Finite Group Databasebeta

← #13562574

Subgroups — #13562574

Order 1792.

1548 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×#2778C211yesmaximal, characteristic
2#11735865C211yesmaximal, characteristic, complemented
3#11735863C211yesmaximal, characteristic, complemented
4#11735701C211yesmaximal, characteristic, complemented
5#11735621C211yesmaximal, characteristic, complemented
6#11735048C211yesmaximal, characteristic, complemented
7#11735007C211yesmaximal, characteristic, complemented
8#11734497C211yesmaximal, characteristic, complemented
9#11734468C211yesmaximal, characteristic, complemented
10#11734405C211yesmaximal, characteristic, complemented
11#11734342C211yesmaximal, characteristic, complemented
12#11734178C211yesmaximal, characteristic
13#11734138C211yesmaximal, characteristic
14#11733199C211yesmaximal, characteristic, complemented
15#11733194C211yesmaximal, characteristic, complemented
16#11733116C211yesmaximal, characteristic, complemented
17#11733061C211yesmaximal, characteristic, complemented
18#11733032C211yesmaximal, characteristic, complemented
19#11732908C211yesmaximal, characteristic, complemented
20#11732315C211yesmaximal, characteristic, complemented
21#11732288C211yesmaximal, characteristic, complemented
22#11732278C211yesmaximal, characteristic, complemented
23#11732272C211yesmaximal, characteristic, complemented
24#11732248C211yesmaximal, characteristic, complemented
25#11732208C211yesmaximal, characteristic, complemented
26#11732108C211yesmaximal, characteristic, complemented
27#11732102C211yesmaximal, characteristic, complemented
28#11732005C211yesmaximal, characteristic, complemented
29#11731860C211yesmaximal, characteristic, complemented
30#11731445C211yesmaximal, characteristic, complemented
31#11731433C211yesmaximal, characteristic, complemented
32C2×D4×Dic7C2211yescharacteristic
33C2×D4×Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C2×#6442C2211yescharacteristic
37C2×#6441C2211yescharacteristic
38C2×#6441C2211yescharacteristic
39C2×#6441C2211yescharacteristic
40C2×#6440C2211yescharacteristic
41C7×#401C2211yescharacteristic
42C7×#400C2211yescharacteristic
43C7×#397C2211yescharacteristic
44C7×#394C2211yescharacteristic
45C7×#394C2211yescharacteristic
46C7×#392C2211yescharacteristic
47C7×#388C2211yescharacteristic
48C7×#388C2211yescharacteristic
49C7×#388C2211yescharacteristic
50C7×#386C2211yescharacteristic
51C7×#386C2211yescharacteristic
52C7×#386C2211yescharacteristic
53C7×#386C2211yescharacteristic
54C7×#385C2211yescharacteristic
55C7×#380C2211yescharacteristic
56#89994C2211yescharacteristic
57#89994C2211yescharacteristic
58#89994C2211yescharacteristic
59#89993C2211yescharacteristic
60#89992C2211yescharacteristic
61#89992C2211yescharacteristic
62#89992C2211yescharacteristic
63#89992C2211yescharacteristic
64#89992C2211yescharacteristic
65#89992C2211yescharacteristic
66#89984C2211yescharacteristic
67#89984C2211yescharacteristic
68#89982C2211yescharacteristic
69#89982C2211yescharacteristic
70#89982C2211yescharacteristic
71C2×C7⋊#95C2211yescharacteristic
72#89758C2211yescharacteristic
73#89757C2211yescharacteristic
74#89757C2211yescharacteristic
75#89757C2211yescharacteristic
76#89756C2211yescharacteristic
77#89756C2211yescharacteristic
78#89755C2211yescharacteristic
79#89755C2211yescharacteristic
80#89754C2211yescharacteristic
81#89754C2211yescharacteristic
82#89750C2211yescharacteristic
83C4⋊C4×Dic7C2211yescharacteristic
84#89746C2211yescharacteristic
85#89746C2211yescharacteristic
86#89744C2211yescharacteristic
87#89744C2211yescharacteristic
88#89725C2211yescharacteristic
89#89725C2211yescharacteristic
90#89725C2211yescharacteristic
91#89725C2211yescharacteristic
92#89724C2211yescharacteristic
93#89724C2211yescharacteristic
94#89724C2211yescharacteristic
95#89723C2211yescharacteristic
96#89723C2211yescharacteristic
97#89723C2211yescharacteristic
98#89723C2211yescharacteristic
99#89723C2211yescharacteristic
100#89722C2211yescharacteristic
101#89722C2211yescharacteristic
102#89722C2211yescharacteristic
103#89722C2211yescharacteristic
104#89722C2211yescharacteristic
105#89721C2211yescharacteristic
106#89721C2211yescharacteristic
107#89720C2211yescharacteristic
108#89720C2211yescharacteristic
109#89720C2211yescharacteristic
110#89719C2211yescharacteristic
111#89719C2211yescharacteristic
112#89718C2211yescharacteristic
113#89718C2211yescharacteristic
114#89718C2211yescharacteristic
