Finite Group Databasebeta

← #13568191

Subgroups — #13568191

Order 1792.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2602C211yesmaximal, characteristic
2#11740288C211yesmaximal, characteristic, complemented
3#11740282C211yesmaximal, characteristic, complemented
4#11739832C211yesmaximal, characteristic, complemented
5#11739764C211yesmaximal, characteristic, complemented
6#11735062C211yesmaximal, characteristic, complemented
7#11735043C211yesmaximal, characteristic, complemented
8#11734508C211yesmaximal, characteristic, complemented
9#11734499C211yesmaximal, characteristic, complemented
10#11734494C211yesmaximal, characteristic, complemented
11#11734472C211yesmaximal, characteristic, complemented
12#11734179C211yesmaximal, characteristic
13#11734170C211yesmaximal, characteristic
14#11733863C211yesmaximal, characteristic, complemented
15#11733836C211yesmaximal, characteristic, complemented
16#11733622C211yesmaximal, characteristic, complemented
17#11733562C211yesmaximal, characteristic, complemented
18#11733267C211yesmaximal, characteristic, complemented
19#11733234C211yesmaximal, characteristic, complemented
20#11733232C211yesmaximal, characteristic, complemented
21#11733212C211yesmaximal, characteristic, complemented
22#11733203C211yesmaximal, characteristic, complemented
23#11733057C211yesmaximal, characteristic, complemented
24#11732737C211yesmaximal, characteristic, complemented
25#11732558C211yesmaximal, characteristic, complemented
26#11732233C211yesmaximal, characteristic, complemented
27#11732168C211yesmaximal, characteristic, complemented
28#11731950C211yesmaximal, characteristic, complemented
29#11731890C211yesmaximal, characteristic, complemented
30#11730939C211yesmaximal, characteristic, complemented
31#11730890C211yesmaximal, characteristic, complemented
32C2×C7×#123C2211yescharacteristic
33C2×C4×C7×D4C2211yescharacteristic
34C2×#6498C2211yescharacteristic
35C2×#6498C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6489C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C2×#6452C2211yescharacteristic
40C2×#6433C2211yescharacteristic
41C7×#397C2211yescharacteristic
42C7×#394C2211yescharacteristic
43C7×#394C2211yescharacteristic
44C7×#392C2211yescharacteristic
45C7×#390C2211yescharacteristic
46C7×#389C2211yescharacteristic
47C7×#388C2211yescharacteristic
48C7×#388C2211yescharacteristic
49C7×#388C2211yescharacteristic
50C7×#387C2211yescharacteristic
51C7×#386C2211yescharacteristic
52C7×#385C2211yescharacteristic
53C4×C7×C22⋊C4C2211yescharacteristic
54#89994C2211yescharacteristic
55#89994C2211yescharacteristic
56#89994C2211yescharacteristic
57#89993C2211yescharacteristic
58#89993C2211yescharacteristic
59#89993C2211yescharacteristic
60#89992C2211yescharacteristic
61#89992C2211yescharacteristic
62#89992C2211yescharacteristic
63#89992C2211yescharacteristic
64#89984C2211yescharacteristic
65#89982C2211yescharacteristic
66#89982C2211yescharacteristic
67C4×C22⋊Dic7C2211yescharacteristic
68C4×C22⋊Dic7C2211yescharacteristic
69#89758C2211yescharacteristic
70#89757C2211yescharacteristic
71#89757C2211yescharacteristic
72#89757C2211yescharacteristic
73#89756C2211yescharacteristic
74#89756C2211yescharacteristic
