Finite Group Databasebeta

← C2×#22600393 #32874060

Subgroups — C2×#22600393 #32874060

Order 18176.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic
2C2×D4×Dic142C211yesmaximal, characteristic
3#22600393C2116yesmaximal, direct product factor
4C2×#17986368C211yesmaximal, characteristic, complemented
5C2×#17986341C211yesmaximal, characteristic, complemented
6C2×#17986330C211yesmaximal, characteristic, complemented
7C2×#17986307C211yesmaximal, characteristic, complemented
8C2×#17986257C211yesmaximal, characteristic, complemented
9C2×#17986240C211yesmaximal, characteristic, complemented
10C2×#17986210C211yesmaximal, characteristic, complemented
11C2×#17986157C211yesmaximal, characteristic, complemented
12C2×#17986157C211yesmaximal, characteristic, complemented
13C2×#17986107C211yesmaximal, characteristic, complemented
14C2×#17986009C211yesmaximal, characteristic, complemented
15C22×#14556053C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C22×Dic284C2211yescharacteristic
20C22×Dic284C2211yescharacteristic
21C22×Dic284C2211yescharacteristic
22#17986689—24no—
23#17986689C2218yes—
24D4×Dic142—24no—
25D4×Dic142C2218yes—
26C2×#14556128C2211yescharacteristic
27C2×#14556127—21no—
28C2×#14556121—21no—
29C2×#14556120C2211yescharacteristic
30C2×#14556118—21no—
31C2×#14556109—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556107C2211yescharacteristic
34C2×#14556107C2211yescharacteristic
35C2×#14556107C2211yescharacteristic
36C2×#14556105—21no—
37C2×#14556105—21no—
38C2×C4×Dic142C2211yescharacteristic
39C2×C4×Dic142C2211yescharacteristic
40C2×D4×Dic71—21no—
41C2×#14556087C2211yescharacteristic
42C2×#14556084—21no—
43C22×C4⋊Dic71C2211yescharacteristic
44#17986368C2218yescomplemented
45#17986341C2218yescomplemented
46#17986330C2218yescomplemented
47#17986307C2218yescomplemented
48#17986257C2218yescomplemented
49#17986240C2218yescomplemented
50#17986210C2218yescomplemented
51#17986157C2218yescomplemented
52#17986157C2218yescomplemented
53#17986107C2218yescomplemented
54C2×#14556062C2211yescharacteristic
55C2×#14556060C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57#17986009C2218yescomplemented
58C2×#14556053C2211yescharacteristic
59C2×#14556053C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556053C2211yescharacteristic
67C2×#14556053C2211yescharacteristic
68C2×#14556053C2218yescomplemented
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yes—
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—24no—
78C22×Dic142—24no—
79C22×Dic142—22no—
80C22×Dic142—22no—
81C22×Dic142—21no—
82C22×Dic142—21no—
83C22×Dic142—42no—
84C22×Dic142—42no—
85C22×Dic142C2311yescharacteristic
86C22×Dic142C2311yescharacteristic
87C22×Dic142C2311yescharacteristic
88C22×Dic142C2314yes—
89C22×Dic142C2314yes—
90C22×Dic142C2311yescharacteristic
91C23×Dic71—21no—
92C23×Dic71—21no—
93C23×Dic71—21no—
94C2×Dic284—24no—
95C2×Dic284—42no—
96C2×Dic284—42no—
97C2×Dic284C2314yes—
98C2×Dic284C2314yes—
99C2×Dic284C2314yes—
100#14556128—22no—
101#14556128C2314yes—
102#14556127—28no—
103#14556121—28no—
104#14556120—22no—
105#14556120C2314yes—
106#14556118—28no—
107#14556109—28no—
108#14556107—22no—
109#14556107—22no—
110#14556107—22no—
111#14556107—22no—
112#14556107C2314yes—