115#89717C2211yescharacteristic
116#89717C2211yescharacteristic
117#89717C2211yescharacteristic
118#89717C2211yescharacteristic
119#89716C2211yescharacteristic
120#89716C2211yescharacteristic
121#89716C2211yescharacteristic
122#89716C2211yescharacteristic
123#89716C2211yescharacteristic
124#89716C2211yescharacteristic
125#89716C2211yescharacteristic
126#89715C2211yescharacteristic
127#89715C2211yescharacteristic
128#89715C2211yescharacteristic
129#89715C2211yescharacteristic
130#89714C2211yescharacteristic
131#89714C2211yescharacteristic
132#89714C2211yescharacteristic
133C22⋊C4×Dic7C2211yescharacteristic
134C22⋊C4×Dic7C2211yescharacteristic
135#89709C2211yescharacteristic
136C4×Dic7⋊C4C2211yescharacteristic
137#89701C2211yescharacteristic
138#89700C2211yescharacteristic
139#89432C2211yescharacteristic
140#89432C2211yescharacteristic
141#89432C2211yescharacteristic
142#89432C2211yescharacteristic
143#89432C2211yescharacteristic
144#89432C2211yescharacteristic
145#89431C2211yescharacteristic
146#89431C2211yescharacteristic
147#89431C2211yescharacteristic
148#89430C2211yescharacteristic
149#89430C2211yescharacteristic
150#89429C2211yescharacteristic
151#89429C2211yescharacteristic
152#89429C2211yescharacteristic
153#89429C2211yescharacteristic
154#89429C2211yescharacteristic
155#89428C2211yescharacteristic
156#89428C2211yescharacteristic
157#89427C2211yescharacteristic
158#89427C2211yescharacteristic
159#89427C2211yescharacteristic
160#89427C2211yescharacteristic
161#89427C2211yescharacteristic
162#89427C2211yescharacteristic
163#89426C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89426C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89425C2211yescharacteristic
174#89425C2211yescharacteristic
175#89424C2211yescharacteristic
176#89424C2211yescharacteristic
177#89423C2211yescharacteristic
178#89423C2211yescharacteristic
179#89423C2211yescharacteristic
180#89422C2211yescharacteristic
181#89421C2211yescharacteristic
182#89420C2211yescharacteristic
183#89419C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#36790—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C22×C7×D4C2311yescharacteristic
190C22×C7×D4C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C23×C4×C7C2311yescharacteristic
193C23×Dic7C2311yescharacteristic
194C23×Dic7C2311yescharacteristic
195C23×Dic7C2311yescharacteristic
196C23×Dic7C2311yescharacteristic
197C23×Dic7C2311yescharacteristic
198C22×Dic14C2311yescharacteristic
199C22×Dic14C2311yescharacteristic
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×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
229C2×C22⋊Dic7C2311yescharacteristic
230C2×C22⋊Dic7C2311yescharacteristic
231C2×C22⋊Dic7C2311yescharacteristic
232C2×C22⋊Dic7C2311yescharacteristic
233C2×C22⋊Dic7C2311yescharacteristic
234C2×C22⋊Dic7C2311yescharacteristic
235C2×C22⋊Dic7C2311yescharacteristic
236C2×C22⋊Dic7C2311yescharacteristic
237D4×Dic7—24no—
238D4×Dic7—24no—
239C2×C4⋊Dic7C2311yescharacteristic
240C2×C4⋊Dic7C2311yescharacteristic
241C2×C4⋊Dic7C2311yescharacteristic
242C2×C4⋊Dic7C2311yescharacteristic
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×C4⋊Dic7C2311yescharacteristic
252#6487—42no—
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×Dic7—42no—
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
285#6442—42no—
286#6441—24no—
287#6441—42no—
288#6441—42no—
289#6440—42no—
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#2855—71no—
353#2852—71no—
354#2778D711yescharacteristic
355#2770—71no—
356#2770—71no—
357#2768—71no—
358#2764—71no—
359#2762—71no—
360#2758—71no—
361#2750—71no—
362#2749—71no—
363#2747—71no—
364#2743—71no—
365#2741—71no—
366#2728—71no—
367#2702—71no—
368#2692—71no—
369#2689—71no—
370#2655—71no—
371#2654—71no—
372#2600—71no—
373#2595—71no—
374#2587—71no—
375#2564—71no—
376#2533—71no—
377#2532—71no—
378#2438—71no—
379#2415—71no—
380#2332—71no—
381#2318—71no—
382#2290—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C24×C7C2411yescharacteristic
386C2×C7×D4—22no—
387C2×C7×D4—22no—
388C2×C7×D4—22no—
389C2×C7×D4—22no—
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—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×Dic7—22no—
414C22×Dic7—22no—
415C22×Dic7—22no—
416C22×Dic7—41no—
417C22×Dic7—41no—
418C22×Dic7—41no—
419C22×Dic7—41no—
420C22×Dic7—41no—
421C22×Dic7—41no—
422C22×Dic7—41no—
423C22×Dic7—41no—
424C22×Dic7—41no—
425C22×Dic7—41no—
426C22×Dic7—41no—
427C22×Dic7#4114yes—
