Finite Group Databasebeta

← C137×#36888 #46886274

Subgroups — C137×#36888 #46886274

Order 35072.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2849×C137C211yesmaximal, characteristic, complemented
2#2848×C137C211yesmaximal, characteristic, complemented
3#2796×C137C211yesmaximal, characteristic, complemented
4#2790×C137C211yesmaximal, characteristic, complemented
5#2779×C137C211yesmaximal, characteristic, complemented
6#2753×C137C211yesmaximal, characteristic, complemented
7#2748×C137C211yesmaximal, characteristic, complemented
8#2740×C137C211yesmaximal, characteristic, complemented
9#2735×C137C211yesmaximal, characteristic, complemented
10#2730×C137C211yesmaximal, characteristic, complemented
11#2720×C137C211yesmaximal, characteristic, complemented
12#2707×C137C211yesmaximal, characteristic, complemented
13#2698×C137C211yesmaximal, characteristic, complemented
14#2695×C137C211yesmaximal, characteristic, complemented
15#2685×C137C211yesmaximal, characteristic, complemented
16#2685×C137C211yesmaximal, characteristic, complemented
17#2678×C137C211yesmaximal, characteristic
18#2672×C137C211yesmaximal, characteristic, complemented
19#2633×C137C211yesmaximal, characteristic, complemented
20#2630×C137C211yesmaximal, characteristic, complemented
21#2578×C137C211yesmaximal, characteristic, complemented
22#2573×C137C211yesmaximal, characteristic, complemented
23#2558×C137C211yesmaximal, characteristic, complemented
24#2556×C137C211yesmaximal, characteristic, complemented
25#2468×C137C211yesmaximal, characteristic, complemented
26#2461×C137C211yesmaximal, characteristic, complemented
27#2454×C137C211yesmaximal, characteristic, complemented
28#2422×C137C211yesmaximal, characteristic, complemented
29#2335×C137C211yesmaximal, characteristic, complemented
30#2334×C137C211yesmaximal, characteristic, complemented
31C4×#120×C137C211yesmaximal, characteristic, complemented
32C24×C4×C137C2211yescharacteristic
33C2×#126×C137C2211yescharacteristic
34C2×#126×C137C2211yescharacteristic
35C2×#125×C137C2211yescharacteristic, complemented
36C2×#125×C137C2211yescharacteristic, complemented
37C2×#124×C137C2211yescharacteristic, complemented
38C2×#123×C137C2211yescharacteristic
39C2×#123×C137C2211yescharacteristic
40C2×#123×C137C2211yescharacteristic
41C2×#123×C137C2211yescharacteristic, complemented
42C2×C22⋊Q8×C137C2211yescharacteristic
43C2×C22⋊Q8×C137C2211yescharacteristic
44C2×C22⋊Q8×C137C2211yescharacteristic
45C2×#121×C137C2211yescharacteristic
46C2×#120×C137C2211yescharacteristic
47C2×#120×C137C2211yescharacteristic
48C2×C4×D4×C137C2211yescharacteristic
49C2×C4×D4×C137C2211yescharacteristic
50C2×C4×D4×C137C2211yescharacteristic
51#400×C137C2211yescharacteristic, complemented
52#400×C137C2211yescharacteristic, complemented
53#400×C137C2211yescharacteristic, complemented
54#400×C137C2211yescharacteristic, complemented
55#399×C137C2211yescharacteristic
56#399×C137C2211yescharacteristic
57#399×C137C2211yescharacteristic
58#399×C137C2211yescharacteristic, complemented
59#399×C137C2211yescharacteristic, complemented
60#398×C137C2211yescharacteristic, complemented
61#398×C137C2211yescharacteristic, complemented
62#398×C137C2211yescharacteristic, complemented
63#398×C137C2211yescharacteristic, complemented
64#398×C137C2211yescharacteristic, complemented
65#398×C137C2211yescharacteristic, complemented
66#397×C137C2211yescharacteristic
67#397×C137C2211yescharacteristic
68#397×C137C2211yescharacteristic
69#397×C137C2211yescharacteristic
70#397×C137C2211yescharacteristic, complemented
71#397×C137C2211yescharacteristic, complemented
72#397×C137C2211yescharacteristic, complemented
73#397×C137C2211yescharacteristic, complemented
74#396×C137C2211yescharacteristic
75#396×C137C2211yescharacteristic
76#396×C137C2211yescharacteristic
77#396×C137C2211yescharacteristic
78#396×C137C2211yescharacteristic
79#396×C137C2211yescharacteristic, complemented
80#396×C137C2211yescharacteristic, complemented
81#396×C137C2211yescharacteristic, complemented
82#396×C137C2211yescharacteristic, complemented
83#395×C137C2211yescharacteristic, complemented
84#395×C137C2211yescharacteristic, complemented
85#394×C137C2211yescharacteristic
86#394×C137C2211yescharacteristic
87#394×C137C2211yescharacteristic
88#394×C137C2211yescharacteristic
89#394×C137C2211yescharacteristic
90#394×C137C2211yescharacteristic
91#394×C137C2211yescharacteristic
92#394×C137C2211yescharacteristic
93#394×C137C2211yescharacteristic
94#394×C137C2211yescharacteristic
95#394×C137C2211yescharacteristic, complemented
96#394×C137C2211yescharacteristic, complemented
97#392×C137C2211yescharacteristic
98#392×C137C2211yescharacteristic
99#391×C137C2211yescharacteristic, complemented
100#390×C137C2211yescharacteristic
101#390×C137C2211yescharacteristic
102#390×C137C2211yescharacteristic
103#390×C137C2211yescharacteristic
104#390×C137C2211yescharacteristic
105#390×C137C2211yescharacteristic
106#389×C137C2211yescharacteristic, complemented
107#389×C137C2211yescharacteristic, complemented
108#389×C137C2211yescharacteristic, complemented
109#389×C137C2211yescharacteristic, complemented
110#389×C137C2211yescharacteristic, complemented
111#389×C137C2211yescharacteristic, complemented
112#388×C137C2211yescharacteristic
113#388×C137C2211yescharacteristic
114#388×C137C2211yescharacteristic
115#388×C137C2211yescharacteristic
116#388×C137C2211yescharacteristic
117#388×C137C2211yescharacteristic
118#388×C137C2211yescharacteristic
119#388×C137C2211yescharacteristic
120#388×C137C2211yescharacteristic
121#388×C137C2211yescharacteristic
122#388×C137C2211yescharacteristic
123#388×C137C2211yescharacteristic
124#388×C137C2211yescharacteristic
125#388×C137C2211yescharacteristic, complemented
126#388×C137C2211yescharacteristic, complemented
127#388×C137C2211yescharacteristic, complemented
128#388×C137C2211yescharacteristic, complemented
129#388×C137C2211yescharacteristic, complemented
130#388×C137C2211yescharacteristic, complemented
