Finite Group Databasebeta

← #14217084

Subgroups — #14217084

Order 1792.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2479C211yesmaximal, characteristic
2#11740543C211yesmaximal, characteristic, complemented
3#11740520C211yesmaximal, characteristic, complemented
4#11739694C211yesmaximal, characteristic, complemented
5#11739674C211yesmaximal, characteristic, complemented
6#11735514C211yesmaximal, characteristic, complemented
7#11735490C211yesmaximal, characteristic, complemented
8#11735478C211yesmaximal, characteristic, complemented
9#11735466C211yesmaximal, characteristic, complemented
10#11735262C211yesmaximal, characteristic, complemented
11#11735237C211yesmaximal, characteristic, complemented
12#11734491C211yesmaximal, characteristic
13#11734385C211yesmaximal, characteristic
14#11733796C211yesmaximal, characteristic
15#11733777C211yesmaximal, characteristic
16#11733546C211yesmaximal, characteristic, complemented
17#11733412C211yesmaximal, characteristic, complemented
18#11733093C211yesmaximal, characteristic, complemented
19#11733053C211yesmaximal, characteristic, complemented
20#11733026C211yesmaximal, characteristic, complemented
21#11733025C211yesmaximal, characteristic, complemented
22#11733009C211yesmaximal, characteristic, complemented
23#11732896C211yesmaximal, characteristic, complemented
24#11732624C211yesmaximal, characteristic, complemented
25#11732416C211yesmaximal, characteristic, complemented
26#11732193C211yesmaximal, characteristic
27#11732125C211yesmaximal, characteristic
28#11731925C211yesmaximal, characteristic, complemented
29#11731845C211yesmaximal, characteristic, complemented
30#11731108C211yesmaximal, characteristic, complemented
31#11731101C211yesmaximal, characteristic, complemented
32C2×C7×#126C2211yescharacteristic
33C2×C7×#117C2211yescharacteristic
34C2×#6499C2211yescharacteristic
35C2×#6499C2211yescharacteristic
36C2×#6453C2211yescharacteristic
37C2×#6452C2211yescharacteristic
38C2×#6452C2211yescharacteristic
39C2×#6451C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6450C2211yescharacteristic
42C2×#6442C2211yescharacteristic
43C2×#6442C2211yescharacteristic
44C2×#6442C2211yescharacteristic
45C2×#6440C2211yescharacteristic
46C2×#6432C2211yescharacteristic
47C7×#399C2211yescharacteristic
48C7×#399C2211yescharacteristic
49C7×#398C2211yescharacteristic
50C7×#394C2211yescharacteristic
51C7×#390C2211yescharacteristic
52C7×#389C2211yescharacteristic
53C7×#388C2211yescharacteristic
54C7×#388C2211yescharacteristic
55C7×#388C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C7×#386C2211yescharacteristic
58C7×#385C2211yescharacteristic
59C4×C7×C4⋊C4C2211yescharacteristic
60#89994C2211yescharacteristic
61#89992C2211yescharacteristic
62#89984C2211yescharacteristic
63C4×C22⋊Dic7C2211yescharacteristic
64C4×C22⋊Dic7C2211yescharacteristic
65C4×C22⋊Dic7C2211yescharacteristic
66#89757C2211yescharacteristic
67#89756C2211yescharacteristic
68#89756C2211yescharacteristic
69#89756C2211yescharacteristic
70#89755C2211yescharacteristic
71#89754C2211yescharacteristic
72#89753C2211yescharacteristic
73#89753C2211yescharacteristic
74#89753C2211yescharacteristic
75#89753C2211yescharacteristic
76#89753C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89752C2211yescharacteristic
80#89751C2211yescharacteristic
81#89750C2211yescharacteristic
82#89750C2211yescharacteristic
83#89750C2211yescharacteristic
84#89750C2211yescharacteristic
85#89749C2211yescharacteristic
86#89748C2211yescharacteristic
87#89748C2211yescharacteristic
88C4⋊C4×Dic7C2211yescharacteristic
89C4⋊C4×Dic7C2211yescharacteristic
90C4⋊C4×Dic7C2211yescharacteristic
91C4⋊C4×Dic7C2211yescharacteristic
92C4⋊C4×Dic7C2211yescharacteristic
93#89746C2211yescharacteristic
94#89745C2211yescharacteristic
95#89745C2211yescharacteristic
96#89745C2211yescharacteristic
97#89744C2211yescharacteristic
98#89744C2211yescharacteristic
99#89744C2211yescharacteristic
100#89725C2211yescharacteristic
101#89724C2211yescharacteristic
102#89723C2211yescharacteristic
103#89723C2211yescharacteristic
104#89723C2211yescharacteristic
105#89723C2211yescharacteristic
106#89723C2211yescharacteristic
107#89723C2211yescharacteristic
108#89723C2211yescharacteristic
109#89723C2211yescharacteristic
110#89723C2211yescharacteristic
111#89723C2211yescharacteristic
112#89722C2211yescharacteristic
113#89721C2211yescharacteristic
114#89721C2211yescharacteristic
115#89721C2211yescharacteristic
116#89721C2211yescharacteristic
117#89720C2211yescharacteristic
118#89720C2211yescharacteristic
119#89720C2211yescharacteristic