75#89756C2211yescharacteristic
76#89756C2211yescharacteristic
77#89756C2211yescharacteristic
78#89755C2211yescharacteristic
79#89755C2211yescharacteristic
80#89754C2211yescharacteristic
81#89753C2211yescharacteristic
82#89753C2211yescharacteristic
83#89753C2211yescharacteristic
84#89753C2211yescharacteristic
85#89750C2211yescharacteristic
86#89750C2211yescharacteristic
87C4⋊C4×Dic7C2211yescharacteristic
88#89744C2211yescharacteristic
89#89744C2211yescharacteristic
90#89744C2211yescharacteristic
91#89744C2211yescharacteristic
92#89725C2211yescharacteristic
93#89725C2211yescharacteristic
94#89725C2211yescharacteristic
95#89725C2211yescharacteristic
96#89724C2211yescharacteristic
97#89724C2211yescharacteristic
98#89724C2211yescharacteristic
99#89724C2211yescharacteristic
100#89724C2211yescharacteristic
101#89723C2211yescharacteristic
102#89723C2211yescharacteristic
103#89723C2211yescharacteristic
104#89723C2211yescharacteristic
105#89723C2211yescharacteristic
106#89723C2211yescharacteristic
107#89723C2211yescharacteristic
108#89723C2211yescharacteristic
109#89723C2211yescharacteristic
110#89723C2211yescharacteristic
111#89722C2211yescharacteristic
112#89722C2211yescharacteristic
113#89722C2211yescharacteristic
114#89721C2211yescharacteristic
115#89721C2211yescharacteristic
116#89721C2211yescharacteristic
117#89720C2211yescharacteristic
118#89720C2211yescharacteristic
119#89720C2211yescharacteristic
120#89720C2211yescharacteristic
121#89720C2211yescharacteristic
122#89720C2211yescharacteristic
123#89720C2211yescharacteristic
124#89720C2211yescharacteristic
125#89720C2211yescharacteristic
126#89720C2211yescharacteristic
127#89718C2211yescharacteristic
128#89718C2211yescharacteristic
129#89718C2211yescharacteristic
130#89717C2211yescharacteristic
131#89717C2211yescharacteristic
132#89717C2211yescharacteristic
133#89716C2211yescharacteristic
134#89716C2211yescharacteristic
135#89716C2211yescharacteristic
136#89716C2211yescharacteristic
137#89715C2211yescharacteristic
138#89715C2211yescharacteristic
139#89715C2211yescharacteristic
140#89714C2211yescharacteristic
141#89714C2211yescharacteristic
142#89714C2211yescharacteristic
143C22⋊C4×Dic7C2211yescharacteristic
144#89707C2211yescharacteristic
145C4×C4⋊Dic7C2211yescharacteristic
146#89705C2211yescharacteristic
147#89705C2211yescharacteristic
148#89705C2211yescharacteristic
149#89705C2211yescharacteristic
150#89705C2211yescharacteristic
151#89705C2211yescharacteristic
152C42×Dic7C2211yescharacteristic
153#89700C2211yescharacteristic
154#89700C2211yescharacteristic
155#89433C2211yescharacteristic
156#89433C2211yescharacteristic
157#89432C2211yescharacteristic
158#89432C2211yescharacteristic
159#89432C2211yescharacteristic
160#89432C2211yescharacteristic
161#89430C2211yescharacteristic
162#89430C2211yescharacteristic
163#89430C2211yescharacteristic
164#89429C2211yescharacteristic
165#89427C2211yescharacteristic
166#89427C2211yescharacteristic
167#89426C2211yescharacteristic
168#89426C2211yescharacteristic
169#89426C2211yescharacteristic
170#89426C2211yescharacteristic
171#89426C2211yescharacteristic
172#89425C2211yescharacteristic
173#89425C2211yescharacteristic
174#89425C2211yescharacteristic
