Finite Group Databasebeta

← C2×#22600789 #32875993

Subgroups — C2×#22600789 #32875993

Order 18176.

1878 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×#17986689C211yesmaximal, characteristic
2#22600789C2116yesmaximal, direct product factor
3C2×#17986405C211yesmaximal, characteristic, complemented
4C2×#17986334C211yesmaximal, characteristic, complemented
5C2×#17986337C211yesmaximal, characteristic, complemented
6C2×#17986329C211yesmaximal, characteristic, complemented
7C2×#17986327C211yesmaximal, characteristic, complemented
8C2×#17986306C211yesmaximal, characteristic, complemented
9C2×#17986281C211yesmaximal, characteristic, complemented
10C2×#17986255C211yesmaximal, characteristic, complemented
11C2×#17986238C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic
14C2×#17986039C211yesmaximal, characteristic, complemented
15C22×#14556059C211yesmaximal, characteristic, complemented
16C2×#554×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986689—24no—
21#17986689C2218yes—
22C2×#14556121—21no—
23C2×#14556120C2211yescharacteristic
24C2×#14556118—21no—
25C2×#14556109—21no—
26C2×#14556107C2211yescharacteristic
27C2×#14556107C2211yescharacteristic
28C2×C4×Dic142C2211yescharacteristic
29C2×#14556087C2211yescharacteristic
30C2×#14556084—21no—
31C22×C4⋊Dic71C2211yescharacteristic
32#17986405C2218yescomplemented
33#17986337C2218yescomplemented
34#17986334C2218yescomplemented
35#17986329C2218yescomplemented
36#17986327C2218yescomplemented
37#17986306C2218yescomplemented
38#17986281C2218yescomplemented
39#17986255C2218yescomplemented
40#17986238C2218yescomplemented
41#17986104C2218yescomplemented
42#17986071C2218yes—
43#17986039C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2218yescomplemented
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556051C2211yescharacteristic
59C2×#14556051C2211yescharacteristic
60C2×#14556051C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yes—
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#125×C71—21no—
68C2×C22⋊Q8×C71—21no—
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C22×C4⋊C4×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C23×Dic71—21no—
79C2×#11765855—24no—
80C2×#11765855C2314yes—
81C2×#11765849—24no—
82C2×#11765849C2314yes—
83C22×C71⋊C8—24no—
84C22×C71⋊C8C2314yes—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89#14556121—28no—
90#14556120—22no—
91#14556120C2314yes—
92#14556118—28no—
93#14556109—28no—
94#14556107—22no—
95#14556107—22no—
96#14556107C2314yes—
97#14556107C2314yes—
98C4×Dic142—22no—
99C4×Dic142C2314yes—
100#14556087—22no—
101#14556087C2314yes—
102#14556084—28no—
103C2×C4⋊Dic71—22no—
104C2×C4⋊Dic71—21no—
105C2×C4⋊Dic71C2314yes—
106C2×C4⋊Dic71C2311yescharacteristic
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2311yescharacteristic
109C2×Dic71⋊C4—21no—
110C2×Dic71⋊C4—21no—
111C2×Dic71⋊C4—21no—
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×C22⋊Dic71—21no—
115C2×C22⋊Dic71—21no—
116C2×C22⋊Dic71—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556059C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556051C2314yes—
133#14556051C2314yes—
134#14556051C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C22×Q8×C71—21no—
139C22×Q8×C71C2311yescharacteristic
140C22×D4×C71D411yescharacteristic
141C23×C4×C71—21no—
142C23×C4×C71—21no—
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C4⋊Q8×C71—22no—
146C4⋊Q8×C71C2314yes—
147#125×C71—28no—
148C22⋊Q8×C71—22no—
149C22⋊Q8×C71—22no—
150C22⋊Q8×C71—28no—
151C22⋊Q8×C71—28no—
152C22⋊Q8×C71C2314yes—
153C22⋊Q8×C71C2314yes—
154C4×Q8×C71—22no—
155C4×Q8×C71C2314yes—
