Finite Group Databasebeta

← C73×#36827 #32946231

Subgroups — C73×#36827 #32946231

Order 18688.

1610 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2855C211yesmaximal, characteristic, complemented
2C73×#2854C211yesmaximal, characteristic
3C73×#2802C211yesmaximal, characteristic, complemented
4C73×#2800C211yesmaximal, characteristic, complemented
5C73×#2792C211yesmaximal, characteristic, complemented
6C73×#2788C211yesmaximal, characteristic, complemented
7C73×#2783C211yesmaximal, characteristic, complemented
8C73×#2780C211yesmaximal, characteristic, complemented
9C73×#2744C211yesmaximal, characteristic, complemented
10C73×#2739C211yesmaximal, characteristic, complemented
11C73×#2729C211yesmaximal, characteristic, complemented
12C73×#2725C211yesmaximal, characteristic, complemented
13C73×#2707C211yesmaximal, characteristic, complemented
14C73×#2701C211yesmaximal, characteristic
15C73×#2695C211yesmaximal, characteristic, complemented
16C73×#2686C211yesmaximal, characteristic
17C73×#2680C211yesmaximal, characteristic, complemented
18C73×#2674C211yesmaximal, characteristic, complemented
19C73×#2654C211yesmaximal, characteristic, complemented
20C73×#2650C211yesmaximal, characteristic, complemented
21C73×#2609C211yesmaximal, characteristic, complemented
22C73×#2601C211yesmaximal, characteristic, complemented
23C73×#2601C211yesmaximal, characteristic, complemented
24C73×#2590C211yesmaximal, characteristic, complemented
25C73×#2560C211yesmaximal, characteristic, complemented
26C73×#2550C211yesmaximal, characteristic, complemented
27C73×#2474C211yesmaximal, characteristic, complemented
28C73×#2470C211yesmaximal, characteristic, complemented
29C73×#2334C211yesmaximal, characteristic, complemented
30C73×#2314C211yesmaximal, characteristic, complemented
31C73×#2296C211yesmaximal, characteristic, complemented
32C2×C4⋊Q8×C73C2211yescharacteristic
33C2×#126×C73C2211yescharacteristic
34C2×#126×C73C2211yescharacteristic
35C2×#125×C73C2211yescharacteristic
36C2×#124×C73C2211yescharacteristic
37C2×#123×C73C2211yescharacteristic
38C2×#123×C73C2211yescharacteristic
39C2×#123×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×C22⋊Q8×C73C2211yescharacteristic
42C2×#121×C73C2211yescharacteristic
43C2×#117×C73C2211yescharacteristic
44C2×#117×C73C2211yescharacteristic
45C2×#117×C73C2211yescharacteristic
46C22×C42×C73C2211yescharacteristic
47#400×C73C2211yescharacteristic
48#400×C73C2211yescharacteristic
49#400×C73C2211yescharacteristic
50#400×C73C2211yescharacteristic
51#400×C73C2211yescharacteristic
52#400×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic
54#399×C73C2211yescharacteristic
55#398×C73C2211yescharacteristic
56#398×C73C2211yescharacteristic
57#398×C73C2211yescharacteristic
58#398×C73C2211yescharacteristic
59#398×C73C2211yescharacteristic
60#398×C73C2211yescharacteristic
61#398×C73C2211yescharacteristic
62#398×C73C2211yescharacteristic
63#398×C73C2211yescharacteristic
64#398×C73C2211yescharacteristic
65#398×C73C2211yescharacteristic
66#397×C73C2211yescharacteristic
67#397×C73C2211yescharacteristic
68#397×C73C2211yescharacteristic
69#397×C73C2211yescharacteristic
70#397×C73C2211yescharacteristic
71#397×C73C2211yescharacteristic
72#397×C73C2211yescharacteristic
73#396×C73C2211yescharacteristic
74#396×C73C2211yescharacteristic
75#396×C73C2211yescharacteristic
76#396×C73C2211yescharacteristic
77#396×C73C2211yescharacteristic
78#396×C73C2211yescharacteristic
79#396×C73C2211yescharacteristic
80#396×C73C2211yescharacteristic
81#396×C73C2211yescharacteristic
82#396×C73C2211yescharacteristic
83#395×C73C2211yescharacteristic
84#395×C73C2211yescharacteristic
85#395×C73C2211yescharacteristic
86#395×C73C2211yescharacteristic
87#394×C73C2211yescharacteristic
88#394×C73C2211yescharacteristic
89#394×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#394×C73C2211yescharacteristic
92#394×C73C2211yescharacteristic
93#393×C73C2211yescharacteristic
94#393×C73C2211yescharacteristic
95#391×C73C2211yescharacteristic
96#391×C73C2211yescharacteristic
97#391×C73C2211yescharacteristic
98#390×C73C2211yescharacteristic
99#390×C73C2211yescharacteristic
100#390×C73C2211yescharacteristic
101#389×C73C2211yescharacteristic
102#389×C73C2211yescharacteristic
103#389×C73C2211yescharacteristic
104#389×C73C2211yescharacteristic
105#389×C73C2211yescharacteristic
106#389×C73C2211yescharacteristic
107#389×C73C2211yescharacteristic
108#389×C73C2211yescharacteristic
109#389×C73C2211yescharacteristic
