Finite Group Databasebeta

← #14216755

Subgroups — #14216755

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2353C211yesmaximal, characteristic, complemented
2#11739857C211yesmaximal, characteristic
3#11739784C211yesmaximal, characteristic, complemented
4#11733305C211yesmaximal, characteristic, complemented
5#11733282C211yesmaximal, characteristic, complemented
6#11732995C211yesmaximal, characteristic, complemented
7#11732896C211yesmaximal, characteristic, complemented
8#11732808C211yesmaximal, characteristic, complemented
9#11732729C211yesmaximal, characteristic, complemented
10#11732519C211yesmaximal, characteristic, complemented
11#11732469C211yesmaximal, characteristic, complemented
12#11732287C211yesmaximal, characteristic, complemented
13#11732168C211yesmaximal, characteristic, complemented
14#11732159C211yesmaximal, characteristic
15#11732158C211yesmaximal, characteristic
16#11731745C211yesmaximal, characteristic, complemented
17#11731719C211yesmaximal, characteristic, complemented
18#11731587C211yesmaximal, characteristic, complemented
19#11731522C211yesmaximal, characteristic, complemented
20#11731489C211yesmaximal, characteristic, complemented
21#11731369C211yesmaximal, characteristic, complemented
22#11731038C211yesmaximal, characteristic, complemented
23#11731021C211yesmaximal, characteristic, complemented
24#11730986C211yesmaximal, characteristic, complemented
25#11730986C211yesmaximal, characteristic, complemented
26#11730907C211yesmaximal, characteristic, complemented
27#11730885C211yesmaximal, characteristic, complemented
28#11730847C211yesmaximal, characteristic, complemented
29#11730830C211yesmaximal, characteristic, complemented
30#11730798C211yesmaximal, characteristic, complemented
31#11730782C211yesmaximal, characteristic, complemented
32C2×C4×C7×D4C2211yescharacteristic
33C2×#6498C2211yescharacteristic
34C2×#6492C2211yescharacteristic
35C2×C4×C22⋊D7C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6446C2211yescharacteristic
38C2×(C22⋊D7)⋊C4C2211yescharacteristic
39C2×#6440C2211yescharacteristic
40C2×#6435C2211yescharacteristic
41C7×#388C2211yescharacteristic
42C7×#388C2211yescharacteristic
43C7×#387C2211yescharacteristic
44C7×#387C2211yescharacteristic
45C7×#386C2211yescharacteristic
46C7×#386C2211yescharacteristic
47C7×#383C2211yescharacteristic
48C7×#381C2211yescharacteristic
49C7×#380C2211yescharacteristic
50C4×C7×C22⋊C4C2211yescharacteristic
51C4×C7×C22⋊C4C2211yescharacteristic
52C4×C7×C22⋊C4C2211yescharacteristic
53C7×#376C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#89995C2211yescharacteristic
56#89994C2211yescharacteristic
57#89992C2211yescharacteristic
58#89985C2211yescharacteristic
59#89985C2211yescharacteristic
60#89984C2211yescharacteristic
61#89983C2211yescharacteristic
62#89983C2211yescharacteristic
63#89983C2211yescharacteristic
64#89982C2211yescharacteristic
65#89982C2211yescharacteristic
66#89982C2211yescharacteristic
67#89982C2211yescharacteristic
68C4×C22⋊Dic7C2211yescharacteristic
69C4×C22⋊Dic7C2211yescharacteristic
70C2×C7⋊#95C2211yescharacteristic
71#89766C2211yescharacteristic
72#89766C2211yescharacteristic
73#89761C2211yescharacteristic
74#89758C2211yescharacteristic
75#89758C2211yescharacteristic
76#89757C2211yescharacteristic
77#89750C2211yescharacteristic
78#89750C2211yescharacteristic
79#89748C2211yescharacteristic
80C4⋊C4×Dic7C2211yescharacteristic
81#89745C2211yescharacteristic
82#89744C2211yescharacteristic
83#89733C2211yescharacteristic
84#89733C2211yescharacteristic
85#89730C2211yescharacteristic
86#89728C2211yescharacteristic
87#89728C2211yescharacteristic
88#89728C2211yescharacteristic
89#89725C2211yescharacteristic
