Finite Group Databasebeta

← #31995255

Subgroups — #31995255

Order 18176.

1598 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986481C211yesmaximal, characteristic
2C2×#17985999C211yesmaximal, characteristic
3C2×#17985994C211yesmaximal, characteristic
4C2×#17985956C211yesmaximal, characteristic, complemented
5#22590694C211yesmaximal, characteristic, complemented
6#22588172C211yesmaximal, characteristic, complemented
7#22588166C211yesmaximal, characteristic, complemented
8#22588164C211yesmaximal, characteristic, complemented
9#103×Dic71C211yesmaximal, characteristic, complemented
10C4×#14556052C211yesmaximal, characteristic, complemented
11C4×#14556048C211yesmaximal, characteristic, complemented
12#22588154C211yesmaximal, characteristic, complemented
13#22588058C211yesmaximal, characteristic, complemented
14#340×D71C211yesmaximal, characteristic, complemented
15C71×#1763C211yesmaximal, characteristic, complemented
16C22×#11765866C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986481—24no—
20#17986481C418yescomplemented
21C2×Q8×Dic71C2211yescharacteristic
22C2×C4×D284—21no—
23C2×C4×D284C2211yescharacteristic
24C2×#14556090—21no—
25C2×#14556090C2211yescharacteristic
26C2×#14556086C2211yescharacteristic
27C2×#14556085—21no—
28C2×#14556085C2211yescharacteristic
29C2×C4⋊C4×D71—21no—
30C2×C4⋊C4×D71C2211yescharacteristic
31C2×C4⋊C4×D71C2211yescharacteristic
32#17985999C418yescomplemented
33#17985994C418yescomplemented
34C2×#14556052C2211yescharacteristic
35C2×#14556052C2211yescharacteristic
36C2×#14556050C2211yescharacteristic
37C2×#14556050C2211yescharacteristic
38C2×#14556048C2211yescharacteristic
39C2×#14556048C2211yescharacteristic
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
64C2×#11765866—22no—
65C2×#11765866—22no—
66C2×#11765866—22no—
67C2×#11765866C2×C414yes—
68C2×#11765866C2×C414yes—
69C2×#11765866C2×C414yes—
70C22×D284—21no—
71C22×D284C2311yescharacteristic
72C22×C4×D71—21no—
73C22×C4×D71—21no—
74C22×C4×D71—21no—
75C22×C4×D71—21no—
76C22×C4×D71—21no—
77C22×C4×D71C2311yescharacteristic
78C2×#11765848—22no—
79C2×#11765848—22no—
80C2×#11765848C2×C414yescomplemented
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C2×C8×D71—22no—
84C2×C8×D71—22no—
85C2×C8×D71C2×C414yescomplemented
86Q8×Dic71—22no—
87Q8×Dic71C2×C414yescomplemented
88C4×D284—28no—
89C4×D284—22no—
90C4×D284C2×C414yescomplemented
91#14556090—28no—
92#14556090—22no—
93#14556090C2×C414yescomplemented
94#14556086—22no—
95#14556086C2×C414yescomplemented
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⋊C4D411yescharacteristic
106C2×Dic71⋊C4D411yescharacteristic
107C4⋊C4×D71—22no—
108C4⋊C4×D71—22no—
109C4⋊C4×D71—28no—
110C4⋊C4×D71C2×C414yes—
111C4⋊C4×D71C2×C414yescomplemented
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4D411yescharacteristic
116C2×(C2×D71)⋊C4D411yescharacteristic
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119C2×C4×Dic71—21no—
120C2×C4×Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71C2311yescharacteristic
123#14556052C2×C414yescomplemented
124#14556052C2×C414yescomplemented
125#14556050C2×C414yescomplemented
126#14556050C2×C414yescomplemented
127#14556048C2×C414yescomplemented