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
441C22×Dic7C2411yescharacteristic
442C22×Dic7C2411yescharacteristic
443C22×Dic7C2411yescharacteristic
444C2×Dic14—22no—
445C2×Dic14—22no—
446C2×Dic14—41no—
447C2×Dic14—41no—
448C2×Dic14—41no—
449C2×Dic14—41no—
450C7×C4⋊C4—41no—
451C7×C4⋊C4—41no—
452C7×C4⋊C4—41no—
453C7×C4⋊C4—41no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—22no—
458C7×C22⋊C4—41no—
459C7×C22⋊C4—41no—
460C7×C22⋊C4—41no—
461C7×C22⋊C4—41no—
462C7×C22⋊C4—41no—
463C7×C22⋊C4—41no—
464C7×C22⋊C4—41no—
465C7×C22⋊C4—41no—
466C7×C22⋊C4—41no—
467C42×C7—41no—
468C22⋊Dic7—22no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—22no—
472C22⋊Dic7—22no—
473C22⋊Dic7—22no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7—41no—
478C22⋊Dic7—41no—
479C22⋊Dic7—41no—
480C22⋊Dic7—41no—
481C22⋊Dic7—41no—
482C22⋊Dic7—41no—
483C22⋊Dic7—41no—
484C22⋊Dic7—41no—
485C22⋊Dic7—41no—
486C22⋊Dic7—41no—
487C4⋊Dic7—22no—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—22no—
491C4⋊Dic7—41no—
492C4⋊Dic7—41no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
495C4⋊Dic7—41no—
496C4⋊Dic7—41no—
497C4⋊Dic7—41no—
498C4⋊Dic7—41no—
499C4⋊Dic7—41no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—22no—
503Dic7⋊C4—22no—
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—22no—
523C4×Dic7—22no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#126—71no—
532C2×C22⋊Q8—71no—
533C2×C22⋊Q8—71no—
534C2×C22⋊Q8—71no—
535C2×C22⋊Q8—71no—
536C2×C4×D4—71no—
537C2×C4×D4—71no—
538C2×#117—71no—
539C22×C42—71no—
540#401C2×D711yescharacteristic
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#400C2×D711yescharacteristic
556#399—71no—
557#399—71no—
558#398—71no—
559#398—71no—
560#398—71no—
561#398—71no—
562#398—71no—
563#398—71no—
564#398—71no—
565#398—71no—
566#398—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397—71no—
571#397—71no—
572#397—71no—
573#397—71no—
574#397C2×D711yescharacteristic
575#396—71no—
576#396—71no—
577#396—71no—
578#395—71no—
579#395—71no—
580#394—71no—
581#394—71no—
582#394—71no—
583#394C2×D711yescharacteristic
584#394C2×D711yescharacteristic
585#393—71no—
586#393—71no—
587#392C2×D711yescharacteristic
588#391—71no—
589#391—71no—
590#391—71no—
591#391—71no—
592#391—71no—
593#391—71no—
594#390—71no—
595#389—71no—
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—71no—
602#388—71no—
603#388—71no—
604#388—71no—
605#388—71no—
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#388C2×D711yescharacteristic
619#388C2×D711yescharacteristic
620#388C2×D711yescharacteristic
621#387—71no—
622#387—71no—
623#387—71no—
624#387—71no—
625#387—71no—
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#386—71no—
643#386—71no—
644#386—71no—
645#386—71no—
646#386—71no—
647#386—71no—
648#386C2×D711yescharacteristic
649#386C2×D711yescharacteristic
650#386C2×D711yescharacteristic
651#386C2×D711yescharacteristic
652#385—71no—
653#385—71no—
654#385—71no—
655#385—71no—
656#385—71no—
657#385—71no—
658#385—71no—
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385C2×D711yescharacteristic
664#383—71no—
665#383—71no—
666#383—71no—
667#383—71no—
668#382—71no—
669#381—71no—
670#381—71no—
671#381—71no—
672#381—71no—
673#380—71no—
674#380—71no—
675#380—71no—
676#380—71no—
677#380—71no—
678#380C2×D711yescharacteristic
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C4⋊C4—71no—
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684#376—71no—
685C2×#95—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×C7C2×#4112yes—
706C23×C72−1+412yes—
707C23×C7C2511yescharacteristic
708C7×D4—44no—
709C7×D4—44no—
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—21no—
745C2×C4×C7—21no—
746C2×C4×C7—44no—
747C2×C4×C7—82no—
748C2×C4×C7H(5,𝔽2)12yes—
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—44no—
796C2×Dic7—44no—
797C2×Dic7—44no—
798C2×Dic7—82no—
799C2×Dic7—82no—
800C2×Dic7C2×#4112yes—
801C2×Dic7C2×#4112yes—
802Dic14—82no—
803Dic14—82no—
804C22×Q8—71no—
805C22×Q8—71no—
806C22×D4C22×D711yescharacteristic
807C22×D4C22×D711yescharacteristic
808C22×D4C22×D711yescharacteristic
809C23×C4—71no—
810C23×C4—71no—
811C23×C4—71no—
812C23×C4—71no—
813C23×C4—71no—
814C23×C4C22×D711yescharacteristic
815C23×C4C22×D711yescharacteristic
816#126—282no—
817C22⋊Q8—144no—
818C22⋊Q8—282no—
819C22⋊Q8—282no—
820C22⋊Q8—282no—
821C4×D4—144no—
822C4×D4—144no—
823#117—282no—
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—71no—
856C2×C4⋊C4—71no—