175#89425C2211yescharacteristic
176#89424C2211yescharacteristic
177#89424C2211yescharacteristic
178#89424C2211yescharacteristic
179#89424C2211yescharacteristic
180#89423C2211yescharacteristic
181#89422C2211yescharacteristic
182#89422C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#36994—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C22×C7×D4C2311yescharacteristic
190C22×C7×D4C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C23×C4×C7C2311yescharacteristic
193C23×Dic7C2311yescharacteristic
194C23×Dic7C2311yescharacteristic
195C23×Dic7C2311yescharacteristic
196C7×#123—24no—
197C4×C7×D4—24no—
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C22⋊C4C2311yescharacteristic
205C2×C7×C22⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4C2311yescharacteristic
213C2×C7×C22⋊C4C2311yescharacteristic
214C2×C7×C22⋊C4C2311yescharacteristic
215C2×C7×C22⋊C4C2311yescharacteristic
216C2×C7×C22⋊C4C2311yescharacteristic
217C2×C42×C7C2311yescharacteristic
218C2×C42×C7C2311yescharacteristic
219C2×C42×C7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C2×C22⋊Dic7C2311yescharacteristic
222C2×C22⋊Dic7C2311yescharacteristic
223C2×C22⋊Dic7C2311yescharacteristic
224C2×C22⋊Dic7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226C2×C22⋊Dic7C2311yescharacteristic
227C2×C22⋊Dic7C2311yescharacteristic
228C2×C22⋊Dic7C2311yescharacteristic
229C2×C22⋊Dic7C2311yescharacteristic
230C2×C22⋊Dic7C2311yescharacteristic
231C2×C22⋊Dic7C2311yescharacteristic
232C2×C22⋊Dic7C2311yescharacteristic
233C2×C22⋊Dic7C2311yescharacteristic
234C2×C22⋊Dic7C2311yescharacteristic
235C2×C22⋊Dic7C2311yescharacteristic
236C2×C22⋊Dic7C2311yescharacteristic
237C2×C22⋊Dic7C2311yescharacteristic
238C2×C22⋊Dic7C2311yescharacteristic
239C2×C22⋊Dic7C2311yescharacteristic
240C2×C22⋊Dic7C2311yescharacteristic
241#6498—42no—
242#6498—42no—
243#6489—42no—
244#6489—42no—
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
252C2×C4⋊Dic7C2311yescharacteristic
253C2×C4⋊Dic7C2311yescharacteristic
254C2×C4⋊Dic7C2311yescharacteristic
255C2×C4⋊Dic7C2311yescharacteristic
256C2×C4⋊Dic7C2311yescharacteristic
257C2×C4⋊Dic7C2311yescharacteristic
258C2×C4⋊Dic7C2311yescharacteristic
259C2×C4⋊Dic7C2311yescharacteristic
260C2×Dic7⋊C4—24no—
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×Dic7⋊C4C2311yescharacteristic
264C2×Dic7⋊C4C2311yescharacteristic
265C2×Dic7⋊C4C2311yescharacteristic
266C2×Dic7⋊C4C2311yescharacteristic
267C2×Dic7⋊C4C2311yescharacteristic
268C2×Dic7⋊C4C2311yescharacteristic
269C2×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
273C2×Dic7⋊C4C2311yescharacteristic
274C2×Dic7⋊C4C2311yescharacteristic
275C2×Dic7⋊C4C2311yescharacteristic
276C2×Dic7⋊C4C2311yescharacteristic
277C2×Dic7⋊C4C2311yescharacteristic
278C2×Dic7⋊C4C2311yescharacteristic
279C2×Dic7⋊C4C2311yescharacteristic
280C2×Dic7⋊C4C2311yescharacteristic
281C2×Dic7⋊C4C2311yescharacteristic
282C2×Dic7⋊C4C2311yescharacteristic
283C2×Dic7⋊C4C2311yescharacteristic
284C2×Dic7⋊C4C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291C2×C4×Dic7C2311yescharacteristic
292C2×C4×Dic7C2311yescharacteristic
293C2×C4×Dic7C2311yescharacteristic
294C2×C4×Dic7C2311yescharacteristic
295C2×C4×Dic7C2311yescharacteristic