156C4×D4×C71—28no—
157C4×D4×C71D414yes—
158C4×D4×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—22no—
162C2×C4⋊C4×C71—22no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2314yes—
169C2×C4⋊C4×C71C2314yes—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C2×Dic142—22no—
180C2×Dic142—22no—
181C2×Dic142—21no—
182C2×Dic142C2412yes—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—24no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—44no—
189#11765855—28no—
190#11765849—28no—
191C2×C71⋊C8—22no—
192C2×C71⋊C8—22no—
193C2×C71⋊C8—22no—
194C2×C71⋊C8—28no—
195C2×C71⋊C8#4114yes—
196C2×C71⋊C8C2412yes—
197C2×C71⋊C8C2412yes—
198C2×C71⋊C8C2412yes—
199C2×C71⋊C8C2412yes—
200C4⋊Dic71—21no—
201C4⋊Dic71—21no—
202C4⋊Dic71—24no—
203C4⋊Dic71—21no—
204C4⋊Dic71C2412yes—
205C4⋊Dic71C2412yes—
206C4⋊Dic71C2412yes—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209Dic71⋊C4—24no—
210Dic71⋊C4—24no—
211Dic71⋊C4—24no—
212C22⋊Dic71—24no—
213C22⋊Dic71—24no—
214C22⋊Dic71—24no—
215C4×Dic71—24no—
216C4×Dic71—24no—
217C24×C71C2×D411yescharacteristic
218C24×C71C2×D411yescharacteristic
219C2×Q8×C71—21no—
220C2×Q8×C71—24no—
221C2×Q8×C71—22no—
222C2×Q8×C71—22no—
223C2×Q8×C71—82no—
224C2×Q8×C71C2412yes—
225C2×D4×C71—24no—
226C2×D4×C71C2×D414yes—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—24no—
236C22×C4×C71—24no—
237C22×C4×C71—82no—
238C22×C4×C71—82no—
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2×D411yescharacteristic
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D412yes—
244C22×C4×C71C2×D412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2411yescharacteristic
248C4⋊C4×C71—21no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71C2×D414yes—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C4⋊C4×C71C2412yes—
261C22⋊C4×C71—24no—
262C22⋊C4×C71—24no—
263C22⋊C4×C71C2×D414yes—
264C22⋊C4×C71C2×D414yes—
265C42×C71—24no—
266C42×C71C2×D412yes—
267C42×C71C2412yes—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71#13714yes—
274C23×C71C22×D412yes—
275C23×C71C22×D412yes—
276C23×C71C22×D411yescharacteristic
277Q8×C71—22no—
278Q8×C71—22no—
279Q8×C71—42no—
280Q8×C71—84no—
281D4×C71—28no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—24no—
287C2×C4×C71—24no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—42no—
297C2×C4×C71—42no—
298C2×C4×C71—42no—
299C2×C4×C71—42no—
300C2×C4×C71—84no—
301C2×C4×C71—84no—
302C2×C4×C71C22×D412yes—
303C2×C4×C71C22×D412yes—
304C2×C4×C71C22×D412yes—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D411yescharacteristic
307C2×C4×C71C2×#4112yes—
308C2×C4×C712−1+412yes—
309C2×C4×C71C2511yescharacteristic
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—42no—
315C2×Dic71—48no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319Dic142—22no—
320Dic142—22no—
321Dic142—42no—
322C71⋊C8—22no—
323C71⋊C8—22no—
324C71⋊C8—22no—
325C71⋊C8C2×#4114yes—
326C22×C71—28no—
327C22×C71—22no—
328C22×C71—22no—
329C22×C71—22no—
330C22×C71—22no—
331C22×C71—22no—
332C22×C71—44no—
333C22×C71#54712yes—
334C22×C71C2×#13714yes—
335C22×C71C2×#13712yes—
336C22×C71#57712yes—
337C22×C71C23×D411yescharacteristic
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—22no—
341C4×C71—22no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71—42no—
345C4×C71—42no—
346C4×C71#54712yes—
347C4×C71C22×#4111yescharacteristic
348C4×C71C2×2−1+411yescharacteristic
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352Dic71—42no—
353C2×#3344—711nomaximal, Sylow
354C2×C71—24no—
355C2×C71—42no—
356C2×C71#334414yescomplemented
357C2×C71C2×#54711yescharacteristic
358C2×C71C22×#13711yescharacteristic