113#14556107C2314yes—
114#14556107C2314yes—
115#14556107C2314yes—
116#14556105—28no—
117#14556105—28no—
118C4×Dic142—22no—
119C4×Dic142—22no—
120C4×Dic142C2314yes—
121C4×Dic142C2314yes—
122D4×Dic71—28no—
123#14556087—22no—
124#14556087C2314yes—
125#14556084—28no—
126C2×C4⋊Dic71—22no—
127C2×C4⋊Dic71—21no—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2314yes—
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C2×Dic71⋊C4—21no—
142C2×Dic71⋊C4—21no—
143C2×C22⋊Dic71—21no—
144C2×C22⋊Dic71—21no—
145C2×C22⋊Dic71—21no—
146C2×C22⋊Dic71—21no—
147C2×C22⋊Dic71—21no—
148C2×C4×Dic71—21no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yes—
152#14556060C2314yes—
153#14556060C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556053C2314yes—
157#14556053C2314yes—
158#14556053C2314yes—
159#14556053C2314yes—
160#14556053C2314yes—
161#14556053C2314yes—
162#14556053C2314yes—
163#14556053C2314yes—
164C22×D4×C71D411yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C2×M16×C71—42no—
168C2×M16×C71C2314yes—
169C22×C8×C71—42no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2314yes—
175C4×D4×C71D414yes—
176C4×D4×C71C2314yes—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C4⋊C8×C71C2314yes—
182C22⋊C8×C71C2314yes—
183C22⋊C8×C71C2314yes—
184#97×C71C2314yes—
185C2×Dic142—21no—
186C2×Dic142—22no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—22no—
193C2×Dic142—28no—
194C2×Dic142—28no—
195C2×Dic142—24no—
196C2×Dic142—24no—
197C2×Dic142—21no—
198C2×Dic142—21no—
199C2×Dic142—21no—
200C2×Dic142—44no—
201C2×Dic142—44no—
202C2×Dic142—48no—
203C2×Dic142—48no—
204C2×Dic142—44no—
205C2×Dic142—44no—
206C2×Dic142#4114yes—
207C2×Dic142C2412yes—
208C2×Dic142C2412yes—
209C2×Dic142C2412yes—
210C2×Dic142C2412yes—
211C22×Dic71—21no—
212C22×Dic71—21no—
213C22×Dic71—21no—
214C22×Dic71—24no—
215C22×Dic71—24no—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71—24no—
219C22×Dic71—21no—
220C22×Dic71—21no—
221C22×Dic71—21no—
222C22×Dic71—44no—
223C22×Dic71—44no—
224C22×Dic71—44no—
225Dic284—28no—
226Dic284—44no—
227Dic284—44no—
228C4⋊Dic71—21no—
229C4⋊Dic71—21no—
230C4⋊Dic71—24no—
231C4⋊Dic71—24no—
232C4⋊Dic71—24no—
233C4⋊Dic71—21no—
234C4⋊Dic71—21no—
235C4⋊Dic71C2412yes—
236C4⋊Dic71C2412yes—
237C4⋊Dic71C2412yes—
238C4⋊Dic71C2412yes—
239Dic71⋊C4—24no—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242Dic71⋊C4—24no—
243Dic71⋊C4—24no—
244Dic71⋊C4—24no—
245Dic71⋊C4—24no—
246Dic71⋊C4—24no—
247C22⋊Dic71—24no—
248C22⋊Dic71—24no—
249C22⋊Dic71—24no—
250C22⋊Dic71—24no—
251C22⋊Dic71—24no—
252C4×Dic71—24no—
253C4×Dic71—24no—
254C4×Dic71—24no—
255C24×C71C2×D411yescharacteristic
256C24×C71C2×D411yescharacteristic
257C2×D4×C71—24no—
258C2×D4×C71C2×D414yes—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D412yes—
266C22×C4×C71C2×D412yes—
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2411yescharacteristic
272M16×C71—44no—
273C2×C8×C71—22no—
274C2×C8×C71—22no—
275C2×C8×C71—22no—
276C2×C8×C71—22no—
277C2×C8×C71—44no—
278C2×C8×C71C2412yes—
279C2×C8×C71C2412yes—
280C2×C8×C71C2412yes—
281C2×C8×C71C2412yes—
282C4⋊C4×C71C2×D414yes—
283C22⋊C4×C71C2×D414yes—
284C22⋊C4×C71C2×D414yes—
285C42×C71C2×D412yes—
286C42×C71C2412yes—
287C23×C71—22no—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71#13714yes—