120#89720C2211yescharacteristic
121#89720C2211yescharacteristic
122#89720C2211yescharacteristic
123#89719C2211yescharacteristic
124#89719C2211yescharacteristic
125#89717C2211yescharacteristic
126#89717C2211yescharacteristic
127#89717C2211yescharacteristic
128#89717C2211yescharacteristic
129#89716C2211yescharacteristic
130#89716C2211yescharacteristic
131#89716C2211yescharacteristic
132#89716C2211yescharacteristic
133#89716C2211yescharacteristic
134#89716C2211yescharacteristic
135#89716C2211yescharacteristic
136#89714C2211yescharacteristic
137C22⋊C4×Dic7C2211yescharacteristic
138C22⋊C4×Dic7C2211yescharacteristic
139C22⋊C4×Dic7C2211yescharacteristic
140C4×C4⋊Dic7C2211yescharacteristic
141C4×C4⋊Dic7C2211yescharacteristic
142C4×C4⋊Dic7C2211yescharacteristic
143C4×C4⋊Dic7C2211yescharacteristic
144#89705C2211yescharacteristic
145#89705C2211yescharacteristic
146#89705C2211yescharacteristic
147#89705C2211yescharacteristic
148#89704C2211yescharacteristic
149#89704C2211yescharacteristic
150C4×Dic7⋊C4C2211yescharacteristic
151C42×Dic7C2211yescharacteristic
152#89700C2211yescharacteristic
153#89700C2211yescharacteristic
154#89700C2211yescharacteristic
155#89433C2211yescharacteristic
156#89432C2211yescharacteristic
157#89429C2211yescharacteristic
158#89428C2211yescharacteristic
159#89428C2211yescharacteristic
160#89428C2211yescharacteristic
161#89427C2211yescharacteristic
162#89427C2211yescharacteristic
163#89427C2211yescharacteristic
164#89426C2211yescharacteristic
165#89426C2211yescharacteristic
166#89426C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89424C2211yescharacteristic
171#89422C2211yescharacteristic
172#89422C2211yescharacteristic
173#89421C2211yescharacteristic
174#89421C2211yescharacteristic
175#89421C2211yescharacteristic
176#89420C2211yescharacteristic
177#89420C2211yescharacteristic
178#89420C2211yescharacteristic
179#89420C2211yescharacteristic
180#89419C2211yescharacteristic
181#89418C2211yescharacteristic
182#89418C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#60042—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×Dic7C2311yescharacteristic
191C22×Dic14C2311yescharacteristic
192C22×Dic14C2311yescharacteristic
193C22×Dic14C2311yescharacteristic
194C7×#126—24no—
195C7×#117—24no—
196C2×C7×C4⋊C4C2311yescharacteristic
197C2×C7×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊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×C42×C7C2311yescharacteristic
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
236#6499—24no—
237#6499—42no—
238C2×C4⋊Dic7C2311yescharacteristic
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
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×Dic7⋊C4C2311yescharacteristic
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
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
295#6453—24no—
296#6452—24no—
297#6452—42no—
298#6451—24no—
299#6450—42no—
300#6450—42no—
301#6442—24no—
302#6442—42no—
303#6442—42no—
304#6440—24no—
305#6432—24no—
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
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356C7⋊#95C2311yescharacteristic
357C7⋊#95C2311yescharacteristic
358#2734—71no—
359#2731—71no—
360#2721—71no—
361#2721—71no—
362#2612—71no—
363#2612—71no—
364#2604—71no—
365#2604—71no—
366#2574—71no—
367#2574—71no—
368#2565—71no—
369#2545—71no—
370#2529—71no—
371#2529—71no—
372#2521—71no—
373#2521—71no—
374#2519—71no—
375#2519—71no—
376#2479—71no—
377#2479D711yescharacteristic
378#2441—71no—
379#2441—71no—
380#2373—71no—
381#2373—71no—
382#2372—71no—
383#2371—71no—
384#2371—71no—
385#2369—71no—
386C4×C4⋊Q8—71no—
387#2298—71no—
388#2298—71no—
389C24×C7C2411yescharacteristic
390C24×C7C2411yescharacteristic
391C2×C7×D4—22no—
392C2×C7×D4—41no—
393C2×C7×D4—41no—
394C22×C4×C7—22no—
395C22×C4×C7—22no—
396C22×C4×C7—41no—
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
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×Dic7—22no—
411C22×Dic7—22no—
412C22×Dic7—41no—
413C22×Dic7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C2×Dic14—22no—
430C2×Dic14—22no—
431C2×Dic14—41no—
432C2×Dic14—41no—
433C2×Dic14—41no—
434C2×Dic14—41no—
435C2×Dic14—41no—
436C2×Dic14—41no—
437C2×Dic14#4114yes—
438C7×C4⋊C4—22no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—22no—
443C7×C4⋊C4—22no—
444C7×C4⋊C4—41no—
445C7×C4⋊C4—41no—
446C7×C4⋊C4—41no—
447C7×C4⋊C4#4114yes—
448C7×C22⋊C4—22no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—22no—
451C7×C22⋊C4—22no—
452C7×C22⋊C4—22no—
