Finite Group Databasebeta

← #31995272

Subgroups — #31995272

Order 18176.

1522 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986475C211yesmaximal, characteristic
2C2×#17986006C211yesmaximal, characteristic
3C2×#103×D71C211yesmaximal, characteristic
4C2×#17985956C211yesmaximal, characteristic
5#22590694C211yesmaximal, characteristic
6#22588172C211yesmaximal, characteristic, complemented
7#22588171C211yesmaximal, characteristic, complemented
8#22588169C211yesmaximal, characteristic, complemented
9C4×#14556051C211yesmaximal, characteristic, complemented
10#103×Dic71C211yesmaximal, characteristic, complemented
11C4×#14556052C211yesmaximal, characteristic, complemented
12#22588159C211yesmaximal, characteristic, complemented
13#22588058C211yesmaximal, characteristic
14#22588055C211yesmaximal, characteristic
15C71×#1763C211yesmaximal, characteristic, complemented
16C22×Q8×D71C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986475—24no—
20#17986475C418yescomplemented
21C2×Q8×Dic71C2211yescharacteristic
22C2×C4×Dic142—21no—
23C2×C4×Dic142C2211yescharacteristic
24C2×#14556093—21no—
25C2×#14556093C2211yescharacteristic
26C2×#14556086—21no—
27C2×#14556086C2211yescharacteristic
28C2×#14556086C2211yescharacteristic
29C2×#14556085—21no—
30C2×#14556085C2211yescharacteristic
31C2×C4⋊C4×D71C2211yescharacteristic
32#17986006C418yescomplemented
33C2×#14556053C2211yescharacteristic
34C2×#14556053C2211yescharacteristic
35C2×#14556052C2211yescharacteristic
36C2×#14556052C2211yescharacteristic
37C2×#14556051C2211yescharacteristic
38C2×#14556051C2211yescharacteristic
39#103×D71C418yescomplemented
40#17985956—24no—
41C2×#14556038C2211yescharacteristic
42C2×C4×C71⋊C8C2211yescharacteristic
43C2×C8×Dic71C2211yescharacteristic
44C4⋊C4×Dic71C2211yescharacteristic
45C4⋊C4×Dic71C2211yescharacteristic
46C4×Dic71⋊C4—21no—
47C4×C4⋊Dic71C2211yescharacteristic
48#17985850—21no—
49C4×(C2×D71)⋊C4—21no—
50#17985846—21no—
51#17985762C2211yescharacteristic
52#17985762C2211yescharacteristic
53#17985761C2211yescharacteristic
54#17985761C2211yescharacteristic
55#17985761C2211yescharacteristic
56#17985761C2211yescharacteristic
57C2×C4×Q8×C71C2211yescharacteristic
58C2×#103×C71C2211yescharacteristic
59C2×#103×C71C2211yescharacteristic
60C2×#97×C71C2211yescharacteristic
61C4×C4⋊C4×C71C2211yescharacteristic
62#340×C71C2211yescharacteristic
63#340×C71C2211yescharacteristic
64C22×Dic142—21no—
65C22×Dic142C2311yescharacteristic
66C2×Q8×D71—22no—
67C2×Q8×D71—22no—
68C2×Q8×D71—22no—
69C2×Q8×D71C2×C414yes—
70C2×Q8×D71C2×C414yes—
71C2×Q8×D71C2×C414yes—
72C22×C4×D71—21no—
73C22×C4×D71—21no—
74C22×C4×D71C2311yescharacteristic
75C2×#11765848—22no—
76C2×#11765848—22no—
77C2×#11765848C2×C414yes—
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C2×C8×D71—22no—
81C2×C8×D71—22no—
82C2×C8×D71C2×C414yes—
83Q8×Dic71—22no—
84Q8×Dic71C2×C414yescomplemented
85C4×Dic142—28no—
86C4×Dic142—22no—
87C4×Dic142C2×C414yescomplemented
88#14556093—28no—
89#14556093—22no—
90#14556093C2×C414yescomplemented
91#14556086—22no—
92#14556086—22no—
93#14556086—28no—
94#14556086C2×C414yes—
95#14556086C2×C414yes—
96#14556085—28no—
97#14556085C2×C414yes—
98#14556085D414yes—
99C2×C4⋊Dic71—21no—
100C2×C4⋊Dic71C2311yescharacteristic