110#389×C73C2211yescharacteristic
111#389×C73C2211yescharacteristic
112#389×C73C2211yescharacteristic
113#389×C73C2211yescharacteristic
114#389×C73C2211yescharacteristic
115#389×C73C2211yescharacteristic
116#389×C73C2211yescharacteristic
117#388×C73C2211yescharacteristic
118#388×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic
122#388×C73C2211yescharacteristic
123#388×C73C2211yescharacteristic
124#388×C73C2211yescharacteristic
125#388×C73C2211yescharacteristic
126#388×C73C2211yescharacteristic
127#388×C73C2211yescharacteristic
128#388×C73C2211yescharacteristic
129#388×C73C2211yescharacteristic
130#388×C73C2211yescharacteristic
131#388×C73C2211yescharacteristic
132#388×C73C2211yescharacteristic
133#388×C73C2211yescharacteristic
134#388×C73C2211yescharacteristic
135#388×C73C2211yescharacteristic
136#388×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×C73C2211yescharacteristic
141#387×C73C2211yescharacteristic
142#387×C73C2211yescharacteristic
143#387×C73C2211yescharacteristic
144#387×C73C2211yescharacteristic
145#387×C73C2211yescharacteristic
146#387×C73C2211yescharacteristic
147#387×C73C2211yescharacteristic
148#387×C73C2211yescharacteristic
149#387×C73C2211yescharacteristic
150#387×C73C2211yescharacteristic
151#387×C73C2211yescharacteristic
152#387×C73C2211yescharacteristic
153#387×C73C2211yescharacteristic
154#387×C73C2211yescharacteristic
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic
157#386×C73C2211yescharacteristic
158#386×C73C2211yescharacteristic
159#386×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic
165#385×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic
167#385×C73C2211yescharacteristic
168#385×C73C2211yescharacteristic
169#385×C73C2211yescharacteristic
170#385×C73C2211yescharacteristic
171#384×C73C2211yescharacteristic
172#382×C73C2211yescharacteristic
173#382×C73C2211yescharacteristic
174#381×C73C2211yescharacteristic
175#381×C73C2211yescharacteristic
176#380×C73C2211yescharacteristic
177#380×C73C2211yescharacteristic
178#380×C73C2211yescharacteristic
179#380×C73C2211yescharacteristic
180C4×C4⋊C4×C73C2211yescharacteristic
181C4×C4⋊C4×C73C2211yescharacteristic
182C4×C4⋊C4×C73C2211yescharacteristic
183C4×C4⋊C4×C73C2211yescharacteristic
184C4×C4⋊C4×C73C2211yescharacteristic
185C4×C4⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C22×Q8×C73C2311yescharacteristic
188C22×Q8×C73C2311yescharacteristic
189C22×D4×C73C2311yescharacteristic
190C22×D4×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C23×C4×C73C2311yescharacteristic
193C23×C4×C73C2311yescharacteristic
194C23×C4×C73C2311yescharacteristic
195C23×C4×C73C2311yescharacteristic
196C23×C4×C73C2311yescharacteristic
197C4⋊Q8×C73—42no—
198#126×C73—24no—
199#126×C73—42no—
200#125×C73—42no—
201#124×C73—42no—
202#123×C73—42no—
203#123×C73—42no—
204#123×C73—42no—
205C22⋊Q8×C73—42no—
206C22⋊Q8×C73—42no—
207#121×C73—42no—
208#117×C73—24no—
209#117×C73—24no—
210#117×C73—42no—
211C2×C4⋊C4×C73C2311yescharacteristic
212C2×C4⋊C4×C73C2311yescharacteristic
213C2×C4⋊C4×C73C2311yescharacteristic
214C2×C4⋊C4×C73C2311yescharacteristic
215C2×C4⋊C4×C73C2311yescharacteristic
216C2×C4⋊C4×C73C2311yescharacteristic
217C2×C4⋊C4×C73C2311yescharacteristic
218C2×C4⋊C4×C73C2311yescharacteristic
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2311yescharacteristic
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2311yescharacteristic
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2311yescharacteristic
231C2×C4⋊C4×C73C2311yescharacteristic
232C2×C4⋊C4×C73C2311yescharacteristic
233C2×C4⋊C4×C73C2311yescharacteristic
234C2×C4⋊C4×C73C2311yescharacteristic
235C2×C4⋊C4×C73C2311yescharacteristic
236C2×C4⋊C4×C73C2311yescharacteristic
237C2×C4⋊C4×C73C2311yescharacteristic
238C2×C4⋊C4×C73C2311yescharacteristic
239C2×C4⋊C4×C73C2311yescharacteristic
240C2×C4⋊C4×C73C2311yescharacteristic
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊C4×C73C2311yescharacteristic
253C2×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C4⋊C4×C73C2311yescharacteristic
256C2×C4⋊C4×C73C2311yescharacteristic
257C2×C4⋊C4×C73C2311yescharacteristic
258C2×C22⋊C4×C73C2311yescharacteristic
259C2×C22⋊C4×C73C2311yescharacteristic
260C2×C22⋊C4×C73C2311yescharacteristic
261C2×C22⋊C4×C73C2311yescharacteristic
262C2×C22⋊C4×C73C2311yescharacteristic
263C2×C22⋊C4×C73C2311yescharacteristic
264C2×C22⋊C4×C73C2311yescharacteristic
265C2×C22⋊C4×C73C2311yescharacteristic
266C2×C22⋊C4×C73C2311yescharacteristic