90#89725C2211yescharacteristic
91#89723C2211yescharacteristic
92#89722C2211yescharacteristic
93#89720C2211yescharacteristic
94#89720C2211yescharacteristic
95#89720C2211yescharacteristic
96#89720C2211yescharacteristic
97#89718C2211yescharacteristic
98#89717C2211yescharacteristic
99#89717C2211yescharacteristic
100#89717C2211yescharacteristic
101#89717C2211yescharacteristic
102#89717C2211yescharacteristic
103#89716C2211yescharacteristic
104#89716C2211yescharacteristic
105#89716C2211yescharacteristic
106#89716C2211yescharacteristic
107#89714C2211yescharacteristic
108#89714C2211yescharacteristic
109C22⋊C4×Dic7C2211yescharacteristic
110C22⋊C4×Dic7C2211yescharacteristic
111C22⋊C4×Dic7C2211yescharacteristic
112#89712C2211yescharacteristic
113C4×(C2×D7)⋊C4C2211yescharacteristic
114C4×(C2×D7)⋊C4C2211yescharacteristic
115C4×(C2×D7)⋊C4C2211yescharacteristic
116#89709C2211yescharacteristic
117#89705C2211yescharacteristic
118#89705C2211yescharacteristic
119#89705C2211yescharacteristic
120#89705C2211yescharacteristic
121#89705C2211yescharacteristic
122#89705C2211yescharacteristic
123#89704C2211yescharacteristic
124C4×Dic7⋊C4C2211yescharacteristic
125C4×Dic7⋊C4C2211yescharacteristic
126C4×Dic7⋊C4C2211yescharacteristic
127C4×Dic7⋊C4C2211yescharacteristic
128C42×Dic7C2211yescharacteristic
129#89700C2211yescharacteristic
130#89700C2211yescharacteristic
131#89447C2211yescharacteristic
132#89442C2211yescharacteristic
133#89441C2211yescharacteristic
134#89441C2211yescharacteristic
135#89441C2211yescharacteristic
136#89441C2211yescharacteristic
137#89440C2211yescharacteristic
138#89440C2211yescharacteristic
139#89439C2211yescharacteristic
140#89439C2211yescharacteristic
141#89438C2211yescharacteristic
142#89436C2211yescharacteristic
143#89436C2211yescharacteristic
144D7×#95C2211yescharacteristic
145C7⋊#401C2211yescharacteristic
146#89432C2211yescharacteristic
147#89432C2211yescharacteristic
148#89432C2211yescharacteristic
149#89432C2211yescharacteristic
150#89432C2211yescharacteristic
151#89432C2211yescharacteristic
152#89431C2211yescharacteristic
153#89431C2211yescharacteristic
154#89431C2211yescharacteristic
155#89431C2211yescharacteristic
156#89430C2211yescharacteristic
157#89430C2211yescharacteristic
158#89430C2211yescharacteristic
159#89430C2211yescharacteristic
160#89430C2211yescharacteristic
161#89430C2211yescharacteristic
162#89427C2211yescharacteristic
163#89427C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89424C2211yescharacteristic
172#89424C2211yescharacteristic
173#89424C2211yescharacteristic
174#89424C2211yescharacteristic
175#89424C2211yescharacteristic
176#89424C2211yescharacteristic
177#89424C2211yescharacteristic
178#89424C2211yescharacteristic
179#89423C2211yescharacteristic
180#89423C2211yescharacteristic
181#89421C2211yescharacteristic
182#89420C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89419C2211yescharacteristic
186#89419C2211yescharacteristic
187#60026—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C23×C4×C7C2311yescharacteristic
193C22×C22⋊D7C2311yescharacteristic
194C22×C22⋊D7C2311yescharacteristic
195C23×Dic7C2311yescharacteristic
196C23×Dic7C2311yescharacteristic
197C22×C4×D7C2311yescharacteristic
198C22×C4×D7C2311yescharacteristic
199C22×C4×D7C2311yescharacteristic
200C4×C7×D4—24no—
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×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C42×C7C2311yescharacteristic
215C2×C42×C7C2311yescharacteristic
216C2×C42×C7C2311yescharacteristic
217C2×C22⋊Dic7C2311yescharacteristic
218C2×C22⋊Dic7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
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
229#6498—24no—
230#6492—24no—