131#388×C137C2211yescharacteristic, complemented
132#387×C137C2211yescharacteristic, complemented
133#387×C137C2211yescharacteristic, complemented
134#387×C137C2211yescharacteristic, complemented
135#387×C137C2211yescharacteristic, complemented
136#387×C137C2211yescharacteristic, complemented
137#387×C137C2211yescharacteristic, complemented
138#387×C137C2211yescharacteristic, complemented
139#387×C137C2211yescharacteristic, complemented
140#387×C137C2211yescharacteristic, complemented
141#386×C137C2211yescharacteristic
142#386×C137C2211yescharacteristic
143#386×C137C2211yescharacteristic
144#386×C137C2211yescharacteristic
145#386×C137C2211yescharacteristic
146#386×C137C2211yescharacteristic
147#386×C137C2211yescharacteristic
148#386×C137C2211yescharacteristic
149#385×C137C2211yescharacteristic
150#385×C137C2211yescharacteristic
151#385×C137C2211yescharacteristic
152#385×C137C2211yescharacteristic
153#385×C137C2211yescharacteristic
154#385×C137C2211yescharacteristic
155#385×C137C2211yescharacteristic
156#385×C137C2211yescharacteristic
157#385×C137C2211yescharacteristic
158#385×C137C2211yescharacteristic
159#385×C137C2211yescharacteristic
160#385×C137C2211yescharacteristic
161#385×C137C2211yescharacteristic
162#385×C137C2211yescharacteristic, complemented
163#385×C137C2211yescharacteristic, complemented
164#385×C137C2211yescharacteristic, complemented
165#384×C137C2211yescharacteristic, complemented
166#383×C137C2211yescharacteristic, complemented
167#382×C137C2211yescharacteristic, complemented
168#381×C137C2211yescharacteristic
169#381×C137C2211yescharacteristic
170#380×C137C2211yescharacteristic
171#380×C137C2211yescharacteristic
172#380×C137C2211yescharacteristic
173#380×C137C2211yescharacteristic, complemented
174#380×C137C2211yescharacteristic, complemented
175#380×C137C2211yescharacteristic, complemented
176#379×C137C2211yescharacteristic
177#379×C137C2211yescharacteristic
178#379×C137C2211yescharacteristic
179#379×C137C2211yescharacteristic
180C4×C4⋊C4×C137C2211yescharacteristic, complemented
181C4×C4⋊C4×C137C2211yescharacteristic, complemented
182C4×C4⋊C4×C137C2211yescharacteristic, complemented
183C4×C22⋊C4×C137C2211yescharacteristic
184C4×C22⋊C4×C137C2211yescharacteristic
185C4×C22⋊C4×C137C2211yescharacteristic
186C4×C22⋊C4×C137C2211yescharacteristic, complemented
187C25×C137C2311yescharacteristic
188C22×Q8×C137C2311yescharacteristic
189C22×D4×C137C2311yescharacteristic
190C22×D4×C137C2311yescharacteristic
191C22×D4×C137C2311yescharacteristic
192C22×D4×C137C2311yescharacteristic
193C22×D4×C137C2311yescharacteristic
194C22×D4×C137C2311yescharacteristic
195C22×D4×C137C2311yescharacteristic
196C23×C4×C137—42no—
197C23×C4×C137—42no—
198C23×C4×C137—42no—
199C23×C4×C137C2311yescharacteristic
200C23×C4×C137C2311yescharacteristic
201C23×C4×C137C2311yescharacteristic
202C23×C4×C137C2311yescharacteristic
203C23×C4×C137C2311yescharacteristic
204C23×C4×C137C2311yescharacteristic
205C23×C4×C137C2311yescharacteristic
206C23×C4×C137C2311yescharacteristic
207#126×C137—24no—
208#126×C137—42no—
209#125×C137—42no—
210#125×C137—42no—
211#124×C137—42no—
212#123×C137—24no—
213#123×C137—42no—
214#123×C137—42no—
215#123×C137—42no—
216C22⋊Q8×C137—42no—
217C22⋊Q8×C137—42no—
218C22⋊Q8×C137—42no—
219#121×C137—42no—
220#120×C137—24no—
221#120×C137—42no—
222C4×D4×C137—42no—
223C4×D4×C137—42no—
224C4×D4×C137—42no—
225C2×C4⋊C4×C137C2311yescharacteristic
226C2×C4⋊C4×C137C2311yescharacteristic
227C2×C4⋊C4×C137C2311yescharacteristic
228C2×C4⋊C4×C137C2311yescharacteristic
229C2×C4⋊C4×C137C2311yescharacteristic
230C2×C4⋊C4×C137C2311yescharacteristic
231C2×C4⋊C4×C137C2311yescharacteristic
232C2×C4⋊C4×C137C2311yescharacteristic
233C2×C4⋊C4×C137C2311yescharacteristic
234C2×C4⋊C4×C137C2311yescharacteristic
235C2×C4⋊C4×C137C2311yescharacteristic
236C2×C4⋊C4×C137C2311yescharacteristic
237C2×C4⋊C4×C137C2311yescharacteristic
238C2×C4⋊C4×C137C2311yescharacteristic
239C2×C4⋊C4×C137C2311yescharacteristic
240C2×C4⋊C4×C137C2311yescharacteristic
241C2×C4⋊C4×C137C2311yescharacteristic
242C2×C4⋊C4×C137C2311yescharacteristic
243C2×C4⋊C4×C137C2311yescharacteristic
244C2×C4⋊C4×C137C2311yescharacteristic
245C2×C4⋊C4×C137C2311yescharacteristic
246C2×C4⋊C4×C137C2311yescharacteristic
247C2×C4⋊C4×C137C2311yescharacteristic
248C2×C4⋊C4×C137C2311yescharacteristic
249C2×C4⋊C4×C137C2311yescharacteristic
250C2×C4⋊C4×C137C2311yescharacteristic
251C2×C4⋊C4×C137C2311yescharacteristic
252C2×C4⋊C4×C137C2311yescharacteristic
253C2×C4⋊C4×C137C2311yescharacteristic
254C2×C4⋊C4×C137C2311yescharacteristic
255C2×C4⋊C4×C137C2311yescharacteristic
256C2×C4⋊C4×C137C2311yescharacteristic
257C2×C4⋊C4×C137C2311yescharacteristic
258C2×C4⋊C4×C137C2311yescharacteristic
259C2×C4⋊C4×C137C2311yescharacteristic
260C2×C4⋊C4×C137C2311yescharacteristic
261C2×C4⋊C4×C137C2311yescharacteristic
262C2×C4⋊C4×C137C2311yescharacteristic
263C2×C22⋊C4×C137C2311yescharacteristic
264C2×C22⋊C4×C137C2311yescharacteristic
265C2×C22⋊C4×C137C2311yescharacteristic
266C2×C22⋊C4×C137C2311yescharacteristic
267C2×C22⋊C4×C137C2311yescharacteristic
268C2×C22⋊C4×C137C2311yescharacteristic
269C2×C22⋊C4×C137C2311yescharacteristic
270C2×C22⋊C4×C137C2311yescharacteristic
271C2×C22⋊C4×C137C2311yescharacteristic
272C2×C22⋊C4×C137C2311yescharacteristic
273C2×C22⋊C4×C137C2311yescharacteristic
274C2×C22⋊C4×C137C2311yescharacteristic
275C2×C22⋊C4×C137C2311yescharacteristic
276C2×C22⋊C4×C137C2311yescharacteristic
277C2×C22⋊C4×C137C2311yescharacteristic
278C2×C22⋊C4×C137C2311yescharacteristic
279C2×C22⋊C4×C137C2311yescharacteristic
280C2×C22⋊C4×C137C2311yescharacteristic
281C2×C22⋊C4×C137C2311yescharacteristic
282C2×C22⋊C4×C137C2311yescharacteristic
283C2×C22⋊C4×C137C2311yescharacteristic
284C2×C22⋊C4×C137C2311yescharacteristic
285C2×C22⋊C4×C137C2311yescharacteristic
286C2×C22⋊C4×C137C2311yescharacteristic
287C2×C22⋊C4×C137C2311yescharacteristic
288C2×C22⋊C4×C137C2311yescharacteristic
289C2×C22⋊C4×C137C2311yescharacteristic
290C2×C22⋊C4×C137C2311yescharacteristic