128#14556048C2×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×C414yescomplemented
148#103×C71C2×C414yescomplemented
149#97×C71—22no—
150#95×C71—21no—
151C23×D71—21no—
152C23×D71C2×D411yescharacteristic
153#11765866—28no—
154#11765866—28no—
155#11765866—28no—
156#11765866C42116yescomplemented
157C2×D284—24no—
158C2×D284—24no—
159C2×D284—24no—
160C2×D284—21no—
161C2×D284—21no—
162C2×D284—21no—
163C2×D284C22×C412yes—
164C2×D284C22×C412yes—
165C2×D284C22×C412yes—
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—24no—
177C2×C4×D71—24no—
178C2×C4×D71—24no—
179C2×C4×D71—81no—
180C2×C4×D71—81no—
181C2×C4×D71—81no—
182C2×C4×D71—81no—
183C2×C4×D71—81no—
184C2×C4×D71—81no—
185C2×C4×D71—81no—
186C2×C4×D71—81no—
187C2×C4×D71C22×C412yes—
188C2×C4×D71C22×C412yes—
189C2×C4×D71C22×C412yes—
190C2×C4×D71C2×D412yes—
191C2×C4×D71#4112yes—
192C2×C4×D71#4112yes—
193#11765848—28no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—21no—
197C2×C71⋊C8—21no—
198C2×C71⋊C8C22×C412yes—
199C2×C71⋊C8C22×C412yes—
200C8×D71—28no—
201C4⋊Dic71—21no—
202C4⋊Dic71—21no—
203C4⋊Dic71—21no—
204C4⋊Dic71—24no—
205C4⋊Dic71C22×C412yes—
206C4⋊Dic71C22×C412yes—
207C4⋊Dic71C22×C412yes—
208Dic71⋊C4—24no—
209Dic71⋊C4—24no—
210Dic71⋊C4C22⋊C414yes—
211Dic71⋊C4C22⋊C414yes—
212(C2×D71)⋊C4—24no—
213(C2×D71)⋊C4—24no—
214(C2×D71)⋊C4—24no—
215(C2×D71)⋊C4C22⋊C414yes—
216(C2×D71)⋊C4C22⋊C414yes—
217C4×Dic71—24no—
218C4×Dic71—24no—
219C4×Dic71—81no—
220C4×Dic71—81no—
221C4×Dic71—81no—
222C4×Dic71C22×C412yes—
223C4×Dic71C2×D412yes—
224C2×Q8×C71—21no—
225C2×Q8×C71—21no—
226C2×Q8×C71—21no—
227C2×Q8×C71C22×C412yes—
228C2×Q8×C71C22×C412yes—
229C2×Q8×C71C22×C412yes—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2411yescharacteristic
237C2×C8×C71—21no—
238C2×C8×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71C22×C412yes—
242C2×C8×C71C22×C412yes—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—21no—
247C4⋊C4×C71C22×C412yes—
248C4⋊C4×C71C22×C412yes—
249C4⋊C4×C71C22×C412yes—
250C42×C71—24no—
251C42×C71—81no—
252C42×C71C22×C412yes—
253C42×C71C2×D412yes—
254C23×C71C22×D411yescharacteristic
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—41no—
263C22×D71—41no—
264C22×D71—41no—
265C22×D71—41no—
266C22×D71C2×C22⋊C412yes—
267C22×D71C4×D412yes—
268C22×D71C4×D412yes—
269Q8×C71—22no—
270Q8×C71—22no—
271Q8×C71—22no—
272Q8×C71C2×C4214yes—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—21no—
277C2×C4×C71—21no—
278C2×C4×C71—21no—
279C2×C4×C71—21no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—41no—
288C2×C4×C71—41no—
289C2×C4×C71C2×C22⋊C412yes—
290C2×C4×C71C2×C22⋊C412yes—
291C2×C4×C71C23×C411yescharacteristic
292C2×C4×C71C23×C411yescharacteristic
293C2×C4×C71C23×C411yescharacteristic
294C2×C4×C71C22×D411yescharacteristic
295C2×C4×C71C2×#4111yescharacteristic
296C2×C4×C71C2×#4111yescharacteristic
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—41no—
305C2×Dic71—41no—
306C2×Dic71—41no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—41no—
310C2×Dic71C2×C22⋊C412yes—
311C2×Dic71C2×C22⋊C412yes—
312C2×Dic71C2×C22⋊C412yes—
313C2×Dic71C4×D412yes—
314C2×Dic71C4×D412yes—
315D284—216no—
316D284—22no—
317D284—22no—
318D284—22no—
