Finite Group Databasebeta

← C137×#36844 #46886230

Subgroups — C137×#36844 #46886230

Order 35072.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2853×C137C211yesmaximal, characteristic, complemented
2#2850×C137C211yesmaximal, characteristic, complemented
3#2803×C137C211yesmaximal, characteristic, complemented
4#2781×C137C211yesmaximal, characteristic, complemented
5#2778×C137C211yesmaximal, characteristic, complemented
6#2767×C137C211yesmaximal, characteristic, complemented
7#2746×C137C211yesmaximal, characteristic, complemented
8#2743×C137C211yesmaximal, characteristic, complemented
9#2732×C137C211yesmaximal, characteristic, complemented
10#2710×C137C211yesmaximal, characteristic, complemented
11#2706×C137C211yesmaximal, characteristic, complemented
12#2699×C137C211yesmaximal, characteristic, complemented
13#2696×C137C211yesmaximal, characteristic, complemented
14#2693×C137C211yesmaximal, characteristic, complemented
15#2688×C137C211yesmaximal, characteristic, complemented
16#2676×C137C211yesmaximal, characteristic, complemented
17#2673×C137C211yesmaximal, characteristic, complemented
18#2673×C137C211yesmaximal, characteristic, complemented
19#2636×C137C211yesmaximal, characteristic, complemented
20#2635×C137C211yesmaximal, characteristic, complemented
21#2529×C137C211yesmaximal, characteristic, complemented
22#2527×C137C211yesmaximal, characteristic, complemented
23#2488×C137C211yesmaximal, characteristic, complemented
24#2468×C137C211yesmaximal, characteristic, complemented
25#2467×C137C211yesmaximal, characteristic, complemented
26#2464×C137C211yesmaximal, characteristic, complemented
27#2456×C137C211yesmaximal, characteristic, complemented
28#2444×C137C211yesmaximal, characteristic, complemented
29#2328×C137C211yesmaximal, characteristic, complemented
30#2325×C137C211yesmaximal, characteristic, complemented
31C4×#121×C137C211yesmaximal, characteristic, complemented
32C2×#127×C137C2211yescharacteristic
33C2×#126×C137C2211yescharacteristic
34C2×#124×C137C2211yescharacteristic
35C2×#123×C137C2211yescharacteristic
36C2×#123×C137C2211yescharacteristic
37C2×#123×C137C2211yescharacteristic
38C2×#123×C137C2211yescharacteristic
39C2×C22⋊Q8×C137C2211yescharacteristic
40C2×C22⋊Q8×C137C2211yescharacteristic
41C2×#121×C137C2211yescharacteristic
42C2×#121×C137C2211yescharacteristic
43C2×#121×C137C2211yescharacteristic
44C2×#121×C137C2211yescharacteristic
45C2×#121×C137C2211yescharacteristic
46C2×#121×C137C2211yescharacteristic
47C2×C4×D4×C137C2211yescharacteristic
48C2×C4×D4×C137C2211yescharacteristic
49C2×C4×D4×C137C2211yescharacteristic
50C2×C4×D4×C137C2211yescharacteristic
51C2×C4×D4×C137C2211yescharacteristic
52C22×C42×C137C2211yescharacteristic
53#401×C137C2211yescharacteristic
54#400×C137C2211yescharacteristic
55#400×C137C2211yescharacteristic
56#400×C137C2211yescharacteristic
57#400×C137C2211yescharacteristic
58#400×C137C2211yescharacteristic
59#400×C137C2211yescharacteristic
60#400×C137C2211yescharacteristic
61#399×C137C2211yescharacteristic
62#399×C137C2211yescharacteristic
63#399×C137C2211yescharacteristic
64#398×C137C2211yescharacteristic
65#398×C137C2211yescharacteristic
66#398×C137C2211yescharacteristic
67#398×C137C2211yescharacteristic
68#397×C137C2211yescharacteristic
69#397×C137C2211yescharacteristic
70#397×C137C2211yescharacteristic
71#397×C137C2211yescharacteristic
72#397×C137C2211yescharacteristic
73#396×C137C2211yescharacteristic
74#396×C137C2211yescharacteristic
75#396×C137C2211yescharacteristic
76#396×C137C2211yescharacteristic
77#394×C137C2211yescharacteristic
78#394×C137C2211yescharacteristic
79#394×C137C2211yescharacteristic
80#394×C137C2211yescharacteristic
81#394×C137C2211yescharacteristic
82#394×C137C2211yescharacteristic
83#394×C137C2211yescharacteristic
84#394×C137C2211yescharacteristic
85#394×C137C2211yescharacteristic
86#394×C137C2211yescharacteristic
87#394×C137C2211yescharacteristic
88#394×C137C2211yescharacteristic
89#393×C137C2211yescharacteristic
90#393×C137C2211yescharacteristic
91#392×C137C2211yescharacteristic
92#392×C137C2211yescharacteristic
93#392×C137C2211yescharacteristic
94#392×C137C2211yescharacteristic
95#392×C137C2211yescharacteristic