453C7×C22⋊C4—22no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—41no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4—41no—
459C42×C7—22no—
460C42×C7—22no—
461C42×C7—22no—
462C42×C7—22no—
463C22⋊Dic7—22no—
464C22⋊Dic7—22no—
465C22⋊Dic7—22no—
466C22⋊Dic7—22no—
467C22⋊Dic7—22no—
468C22⋊Dic7—22no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—22no—
472C22⋊Dic7—22no—
473C22⋊Dic7—41no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7—41no—
478C4⋊Dic7—22no—
479C4⋊Dic7—22no—
480C4⋊Dic7—22no—
481C4⋊Dic7—22no—
482C4⋊Dic7—22no—
483C4⋊Dic7—22no—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—22no—
487C4⋊Dic7—22no—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—41no—
491C4⋊Dic7—41no—
492Dic7⋊C4—22no—
493Dic7⋊C4—22no—
494Dic7⋊C4—22no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—41no—
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#4114yes—
514C4×Dic7—22no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—22no—
525C4×Dic7—22no—
526C4×Dic7—22no—
527C4×Dic7—22no—
528C4×Dic7—22no—
529C4×Dic7—22no—
530C4×Dic7—41no—
531C4×Dic7—41no—
532C4×Dic7—41no—
533C4×Dic7—41no—
534C4×Dic7—41no—
535C2×C4⋊Q8—71no—
536C2×C4⋊Q8—71no—
537C2×#126—71no—
538C2×#126—71no—
539C2×#126—71no—
540C2×#126C2×D711yescharacteristic
541C2×#125—71no—
542C2×#125—71no—
543C2×#125—71no—
544C2×#124—71no—
545C2×#124—71no—
546C2×C4×Q8—71no—
547C2×C4×Q8—71no—
548C2×#117—71no—
549C2×#117C2×D711yescharacteristic
550#400—71no—
551#400—71no—
552#399—71no—
553#399—71no—
554#399—71no—
555#399—71no—
556#399C2×D711yescharacteristic
557#399C2×D711yescharacteristic
558#398—71no—
559#398—71no—
560#398—71no—
561#398—71no—
562#398—71no—
563#398—71no—
564#398—71no—
565#398C2×D711yescharacteristic
566#397—71no—
567#397—71no—
568#396—71no—
569#396—71no—
570#396—71no—
571#396—71no—
572#396—71no—
573#396—71no—
574#395—71no—
575#395—71no—
576#395—71no—
577#395—71no—
578#394—71no—
579#394C2×D711yescharacteristic
580#393—71no—
581#393—71no—
582#391—71no—
583#391—71no—
584#391—71no—
585#391—71no—
586#391—71no—
587#391—71no—
588#391—71no—
589#390C2×D711yescharacteristic
590#389—71no—
591#389—71no—
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#389C2×D711yescharacteristic
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#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#387C2×D711yescharacteristic
652#386—71no—
653#386C2×D711yescharacteristic
654#385—71no—
655#385C2×D711yescharacteristic
656#384—71no—
657#384—71no—
658#382—71no—
659#382—71no—
660#382—71no—
661#380—71no—
662#380—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C4⋊C4—71no—
668C4×C4⋊C4—71no—
669C4×C4⋊C4—71no—
670C4×C4⋊C4—71no—
671C4×C4⋊C4—71no—
672C4×C4⋊C4—71no—
673C4×C4⋊C4—71no—
674C4×C4⋊C4—71no—
675C4×C4⋊C4—71no—
676C4×C4⋊C4C2×D711yescharacteristic
677C4×C22⋊C4—71no—
678C4×C22⋊C4—71no—
679C4×C22⋊C4—71no—
680C4×C22⋊C4—71no—
681C4×C22⋊C4—71no—
682C4×C22⋊C4—71no—
683#376—71no—
684#376—71no—
685#376—71no—
686#376—71no—
687#376—71no—
688#376—71no—
689C43—71no—
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×C7C2511yescharacteristic
705C7×D4—82no—
706C2×C4×C7—21no—
707C2×C4×C7—21no—
708C2×C4×C7—21no—
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—44no—
740C2×C4×C7C2×#4112yes—
741C2×C4×C7C2×#4112yes—
742C2×C4×C7C2×#4112yes—
743C2×C4×C7C2×#4112yes—
744C2×C4×C7C2×#4112yes—
745C2×C4×C72−1+412yes—
746C2×Dic7—21no—
747C2×Dic7—21no—
748C2×Dic7—21no—
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—44no—
789C2×Dic7C2×#4112yes—
790C2×Dic7C2×#4112yes—
791C2×Dic7C2×#4112yes—
792C2×Dic7C2×#4112yes—
793C2×Dic7H(5,𝔽2)12yes—
794C2×Dic72−1+412yes—
795Dic14—44no—
796Dic14—44no—
797Dic14—82no—
798C22×Q8—71no—
799C22×Q8—71no—
800C22×Q8—71no—
801C22×D4C22×D711yescharacteristic
802C23×C4—71no—
803C23×C4C22×D711yescharacteristic
804C4⋊Q8—144no—
805C4⋊Q8—144no—
806#126—24no—
807#126—144no—
808#126—282no—
809#126—282no—
810#125—144no—
811#125—144no—
812#125—282no—
813#124—144no—
814#124—282no—
815C4×Q8—282no—
816C4×Q8—282no—
817#117—24no—
818#117—144no—
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⋊C4C22×D711yescharacteristic
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×C4⋊C4C22×D711yescharacteristic
863C2×C4⋊C4C22×D711yescharacteristic
864C2×C4⋊C4C22×D711yescharacteristic
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×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×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
907C2×C42—71no—
908C2×C42—71no—
909C2×C42—71no—
910C2×C42—71no—
911C2×C42—71no—
912C2×C42C22×D711yescharacteristic
913C2×C42C22×D711yescharacteristic
914C2×C42C22×D711yescharacteristic
915C2×C42C22×D711yescharacteristic