267C2×C22⋊C4×C73C2311yescharacteristic
268C2×C22⋊C4×C73C2311yescharacteristic
269C2×C22⋊C4×C73C2311yescharacteristic
270C2×C22⋊C4×C73C2311yescharacteristic
271C2×C22⋊C4×C73C2311yescharacteristic
272C2×C22⋊C4×C73C2311yescharacteristic
273C2×C22⋊C4×C73C2311yescharacteristic
274C2×C22⋊C4×C73C2311yescharacteristic
275C2×C22⋊C4×C73C2311yescharacteristic
276C2×C22⋊C4×C73C2311yescharacteristic
277C2×C22⋊C4×C73C2311yescharacteristic
278C2×C22⋊C4×C73C2311yescharacteristic
279C2×C22⋊C4×C73C2311yescharacteristic
280C2×C22⋊C4×C73C2311yescharacteristic
281C2×C22⋊C4×C73C2311yescharacteristic
282C2×C22⋊C4×C73C2311yescharacteristic
283C2×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C42×C73—42no—
293C2×C42×C73C2311yescharacteristic
294C2×C42×C73C2311yescharacteristic
295C2×C42×C73C2311yescharacteristic
296C2×C42×C73C2311yescharacteristic
297C2×C42×C73C2311yescharacteristic
298C2×C42×C73C2311yescharacteristic
299C2×C42×C73C2311yescharacteristic
300C2×C42×C73C2311yescharacteristic
301C2×C42×C73C2311yescharacteristic
302C2×C42×C73C2311yescharacteristic
303C2×C42×C73C2311yescharacteristic
304C2×C42×C73C2311yescharacteristic
305C2×C42×C73C2311yescharacteristic
306C2×C42×C73C2311yescharacteristic
307#95×C73C2311yescharacteristic
308#95×C73C2311yescharacteristic
309#95×C73C2311yescharacteristic
310#95×C73C2311yescharacteristic
311#95×C73C2311yescharacteristic
312#95×C73C2311yescharacteristic
313#95×C73C2311yescharacteristic
314#95×C73C2311yescharacteristic
315#95×C73C2311yescharacteristic
316#95×C73C2311yescharacteristic
317#95×C73C2311yescharacteristic
318#95×C73C2311yescharacteristic
319#95×C73C2311yescharacteristic
320#95×C73C2311yescharacteristic
321#95×C73C2311yescharacteristic
322#95×C73C2311yescharacteristic
323#95×C73C2311yescharacteristic
324#95×C73C2311yescharacteristic
325#95×C73C2311yescharacteristic
326#95×C73C2311yescharacteristic
327#95×C73C2311yescharacteristic
328#95×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357C24×C73C2411yescharacteristic
358C24×C73C2411yescharacteristic
359C24×C73C2411yescharacteristic
360C2×Q8×C73—22no—
361C2×Q8×C73—41no—
362C2×Q8×C73—41no—
363C2×Q8×C73—41no—
364C2×Q8×C73—41no—
365C2×Q8×C73—41no—
366C2×D4×C73—22no—
367C2×D4×C73—22no—
368C2×D4×C73—22no—
369C2×D4×C73—41no—
370C2×D4×C73—41no—
371C2×D4×C73—41no—
372C2×D4×C73—41no—
373C2×D4×C73—41no—
374C2×D4×C73—41no—
375C22×C4×C73—22no—
376C22×C4×C73—22no—
377C22×C4×C73—22no—
378C22×C4×C73—22no—
379C22×C4×C73—22no—
380C22×C4×C73—22no—
381C22×C4×C73—22no—
382C22×C4×C73—22no—
383C22×C4×C73—41no—
384C22×C4×C73—41no—
385C22×C4×C73—41no—
386C22×C4×C73—41no—
387C22×C4×C73—41no—
388C22×C4×C73—41no—
389C22×C4×C73—41no—
390C22×C4×C73C2411yescharacteristic
391C22×C4×C73C2411yescharacteristic
392C22×C4×C73C2411yescharacteristic
393C22×C4×C73C2411yescharacteristic
394C22×C4×C73C2411yescharacteristic
395C22×C4×C73C2411yescharacteristic
396C22×C4×C73C2411yescharacteristic
397C22×C4×C73C2411yescharacteristic
398C22×C4×C73C2411yescharacteristic
399C22×C4×C73C2411yescharacteristic
400C22×C4×C73C2411yescharacteristic
401C22×C4×C73C2411yescharacteristic
402C22×C4×C73C2411yescharacteristic
403C22×C4×C73C2411yescharacteristic
404C22×C4×C73C2411yescharacteristic
405C22×C4×C73C2411yescharacteristic
406C22×C4×C73C2411yescharacteristic
407C22×C4×C73C2411yescharacteristic
408C22×C4×C73C2411yescharacteristic
409C22×C4×C73C2411yescharacteristic
410C22×C4×C73C2411yescharacteristic
411C22×C4×C73C2411yescharacteristic
412C22×C4×C73C2411yescharacteristic
413C22×C4×C73C2411yescharacteristic
414C22×C4×C73C2411yescharacteristic
415C22×C4×C73C2411yescharacteristic
416C22×C4×C73C2411yescharacteristic
417C22×C4×C73C2411yescharacteristic
418C4⋊C4×C73—22no—
419C4⋊C4×C73—22no—
420C4⋊C4×C73—22no—
421C4⋊C4×C73—22no—
422C4⋊C4×C73—22no—
423C4⋊C4×C73—22no—
424C4⋊C4×C73—22no—
425C4⋊C4×C73—22no—
426C4⋊C4×C73—22no—
427C4⋊C4×C73—22no—
428C4⋊C4×C73—22no—
429C4⋊C4×C73—22no—
430C4⋊C4×C73—22no—
431C4⋊C4×C73—22no—
432C4⋊C4×C73—22no—
433C4⋊C4×C73—22no—
434C4⋊C4×C73—22no—
435C4⋊C4×C73—41no—
436C4⋊C4×C73—41no—
437C4⋊C4×C73—41no—
438C4⋊C4×C73—41no—
439C4⋊C4×C73—41no—
440C4⋊C4×C73—41no—
441C4⋊C4×C73—41no—
442C4⋊C4×C73—41no—
443C4⋊C4×C73—41no—
444C4⋊C4×C73—41no—
445C4⋊C4×C73—41no—
446C4⋊C4×C73—41no—
447C4⋊C4×C73—41no—
448C4⋊C4×C73—41no—
449C4⋊C4×C73—41no—
450C4⋊C4×C73—41no—
451C4⋊C4×C73—41no—
452C4⋊C4×C73—41no—
453C4⋊C4×C73—41no—
454C4⋊C4×C73—41no—
455C4⋊C4×C73—41no—
456C4⋊C4×C73—41no—
457C4⋊C4×C73—41no—
458C4⋊C4×C73—41no—