291C2×C22⋊C4×C137C2311yescharacteristic
292C2×C22⋊C4×C137C2311yescharacteristic
293C2×C22⋊C4×C137C2311yescharacteristic
294C2×C22⋊C4×C137C2311yescharacteristic
295C2×C22⋊C4×C137C2311yescharacteristic
296C2×C22⋊C4×C137C2311yescharacteristic
297C2×C22⋊C4×C137C2311yescharacteristic
298C2×C22⋊C4×C137C2311yescharacteristic
299C2×C22⋊C4×C137C2311yescharacteristic
300C2×C22⋊C4×C137C2311yescharacteristic
301C2×C22⋊C4×C137C2311yescharacteristic
302C2×C22⋊C4×C137C2311yescharacteristic
303C2×C22⋊C4×C137C2311yescharacteristic
304C2×C22⋊C4×C137C2311yescharacteristic
305C2×C22⋊C4×C137C2311yescharacteristic
306C2×C22⋊C4×C137C2311yescharacteristic
307C2×C22⋊C4×C137C2311yescharacteristic
308C2×C22⋊C4×C137C2311yescharacteristic
309C2×C22⋊C4×C137C2311yescharacteristic
310C2×C22⋊C4×C137C2311yescharacteristic
311C2×C22⋊C4×C137C2311yescharacteristic
312C2×C22⋊C4×C137C2311yescharacteristic
313C2×C42×C137C2311yescharacteristic
314C2×C42×C137C2311yescharacteristic
315C2×C42×C137C2311yescharacteristic
316C2×C42×C137C2311yescharacteristic
317C2×C42×C137C2311yescharacteristic
318C2×C42×C137C2311yescharacteristic
319C2×C42×C137C2311yescharacteristic
320C2×C42×C137C2311yescharacteristic
321C2×C42×C137C2311yescharacteristic
322C2×C42×C137C2311yescharacteristic
323#95×C137C2311yescharacteristic
324#95×C137C2311yescharacteristic
325#95×C137C2311yescharacteristic
326#95×C137C2311yescharacteristic
327#95×C137C2311yescharacteristic
328#95×C137C2311yescharacteristic
329#95×C137C2311yescharacteristic
330#95×C137C2311yescharacteristic
331#95×C137C2311yescharacteristic
332#95×C137C2311yescharacteristic
333#95×C137C2311yescharacteristic
334#95×C137C2311yescharacteristic
335#95×C137C2311yescharacteristic
336#95×C137C2311yescharacteristic
337#95×C137C2311yescharacteristic
338#95×C137C2311yescharacteristic
339#95×C137C2311yescharacteristic
340#95×C137C2311yescharacteristic
341#95×C137C2311yescharacteristic
342#95×C137C2311yescharacteristic
343#95×C137C2311yescharacteristic
344#95×C137C2311yescharacteristic
345#95×C137C2311yescharacteristic
346#95×C137C2311yescharacteristic
347#95×C137C2311yescharacteristic
348#95×C137C2311yescharacteristic
349#95×C137C2311yescharacteristic
350#95×C137C2311yescharacteristic
351#95×C137C2311yescharacteristic
352#95×C137C2311yescharacteristic
353#95×C137C2311yescharacteristic
354#95×C137C2311yescharacteristic
355#95×C137C2311yescharacteristic
356#95×C137C2311yescharacteristic
357#95×C137C2311yescharacteristic
358#95×C137C2311yescharacteristic
359#95×C137C2311yescharacteristic
360#95×C137C2311yescharacteristic
361#95×C137C2311yescharacteristic
362#95×C137C2311yescharacteristic
363C24×C137—22no—
364C24×C137—22no—
365C24×C137—22no—
366C24×C137—41no—
367C24×C137—41no—
368C24×C137—41no—
369C24×C137—41no—
370C24×C137C2411yescharacteristic
371C24×C137C2411yescharacteristic
372C24×C137C2411yescharacteristic
373C24×C137C2411yescharacteristic
374C24×C137C2411yescharacteristic
375C2×Q8×C137—22no—
376C2×Q8×C137—41no—
377C2×Q8×C137—41no—
378C2×D4×C137—22no—
379C2×D4×C137—22no—
380C2×D4×C137—22no—
381C2×D4×C137—22no—
382C2×D4×C137—22no—
383C2×D4×C137—22no—
384C2×D4×C137—22no—
385C2×D4×C137—22no—
386C2×D4×C137—41no—
387C2×D4×C137—41no—
388C2×D4×C137—41no—
389C2×D4×C137—41no—
390C2×D4×C137—41no—
391C2×D4×C137—41no—
392C2×D4×C137—41no—
393C2×D4×C137—41no—
394C2×D4×C137—41no—
395C2×D4×C137—41no—
396C2×D4×C137—41no—
397C2×D4×C137—41no—
398C2×D4×C137—41no—
399C22×C4×C137—22no—
400C22×C4×C137—22no—
401C22×C4×C137—22no—
402C22×C4×C137—22no—
403C22×C4×C137—22no—
404C22×C4×C137—22no—
405C22×C4×C137—22no—
406C22×C4×C137—22no—
407C22×C4×C137—22no—
408C22×C4×C137—22no—
409C22×C4×C137—41no—
410C22×C4×C137—41no—
411C22×C4×C137—41no—
412C22×C4×C137—41no—
413C22×C4×C137—41no—
414C22×C4×C137—41no—
415C22×C4×C137—41no—
416C22×C4×C137—41no—
417C22×C4×C137—41no—
418C22×C4×C137—41no—
419C22×C4×C137—41no—
420C22×C4×C137—41no—
421C22×C4×C137—41no—
422C22×C4×C137—41no—
423C22×C4×C137—416no—
424C22×C4×C137C2411yescharacteristic
425C22×C4×C137C2411yescharacteristic
426C22×C4×C137C2411yescharacteristic
427C22×C4×C137C2411yescharacteristic
428C22×C4×C137C2411yescharacteristic
429C22×C4×C137C2411yescharacteristic
430C22×C4×C137C2411yescharacteristic
431C22×C4×C137C2411yescharacteristic
432C22×C4×C137C2411yescharacteristic
433C22×C4×C137C2411yescharacteristic
434C22×C4×C137C2411yescharacteristic
435C22×C4×C137C2411yescharacteristic
436C22×C4×C137C2411yescharacteristic
437C22×C4×C137C2411yescharacteristic
438C22×C4×C137C2411yescharacteristic
439C22×C4×C137C2411yescharacteristic
440C22×C4×C137C2411yescharacteristic
441C22×C4×C137C2411yescharacteristic
442C22×C4×C137C2411yescharacteristic
443C22×C4×C137C2411yescharacteristic
444C22×C4×C137C2411yescharacteristic
445C22×C4×C137C2411yescharacteristic
446C22×C4×C137C2411yescharacteristic
447C22×C4×C137C2411yescharacteristic
448C22×C4×C137C2411yescharacteristic
449C22×C4×C137C2411yescharacteristic
450C4⋊C4×C137—22no—
451C4⋊C4×C137—22no—
452C4⋊C4×C137—22no—
453C4⋊C4×C137—22no—
454C4⋊C4×C137—22no—
455C4⋊C4×C137—22no—
456C4⋊C4×C137—22no—
457C4⋊C4×C137—22no—
458C4⋊C4×C137—22no—
459C4⋊C4×C137—22no—
460C4⋊C4×C137—22no—
461C4⋊C4×C137—41no—
462C4⋊C4×C137—41no—
463C4⋊C4×C137—41no—
464C4⋊C4×C137—41no—
465C4⋊C4×C137—41no—
466C4⋊C4×C137—41no—
467C4⋊C4×C137—41no—
468C4⋊C4×C137—41no—
469C4⋊C4×C137—41no—
470C4⋊C4×C137—41no—
471C4⋊C4×C137—41no—
472C4⋊C4×C137—41no—
473C4⋊C4×C137—41no—
474C4⋊C4×C137—41no—
475C4⋊C4×C137—41no—
476C4⋊C4×C137—41no—
477C4⋊C4×C137—41no—
478C4⋊C4×C137—41no—
479C4⋊C4×C137—41no—
480C4⋊C4×C137—41no—
481C4⋊C4×C137—41no—
482C4⋊C4×C137—41no—
483C4⋊C4×C137—41no—
484C4⋊C4×C137—41no—
485C4⋊C4×C137—41no—
486C4⋊C4×C137—41no—
487C4⋊C4×C137—41no—
488C22⋊C4×C137—22no—
489C22⋊C4×C137—22no—
490C22⋊C4×C137—22no—
491C22⋊C4×C137—22no—
492C22⋊C4×C137—22no—
493C22⋊C4×C137—22no—
494C22⋊C4×C137—22no—
495C22⋊C4×C137—22no—
496C22⋊C4×C137—22no—
497C22⋊C4×C137—22no—
498C22⋊C4×C137—22no—
499C22⋊C4×C137—22no—
500C22⋊C4×C137—22no—
501C22⋊C4×C137—22no—
502C22⋊C4×C137—22no—
