Finite Group Databasebeta

← C2×#22600909 #32876140

Subgroups — C2×#22600909 #32876140

Order 18176.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic
2#22600909C2116yesmaximal, direct product factor
3C2×#17986398C211yesmaximal, characteristic, complemented
4C2×#17986334C211yesmaximal, characteristic, complemented
5C2×#17986332C211yesmaximal, characteristic, complemented
6C2×#17986340C211yesmaximal, characteristic, complemented
7C2×#17986337C211yesmaximal, characteristic, complemented
8C2×#17986306C211yesmaximal, characteristic, complemented
9C2×#17986303C211yesmaximal, characteristic, complemented
10C2×#17986255C211yesmaximal, characteristic, complemented
11C2×#17986255C211yesmaximal, characteristic, complemented
12C2×C4×#11765855C211yesmaximal, characteristic, complemented
13C2×#17986077C211yesmaximal, characteristic
14C2×#17986042C211yesmaximal, characteristic, complemented
15C2×#17986039C211yesmaximal, characteristic, complemented
16C2×#552×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C22×#11765849C2211yescharacteristic
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#17986398C2218yescomplemented
33#17986340C2218yescomplemented
34#17986337C2218yescomplemented
35#17986334C2218yescomplemented
36#17986332C2218yescomplemented
37#17986306C2218yescomplemented
38#17986303C2218yescomplemented
39#17986255C2218yescomplemented
40#17986255C2218yescomplemented
41C4×#11765855C2218yescomplemented
42#17986077C2218yes—
43#17986042C2218yescomplemented
44#17986039C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556061C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
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×C4×C71⋊C8C2211yescharacteristic
64#552×C71—24no—
65#552×C71C2218yes—
66C2×#126×C71—21no—
67C2×#125×C71—21no—
68C2×#125×C71C2211yescharacteristic
69C2×#123×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71C2211yescharacteristic
74C2×#117×C71—21no—
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C23×Dic71—21no—
79C2×#11765855—24no—
80C2×#11765855C2314yes—
81C2×#11765849—24no—
82C2×#11765849—24no—
83C2×#11765849C2314yes—
84C2×#11765849C2314yes—
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#14556061C2314yes—
123#14556061C2314yes—
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—
137C4×C71⋊C8C2314yes—
138C22×Q8×C71C2311yescharacteristic
139C22×D4×C71D411yescharacteristic
140C23×C4×C71—21no—
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143#126×C71—28no—
144#125×C71—28no—
145#125×C71—22no—
146#125×C71C2314yes—
147#123×C71—28no—
148C22⋊Q8×C71—22no—
149C22⋊Q8×C71—22no—
150C22⋊Q8×C71C2314yes—
151C22⋊Q8×C71C2314yes—
152C4×Q8×C71—22no—
153C4×Q8×C71C2314yes—
154C4×D4×C71D414yes—
155C4×D4×C71C2314yes—
156#117×C71—22no—
157#117×C71—28no—
158#117×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—22no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71C2314yes—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71D411yescharacteristic
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C42×C71—21no—
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—
191#11765849—28no—
192C2×C71⋊C8—22no—
193C2×C71⋊C8—22no—
194C2×C71⋊C8—22no—
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—22no—
221C2×Q8×C71—22no—
222C2×Q8×C71C2412yes—
223C2×D4×C71—42no—
224C2×D4×C71C2×D414yes—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—24no—
234C22×C4×C71—44no—
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D412yes—
240C22×C4×C71C2×D412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2411yescharacteristic
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71—24no—
247C4⋊C4×C71—24no—
248C4⋊C4×C71—24no—
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71C2×D414yes—
254C4⋊C4×C71C2412yes—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2412yes—
257C22⋊C4×C71—24no—
258C22⋊C4×C71—24no—
259C22⋊C4×C71—24no—
260C22⋊C4×C71C2×D414yes—
261C22⋊C4×C71C2×D414yes—
262C42×C71—24no—
263C42×C71—24no—
264C42×C71C2×D412yes—
265C42×C71C2412yes—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71C22×D412yes—
273C23×C71C22×D412yes—
274C23×C71C22×D411yescharacteristic
275Q8×C71—22no—
276Q8×C71—22no—
277Q8×C71—42no—
278D4×C71—44no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—24no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—48no—