96#392×C137C2211yescharacteristic
97#392×C137C2211yescharacteristic
98#392×C137C2211yescharacteristic
99#392×C137C2211yescharacteristic
100#392×C137C2211yescharacteristic
101#391×C137C2211yescharacteristic
102#391×C137C2211yescharacteristic
103#390×C137C2211yescharacteristic
104#390×C137C2211yescharacteristic
105#390×C137C2211yescharacteristic
106#390×C137C2211yescharacteristic
107#390×C137C2211yescharacteristic
108#389×C137C2211yescharacteristic
109#389×C137C2211yescharacteristic
110#388×C137C2211yescharacteristic
111#388×C137C2211yescharacteristic
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
126#388×C137C2211yescharacteristic
127#388×C137C2211yescharacteristic
128#388×C137C2211yescharacteristic
129#387×C137C2211yescharacteristic
130#387×C137C2211yescharacteristic
131#387×C137C2211yescharacteristic
132#387×C137C2211yescharacteristic
133#387×C137C2211yescharacteristic
134#387×C137C2211yescharacteristic
135#387×C137C2211yescharacteristic
136#387×C137C2211yescharacteristic
137#387×C137C2211yescharacteristic
138#387×C137C2211yescharacteristic
139#386×C137C2211yescharacteristic
140#386×C137C2211yescharacteristic
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#386×C137C2211yescharacteristic
150#386×C137C2211yescharacteristic
151#386×C137C2211yescharacteristic
152#386×C137C2211yescharacteristic
153#386×C137C2211yescharacteristic
154#386×C137C2211yescharacteristic
155#386×C137C2211yescharacteristic
156#386×C137C2211yescharacteristic
157#386×C137C2211yescharacteristic
158#386×C137C2211yescharacteristic
159#386×C137C2211yescharacteristic
160#386×C137C2211yescharacteristic
161#386×C137C2211yescharacteristic
162#386×C137C2211yescharacteristic
163#385×C137C2211yescharacteristic
164#385×C137C2211yescharacteristic
165#385×C137C2211yescharacteristic
166#385×C137C2211yescharacteristic
167#385×C137C2211yescharacteristic
168#385×C137C2211yescharacteristic
169#385×C137C2211yescharacteristic
170#385×C137C2211yescharacteristic
171#382×C137C2211yescharacteristic
172#382×C137C2211yescharacteristic
173#382×C137C2211yescharacteristic
174#381×C137C2211yescharacteristic
175#381×C137C2211yescharacteristic
176#381×C137C2211yescharacteristic
177#381×C137C2211yescharacteristic
178#380×C137C2211yescharacteristic
179#380×C137C2211yescharacteristic
180#380×C137C2211yescharacteristic
181#380×C137C2211yescharacteristic
182C4×C4⋊C4×C137C2211yescharacteristic
183C4×C22⋊C4×C137C2211yescharacteristic
184C4×C22⋊C4×C137C2211yescharacteristic
185#376×C137C2211yescharacteristic
186C2×#95×C137C2211yescharacteristic
187C22×Q8×C137C2311yescharacteristic
188C22×D4×C137C2311yescharacteristic
189C22×D4×C137C2311yescharacteristic
190C22×D4×C137C2311yescharacteristic
191C22×D4×C137C2311yescharacteristic
192C22×D4×C137C2311yescharacteristic
193C22×D4×C137C2311yescharacteristic
194C22×D4×C137C2311yescharacteristic
195C22×D4×C137C2311yescharacteristic
196C22×D4×C137C2311yescharacteristic
197C22×D4×C137C2311yescharacteristic
198C22×D4×C137C2311yescharacteristic
199C22×D4×C137C2311yescharacteristic
200C22×D4×C137C2311yescharacteristic
201C22×D4×C137C2311yescharacteristic
202C22×D4×C137C2311yescharacteristic
203C23×C4×C137C2311yescharacteristic
204C23×C4×C137C2311yescharacteristic
205C23×C4×C137C2311yescharacteristic
206C23×C4×C137C2311yescharacteristic
207C23×C4×C137C2311yescharacteristic
208C23×C4×C137C2311yescharacteristic
209C23×C4×C137C2311yescharacteristic
210C23×C4×C137C2311yescharacteristic
211C23×C4×C137C2311yescharacteristic
212C23×C4×C137C2311yescharacteristic
213#127×C137—24no—
214#126×C137—42no—
215#124×C137—42no—
216#123×C137—42no—
217#123×C137—42no—
218#123×C137—42no—
219#123×C137—42no—
220C22⋊Q8×C137—42no—
221C22⋊Q8×C137—42no—
222#121×C137—24no—
223#121×C137—24no—
224#121×C137—42no—
225#121×C137—42no—
226#121×C137—42no—
227#121×C137—42no—
228C4×D4×C137—42no—
229C4×D4×C137—42no—
230C4×D4×C137—42no—
231C4×D4×C137—42no—
232C4×D4×C137—42no—
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×C22⋊C4×C137C2311yescharacteristic
260C2×C22⋊C4×C137C2311yescharacteristic
261C2×C22⋊C4×C137C2311yescharacteristic
262C2×C22⋊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×C42×C137—42no—