296#6452—42no—
297#6433—42no—
298C7×#95C2311yescharacteristic
299C7×#95C2311yescharacteristic
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7×#95C2311yescharacteristic
303C7×#95C2311yescharacteristic
304C7×#95C2311yescharacteristic
305C7×#95C2311yescharacteristic
306C7⋊#95C2311yescharacteristic
307C7⋊#95C2311yescharacteristic
308C7⋊#95C2311yescharacteristic
309C7⋊#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352#2865—71no—
353#2864—71no—
354#2802—71no—
355#2800—71no—
356#2793—71no—
357#2790—71no—
358#2777—71no—
359#2772—71no—
360#2771—71no—
361#2761—71no—
362#2752—71no—
363#2750—71no—
364#2740—71no—
365#2738—71no—
366#2719—71no—
367#2707—71no—
368#2707—71no—
369#2706—71no—
370#2652—71no—
371#2649—71no—
372#2602D711yescharacteristic
373#2590—71no—
374#2579—71no—
375#2577—71no—
376#2475—71no—
377#2470—71no—
378#2441—71no—
379#2413—71no—
380#2335—71no—
381#2313—71no—
382#2293—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C24×C7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—22no—
388C2×C7×D4—22no—
389C2×C7×D4—41no—
390C2×C7×D4—41no—
391C2×C7×D4—41no—
392C2×C7×D4—41no—
393C2×C7×D4—41no—
394C2×C7×D4—41no—
395C22×C4×C7—22no—
396C22×C4×C7—41no—
397C22×C4×C7—41no—
398C22×C4×C7—41no—
399C22×C4×C7—41no—
400C22×C4×C7#4114yes—
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C22×C4×C7C2411yescharacteristic
410C22×C4×C7C2411yescharacteristic
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2411yescharacteristic
413C22×Dic7—22no—
414C22×Dic7—22no—
415C22×Dic7—41no—
416C22×Dic7—41no—
417C22×Dic7—41no—
418C22×Dic7—41no—
419C22×Dic7—41no—
420C22×Dic7—41no—
421C22×Dic7—41no—
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C22×Dic7C2411yescharacteristic
431C22×Dic7C2411yescharacteristic
432C22×Dic7C2411yescharacteristic
433C22×Dic7C2411yescharacteristic
434C22×Dic7C2411yescharacteristic
435C22×Dic7C2411yescharacteristic
436C22×Dic7C2411yescharacteristic
437C22×Dic7C2411yescharacteristic
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—41no—
443C7×C4⋊C4—41no—
444C7×C22⋊C4—22no—
445C7×C22⋊C4—22no—
446C7×C22⋊C4—22no—
447C7×C22⋊C4—22no—
448C7×C22⋊C4—22no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—41no—
451C7×C22⋊C4—41no—
452C7×C22⋊C4—41no—
453C7×C22⋊C4—41no—
454C7×C22⋊C4—41no—
455C7×C22⋊C4—41no—
456C7×C22⋊C4—41no—
457C42×C7—22no—
458C42×C7—41no—
459C42×C7—41no—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—22no—
463C22⋊Dic7—41no—
464C22⋊Dic7—41no—
465C22⋊Dic7—41no—
466C22⋊Dic7—41no—
467C22⋊Dic7—41no—
468C22⋊Dic7—41no—
469C22⋊Dic7—41no—
470C22⋊Dic7—41no—
471C22⋊Dic7—41no—
472C22⋊Dic7—41no—
473C22⋊Dic7—41no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7—41no—
478C22⋊Dic7—41no—
479C22⋊Dic7—41no—
480C22⋊Dic7—41no—
481C4⋊Dic7—22no—
482C4⋊Dic7—22no—
483C4⋊Dic7—22no—
484C4⋊Dic7—41no—
485C4⋊Dic7—41no—
486C4⋊Dic7—41no—
487C4⋊Dic7—41no—
488C4⋊Dic7—41no—
489C4⋊Dic7—41no—
490C4⋊Dic7—41no—
491C4⋊Dic7—41no—
492C4⋊Dic7—41no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
495C4⋊Dic7—41no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—22no—
503Dic7⋊C4—41no—
504Dic7⋊C4—41no—
505Dic7⋊C4—41no—
506Dic7⋊C4—41no—
507Dic7⋊C4—41no—
508Dic7⋊C4—41no—
509Dic7⋊C4—41no—
510Dic7⋊C4—41no—