503C22⋊C4×C137—41no—
504C22⋊C4×C137—41no—
505C22⋊C4×C137—41no—
506C22⋊C4×C137—41no—
507C22⋊C4×C137—41no—
508C22⋊C4×C137—41no—
509C22⋊C4×C137—41no—
510C22⋊C4×C137—41no—
511C22⋊C4×C137—41no—
512C22⋊C4×C137—41no—
513C22⋊C4×C137—41no—
514C22⋊C4×C137—41no—
515C22⋊C4×C137—41no—
516C22⋊C4×C137—41no—
517C22⋊C4×C137—41no—
518C22⋊C4×C137—41no—
519C22⋊C4×C137—41no—
520C22⋊C4×C137—41no—
521C22⋊C4×C137—41no—
522C22⋊C4×C137—41no—
523C22⋊C4×C137—41no—
524C22⋊C4×C137—41no—
525C22⋊C4×C137—41no—
526C22⋊C4×C137—41no—
527C22⋊C4×C137—41no—
528C22⋊C4×C137—41no—
529C22⋊C4×C137—41no—
530C22⋊C4×C137—41no—
531C22⋊C4×C137—41no—
532C22⋊C4×C137—41no—
533C22⋊C4×C137—41no—
534C22⋊C4×C137—41no—
535C22⋊C4×C137—41no—
536C22⋊C4×C137—41no—
537C22⋊C4×C137#4114yes—
538C42×C137—22no—
539C42×C137—22no—
540C42×C137—41no—
541C42×C137—41no—
542C42×C137—41no—
543C42×C137—41no—
544C42×C137—41no—
545C42×C137—41no—
546C42×C137—41no—
547C42×C137—41no—
548C23×C137—21no—
549C23×C137—21no—
550C23×C137—21no—
551C23×C137—21no—
552C23×C137—21no—
553C23×C137—21no—
554C23×C137—21no—
555C23×C137—21no—
556C23×C137—21no—
557C23×C137—21no—
558C23×C137—21no—
559C23×C137—21no—
560C23×C137—21no—
561C23×C137—21no—
562C23×C137—21no—
563C23×C137—21no—
564C23×C137—21no—
565C23×C137—21no—
566C23×C137—21no—
567C23×C137—21no—
568C23×C137—21no—
569C23×C137—21no—
570C23×C137—21no—
571C23×C137—21no—
572C23×C137—21no—
573C23×C137—21no—
574C23×C137—21no—
575C23×C137—21no—
576C23×C137—21no—
577C23×C137—21no—
578C23×C137—21no—
579C23×C137—21no—
580C23×C137—44no—
581C23×C137—44no—
582C23×C137—44no—
583C23×C137—44no—
584C23×C137—44no—
585C23×C137—44no—
586C23×C137—44no—
587C23×C137C2×#4112yes—
588C23×C137H(5,𝔽2)12yes—
589C23×C1372−1+412yes—
590C23×C137C2511yescharacteristic
591Q8×C137—82no—
592D4×C137—44no—
593D4×C137—44no—
594D4×C137—44no—
595D4×C137—82no—
596D4×C137—82no—
597D4×C137—82no—
598D4×C137—82no—
599C2×C4×C137—21no—
600C2×C4×C137—21no—
601C2×C4×C137—21no—
602C2×C4×C137—21no—
603C2×C4×C137—21no—
604C2×C4×C137—21no—
605C2×C4×C137—21no—
606C2×C4×C137—21no—
607C2×C4×C137—21no—
608C2×C4×C137—21no—
609C2×C4×C137—21no—
610C2×C4×C137—21no—
611C2×C4×C137—21no—
612C2×C4×C137—21no—
613C2×C4×C137—21no—
614C2×C4×C137—21no—
615C2×C4×C137—21no—
616C2×C4×C137—21no—
617C2×C4×C137—21no—
618C2×C4×C137—21no—
619C2×C4×C137—21no—
620C2×C4×C137—21no—
621C2×C4×C137—21no—
622C2×C4×C137—21no—
623C2×C4×C137—21no—
624C2×C4×C137—21no—
625C2×C4×C137—21no—
626C2×C4×C137—21no—
627C2×C4×C137—21no—
628C2×C4×C137—21no—
629C2×C4×C137—21no—
630C2×C4×C137—21no—
631C2×C4×C137—21no—
632C2×C4×C137—21no—
633C2×C4×C137—21no—
634C2×C4×C137—21no—
635C2×C4×C137—21no—
636C2×C4×C137—21no—
637C2×C4×C137—21no—
638C2×C4×C137—21no—
639C2×C4×C137—21no—
640C2×C4×C137—21no—
641C2×C4×C137—21no—
642C2×C4×C137—21no—
643C2×C4×C137—21no—
644C2×C4×C137—21no—
645C2×C4×C137—21no—
646C2×C4×C137—21no—
647C2×C4×C137—21no—
648C2×C4×C137—21no—
649C2×C4×C137—21no—
650C2×C4×C137—21no—
651C2×C4×C137—21no—
652C2×C4×C137—21no—
653C2×C4×C137—21no—
654C2×C4×C137—21no—
655C2×C4×C137—21no—
656C2×C4×C137—21no—
657C2×C4×C137—21no—
658C2×C4×C137—21no—
659C2×C4×C137—21no—
660C2×C4×C137—21no—
661C2×C4×C137—21no—
662C2×C4×C137—21no—
663C2×C4×C137—21no—
664C2×C4×C137—21no—
665C2×C4×C137—21no—
666C2×C4×C137—21no—
667C2×C4×C137—21no—
668C2×C4×C137—21no—
669C2×C4×C137—21no—
670C2×C4×C137—21no—
671C2×C4×C137—21no—
672C2×C4×C137—21no—
673C2×C4×C137—44no—
674C2×C4×C137—44no—
675C2×C4×C137—44no—
676C2×C4×C137—44no—
677C2×C4×C137—44no—
678C2×C4×C137—44no—
679C2×C4×C137—82no—
680C2×C4×C137—82no—
681C2×C4×C137C2×#4112yes—
682C2×C4×C137C2×#4112yes—
683C2×C4×C137H(5,𝔽2)12yes—
684C2×C4×C137H(5,𝔽2)12yes—
685C22×C137—22no—
686C22×C137—22no—
687C22×C137—22no—
688C22×C137—22no—
689C22×C137—22no—
690C22×C137—22no—
691C22×C137—22no—
692C22×C137—22no—
693C22×C137—22no—
694C22×C137—416no—
695C22×C137—41no—
696C22×C137—41no—
697C22×C137—41no—
698C22×C137—41no—
699C22×C137—41no—
700C22×C137—41no—
701C22×C137—41no—
702C22×C137—41no—
703C22×C137—41no—
704C22×C137—41no—
705C22×C137—41no—
706C22×C137—41no—
707C22×C137—41no—
708C22×C137—41no—
709C22×C137—41no—
710C22×C137—41no—
711C22×C137—41no—
712C22×C137—41no—
713C22×C137—41no—
714C22×C137—41no—
715C22×C137—41no—
716C22×C137—41no—
717C22×C137—41no—
718C22×C137—41no—
719C22×C137—41no—
720C22×C137—41no—
721C22×C137C22×#4111yescharacteristic
722C22×C137C2×H(5,𝔽2)11yescharacteristic
723C22×C137C2×H(5,𝔽2)11yescharacteristic
724C22×C137C2×H(5,𝔽2)11yescharacteristic
725C22×C137C2×2−1+411yescharacteristic
726C22×C137#58511yescharacteristic
727C22×C137#58511yescharacteristic
728C4×C137—22no—
729C4×C137—22no—
730C4×C137—22no—
731C4×C137—22no—
732C4×C137—41no—
733C4×C137—41no—
734C4×C137—41no—
735C4×C137—41no—
736C4×C137—41no—
737C4×C137—41no—
738C4×C137—41no—
739C4×C137—41no—
740C4×C137—41no—
741C4×C137—41no—
742C4×C137—41no—
743C4×C137—41no—
744C4×C137—41no—
745C4×C137—41no—
746C4×C137—41no—
747C4×C137—41no—
748C4×C137—41no—
749C4×C137—41no—
750C4×C137—41no—
751C4×C137—41no—
752C4×C137—41no—
753C4×C137—41no—
754C2×C137—42no—
755C2×C137—42no—
756C2×C137—42no—
757C2×C137—81no—
758C2×C137—81no—
759C2×C137#346011yescharacteristic
760C2×C137#351311yescharacteristic
761C2×C137#352011yescharacteristic
762C2×C137#353211yescharacteristic
763C2×C137#353511yescharacteristic
764C2×C137#353911yescharacteristic
765C2×C137#354111yescharacteristic
766#36888C13711yesmaximal, characteristic, direct product factor, Sylow
767C137#3688811yescharacteristic, direct product factor, Sylow
768#2849C2×C13711yescharacteristic, complemented
769#2848C2×C13711yescharacteristic, complemented
770#2796C2×C13711yescharacteristic, complemented
771#2790C2×C13711yescharacteristic, complemented
772#2779C2×C13711yescharacteristic, complemented
773#2753C2×C13711yescharacteristic, complemented
774#2748C2×C13711yescharacteristic, complemented
775#2740C2×C13711yescharacteristic, complemented
776#2735C2×C13711yescharacteristic, complemented
777#2730C2×C13711yescharacteristic, complemented
778#2720C2×C13711yescharacteristic, complemented