294C2×C4×C71—42no—
295C2×C4×C71—42no—
296C2×C4×C71—42no—
297C2×C4×C71—42no—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D412yes—
300C2×C4×C71C22×D412yes—
301C2×C4×C71C22×D412yes—
302C2×C4×C71C22×D411yescharacteristic
303C2×C4×C71C2×#4112yes—
304C2×C4×C712−1+412yes—
305C2×C4×C71C2511yescharacteristic
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—48no—
311C2×Dic71—42no—
312C2×Dic71—42no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315Dic142—22no—
316Dic142—22no—
317Dic142—42no—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C71⋊C8—22no—
321C71⋊C8C2×#4114yes—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—22no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—44no—
329C22×C71—44no—
330C22×C71#54712yes—
331C22×C71#57512yes—
332C22×C71#57812yes—
333C22×C71C23×D411yescharacteristic
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—22no—
337C4×C71—22no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71—42no—
341C4×C71—42no—
342C4×C71#54712yes—
343C4×C71C22×#4111yescharacteristic
344C4×C71C2×2−1+411yescharacteristic
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71—42no—
349C2×#3352—711nomaximal, Sylow
350C2×C71—42no—
351C2×C71—42no—
352C2×C71#335214yescomplemented
353C2×C71C2×#54711yescharacteristic
354C2×C71C2×#57511yescharacteristic
355C2×C71C2×#57811yescharacteristic
356C2×#552—711no—
357C2×#552D7111yescharacteristic
358#3352—7116no—
359C2×#499—711no—
360C2×#484—711no—
361C2×#484—711no—
362C2×#485—711no—
363C2×#485—711no—
364C2×#479—711no—
365C2×#479—711no—
366C2×#470—711no—
367C2×#470—711no—
368C2×C4×Q16—711no—
369C2×#436—711no—
370C2×#428—711no—
371C2×#428—711no—
372C71C2×#335211yescharacteristic, complemented, Sylow
373C22×Q16—711no—
374C22×M16—711no—
375C22×M16—711no—
376#552—24no—
377#552—718no—
378#552—1424no—
379#552C2×D7118yes—
380C2×#126—21no—
381C2×#126—1421no—
382C2×#125—21no—
383C2×#125—711no—
384C2×#125—1421no—
385C2×#125C2×D7111yescharacteristic
386C2×#123—21no—
387C2×#123—1421no—
388C2×C22⋊Q8—711no—
389C2×C22⋊Q8—711no—
390C2×C22⋊Q8C2×D7111yescharacteristic
391C2×C22⋊Q8C2×D7111yescharacteristic
392C2×C4×Q8—711no—
393C2×C4×Q8C2×D7111yescharacteristic
394C2×C4×D4C2×D7111yescharacteristic
395C2×#117—21no—
396C2×#117—711no—
397C2×#117—1421no—
398C2×#117C2×D7111yescharacteristic
399C22×C4⋊C4—711no—
400C22×C4⋊C4C2×D7111yescharacteristic
401#499—718no—
402#485—718no—
403#485—718no—
404#484—718no—
405#484—718no—
406#479—718no—
407#479—718no—
408#470—718no—
409#470—718no—
410C4×Q16—718no—
411#436—718no—
412#428—718no—
413#428—718no—
414C2×#107—711no—
415C2×#107—711no—
416C2×#107—711no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#106—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×C4⋊C8—711no—
424C2×#103—711no—
425C2×#103—711no—
426C2×#103—711no—
427C2×#103—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×C22⋊C8—711no—
431C2×C22⋊C8—711no—
432C2×C4×C8—711no—
433C22×Q8—711no—
434C22×Q8C22×D7111yescharacteristic
435C22×D4C22⋊D7111yescharacteristic
436C23×C4—21no—
437C23×C4—1421no—
438C23×C4C22×D7111yescharacteristic
439C23×C4C22×D7111yescharacteristic
440C2×Q16—714no—
441C2×Q16—1424no—
442C2×M16—714no—
443C2×M16—714no—
444C2×M16—1424no—
445C2×M16—1424no—
446C22×C8—711no—
447C22×C8—711no—
448C22×C8—711no—
449C22×C8—711no—
450#126—28no—
451#126—1428no—
452#125—28no—
453#125—22no—
454#125—714no—
455#125—1428no—
456#125—1422no—
457#125C22×D7114yes—
458#123—28no—
459#123—1428no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—714no—
463C22⋊Q8—714no—
464C22⋊Q8—1422no—
465C22⋊Q8—1422no—
466C22⋊Q8C22×D7114yes—
467C22⋊Q8C22×D7114yes—
468C4×Q8—22no—
469C4×Q8—714no—
470C4×Q8—1422no—
471C4×Q8C22×D7114yes—
472C4×D4C22⋊D7114yes—
473C4×D4C22×D7114yes—
474#117—22no—
475#117—28no—
476#117—714no—
477#117—1422no—
478#117—1428no—
479#117C22×D7114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—714no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1422no—
493C2×C4⋊C4—1421no—
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×C4⋊C4C22×D7114yes—
502C2×C4⋊C4C22×D7111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1421no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4C22⋊D7111yescharacteristic