101C2×C4⋊Dic71C2311yescharacteristic
102C2×C4⋊Dic71C2311yescharacteristic
103C2×Dic71⋊C4—21no—
104C2×Dic71⋊C4—21no—
105C2×Dic71⋊C4—21no—
106C2×Dic71⋊C4D411yescharacteristic
107C2×Dic71⋊C4D411yescharacteristic
108C4⋊C4×D71—22no—
109C4⋊C4×D71C2×C414yes—
110C2×(C2×D71)⋊C4—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×(C2×D71)⋊C4D411yescharacteristic
113C2×(C2×D71)⋊C4D411yescharacteristic
114C2×C4×Dic71—21no—
115C2×C4×Dic71—21no—
116C2×C4×Dic71—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119C2×C4×Dic71—21no—
120C2×C4×Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71C2311yescharacteristic
123#14556053C2×C414yes—
124#14556053C2×C414yescomplemented
125#14556052C2×C414yes—
126#14556052C2×C414yescomplemented
127#14556051C2×C414yes—
128#14556051C2×C414yescomplemented
129#14556038—22no—
130C4×C71⋊C8—22no—
131C8×Dic71—22no—
132C71⋊#95—21no—
133C71⋊#95—21no—
134C71⋊#95—21no—
135C22×Q8×C71C2311yescharacteristic
136C22×C8×C71C2311yescharacteristic
137C22×C8×C71C2311yescharacteristic
138C4×Q8×C71—22no—
139C4×Q8×C71C2×C414yescomplemented
140C2×C4⋊C4×C71—21no—
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2311yescharacteristic
143C2×C4⋊C4×C71C2311yescharacteristic
144C2×C42×C71—21no—
145C2×C42×C71—21no—
146C2×C42×C71C2311yescharacteristic
147#103×C71C2×C414yes—
148#103×C71C2×C414yescomplemented
149#97×C71—22no—
150#95×C71—21no—
151C23×D71C2×D411yescharacteristic
152C2×Dic142—21no—
153C2×Dic142—21no—
154C2×Dic142—21no—
155C2×Dic142—24no—
156C2×Dic142—24no—
157C2×Dic142—24no—
158C2×Dic142C22×C412yes—
159C2×Dic142C22×C412yes—
160C2×Dic142C22×C412yes—
161Q8×D71—28no—
162Q8×D71—28no—
163Q8×D71—28no—
164Q8×D71C42116yescomplemented
165C22×Dic71—21no—
166C22×Dic71—21no—
167C22×Dic71—21no—
168C22×Dic71—21no—
169C22×Dic71C2×D411yescharacteristic
170C22×Dic71C2×D411yescharacteristic
171C22×Dic71C2×D411yescharacteristic
172C2×C4×D71—24no—
173C2×C4×D71—24no—
174C2×C4×D71—24no—
175C2×C4×D71—24no—
176C2×C4×D71—81no—
177C2×C4×D71—81no—
178C2×C4×D71C22×C412yes—
179C2×C4×D71C22×C412yes—
180C2×C4×D71C22×C412yes—
181C2×C4×D71C2×D412yes—
182C2×C4×D71#4112yes—
183C2×C4×D71#4112yes—
184#11765848—28no—
185C2×C71⋊C8—21no—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8C22×C412yes—
190C2×C71⋊C8C22×C412yes—
191C8×D71—28no—
192C4⋊Dic71—21no—
193C4⋊Dic71—21no—
194C4⋊Dic71—21no—
195C4⋊Dic71—24no—
196C4⋊Dic71C22×C412yes—
197C4⋊Dic71C22×C412yes—
198C4⋊Dic71C22×C412yes—
199Dic71⋊C4—24no—
200Dic71⋊C4—24no—
201Dic71⋊C4—24no—
202Dic71⋊C4C22⋊C414yes—
203Dic71⋊C4C22⋊C414yes—
204(C2×D71)⋊C4—24no—
205(C2×D71)⋊C4—24no—
206(C2×D71)⋊C4C22⋊C414yes—
207(C2×D71)⋊C4C22⋊C414yes—
208C4×Dic71—24no—
209C4×Dic71—24no—
210C4×Dic71—24no—
211C4×Dic71—24no—
212C4×Dic71—24no—
213C4×Dic71—81no—
214C4×Dic71—81no—
215C4×Dic71—81no—
216C4×Dic71C22×C412yes—
217C4×Dic71C2×D412yes—
218C2×Q8×C71—21no—
219C2×Q8×C71—21no—
220C2×Q8×C71—21no—
221C2×Q8×C71C22×C412yes—
222C2×Q8×C71C22×C412yes—
223C2×Q8×C71C22×C412yes—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2411yescharacteristic
231C2×C8×C71—21no—
232C2×C8×C71—21no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71C22×C412yes—
236C2×C8×C71C22×C412yes—
237C4⋊C4×C71—24no—
238C4⋊C4×C71—21no—
239C4⋊C4×C71—21no—
240C4⋊C4×C71—21no—
241C4⋊C4×C71C22×C412yes—
242C4⋊C4×C71C22×C412yes—
