Finite Group Databasebeta

← #31995253

Subgroups — #31995253

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×#17986478C211yesmaximal, characteristic
2C2×#17985997C211yesmaximal, characteristic
3C2×#17985992C211yesmaximal, characteristic
4C2×#17985956C211yesmaximal, characteristic, complemented
5#22590694C211yesmaximal, characteristic, complemented
6#22588171C211yesmaximal, characteristic, complemented
7#22588169C211yesmaximal, characteristic, complemented
8#22588167C211yesmaximal, characteristic, complemented
9C4×#14556051C211yesmaximal, characteristic, complemented
10#22588159C211yesmaximal, characteristic, complemented
11#102×Dic71C211yesmaximal, characteristic, complemented
12C4×#14556049C211yesmaximal, characteristic, complemented
13#22588058C211yesmaximal, characteristic, complemented
14#340×D71C211yesmaximal, characteristic, complemented
15C71×#1762C211yesmaximal, characteristic, complemented
16C22×#11765864C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986478—24no—
20#17986478C418yescomplemented
21C2×C4×Dic142C2211yescharacteristic
22C2×#14556093C2211yescharacteristic
23C2×D4×Dic71C2211yescharacteristic
24C2×C4×C22⋊D71—21no—
25C2×(C22⋊D71)⋊C4—21no—
26C2×#14556086C2211yescharacteristic
27C2×#14556085C2211yescharacteristic
28C2×#14556084—21no—
29C22×Dic71⋊C4—21no—
30C2×C4⋊C4×D71C2211yescharacteristic
31C2×C4⋊C4×D71C2211yescharacteristic
32#17985997C418yescomplemented
33#17985992C418yescomplemented
34C2×#14556053C2211yescharacteristic
35C2×#14556053C2211yescharacteristic
36C2×#14556051C2211yescharacteristic
37C2×#14556051C2211yescharacteristic
38C2×#14556049C2211yescharacteristic
39C2×#14556049C2211yescharacteristic
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×D4×C71C2211yescharacteristic
58C2×#102×C71C2211yescharacteristic
59C2×#102×C71C2211yescharacteristic
60C2×#97×C71C2211yescharacteristic
61C4×C4⋊C4×C71C2211yescharacteristic
62#340×C71C2211yescharacteristic
63#340×C71C2211yescharacteristic
64C2×#11765864—22no—
65C2×#11765864—22no—
66C2×#11765864—22no—
67C2×#11765864C2×C414yes—
68C2×#11765864C2×C414yes—
69C2×#11765864C2×C414yes—
70C22×Dic142C2311yescharacteristic
71C22×C22⋊D71—21no—
72C23×Dic71—21no—
73C23×Dic71—21no—
74C22×C4×D71—21no—
75C22×C4×D71—21no—
76C22×C4×D71C2311yescharacteristic
77C2×#11765848—22no—
78C2×#11765848—22no—
79C2×#11765848C2×C414yescomplemented
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C2×C8×D71—22no—
83C2×C8×D71—22no—
84C2×C8×D71C2×C414yescomplemented
85C4×Dic142—22no—
86C4×Dic142C2×C414yescomplemented
87#14556093—22no—
88#14556093C2×C414yescomplemented
89D4×Dic71—22no—
90D4×Dic71C2×C414yescomplemented
91C4×C22⋊D71—28no—
92(C22⋊D71)⋊C4—28no—
93#14556086—22no—
94#14556086C2×C414yescomplemented
95#14556085C2×C414yes—
96#14556085D414yes—
97#14556084—28no—
98C2×C4⋊Dic71C2311yescharacteristic
99C2×C4⋊Dic71C2311yescharacteristic
100C2×C4⋊Dic71C2311yescharacteristic
101C2×Dic71⋊C4—21no—
102C2×Dic71⋊C4—21no—
103C2×Dic71⋊C4—21no—
104C2×Dic71⋊C4—28no—
105C2×Dic71⋊C4—21no—
106C2×Dic71⋊C4D411yescharacteristic
107C2×Dic71⋊C4D411yescharacteristic
108C4⋊C4×D71—22no—
109C4⋊C4×D71—22no—
110C4⋊C4×D71C2×C414yes—
111C4⋊C4×D71C2×C414yescomplemented
112C2×C22⋊Dic71—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4D411yescharacteristic
115C2×(C2×D71)⋊C4D411yescharacteristic
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×C414yescomplemented
124#14556053C2×C414yescomplemented
125#14556051C2×C414yescomplemented
126#14556051C2×C414yescomplemented
127#14556049C2×C414yescomplemented
128#14556049C2×C414yescomplemented
129#14556038—22no—
130C4×C71⋊C8—22no—
131C8×Dic71—22no—
132C71⋊#95—21no—
133C71⋊#95—21no—
134C71⋊#95—21no—