779#2707C2×C13711yescharacteristic, complemented
780#2698C2×C13711yescharacteristic, complemented
781#2695C2×C13711yescharacteristic, complemented
782#2685C2×C13711yescharacteristic, complemented
783#2685C2×C13711yescharacteristic, complemented
784#2678C2×C13711yescharacteristic
785#2672C2×C13711yescharacteristic, complemented
786#2633C2×C13711yescharacteristic, complemented
787#2630C2×C13711yescharacteristic, complemented
788#2578C2×C13711yescharacteristic, complemented
789#2573C2×C13711yescharacteristic, complemented
790#2558C2×C13711yescharacteristic, complemented
791#2556C2×C13711yescharacteristic, complemented
792#2468C2×C13711yescharacteristic, complemented
793#2461C2×C13711yescharacteristic, complemented
794#2454C2×C13711yescharacteristic, complemented
795#2422C2×C13711yescharacteristic, complemented
796#2335C2×C13711yescharacteristic, complemented
797#2334C2×C13711yescharacteristic, complemented
798C4×#120C2×C13711yescharacteristic, complemented
799C24×C4C22×C13711yescharacteristic
800C2×#126C22×C13711yescharacteristic
801C2×#126C22×C13711yescharacteristic
802C2×#125C22×C13711yescharacteristic, complemented
803C2×#125C22×C13711yescharacteristic, complemented
804C2×#124C22×C13711yescharacteristic, complemented
805C2×#123C22×C13711yescharacteristic
806C2×#123C22×C13711yescharacteristic
807C2×#123C22×C13711yescharacteristic
808C2×#123C22×C13711yescharacteristic, complemented
809C2×C22⋊Q8C22×C13711yescharacteristic
810C2×C22⋊Q8C22×C13711yescharacteristic
811C2×C22⋊Q8C22×C13711yescharacteristic
812C2×#121C22×C13711yescharacteristic
813C2×#120C22×C13711yescharacteristic
814C2×#120C22×C13711yescharacteristic
815C2×C4×D4C22×C13711yescharacteristic
816C2×C4×D4C22×C13711yescharacteristic
817C2×C4×D4C22×C13711yescharacteristic
818#400C22×C13711yescharacteristic, complemented
819#400C22×C13711yescharacteristic, complemented
820#400C22×C13711yescharacteristic, complemented
821#400C22×C13711yescharacteristic, complemented
822#399C22×C13711yescharacteristic
823#399C22×C13711yescharacteristic
824#399C22×C13711yescharacteristic
825#399C22×C13711yescharacteristic, complemented
826#399C22×C13711yescharacteristic, complemented
827#398C22×C13711yescharacteristic, complemented
828#398C22×C13711yescharacteristic, complemented
829#398C22×C13711yescharacteristic, complemented
830#398C22×C13711yescharacteristic, complemented
831#398C22×C13711yescharacteristic, complemented
832#398C22×C13711yescharacteristic, complemented
833#397C22×C13711yescharacteristic
834#397C22×C13711yescharacteristic
835#397C22×C13711yescharacteristic
836#397C22×C13711yescharacteristic
837#397C22×C13711yescharacteristic, complemented
838#397C22×C13711yescharacteristic, complemented
839#397C22×C13711yescharacteristic, complemented
840#397C22×C13711yescharacteristic, complemented
841#396C22×C13711yescharacteristic
842#396C22×C13711yescharacteristic
843#396C22×C13711yescharacteristic
844#396C22×C13711yescharacteristic
845#396C22×C13711yescharacteristic
846#396C22×C13711yescharacteristic, complemented
847#396C22×C13711yescharacteristic, complemented
848#396C22×C13711yescharacteristic, complemented
849#396C22×C13711yescharacteristic, complemented
850#395C22×C13711yescharacteristic, complemented
851#395C22×C13711yescharacteristic, complemented
852#394C22×C13711yescharacteristic
853#394C22×C13711yescharacteristic
854#394C22×C13711yescharacteristic
855#394C22×C13711yescharacteristic
856#394C22×C13711yescharacteristic
857#394C22×C13711yescharacteristic
858#394C22×C13711yescharacteristic
859#394C22×C13711yescharacteristic
860#394C22×C13711yescharacteristic
861#394C22×C13711yescharacteristic
862#394C22×C13711yescharacteristic, complemented
863#394C22×C13711yescharacteristic, complemented
864#392C22×C13711yescharacteristic
865#392C22×C13711yescharacteristic
866#391C22×C13711yescharacteristic, complemented
867#390C22×C13711yescharacteristic
868#390C22×C13711yescharacteristic
869#390C22×C13711yescharacteristic
870#390C22×C13711yescharacteristic
871#390C22×C13711yescharacteristic
872#390C22×C13711yescharacteristic
873#389C22×C13711yescharacteristic, complemented
874#389C22×C13711yescharacteristic, complemented
875#389C22×C13711yescharacteristic, complemented
876#389C22×C13711yescharacteristic, complemented
877#389C22×C13711yescharacteristic, complemented
878#389C22×C13711yescharacteristic, complemented
879#388C22×C13711yescharacteristic
880#388C22×C13711yescharacteristic
881#388C22×C13711yescharacteristic
882#388C22×C13711yescharacteristic
883#388C22×C13711yescharacteristic
884#388C22×C13711yescharacteristic
885#388C22×C13711yescharacteristic
886#388C22×C13711yescharacteristic
887#388C22×C13711yescharacteristic
888#388C22×C13711yescharacteristic
889#388C22×C13711yescharacteristic
890#388C22×C13711yescharacteristic
891#388C22×C13711yescharacteristic
892#388C22×C13711yescharacteristic, complemented
893#388C22×C13711yescharacteristic, complemented
894#388C22×C13711yescharacteristic, complemented
895#388C22×C13711yescharacteristic, complemented
896#388C22×C13711yescharacteristic, complemented
897#388C22×C13711yescharacteristic, complemented
898#388C22×C13711yescharacteristic, complemented
899#387C22×C13711yescharacteristic, complemented
900#387C22×C13711yescharacteristic, complemented
901#387C22×C13711yescharacteristic, complemented
902#387C22×C13711yescharacteristic, complemented
903#387C22×C13711yescharacteristic, complemented
904#387C22×C13711yescharacteristic, complemented
905#387C22×C13711yescharacteristic, complemented
906#387C22×C13711yescharacteristic, complemented
907#387C22×C13711yescharacteristic, complemented
908#386C22×C13711yescharacteristic
909#386C22×C13711yescharacteristic
910#386C22×C13711yescharacteristic
911#386C22×C13711yescharacteristic
912#386C22×C13711yescharacteristic
913#386C22×C13711yescharacteristic
914#386C22×C13711yescharacteristic
915#386C22×C13711yescharacteristic
916#385C22×C13711yescharacteristic
917#385C22×C13711yescharacteristic
918#385C22×C13711yescharacteristic