310C2×C42×C137C2311yescharacteristic
311C2×C42×C137C2311yescharacteristic
312C2×C42×C137C2311yescharacteristic
313C2×C42×C137C2311yescharacteristic
314C2×C42×C137C2311yescharacteristic
315C2×C42×C137C2311yescharacteristic
316C2×C42×C137C2311yescharacteristic
317C2×C42×C137C2311yescharacteristic
318C2×C42×C137C2311yescharacteristic
319#95×C137C2311yescharacteristic
320#95×C137C2311yescharacteristic
321#95×C137C2311yescharacteristic
322#95×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×C137C2411yescharacteristic
364C24×C137C2411yescharacteristic
365C24×C137C2411yescharacteristic
366C24×C137C2411yescharacteristic
367C24×C137C2411yescharacteristic
368C24×C137C2411yescharacteristic
369C2×Q8×C137—22no—
370C2×Q8×C137—41no—
371C2×Q8×C137—41no—
372C2×D4×C137—22no—
373C2×D4×C137—22no—
374C2×D4×C137—22no—
375C2×D4×C137—22no—
376C2×D4×C137—22no—
377C2×D4×C137—22no—
378C2×D4×C137—22no—
379C2×D4×C137—22no—
380C2×D4×C137—22no—
381C2×D4×C137—22no—
382C2×D4×C137—22no—
383C2×D4×C137—41no—
384C2×D4×C137—41no—
385C2×D4×C137—41no—
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—
399C2×D4×C137—41no—
400C2×D4×C137—41no—
401C2×D4×C137—41no—
402C2×D4×C137—41no—
403C2×D4×C137—41no—
404C2×D4×C137—41no—
405C2×D4×C137—41no—
406C2×D4×C137—41no—
407C2×D4×C137—41no—
408C2×D4×C137—41no—
409C2×D4×C137—41no—
410C2×D4×C137—41no—
411C2×D4×C137—41no—
412C2×D4×C137—41no—
413C2×D4×C137—41no—
414C2×D4×C137—41no—
415C2×D4×C137—41no—
416C2×D4×C137#4114yes—
417C22×C4×C137—22no—
418C22×C4×C137—22no—
419C22×C4×C137—22no—
420C22×C4×C137—22no—
421C22×C4×C137—22no—
422C22×C4×C137—22no—
423C22×C4×C137—22no—
424C22×C4×C137—41no—
425C22×C4×C137—41no—
426C22×C4×C137—41no—
427C22×C4×C137—41no—
428C22×C4×C137—41no—
429C22×C4×C137—41no—
430C22×C4×C137—41no—
431C22×C4×C137—41no—
432C22×C4×C137—41no—
433C22×C4×C137—41no—
434C22×C4×C137—41no—
435C22×C4×C137—41no—
436C22×C4×C137—41no—
437C22×C4×C137—41no—
438C22×C4×C137—41no—
439C22×C4×C137—41no—
440C22×C4×C137—41no—
441C22×C4×C137—41no—
442C22×C4×C137—41no—
443C22×C4×C137—41no—
444C22×C4×C137—41no—
445C22×C4×C137—41no—
446C22×C4×C137—41no—
447C22×C4×C137C2411yescharacteristic
448C22×C4×C137C2411yescharacteristic
449C22×C4×C137C2411yescharacteristic
450C22×C4×C137C2411yescharacteristic
451C22×C4×C137C2411yescharacteristic
452C22×C4×C137C2411yescharacteristic
453C22×C4×C137C2411yescharacteristic
454C22×C4×C137C2411yescharacteristic
455C22×C4×C137C2411yescharacteristic
456C22×C4×C137C2411yescharacteristic
457C22×C4×C137C2411yescharacteristic
458C22×C4×C137C2411yescharacteristic
459C22×C4×C137C2411yescharacteristic
460C22×C4×C137C2411yescharacteristic
461C22×C4×C137C2411yescharacteristic
462C22×C4×C137C2411yescharacteristic
463C22×C4×C137C2411yescharacteristic
464C22×C4×C137C2411yescharacteristic
465C22×C4×C137C2411yescharacteristic
466C22×C4×C137C2411yescharacteristic
467C22×C4×C137C2411yescharacteristic
468C22×C4×C137C2411yescharacteristic
469C22×C4×C137C2411yescharacteristic
470C22×C4×C137C2411yescharacteristic
471C22×C4×C137C2411yescharacteristic
472C4⋊C4×C137—22no—
473C4⋊C4×C137—22no—
474C4⋊C4×C137—22no—
475C4⋊C4×C137—22no—
476C4⋊C4×C137—22no—
477C4⋊C4×C137—22no—
478C4⋊C4×C137—22no—
479C4⋊C4×C137—22no—
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—
488C4⋊C4×C137—41no—
489C4⋊C4×C137—41no—
490C4⋊C4×C137—41no—
491C4⋊C4×C137—41no—
492C4⋊C4×C137—41no—
493C4⋊C4×C137—41no—
494C4⋊C4×C137—41no—
495C4⋊C4×C137—41no—
496C4⋊C4×C137—41no—
497C4⋊C4×C137—41no—
498C22⋊C4×C137—22no—
499C22⋊C4×C137—22no—
500C22⋊C4×C137—22no—
501C22⋊C4×C137—22no—
502C22⋊C4×C137—22no—
503C22⋊C4×C137—22no—
504C22⋊C4×C137—22no—
505C22⋊C4×C137—22no—
506C22⋊C4×C137—22no—
507C22⋊C4×C137—22no—
508C22⋊C4×C137—22no—
509C22⋊C4×C137—22no—
510C22⋊C4×C137—22no—
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—41no—
538C22⋊C4×C137—41no—
539C22⋊C4×C137—41no—
540C22⋊C4×C137—41no—
541C22⋊C4×C137—41no—
542C22⋊C4×C137—41no—
543C22⋊C4×C137—41no—
544C22⋊C4×C137—41no—
545C22⋊C4×C137—41no—
546C22⋊C4×C137—41no—
547C22⋊C4×C137—41no—
548C42×C137—22no—
549C42×C137—22no—
550C42×C137—22no—
551C42×C137—22no—
552C42×C137—22no—
553C42×C137—41no—
554C42×C137—41no—
555C42×C137—41no—
556C42×C137—41no—