135C22×D4×C71C2311yescharacteristic
136C23×C4×C71—21no—
137C22×C8×C71C2311yescharacteristic
138C22×C8×C71C2311yescharacteristic
139C4×D4×C71—22no—
140C4×D4×C71C2×C414yescomplemented
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2311yescharacteristic
143C2×C4⋊C4×C71C2311yescharacteristic
144C2×C22⋊C4×C71—21no—
145C2×C42×C71—21no—
146C2×C42×C71C2311yescharacteristic
147#102×C71C2×C414yescomplemented
148#102×C71C2×C414yescomplemented
149#97×C71—22no—
150#95×C71—21no—
151C23×D71C2×D411yescharacteristic
152#11765864—28no—
153#11765864—28no—
154#11765864—28no—
155#11765864C42116yescomplemented
156C2×Dic142—21no—
157C2×Dic142—21no—
158C2×Dic142—21no—
159C2×Dic142C22×C412yes—
160C2×Dic142C22×C412yes—
161C2×Dic142C22×C412yes—
162C2×C22⋊D71—24no—
163C2×C22⋊D71—24no—
164C2×C22⋊D71—24no—
165C22×Dic71—21no—
166C22×Dic71—24no—
167C22×Dic71—24no—
168C22×Dic71—24no—
169C22×Dic71—21no—
170C22×Dic71—21no—
171C22×Dic71—21no—
172C22×Dic71—24no—
173C22×Dic71—81no—
174C22×Dic71—81no—
175C22×Dic71C2×D411yescharacteristic
176C22×Dic71C2×D411yescharacteristic
177C22×Dic71C2×D411yescharacteristic
178C2×C4×D71—24no—
179C2×C4×D71—24no—
180C2×C4×D71—81no—
181C2×C4×D71—81no—
182C2×C4×D71—81no—
183C2×C4×D71—81no—
184C2×C4×D71C22×C412yes—
185C2×C4×D71C22×C412yes—
186C2×C4×D71C22×C412yes—
187C2×C4×D71C2×D412yes—
188C2×C4×D71#4112yes—
189C2×C4×D71#4112yes—
190#11765848—28no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8—21no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8C22×C412yes—
196C2×C71⋊C8C22×C412yes—
197C8×D71—28no—
198C4⋊Dic71—21no—
199C4⋊Dic71—21no—
200C4⋊Dic71—21no—
201C4⋊Dic71C22×C412yes—
202C4⋊Dic71C22×C412yes—
203C4⋊Dic71C22×C412yes—
204Dic71⋊C4—24no—
205Dic71⋊C4—24no—
206Dic71⋊C4—24no—
207Dic71⋊C4—24no—
208Dic71⋊C4C22⋊C414yes—
209Dic71⋊C4C22⋊C414yes—
210C22⋊Dic71—24no—
211(C2×D71)⋊C4—24no—
212(C2×D71)⋊C4C22⋊C414yes—
213(C2×D71)⋊C4C22⋊C414yes—
214C4×Dic71—24no—
215C4×Dic71—24no—
216C4×Dic71—24no—
217C4×Dic71—81no—
218C4×Dic71—81no—
219C4×Dic71—81no—
220C4×Dic71C22×C412yes—
221C4×Dic71C2×D412yes—
222C24×C71—21no—
223C2×D4×C71—21no—
224C2×D4×C71—21no—
225C2×D4×C71—21no—
226C2×D4×C71C22×C412yes—
227C2×D4×C71C22×C412yes—
228C2×D4×C71C22×C412yes—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—24no—
233C22×C4×C71—81no—
234C22×C4×C71—81no—
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2411yescharacteristic
238C2×C8×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71—21no—
242C2×C8×C71C22×C412yes—
243C2×C8×C71C22×C412yes—
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—21no—
247C4⋊C4×C71C22×C412yes—
248C4⋊C4×C71C22×C412yes—
249C4⋊C4×C71C22×C412yes—
250C22⋊C4×C71—24no—
251C42×C71—81no—
252C42×C71C22×C412yes—
253C42×C71C2×D412yes—
254C23×C71—22no—
255C23×C71—22no—
256C23×C71—22no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—41no—
260C23×C71—41no—
261C23×C71C22×D411yescharacteristic
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71C2×C22⋊C412yes—
267C22×D71C4×D412yes—
268C22×D71C4×D412yes—
269D4×C71—22no—
270D4×C71—22no—
271D4×C71—22no—
272D4×C71C2×C4214yes—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—21no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—41no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—84no—
287C2×C4×C71C2×C22⋊C412yes—
288C2×C4×C71C2×C22⋊C412yes—
289C2×C4×C71C23×C411yescharacteristic
290C2×C4×C71C23×C411yescharacteristic
291C2×C4×C71C23×C411yescharacteristic
292C2×C4×C71C22×D411yescharacteristic
293C2×C4×C71C2×#4111yescharacteristic
294C2×C4×C71C2×#4111yescharacteristic
295C22⋊D71—216no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—216no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—41no—