511Dic7⋊C4—41no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4—41no—
515Dic7⋊C4—41no—
516Dic7⋊C4—41no—
517Dic7⋊C4—41no—
518Dic7⋊C4—41no—
519Dic7⋊C4—41no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—41no—
523C4×Dic7—41no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#125—71no—
532C2×#125—71no—
533C2×#123—71no—
534C2×#123—71no—
535C2×#123C2×D711yescharacteristic
536C2×C4×D4C2×D711yescharacteristic
537C2×#117—71no—
538C2×#117—71no—
539C22×C4⋊C4—71no—
540#400—71no—
541#400—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#400—71no—
549#399—71no—
550#399—71no—
551#399—71no—
552#398—71no—
553#398—71no—
554#398—71no—
555#398—71no—
556#398—71no—
557#398—71no—
558#398—71no—
559#398—71no—
560#398—71no—
561#398—71no—
562#397—71no—
563#397—71no—
564#397—71no—
565#397—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397—71no—
571#397C2×D711yescharacteristic
572#396—71no—
573#396—71no—
574#396—71no—
575#396—71no—
576#396—71no—
577#396—71no—
578#396—71no—
579#396—71no—
580#396—71no—
581#396—71no—
582#394—71no—
583#394—71no—
584#394—71no—
585#394C2×D711yescharacteristic
586#394C2×D711yescharacteristic
587#392C2×D711yescharacteristic
588#390—71no—
589#390—71no—
590#390—71no—
591#390C2×D711yescharacteristic
592#389—71no—
593#389—71no—
594#389—71no—
595#389—71no—
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389C2×D711yescharacteristic
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388—71no—
611#388—71no—
612#388—71no—
613#388—71no—
614#388—71no—
615#388—71no—
616#388—71no—
617#388—71no—
618#388—71no—
619#388—71no—
620#388—71no—
621#388—71no—
622#388—71no—
623#388C2×D711yescharacteristic
624#388C2×D711yescharacteristic
625#388C2×D711yescharacteristic
626#387—71no—
627#387—71no—
628#387—71no—
629#387—71no—
630#387—71no—
631#387—71no—
632#387—71no—
633#387—71no—
634#387—71no—
635#387—71no—
636#387—71no—
637#387—71no—
638#387—71no—
639#387—71no—
640#387—71no—
641#387—71no—
642#387—71no—
643#387—71no—
644#387—71no—
645#387—71no—
646#387—71no—
647#387—71no—
648#387—71no—
649#387—71no—
650#387—71no—
651#387—71no—
652#387—71no—
653#387C2×D711yescharacteristic
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#386C2×D711yescharacteristic
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385—71no—
667#385C2×D711yescharacteristic
668#384—71no—
669#383—71no—
670#382—71no—
671#382—71no—
672#381—71no—
673#381—71no—
674#381—71no—
675#380—71no—
676#380—71no—
677#380—71no—
678#380—71no—
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C4×C22⋊C4C2×D711yescharacteristic
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7—21no—
697C23×C7—21no—
698C23×C7—21no—
699C23×C7—21no—
700C23×C7—21no—
701C23×C7—21no—
702C23×C7—21no—
703C23×C7—21no—
704C23×C7—21no—
705C23×C7—21no—
706C23×C7C2×#4112yes—
707C23×C7C2511yescharacteristic
708C7×D4—44no—
709C7×D4—82no—
710C7×D4—82no—
711C2×C4×C7—21no—
712C2×C4×C7—21no—
713C2×C4×C7—21no—
714C2×C4×C7—21no—
715C2×C4×C7—21no—
716C2×C4×C7—21no—
717C2×C4×C7—21no—
718C2×C4×C7—21no—
719C2×C4×C7—21no—
720C2×C4×C7—21no—
721C2×C4×C7—21no—
722C2×C4×C7—21no—
723C2×C4×C7—21no—
724C2×C4×C7—21no—
725C2×C4×C7—21no—
726C2×C4×C7—21no—
727C2×C4×C7—21no—
728C2×C4×C7—21no—
729C2×C4×C7—21no—
730C2×C4×C7—21no—