243C4⋊C4×C71C22×C412yes—
244C42×C71—24no—
245C42×C71—81no—
246C42×C71C22×C412yes—
247C42×C71C2×D412yes—
248C23×C71C22×D411yescharacteristic
249C22×D71—21no—
250C22×D71—21no—
251C22×D71—21no—
252C22×D71—21no—
253C22×D71C2×C22⋊C412yes—
254C22×D71C4×D412yes—
255C22×D71C4×D412yes—
256Q8×C71—22no—
257Q8×C71—22no—
258Q8×C71—22no—
259Q8×C71C2×C4214yes—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71C2×C22⋊C412yes—
277C2×C4×C71C2×C22⋊C412yes—
278C2×C4×C71C23×C411yescharacteristic
279C2×C4×C71C23×C411yescharacteristic
280C2×C4×C71C23×C411yescharacteristic
281C2×C4×C71C22×D411yescharacteristic
282C2×C4×C71C2×#4111yescharacteristic
283C2×C4×C71C2×#4111yescharacteristic
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—21no—
288C2×Dic71—21no—
289C2×Dic71—21no—
290C2×Dic71—21no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71C2×C22⋊C412yes—
301C2×Dic71C2×C22⋊C412yes—
302C2×Dic71C2×C22⋊C412yes—
303C2×Dic71C4×D412yes—
304C2×Dic71C4×D412yes—
305C4×D71—216no—
306C4×D71—84no—
307C4×D71C2×C4214yes—
308C4×D71#11714yes—
309C4×D71C4×D414yes—
310C4×D71C4×D414yes—
311Dic142—22no—
312Dic142—22no—
313Dic142—22no—
314Dic142—216no—
315Dic142C2×C4214yes—
316C8×C71—22no—
317C8×C71—22no—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C22×C71C22×C22⋊C411yescharacteristic
321C22×C71C2×C4×D411yescharacteristic
322C22×C71C2×C4×D411yescharacteristic
323C22×C71#57711yescharacteristic
324C22×C71#57711yescharacteristic
325C22×C71#57811yescharacteristic
326C22×C71#57811yescharacteristic
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71C4×C22⋊C414yes—
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—24no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71C22×C4211yescharacteristic
341C4×C71C2×#11711yescharacteristic
342C4×C71C2×C4×D411yescharacteristic
343C4×C71C2×C4×D411yescharacteristic
344Dic71—22no—
345Dic71—22no—
346Dic71—24no—
347Dic71—42no—
348Dic71—42no—
349Dic71—42no—
350Dic71C4×C22⋊C414yes—
351#20417—711nomaximal, Sylow
352C2×C71C2×C4×C22⋊C411yescharacteristic
353C2×C71#289811yescharacteristic
354C2×C71#289811yescharacteristic
355C2×C71#294711yescharacteristic
356C2×C71#294711yescharacteristic
357C2×C71#294911yescharacteristic
358C2×C71#295011yescharacteristic
359D71—24no—
360C2×#519—711no—
361C2×#419—711no—
362C22×#103—711no—
363C2×#405—711no—
364#2274—711no—
365#1763—711no—
366#1763—711no—
367#1763—711no—
368#1763D7111yescharacteristic, complemented
369C4×#103—711no—
370C4×#103—711no—
371C4×#103—711no—
372C4×#103—711no—
373#1736—711no—
374#1735—711no—
375C71#2041711yescharacteristic, complemented, Sylow
376C23×Q8—711no—
377C22×M16—711no—
378C23×C8—711no—
379#519—718no—
380#519—1424no—
381C2×C4×Q8—711no—
382C2×C4×Q8—711no—
383C2×C4×Q8—711no—
384C2×C4×Q8—1421no—
385C2×C4×Q8—1421no—
386C2×C4×Q8C2×D7111yescharacteristic
387C2×#117—711no—
388C2×#117—711no—
389C2×#117—711no—
390C2×#117—1421no—
391C2×#117—1421no—
392C22×C4⋊C4—711no—
393#419—718no—
394C2×#103—711no—
395C2×#103—711no—
396C2×#103—711no—
397C2×#103—711no—
398C2×#103—711no—
399C2×#103—711no—
400C2×#103—718no—
401C2×#103C2×D7111yescharacteristic
402C2×#103C2×D7111yescharacteristic
403#405—1424no—
404C2×#97—711no—
405C2×#97C2×D7111yescharacteristic
406C2×C4×C8—711no—
407C2×C4×C8—711no—
408C4×C4⋊C4—711no—
409C4×C4⋊C4—711no—