319D284C2×C4214yes—
320C4×D71—216no—
321C4×D71—84no—
322C4×D71—84no—
323C4×D71—84no—
324C4×D71—84no—
325C4×D71C2×C4214yes—
326C4×D71#11714yes—
327C4×D71C4×D414yes—
328C4×D71C4×D414yes—
329C8×C71—22no—
330C8×C71—22no—
331C71⋊C8—22no—
332C71⋊C8—22no—
333C22×C71C22×C22⋊C411yescharacteristic
334C22×C71C2×C4×D411yescharacteristic
335C22×C71C2×C4×D411yescharacteristic
336C22×C71#57611yescharacteristic
337C22×C71#57711yescharacteristic
338C22×C71#57711yescharacteristic
339C22×C71#57811yescharacteristic
340C2×D71—22no—
341C2×D71—22no—
342C2×D71—22no—
343C2×D71—22no—
344C2×D71—22no—
345C2×D71—22no—
346C2×D71—24no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—42no—
350C2×D71—42no—
351C2×D71—42no—
352C2×D71—42no—
353C2×D71C4×C22⋊C414yes—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—24no—
357C4×C71—42no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71C22×C4211yescharacteristic
361C4×C71C2×#11711yescharacteristic
362C4×C71C2×C4×D411yescharacteristic
363C4×C71C2×C4×D411yescharacteristic
364Dic71—22no—
365Dic71—22no—
366Dic71—42no—
367Dic71—42no—
368Dic71—42no—
369Dic71C4×C22⋊C414yes—
370#20415—711nomaximal, Sylow
371C2×C71C2×C4×C22⋊C411yescharacteristic
372C2×C71#289711yescharacteristic
373C2×C71#289811yescharacteristic
374C2×C71#294611yescharacteristic
375C2×C71#294711yescharacteristic
376C2×C71#295111yescharacteristic
377C2×C71#295211yescharacteristic
378D71—24no—
379D71—44no—
380C2×#520—711no—
381C2×#417—711no—
382C2×#416—711no—
383C2×#405—711no—
384#2274—711no—
385#1763—711no—
386#1763D7111yescharacteristic, complemented
387#1762—711no—
388#1762—711no—
389C4×#103—711no—
390C4×#103—711no—
391C4×#102—711no—
392C4×#102—711no—
393#1736—711no—
394C2×#340—711no—
395C71#2041511yescharacteristic, complemented, Sylow
396C22×#41—711no—
397C22×M16—711no—
398C23×C8—711no—
399#520—718no—
400#520—1424no—
401C2×C4×Q8—711no—
402C2×C4×Q8C2×D7111yescharacteristic
403C2×C4×D4—711no—
404C2×C4×D4—711no—
405C2×C4×D4—1421no—
406C2×C4×D4—1421no—
407C2×#117—711no—
408C2×#117—711no—
409C2×#117—1421no—
410C22×C4⋊C4—711no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—1421no—
413#417—718no—
414#416—718no—
415C2×#103—711no—
416C2×#103—711no—
417C2×#103C2×D7111yescharacteristic
418C2×#103C2×D7111yescharacteristic
419C2×#102—711no—
420C2×#102—711no—
421C2×#102—711no—
422C2×#102—711no—
423#405—1424no—
424C2×#97—711no—
425C2×#97C2×D7111yescharacteristic
426C2×C4×C8—711no—
427C2×C4×C8—711no—
428C4×C4⋊C4—711no—
429C4×C4⋊C4—711no—
430C4×C4⋊C4—711no—
431C4×C4⋊C4—1421no—
432C4×C4⋊C4—1421no—
433C4×C4⋊C4C2×D7111yescharacteristic
434C4×C22⋊C4—1421no—
435C4×C22⋊C4—1421no—
436#340—711no—
437#340—711no—
438#340—711no—
439#340—711no—
440#340—711no—
441#340—711no—
442#340C2×D7111yescharacteristic
443#340C2×D7111yescharacteristic
444C2×#41—714no—
445C2×#41—714no—
446C2×#41—714no—
447C2×#41—1422no—
448C2×#41—1422no—
449C2×#41—1422no—
450C22×Q8C22×D7111yescharacteristic
451C22×D4—711no—
452C22×D4—1421no—
453C23×C4—711no—
454C23×C4—1421no—
455C23×C4—1421no—
456C23×C4—1421no—
457C23×C4—1421no—
458C23×C4—1421no—
459C2×M16—714no—
460C2×M16—1422no—
461C2×M16—1422no—
462C22×C8—711no—
463C22×C8—711no—
464C22×C8—714no—
465C22×C8—1422no—