731C2×C4×C7—21no—
732C2×C4×C7—21no—
733C2×C4×C7—21no—
734C2×C4×C7—21no—
735C2×C4×C7—21no—
736C2×C4×C7—21no—
737C2×C4×C7—21no—
738C2×C4×C7—21no—
739C2×C4×C7—21no—
740C2×C4×C7—21no—
741C2×C4×C7—21no—
742C2×C4×C7—21no—
743C2×C4×C7—21no—
744C2×C4×C7—44no—
745C2×C4×C7—44no—
746C2×C4×C7C2×#4112yes—
747C2×C4×C7C2×#4112yes—
748C2×C4×C72−1+412yes—
749C2×Dic7—21no—
750C2×Dic7—21no—
751C2×Dic7—21no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7—21no—
781C2×Dic7—21no—
782C2×Dic7—21no—
783C2×Dic7—21no—
784C2×Dic7—21no—
785C2×Dic7—21no—
786C2×Dic7—21no—
787C2×Dic7—21no—
788C2×Dic7—21no—
789C2×Dic7—21no—
790C2×Dic7—21no—
791C2×Dic7—21no—
792C2×Dic7—21no—
793C2×Dic7—21no—
794C2×Dic7—21no—
795C2×Dic7—21no—
796C2×Dic7—44no—
797C2×Dic7—82no—
798C2×Dic7—82no—
799C2×Dic7H(5,𝔽2)12yes—
800C22×D4C22×D711yescharacteristic
801C22×D4C22×D711yescharacteristic
802C22×D4C22×D711yescharacteristic
803C23×C4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4C22×D711yescharacteristic
807C23×C4C22×D711yescharacteristic
808#125—282no—
809#125—282no—
810#123—24no—
811#123—282no—
812#123—282no—
813C4×D4—24no—
814#117—282no—
815#117—282no—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—71no—
818C2×C4⋊C4—71no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—71no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—71no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—71no—
839C2×C4⋊C4—71no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—71no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—71no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—71no—
850C2×C4⋊C4—71no—
851C2×C4⋊C4—71no—
852C2×C4⋊C4—71no—
853C2×C4⋊C4—71no—
854C2×C4⋊C4—71no—
855C2×C4⋊C4—144no—
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
860C2×C4⋊C4C22×D711yescharacteristic
861C2×C4⋊C4C22×D711yescharacteristic
862C2×C22⋊C4—71no—
863C2×C22⋊C4—71no—
864C2×C22⋊C4—71no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4—71no—
867C2×C22⋊C4—71no—
868C2×C22⋊C4—71no—
869C2×C22⋊C4—71no—
870C2×C22⋊C4—71no—
871C2×C22⋊C4—71no—
872C2×C22⋊C4—71no—
873C2×C22⋊C4—71no—
874C2×C22⋊C4—71no—
875C2×C22⋊C4—71no—
876C2×C22⋊C4—71no—
877C2×C22⋊C4—71no—
878C2×C22⋊C4—71no—
879C2×C22⋊C4—71no—
880C2×C22⋊C4—71no—
881C2×C22⋊C4—71no—
882C2×C22⋊C4—71no—
883C2×C22⋊C4C22×D711yescharacteristic
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
891C2×C22⋊C4C22×D711yescharacteristic
892C2×C22⋊C4C22×D711yescharacteristic
893C2×C22⋊C4C22×D711yescharacteristic
894C2×C22⋊C4C22×D711yescharacteristic
895C2×C22⋊C4C22×D711yescharacteristic
896C2×C42—71no—
897C2×C42—71no—
898C2×C42—71no—
899C2×C42—71no—
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
907C2×C42C22×D711yescharacteristic
908C2×C42C22×D711yescharacteristic
909C2×C42C22×D711yescharacteristic
910#95—71no—
911#95—71no—
912#95—71no—
913#95—71no—
914#95—71no—
915#95—71no—
916#95—71no—
917#95—71no—
918#95—71no—
919#95—71no—
920#95—71no—
921#95—71no—
922#95—71no—
923#95—71no—
924#95—71no—
925#95—71no—
926#95—71no—
927#95—71no—
928#95—71no—
929#95—71no—
930#95—71no—
931#95—71no—
932#95—71no—
933#95—71no—
934#95—71no—
935#95—71no—
936#95—71no—
937#95—71no—
938#95—71no—
939#95—71no—
940#95—71no—
941#95—71no—
942#95—71no—
943#95—71no—