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#95—71no—
957#95—71no—
958#95—71no—
959#95—71no—
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—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×C7C22×#4111yescharacteristic
983C22×C7C22×#4111yescharacteristic
984C22×C7C22×#4111yescharacteristic
985C22×C7C2×H(5,𝔽2)11yescharacteristic
986C22×C7C2×2−1+411yescharacteristic
987C22×C7C2×2−1+411yescharacteristic
988C22×C7#58511yescharacteristic
989C4×C7—22no—
990C4×C7—22no—
991C4×C7—22no—
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—
1002Dic7—22no—
1003Dic7—22no—
1004Dic7—22no—
1005Dic7—22no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—41no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018C24C23×D711yescharacteristic
1019C24C23×D711yescharacteristic
1020C2×Q8—74no—
1021C2×Q8—142no—
1022C2×Q8—142no—
1023C2×Q8—281no—
1024C2×Q8—281no—
1025C2×Q8—281no—
1026C2×Q8—281no—
1027C2×Q8—281no—
1028C2×Q8—281no—
1029C2×D4—22no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—41no—
1035C22×C4—71no—
1036C22×C4—71no—
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—142no—
1052C22×C4—142no—
1053C22×C4—281no—
1054C22×C4C23×D711yescharacteristic
1055C22×C4C23×D711yescharacteristic
1056C22×C4C23×D711yescharacteristic
1057C22×C4C23×D711yescharacteristic
1058C22×C4C23×D711yescharacteristic
1059C22×C4C23×D711yescharacteristic
1060C22×C4C23×D711yescharacteristic
1061C22×C4C23×D711yescharacteristic
1062C22×C4C23×D711yescharacteristic
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—74no—
1077C4⋊C4—142no—
1078C4⋊C4—142no—
1079C4⋊C4—142no—
1080C4⋊C4—142no—
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—142no—
1092C4⋊C4—142no—
1093C4⋊C4—142no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—142no—
1097C4⋊C4—142no—
1098C4⋊C4—142no—
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#115914yes—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—22no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—142no—
1125C22⋊C4—142no—
1126C22⋊C4—142no—
1127C22⋊C4—142no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—281no—
1135C22⋊C4—281no—
1136C22⋊C4—281no—
1137C22⋊C4—281no—
1138C22⋊C4—281no—
1139C42—22no—
1140C42—22no—
1141C42—22no—
1142C42—22no—
1143C42—142no—
1144C42—142no—
1145C42—142no—
1146C42—142no—
1147C42—142no—
1148C42—142no—
1149C42—142no—
1150C42—142no—
1151C42—142no—
1152C42—142no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—281no—
1160C42—281no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C2×C7—81no—
1165C2×C7—81no—
1166C2×C7#348211yescharacteristic
1167C2×C7#348211yescharacteristic
1168C2×C7#348311yescharacteristic
1169C2×C7#349511yescharacteristic
1170C2×C7#349511yescharacteristic
1171C2×C7#350511yescharacteristic
1172C2×C7#354411yescharacteristic
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23C24×D711yescharacteristic
1188Q8—284no—
1189Q8—284no—
1190Q8—562no—
1191D4—82no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
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—44no—
1226C2×C4—72no—
1227C2×C4—72no—
1228C2×C4—72no—
1229C2×C4—72no—
1230C2×C4—72no—
1231C2×C4—72no—
1232C2×C4—141no—
1233C2×C4—141no—
1234C2×C4—141no—
1235C2×C4—141no—
1236C2×C4—141no—
1237C2×C4—141no—
1238C2×C4—141no—
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—284no—
1275C2×C4C2×#115912yes—
1276C2×C4C2×#115912yes—
1277C2×C4C2×#115912yes—
1278C2×C4D7×#4112yes—
1279C2×C4D7×#4112yes—
1280C2×C4#655412yes—
1281C7#6004211yescharacteristic, complemented, Sylow
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22C22×#115911yescharacteristic
1297C22C2×D7×#4111yescharacteristic
1298C22C2×D7×#4111yescharacteristic
1299C22C2×#655411yescharacteristic
1300C22#9061611yescharacteristic
1301C22D7×H(5,𝔽2)11yescharacteristic
1302C22D7×2−1+411yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—22no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—142no—
1317C4—142no—
1318C4—142no—
1319C4—142no—
1320C4—142no—
1321C4—142no—
1322C4—281no—
1323C4—281no—
1324C4—281no—
1325C4—281no—
1326C4—281no—
1327C4—281no—
1328C4—281no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C2—81no—
1333C2—81no—
1334C2#1174309611yescharacteristic
1335C2#1174322211yescharacteristic
1336C2#1174363211yescharacteristic
1337C2#1174374411yescharacteristic
1338C2#1174383611yescharacteristic
1339C2#1174388511yescharacteristic
1340C2#1174389911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2479C2
prime radicalC22×C7×D4C23
hypercenter#2479D7
hypocenterC7#60042
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2479