459C4⋊C4×C73—41no—
460C4⋊C4×C73—41no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73—41no—
464C4⋊C4×C73—41no—
465C22⋊C4×C73—22no—
466C22⋊C4×C73—22no—
467C22⋊C4×C73—22no—
468C22⋊C4×C73—22no—
469C22⋊C4×C73—22no—
470C22⋊C4×C73—22no—
471C22⋊C4×C73—22no—
472C22⋊C4×C73—22no—
473C22⋊C4×C73—22no—
474C22⋊C4×C73—22no—
475C22⋊C4×C73—22no—
476C22⋊C4×C73—22no—
477C22⋊C4×C73—22no—
478C22⋊C4×C73—22no—
479C22⋊C4×C73—22no—
480C22⋊C4×C73—41no—
481C22⋊C4×C73—41no—
482C22⋊C4×C73—41no—
483C22⋊C4×C73—41no—
484C22⋊C4×C73—41no—
485C22⋊C4×C73—41no—
486C22⋊C4×C73—41no—
487C22⋊C4×C73—41no—
488C22⋊C4×C73—41no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C22⋊C4×C73—41no—
498C22⋊C4×C73—41no—
499C42×C73—22no—
500C42×C73—22no—
501C42×C73—41no—
502C42×C73—41no—
503C42×C73—41no—
504C42×C73—41no—
505C42×C73—41no—
506C42×C73—41no—
507C42×C73—41no—
508C42×C73—41no—
509C42×C73—41no—
510C42×C73—41no—
511C42×C73—41no—
512C42×C73#4114yes—
513C23×C73—21no—
514C23×C73—21no—
515C23×C73—21no—
516C23×C73—21no—
517C23×C73—21no—
518C23×C73—21no—
519C23×C73—21no—
520C23×C73—21no—
521C23×C73—21no—
522C23×C73—21no—
523C23×C73—21no—
524C23×C73—21no—
525C23×C73—21no—
526C23×C73—21no—
527C23×C73—21no—
528C23×C73—21no—
529C23×C73—21no—
530C23×C73—21no—
531C23×C73—21no—
532C23×C73—21no—
533C23×C73H(5,𝔽2)12yes—
534C23×C73C2511yescharacteristic
535Q8×C73—82no—
536Q8×C73—82no—
537D4×C73—82no—
538D4×C73—82no—
539D4×C73—82no—
540C2×C4×C73—28no—
541C2×C4×C73—21no—
542C2×C4×C73—21no—
543C2×C4×C73—21no—
544C2×C4×C73—21no—
545C2×C4×C73—21no—
546C2×C4×C73—21no—
547C2×C4×C73—21no—
548C2×C4×C73—21no—
549C2×C4×C73—21no—
550C2×C4×C73—21no—
551C2×C4×C73—21no—
552C2×C4×C73—21no—
553C2×C4×C73—21no—
554C2×C4×C73—21no—
555C2×C4×C73—21no—
556C2×C4×C73—21no—
557C2×C4×C73—21no—
558C2×C4×C73—21no—
559C2×C4×C73—21no—
560C2×C4×C73—21no—
561C2×C4×C73—21no—
562C2×C4×C73—21no—
563C2×C4×C73—21no—
564C2×C4×C73—21no—
565C2×C4×C73—21no—
566C2×C4×C73—21no—
567C2×C4×C73—21no—
568C2×C4×C73—21no—
569C2×C4×C73—21no—
570C2×C4×C73—21no—
571C2×C4×C73—21no—
572C2×C4×C73—21no—
573C2×C4×C73—21no—
574C2×C4×C73—21no—
575C2×C4×C73—21no—
576C2×C4×C73—21no—
577C2×C4×C73—21no—
578C2×C4×C73—21no—
579C2×C4×C73—21no—
580C2×C4×C73—21no—
581C2×C4×C73—21no—
582C2×C4×C73—21no—
583C2×C4×C73—21no—
584C2×C4×C73—21no—
585C2×C4×C73—21no—
586C2×C4×C73—21no—
587C2×C4×C73—21no—
588C2×C4×C73—21no—
589C2×C4×C73—21no—
590C2×C4×C73—21no—
591C2×C4×C73—21no—
592C2×C4×C73—21no—
593C2×C4×C73—21no—
594C2×C4×C73—21no—
595C2×C4×C73—21no—
596C2×C4×C73—21no—
597C2×C4×C73—21no—
598C2×C4×C73—21no—
599C2×C4×C73—21no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—44no—
620C2×C4×C73—44no—
621C2×C4×C73—44no—
622C2×C4×C73—82no—
623C2×C4×C73C2×#4112yes—
624C2×C4×C73C2×#4112yes—
625C2×C4×C73C2×#4112yes—
626C2×C4×C73H(5,𝔽2)12yes—
627C2×C4×C732−1+412yes—
628C2×C4×C732−1+412yes—
629C22×C73—22no—
630C22×C73—22no—
631C22×C73—22no—
632C22×C73—41no—
633C22×C73—41no—
634C22×C73—41no—
635C22×C73—41no—
636C22×C73—41no—
637C22×C73—41no—
638C22×C73—41no—
639C22×C73—41no—
640C22×C73—41no—
641C22×C73—41no—
642C22×C73—41no—
643C22×C73—41no—
644C22×C73—41no—
645C22×C73—41no—
646C22×C73—41no—
647C22×C73—41no—
648C22×C73—41no—
649C22×C73—41no—
650C22×C73C22×#4111yescharacteristic
651C22×C73C2×H(5,𝔽2)11yescharacteristic
652C22×C73C2×H(5,𝔽2)11yescharacteristic
653C22×C73C2×2−1+411yescharacteristic
654C22×C73C2×2−1+411yescharacteristic
655C22×C73#58511yescharacteristic
656C22×C73#58511yescharacteristic
657C4×C73—22no—
658C4×C73—22no—
659C4×C73—22no—
660C4×C73—22no—
661C4×C73—22no—
662C4×C73—22no—
663C4×C73—41no—
664C4×C73—41no—
665C4×C73—41no—
666C4×C73—41no—
667C4×C73—41no—
668C4×C73—41no—
669C4×C73—41no—
670C4×C73—41no—
671C4×C73—41no—
672C4×C73—41no—
673C4×C73—41no—
674C4×C73—41no—
675C4×C73—41no—
676C4×C73—41no—
677C4×C73—41no—
678C4×C73—41no—
679C4×C73—41no—
680C4×C73—41no—
681C4×C73—41no—
682C4×C73—41no—
683C4×C73—41no—
684C4×C73—41no—
685#36827C7311yesmaximal, characteristic, direct product factor, Sylow
686C2×C73—42no—
687C2×C73—81no—
688C2×C73—81no—
689C2×C73#345511yescharacteristic
690C2×C73#349211yescharacteristic
691C2×C73#351111yescharacteristic
692C2×C73#353411yescharacteristic
693C2×C73#353511yescharacteristic
694C2×C73#354711yescharacteristic
695C2×C73#355511yescharacteristic
696#2855C2×C7311yescharacteristic, complemented
697#2854C2×C7311yescharacteristic
698#2802C2×C7311yescharacteristic, complemented
699#2800C2×C7311yescharacteristic, complemented