919#385C22×C13711yescharacteristic
920#385C22×C13711yescharacteristic
921#385C22×C13711yescharacteristic
922#385C22×C13711yescharacteristic
923#385C22×C13711yescharacteristic
924#385C22×C13711yescharacteristic
925#385C22×C13711yescharacteristic
926#385C22×C13711yescharacteristic
927#385C22×C13711yescharacteristic
928#385C22×C13711yescharacteristic
929#385C22×C13711yescharacteristic, complemented
930#385C22×C13711yescharacteristic, complemented
931#385C22×C13711yescharacteristic, complemented
932#384C22×C13711yescharacteristic, complemented
933#383C22×C13711yescharacteristic, complemented
934#382C22×C13711yescharacteristic, complemented
935#381C22×C13711yescharacteristic
936#381C22×C13711yescharacteristic
937#380C22×C13711yescharacteristic
938#380C22×C13711yescharacteristic
939#380C22×C13711yescharacteristic
940#380C22×C13711yescharacteristic, complemented
941#380C22×C13711yescharacteristic, complemented
942#380C22×C13711yescharacteristic, complemented
943#379C22×C13711yescharacteristic
944#379C22×C13711yescharacteristic
945#379C22×C13711yescharacteristic
946#379C22×C13711yescharacteristic
947C4×C4⋊C4C22×C13711yescharacteristic, complemented
948C4×C4⋊C4C22×C13711yescharacteristic, complemented
949C4×C4⋊C4C22×C13711yescharacteristic, complemented
950C4×C22⋊C4C22×C13711yescharacteristic
951C4×C22⋊C4C22×C13711yescharacteristic
952C4×C22⋊C4C22×C13711yescharacteristic
953C4×C22⋊C4C22×C13711yescharacteristic, complemented
954C25C23×C13711yescharacteristic
955C22×Q8C23×C13711yescharacteristic
956C22×D4C23×C13711yescharacteristic
957C22×D4C23×C13711yescharacteristic
958C22×D4C23×C13711yescharacteristic
959C22×D4C23×C13711yescharacteristic
960C22×D4C23×C13711yescharacteristic
961C22×D4C23×C13711yescharacteristic
962C22×D4C23×C13711yescharacteristic
963C23×C4—42no—
964C23×C4—42no—
965C23×C4—42no—
966C23×C4C23×C13711yescharacteristic
967C23×C4C23×C13711yescharacteristic
968C23×C4C23×C13711yescharacteristic
969C23×C4C23×C13711yescharacteristic
970C23×C4C23×C13711yescharacteristic
971C23×C4C23×C13711yescharacteristic
972C23×C4C23×C13711yescharacteristic
973C23×C4C23×C13711yescharacteristic
974#126—24no—
975#126—42no—
976#125—42no—
977#125—42no—
978#124—42no—
979#123—24no—
980#123—42no—
981#123—42no—
982#123—42no—
983C22⋊Q8—42no—
984C22⋊Q8—42no—
985C22⋊Q8—42no—
986#121—42no—
987#120—24no—
988#120—42no—
989C4×D4—42no—
990C4×D4—42no—
991C4×D4—42no—
992C2×C4⋊C4C23×C13711yescharacteristic
993C2×C4⋊C4C23×C13711yescharacteristic
994C2×C4⋊C4C23×C13711yescharacteristic
995C2×C4⋊C4C23×C13711yescharacteristic
996C2×C4⋊C4C23×C13711yescharacteristic
997C2×C4⋊C4C23×C13711yescharacteristic
998C2×C4⋊C4C23×C13711yescharacteristic
999C2×C4⋊C4C23×C13711yescharacteristic
1000C2×C4⋊C4C23×C13711yescharacteristic
1001C2×C4⋊C4C23×C13711yescharacteristic
1002C2×C4⋊C4C23×C13711yescharacteristic
1003C2×C4⋊C4C23×C13711yescharacteristic
1004C2×C4⋊C4C23×C13711yescharacteristic
1005C2×C4⋊C4C23×C13711yescharacteristic
1006C2×C4⋊C4C23×C13711yescharacteristic
1007C2×C4⋊C4C23×C13711yescharacteristic
1008C2×C4⋊C4C23×C13711yescharacteristic
1009C2×C4⋊C4C23×C13711yescharacteristic
1010C2×C4⋊C4C23×C13711yescharacteristic
1011C2×C4⋊C4C23×C13711yescharacteristic
1012C2×C4⋊C4C23×C13711yescharacteristic
1013C2×C4⋊C4C23×C13711yescharacteristic
1014C2×C4⋊C4C23×C13711yescharacteristic
1015C2×C4⋊C4C23×C13711yescharacteristic
1016C2×C4⋊C4C23×C13711yescharacteristic
1017C2×C4⋊C4C23×C13711yescharacteristic
1018C2×C4⋊C4C23×C13711yescharacteristic
1019C2×C4⋊C4C23×C13711yescharacteristic
1020C2×C4⋊C4C23×C13711yescharacteristic
1021C2×C4⋊C4C23×C13711yescharacteristic
1022C2×C4⋊C4C23×C13711yescharacteristic
1023C2×C4⋊C4C23×C13711yescharacteristic
1024C2×C4⋊C4C23×C13711yescharacteristic
1025C2×C4⋊C4C23×C13711yescharacteristic
1026C2×C4⋊C4C23×C13711yescharacteristic
1027C2×C4⋊C4C23×C13711yescharacteristic
1028C2×C4⋊C4C23×C13711yescharacteristic
1029C2×C4⋊C4C23×C13711yescharacteristic
1030C2×C22⋊C4C23×C13711yescharacteristic
1031C2×C22⋊C4C23×C13711yescharacteristic
1032C2×C22⋊C4C23×C13711yescharacteristic
1033C2×C22⋊C4C23×C13711yescharacteristic
1034C2×C22⋊C4C23×C13711yescharacteristic
1035C2×C22⋊C4C23×C13711yescharacteristic
1036C2×C22⋊C4C23×C13711yescharacteristic
1037C2×C22⋊C4C23×C13711yescharacteristic
1038C2×C22⋊C4C23×C13711yescharacteristic
1039C2×C22⋊C4C23×C13711yescharacteristic
1040C2×C22⋊C4C23×C13711yescharacteristic
1041C2×C22⋊C4C23×C13711yescharacteristic
1042C2×C22⋊C4C23×C13711yescharacteristic
1043C2×C22⋊C4C23×C13711yescharacteristic
1044C2×C22⋊C4C23×C13711yescharacteristic
1045C2×C22⋊C4C23×C13711yescharacteristic
1046C2×C22⋊C4C23×C13711yescharacteristic
1047C2×C22⋊C4C23×C13711yescharacteristic
1048C2×C22⋊C4C23×C13711yescharacteristic
1049C2×C22⋊C4C23×C13711yescharacteristic
1050C2×C22⋊C4C23×C13711yescharacteristic
1051C2×C22⋊C4C23×C13711yescharacteristic
1052C2×C22⋊C4C23×C13711yescharacteristic
1053C2×C22⋊C4C23×C13711yescharacteristic
1054C2×C22⋊C4C23×C13711yescharacteristic
1055C2×C22⋊C4C23×C13711yescharacteristic
1056C2×C22⋊C4C23×C13711yescharacteristic
1057C2×C22⋊C4C23×C13711yescharacteristic
1058C2×C22⋊C4C23×C13711yescharacteristic
1059C2×C22⋊C4C23×C13711yescharacteristic
1060C2×C22⋊C4C23×C13711yescharacteristic
1061C2×C22⋊C4C23×C13711yescharacteristic
1062C2×C22⋊C4C23×C13711yescharacteristic
1063C2×C22⋊C4C23×C13711yescharacteristic
1064C2×C22⋊C4C23×C13711yescharacteristic
1065C2×C22⋊C4C23×C13711yescharacteristic
1066C2×C22⋊C4C23×C13711yescharacteristic
1067C2×C22⋊C4C23×C13711yescharacteristic
1068C2×C22⋊C4C23×C13711yescharacteristic
1069C2×C22⋊C4C23×C13711yescharacteristic
1070C2×C22⋊C4C23×C13711yescharacteristic
1071C2×C22⋊C4C23×C13711yescharacteristic
1072C2×C22⋊C4C23×C13711yescharacteristic
1073C2×C22⋊C4C23×C13711yescharacteristic
1074C2×C22⋊C4C23×C13711yescharacteristic
1075C2×C22⋊C4C23×C13711yescharacteristic
1076C2×C22⋊C4C23×C13711yescharacteristic
1077C2×C22⋊C4C23×C13711yescharacteristic
1078C2×C22⋊C4C23×C13711yescharacteristic
1079C2×C22⋊C4C23×C13711yescharacteristic