231C4×C22⋊D7—24no—
232C2×(C2×D7)⋊C4C2311yescharacteristic
233C2×(C2×D7)⋊C4C2311yescharacteristic
234C2×(C2×D7)⋊C4C2311yescharacteristic
235C2×(C2×D7)⋊C4C2311yescharacteristic
236C2×(C2×D7)⋊C4C2311yescharacteristic
237C2×(C2×D7)⋊C4C2311yescharacteristic
238C2×(C2×D7)⋊C4C2311yescharacteristic
239C2×(C2×D7)⋊C4C2311yescharacteristic
240C2×(C2×D7)⋊C4C2311yescharacteristic
241C2×(C2×D7)⋊C4C2311yescharacteristic
242#6489—24no—
243C2×C4⋊Dic7C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2311yescharacteristic
255C2×Dic7⋊C4C2311yescharacteristic
256C2×Dic7⋊C4C2311yescharacteristic
257C2×Dic7⋊C4C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
260C2×Dic7⋊C4C2311yescharacteristic
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×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286#6446—24no—
287(C22⋊D7)⋊C4—24no—
288#6440—24no—
289#6435—24no—
290C7×#95C2311yescharacteristic
291C7×#95C2311yescharacteristic
292C7×#95C2311yescharacteristic
293C7×#95C2311yescharacteristic
294C7×#95C2311yescharacteristic
295C7×#95C2311yescharacteristic
296C7×#95C2311yescharacteristic
297C7×#95C2311yescharacteristic
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#2810—71no—
353#2750—71no—
354#2750—71no—
355#2750—71no—
356#2573—71no—
357#2573—71no—
358#2573—71no—
359#2533—71no—
360#2533—71no—
361#2533—71no—
362#2497—71no—
363#2497—71no—
364#2497—71no—
365#2493—71no—
366#2493—71no—
367#2493—71no—
368#2470—71no—
369#2470—71no—
370#2470—71no—
371#2457—71no—
372#2457—71no—
373#2457—71no—
374#2359—71no—
375#2359—71no—
376#2359—71no—
377#2353—71no—
378#2353—71no—
379#2353D711yescharacteristic, complemented
380#2298—71no—
381#2298—71no—
382#2298—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—22no—
388C2×C7×D4—41no—
389C22×C4×C7—22no—
390C22×C4×C7—22no—
391C22×C4×C7—22no—
392C22×C4×C7—22no—
393C22×C4×C7—22no—
394C22×C4×C7—41no—
395C22×C4×C7—41no—
396C22×C4×C7—41no—
397C22×C4×C7—41no—
398C22×C4×C7—41no—
399C22×C4×C7—41no—
400C22×C4×C7—41no—
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×C4×C7C2411yescharacteristic
414C2×C22⋊D7—22no—
415C2×C22⋊D7—22no—
416C2×C22⋊D7—22no—
417C2×C22⋊D7—22no—
418C2×C22⋊D7—41no—
419C2×C22⋊D7—41no—
420C22×Dic7—22no—
421C22×Dic7—22no—
422C22×Dic7—22no—
423C22×Dic7—41no—
424C22×Dic7—41no—
425C22×Dic7—41no—
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C22×Dic7C2411yescharacteristic
431C22×Dic7C2411yescharacteristic
432C22×Dic7C2411yescharacteristic
433C22×Dic7C2411yescharacteristic
434C22×Dic7C2411yescharacteristic
435C22×Dic7C2411yescharacteristic
436C22×Dic7C2411yescharacteristic
437C22×Dic7C2411yescharacteristic
438C22×Dic7C2411yescharacteristic
439C22×Dic7C2411yescharacteristic
440C22×Dic7C2411yescharacteristic
441C2×C4×D7—22no—
442C2×C4×D7—22no—
443C2×C4×D7—22no—
444C2×C4×D7—22no—
445C2×C4×D7—41no—
446C2×C4×D7—41no—
447C2×C4×D7—41no—
448C2×C4×D7—41no—
449C2×C4×D7—41no—
450C7×C4⋊C4—22no—
451C7×C4⋊C4—41no—
452C7×C4⋊C4—41no—
453C7×C22⋊C4—22no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—41no—
456C7×C22⋊C4—41no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4—41no—
459C7×C22⋊C4—41no—
460C7×C22⋊C4#4114yes—
461C42×C7—22no—
462C42×C7—22no—
463C42×C7—41no—
464C42×C7—41no—
465C42×C7—41no—
466C22⋊Dic7—22no—
467C22⋊Dic7—22no—
468C22⋊Dic7—22no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—22no—
472C22⋊Dic7—41no—
473C22⋊Dic7—41no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7#4114yes—
478(C2×D7)⋊C4—22no—
479(C2×D7)⋊C4—22no—
480(C2×D7)⋊C4—22no—
481(C2×D7)⋊C4—22no—
482(C2×D7)⋊C4—41no—
483(C2×D7)⋊C4—41no—
484(C2×D7)⋊C4—41no—
485(C2×D7)⋊C4—41no—
486(C2×D7)⋊C4—41no—
487(C2×D7)⋊C4#4114yes—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—22no—