Complements

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

NH ≅ G/Ntype
2. #11740543C2semidirect
3. #11740520C2semidirect
4. #11739694C2semidirect
5. #11739674C2semidirect
6. #11735514C2semidirect
7. #11735490C2semidirect
8. #11735478C2semidirect
9. #11735466C2semidirect
10. #11735262C2semidirect
11. #11735237C2semidirect
16. #11733546C2semidirect
17. #11733412C2semidirect
18. #11733093C2semidirect
19. #11733053C2semidirect
20. #11733026C2semidirect
21. #11733025C2semidirect
22. #11733009C2semidirect
23. #11732896C2semidirect
24. #11732624C2semidirect
25. #11732416C2semidirect
28. #11731925C2semidirect
29. #11731845C2semidirect
30. #11731108C2semidirect
31. #11731101C2semidirect
1281. C7#60042semidirect

Maximal subgroups

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

subgroupindex
C7×#24792
#117405432
#117405202
#117396942
#117396742
#117355142
#117354902
#117354782
#117354662
#117352622
#117352372
#117344912
#117343852
#117337962
#117337772
#117335462
#117334122
#117330932
#117330532
#117330262
#117330252
#117330092
#117328962
#117326242
#117324162
#117321932
#117321252
#117319252
#117318452
#117311082
#117311012
#600427