700#2792C2×C7311yescharacteristic, complemented
701#2788C2×C7311yescharacteristic, complemented
702#2783C2×C7311yescharacteristic, complemented
703#2780C2×C7311yescharacteristic, complemented
704#2744C2×C7311yescharacteristic, complemented
705#2739C2×C7311yescharacteristic, complemented
706#2729C2×C7311yescharacteristic, complemented
707#2725C2×C7311yescharacteristic, complemented
708#2707C2×C7311yescharacteristic, complemented
709#2701C2×C7311yescharacteristic
710#2695C2×C7311yescharacteristic, complemented
711#2686C2×C7311yescharacteristic
712#2680C2×C7311yescharacteristic, complemented
713#2674C2×C7311yescharacteristic, complemented
714#2654C2×C7311yescharacteristic, complemented
715#2650C2×C7311yescharacteristic, complemented
716#2609C2×C7311yescharacteristic, complemented
717#2601C2×C7311yescharacteristic, complemented
718#2601C2×C7311yescharacteristic, complemented
719#2590C2×C7311yescharacteristic, complemented
720#2560C2×C7311yescharacteristic, complemented
721#2550C2×C7311yescharacteristic, complemented
722#2474C2×C7311yescharacteristic, complemented
723#2470C2×C7311yescharacteristic, complemented
724#2334C2×C7311yescharacteristic, complemented
725#2314C2×C7311yescharacteristic, complemented
726#2296C2×C7311yescharacteristic, complemented
727C73#3682711yescharacteristic, direct product factor, Sylow
728C2×C4⋊Q8C22×C7311yescharacteristic
729C2×#126C22×C7311yescharacteristic
730C2×#126C22×C7311yescharacteristic
731C2×#125C22×C7311yescharacteristic
732C2×#124C22×C7311yescharacteristic
733C2×#123C22×C7311yescharacteristic
734C2×#123C22×C7311yescharacteristic
735C2×#123C22×C7311yescharacteristic
736C2×C22⋊Q8C22×C7311yescharacteristic
737C2×C22⋊Q8C22×C7311yescharacteristic
738C2×#121C22×C7311yescharacteristic
739C2×#117C22×C7311yescharacteristic
740C2×#117C22×C7311yescharacteristic
741C2×#117C22×C7311yescharacteristic
742C22×C42C22×C7311yescharacteristic
743#400C22×C7311yescharacteristic
744#400C22×C7311yescharacteristic
745#400C22×C7311yescharacteristic
746#400C22×C7311yescharacteristic
747#400C22×C7311yescharacteristic
748#400C22×C7311yescharacteristic
749#400C22×C7311yescharacteristic
750#399C22×C7311yescharacteristic
751#398C22×C7311yescharacteristic
752#398C22×C7311yescharacteristic
753#398C22×C7311yescharacteristic
754#398C22×C7311yescharacteristic
755#398C22×C7311yescharacteristic
756#398C22×C7311yescharacteristic
757#398C22×C7311yescharacteristic
758#398C22×C7311yescharacteristic
759#398C22×C7311yescharacteristic
760#398C22×C7311yescharacteristic
761#398C22×C7311yescharacteristic
762#397C22×C7311yescharacteristic
763#397C22×C7311yescharacteristic
764#397C22×C7311yescharacteristic
765#397C22×C7311yescharacteristic
766#397C22×C7311yescharacteristic
767#397C22×C7311yescharacteristic
768#397C22×C7311yescharacteristic
769#396C22×C7311yescharacteristic
770#396C22×C7311yescharacteristic
771#396C22×C7311yescharacteristic
772#396C22×C7311yescharacteristic
773#396C22×C7311yescharacteristic
774#396C22×C7311yescharacteristic
775#396C22×C7311yescharacteristic
776#396C22×C7311yescharacteristic
777#396C22×C7311yescharacteristic
778#396C22×C7311yescharacteristic
779#395C22×C7311yescharacteristic
780#395C22×C7311yescharacteristic
781#395C22×C7311yescharacteristic
782#395C22×C7311yescharacteristic
783#394C22×C7311yescharacteristic
784#394C22×C7311yescharacteristic
785#394C22×C7311yescharacteristic
786#394C22×C7311yescharacteristic
787#394C22×C7311yescharacteristic
788#394C22×C7311yescharacteristic
789#393C22×C7311yescharacteristic
790#393C22×C7311yescharacteristic
791#391C22×C7311yescharacteristic
792#391C22×C7311yescharacteristic
793#391C22×C7311yescharacteristic
794#390C22×C7311yescharacteristic
795#390C22×C7311yescharacteristic
796#390C22×C7311yescharacteristic
797#389C22×C7311yescharacteristic
798#389C22×C7311yescharacteristic
799#389C22×C7311yescharacteristic
800#389C22×C7311yescharacteristic
801#389C22×C7311yescharacteristic
802#389C22×C7311yescharacteristic
803#389C22×C7311yescharacteristic
804#389C22×C7311yescharacteristic
805#389C22×C7311yescharacteristic
806#389C22×C7311yescharacteristic
807#389C22×C7311yescharacteristic
808#389C22×C7311yescharacteristic
809#389C22×C7311yescharacteristic
810#389C22×C7311yescharacteristic
811#389C22×C7311yescharacteristic
812#389C22×C7311yescharacteristic
813#388C22×C7311yescharacteristic
814#388C22×C7311yescharacteristic
815#388C22×C7311yescharacteristic
816#388C22×C7311yescharacteristic
817#388C22×C7311yescharacteristic
