Finite Group Databasebeta

← C2×#22597156 #32861523

Subgroups — C2×#22597156 #32861523

Order 18176.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556160C211yesmaximal, characteristic
2C2×C4×#11765866C211yesmaximal, characteristic
3C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
4#22597156C2116yesmaximal, direct product factor
5C2×#17986104C211yesmaximal, characteristic, complemented
6C2×#17986101C211yesmaximal, characteristic, complemented
7C2×#17986097C211yesmaximal, characteristic, complemented
8C2×Q16×Dic71C211yesmaximal, characteristic, complemented
9C2×#17986091C211yesmaximal, characteristic, complemented
10C2×#17986086C211yesmaximal, characteristic, complemented
11C2×#17986084C211yesmaximal, characteristic, complemented
12C2×#17986038C211yesmaximal, characteristic, complemented
13C2×#17985999C211yesmaximal, characteristic
14C2×#17986006C211yesmaximal, characteristic, complemented
15C2×#17985951C211yesmaximal, characteristic, complemented
16C2×#441×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×Q8×D71C2211yescharacteristic
19C2×#14556160C4116yescomplemented
20C2×#14556160C2218yes—
21C22×#11765855C2211yescharacteristic
22C22×#11765854C2211yescharacteristic
23C22×#11765852C2211yescharacteristic
24C22×#11765848C2211yescharacteristic
25C22×#11765848C2211yescharacteristic
26C4×#11765866—24no—
27C4×#11765866C2218yes—
28C2×Q8×Dic71C2211yescharacteristic
29C2×Q8×Dic71C2211yescharacteristic
30C2×C4×Dic142—21no—
31C2×C4×Dic142C2211yescharacteristic
32C2×#14556093—21no—
33C2×#14556093C2211yescharacteristic
34C4×Q8×D71—24no—
35C4×Q8×D71C2218yescomplemented
36C2×C4×D284—21no—
37C2×C4×D284C2211yescharacteristic
38C2×#14556090—21no—
39C2×#14556090C2211yescharacteristic
40C2×#14556086—21no—
41C2×#14556086C2211yescharacteristic
42C2×C4⋊C4×D71—21no—
43C2×C4⋊C4×D71C2211yescharacteristic
44C2×C42×D71—21no—
45C2×C42×D71—21no—
46C2×C42×D71C2211yescharacteristic
47#17986104C2218yescomplemented
48#17986101C2218yescomplemented
49#17986097C2218yescomplemented
50Q16×Dic71C2218yescomplemented
51#17986091C2218yescomplemented
52#17986086C2218yescomplemented
53#17986084C2218yescomplemented
54#17986038C2218yescomplemented
55C2×#14556062C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58#17986006C2218yescomplemented
59#17985999C2218yes—
60C2×#14556053C2211yescharacteristic
61C2×#14556052C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66#17985951C2218yescomplemented
67C2×#14556039C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C8×Dic71C2211yescharacteristic
70C22×Q16×C71C2211yescharacteristic
71C2×C4×Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73#441×C71C2218yescomplemented
74C2×#106×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#103×C71C2211yescharacteristic
77C2×#97×C71C2211yescharacteristic
78C2×#11765866—22no—
79C2×#11765866—24no—
80C2×#11765866C2×C418yes—
81C2×#11765866C2314yes—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C2×Q8×D71—22no—
85C2×Q8×D71—24no—
86C2×Q8×D71C2×C418yescomplemented
87C2×Q8×D71C2314yes—
88C22×D284—21no—
89C22×D284C2311yescharacteristic