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—21no—
581C23×C137—21no—
582C23×C137—21no—
583C23×C137—21no—
584C23×C137—21no—
585C23×C137—21no—
586C23×C137—21no—
587C23×C137—21no—
588C23×C137—21no—
589C23×C137—21no—
590C23×C137—21no—
591C23×C137—21no—
592C23×C137—21no—
593C23×C137—21no—
594C23×C137—21no—
595C23×C137—21no—
596C23×C137—21no—
597C23×C137C2×#4112yes—
598C23×C137C2×#4112yes—
599C23×C137C2511yescharacteristic
600Q8×C137—82no—
601D4×C137—44no—
602D4×C137—44no—
603D4×C137—44no—
604D4×C137—44no—
605D4×C137—44no—
606D4×C137—82no—
607D4×C137—82no—
608D4×C137—82no—
609D4×C137—82no—
610D4×C137—82no—
611D4×C137—82no—
612D4×C137—82no—
613D4×C137—82no—
614D4×C137—82no—
615D4×C137—82no—
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—21no—
674C2×C4×C137—21no—
675C2×C4×C137—21no—
676C2×C4×C137—21no—
677C2×C4×C137—21no—
678C2×C4×C137—21no—
679C2×C4×C137—21no—
680C2×C4×C137—21no—
681C2×C4×C137—21no—
682C2×C4×C137—21no—
683C2×C4×C137—21no—
684C2×C4×C137—21no—
685C2×C4×C137—21no—
686C2×C4×C137—21no—
687C2×C4×C137—44no—
688C2×C4×C137—44no—
689C2×C4×C137—44no—
690C2×C4×C137—82no—
691C2×C4×C137—82no—
692C2×C4×C137—82no—
693C2×C4×C137—82no—
694C2×C4×C137—82no—
695C2×C4×C137—82no—
696C2×C4×C137—82no—
697C2×C4×C137C2×#4112yes—
698C2×C4×C137H(5,𝔽2)12yes—
699C2×C4×C137H(5,𝔽2)12yes—
700C2×C4×C137H(5,𝔽2)12yes—
701C22×C137—22no—
702C22×C137—22no—
703C22×C137—22no—
704C22×C137—22no—
705C22×C137—22no—
706C22×C137—22no—
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×C137—41no—
722C22×C137—41no—
723C22×C137—41no—
724C22×C137—41no—
725C22×C137—41no—
726C22×C137—41no—
727C22×C137—41no—
728C22×C137—41no—
729C22×C137—41no—
730C22×C137—41no—
731C22×C137—41no—
732C22×C137—41no—
733C22×C137—41no—
734C22×C137—41no—
735C22×C137—41no—
736C22×C137—41no—
737C22×C137—41no—
738C22×C137—41no—
739C22×C137—41no—
740C22×C137—41no—
741C22×C137—41no—
742C22×C137—41no—
743C22×C137C22×#4111yescharacteristic
744C22×C137C2×H(5,𝔽2)11yescharacteristic
745C22×C137C2×H(5,𝔽2)11yescharacteristic
746C22×C137C2×H(5,𝔽2)11yescharacteristic
747C22×C137#58511yescharacteristic
748C22×C137#58511yescharacteristic
749C22×C137#58511yescharacteristic
750C4×C137—22no—
751C4×C137—22no—
752C4×C137—22no—
753C4×C137—22no—
754C4×C137—41no—
755C4×C137—41no—
756C4×C137—41no—
757C4×C137—41no—
758C4×C137—41no—
759C4×C137—41no—
760C4×C137—41no—
761C4×C137—41no—
762C4×C137—41no—
763C4×C137—41no—
764C4×C137—41no—
765C4×C137—41no—
766C4×C137—41no—
767C4×C137—41no—
768C4×C137—41no—
769C4×C137—41no—
770C4×C137—41no—
771C4×C137—41no—
772C4×C137—41no—
773C4×C137—41no—
774C4×C137—41no—
775C2×C137—42no—
776C2×C137—42no—
777C2×C137—81no—
778C2×C137—81no—
779C2×C137—81no—
780C2×C137—81no—
781C2×C137#345911yescharacteristic
782C2×C137#351311yescharacteristic
783C2×C137#351411yescharacteristic
784C2×C137#354211yescharacteristic
785C2×C137#354211yescharacteristic
786C2×C137#354611yescharacteristic
787C2×C137#356711yescharacteristic
788#36844C13711yesmaximal, characteristic, direct product factor, Sylow
789C137#3684411yescharacteristic, direct product factor, Sylow
790#2853C2×C13711yescharacteristic, complemented
791#2850C2×C13711yescharacteristic, complemented
792#2803C2×C13711yescharacteristic, complemented
793#2781C2×C13711yescharacteristic, complemented
794#2778C2×C13711yescharacteristic, complemented
795#2767C2×C13711yescharacteristic, complemented
796#2746C2×C13711yescharacteristic, complemented
797#2743C2×C13711yescharacteristic, complemented
798#2732C2×C13711yescharacteristic, complemented
799#2710C2×C13711yescharacteristic, complemented
800#2706C2×C13711yescharacteristic, complemented
801#2699C2×C13711yescharacteristic, complemented
802#2696C2×C13711yescharacteristic, complemented
803#2693C2×C13711yescharacteristic, complemented
804#2688C2×C13711yescharacteristic, complemented
805#2676C2×C13711yescharacteristic, complemented
806#2673C2×C13711yescharacteristic, complemented
807#2673C2×C13711yescharacteristic, complemented
808#2636C2×C13711yescharacteristic, complemented
809#2635C2×C13711yescharacteristic, complemented
810#2529C2×C13711yescharacteristic, complemented
811#2527C2×C13711yescharacteristic, complemented