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—22no—
504Dic7⋊C4—22no—
505Dic7⋊C4—22no—
506Dic7⋊C4—22no—
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—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—22no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#123—71no—
532C2×#123—71no—
533C2×#123—71no—
534C2×C4×D4—71no—
535C2×C4×D4—71no—
536C2×C4×D4C2×D711yescharacteristic
537C2×#117—71no—
538C2×#117—71no—
539C2×#117—71no—
540#401—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#400—71no—
550#400—71no—
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400—71no—
556#400—71no—
557#400—71no—
558#400—71no—
559#397—71no—
560#397—71no—
561#397—71no—
562#396—71no—
563#396—71no—
564#396—71no—
565#396—71no—
566#396—71no—
567#396—71no—
568#394—71no—
569#394—71no—
570#394—71no—
571#392—71no—
572#389—71no—
573#389—71no—
574#389—71no—
575#389—71no—
576#389—71no—
577#389—71no—
578#389—71no—
579#389—71no—
580#389—71no—
581#388—71no—
582#388—71no—
583#388—71no—
584#388—71no—
585#388—71no—
586#388—71no—
587#388—71no—
588#388—71no—
589#388—71no—
590#388—71no—
591#388—71no—
592#388—71no—
593#388—71no—
594#388—71no—
595#388—71no—
596#388—71no—
597#388C2×D711yescharacteristic
598#388C2×D711yescharacteristic
599#387—71no—
600#387—71no—
601#387—71no—
602#387—71no—
603#387—71no—
604#387—71no—
605#387—71no—
606#387—71no—
607#387—71no—
608#387—71no—
609#387—71no—
610#387—71no—
611#387—71no—
612#387—71no—
613#387—71no—
614#387—71no—
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387—71no—
623#387—71no—
624#387C2×D711yescharacteristic
625#387C2×D711yescharacteristic
626#386—71no—
627#386—71no—
628#386—71no—
629#386—71no—
630#386—71no—
631#386—71no—
632#386—71no—
633#386C2×D711yescharacteristic
634#386C2×D711yescharacteristic
635#385—71no—
636#385—71no—
637#385—71no—
638#385—71no—
639#385—71no—
640#385—71no—
641#385—71no—
642#385—71no—
643#385—71no—
644#384—71no—
645#383—71no—
646#383—71no—
647#383—71no—
648#383C2×D711yescharacteristic
649#381—71no—
650#381—71no—
651#381—71no—
652#381—71no—
653#381—71no—
654#381C2×D711yescharacteristic
655#380—71no—
656#380—71no—
657#380—71no—
658#380—71no—
659#380—71no—
660#380C2×D711yescharacteristic
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C22⋊C4—71no—
668C4×C22⋊C4—71no—
669C4×C22⋊C4—71no—
670C4×C22⋊C4—71no—
671C4×C22⋊C4—71no—
672C4×C22⋊C4—71no—
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4C2×D711yescharacteristic
677C4×C22⋊C4C2×D711yescharacteristic
678C4×C22⋊C4C2×D711yescharacteristic
679#376—71no—
680#376—71no—
681#376C2×D711yescharacteristic
682C2×#95—71no—
683C2×#95—71no—
684C2×#95C2×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×C7C2×#4112yes—
699C23×C7C2×#4112yes—
700C23×C7C2511yescharacteristic
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7—21no—
707C22×D7C2×#4112yes—
708C7×D4—44no—
709C2×C4×C7—21no—
710C2×C4×C7—21no—
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—21no—
745C2×C4×C7—44no—
746C2×C4×C7—82no—
747C2×C4×C7—82no—
748C2×C4×C7—82no—
749C2×C4×C7C2×#4112yes—
750C2×C4×C7C2×#4112yes—
751C2×C4×C7C2×#4112yes—
752C22⋊D7—44no—
753C22⋊D7—44no—
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×Dic7C2×#4112yes—
799C2×Dic7C2×#4112yes—
800C2×Dic7C2×#4112yes—
801C4×D7—44no—
802C4×D7—82no—
803C4×D7—82no—
804C22×D4—71no—
805C22×D4—71no—
806C22×D4C22×D711yescharacteristic
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4—71no—
812C23×C4C22×D711yescharacteristic
813C23×C4C22×D711yescharacteristic
814C23×C4C22×D711yescharacteristic
815C23×C4C22×D711yescharacteristic
816#123—144no—
817#123—144no—
818#123—144no—
819C4×D4—24no—
820C4×D4—144no—
821C4×D4—144no—
822#117—144no—
823#117—144no—
824#117—144no—
