Finite Group Databasebeta

← C2×#22600869 #32876078

Subgroups — C2×#22600869 #32876078

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×#17986723C211yesmaximal, characteristic
2C2×#17986687C211yesmaximal, characteristic
3#22600869C2116yesmaximal, direct product factor
4C2×#17986336C211yesmaximal, characteristic, complemented
5C2×#17986343C211yesmaximal, characteristic, complemented
6C2×#17986343C211yesmaximal, characteristic, complemented
7C2×#17986342C211yesmaximal, characteristic, complemented
8C2×#17986303C211yesmaximal, characteristic, complemented
9C2×#17986291C211yesmaximal, characteristic, complemented
10C2×#17986258C211yesmaximal, characteristic, complemented
11C2×#17986241C211yesmaximal, characteristic, complemented
12C2×#17986107C211yesmaximal, characteristic, complemented
13C2×#17986072C211yesmaximal, characteristic
14C2×#17986040C211yesmaximal, characteristic, complemented
15C2×#17986034C211yesmaximal, characteristic, complemented
16C2×#501×C71C211yesmaximal, characteristic, complemented
17C22×Dic284C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986723—24no—
21#17986723C2218yes—
22#17986687—24no—
23#17986687C2218yes—
24C2×#14556123—21no—
25C2×#14556123—21no—
26C2×#14556123—21no—
27C2×#14556119—21no—
28C2×#14556117—21no—
29C2×#14556113—21no—
30C2×#14556108C2211yescharacteristic
31C2×#14556108C2211yescharacteristic
32C2×#14556108C2211yescharacteristic
33C2×#14556108C2211yescharacteristic
34C2×Q8×Dic71—21no—
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×Dic142C2211yescharacteristic
37C2×C4×D284C2211yescharacteristic
38C2×#14556086—21no—
39C2×#14556086C2211yescharacteristic
40C2×#14556086C2211yescharacteristic
41C2×#14556086C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986343C2218yescomplemented
44#17986343C2218yescomplemented
45#17986342C2218yescomplemented
46#17986336C2218yescomplemented
47#17986303C2218yescomplemented
48#17986291C2218yescomplemented
49#17986258C2218yescomplemented
50#17986241C2218yescomplemented
51#17986107C2218yescomplemented
52#17986072C2218yes—
53#17986040C2218yescomplemented
54#17986034C2218yescomplemented
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×C4⋊(C71⋊C8)C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556051C2211yescharacteristic
65C2×#14556051C2211yescharacteristic
66C2×#14556051C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×#125×C71C2211yescharacteristic
71#501×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#106×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C22×D284D411yescharacteristic
80C22×C4×D71—21no—
81C22×C4×D71C2311yescharacteristic
82C22×C4×D71C2311yescharacteristic
83C2×Dic284—24no—
84C2×Dic284C2314yes—
85C2×#11765848—24no—
86C2×#11765848C2314yes—
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89C2×C8×D71—24no—
90C2×C8×D71C2314yes—
91#14556123—28no—
92#14556123—28no—
93#14556123—28no—
94#14556119—28no—
95#14556117—28no—
96#14556113—28no—
97#14556108—22no—
98#14556108—22no—
99#14556108—22no—
100#14556108—22no—
101#14556108C2314yes—
102#14556108C2314yes—
103#14556108C2314yes—
104#14556108C2314yes—
105Q8×Dic71—28no—
106C4×Dic142—22no—
107C4×Dic142—22no—
108C4×Dic142C2314yes—
109C4×Dic142C2314yes—
110C4×D284D414yes—
111C4×D284C2314yes—
112#14556086—22no—
113#14556086—22no—
114#14556086—22no—
115#14556086—28no—
116#14556086C2314yes—
117#14556086C2314yes—
118#14556086C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71—21no—
123C2×C4⋊Dic71D411yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C4⋊C4×D71—22no—
130C4⋊C4×D71C2314yes—
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×(C2×D71)⋊C4D411yescharacteristic
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71—21no—
145#14556061C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556060C2314yes—
149#14556059C2314yes—
150C4⋊(C71⋊C8)C2314yes—
151#14556053C2314yes—
152#14556053C2314yes—
153#14556051C2314yes—