812#2488C2×C13711yescharacteristic, complemented
813#2468C2×C13711yescharacteristic, complemented
814#2467C2×C13711yescharacteristic, complemented
815#2464C2×C13711yescharacteristic, complemented
816#2456C2×C13711yescharacteristic, complemented
817#2444C2×C13711yescharacteristic, complemented
818#2328C2×C13711yescharacteristic, complemented
819#2325C2×C13711yescharacteristic, complemented
820C4×#121C2×C13711yescharacteristic, complemented
821C2×#127C22×C13711yescharacteristic
822C2×#126C22×C13711yescharacteristic
823C2×#124C22×C13711yescharacteristic
824C2×#123C22×C13711yescharacteristic
825C2×#123C22×C13711yescharacteristic
826C2×#123C22×C13711yescharacteristic
827C2×#123C22×C13711yescharacteristic
828C2×C22⋊Q8C22×C13711yescharacteristic
829C2×C22⋊Q8C22×C13711yescharacteristic
830C2×#121C22×C13711yescharacteristic
831C2×#121C22×C13711yescharacteristic
832C2×#121C22×C13711yescharacteristic
833C2×#121C22×C13711yescharacteristic
834C2×#121C22×C13711yescharacteristic
835C2×#121C22×C13711yescharacteristic
836C2×C4×D4C22×C13711yescharacteristic
837C2×C4×D4C22×C13711yescharacteristic
838C2×C4×D4C22×C13711yescharacteristic
839C2×C4×D4C22×C13711yescharacteristic
840C2×C4×D4C22×C13711yescharacteristic
841C22×C42C22×C13711yescharacteristic
842#401C22×C13711yescharacteristic
843#400C22×C13711yescharacteristic
844#400C22×C13711yescharacteristic
845#400C22×C13711yescharacteristic
846#400C22×C13711yescharacteristic
847#400C22×C13711yescharacteristic
848#400C22×C13711yescharacteristic
849#400C22×C13711yescharacteristic
850#399C22×C13711yescharacteristic
851#399C22×C13711yescharacteristic
852#399C22×C13711yescharacteristic
853#398C22×C13711yescharacteristic
854#398C22×C13711yescharacteristic
855#398C22×C13711yescharacteristic
856#398C22×C13711yescharacteristic
857#397C22×C13711yescharacteristic
858#397C22×C13711yescharacteristic
859#397C22×C13711yescharacteristic
860#397C22×C13711yescharacteristic
861#397C22×C13711yescharacteristic
862#396C22×C13711yescharacteristic
863#396C22×C13711yescharacteristic
864#396C22×C13711yescharacteristic
865#396C22×C13711yescharacteristic
866#394C22×C13711yescharacteristic
867#394C22×C13711yescharacteristic
868#394C22×C13711yescharacteristic
869#394C22×C13711yescharacteristic
870#394C22×C13711yescharacteristic
871#394C22×C13711yescharacteristic
872#394C22×C13711yescharacteristic
873#394C22×C13711yescharacteristic
874#394C22×C13711yescharacteristic
875#394C22×C13711yescharacteristic
876#394C22×C13711yescharacteristic
877#394C22×C13711yescharacteristic
878#393C22×C13711yescharacteristic
879#393C22×C13711yescharacteristic
880#392C22×C13711yescharacteristic
881#392C22×C13711yescharacteristic
882#392C22×C13711yescharacteristic
883#392C22×C13711yescharacteristic
884#392C22×C13711yescharacteristic
885#392C22×C13711yescharacteristic
886#392C22×C13711yescharacteristic
887#392C22×C13711yescharacteristic
888#392C22×C13711yescharacteristic
889#392C22×C13711yescharacteristic
890#391C22×C13711yescharacteristic
891#391C22×C13711yescharacteristic
892#390C22×C13711yescharacteristic
893#390C22×C13711yescharacteristic
894#390C22×C13711yescharacteristic
895#390C22×C13711yescharacteristic
896#390C22×C13711yescharacteristic
897#389C22×C13711yescharacteristic
898#389C22×C13711yescharacteristic
899#388C22×C13711yescharacteristic
900#388C22×C13711yescharacteristic
901#388C22×C13711yescharacteristic
902#388C22×C13711yescharacteristic
903#388C22×C13711yescharacteristic
904#388C22×C13711yescharacteristic
905#388C22×C13711yescharacteristic
906#388C22×C13711yescharacteristic
907#388C22×C13711yescharacteristic
908#388C22×C13711yescharacteristic
909#388C22×C13711yescharacteristic
910#388C22×C13711yescharacteristic
911#388C22×C13711yescharacteristic
912#388C22×C13711yescharacteristic
913#388C22×C13711yescharacteristic
914#388C22×C13711yescharacteristic
915#388C22×C13711yescharacteristic
916#388C22×C13711yescharacteristic
917#388C22×C13711yescharacteristic
918#387C22×C13711yescharacteristic
919#387C22×C13711yescharacteristic
920#387C22×C13711yescharacteristic
921#387C22×C13711yescharacteristic
922#387C22×C13711yescharacteristic
923#387C22×C13711yescharacteristic
924#387C22×C13711yescharacteristic