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⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C22⋊C4—71no—
859C2×C22⋊C4—71no—
860C2×C22⋊C4—71no—
861C2×C22⋊C4—71no—
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⋊C4C22×D711yescharacteristic
881C2×C22⋊C4C22×D711yescharacteristic
882C2×C22⋊C4C22×D711yescharacteristic
883C2×C22⋊C4C22×D711yescharacteristic
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C42—71no—
889C2×C42—71no—
890C2×C42—71no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—71no—
894C2×C42—71no—
895C2×C42—71no—
896C2×C42—71no—
897C2×C42—71no—
898C2×C42—71no—
899C2×C42—71no—
900C2×C42—71no—
901C2×C42C22×D711yescharacteristic
902C2×C42C22×D711yescharacteristic
903C2×C42C22×D711yescharacteristic
904C2×C42C22×D711yescharacteristic
905C2×C42C22×D711yescharacteristic
906#95—71no—
907#95—71no—
908#95—71no—
909#95—71no—
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#95C22×D711yescharacteristic
955#95C22×D711yescharacteristic
956#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964#95C22×D711yescharacteristic
965#95C22×D711yescharacteristic
966#95C22×D711yescharacteristic
967#95C22×D711yescharacteristic
968C22×C7—22no—
969C22×C7—22no—
970C22×C7—22no—
971C22×C7—22no—
972C22×C7—22no—
973C22×C7—22no—
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×C7C22×#4111yescharacteristic
983C22×C7C22×#4111yescharacteristic
984C22×C7C22×#4111yescharacteristic
985C22×C7#58511yescharacteristic
986C22×C7#58511yescharacteristic
987C22×C7#58511yescharacteristic
988C22×C7#58511yescharacteristic
989C2×D7—22no—
990C2×D7—22no—
991C2×D7—22no—
992C2×D7—41no—
993C2×D7—41no—
994C2×D7—41no—
995C2×D7—41no—
996C4×C7—22no—
997C4×C7—22no—
998C4×C7—22no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006C4×C7—41no—
1007C4×C7—41no—
1008C4×C7—41no—
1009Dic7—22no—
1010Dic7—22no—
1011Dic7—22no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022Dic7—41no—
1023Dic7—41no—
1024C24—71no—
1025C24C23×D711yescharacteristic
1026C24C23×D711yescharacteristic
1027C2×D4—22no—
1028C2×D4—22no—
1029C2×D4—41no—
1030C2×D4—142no—
1031C2×D4—142no—
1032C2×D4—142no—
1033C2×D4—142no—
1034C2×D4—281no—
1035C2×D4—281no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—71no—
1055C22×C4—71no—
1056C22×C4—71no—
1057C22×C4—71no—
1058C22×C4—71no—
1059C22×C4—71no—
1060C22×C4—71no—
1061C22×C4—71no—
1062C22×C4—71no—
1063C22×C4—142no—
1064C22×C4—142no—
1065C22×C4—142no—
1066C22×C4—142no—
1067C22×C4—142no—
1068C22×C4—142no—
1069C22×C4—142no—
1070C22×C4—281no—
1071C22×C4—281no—
1072C22×C4—281no—
1073C22×C4—281no—
1074C22×C4—281no—
1075C22×C4—281no—
1076C22×C4—281no—
1077C22×C4—281no—
1078C22×C4C23×D711yescharacteristic
1079C22×C4C23×D711yescharacteristic
1080C22×C4C23×D711yescharacteristic
1081C22×C4C23×D711yescharacteristic
1082C22×C4C23×D711yescharacteristic
1083C22×C4C23×D711yescharacteristic
1084C22×C4C23×D711yescharacteristic
1085C22×C4C23×D711yescharacteristic
1086C22×C4C23×D711yescharacteristic
1087C22×C4C23×D711yescharacteristic
1088C22×C4C23×D711yescharacteristic
1089C22×C4C23×D711yescharacteristic
1090C22×C4C23×D711yescharacteristic
1091C4⋊C4—22no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—142no—
1097C4⋊C4—142no—
1098C4⋊C4—142no—
1099C4⋊C4—142no—
1100C4⋊C4—142no—
1101C4⋊C4—142no—
1102C4⋊C4—142no—
1103C4⋊C4—142no—
1104C4⋊C4—142no—
1105C4⋊C4—142no—
1106C4⋊C4—142no—
1107C4⋊C4—142no—
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—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—74no—
1132C22⋊C4—74no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—142no—
1137C22⋊C4—142no—
1138C22⋊C4—142no—
1139C22⋊C4—142no—
1140C22⋊C4—142no—
1141C22⋊C4—142no—
1142C22⋊C4—142no—