818#388C22×C7311yescharacteristic
819#388C22×C7311yescharacteristic
820#388C22×C7311yescharacteristic
821#388C22×C7311yescharacteristic
822#388C22×C7311yescharacteristic
823#388C22×C7311yescharacteristic
824#388C22×C7311yescharacteristic
825#388C22×C7311yescharacteristic
826#388C22×C7311yescharacteristic
827#388C22×C7311yescharacteristic
828#388C22×C7311yescharacteristic
829#388C22×C7311yescharacteristic
830#388C22×C7311yescharacteristic
831#388C22×C7311yescharacteristic
832#388C22×C7311yescharacteristic
833#387C22×C7311yescharacteristic
834#387C22×C7311yescharacteristic
835#387C22×C7311yescharacteristic
836#387C22×C7311yescharacteristic
837#387C22×C7311yescharacteristic
838#387C22×C7311yescharacteristic
839#387C22×C7311yescharacteristic
840#387C22×C7311yescharacteristic
841#387C22×C7311yescharacteristic
842#387C22×C7311yescharacteristic
843#387C22×C7311yescharacteristic
844#387C22×C7311yescharacteristic
845#387C22×C7311yescharacteristic
846#387C22×C7311yescharacteristic
847#387C22×C7311yescharacteristic
848#387C22×C7311yescharacteristic
849#387C22×C7311yescharacteristic
850#387C22×C7311yescharacteristic
851#386C22×C7311yescharacteristic
852#386C22×C7311yescharacteristic
853#386C22×C7311yescharacteristic
854#386C22×C7311yescharacteristic
855#386C22×C7311yescharacteristic
856#385C22×C7311yescharacteristic
857#385C22×C7311yescharacteristic
858#385C22×C7311yescharacteristic
859#385C22×C7311yescharacteristic
860#385C22×C7311yescharacteristic
861#385C22×C7311yescharacteristic
862#385C22×C7311yescharacteristic
863#385C22×C7311yescharacteristic
864#385C22×C7311yescharacteristic
865#385C22×C7311yescharacteristic
866#385C22×C7311yescharacteristic
867#384C22×C7311yescharacteristic
868#382C22×C7311yescharacteristic
869#382C22×C7311yescharacteristic
870#381C22×C7311yescharacteristic
871#381C22×C7311yescharacteristic
872#380C22×C7311yescharacteristic
873#380C22×C7311yescharacteristic
874#380C22×C7311yescharacteristic
875#380C22×C7311yescharacteristic
876C4×C4⋊C4C22×C7311yescharacteristic
877C4×C4⋊C4C22×C7311yescharacteristic
878C4×C4⋊C4C22×C7311yescharacteristic
879C4×C4⋊C4C22×C7311yescharacteristic
880C4×C4⋊C4C22×C7311yescharacteristic
881C4×C4⋊C4C22×C7311yescharacteristic
882C4×C22⋊C4C22×C7311yescharacteristic
883C22×Q8C23×C7311yescharacteristic
884C22×Q8C23×C7311yescharacteristic
885C22×D4C23×C7311yescharacteristic
886C22×D4C23×C7311yescharacteristic
887C22×D4C23×C7311yescharacteristic
888C23×C4C23×C7311yescharacteristic
889C23×C4C23×C7311yescharacteristic
890C23×C4C23×C7311yescharacteristic
891C23×C4C23×C7311yescharacteristic
892C23×C4C23×C7311yescharacteristic
893C4⋊Q8—42no—
894#126—24no—
895#126—42no—
896#125—42no—
897#124—42no—
898#123—42no—
899#123—42no—
900#123—42no—
901C22⋊Q8—42no—
902C22⋊Q8—42no—
903#121—42no—
904#117—24no—
905#117—24no—
906#117—42no—
907C2×C4⋊C4C23×C7311yescharacteristic
908C2×C4⋊C4C23×C7311yescharacteristic
909C2×C4⋊C4C23×C7311yescharacteristic
910C2×C4⋊C4C23×C7311yescharacteristic
911C2×C4⋊C4C23×C7311yescharacteristic
912C2×C4⋊C4C23×C7311yescharacteristic
913C2×C4⋊C4C23×C7311yescharacteristic
914C2×C4⋊C4C23×C7311yescharacteristic
915C2×C4⋊C4C23×C7311yescharacteristic
916C2×C4⋊C4C23×C7311yescharacteristic
917C2×C4⋊C4C23×C7311yescharacteristic
918C2×C4⋊C4C23×C7311yescharacteristic
919C2×C4⋊C4C23×C7311yescharacteristic
920C2×C4⋊C4C23×C7311yescharacteristic
921C2×C4⋊C4C23×C7311yescharacteristic
922C2×C4⋊C4C23×C7311yescharacteristic
923C2×C4⋊C4C23×C7311yescharacteristic
924C2×C4⋊C4C23×C7311yescharacteristic
925C2×C4⋊C4C23×C7311yescharacteristic
926C2×C4⋊C4C23×C7311yescharacteristic
927C2×C4⋊C4C23×C7311yescharacteristic
928C2×C4⋊C4C23×C7311yescharacteristic
929C2×C4⋊C4C23×C7311yescharacteristic
930C2×C4⋊C4C23×C7311yescharacteristic
931C2×C4⋊C4C23×C7311yescharacteristic
932C2×C4⋊C4C23×C7311yescharacteristic
933C2×C4⋊C4C23×C7311yescharacteristic
934C2×C4⋊C4C23×C7311yescharacteristic
935C2×C4⋊C4C23×C7311yescharacteristic
936C2×C4⋊C4C23×C7311yescharacteristic
937C2×C4⋊C4C23×C7311yescharacteristic
938C2×C4⋊C4C23×C7311yescharacteristic
939C2×C4⋊C4C23×C7311yescharacteristic
940C2×C4⋊C4C23×C7311yescharacteristic
941C2×C4⋊C4C23×C7311yescharacteristic
942C2×C4⋊C4C23×C7311yescharacteristic
943C2×C4⋊C4C23×C7311yescharacteristic
944C2×C4⋊C4C23×C7311yescharacteristic
945C2×C4⋊C4C23×C7311yescharacteristic
946C2×C4⋊C4C23×C7311yescharacteristic
947C2×C4⋊C4C23×C7311yescharacteristic
948C2×C4⋊C4C23×C7311yescharacteristic
949C2×C4⋊C4C23×C7311yescharacteristic