466C22×C8—1422no—
467C22×C8C22×D7111yescharacteristic
468C22×C8C22×D7111yescharacteristic
469C4×Q8—22no—
470C4×Q8—714no—
471C4×Q8—1422no—
472C4×Q8C4×D7114yescomplemented
473C4×D4—714no—
474C4×D4—714no—
475C4×D4—1428no—
476C4×D4—1422no—
477C4×D4—1428no—
478C4×D4—1422no—
479#117—714no—
480#117—714no—
481#117—714no—
482#117—1428no—
483#117—1422no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—714no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—1428no—
493C2×C4⋊C4—1422no—
494C2×C4⋊C4—1422no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—711no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4—1421no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—711no—
509C2×C42—1421no—
510C2×C42—1421no—
511C2×C42—1421no—
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42C22×D7111yescharacteristic
515#103—714no—
516#103—714no—
517#103C4×D7114yescomplemented
518#103C4×D7114yescomplemented
519#102—714no—
520#102—714no—
521#102—714no—
522#102—714no—
523#97—22no—
524#97—1422no—
525C4×C8—1422no—
526C4×C8—1422no—
527#95—21no—
528#95—1421no—
529#95—1421no—
530#95—1421no—
531C24—711no—
532C24—1421no—
533#41—7116no—
534#41—1428no—
535#41—1428no—
536#41—1428no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D7112yes—
541C2×Q8C2×C4×D7112yes—
542C2×Q8C2×C4×D7112yes—
543C2×D4—712no—
544C2×D4—712no—
545C2×D4—712no—
546C2×D4—1424no—
547C2×D4—1424no—
548C2×D4—1424no—
549C2×D4—1421no—
550C2×D4—1421no—
551C2×D4—1421no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—5681no—
557C22×C4—5681no—
558C22×C4—5681no—
559C22×C4—5681no—
560C22×C4—5681no—
561C22×C4—5681no—
562C22×C4—5681no—
563C22×C4—5681no—
564C22×C4—711no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—711no—
572C22×C4—711no—
573C22×C4—1424no—
574C22×C4—1424no—
575C22×C4—1424no—
576C22×C4—1424no—
577C22×C4—1424no—
578C22×C4—1424no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1421no—
582C22×C4—1424no—
583C22×C4D4×D7111yescharacteristic
584C22×C4D4×D7111yescharacteristic
585C22×C4C23×D7111yescharacteristic
586M16—1428no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—712no—
592C2×C8—712no—
593C2×C8—1428no—
594C2×C8—1421no—
595C2×C8—1421no—
596C2×C8—1421no—
597C2×C8—1421no—
598C2×C8C2×C4×D7112yes—
599C2×C8C2×C4×D7112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—714no—
605C4⋊C4—714no—
606C4⋊C4—712no—
607C4⋊C4—712no—
608C4⋊C4—712no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1421no—
613C4⋊C4—1421no—
614C4⋊C4—1421no—
615C4⋊C4C2×C4×D7112yes—
616C4⋊C4C2×C4×D7112yes—
617C4⋊C4C2×C4×D7112yes—
618C22⋊C4—714no—
619C22⋊C4—714no—
620C22⋊C4—1424no—
621C22⋊C4—1424no—
622C22⋊C4—1424no—
623C42—24no—
624C42—81no—
625C42—5681no—
626C42—5681no—
627C42—5681no—
628C42—712no—
629C42—712no—
630C42—1424no—
631C42—1424no—
632C42C2×C4×D7112yes—
633C42D4×D7112yes—
634C23—2841no—
635C23—2841no—
636C23—2841no—
637C23—2841no—
638C23—712no—
639C23—712no—
640C23—712no—
641C23—1422no—
642C23—1422no—
643C23—1422no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23C2×D4×D7111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C42×D7114yes—
653D4—714no—
654D4—14216no—
655D4—1422no—
656D4—1422no—
657D4—1422no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