154#14556051C2314yes—
155#14556051C2314yes—
156#14556051C2314yes—
157(C2×D71)⋊C8C2314yes—
158(C2×D71)⋊C8C2314yes—
159C22×Q8×C71—21no—
160C22×C8×C71C2311yescharacteristic
161C22×C8×C71C2311yescharacteristic
162C4⋊Q8×C71—22no—
163C4⋊Q8×C71C2314yes—
164#125×C71—22no—
165#125×C71C2314yes—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71C2311yescharacteristic
174#107×C71C2314yes—
175#107×C71C2314yes—
176#106×C71C2314yes—
177#106×C71C2314yes—
178#97×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C23×D71C2×D411yescharacteristic
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142—21no—
187C2×Dic142C2412yes—
188C2×Dic142C2412yes—
189C2×D284—42no—
190C2×D284C2×D414yes—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C2×C4×D71—22no—
198C2×C4×D71—22no—
199C2×C4×D71—22no—
200C2×C4×D71—22no—
201C2×C4×D71—24no—
202C2×C4×D71—44no—
203C2×C4×D71C2×D412yes—
204C2×C4×D71C2×D412yes—
205C2×C4×D71C2412yes—
206C2×C4×D71C2412yes—
207Dic284—28no—
208#11765848—28no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8—22no—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C8×D71—28no—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71—24no—
219C4⋊Dic71—24no—
220C4⋊Dic71C2×D414yes—
221C4⋊Dic71C2412yes—
222C4⋊Dic71C2412yes—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4C2×D414yes—
234(C2×D71)⋊C4C2×D414yes—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71—24no—
238C4×Dic71—24no—
239C4×Dic71—24no—
240C2×Q8×C71—24no—
241C2×Q8×C71—44no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2411yescharacteristic
249C2×C8×C71—22no—
250C2×C8×C71#4114yes—
251C2×C8×C71C2412yes—
252C2×C8×C71C2412yes—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C42×C71C2×D412yes—
265C42×C71C2412yes—
266C23×C71C22×D411yescharacteristic
267C22×D71—22no—
268C22×D71—22no—
269C22×D71—22no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71C22×D412yes—
274C22×D71C22×D412yes—
275Q8×C71—48no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71—42no—
285C2×C4×C71—42no—
286C2×C4×C71C22×D412yes—
287C2×C4×C71C22×D412yes—
288C2×C4×C71C22×D411yescharacteristic
289C2×C4×C71C2×#4112yes—
290C2×C4×C712−1+412yes—
291C2×C4×C71C2511yescharacteristic
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71C22×D412yes—
303C2×Dic71C22×D412yes—
304D284—44no—
305C4×D71—24no—
306C4×D71—24no—
307C4×D71—22no—
308C4×D71—22no—
309C4×D71—22no—
310C4×D71—22no—
311C4×D71—48no—
312Dic142—22no—
313Dic142—22no—
314Dic142—22no—
315Dic142—22no—
316Dic142—42no—
317Dic142—42no—
318C8×C71—22no—
319C8×C71C2×#4114yes—
320C71⋊C8—22no—
321C71⋊C8—22no—
322C22×C71#54712yes—
323C22×C71#57512yes—
324C22×C71#57812yes—
325C22×C71C23×D411yescharacteristic
326C2×D71—22no—
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—44no—
333C2×D71—44no—
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71#54712yes—
341C4×C71C22×#4111yescharacteristic
342C4×C71C2×2−1+411yescharacteristic
343Dic71—22no—
344Dic71—22no—
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71—42no—
349C2×#3349—711nomaximal, Sylow
350C2×C71#334914yescomplemented
351C2×C71C2×#54711yescharacteristic
352C2×C71C2×#57511yescharacteristic
353C2×C71C2×#57811yescharacteristic
354D71—42no—
355D71—42no—
356C2×#556—711no—
357C2×#552—711no—
358#3349—7116no—
359C2×#501D7111yescharacteristic, complemented
360C2×#484—711no—
361C2×#485—711no—
362C2×#485—711no—
363C2×#485—711no—
364C2×#479—711no—
365C2×#477—711no—
366C2×#470—711no—
367C2×#467—711no—
368C2×#441—711no—
369C2×#435—711no—
370C2×#428—711no—
371C2×#427—711no—
372C71C2×#334911yescharacteristic, complemented, Sylow
373C22×Q16—711no—
374C22×M16—711no—
375C23×C8—711no—
376#556—718no—
377#556—1424no—
378#552—718no—
379#552—1424no—
380C2×C4⋊Q8C2×D7111yescharacteristic
381C2×#126—1421no—
382C2×#126—1421no—
383C2×#126—1421no—
384C2×#125—1421no—
385C2×#125C2×D7111yescharacteristic
386C2×#124—1421no—
387C2×#123—1421no—