950C2×C4⋊C4C23×C7311yescharacteristic
951C2×C4⋊C4C23×C7311yescharacteristic
952C2×C4⋊C4C23×C7311yescharacteristic
953C2×C4⋊C4C23×C7311yescharacteristic
954C2×C22⋊C4C23×C7311yescharacteristic
955C2×C22⋊C4C23×C7311yescharacteristic
956C2×C22⋊C4C23×C7311yescharacteristic
957C2×C22⋊C4C23×C7311yescharacteristic
958C2×C22⋊C4C23×C7311yescharacteristic
959C2×C22⋊C4C23×C7311yescharacteristic
960C2×C22⋊C4C23×C7311yescharacteristic
961C2×C22⋊C4C23×C7311yescharacteristic
962C2×C22⋊C4C23×C7311yescharacteristic
963C2×C22⋊C4C23×C7311yescharacteristic
964C2×C22⋊C4C23×C7311yescharacteristic
965C2×C22⋊C4C23×C7311yescharacteristic
966C2×C22⋊C4C23×C7311yescharacteristic
967C2×C22⋊C4C23×C7311yescharacteristic
968C2×C22⋊C4C23×C7311yescharacteristic
969C2×C22⋊C4C23×C7311yescharacteristic
970C2×C22⋊C4C23×C7311yescharacteristic
971C2×C22⋊C4C23×C7311yescharacteristic
972C2×C22⋊C4C23×C7311yescharacteristic
973C2×C22⋊C4C23×C7311yescharacteristic
974C2×C22⋊C4C23×C7311yescharacteristic
975C2×C22⋊C4C23×C7311yescharacteristic
976C2×C22⋊C4C23×C7311yescharacteristic
977C2×C22⋊C4C23×C7311yescharacteristic
978C2×C22⋊C4C23×C7311yescharacteristic
979C2×C22⋊C4C23×C7311yescharacteristic
980C2×C22⋊C4C23×C7311yescharacteristic
981C2×C22⋊C4C23×C7311yescharacteristic
982C2×C22⋊C4C23×C7311yescharacteristic
983C2×C22⋊C4C23×C7311yescharacteristic
984C2×C22⋊C4C23×C7311yescharacteristic
985C2×C22⋊C4C23×C7311yescharacteristic
986C2×C22⋊C4C23×C7311yescharacteristic
987C2×C22⋊C4C23×C7311yescharacteristic
988C2×C42—42no—
989C2×C42C23×C7311yescharacteristic
990C2×C42C23×C7311yescharacteristic
991C2×C42C23×C7311yescharacteristic
992C2×C42C23×C7311yescharacteristic
993C2×C42C23×C7311yescharacteristic
994C2×C42C23×C7311yescharacteristic
995C2×C42C23×C7311yescharacteristic
996C2×C42C23×C7311yescharacteristic
997C2×C42C23×C7311yescharacteristic
998C2×C42C23×C7311yescharacteristic
999C2×C42C23×C7311yescharacteristic
1000C2×C42C23×C7311yescharacteristic
1001C2×C42C23×C7311yescharacteristic
1002C2×C42C23×C7311yescharacteristic
1003#95C23×C7311yescharacteristic
1004#95C23×C7311yescharacteristic
1005#95C23×C7311yescharacteristic
1006#95C23×C7311yescharacteristic
1007#95C23×C7311yescharacteristic
1008#95C23×C7311yescharacteristic
1009#95C23×C7311yescharacteristic
1010#95C23×C7311yescharacteristic
1011#95C23×C7311yescharacteristic
1012#95C23×C7311yescharacteristic
1013#95C23×C7311yescharacteristic
1014#95C23×C7311yescharacteristic
1015#95C23×C7311yescharacteristic
1016#95C23×C7311yescharacteristic
1017#95C23×C7311yescharacteristic
1018#95C23×C7311yescharacteristic
1019#95C23×C7311yescharacteristic
1020#95C23×C7311yescharacteristic
1021#95C23×C7311yescharacteristic
1022#95C23×C7311yescharacteristic
1023#95C23×C7311yescharacteristic
1024#95C23×C7311yescharacteristic
1025#95C23×C7311yescharacteristic
1026#95C23×C7311yescharacteristic
1027#95C23×C7311yescharacteristic
1028#95C23×C7311yescharacteristic
1029#95C23×C7311yescharacteristic
1030#95C23×C7311yescharacteristic
1031#95C23×C7311yescharacteristic
1032#95C23×C7311yescharacteristic
1033#95C23×C7311yescharacteristic
1034#95C23×C7311yescharacteristic
1035#95C23×C7311yescharacteristic
1036#95C23×C7311yescharacteristic
1037#95C23×C7311yescharacteristic
1038#95C23×C7311yescharacteristic
1039#95C23×C7311yescharacteristic
1040#95C23×C7311yescharacteristic
1041#95C23×C7311yescharacteristic
1042#95C23×C7311yescharacteristic
1043#95C23×C7311yescharacteristic
1044#95C23×C7311yescharacteristic
1045#95C23×C7311yescharacteristic
1046#95C23×C7311yescharacteristic
1047#95C23×C7311yescharacteristic
1048#95C23×C7311yescharacteristic
1049#95C23×C7311yescharacteristic
1050#95C23×C7311yescharacteristic
1051#95C23×C7311yescharacteristic
1052#95C23×C7311yescharacteristic
1053C24C24×C7311yescharacteristic
1054C24C24×C7311yescharacteristic
1055C24C24×C7311yescharacteristic
1056C2×Q8—22no—
1057C2×Q8—41no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×D4—22no—
1063C2×D4—22no—
1064C2×D4—22no—
1065C2×D4—41no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—41no—
1069C2×D4—41no—
1070C2×D4—41no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4C24×C7311yescharacteristic
1087C22×C4C24×C7311yescharacteristic
1088C22×C4C24×C7311yescharacteristic
1089C22×C4C24×C7311yescharacteristic
1090C22×C4C24×C7311yescharacteristic
1091C22×C4C24×C7311yescharacteristic
1092C22×C4C24×C7311yescharacteristic
1093C22×C4C24×C7311yescharacteristic
1094C22×C4C24×C7311yescharacteristic
1095C22×C4C24×C7311yescharacteristic