293C23×C71C22×D412yes—
294C23×C71C22×D412yes—
295C23×C71C22×D411yescharacteristic
296D4×C71—28no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—24no—
302C2×C4×C71—24no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D411yescharacteristic
312C2×C4×C71C2×#4112yes—
313C2×C4×C71H(5,𝔽2)12yes—
314C2×C4×C71C2511yescharacteristic
315C2×Dic71—24no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—48no—
325C2×Dic71—48no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—48no—
330C2×Dic71—42no—
331C2×Dic71—42no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334Dic142—24no—
335Dic142—22no—
336Dic142—22no—
337Dic142—22no—
338Dic142—22no—
339Dic142—22no—
340Dic142—22no—
341Dic142—22no—
342Dic142—48no—
343Dic142—48no—
344Dic142—42no—
345Dic142—42no—
346Dic142—42no—
347Dic142C2×#4114yes—
348C8×C71—22no—
349C8×C71—22no—
350C8×C71—22no—
351C8×C71—22no—
352C22×C71—22no—
353C22×C71—28no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71—44no—
359C22×C71#54612yes—
360C22×C71C2×#13714yes—
361C22×C71C2×#13712yes—
362C22×C71#57812yes—
363C22×C71C23×D411yescharacteristic
364C4×C71—22no—
365C4×C71—22no—
366C4×C71—22no—
367C4×C71—22no—
368C4×C71#54612yes—
369C4×C71C22×#4111yescharacteristic
370C4×C71C2×H(5,𝔽2)11yescharacteristic
371Dic71—24no—
372Dic71—42no—
373Dic71—42no—
374Dic71—42no—
375Dic71—42no—
376Dic71—42no—
377Dic71—42no—
378Dic71—42no—
379C2×#3312—711nomaximal, Sylow
380C2×C71—24no—
381C2×C71—42no—
382C2×C71#331214yescomplemented
383C2×C71C2×#54611yescharacteristic
384C2×C71C22×#13711yescharacteristic
385C2×C71C2×#57811yescharacteristic
386C2×#552—711no—
387C2×D4×Q8—711no—
388#3312—7116no—
389C2×#491—711no—
390C2×#485—711no—
391C2×#483—711no—
392C2×#479—711no—
393C2×#470—711no—
394C2×#467—711no—
395C2×#462—711no—
396C2×#451—711no—
397C2×#451—711no—
398C2×#441—711no—
399C2×#435D7111yescharacteristic
400C2×#419—711no—
401C22×#103—711no—
402C71C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8—711no—
404C23×Q8—711no—
405C22×Q16—711no—
406C22×Q16—711no—
407C22×Q16—711no—
408C22×M16C2×D7111yescharacteristic
409C23×C8C2×D7111yescharacteristic
410#552—718no—
411#552—1424no—
412D4×Q8—718no—
413D4×Q8—1424no—
414C2×C4⋊Q8—711no—
415C2×C4⋊Q8—1421no—
416C2×#126—1421no—
417C2×#125—711no—
418C2×#125—1421no—
419C2×#123—1421no—
420C2×C22⋊Q8—711no—
421C2×C22⋊Q8—711no—
422C2×C22⋊Q8—711no—
423C2×C22⋊Q8—711no—
424C2×C22⋊Q8—1421no—
425C2×C22⋊Q8—1421no—
426C2×C4×Q8—711no—
427C2×C4×Q8—711no—
428C2×C4×D4—1421no—
429C2×C4×D4C2×D7111yescharacteristic
430C2×#117—711no—
431C2×#117—1421no—
432C22×C4⋊C4—711no—
433#491—718no—
434#485—718no—
435#483—718no—
436#479—718no—
437#470—718no—
438#467—718no—
439#462—718no—
440#451—718no—
441#451—718no—
442#441—718no—
443#435C2×D7118yes—
444C2×#107—711no—
445C2×#106—711no—
446C2×#106—711no—
447C2×C4⋊C8C2×D7111yescharacteristic
448#419—718no—
449C2×#103—711no—
450C2×#103—711no—
451C2×#103—711no—
452C2×#103—711no—
453C2×#103—711no—
454C2×#103—711no—
455C2×#103—711no—
456C2×#103—711no—
457C2×#103—711no—
458C2×#103—718no—
459C2×#103—711no—
460C2×C22⋊C8C2×D7111yescharacteristic
461C2×C22⋊C8C2×D7111yescharacteristic
462C2×#97C2×D7111yescharacteristic
463C22×Q8—2842no—
464C22×Q8—2842no—
465C22×Q8—714no—