359C2×C71C2×#57711yescharacteristic
360C2×#554D7111yescharacteristic
361C2×#552—711no—
362#3344—7116no—
363C2×#501—711no—
364C2×#484—711no—
365C2×#485—711no—
366C2×#483—711no—
367C2×#483—711no—
368C2×#479—711no—
369C2×#475—711no—
370C2×#470—711no—
371C2×#467—711no—
372C2×#441—711no—
373C2×#435—711no—
374C2×#428—711no—
375C22×#106—711no—
376C71C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—711no—
378C22×M16—711no—
379C23×C8—711no—
380#554—24no—
381#554C2×D7118yes—
382#552—718no—
383#552—1424no—
384C2×C4⋊Q8C2×D7111yescharacteristic
385C2×#126—1421no—
386C2×#125—21no—
387C2×#125—711no—
388C2×#125—1421no—
389C2×#123—1421no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—21no—
392C2×C22⋊Q8—711no—
393C2×C22⋊Q8—711no—
394C2×C22⋊Q8C2×D7111yescharacteristic
395C2×C22⋊Q8C2×D7111yescharacteristic
396C2×C4×Q8—711no—
397C2×C4×Q8C2×D7111yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C2×D7111yescharacteristic
400C2×#117—711no—
401C2×#117—1421no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4C2×D7111yescharacteristic
404C22×C4⋊C4C2×D7111yescharacteristic
405#501—718no—
406#485—718no—
407#484—718no—
408#483—718no—
409#483—718no—
410#479—718no—
411#475—718no—
412#470—718no—
413#467—718no—
414#441—718no—
415#435—718no—
416#428—718no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—718no—
425C2×#106—711no—
426C2×#106—711no—
427C2×C4⋊C8—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×#103—711no—
431C2×#103—711no—
432C2×#103—711no—
433C2×#103—711no—
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×#97—711no—
437C22×Q8—21no—
438C22×Q8—711no—
439C22×Q8C22×D7111yescharacteristic
440C22×D4C22⋊D7111yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1421no—
444C23×C4C22×D7111yescharacteristic
445C23×C4C22×D7111yescharacteristic
446C2×Q16—714no—
447C2×Q16—1424no—
448C2×M16—714no—
449C2×M16—1424no—
450C22×C8—711no—
451C22×C8—711no—
452C22×C8—714no—
453C22×C8—711no—
454C22×C8—711no—
455C22×C8—1424no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D7114yes—
458#126—1428no—
459#125—28no—
460#125—714no—
461#125—1428no—
462#125—1422no—
463#123—1428no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—714no—
469C22⋊Q8—714no—
470C22⋊Q8—1422no—
471C22⋊Q8—1422no—
472C22⋊Q8C22×D7114yes—
473C22⋊Q8C22×D7114yes—
474C4×Q8—22no—
475C4×Q8—714no—
476C4×Q8—1422no—
477C4×Q8C22×D7114yes—
478C4×D4—28no—
479C4×D4C22⋊D7114yes—
480C4×D4C22×D7114yes—
481#117—714no—
482#117—1422no—
483#117—1428no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—711no—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—714no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1422no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4C22⋊D7111yescharacteristic
504C2×C4⋊C4C22×D7111yescharacteristic
505C2×C4⋊C4C22×D7111yescharacteristic
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C4⋊C4C22×D7114yes—
508C2×C4⋊C4C22×D7114yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4C22⋊D7111yescharacteristic
515C2×C22⋊C4C22⋊D7111yescharacteristic
516C2×C42—21no—
517C2×C42—1421no—
518C2×C42—1421no—
519C2×C42C22×D7111yescharacteristic
520#107—714no—
521#107—714no—
522#107—714no—
523#106—714no—
524#106—714no—
525#106—714no—
526#106—714no—
527#106—714no—
528#106—714no—
529C4⋊C8—714no—
530#103—714no—
531#103—714no—
532#103—714no—
533#103—714no—
534#103—714no—
535#103—714no—
536C22⋊C8—714no—
537C22⋊C8—714no—
538#97—714no—
539C24C2×C22⋊D7111yescharacteristic
540C24C2×C22⋊D7111yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—712no—
547C2×Q8—1422no—
548C2×Q8—1422no—
549C2×Q8—1421no—