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#115714yes—
1154C42—22no—
1155C42—22no—
1156C42—41no—
1157C42—41no—
1158C42—41no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—142no—
1163C42—142no—
1164C42—142no—
1165C42—142no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C42—281no—
1171C42—281no—
1172C2×C7—42no—
1173C2×C7—42no—
1174C2×C7#347511yescharacteristic
1175C2×C7#347511yescharacteristic
1176C2×C7#347511yescharacteristic
1177C2×C7#352111yescharacteristic
1178C2×C7#352111yescharacteristic
1179C2×C7#352111yescharacteristic
1180C2×C7#356711yescharacteristic
1181D7—42no—
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—72no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23—141no—
1199C23—141no—
1200C23—141no—
1201C23C2×#115712yes—
1202C23D7×#4112yes—
1203C23C24×D711yescharacteristic
1204D4—44no—
1205D4—284no—
1206D4—284no—
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—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—44no—
1244C2×C4—72no—
1245C2×C4—72no—
1246C2×C4—72no—
1247C2×C4—82no—
1248C2×C4—82no—
1249C2×C4—82no—
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—141no—
1287C2×C4—141no—
1288C2×C4—141no—
1289C2×C4—141no—
1290C2×C4—141no—
1291C2×C4—141no—
1292C2×C4—284no—
1293C2×C4—284no—
1294C2×C4—562no—
1295C2×C4—562no—
1296C2×C4—562no—
1297C2×C4C2×#115712yes—
1298C2×C4C2×#115712yes—
1299C2×C4D7×#4112yes—
1300C7#6002611yescharacteristic, complemented, Sylow
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—142no—
1316C22—142no—
1317C22—142no—
1318C22—281no—
1319C22—281no—
1320C22—281no—
1321C22—281no—
1322C22C22×#115711yescharacteristic
1323C22C2×D7×#4111yescharacteristic
1324C22C2×D7×#4111yescharacteristic
1325C22#9061611yescharacteristic
1326C22#9061611yescharacteristic
1327C22#9061811yescharacteristic
1328C22#9061811yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—142no—
1343C4—142no—
1344C4—142no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C4—281no—
1350C4—281no—
1351C4—281no—
1352C4—281no—
1353C4—281no—
1354C4—281no—
1355C4—281no—
1356C4—281no—
1357C2—42no—
1358C2—42no—
1359C2—282no—
1360C2#1174281211yescharacteristic
1361C2#1174290911yescharacteristic
1362C2#1174293311yescharacteristic
1363C2#1174385811yescharacteristic
1364C2#1174386711yescharacteristic
1365C2#1174395811yescharacteristic
1366C2#1174397511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2353C2
prime radical#89995C22
hypercenter#2353D7
hypocenterC7#60026
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
1. C7×#2353C2semidirect
3. #11739784C2semidirect
4. #11733305C2semidirect
5. #11733282C2semidirect
6. #11732995C2semidirect
7. #11732896C2semidirect
8. #11732808C2semidirect
9. #11732729C2semidirect
10. #11732519C2semidirect
11. #11732469C2semidirect
12. #11732287C2semidirect
13. #11732168C2semidirect
16. #11731745C2semidirect
17. #11731719C2semidirect
18. #11731587C2semidirect
19. #11731522C2semidirect
20. #11731489C2semidirect
21. #11731369C2semidirect
22. #11731038C2semidirect
23. #11731021C2semidirect
24. #11730986C2semidirect
25. #11730986C2semidirect
26. #11730907C2semidirect
27. #11730885C2semidirect
28. #11730847C2semidirect
29. #11730830C2semidirect
30. #11730798C2semidirect
31. #11730782C2semidirect
379. #2353D7semidirect
1300. C7#60026semidirect

Maximal subgroups

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

subgroupindex
C7×#23532
#117398572
#117397842
#117333052
#117332822
#117329952
#117328962
#117328082
#117327292
#117325192
#117324692
#117322872
#117321682
#117321592
#117321582
#117317452
#117317192
#117315872
#117315222
#117314892
#117313692
#117310382
#117310212
#117309862
#117309072
#117308852
#117308472
#117308302
#117307982
#117307822
#600267