466C22×Q8—714no—
467C22×Q8—711no—
468C22×Q8—711no—
469C22×Q8—711no—
470C22×Q8—711no—
471C22×Q8—1424no—
472C22×Q8—1424no—
473C22×Q8—1421no—
474C22×Q8—1421no—
475C22×Q8—1422no—
476C22×Q8—1422no—
477C22×D4D28411yescharacteristic
478C23×C4—1421no—
479C23×C4—1421no—
480C23×C4—1421no—
481C23×C4C22×D7111yescharacteristic
482C23×C4C22×D7111yescharacteristic
483C2×Q16—2842no—
484C2×Q16—2842no—
485C2×Q16—714no—
486C2×Q16—714no—
487C2×Q16—714no—
488C2×Q16—1424no—
489C2×M16—42no—
490C2×M16C22×D7114yes—
491C22×C8—42no—
492C22×C8C22×D7111yescharacteristic
493C22×C8C22×D7111yescharacteristic
494C22×C8C22×D7111yescharacteristic
495C22×C8C22×D7111yescharacteristic
496C22×C8C22×D7114yes—
497C4⋊Q8—714no—
498C4⋊Q8—1428no—
499C4⋊Q8—1422no—
500#126—1428no—
501#125—714no—
502#125—1428no—
503#125—1422no—
504#123—1428no—
505C22⋊Q8—714no—
506C22⋊Q8—714no—
507C22⋊Q8—714no—
508C22⋊Q8—714no—
509C22⋊Q8—1422no—
510C22⋊Q8—1422no—
511C22⋊Q8—1422no—
512C22⋊Q8—1422no—
513C22⋊Q8—1428no—
514C22⋊Q8—1428no—
515C4×Q8—714no—
516C4×Q8—714no—
517C4×Q8—1422no—
518C4×Q8—1422no—
519C4×D4—1428no—
520C4×D4D28414yes—
521C4×D4C22×D7114yes—
522#117—714no—
523#117—1422no—
524#117—1428no—
525C2×C4⋊C4—711no—
526C2×C4⋊C4—711no—
527C2×C4⋊C4—714no—
528C2×C4⋊C4—711no—
529C2×C4⋊C4—711no—
530C2×C4⋊C4—1421no—
531C2×C4⋊C4—1422no—
532C2×C4⋊C4—1421no—
533C2×C4⋊C4—1421no—
534C2×C4⋊C4—1421no—
535C2×C4⋊C4—1421no—
536C2×C4⋊C4—1421no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4D28411yescharacteristic
543C2×C22⋊C4—1421no—
544C2×C22⋊C4—1421no—
545C2×C22⋊C4—1421no—
546C2×C22⋊C4—1421no—
547C2×C22⋊C4—1421no—
548C2×C22⋊C4D28411yescharacteristic
549C2×C22⋊C4D28411yescharacteristic
550C2×C42—1421no—
551C2×C42—1421no—
552C2×C42—1421no—
553C2×C42C22×D7111yescharacteristic
554#107—714no—
555#106—714no—
556#106—714no—
557C4⋊C8C22×D7114yes—
558#103—714no—
559#103—714no—
560#103—714no—
561#103—714no—
562#103—714no—
563#103—714no—
564#103—714no—
565#103—714no—
566#103—714no—
567#103—714no—
568C22⋊C8C22×D7114yes—
569C22⋊C8C22×D7114yes—
570#97C22×D7114yes—
571C24C2×D28411yescharacteristic
572C24C2×D28411yescharacteristic
573C2×Q8—2848no—
574C2×Q8—2848no—
575C2×Q8—2844no—
576C2×Q8—2844no—
577C2×Q8—2844no—
578C2×Q8—2844no—
579C2×Q8—714no—
580C2×Q8—712no—
581C2×Q8—712no—
582C2×Q8—712no—
583C2×Q8—712no—
584C2×Q8—1428no—
585C2×Q8—1428no—
586C2×Q8—1422no—
587C2×Q8—1422no—
588C2×Q8—1422no—
589C2×Q8—1422no—
590C2×Q8—1422no—
591C2×Q8—1422no—
592C2×Q8—1421no—
593C2×Q8—1421no—
594C2×Q8—1421no—
595C2×Q8—1424no—
596C2×Q8—1424no—
597C2×Q8—1421no—
598C2×Q8—1422no—
599C2×D4—24no—
600C2×D4C2×D28414yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—2844no—
606C22×C4—2844no—
607C22×C4—2844no—
608C22×C4—1424no—
609C22×C4—1424no—
610C22×C4—1424no—
611C22×C4—1421no—
612C22×C4—1421no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1421no—
617C22×C4—1421no—
618C22×C4—1421no—
619C22×C4C2×D28412yes—
620C22×C4C2×D28412yes—
621C22×C4C2×D28411yescharacteristic
622C22×C4C2×D28411yescharacteristic
623C22×C4C2×D28411yescharacteristic
624C22×C4C2×D28411yescharacteristic
625C22×C4C23×D7112yes—
626C22×C4C23×D7112yes—
627C22×C4C23×D7111yescharacteristic
628Q16—2844no—
629Q16—2844no—
630Q16—1428no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D7112yes—