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—21no—
93C22×C4×D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71D411yescharacteristic
96C22×C4×D71D411yescharacteristic
97C22×C4×D71C2311yescharacteristic
98#14556160C2×C4164yescomplemented
99C2×#11765855C2×C418yescomplemented
100C2×#11765855C2314yes—
101C2×#11765854C2×C418yescomplemented
102C2×#11765854C2314yes—
103C2×#11765852C2×C418yescomplemented
104C2×#11765852C2314yes—
105C2×#11765848—24no—
106C2×#11765848C2×C418yescomplemented
107C2×#11765848C2314yes—
108C2×#11765848C2314yes—
109C22×C71⋊C8C2311yescharacteristic
110C22×C71⋊C8C2311yescharacteristic
111Q8×Dic71—22no—
112Q8×Dic71—22no—
113Q8×Dic71C2314yes—
114Q8×Dic71C2314yes—
115C4×Dic142—28no—
116C4×Dic142—22no—
117C4×Dic142C2314yes—
118#14556093—22no—
119#14556093—28no—
120#14556093C2314yes—
121C4×D284—28no—
122C4×D284—22no—
123C4×D284C2314yes—
124#14556090—28no—
125#14556090—22no—
126#14556090C2314yes—
127#14556086—22no—
128#14556086—28no—
129#14556086C2314yes—
130C2×C4⋊Dic71—21no—
131C2×C4⋊Dic71—21no—
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C4⋊C4×D71—28no—
138C4⋊C4×D71—22no—
139C4⋊C4×D71C2314yes—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71—21no—
148C2×C4×Dic71D411yescharacteristic
149C2×C4×Dic71D411yescharacteristic
150C2×C4×Dic71C2311yescharacteristic
151C42×D71—28no—
152C42×D71—28no—
153C42×D71D414yes—
154C42×D71C2314yes—
155#14556062C2314yes—
156#14556061C2314yes—
157#14556059C2314yes—
158#14556053C2314yes—
159#14556052C2314yes—
160#14556052C2314yes—
161#14556051C2314yes—
162#14556050C2314yes—
163#14556048C2314yes—
164#14556039C2314yes—
165C8×Dic71C2314yes—
166C8×Dic71C2314yes—
167C22×Q8×C71C2311yescharacteristic
168C22×Q8×C71C2311yescharacteristic
169C2×Q16×C71C2×C418yescomplemented
170C2×Q16×C71C2314yes—
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2311yescharacteristic
173C4×Q8×C71—22no—
174C4×Q8×C71—22no—
175C4×Q8×C71C2314yes—
176C4×Q8×C71C2314yes—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71—21no—
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C4⋊C4×C71C2311yescharacteristic
181C2×C42×C71—21no—
182C2×C42×C71—21no—
183C2×C42×C71C2311yescharacteristic
184#106×C71C2314yes—
185#103×C71C2314yes—
186#103×C71C2314yes—
187#97×C71C2314yes—
188C23×D71—21no—
189C23×D71C2×D411yescharacteristic
190#11765866—216no—
191#11765866—28no—
192#11765866C22×C4116yes—
193C2×Dic142—21no—
194C2×Dic142—22no—
195C2×Dic142—28no—
196C2×Dic142—24no—
197C2×Dic142C22×C414yes—
198C2×Dic142C2412yes—
199Q8×D71—216no—
200Q8×D71—28no—
201Q8×D71C22×C4116yescomplemented
202C2×D284—28no—
203C2×D284—24no—
204C2×D284—21no—
205C2×D284—22no—
206C2×D284C22×C414yes—
207C2×D284C2412yes—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71C2×D411yescharacteristic
212C22×Dic71C2×D411yescharacteristic
213C22×Dic71C2×D411yescharacteristic
214C2×C4×D71—28no—
215C2×C4×D71—24no—
216C2×C4×D71—28no—
217C2×C4×D71—24no—
218C2×C4×D71—24no—
219C2×C4×D71—24no—
220C2×C4×D71—24no—
221C2×C4×D71—24no—
222C2×C4×D71—42no—
223C2×C4×D71—44no—
224C2×C4×D71—44no—
225C2×C4×D71—44no—