944#95—71no—
945#95—71no—
946#95—71no—
947#95—71no—
948#95—71no—
949#95—71no—
950#95—71no—
951#95—71no—
952#95—71no—
953#95—71no—
954#95—71no—
955#95—71no—
956#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964C22×C7—22no—
965C22×C7—22no—
966C22×C7—22no—
967C22×C7—41no—
968C22×C7—41no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7—41no—
978C22×C7—41no—
979C22×C7—41no—
980C22×C7—41no—
981C22×C7—41no—
982C22×C7—41no—
983C22×C7—41no—
984C22×C7—41no—
985C22×C7C22×#4111yescharacteristic
986C22×C7C2×H(5,𝔽2)11yescharacteristic
987C22×C7C2×2−1+411yescharacteristic
988C22×C7#58511yescharacteristic
989C22×C7#58511yescharacteristic
990C22×C7#58511yescharacteristic
991C22×C7#58511yescharacteristic
992C4×C7—22no—
993C4×C7—22no—
994C4×C7—22no—
995C4×C7—41no—
996C4×C7—41no—
997C4×C7—41no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004Dic7—22no—
1005Dic7—41no—
1006Dic7—41no—
1007Dic7—41no—
1008Dic7—41no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020C24C23×D711yescharacteristic
1021C24C23×D711yescharacteristic
1022C24C23×D711yescharacteristic
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C22×C4—22no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—71no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—71no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—142no—
1054C22×C4—142no—
1055C22×C4—281no—
1056C22×C4—281no—
1057C22×C4—281no—
1058C22×C4—281no—
1059C22×C4—281no—
1060C22×C4—281no—
1061C22×C4—281no—
1062C22×C4#115914yes—
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C22×C4C23×D711yescharacteristic
1068C22×C4C23×D711yescharacteristic
1069C22×C4C23×D711yescharacteristic
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—142no—
1082C4⋊C4—142no—
1083C4⋊C4—142no—
1084C4⋊C4—142no—
1085C4⋊C4—142no—
1086C4⋊C4—142no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—142no—
1090C4⋊C4—142no—
1091C4⋊C4—281no—
1092C4⋊C4—281no—
1093C4⋊C4—281no—
1094C4⋊C4—281no—
1095C4⋊C4—281no—
1096C4⋊C4—281no—
1097C4⋊C4—281no—
1098C4⋊C4—281no—
1099C4⋊C4—281no—
1100C4⋊C4—281no—
1101C4⋊C4—281no—
1102C4⋊C4—281no—
1103C4⋊C4—281no—
1104C4⋊C4—281no—
1105C4⋊C4—281no—
1106C4⋊C4—281no—
1107C4⋊C4—281no—
1108C4⋊C4—281no—
1109C4⋊C4—281no—
1110C4⋊C4—281no—
1111C4⋊C4—281no—
1112C4⋊C4—281no—
1113C4⋊C4—281no—
1114C4⋊C4—281no—
1115C4⋊C4—281no—
1116C4⋊C4—281no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—281no—
1137C22⋊C4—281no—
1138C22⋊C4—281no—
1139C22⋊C4—281no—
1140C22⋊C4—281no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C22⋊C4—281no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C42—22no—
1155C42—41no—
1156C42—41no—
1157C42—142no—
1158C42—142no—
1159C42—281no—
1160C42—281no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7—42no—
1169C2×C7—81no—
1170C2×C7—81no—
1171C2×C7#345511yescharacteristic
1172C2×C7#349511yescharacteristic
1173C2×C7#350511yescharacteristic
1174C2×C7#355711yescharacteristic
1175C2×C7#355911yescharacteristic
1176C2×C7#356211yescharacteristic
1177C2×C7#356711yescharacteristic
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23C2×#115912yes—
1199C23C24×D711yescharacteristic
1200D4—44no—
1201D4—82no—
1202D4—82no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—72no—
1239C2×C4—141no—