410C4×C4⋊C4—711no—
411C4×C4⋊C4—1421no—
412C4×C4⋊C4—1421no—
413C4×C4⋊C4C2×D7111yescharacteristic
414C4×C22⋊C4—1421no—
415C4×C22⋊C4—1421no—
416#340—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420#340—711no—
421#340—711no—
422#340C2×D7111yescharacteristic
423#340C2×D7111yescharacteristic
424C22×Q8—714no—
425C22×Q8—714no—
426C22×Q8—714no—
427C22×Q8—711no—
428C22×Q8—1421no—
429C22×Q8—1422no—
430C22×Q8—1422no—
431C22×Q8—1422no—
432C22×Q8C22×D7111yescharacteristic
433C23×C4—711no—
434C23×C4—1421no—
435C23×C4—1421no—
436C2×M16—714no—
437C2×M16—1422no—
438C2×M16—1422no—
439C22×C8—711no—
440C22×C8—711no—
441C22×C8—714no—
442C22×C8—1422no—
443C22×C8—1422no—
444C22×C8C22×D7111yescharacteristic
445C22×C8C22×D7111yescharacteristic
446C4×Q8—22no—
447C4×Q8—714no—
448C4×Q8—714no—
449C4×Q8—714no—
450C4×Q8—1428no—
451C4×Q8—1422no—
452C4×Q8—1422no—
453C4×Q8—1428no—
454C4×Q8—1422no—
455C4×Q8C4×D7114yescomplemented
456#117—714no—
457#117—714no—
458#117—714no—
459#117—714no—
460#117—1428no—
461#117—1428no—
462#117—1422no—
463#117—1422no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—711no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—1422no—
472C2×C4⋊C4—1421no—
473C2×C4⋊C4—1421no—
474C2×C4⋊C4—1421no—
475C2×C4⋊C4—1421no—
476C2×C4⋊C4C22×D7111yescharacteristic
477C2×C4⋊C4C22×D7111yescharacteristic
478C2×C4⋊C4C22×D7111yescharacteristic
479C2×C22⋊C4—711no—
480C2×C22⋊C4—711no—
481C2×C22⋊C4—1421no—
482C2×C22⋊C4—1421no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—711no—
486C2×C42—1421no—
487C2×C42—1421no—
488C2×C42—1421no—
489C2×C42—1421no—
490C2×C42—1421no—
491C2×C42—1421no—
492C2×C42—1421no—
493C2×C42—1421no—
494C2×C42C22×D7111yescharacteristic
495#103—714no—
496#103—714no—
497#103—714no—
498#103—714no—
499#103—714no—
500#103—714no—
501#103C4×D7114yes—
502#103C4×D7114yescomplemented
503#97—22no—
504#97—1422no—
505C4×C8—1422no—
506C4×C8—1422no—
507#95—21no—
508#95—1421no—
509#95—1421no—
510#95—1421no—
511C24—711no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—7116no—
516C2×Q8—712no—
517C2×Q8—712no—
518C2×Q8—712no—
519C2×Q8—1424no—
520C2×Q8—1424no—
521C2×Q8—1424no—
522C2×Q8—1428no—
523C2×Q8—1428no—
524C2×Q8—1428no—
525C2×Q8—1421no—
526C2×Q8—1421no—
527C2×Q8—1421no—
528C2×Q8C2×C4×D7112yes—
529C2×Q8C2×C4×D7112yes—
530C2×Q8C2×C4×D7112yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—5681no—
536C22×C4—5681no—
537C22×C4—711no—
538C22×C4—712no—
539C22×C4—712no—
540C22×C4—712no—
541C22×C4—712no—
542C22×C4—712no—
543C22×C4—712no—
544C22×C4—711no—
545C22×C4—711no—
546C22×C4—1424no—
547C22×C4—1424no—
548C22×C4—1424no—
549C22×C4—1424no—
550C22×C4—1421no—
551C22×C4—1421no—
552C22×C4—1421no—
553C22×C4—1421no—
554C22×C4D4×D7111yescharacteristic
555C22×C4D4×D7111yescharacteristic
556C22×C4C23×D7111yescharacteristic
557M16—1428no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—712no—
563C2×C8—712no—
564C2×C8—1428no—
565C2×C8—1421no—
566C2×C8—1421no—
567C2×C8—1421no—
568C2×C8—1421no—
569C2×C8C2×C4×D7112yes—
570C2×C8C2×C4×D7112yes—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—24no—
575C4⋊C4—714no—
576C4⋊C4—714no—
577C4⋊C4—712no—
578C4⋊C4—712no—
579C4⋊C4—712no—
580C4⋊C4—1424no—
581C4⋊C4—1424no—
582C4⋊C4—1424no—
583C4⋊C4—1421no—
584C4⋊C4—1421no—
585C4⋊C4—1421no—