226C2×C4×D71C22×C414yes—
227C2×C4×D71C2×D414yes—
228C2×C4×D71C2×D414yes—
229C2×C4×D71C2×D412yes—
230C2×C4×D71#4114yes—
231C2×C4×D71C2412yes—
232#11765855C22×C4116yescomplemented
233#11765854C22×C4116yescomplemented
234#11765852C22×C4116yescomplemented
235#11765848—28no—
236#11765848C22×C4116yescomplemented
237C2×C71⋊C8—22no—
238C2×C71⋊C8C22×C414yes—
239C2×C71⋊C8C2412yes—
240C2×C71⋊C8C2412yes—
241C4⋊Dic71—21no—
242C4⋊Dic71—21no—
243C4⋊Dic71—24no—
244C4⋊Dic71—24no—
245C4⋊Dic71C2412yes—
246C4⋊Dic71C2412yes—
247Dic71⋊C4—24no—
248Dic71⋊C4—24no—
249Dic71⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253C4×Dic71—24no—
254C4×Dic71—24no—
255C4×Dic71—24no—
256C4×Dic71—24no—
257C4×Dic71—24no—
258C4×Dic71C2×D414yes—
259C4×Dic71C2×D412yes—
260C4×Dic71C2×D414yes—
261C4×Dic71C2412yes—
262C2×Q8×C71—21no—
263C2×Q8×C71—21no—
264C2×Q8×C71—22no—
265C2×Q8×C71—22no—
266C2×Q8×C71C22×C414yes—
267C2×Q8×C71C22×C414yes—
268C2×Q8×C71C2412yes—
269C2×Q8×C71C2412yes—
270C22×C4×C71—21no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2411yescharacteristic
277Q16×C71C22×C4116yescomplemented
278C2×C8×C71—22no—
279C2×C8×C71C22×C414yes—
280C2×C8×C71C2412yes—
281C2×C8×C71C2412yes—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—24no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71C2412yes—
287C4⋊C4×C71C2412yes—
288C42×C71—24no—
289C42×C71—24no—
290C42×C71C2×D412yes—
291C42×C71C2412yes—
292C23×C71C22×D411yescharacteristic
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—24no—
296C22×D71—22no—
297C22×D71—42no—
298C22×D71—42no—
299C22×D71C4×D414yes—
300C22×D71C22×D412yes—
301Q8×C71—24no—
302Q8×C71—24no—
303Q8×C71—22no—
304Q8×C71—22no—
305Q8×C71C23×C414yes—
306Q8×C71C23×C414yes—
307C2×C4×C71—24no—
308C2×C4×C71—24no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71C23×C412yes—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D411yescharacteristic
321C2×C4×C71C2×#4112yes—
322C2×C4×C71C2511yescharacteristic
323C2×Dic71—24no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71C4×D414yes—
331C2×Dic71#13714yescomplemented
332C2×Dic71C22×D412yes—
333C2×Dic71C22×D412yes—
334C2×Dic71C22×D412yes—
335D284—216no—
336D284—24no—
337D284—22no—
338D284C23×C414yes—
339C4×D71—216no—
340C4×D71—216no—
341C4×D71—28no—
342C4×D71—44no—
343C4×D71—48no—
344C4×D71—48no—
345C4×D71—48no—
346C4×D71C4×D418yes—
347C4×D71C23×C414yes—
348C4×D71C2×#4114yes—
349Dic142—24no—
350Dic142—22no—
351Dic142—216no—
352Dic142C23×C414yes—
353C8×C71—22no—
354C8×C71C23×C414yes—
355C71⋊C8—22no—
356C71⋊C8C23×C414yes—
357C22×C71C2×C4×D412yes—
358C22×C71C2×#13712yes—
359C22×C71#57512yes—
360C22×C71C23×D411yescharacteristic
361C2×D71—28no—
362C2×D71—22no—
363C2×D71—22no—
364C2×D71—24no—
365C2×D71—48no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71C2×C4×D414yes—
369C4×C71—24no—
370C4×C71—24no—
371C4×C71—22no—
372C4×C71—22no—
373C4×C71—42no—
374C4×C71—42no—
375C4×C71C2×C4×D412yes—
376C4×C71C24×C411yescharacteristic
377C4×C71C22×#4111yescharacteristic
378Dic71—24no—
379Dic71—22no—
380Dic71—42no—
381Dic71—42no—
382Dic71C2×C4×D414yes—