310C2×Dic71—41no—
311C2×Dic71—41no—
312C2×Dic71—41no—
313C2×Dic71—84no—
314C2×Dic71C2×C22⋊C412yes—
315C2×Dic71C2×C22⋊C412yes—
316C2×Dic71C2×C22⋊C412yes—
317C2×Dic71C4×D412yes—
318C2×Dic71C4×D412yes—
319C4×D71—84no—
320C4×D71—84no—
321C4×D71C2×C4214yes—
322C4×D71#11714yes—
323C4×D71C4×D414yes—
324C4×D71C4×D414yes—
325Dic142—22no—
326Dic142—22no—
327Dic142—22no—
328Dic142C2×C4214yes—
329C8×C71—22no—
330C8×C71—22no—
331C71⋊C8—22no—
332C71⋊C8—22no—
333C22×C71—24no—
334C22×C71—42no—
335C22×C71—42no—
336C22×C71—42no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71C22×C22⋊C411yescharacteristic
341C22×C71C2×C4×D411yescharacteristic
342C22×C71C2×C4×D411yescharacteristic
343C22×C71#57611yescharacteristic
344C22×C71#57711yescharacteristic
345C22×C71#57711yescharacteristic
346C22×C71#57811yescharacteristic
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—22no—
350C2×D71—22no—
351C2×D71—22no—
352C2×D71—22no—
353C2×D71C4×C22⋊C414yes—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71—42no—
359C4×C71C22×C4211yescharacteristic
360C4×C71C2×#11711yescharacteristic
361C4×C71C2×C4×D411yescharacteristic
362C4×C71C2×C4×D411yescharacteristic
363Dic71—22no—
364Dic71—22no—
365Dic71—24no—
366Dic71—42no—
367Dic71—42no—
368Dic71—42no—
369Dic71C4×C22⋊C414yes—
370#20415—711nomaximal, Sylow
371C2×C71—44no—
372C2×C71C2×C4×C22⋊C411yescharacteristic
373C2×C71#289711yescharacteristic
374C2×C71#289811yescharacteristic
375C2×C71#294611yescharacteristic
376C2×C71#294711yescharacteristic
377C2×C71#295111yescharacteristic
378C2×C71#295211yescharacteristic
379D71—24no—
380C2×#520—711no—
381C2×#417—711no—
382C2×#416—711no—
383C2×#405—711no—
384#2274—711no—
385#1763—711no—
386#1763—711no—
387#1762—711no—
388#1762D7111yescharacteristic, complemented
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×Q8—711no—
403C2×C4×D4—711no—
404C2×C4×D4—1421no—
405C2×C4×D4—1421no—
406C2×C4×D4C2×D7111yescharacteristic
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×#103—711no—
418C2×#103—711no—
419C2×#102—711no—
420C2×#102—711no—
421C2×#102C2×D7111yescharacteristic
422C2×#102C2×D7111yescharacteristic
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×Q8—711no—
451C22×D4—1421no—
452C22×D4C22×D7111yescharacteristic
453C23×C4—21no—
454C23×C4—711no—
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—714no—
470C4×Q8—714no—
471C4×Q8—1422no—
472C4×Q8—1422no—
473C4×D4—22no—
474C4×D4—714no—
475C4×D4—1422no—
476C4×D4—1428no—
477C4×D4—1428no—
478C4×D4C4×D7114yescomplemented
479#117—714no—
480#117—714no—
481#117—714no—
482#117—1428no—
483#117—1422no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—714no—
490C2×C4⋊C4—714no—
491C2×C4⋊C4—1422no—
492C2×C4⋊C4—1422no—
493C2×C4⋊C4—1428no—
494C2×C4⋊C4—1421no—
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—21no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4—711no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C42—21no—
507C2×C42—711no—
508C2×C42—1421no—
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#103—714no—
518#103—714no—
519#102—714no—
520#102—714no—
521#102C4×D7114yescomplemented
522#102C4×D7114yescomplemented
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—21no—
532C24—711no—
533#41—7116no—
534#41—1428no—
535#41—1428no—
536#41—1428no—
537C2×Q8—712no—
538C2×Q8—712no—
539C2×Q8—712no—
540C2×Q8—1421no—
541C2×Q8—1421no—
542C2×Q8—1421no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—1424no—
547C2×D4—1424no—
548C2×D4—1424no—
549C2×D4C2×C4×D7112yes—
550C2×D4C2×C4×D7112yes—
551C2×D4C2×C4×D7112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—81no—
557C22×C4—81no—
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—1421no—