510C2×C22⋊C4C22⋊D7111yescharacteristic
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—1421no—
514C2×C42—1421no—
515C2×C42C22×D7111yescharacteristic
516#107—714no—
517#107—714no—
518#107—714no—
519#107—714no—
520#107—714no—
521#106—714no—
522#106—714no—
523#106—714no—
524#106—714no—
525C4⋊C8—714no—
526#103—714no—
527#103—714no—
528#103—714no—
529#103—714no—
530#103—714no—
531#103—714no—
532C22⋊C8—714no—
533C22⋊C8—714no—
534C4×C8—714no—
535C24C2×C22⋊D7111yescharacteristic
536C24C2×C22⋊D7111yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—712no—
541C2×Q8—1422no—
542C2×Q8—1422no—
543C2×Q8—1421no—
544C2×Q8C23×D7112yes—
545C2×D4—42no—
546C2×D4C2×C22⋊D7114yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—44no—
557C22×C4—2844no—
558C22×C4—1424no—
559C22×C4—1421no—
560C22×C4—1421no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4C2×C22⋊D7112yes—
564C22×C4C2×C22⋊D7112yes—
565C22×C4C2×C22⋊D7111yescharacteristic
566C22×C4C2×C22⋊D7111yescharacteristic
567C22×C4C2×C22⋊D7111yescharacteristic
568C22×C4C2×C22⋊D7111yescharacteristic
569C22×C4C23×D7112yes—
570C22×C4C23×D7112yes—
571C22×C4C23×D7111yescharacteristic
572Q16—1428no—
573M16—1428no—
574M16—1428no—
575C2×C8—714no—
576C2×C8—712no—
577C2×C8—712no—
578C2×C8—712no—
579C2×C8—712no—
580C2×C8—1422no—
581C2×C8—1422no—
582C2×C8—1422no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—712no—
593C4⋊C4—712no—
594C4⋊C4—712no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1421no—
601C4⋊C4—1421no—
602C4⋊C4—1424no—
603C4⋊C4—1421no—
604C4⋊C4C2×C22⋊D7114yes—
605C4⋊C4C23×D7112yes—
606C4⋊C4C23×D7112yes—
607C4⋊C4C23×D7112yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—1424no—
612C22⋊C4—1424no—
613C22⋊C4—1424no—
614C22⋊C4C2×C22⋊D7114yes—
615C22⋊C4C2×C22⋊D7114yes—
616C42—24no—
617C42—24no—
618C42—1424no—
619C42—1424no—
620C42C2×C22⋊D7112yes—
621C42C23×D7112yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D7112yes—
629C23C22×C22⋊D7112yes—
630C23C22×C22⋊D7111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—2842no—
635Q8—1422no—
636Q8—1422no—
637D4—44no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—2848no—
658C2×C4—2842no—
659C2×C4—2842no—
660C2×C4—2842no—
661C2×C4—2842no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4C22×C22⋊D7112yes—
667C2×C4C22×C22⋊D7112yes—
668C2×C4C22×C22⋊D7112yes—
669C2×C4C22×C22⋊D7112yes—
670C2×C4C22×C22⋊D7111yescharacteristic
671C2×C4#41×D7112yes—
672C2×C4#1455617512yes—
673C2×C4C24×D7111yescharacteristic
674C8—714no—
675C8—1422no—
676C8—1422no—
677C8—1422no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1798664812yes—
687C22#1798679712yes—
688C22#1798681412yes—
689C22C23×C22⋊D7111yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2842no—
699C4—2842no—
700C4—2842no—
701C4—2842no—
702C4#1798664812yes—
703C4C2×#41×D7111yescharacteristic
704C4C2×#1455617511yescharacteristic
705C2—42no—
706C2—42no—
707C2#2260090914yesdirect product factor
708C2C2×#1798664811yescharacteristic
709C2C2×#1798679711yescharacteristic
710C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#552×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
hypercenterC2×#552D71
hypocenterC71C2×#3352
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22600909C2direct (N × H)
3. C2×#17986398C2semidirect
4. C2×#17986334C2semidirect
5. C2×#17986332C2semidirect
6. C2×#17986340C2semidirect
7. C2×#17986337C2semidirect
8. C2×#17986306C2semidirect
9. C2×#17986303C2semidirect
10. C2×#17986255C2semidirect
11. C2×#17986255C2semidirect
12. C2×C4×#11765855C2semidirect
14. C2×#17986042C2semidirect
15. C2×#17986039C2semidirect
32. #17986398C22semidirect
33. #17986340C22semidirect
34. #17986337C22semidirect
35. #17986334C22semidirect
36. #17986332C22semidirect
37. #17986306C22semidirect
38. #17986303C22semidirect
39. #17986255C22semidirect
40. #17986255C22semidirect
41. C4×#11765855C22semidirect
43. #17986042C22semidirect
44. #17986039C22semidirect
352. C2×C71#3352semidirect
372. C71C2×#3352semidirect
707. C2#22600909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
#226009092
C2×#179863982
C2×#179863342
C2×#179863322
C2×#179863402
C2×#179863372
C2×#179863062
C2×#179863032
C2×#179862552
C2×C4×#117658552
C2×#179860772
C2×#179860422
C2×#179860392
C2×#552×C712
C2×#335271