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
860C2×C4⋊C4C22×D711yescharacteristic
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×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
891C2×C22⋊C4C22×D711yescharacteristic
892C2×C22⋊C4C22×D711yescharacteristic
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×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—282no—
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#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
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×C7—41no—
983C22×C7—41no—
984C22×C7—41no—
985C22×C7—41no—
986C22×C7—41no—
987C22×C7—41no—
988C22×C7—41no—
989C22×C7C22×#4111yescharacteristic
990C22×C7C2×H(5,𝔽2)11yescharacteristic
991C22×C7C2×2−1+411yescharacteristic
992C22×C7#58511yescharacteristic
993C22×C7#58511yescharacteristic
994C22×C7#58511yescharacteristic
995C22×C7#58511yescharacteristic
996C4×C7—22no—
997C4×C7—41no—
998C4×C7—41no—
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—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022Dic7—41no—
1023Dic7—41no—
1024C24C23×D711yescharacteristic
1025C24C23×D711yescharacteristic
1026C24C23×D711yescharacteristic
1027C2×Q8—142no—
1028C2×Q8—142no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×Q8—281no—
1032C2×Q8—281no—
1033C2×D4—22no—
1034C2×D4—22no—
1035C2×D4—22no—
1036C2×D4—22no—
1037C2×D4—41no—
1038C2×D4—41no—
1039C2×D4—41no—
1040C2×D4—41no—
1041C2×D4—41no—
1042C22×C4—22no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—74no—
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—71no—
1064C22×C4—71no—
1065C22×C4—142no—
1066C22×C4—142no—
1067C22×C4—142no—
1068C22×C4—281no—
1069C22×C4—281no—
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×C4—281no—
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—41no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
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—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—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C4⋊C4—281no—
1125C4⋊C4—281no—
1126C4⋊C4—281no—
1127C4⋊C4—281no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—142no—
1142C22⋊C4—142no—
1143C22⋊C4—142no—
1144C22⋊C4—142no—
1145C22⋊C4—142no—
1146C22⋊C4—142no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C22⋊C4—281no—
1155C22⋊C4—281no—
1156C22⋊C4—281no—
1157C22⋊C4—281no—
1158C22⋊C4—281no—
1159C22⋊C4—281no—
1160C42—41no—
1161C42—142no—
1162C42—142no—
1163C42—142no—
1164C42—142no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C42—281no—
1171C42—281no—
1172C2×C7—42no—
1173C2×C7—42no—
1174C2×C7—81no—
1175C2×C7#345511yescharacteristic
1176C2×C7#349511yescharacteristic
1177C2×C7#350511yescharacteristic
1178C2×C7#353311yescharacteristic
1179C2×C7#354111yescharacteristic
1180C2×C7#356411yescharacteristic
1181C2×C7#356611yescharacteristic
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—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23D7×#4112yes—
1202C23#655412yes—
1203C23C24×D711yescharacteristic
1204Q8—562no—
1205Q8—562no—
1206D4—44no—
1207D4—44no—
1208D4—82no—
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—21no—
1244C2×C4—44no—
1245C2×C4—72no—
1246C2×C4—72no—
1247C2×C4—82no—
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—141no—
1287C2×C4—141no—
1288C2×C4—141no—
1289C2×C4—141no—
1290C2×C4—141no—
1291C2×C4—141no—
1292C2×C4—141no—
1293C2×C4—141no—
1294C2×C4—284no—
1295C2×C4—284no—
1296C2×C4—284no—
1297C2×C4—562no—
1298C2×C4—562no—
1299C2×C4#655312yes—
1300C7#3679011yescharacteristic, 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—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22C2×D7×#4111yescharacteristic
1323C22C2×#655311yescharacteristic
1324C22C2×#655411yescharacteristic
1325C22#9061811yescharacteristic
1326C22#9061811yescharacteristic
1327C22#9061811yescharacteristic
1328C22#9061811yescharacteristic
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—142no—
1342C4—142no—
1343C4—281no—
1344C4—281no—
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—81no—
1360C2#1174345511yescharacteristic
1361C2#1174346211yescharacteristic
1362C2#1174347611yescharacteristic
1363C2#1174386111yescharacteristic
1364C2#1174396111yescharacteristic
1365C2#1174397911yescharacteristic
1366C2#1174414611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2778C2
prime radicalC7×#392C22
hypercenter#2778D7
hypocenterC7#36790
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2778