586C4⋊C4—1424no—
587C4⋊C4C2×C4×D7112yes—
588C4⋊C4C2×C4×D7112yes—
589C4⋊C4C2×C4×D7112yes—
590C22⋊C4—714no—
591C22⋊C4—714no—
592C22⋊C4—1424no—
593C22⋊C4—1424no—
594C42—24no—
595C42—81no—
596C42—5681no—
597C42—5681no—
598C42—5681no—
599C42—712no—
600C42—712no—
601C42—1424no—
602C42—1424no—
603C42—1424no—
604C42—1424no—
605C42—1424no—
606C42C2×C4×D7112yes—
607C42D4×D7112yes—
608C23—712no—
609C23—712no—
610C23—712no—
611C23—1421no—
612C23—1421no—
613C23—1421no—
614C23—1421no—
615C23C2×D4×D7111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—714no—
620Q8—14216no—
621Q8—1422no—
622Q8—1422no—
623Q8—1422no—
624Q8C42×D7114yes—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—5684no—
648C2×C4—712no—
649C2×C4—712no—
650C2×C4—712no—
651C2×C4—714no—
652C2×C4—714no—
653C2×C4—714no—
654C2×C4—714no—
655C2×C4—712no—
656C2×C4—712no—
657C2×C4—14216no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1421no—
665C2×C4—1421no—
666C2×C4—1421no—
667C2×C4—1421no—
668C2×C4C22⋊C4×D7112yes—
669C2×C4C22⋊C4×D7112yes—
670C2×C4C22×C4×D7111yescharacteristic
671C2×C4C22×C4×D7111yescharacteristic
672C2×C4C22×C4×D7111yescharacteristic
673C2×C4C2×D4×D7111yescharacteristic
674C2×C4#41×D7111yescharacteristic
675C2×C4#41×D7111yescharacteristic
676C8—22no—
677C8—22no—
678C8—1422no—
679C8—1422no—
680C22—714no—
681C22—1422no—
682C22—1422no—
683C22—1422no—
684C22—1422no—
685C22—1422no—
686C22—1422no—
687C22C2×C22⋊C4×D7111yescharacteristic
688C22C4×D4×D7111yescharacteristic
689C22C4×D4×D7111yescharacteristic
690C22#1798680811yescharacteristic
691C22#1798680911yescharacteristic
692C22#1798681511yescharacteristic
693C22#1798681511yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—2842no—
701C4—2842no—
702C4—2842no—
703C4—714no—
704C4—1422no—
705C4—1422no—
706C4—1424no—
707C4C2×C42×D7111yescharacteristic
708C4#117×D7111yescharacteristic
709C4C4×D4×D7111yescharacteristic
710C4C4×D4×D7111yescharacteristic
711C2—1424no—
712C2C4×C22⋊C4×D7111yescharacteristic
713C2#2259687111yescharacteristic
714C2#2259687211yescharacteristic
715C2#2259718011yescharacteristic
716C2#2259718211yescharacteristic
717C2#2259719611yescharacteristic
718C2#2259720511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC71×#1763C2
socleC23×C71C22×D4
prime radicalC23×D71C2×D4
cosocleC22×C4×C71C24
hypercenter#1763D71
hypocenterC71#20417
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
6. #22588172C2semidirect
7. #22588171C2semidirect
8. #22588169C2semidirect
9. C4×#14556051C2semidirect
10. #103×Dic71C2semidirect
11. C4×#14556052C2semidirect
12. #22588159C2semidirect
15. C71×#1763C2semidirect
20. #17986475C4semidirect
32. #17986006C4semidirect
39. #103×D71C4semidirect
84. Q8×Dic71C2×C4semidirect
87. C4×Dic142C2×C4semidirect
90. #14556093C2×C4semidirect
124. #14556053C2×C4semidirect
126. #14556052C2×C4semidirect
128. #14556051C2×C4semidirect
139. C4×Q8×C71C2×C4semidirect
148. #103×C71C2×C4semidirect
164. Q8×D71C42semidirect
368. #1763D71semidirect
375. C71#20417semidirect
455. C4×Q8C4×D71semidirect
502. #103C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864752
C2×#179860062
C2×#103×D712
C2×#179859562
#225906942
#225881722
#225881712
#225881692
C4×#145560512
#103×Dic712
C4×#145560522
#225881592
#225880582
#225880552
C71×#17632
#2041771