576C22×C4—1421no—
577C22×C4—1421no—
578C22×C4—1424no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4—1424no—
582C22×C4—1421no—
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—714no—
604C4⋊C4—714no—
605C4⋊C4—712no—
606C4⋊C4—712no—
607C4⋊C4—712no—
608C4⋊C4—1424no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1421no—
612C4⋊C4—1421no—
613C4⋊C4—1421no—
614C4⋊C4—1424no—
615C4⋊C4C2×C4×D7112yes—
616C4⋊C4C2×C4×D7112yes—
617C4⋊C4C2×C4×D7112yes—
618C22⋊C4—24no—
619C22⋊C4—714no—
620C22⋊C4—714no—
621C22⋊C4—1424no—
622C22⋊C4—1424no—
623C42—81no—
624C42—5681no—
625C42—5681no—
626C42—5681no—
627C42—712no—
628C42—712no—
629C42—1424no—
630C42—1424no—
631C42—1424no—
632C42C2×C4×D7112yes—
633C42D4×D7112yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—712no—
642C23—712no—
643C23—712no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23C2×D4×D7111yescharacteristic
649Q8—714no—
650Q8—1422no—
651Q8—1422no—
652Q8—1422no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—14216no—
657D4C42×D7114yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—2841no—
673C2×C4—2841no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
678C2×C4—5684no—
679C2×C4—5684no—
680C2×C4—5684no—
681C2×C4—712no—
682C2×C4—712no—
683C2×C4—712no—
684C2×C4—714no—
685C2×C4—714no—
686C2×C4—714no—
687C2×C4—714no—
688C2×C4—712no—
689C2×C4—712no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
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—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—714no—
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#1798680911yescharacteristic
732C22#1798680911yescharacteristic
733C22#1798681511yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2842no—
740C4—2842no—
741C4—2842no—
742C4—714no—
743C4—1422no—
744C4—1422no—
745C4—1424no—
746C4C2×C42×D7111yescharacteristic
747C4#117×D7111yescharacteristic
748C4C4×D4×D7111yescharacteristic
749C4C4×D4×D7111yescharacteristic
750C2—44no—
751C2—1424no—
752C2C4×C22⋊C4×D7111yescharacteristic
753C2#2259686511yescharacteristic
754C2#2259687111yescharacteristic
755C2#2259716911yescharacteristic
756C2#2259718011yescharacteristic
757C2#2259721211yescharacteristic
758C2#2259722211yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC71×#1762C2
socleC23×C71C22×D4
prime radicalC22×#11765864C22
cosocleC22×C4×C71C24
hypercenter#1762D71
hypocenterC71#20415
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. C2×#17985956C2semidirect
5. #22590694C2semidirect
6. #22588171C2semidirect
7. #22588169C2semidirect
8. #22588167C2semidirect
9. C4×#14556051C2semidirect
10. #22588159C2semidirect
11. #102×Dic71C2semidirect
12. C4×#14556049C2semidirect
13. #22588058C2semidirect
14. #340×D71C2semidirect
15. C71×#1762C2semidirect
20. #17986478C4semidirect
32. #17985997C4semidirect
33. #17985992C4semidirect
79. C2×#11765848C2×C4semidirect
84. C2×C8×D71C2×C4semidirect
86. C4×Dic142C2×C4semidirect
88. #14556093C2×C4semidirect
90. D4×Dic71C2×C4semidirect
94. #14556086C2×C4semidirect
111. C4⋊C4×D71C2×C4semidirect
123. #14556053C2×C4semidirect
124. #14556053C2×C4semidirect
125. #14556051C2×C4semidirect
126. #14556051C2×C4semidirect
127. #14556049C2×C4semidirect
128. #14556049C2×C4semidirect
140. C4×D4×C71C2×C4semidirect
147. #102×C71C2×C4semidirect
148. #102×C71C2×C4semidirect
155. #11765864C42semidirect
388. #1762D71semidirect
395. C71#20415semidirect
478. C4×D4C4×D71semidirect
521. #102C4×D71semidirect
522. #102C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179864782
C2×#179859972
C2×#179859922
C2×#179859562
#225906942
#225881712
#225881692
#225881672
C4×#145560512
#225881592
#102×Dic712
C4×#145560492
#225880582
#340×D712
C71×#17622
#2041571