925#387C22×C13711yescharacteristic
926#387C22×C13711yescharacteristic
927#387C22×C13711yescharacteristic
928#386C22×C13711yescharacteristic
929#386C22×C13711yescharacteristic
930#386C22×C13711yescharacteristic
931#386C22×C13711yescharacteristic
932#386C22×C13711yescharacteristic
933#386C22×C13711yescharacteristic
934#386C22×C13711yescharacteristic
935#386C22×C13711yescharacteristic
936#386C22×C13711yescharacteristic
937#386C22×C13711yescharacteristic
938#386C22×C13711yescharacteristic
939#386C22×C13711yescharacteristic
940#386C22×C13711yescharacteristic
941#386C22×C13711yescharacteristic
942#386C22×C13711yescharacteristic
943#386C22×C13711yescharacteristic
944#386C22×C13711yescharacteristic
945#386C22×C13711yescharacteristic
946#386C22×C13711yescharacteristic
947#386C22×C13711yescharacteristic
948#386C22×C13711yescharacteristic
949#386C22×C13711yescharacteristic
950#386C22×C13711yescharacteristic
951#386C22×C13711yescharacteristic
952#385C22×C13711yescharacteristic
953#385C22×C13711yescharacteristic
954#385C22×C13711yescharacteristic
955#385C22×C13711yescharacteristic
956#385C22×C13711yescharacteristic
957#385C22×C13711yescharacteristic
958#385C22×C13711yescharacteristic
959#385C22×C13711yescharacteristic
960#382C22×C13711yescharacteristic
961#382C22×C13711yescharacteristic
962#382C22×C13711yescharacteristic
963#381C22×C13711yescharacteristic
964#381C22×C13711yescharacteristic
965#381C22×C13711yescharacteristic
966#381C22×C13711yescharacteristic
967#380C22×C13711yescharacteristic
968#380C22×C13711yescharacteristic
969#380C22×C13711yescharacteristic
970#380C22×C13711yescharacteristic
971C4×C4⋊C4C22×C13711yescharacteristic
972C4×C22⋊C4C22×C13711yescharacteristic
973C4×C22⋊C4C22×C13711yescharacteristic
974#376C22×C13711yescharacteristic
975C2×#95C22×C13711yescharacteristic
976C22×Q8C23×C13711yescharacteristic
977C22×D4C23×C13711yescharacteristic
978C22×D4C23×C13711yescharacteristic
979C22×D4C23×C13711yescharacteristic
980C22×D4C23×C13711yescharacteristic
981C22×D4C23×C13711yescharacteristic
982C22×D4C23×C13711yescharacteristic
983C22×D4C23×C13711yescharacteristic
984C22×D4C23×C13711yescharacteristic
985C22×D4C23×C13711yescharacteristic
986C22×D4C23×C13711yescharacteristic
987C22×D4C23×C13711yescharacteristic
988C22×D4C23×C13711yescharacteristic
989C22×D4C23×C13711yescharacteristic
990C22×D4C23×C13711yescharacteristic
991C22×D4C23×C13711yescharacteristic
992C23×C4C23×C13711yescharacteristic
993C23×C4C23×C13711yescharacteristic
994C23×C4C23×C13711yescharacteristic
995C23×C4C23×C13711yescharacteristic
996C23×C4C23×C13711yescharacteristic
997C23×C4C23×C13711yescharacteristic
998C23×C4C23×C13711yescharacteristic
999C23×C4C23×C13711yescharacteristic
1000C23×C4C23×C13711yescharacteristic
1001C23×C4C23×C13711yescharacteristic
1002#127—24no—
1003#126—42no—
1004#124—42no—
1005#123—42no—
1006#123—42no—
1007#123—42no—
1008#123—42no—
1009C22⋊Q8—42no—
1010C22⋊Q8—42no—
1011#121—24no—
1012#121—24no—
1013#121—42no—
1014#121—42no—
1015#121—42no—
1016#121—42no—
1017C4×D4—42no—
1018C4×D4—42no—
1019C4×D4—42no—
1020C4×D4—42no—
1021C4×D4—42no—
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×C4⋊C4C23×C13711yescharacteristic
1031C2×C4⋊C4C23×C13711yescharacteristic
1032C2×C4⋊C4C23×C13711yescharacteristic
1033C2×C4⋊C4C23×C13711yescharacteristic
1034C2×C4⋊C4C23×C13711yescharacteristic
1035C2×C4⋊C4C23×C13711yescharacteristic
1036C2×C4⋊C4C23×C13711yescharacteristic
1037C2×C4⋊C4C23×C13711yescharacteristic
1038C2×C4⋊C4C23×C13711yescharacteristic
1039C2×C4⋊C4C23×C13711yescharacteristic
1040C2×C4⋊C4C23×C13711yescharacteristic
1041C2×C4⋊C4C23×C13711yescharacteristic
1042C2×C4⋊C4C23×C13711yescharacteristic
1043C2×C4⋊C4C23×C13711yescharacteristic
1044C2×C4⋊C4C23×C13711yescharacteristic
1045C2×C4⋊C4C23×C13711yescharacteristic
1046C2×C4⋊C4C23×C13711yescharacteristic
1047C2×C4⋊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×C22⋊C4C23×C13711yescharacteristic
1081C2×C22⋊C4C23×C13711yescharacteristic
1082C2×C22⋊C4C23×C13711yescharacteristic
1083C2×C22⋊C4C23×C13711yescharacteristic
1084C2×C22⋊C4C23×C13711yescharacteristic
1085C2×C22⋊C4C23×C13711yescharacteristic
1086C2×C22⋊C4C23×C13711yescharacteristic