1080C2×C42C23×C13711yescharacteristic
1081C2×C42C23×C13711yescharacteristic
1082C2×C42C23×C13711yescharacteristic
1083C2×C42C23×C13711yescharacteristic
1084C2×C42C23×C13711yescharacteristic
1085C2×C42C23×C13711yescharacteristic
1086C2×C42C23×C13711yescharacteristic
1087C2×C42C23×C13711yescharacteristic
1088C2×C42C23×C13711yescharacteristic
1089C2×C42C23×C13711yescharacteristic
1090#95C23×C13711yescharacteristic
1091#95C23×C13711yescharacteristic
1092#95C23×C13711yescharacteristic
1093#95C23×C13711yescharacteristic
1094#95C23×C13711yescharacteristic
1095#95C23×C13711yescharacteristic
1096#95C23×C13711yescharacteristic
1097#95C23×C13711yescharacteristic
1098#95C23×C13711yescharacteristic
1099#95C23×C13711yescharacteristic
1100#95C23×C13711yescharacteristic
1101#95C23×C13711yescharacteristic
1102#95C23×C13711yescharacteristic
1103#95C23×C13711yescharacteristic
1104#95C23×C13711yescharacteristic
1105#95C23×C13711yescharacteristic
1106#95C23×C13711yescharacteristic
1107#95C23×C13711yescharacteristic
1108#95C23×C13711yescharacteristic
1109#95C23×C13711yescharacteristic
1110#95C23×C13711yescharacteristic
1111#95C23×C13711yescharacteristic
1112#95C23×C13711yescharacteristic
1113#95C23×C13711yescharacteristic
1114#95C23×C13711yescharacteristic
1115#95C23×C13711yescharacteristic
1116#95C23×C13711yescharacteristic
1117#95C23×C13711yescharacteristic
1118#95C23×C13711yescharacteristic
1119#95C23×C13711yescharacteristic
1120#95C23×C13711yescharacteristic
1121#95C23×C13711yescharacteristic
1122#95C23×C13711yescharacteristic
1123#95C23×C13711yescharacteristic
1124#95C23×C13711yescharacteristic
1125#95C23×C13711yescharacteristic
1126#95C23×C13711yescharacteristic
1127#95C23×C13711yescharacteristic
1128#95C23×C13711yescharacteristic
1129#95C23×C13711yescharacteristic
1130C24—22no—
1131C24—22no—
1132C24—22no—
1133C24—41no—
1134C24—41no—
1135C24—41no—
1136C24—41no—
1137C24C24×C13711yescharacteristic
1138C24C24×C13711yescharacteristic
1139C24C24×C13711yescharacteristic
1140C24C24×C13711yescharacteristic
1141C24C24×C13711yescharacteristic
1142C2×Q8—22no—
1143C2×Q8—41no—
1144C2×Q8—41no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C2×D4—22no—
1151C2×D4—22no—
1152C2×D4—22no—
1153C2×D4—41no—
1154C2×D4—41no—
1155C2×D4—41no—
1156C2×D4—41no—
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C22×C4—22no—
1167C22×C4—22no—
1168C22×C4—22no—
1169C22×C4—22no—
1170C22×C4—22no—
1171C22×C4—22no—
1172C22×C4—22no—
1173C22×C4—22no—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—41no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—41no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—416no—
1191C22×C4C24×C13711yescharacteristic
1192C22×C4C24×C13711yescharacteristic
1193C22×C4C24×C13711yescharacteristic
1194C22×C4C24×C13711yescharacteristic
1195C22×C4C24×C13711yescharacteristic
1196C22×C4C24×C13711yescharacteristic
1197C22×C4C24×C13711yescharacteristic
1198C22×C4C24×C13711yescharacteristic
1199C22×C4C24×C13711yescharacteristic
1200C22×C4C24×C13711yescharacteristic
1201C22×C4C24×C13711yescharacteristic
1202C22×C4C24×C13711yescharacteristic
1203C22×C4C24×C13711yescharacteristic
1204C22×C4C24×C13711yescharacteristic
1205C22×C4C24×C13711yescharacteristic
1206C22×C4C24×C13711yescharacteristic
1207C22×C4C24×C13711yescharacteristic
1208C22×C4C24×C13711yescharacteristic
1209C22×C4C24×C13711yescharacteristic
1210C22×C4C24×C13711yescharacteristic
1211C22×C4C24×C13711yescharacteristic
1212C22×C4C24×C13711yescharacteristic
1213C22×C4C24×C13711yescharacteristic
1214C22×C4C24×C13711yescharacteristic
1215C22×C4C24×C13711yescharacteristic
1216C22×C4C24×C13711yescharacteristic
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—41no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—41no—
1243C4⋊C4—41no—
1244C4⋊C4—41no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—41no—
1249C4⋊C4—41no—
1250C4⋊C4—41no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C22⋊C4—22no—
1256C22⋊C4—22no—
1257C22⋊C4—22no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—22no—
1262C22⋊C4—22no—
1263C22⋊C4—22no—
1264C22⋊C4—22no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—22no—
1268C22⋊C4—22no—
1269C22⋊C4—22no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C22⋊C4—41no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4#41×C13714yes—
1305C42—22no—
1306C42—22no—
1307C42—41no—
1308C42—41no—
1309C42—41no—
1310C42—41no—
1311C42—41no—
1312C42—41no—
1313C42—41no—
1314C42—41no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—44no—
1348C23—44no—
1349C23—44no—
1350C23—44no—
1351C23—44no—
1352C23—44no—
1353C23—44no—
1354C23C2×#41×C13712yes—
1355C23H(5,𝔽2)×C13712yes—
1356C232−1+4×C13712yes—
1357C23C25×C13711yescharacteristic
1358Q8—82no—
1359D4—44no—
1360D4—44no—
1361D4—44no—
1362D4—82no—
1363D4—82no—
1364D4—82no—
1365D4—82no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—44no—
1441C2×C4—44no—
1442C2×C4—44no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—44no—
1446C2×C4—82no—
1447C2×C4—82no—
1448C2×C4C2×#41×C13712yes—
1449C2×C4C2×#41×C13712yes—
1450C2×C4H(5,𝔽2)×C13712yes—
1451C2×C4H(5,𝔽2)×C13712yes—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—22no—
1459C22—22no—
1460C22—22no—
1461C22—416no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22—41no—
1485C22—41no—
1486C22—41no—
1487C22—41no—
1488C22C22×#41×C13711yescharacteristic
1489C22C2×H(5,𝔽2)×C13711yescharacteristic
1490C22C2×H(5,𝔽2)×C13711yescharacteristic
1491C22C2×H(5,𝔽2)×C13711yescharacteristic
1492C22C2×2−1+4×C13711yescharacteristic
1493C22#585×C13711yescharacteristic
1494C22#585×C13711yescharacteristic
1495C4—22no—
1496C4—22no—
1497C4—22no—
1498C4—22no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—41no—
1518C4—41no—
1519C4—41no—
1520C4—41no—
1521C2—42no—
1522C2—42no—
1523C2—42no—
1524C2—81no—
1525C2—81no—
1526C2#3460×C13711yescharacteristic
1527C2#3513×C13711yescharacteristic
1528C2#3520×C13711yescharacteristic
1529C2#3532×C13711yescharacteristic
1530C2#3535×C13711yescharacteristic