Complements

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

NH ≅ G/Ntype
2. #11735865C2semidirect
3. #11735863C2semidirect
4. #11735701C2semidirect
5. #11735621C2semidirect
6. #11735048C2semidirect
7. #11735007C2semidirect
8. #11734497C2semidirect
9. #11734468C2semidirect
10. #11734405C2semidirect
11. #11734342C2semidirect
14. #11733199C2semidirect
15. #11733194C2semidirect
16. #11733116C2semidirect
17. #11733061C2semidirect
18. #11733032C2semidirect
19. #11732908C2semidirect
20. #11732315C2semidirect
21. #11732288C2semidirect
22. #11732278C2semidirect
23. #11732272C2semidirect
24. #11732248C2semidirect
25. #11732208C2semidirect
26. #11732108C2semidirect
27. #11732102C2semidirect
28. #11732005C2semidirect
29. #11731860C2semidirect
30. #11731445C2semidirect
31. #11731433C2semidirect
1300. C7#36790semidirect

Maximal subgroups

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

subgroupindex
C7×#27782
#117358652
#117358632
#117357012
#117356212
#117350482
#117350072
#117344972
#117344682
#117344052
#117343422
#117341782
#117341382
#117331992
#117331942
#117331162
#117330612
#117330322
#117329082
#117323152
#117322882
#117322782
#117322722
#117322482
#117322082
#117321082
#117321022
#117320052
#117318602
#117314452
#117314332
#367907