550C2×Q8C23×D7112yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D7114yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—2844no—
566C22×C4—1424no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1421no—
570C22×C4—1421no—
571C22×C4C2×C22⋊D7112yes—
572C22×C4C2×C22⋊D7112yes—
573C22×C4C2×C22⋊D7111yescharacteristic
574C22×C4C2×C22⋊D7111yescharacteristic
575C22×C4C2×C22⋊D7111yescharacteristic
576C22×C4C2×C22⋊D7111yescharacteristic
577C22×C4C23×D7112yes—
578C22×C4C23×D7112yes—
579C22×C4C23×D7111yescharacteristic
580Q16—1428no—
581M16—1428no—
582C2×C8—714no—
583C2×C8—712no—
584C2×C8—712no—
585C2×C8—712no—
586C2×C8—712no—
587C2×C8—1428no—
588C2×C8—1422no—
589C2×C8—1422no—
590C2×C8—1422no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—712no—
601C4⋊C4—712no—
602C4⋊C4—712no—
603C4⋊C4—1424no—
604C4⋊C4—1424no—
605C4⋊C4—1424no—
606C4⋊C4—1424no—
607C4⋊C4—1424no—
608C4⋊C4—1421no—
609C4⋊C4—1421no—
610C4⋊C4—1424no—
611C4⋊C4—1421no—
612C4⋊C4C2×C22⋊D7114yes—
613C4⋊C4C23×D7112yes—
614C4⋊C4C23×D7112yes—
615C4⋊C4C23×D7112yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4—1424no—
621C22⋊C4C2×C22⋊D7114yes—
622C22⋊C4C2×C22⋊D7114yes—
623C42—24no—
624C42—1424no—
625C42—1424no—
626C42C2×C22⋊D7112yes—
627C42C23×D7112yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1455615914yes—
634C23C22×C22⋊D7112yes—
635C23C22×C22⋊D7112yes—
636C23C22×C22⋊D7111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—2842no—
642Q8—1422no—
643Q8—1422no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—2842no—
666C2×C4—2848no—
667C2×C4—2842no—
668C2×C4—2842no—
669C2×C4—2842no—
670C2×C4—1422no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4C22×C22⋊D7112yes—
675C2×C4C22×C22⋊D7112yes—
676C2×C4C22×C22⋊D7112yes—
677C2×C4C22×C22⋊D7112yes—
678C2×C4C22×C22⋊D7111yescharacteristic
679C2×C4#41×D7112yes—
680C2×C4#1455617512yes—
681C2×C4C24×D7111yescharacteristic
682C8—714no—
683C8—1422no—
684C8—1422no—
685C8—1422no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1798664812yes—
694C22C2×#1455615914yes—
695C22C2×#1455615912yes—
696C22#1798681012yes—
697C22C23×C22⋊D7111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2842no—
707C4—2842no—
708C4—2842no—
709C4—2842no—
710C4#1798664812yes—
711C4C2×#41×D7111yescharacteristic
712C4C2×#1455617511yescharacteristic
713C2—24no—
714C2—42no—
715C2#2260078914yesdirect product factor
716C2C2×#1798664811yescharacteristic
717C2C22×#1455615911yescharacteristic
718C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
hypercenterC2×#554D71
hypocenterC71C2×#3344
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22600789C2direct (N × H)
3. C2×#17986405C2semidirect
4. C2×#17986334C2semidirect
5. C2×#17986337C2semidirect
6. C2×#17986329C2semidirect
7. C2×#17986327C2semidirect
8. C2×#17986306C2semidirect
9. C2×#17986281C2semidirect
10. C2×#17986255C2semidirect
11. C2×#17986238C2semidirect
12. C2×#17986104C2semidirect
14. C2×#17986039C2semidirect
15. C22×#14556059C2semidirect
32. #17986405C22semidirect
33. #17986337C22semidirect
34. #17986334C22semidirect
35. #17986329C22semidirect
36. #17986327C22semidirect
37. #17986306C22semidirect
38. #17986281C22semidirect
39. #17986255C22semidirect
40. #17986238C22semidirect
41. #17986104C22semidirect
43. #17986039C22semidirect
53. C2×#14556059C22semidirect
356. C2×C71#3344semidirect
376. C71C2×#3344semidirect
715. C2#22600789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
#226007892
C2×#179864052
C2×#179863342
C2×#179863372
C2×#179863292
C2×#179863272
C2×#179863062
C2×#179862812
C2×#179862552
C2×#179862382
C2×#179861042
C2×#179860712
C2×#179860392
C22×#145560592
C2×#554×C712
C2×#334471