1087C2×C22⋊C4C23×C13711yescharacteristic
1088C2×C22⋊C4C23×C13711yescharacteristic
1089C2×C22⋊C4C23×C13711yescharacteristic
1090C2×C22⋊C4C23×C13711yescharacteristic
1091C2×C22⋊C4C23×C13711yescharacteristic
1092C2×C22⋊C4C23×C13711yescharacteristic
1093C2×C22⋊C4C23×C13711yescharacteristic
1094C2×C22⋊C4C23×C13711yescharacteristic
1095C2×C22⋊C4C23×C13711yescharacteristic
1096C2×C22⋊C4C23×C13711yescharacteristic
1097C2×C22⋊C4C23×C13711yescharacteristic
1098C2×C42—42no—
1099C2×C42C23×C13711yescharacteristic
1100C2×C42C23×C13711yescharacteristic
1101C2×C42C23×C13711yescharacteristic
1102C2×C42C23×C13711yescharacteristic
1103C2×C42C23×C13711yescharacteristic
1104C2×C42C23×C13711yescharacteristic
1105C2×C42C23×C13711yescharacteristic
1106C2×C42C23×C13711yescharacteristic
1107C2×C42C23×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
1130#95C23×C13711yescharacteristic
1131#95C23×C13711yescharacteristic
1132#95C23×C13711yescharacteristic
1133#95C23×C13711yescharacteristic
1134#95C23×C13711yescharacteristic
1135#95C23×C13711yescharacteristic
1136#95C23×C13711yescharacteristic
1137#95C23×C13711yescharacteristic
1138#95C23×C13711yescharacteristic
1139#95C23×C13711yescharacteristic
1140#95C23×C13711yescharacteristic
1141#95C23×C13711yescharacteristic
1142#95C23×C13711yescharacteristic
1143#95C23×C13711yescharacteristic
1144#95C23×C13711yescharacteristic
1145#95C23×C13711yescharacteristic
1146#95C23×C13711yescharacteristic
1147#95C23×C13711yescharacteristic
1148#95C23×C13711yescharacteristic
1149#95C23×C13711yescharacteristic
1150#95C23×C13711yescharacteristic
1151#95C23×C13711yescharacteristic
1152C24C24×C13711yescharacteristic
1153C24C24×C13711yescharacteristic
1154C24C24×C13711yescharacteristic
1155C24C24×C13711yescharacteristic
1156C24C24×C13711yescharacteristic
1157C24C24×C13711yescharacteristic
1158C2×Q8—22no—
1159C2×Q8—41no—
1160C2×Q8—41no—
1161C2×D4—22no—
1162C2×D4—22no—
1163C2×D4—22no—
1164C2×D4—22no—
1165C2×D4—22no—
1166C2×D4—22no—
1167C2×D4—22no—
1168C2×D4—22no—
1169C2×D4—22no—
1170C2×D4—22no—
1171C2×D4—22no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4—41no—
1178C2×D4—41no—
1179C2×D4—41no—
1180C2×D4—41no—
1181C2×D4—41no—
1182C2×D4—41no—
1183C2×D4—41no—
1184C2×D4—41no—
1185C2×D4—41no—
1186C2×D4—41no—
1187C2×D4—41no—
1188C2×D4—41no—
1189C2×D4—41no—
1190C2×D4—41no—
1191C2×D4—41no—
1192C2×D4—41no—
1193C2×D4—41no—
1194C2×D4—41no—
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—41no—
1202C2×D4—41no—
1203C2×D4—41no—
1204C2×D4—41no—
1205C2×D4#41×C13714yes—
1206C22×C4—22no—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—22no—
1213C22×C4—41no—
1214C22×C4—41no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4C24×C13711yescharacteristic
1237C22×C4C24×C13711yescharacteristic
1238C22×C4C24×C13711yescharacteristic
1239C22×C4C24×C13711yescharacteristic
1240C22×C4C24×C13711yescharacteristic
1241C22×C4C24×C13711yescharacteristic
1242C22×C4C24×C13711yescharacteristic
1243C22×C4C24×C13711yescharacteristic
1244C22×C4C24×C13711yescharacteristic
1245C22×C4C24×C13711yescharacteristic
1246C22×C4C24×C13711yescharacteristic
1247C22×C4C24×C13711yescharacteristic
1248C22×C4C24×C13711yescharacteristic
1249C22×C4C24×C13711yescharacteristic
1250C22×C4C24×C13711yescharacteristic
1251C22×C4C24×C13711yescharacteristic
1252C22×C4C24×C13711yescharacteristic
1253C22×C4C24×C13711yescharacteristic
1254C22×C4C24×C13711yescharacteristic
1255C22×C4C24×C13711yescharacteristic
1256C22×C4C24×C13711yescharacteristic
1257C22×C4C24×C13711yescharacteristic
1258C22×C4C24×C13711yescharacteristic
1259C22×C4C24×C13711yescharacteristic
1260C22×C4C24×C13711yescharacteristic
1261C4⋊C4—22no—
1262C4⋊C4—22no—
1263C4⋊C4—22no—
1264C4⋊C4—22no—
1265C4⋊C4—22no—
1266C4⋊C4—22no—
1267C4⋊C4—22no—
1268C4⋊C4—22no—
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—41no—
1277C4⋊C4—41no—
1278C4⋊C4—41no—
1279C4⋊C4—41no—
1280C4⋊C4—41no—
1281C4⋊C4—41no—
1282C4⋊C4—41no—
1283C4⋊C4—41no—
1284C4⋊C4—41no—
1285C4⋊C4—41no—
1286C4⋊C4—41no—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—22no—
1290C22⋊C4—22no—
1291C22⋊C4—22no—
1292C22⋊C4—22no—
1293C22⋊C4—22no—
1294C22⋊C4—22no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—41no—