383Dic71C2×#13714yescomplemented
384C2×C4×#137—711nomaximal, Sylow
385C2×C71C4×#13714yescomplemented
386C2×C71C22×C4×D411yescharacteristic
387C2×C71C22×#13711yescharacteristic
388C2×C71C2×#57511yescharacteristic
389D71—24no—
390D71—44no—
391C22×#137—711no—
392C2×C4×#41—711no—
393C22×C4×Q8—711no—
394C4×#137—7116no—
395C2×#441—711no—
396C2×#441D7111yescharacteristic, complemented
397C2×#440—711no—
398C2×#440—711no—
399C2×C4×Q16—711no—
400C2×C4×Q16—711no—
401C2×C4×SD16—711no—
402C2×C4×SD16—711no—
403C2×#428—711no—
404C2×#417—711no—
405C2×#419—711no—
406C2×C4×M16—711no—
407C71C2×C4×#13711yescharacteristic, complemented, Sylow
408C22×#41—711no—
409C23×Q8—711no—
410C2×#137—7116no—
411C2×#137—718no—
412C22×Q16—711no—
413C22×Q16C2×D7111yescharacteristic
414C22×SD16—711no—
415C22×SD16—711no—
416C22×M16—711no—
417C22×M16—711no—
418C4×#41—718no—
419C4×#41—1424no—
420C2×C4×Q8—711no—
421C2×C4×Q8—711no—
422C2×C4×Q8—718no—
423C2×C4×Q8—711no—
424C2×C4×Q8—711no—
425C2×C4×Q8—1421no—
426C2×C4×Q8—1421no—
427C2×C4×Q8—1424no—
428C2×C4×Q8C2×D7111yescharacteristic
429C2×C4×Q8C2×D7111yescharacteristic
430C2×C4×D4—711no—
431C2×C4×D4—711no—
432C2×C4×D4—1421no—
433C2×C4×D4—1421no—
434C2×#117—711no—
435C2×#117—1421no—
436C22×C4⋊C4—711no—
437C22×C4⋊C4—1421no—
438C22×C42—711no—
439C22×C42—1421no—
440C22×C42—1421no—
441#441—718no—
442#441C2×D7118yescomplemented
443#440—718no—
444#440—718no—
445C4×Q16—718no—
446C4×Q16—718no—
447C4×SD16—718no—
448C4×SD16—718no—
449#428—718no—
450C2×#107—711no—
451C2×#107—711no—
452C2×#106—711no—
453C2×#106C2×D7111yescharacteristic
454#419—718no—
455#417—718no—
456C2×#103—711no—
457C2×#103—711no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103C2×D7111yescharacteristic
461C2×#103C2×D7111yescharacteristic
462C2×#102—711no—
463C2×#102—711no—
464C4×M16—718no—
465C2×#97—711no—
466C2×#97C2×D7111yescharacteristic
467C2×C4×C8—711no—
468C2×C4×C8—711no—
469C2×#41—718no—
470C2×#41—714no—
471C2×#41—1422no—
472C2×#41—1424no—
473C22×Q8—718no—
474C22×Q8—714no—
475C22×Q8—711no—
476C22×Q8—1421no—
477C22×Q8—1422no—
478C22×Q8—1424no—
479C22×Q8C22×D7111yescharacteristic
480C22×Q8C22×D7111yescharacteristic
481C22×D4—711no—
482C22×D4—1421no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—1421no—
487C23×C4—1421no—
488C23×C4—1421no—
489C23×C4—1421no—
490C23×C4—1421no—
491#137—7164no—
492C2×Q16—718no—
493C2×Q16—714no—
494C2×Q16C4×D7118yescomplemented
495C2×Q16C22×D7114yes—
496C2×SD16—718no—
497C2×SD16—714no—
498C2×SD16—718no—
499C2×SD16—714no—
500C2×M16—718no—
501C2×M16—714no—
502C2×M16—714no—
503C2×M16—1424no—
504C22×C8—711no—
505C22×C8—711no—
506C22×C8C22×D7111yescharacteristic
507C22×C8C22×D7111yescharacteristic
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—714no—
511C4×Q8—714no—
512C4×Q8—714no—
513C4×Q8—714no—
514C4×Q8—1428no—
515C4×Q8—1428no—
516C4×Q8—1422no—
517C4×Q8—1422no—
518C4×Q8—1422no—
519C4×Q8—1422no—
520C4×Q8C22×D7114yes—
521C4×Q8C22×D7114yes—
522C4×D4—714no—
523C4×D4—714no—
524C4×D4—1428no—
525C4×D4—1422no—
526C4×D4—1428no—
527C4×D4—1422no—
528#117—714no—
529#117—1428no—