1531C2#3539×C13711yescharacteristic
1532C2#3541×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C25
commutator, Frattini, cosocleC23C25×C137
prime radical#2678×C137C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #2849×C137C2semidirect
2. #2848×C137C2semidirect
3. #2796×C137C2semidirect
4. #2790×C137C2semidirect
5. #2779×C137C2semidirect
6. #2753×C137C2semidirect
7. #2748×C137C2semidirect
8. #2740×C137C2semidirect
9. #2735×C137C2semidirect
10. #2730×C137C2semidirect
11. #2720×C137C2semidirect
12. #2707×C137C2semidirect
13. #2698×C137C2semidirect
14. #2695×C137C2semidirect
15. #2685×C137C2semidirect
16. #2685×C137C2semidirect
18. #2672×C137C2semidirect
19. #2633×C137C2semidirect
20. #2630×C137C2semidirect
21. #2578×C137C2semidirect
22. #2573×C137C2semidirect
23. #2558×C137C2semidirect
24. #2556×C137C2semidirect
25. #2468×C137C2semidirect
26. #2461×C137C2semidirect
27. #2454×C137C2semidirect
28. #2422×C137C2semidirect
29. #2335×C137C2semidirect
30. #2334×C137C2semidirect
31. C4×#120×C137C2semidirect
35. C2×#125×C137C22semidirect
36. C2×#125×C137C22semidirect
37. C2×#124×C137C22semidirect
41. C2×#123×C137C22semidirect
51. #400×C137C22semidirect
52. #400×C137C22semidirect
53. #400×C137C22semidirect
54. #400×C137C22semidirect
58. #399×C137C22semidirect
59. #399×C137C22semidirect
60. #398×C137C22semidirect
61. #398×C137C22semidirect
62. #398×C137C22semidirect
63. #398×C137C22semidirect
64. #398×C137C22semidirect
65. #398×C137C22semidirect
70. #397×C137C22semidirect
71. #397×C137C22semidirect
72. #397×C137C22semidirect
73. #397×C137C22semidirect
79. #396×C137C22semidirect
80. #396×C137C22semidirect
81. #396×C137C22semidirect
82. #396×C137C22semidirect
83. #395×C137C22semidirect
84. #395×C137C22semidirect
95. #394×C137C22semidirect
96. #394×C137C22semidirect
99. #391×C137C22semidirect
106. #389×C137C22semidirect
107. #389×C137C22semidirect
108. #389×C137C22semidirect
109. #389×C137C22semidirect
110. #389×C137C22semidirect
111. #389×C137C22semidirect
125. #388×C137C22semidirect
126. #388×C137C22semidirect
127. #388×C137C22semidirect
128. #388×C137C22semidirect
129. #388×C137C22semidirect
130. #388×C137C22semidirect
131. #388×C137C22semidirect
132. #387×C137C22semidirect
133. #387×C137C22semidirect
134. #387×C137C22semidirect
135. #387×C137C22semidirect
136. #387×C137C22semidirect
137. #387×C137C22semidirect
138. #387×C137C22semidirect
139. #387×C137C22semidirect
140. #387×C137C22semidirect
162. #385×C137C22semidirect
163. #385×C137C22semidirect
164. #385×C137C22semidirect
165. #384×C137C22semidirect
166. #383×C137C22semidirect
167. #382×C137C22semidirect
173. #380×C137C22semidirect
174. #380×C137C22semidirect
175. #380×C137C22semidirect
180. C4×C4⋊C4×C137C22semidirect
181. C4×C4⋊C4×C137C22semidirect
182. C4×C4⋊C4×C137C22semidirect
186. C4×C22⋊C4×C137C22semidirect
766. #36888C137direct (N × H)
767. C137#36888direct (N × H)
768. #2849C2×C137semidirect
769. #2848C2×C137semidirect
770. #2796C2×C137semidirect
771. #2790C2×C137semidirect
772. #2779C2×C137semidirect
773. #2753C2×C137semidirect
774. #2748C2×C137semidirect
775. #2740C2×C137semidirect
776. #2735C2×C137semidirect
777. #2730C2×C137semidirect
778. #2720C2×C137semidirect
779. #2707C2×C137semidirect
780. #2698C2×C137semidirect
781. #2695C2×C137semidirect
782. #2685C2×C137semidirect
783. #2685C2×C137semidirect
785. #2672C2×C137semidirect
786. #2633C2×C137semidirect
787. #2630C2×C137semidirect
788. #2578C2×C137semidirect
789. #2573C2×C137semidirect
790. #2558C2×C137semidirect
791. #2556C2×C137semidirect
792. #2468C2×C137semidirect
793. #2461C2×C137semidirect
794. #2454C2×C137semidirect
795. #2422C2×C137semidirect
796. #2335C2×C137semidirect
797. #2334C2×C137semidirect
798. C4×#120C2×C137semidirect
802. C2×#125C22×C137semidirect
803. C2×#125C22×C137semidirect
804. C2×#124C22×C137semidirect
808. C2×#123C22×C137semidirect
818. #400C22×C137semidirect
819. #400C22×C137semidirect
820. #400C22×C137semidirect
821. #400C22×C137semidirect
825. #399C22×C137semidirect
826. #399C22×C137semidirect
827. #398C22×C137semidirect
828. #398C22×C137semidirect
829. #398C22×C137semidirect
830. #398C22×C137semidirect
831. #398C22×C137semidirect
832. #398C22×C137semidirect
837. #397C22×C137semidirect
838. #397C22×C137semidirect
839. #397C22×C137semidirect
840. #397C22×C137semidirect
846. #396C22×C137semidirect
847. #396C22×C137semidirect
848. #396C22×C137semidirect
849. #396C22×C137semidirect
850. #395C22×C137semidirect
851. #395C22×C137semidirect
862. #394C22×C137semidirect
863. #394C22×C137semidirect
866. #391C22×C137semidirect
873. #389C22×C137semidirect
874. #389C22×C137semidirect
875. #389C22×C137semidirect
876. #389C22×C137semidirect
877. #389C22×C137semidirect
878. #389C22×C137semidirect
892. #388C22×C137semidirect
893. #388C22×C137semidirect
894. #388C22×C137semidirect
895. #388C22×C137semidirect
896. #388C22×C137semidirect
897. #388C22×C137semidirect
898. #388C22×C137semidirect
899. #387C22×C137semidirect
900. #387C22×C137semidirect
901. #387C22×C137semidirect
902. #387C22×C137semidirect
903. #387C22×C137semidirect
904. #387C22×C137semidirect
905. #387C22×C137semidirect
906. #387C22×C137semidirect
907. #387C22×C137semidirect
929. #385C22×C137semidirect
930. #385C22×C137semidirect
931. #385C22×C137semidirect
932. #384C22×C137semidirect
933. #383C22×C137semidirect
934. #382C22×C137semidirect
940. #380C22×C137semidirect
941. #380C22×C137semidirect
942. #380C22×C137semidirect
947. C4×C4⋊C4C22×C137semidirect
948. C4×C4⋊C4C22×C137semidirect
949. C4×C4⋊C4C22×C137semidirect
953. C4×C22⋊C4C22×C137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#2849×C1372
#2848×C1372
#2796×C1372
#2790×C1372
#2779×C1372
#2753×C1372
#2748×C1372
#2740×C1372
#2735×C1372
#2730×C1372
#2720×C1372
#2707×C1372
#2698×C1372
#2695×C1372
#2685×C1372
#2678×C1372
#2672×C1372
#2633×C1372
#2630×C1372
#2578×C1372
#2573×C1372
#2558×C1372
#2556×C1372
#2468×C1372
#2461×C1372
#2454×C1372
#2422×C1372
#2335×C1372
#2334×C1372
C4×#120×C1372
#36888137