1311C22⋊C4—41no—
1312C22⋊C4—41no—
1313C22⋊C4—41no—
1314C22⋊C4—41no—
1315C22⋊C4—41no—
1316C22⋊C4—41no—
1317C22⋊C4—41no—
1318C22⋊C4—41no—
1319C22⋊C4—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C42—22no—
1338C42—22no—
1339C42—22no—
1340C42—22no—
1341C42—22no—
1342C42—41no—
1343C42—41no—
1344C42—41no—
1345C42—41no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23C2×#41×C13712yes—
1387C23C2×#41×C13712yes—
1388C23C25×C13711yescharacteristic
1389Q8—82no—
1390D4—44no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—44no—
1395D4—82no—
1396D4—82no—
1397D4—82no—
1398D4—82no—
1399D4—82no—
1400D4—82no—
1401D4—82no—
1402D4—82no—
1403D4—82no—
1404D4—82no—
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—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—44no—
1477C2×C4—44no—
1478C2×C4—44no—
1479C2×C4—82no—
1480C2×C4—82no—
1481C2×C4—82no—
1482C2×C4—82no—
1483C2×C4—82no—
1484C2×C4—82no—
1485C2×C4—82no—
1486C2×C4C2×#41×C13712yes—
1487C2×C4H(5,𝔽2)×C13712yes—
1488C2×C4H(5,𝔽2)×C13712yes—
1489C2×C4H(5,𝔽2)×C13712yes—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22C22×#41×C13711yescharacteristic
1533C22C2×H(5,𝔽2)×C13711yescharacteristic
1534C22C2×H(5,𝔽2)×C13711yescharacteristic
1535C22C2×H(5,𝔽2)×C13711yescharacteristic
1536C22#585×C13711yescharacteristic
1537C22#585×C13711yescharacteristic
1538C22#585×C13711yescharacteristic
1539C4—22no—
1540C4—22no—
1541C4—22no—
1542C4—22no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—41no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C2—42no—
1565C2—42no—
1566C2—81no—
1567C2—81no—
1568C2—81no—
1569C2—81no—
1570C2#3459×C13711yescharacteristic
1571C2#3513×C13711yescharacteristic
1572C2#3514×C13711yescharacteristic
1573C2#3542×C13711yescharacteristic
1574C2#3542×C13711yescharacteristic
1575C2#3546×C13711yescharacteristic
1576C2#3567×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C25
commutator, Frattini, cosocleC23C25×C137
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2853×C137C2semidirect
2. #2850×C137C2semidirect
3. #2803×C137C2semidirect
4. #2781×C137C2semidirect
5. #2778×C137C2semidirect
6. #2767×C137C2semidirect
7. #2746×C137C2semidirect
8. #2743×C137C2semidirect
9. #2732×C137C2semidirect
10. #2710×C137C2semidirect
11. #2706×C137C2semidirect
12. #2699×C137C2semidirect
13. #2696×C137C2semidirect
14. #2693×C137C2semidirect
15. #2688×C137C2semidirect
16. #2676×C137C2semidirect
17. #2673×C137C2semidirect
18. #2673×C137C2semidirect
19. #2636×C137C2semidirect
20. #2635×C137C2semidirect
21. #2529×C137C2semidirect
22. #2527×C137C2semidirect
23. #2488×C137C2semidirect
24. #2468×C137C2semidirect
25. #2467×C137C2semidirect
26. #2464×C137C2semidirect
27. #2456×C137C2semidirect
28. #2444×C137C2semidirect
29. #2328×C137C2semidirect
30. #2325×C137C2semidirect
31. C4×#121×C137C2semidirect
788. #36844C137direct (N × H)
789. C137#36844direct (N × H)
790. #2853C2×C137semidirect
791. #2850C2×C137semidirect
792. #2803C2×C137semidirect
793. #2781C2×C137semidirect
794. #2778C2×C137semidirect
795. #2767C2×C137semidirect
796. #2746C2×C137semidirect
797. #2743C2×C137semidirect
798. #2732C2×C137semidirect
799. #2710C2×C137semidirect
800. #2706C2×C137semidirect
801. #2699C2×C137semidirect
802. #2696C2×C137semidirect
803. #2693C2×C137semidirect
804. #2688C2×C137semidirect
805. #2676C2×C137semidirect
806. #2673C2×C137semidirect
807. #2673C2×C137semidirect
808. #2636C2×C137semidirect
809. #2635C2×C137semidirect
810. #2529C2×C137semidirect
811. #2527C2×C137semidirect
812. #2488C2×C137semidirect
813. #2468C2×C137semidirect
814. #2467C2×C137semidirect
815. #2464C2×C137semidirect
816. #2456C2×C137semidirect
817. #2444C2×C137semidirect
818. #2328C2×C137semidirect
819. #2325C2×C137semidirect
820. C4×#121C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2853×C1372
#2850×C1372
#2803×C1372
#2781×C1372
#2778×C1372
#2767×C1372
#2746×C1372
#2743×C1372
#2732×C1372
#2710×C1372
#2706×C1372
#2699×C1372
#2696×C1372
#2693×C1372
#2688×C1372
#2676×C1372
#2673×C1372
#2636×C1372
#2635×C1372
#2529×C1372
#2527×C1372
#2488×C1372
#2468×C1372
#2467×C1372
#2464×C1372
#2456×C1372
#2444×C1372
#2328×C1372
#2325×C1372
C4×#121×C1372
#36844137