530#117—1422no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—711no—
534C2×C4⋊C4—711no—
535C2×C4⋊C4—714no—
536C2×C4⋊C4—1422no—
537C2×C4⋊C4—1428no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C4⋊C4C22×D7111yescharacteristic
545C2×C22⋊C4—1421no—
546C2×C22⋊C4—1421no—
547C2×C22⋊C4—1421no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—711no—
551C2×C42—711no—
552C2×C42—711no—
553C2×C42—714no—
554C2×C42—714no—
555C2×C42—1428no—
556C2×C42—1428no—
557C2×C42—1421no—
558C2×C42—1421no—
559C2×C42—1421no—
560C2×C42—1421no—
561C2×C42—1421no—
562C2×C42C22×D7111yescharacteristic
563#107—714no—
564#107—714no—
565#106—714no—
566#106C22×D7114yes—
567#103—714no—
568#103—714no—
569#103—714no—
570#103—714no—
571#103C22×D7114yes—
572#103C22×D7114yes—
573#102—714no—
574#102—714no—
575#97—714no—
576#97C22×D7114yes—
577C4×C8—714no—
578C4×C8—714no—
579C24—711no—
580C24—1421no—
581#41—7116no—
582#41—1428no—
583#41—14216no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—7116no—
589C2×Q8—714no—
590C2×Q8—712no—
591C2×Q8—1424no—
592C2×Q8—1428no—
593C2×Q8—1428no—
594C2×Q8—14216no—
595C2×Q8—1421no—
596C2×Q8—1422no—
597C2×Q8C2×C4×D7114yes—
598C2×Q8C2×C4×D7114yes—
599C2×Q8C23×D7112yes—
600C2×Q8C23×D7112yes—
601C2×D4—714no—
602C2×D4—712no—
603C2×D4—1424no—
604C2×D4—1428no—
605C2×D4—1421no—
606C2×D4—1422no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—2844no—
612C22×C4—2842no—
613C22×C4—2844no—
614C22×C4—2844no—
615C22×C4—714no—
616C22×C4—711no—
617C22×C4—711no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—714no—
621C22×C4—712no—
622C22×C4—711no—
623C22×C4—714no—
624C22×C4—1424no—
625C22×C4—1424no—
626C22×C4—1424no—
627C22×C4—1424no—
628C22×C4—1428no—
629C22×C4—1424no—
630C22×C4—1428no—
631C22×C4—1421no—
632C22×C4—1421no—
633C22×C4—1424no—
634C22×C4—1421no—
635C22×C4D4×D7111yescharacteristic
636C22×C4D4×D7111yescharacteristic
637C22×C4C23×D7111yescharacteristic
638Q16—7116no—
639Q16C2×C4×D71116yescomplemented
640SD16—7116no—
641SD16—7116no—
642M16—7116no—
643M16—1428no—
644C2×C8—22no—
645C2×C8—714no—
646C2×C8—712no—
647C2×C8—712no—
648C2×C8—1422no—
649C2×C8C2×C4×D7114yes—
650C2×C8C23×D7112yes—
651C2×C8C23×D7112yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—712no—
657C4⋊C4—712no—
658C4⋊C4—1424no—
659C4⋊C4—1424no—
660C4⋊C4—1424no—
661C4⋊C4—1424no—
662C4⋊C4—1424no—
663C4⋊C4—1421no—
664C4⋊C4—1421no—
665C4⋊C4C23×D7112yes—
666C4⋊C4C23×D7112yes—
667C22⋊C4—1424no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C42—24no—
671C42—24no—
672C42—714no—
673C42—714no—
674C42—712no—
675C42—712no—
676C42—1424no—
677C42—1424no—
678C42—1424no—
679C42—1424no—
680C42—1424no—
681C42D4×D7112yes—
682C42C23×D7112yes—
683C23—2842no—
684C23—2842no—
685C23—712no—
686C23—714no—
687C23—1422no—
688C23—1424no—
689C23—1422no—
690C23—1422no—
691C23C2×D4×D7111yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—24no—
695Q8—24no—
696Q8—714no—
697Q8—14216no—
698Q8—1422no—
699Q8—1424no—
700Q8C22×C4×D7114yes—
701Q8C22×C4×D7114yes—
702D4—714no—
703D4—14216no—
704D4—1422no—
705D4—1424no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—2848no—