678C2×C4—2841no—
679C2×C4—2841no—
680C2×C4—5684no—
681C2×C4—5684no—
682C2×C4—5684no—
683C2×C4—5684no—
684C2×C4—712no—
685C2×C4—712no—
686C2×C4—712no—
687C2×C4—714no—
688C2×C4—714no—
689C2×C4—714no—
690C2×C4—714no—
691C2×C4—712no—
692C2×C4—712no—
693C2×C4—14216no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1421no—
698C2×C4—1421no—
699C2×C4—1421no—
700C2×C4—1421no—
701C2×C4C22⋊C4×D7112yes—
702C2×C4C22⋊C4×D7112yes—
703C2×C4C22×C4×D7111yescharacteristic
704C2×C4C22×C4×D7111yescharacteristic
705C2×C4C22×C4×D7111yescharacteristic
706C2×C4C2×D4×D7111yescharacteristic
707C2×C4#41×D7111yescharacteristic
708C2×C4#41×D7111yescharacteristic
709C8—22no—
710C8—22no—
711C8—1422no—
712C8—1422no—
713C22—2842no—
714C22—2842no—
715C22—2842no—
716C22—2842no—
717C22—2842no—
718C22—2842no—
719C22—714no—
720C22—1424no—
721C22—1422no—
722C22—1422no—
723C22—1422no—
724C22—1422no—
725C22—1422no—
726C22—1422no—
727C22C2×C22⋊C4×D7111yescharacteristic
728C22C4×D4×D7111yescharacteristic
729C22C4×D4×D7111yescharacteristic
730C22#1798680311yescharacteristic
731C22#1798680811yescharacteristic
732C22#1798680811yescharacteristic
733C22#1798681511yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—2842no—
741C4—2842no—
742C4—2842no—
743C4—714no—
744C4—1422no—
745C4—1422no—
746C4C2×C42×D7111yescharacteristic
747C4#117×D7111yescharacteristic
748C4C4×D4×D7111yescharacteristic
749C4C4×D4×D7111yescharacteristic
750C2—2844no—
751C2—1424no—
752C2C4×C22⋊C4×D7111yescharacteristic
753C2#2259686411yescharacteristic
754C2#2259687211yescharacteristic
755C2#2259717111yescharacteristic
756C2#2259718211yescharacteristic
757C2#2259721211yescharacteristic
758C2#2259722011yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC71×#1763C2
socleC23×C71C22×D4
prime radicalC22×#11765866C22
cosocleC22×C4×C71C24
hypercenter#1763D71
hypocenterC71#20415
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
4. C2×#17985956C2semidirect
5. #22590694C2semidirect
6. #22588172C2semidirect
7. #22588166C2semidirect
8. #22588164C2semidirect
9. #103×Dic71C2semidirect
10. C4×#14556052C2semidirect
11. C4×#14556048C2semidirect
12. #22588154C2semidirect
13. #22588058C2semidirect
14. #340×D71C2semidirect
15. C71×#1763C2semidirect
20. #17986481C4semidirect
32. #17985999C4semidirect
33. #17985994C4semidirect
80. C2×#11765848C2×C4semidirect
85. C2×C8×D71C2×C4semidirect
87. Q8×Dic71C2×C4semidirect
90. C4×D284C2×C4semidirect
93. #14556090C2×C4semidirect
95. #14556086C2×C4semidirect
111. C4⋊C4×D71C2×C4semidirect
123. #14556052C2×C4semidirect
124. #14556052C2×C4semidirect
125. #14556050C2×C4semidirect
126. #14556050C2×C4semidirect
127. #14556048C2×C4semidirect
128. #14556048C2×C4semidirect
139. C4×Q8×C71C2×C4semidirect
147. #103×C71C2×C4semidirect
148. #103×C71C2×C4semidirect
156. #11765866C42semidirect
386. #1763D71semidirect
395. C71#20415semidirect
472. C4×Q8C4×D71semidirect
517. #103C4×D71semidirect
518. #103C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864812
C2×#179859992
C2×#179859942
C2×#179859562
#225906942
#225881722
#225881662
#225881642
#103×Dic712
C4×#145560522
C4×#145560482
#225881542
#225880582
#340×D712
C71×#17632
#2041571