1096C22×C4C24×C7311yescharacteristic
1097C22×C4C24×C7311yescharacteristic
1098C22×C4C24×C7311yescharacteristic
1099C22×C4C24×C7311yescharacteristic
1100C22×C4C24×C7311yescharacteristic
1101C22×C4C24×C7311yescharacteristic
1102C22×C4C24×C7311yescharacteristic
1103C22×C4C24×C7311yescharacteristic
1104C22×C4C24×C7311yescharacteristic
1105C22×C4C24×C7311yescharacteristic
1106C22×C4C24×C7311yescharacteristic
1107C22×C4C24×C7311yescharacteristic
1108C22×C4C24×C7311yescharacteristic
1109C22×C4C24×C7311yescharacteristic
1110C22×C4C24×C7311yescharacteristic
1111C22×C4C24×C7311yescharacteristic
1112C22×C4C24×C7311yescharacteristic
1113C22×C4C24×C7311yescharacteristic
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—22no—
1130C4⋊C4—22no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—41no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—41no—
1161C22⋊C4—22no—
1162C22⋊C4—22no—
1163C22⋊C4—22no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
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—41no—
1191C22⋊C4—41no—
1192C22⋊C4—41no—
1193C22⋊C4—41no—
1194C22⋊C4—41no—
1195C42—22no—
1196C42—22no—
1197C42—41no—
1198C42—41no—
1199C42—41no—
1200C42—41no—
1201C42—41no—
1202C42—41no—
1203C42—41no—
1204C42—41no—
1205C42—41no—
1206C42—41no—
1207C42—41no—
1208C42#41×C7314yes—
1209C23—21no—
1210C23—21no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23—21no—
1229C23H(5,𝔽2)×C7312yes—
1230C23C25×C7311yescharacteristic
1231Q8—82no—
1232Q8—82no—
1233D4—82no—
1234D4—82no—
1235D4—82no—
1236C2×C4—28no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—44no—
1316C2×C4—44no—
1317C2×C4—44no—
1318C2×C4—82no—
1319C2×C4C2×#41×C7312yes—
1320C2×C4C2×#41×C7312yes—
1321C2×C4C2×#41×C7312yes—
1322C2×C4H(5,𝔽2)×C7312yes—
1323C2×C42−1+4×C7312yes—
1324C2×C42−1+4×C7312yes—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22C22×#41×C7311yescharacteristic
1347C22C2×H(5,𝔽2)×C7311yescharacteristic
1348C22C2×H(5,𝔽2)×C7311yescharacteristic
1349C22C2×2−1+4×C7311yescharacteristic
1350C22C2×2−1+4×C7311yescharacteristic
1351C22#585×C7311yescharacteristic
1352C22#585×C7311yescharacteristic
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C2—42no—
1382C2—81no—
1383C2—81no—
1384C2C73×#345511yescharacteristic
1385C2C73×#349211yescharacteristic
1386C2C73×#351111yescharacteristic
1387C2C73×#353411yescharacteristic
1388C2C73×#353511yescharacteristic
1389C2C73×#354711yescharacteristic
1390C2C73×#355511yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC2×#121×C73C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2855C2semidirect
3. C73×#2802C2semidirect
4. C73×#2800C2semidirect
5. C73×#2792C2semidirect
6. C73×#2788C2semidirect
7. C73×#2783C2semidirect
8. C73×#2780C2semidirect
9. C73×#2744C2semidirect
10. C73×#2739C2semidirect
11. C73×#2729C2semidirect
12. C73×#2725C2semidirect
13. C73×#2707C2semidirect
15. C73×#2695C2semidirect
17. C73×#2680C2semidirect
18. C73×#2674C2semidirect
19. C73×#2654C2semidirect
20. C73×#2650C2semidirect
21. C73×#2609C2semidirect
22. C73×#2601C2semidirect
23. C73×#2601C2semidirect
24. C73×#2590C2semidirect
25. C73×#2560C2semidirect
26. C73×#2550C2semidirect
27. C73×#2474C2semidirect
28. C73×#2470C2semidirect
29. C73×#2334C2semidirect
30. C73×#2314C2semidirect
31. C73×#2296C2semidirect
685. #36827C73direct (N × H)
696. #2855C2×C73semidirect
698. #2802C2×C73semidirect
699. #2800C2×C73semidirect
700. #2792C2×C73semidirect
701. #2788C2×C73semidirect
702. #2783C2×C73semidirect
703. #2780C2×C73semidirect
704. #2744C2×C73semidirect
705. #2739C2×C73semidirect
706. #2729C2×C73semidirect
707. #2725C2×C73semidirect
708. #2707C2×C73semidirect
710. #2695C2×C73semidirect
712. #2680C2×C73semidirect
713. #2674C2×C73semidirect
714. #2654C2×C73semidirect
715. #2650C2×C73semidirect
716. #2609C2×C73semidirect
717. #2601C2×C73semidirect
718. #2601C2×C73semidirect
719. #2590C2×C73semidirect
720. #2560C2×C73semidirect
721. #2550C2×C73semidirect
722. #2474C2×C73semidirect
723. #2470C2×C73semidirect
724. #2334C2×C73semidirect
725. #2314C2×C73semidirect
726. #2296C2×C73semidirect
727. C73#36827direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28552
C73×#28542
C73×#28022
C73×#28002
C73×#27922
C73×#27882
C73×#27832
C73×#27802
C73×#27442
C73×#27392
C73×#27292
C73×#27252
C73×#27072
C73×#27012
C73×#26952
C73×#26862
C73×#26802
C73×#26742
C73×#26542
C73×#26502
C73×#26092
C73×#26012
C73×#25902
C73×#25602
C73×#25502
C73×#24742
C73×#24702
C73×#23342
C73×#23142
C73×#22962
#3682773