717C2×C4—2844no—
718C2×C4—2848no—
719C2×C4—2848no—
720C2×C4—2842no—
721C2×C4—2842no—
722C2×C4—712no—
723C2×C4—712no—
724C2×C4—714no—
725C2×C4—714no—
726C2×C4—714no—
727C2×C4—714no—
728C2×C4—718no—
729C2×C4—712no—
730C2×C4—1428no—
731C2×C4—14216no—
732C2×C4—14216no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1424no—
737C2×C4—1422no—
738C2×C4C22×C4×D7112yes—
739C2×C4C2×D4×D7112yes—
740C2×C4C2×D4×D7112yes—
741C2×C4C2×D4×D7111yescharacteristic
742C2×C4#41×D7112yes—
743C2×C4C24×D7111yescharacteristic
744C8—22no—
745C8—714no—
746C8—1422no—
747C8C22×C4×D7114yes—
748C22—2848no—
749C22—2842no—
750C22—2842no—
751C22—714no—
752C22—1424no—
753C22—1428no—
754C22—1422no—
755C22—1422no—
756C22C4×D4×D7112yes—
757C22#137×D7112yes—
758C22#1798679812yes—
759C22C22×D4×D7111yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—2842no—
767C4—2842no—
768C4—714no—
769C4—714no—
770C4—1424no—
771C4—1422no—
772C4C4×D4×D7112yes—
773C4C23×C4×D7111yescharacteristic
774C4C2×#41×D7111yescharacteristic
775C2—2844no—
776C2—1424no—
777C2#2259715614yesdirect product factor
778C2C2×C4×D4×D7111yescharacteristic
779C2C2×#137×D7111yescharacteristic
780C2C2×#1798679811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#441×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765866C22
cosocleC2×C4×C71C25
hypercenterC2×#441D71
hypocenterC71C2×C4×#137
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D71C2semidirect
4. #22597156C2direct (N × H)
5. C2×#17986104C2semidirect
6. C2×#17986101C2semidirect
7. C2×#17986097C2semidirect
8. C2×Q16×Dic71C2semidirect
9. C2×#17986091C2semidirect
10. C2×#17986086C2semidirect
11. C2×#17986084C2semidirect
12. C2×#17986038C2semidirect
14. C2×#17986006C2semidirect
15. C2×#17985951C2semidirect
16. C2×#441×C71C2semidirect
19. C2×#14556160C4semidirect
35. C4×Q8×D71C22semidirect
47. #17986104C22semidirect
48. #17986101C22semidirect
49. #17986097C22semidirect
50. Q16×Dic71C22semidirect
51. #17986091C22semidirect
52. #17986086C22semidirect
53. #17986084C22semidirect
54. #17986038C22semidirect
58. #17986006C22semidirect
66. #17985951C22semidirect
73. #441×C71C22semidirect
86. C2×Q8×D71C2×C4semidirect
98. #14556160C2×C4semidirect
99. C2×#11765855C2×C4semidirect
101. C2×#11765854C2×C4semidirect
103. C2×#11765852C2×C4semidirect
106. C2×#11765848C2×C4semidirect
169. C2×Q16×C71C2×C4semidirect
201. Q8×D71C22×C4semidirect
232. #11765855C22×C4semidirect
233. #11765854C22×C4semidirect
234. #11765852C22×C4semidirect
236. #11765848C22×C4semidirect
277. Q16×C71C22×C4semidirect
331. C2×Dic71#137semidirect
383. Dic71C2×#137semidirect
385. C2×C71C4×#137semidirect
396. C2×#441D71semidirect
407. C71C2×C4×#137semidirect
442. #441C2×D71semidirect
494. C2×Q16C4×D71semidirect
639. Q16C2×C4×D71semidirect
777. C2#22597156direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561602
C2×C4×#117658662
C2×C4×Q8×D712
#225971562
C2×#179861042
C2×#179861012
C2×#179860972
C2×Q16×Dic712
C2×#179860912
C2×#179860862
C2×#179860842
C2×#179860382
C2×#179859992
C2×#179860062
C2×#179859512
C2×#441×C712
C2×C4×#13771