1240C2×C4—141no—
1241C2×C4—141no—
1242C2×C4—141no—
1243C2×C4—141no—
1244C2×C4—141no—
1245C2×C4—141no—
1246C2×C4—141no—
1247C2×C4—141no—
1248C2×C4—141no—
1249C2×C4—141no—
1250C2×C4—141no—
1251C2×C4—141no—
1252C2×C4—141no—
1253C2×C4—141no—
1254C2×C4—141no—
1255C2×C4—141no—
1256C2×C4—141no—
1257C2×C4—141no—
1258C2×C4—141no—
1259C2×C4—141no—
1260C2×C4—141no—
1261C2×C4—141no—
1262C2×C4—141no—
1263C2×C4—141no—
1264C2×C4—141no—
1265C2×C4—141no—
1266C2×C4—141no—
1267C2×C4—141no—
1268C2×C4—141no—
1269C2×C4—141no—
1270C2×C4—141no—
1271C2×C4—141no—
1272C2×C4—141no—
1273C2×C4—141no—
1274C2×C4—141no—
1275C2×C4—141no—
1276C2×C4—141no—
1277C2×C4—141no—
1278C2×C4—141no—
1279C2×C4—141no—
1280C2×C4—141no—
1281C2×C4—141no—
1282C2×C4—141no—
1283C2×C4—141no—
1284C2×C4—141no—
1285C2×C4—141no—
1286C2×C4—284no—
1287C2×C4—562no—
1288C2×C4—562no—
1289C2×C4C2×#115912yes—
1290C2×C4C2×#115912yes—
1291C2×C4#655412yes—
1292C7#3699411yescharacteristic, complemented, Sylow
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22C22×#115911yescharacteristic
1315C22C2×#655411yescharacteristic
1316C22#9061611yescharacteristic
1317C22#9061611yescharacteristic
1318C22#9061611yescharacteristic
1319C22D7×H(5,𝔽2)11yescharacteristic
1320C22#9061811yescharacteristic
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—142no—
1334C4—281no—
1335C4—281no—
1336C4—281no—
1337C4—281no—
1338C4—281no—
1339C4—281no—
1340C4—281no—
1341C4—281no—
1342C4—281no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C2—42no—
1350C2—81no—
1351C2—81no—
1352C2#1174309611yescharacteristic
1353C2#1174330411yescharacteristic
1354C2#1174336711yescharacteristic
1355C2#1174387711yescharacteristic
1356C2#1174397511yescharacteristic
1357C2#1174398711yescharacteristic
1358C2#1174412711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2602C2
prime radicalC7×#392C22
hypercenter#2602D7
hypocenterC7#36994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2602

Complements

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

NH ≅ G/Ntype
2. #11740288C2semidirect
3. #11740282C2semidirect
4. #11739832C2semidirect
5. #11739764C2semidirect
6. #11735062C2semidirect
7. #11735043C2semidirect
8. #11734508C2semidirect
9. #11734499C2semidirect
10. #11734494C2semidirect
11. #11734472C2semidirect
14. #11733863C2semidirect
15. #11733836C2semidirect
16. #11733622C2semidirect
17. #11733562C2semidirect
18. #11733267C2semidirect
19. #11733234C2semidirect
20. #11733232C2semidirect
21. #11733212C2semidirect
22. #11733203C2semidirect
23. #11733057C2semidirect
24. #11732737C2semidirect
25. #11732558C2semidirect
26. #11732233C2semidirect
27. #11732168C2semidirect
28. #11731950C2semidirect
29. #11731890C2semidirect
30. #11730939C2semidirect
31. #11730890C2semidirect
1292. C7#36994semidirect

Maximal subgroups

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

subgroupindex
C7×#26022
#117402882
#117402822
#117398322
#117397642
#117350622
#117350432
#117345082
#117344992
#117344942
#117344722
#117341792
#117341702
#117338632
#117338362
#117336222
#117335622
#117332672
#117332342
#117332322
#117332122
#117332032
#117330572
#117327372
#117325582
#117322332
#117321682
#117319502
#117318902
#117309392
#117308902
#369947