638C2×C8C23×D7112yes—
639C2×C8C23×D7112yes—
640C2×C8C23×D7112yes—
641C4⋊C4—712no—
642C4⋊C4—712no—
643C4⋊C4—712no—
644C4⋊C4—712no—
645C4⋊C4—1424no—
646C4⋊C4—1424no—
647C4⋊C4—1424no—
648C4⋊C4—1424no—
649C4⋊C4—1424no—
650C4⋊C4—1424no—
651C4⋊C4—1424no—
652C4⋊C4—1424no—
653C4⋊C4—1421no—
654C4⋊C4—1421no—
655C4⋊C4—1424no—
656C4⋊C4—1421no—
657C4⋊C4—1421no—
658C4⋊C4—1424no—
659C4⋊C4—1424no—
660C4⋊C4C2×D28414yes—
661C22⋊C4—1424no—
662C22⋊C4—1424no—
663C22⋊C4—1424no—
664C22⋊C4—1424no—
665C22⋊C4—1424no—
666C22⋊C4C2×D28414yes—
667C22⋊C4C2×D28414yes—
668C42—1424no—
669C42—1424no—
670C42—1424no—
671C42C2×D28412yes—
672C42C23×D7112yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1455616114yes—
679C23C22×D28412yes—
680C23C22×D28412yes—
681C23C22×D28411yescharacteristic
682Q8—2848no—
683Q8—2848no—
684Q8—2842no—
685Q8—2842no—
686Q8—2842no—
687Q8—714no—
688Q8—1422no—
689Q8—1422no—
690Q8—1422no—
691Q8—1422no—
692Q8—1422no—
693Q8—1422no—
694Q8—1422no—
695Q8—1424no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—2842no—
708C2×C4—2842no—
709C2×C4—2842no—
710C2×C4—2842no—
711C2×C4—2842no—
712C2×C4—2848no—
713C2×C4—2842no—
714C2×C4—2842no—
715C2×C4—2848no—
716C2×C4—2848no—
717C2×C4—1422no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
725C2×C4—1424no—
726C2×C4C22×D28412yes—
727C2×C4C22×D28412yes—
728C2×C4C22×D28412yes—
729C2×C4C22×D28412yes—
730C2×C4C22×D28411yescharacteristic
731C2×C4#41×D7112yes—
732C2×C4#1455617312yes—
733C2×C4C24×D7111yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1798664412yes—
746C22C2×#1455616114yes—
747C22C2×#1455616112yes—
748C22#1798681612yes—
749C22C23×D28411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—2842no—
755C4—2842no—
756C4—2842no—
757C4—2842no—
758C4—2842no—
759C4—2842no—
760C4—2842no—
761C4—1424no—
762C4#1798664412yes—
763C4C2×#41×D7111yescharacteristic
764C4C2×#1455617311yescharacteristic
765C2—24no—
766C2—42no—
767C2#2260039314yesdirect product factor
768C2C2×#1798664411yescharacteristic
769C2C22×#1455616111yescharacteristic
770C2C2×#1798681611yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
hypercenterC2×#435D71
hypocenterC71C2×#3312
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #22600393C2direct (N × H)
4. C2×#17986368C2semidirect
5. C2×#17986341C2semidirect
6. C2×#17986330C2semidirect
7. C2×#17986307C2semidirect
8. C2×#17986257C2semidirect
9. C2×#17986240C2semidirect
10. C2×#17986210C2semidirect
11. C2×#17986157C2semidirect
12. C2×#17986157C2semidirect
13. C2×#17986107C2semidirect
14. C2×#17986009C2semidirect
15. C22×#14556053C2semidirect
44. #17986368C22semidirect
45. #17986341C22semidirect
46. #17986330C22semidirect
47. #17986307C22semidirect
48. #17986257C22semidirect
49. #17986240C22semidirect
50. #17986210C22semidirect
51. #17986157C22semidirect
52. #17986157C22semidirect
53. #17986107C22semidirect
57. #17986009C22semidirect
68. C2×#14556053C22semidirect
382. C2×C71#3312semidirect
402. C71C2×#3312semidirect
767. C2#22600393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
C2×D4×Dic1422
#226003932
C2×#179863682
C2×#179863412
C2×#179863302
C2×#179863072
C2×#179862572
C2×#179862402
C2×#179862102
C2×#179861572
C2×#179861072
C2×#179860092
C22×#145560532
C2×#435×C712
C2×#331271