388C2×C22⋊Q8—711no—
389C2×C22⋊Q8—711no—
390C2×C22⋊Q8—711no—
391C2×C22⋊Q8—711no—
392C2×C4×Q8—711no—
393C2×C4×Q8—711no—
394C2×C4×Q8—1421no—
395C2×C4×D4—711no—
396C2×#117—711no—
397C2×#117—711no—
398C2×#117—711no—
399C2×#117—1421no—
400C22×C4⋊C4—711no—
401#501C2×D7118yescomplemented
402#485—718no—
403#485—718no—
404#485—718no—
405#484—718no—
406#479—718no—
407#477—718no—
408#470—718no—
409#467—718no—
410#441—718no—
411#435—718no—
412#428—718no—
413#427—718no—
414C2×#107—711no—
415C2×#107—711no—
416C2×#107—711no—
417C2×#107C2×D7111yescharacteristic
418C2×#107C2×D7111yescharacteristic
419C2×#106—711no—
420C2×#106—711no—
421C2×#106C2×D7111yescharacteristic
422C2×#106C2×D7111yescharacteristic
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×#97C2×D7111yescharacteristic
433C22×Q8—21no—
434C22×Q8—711no—
435C22×Q8—711no—
436C22×D4—711no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—1421no—
440C2×Q16—714no—
441C2×Q16—1424no—
442C2×M16—714no—
443C2×M16—1424no—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8—714no—
447C22×C8—1424no—
448C22×C8C22×D7111yescharacteristic
449C22×C8C22×D7111yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8C22×D7114yes—
452#126—1428no—
453#126—1428no—
454#126—1428no—
455#125—22no—
456#125—1428no—
457#125C22×D7114yes—
458#124—1428no—
459#123—1428no—
460C22⋊Q8—714no—
461C22⋊Q8—714no—
462C22⋊Q8—714no—
463C22⋊Q8—714no—
464C22⋊Q8—1422no—
465C22⋊Q8—1422no—
466C22⋊Q8—1422no—
467C22⋊Q8—1422no—
468C4×Q8—714no—
469C4×Q8—714no—
470C4×Q8—1428no—
471C4×Q8—1422no—
472C4×Q8—1422no—
473C4×D4—714no—
474C4×D4—714no—
475#117—714no—
476#117—714no—
477#117—714no—
478#117—1428no—
479#117—1422no—
480#117—1422no—
481#117—1422no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4—1422no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4C22×D7111yescharacteristic
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—711no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4—1421no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C42—1421no—
511C2×C42—1421no—
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42—1421no—
515C2×C42C22×D7111yescharacteristic
516#107—714no—
517#107—714no—
518#107—714no—
519#107C22×D7114yes—
520#107C22×D7114yes—
521#106—714no—
522#106—714no—
523#106C22×D7114yes—
524#106C22×D7114yes—
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—
534#97C22×D7114yes—
535C24—711no—
536C24—711no—
537C2×Q8—24no—
538C2×Q8—44no—
539C2×Q8—712no—
540C2×Q8—712no—
541C2×Q8—1422no—
542C2×Q8—1422no—
543C2×Q8—1422no—
544C2×Q8—1422no—
545C2×Q8—1421no—
546C2×Q8—1421no—
547C2×D4—2842no—
548C2×D4—714no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—2844no—
554C22×C4—711no—
555C22×C4—711no—
556C22×C4—712no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—1424no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1422no—
566C22×C4—1422no—
567C22×C4—1422no—
568C22×C4—1422no—
569C22×C4D4×D7111yescharacteristic
570C22×C4D4×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572Q16—1428no—
573M16—1428no—
574C2×C8—22no—
575C2×C8—712no—
576C2×C8—712no—
577C2×C8—1422no—
578C2×C8—1422no—
579C2×C8—1428no—
580C2×C8#1176586614yes—
581C2×C8C23×D7112yes—
582C2×C8C23×D7112yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—714no—
591C4⋊C4—712no—
592C4⋊C4—712no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1421no—
601C4⋊C4—1421no—
602C4⋊C4C23×D7112yes—
603C4⋊C4C23×D7112yes—
604C4⋊C4C23×D7112yes—
605C4⋊C4C23×D7112yes—
606C22⋊C4—714no—
607C22⋊C4—714no—
608C22⋊C4—1424no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C22⋊C4—1424no—
612C22⋊C4—1424no—
613C22⋊C4—1424no—
614C22⋊C4—1424no—
615C42—1424no—
616C42—1424no—
617C42—1424no—
618C42—1424no—
619C42—1424no—
620C42D4×D7112yes—
621C42C23×D7112yes—
622C23—712no—
623C23—712no—
624C23—1422no—
625C23—1422no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23—1422no—
630C23C2×D4×D7111yescharacteristic
631Q8—48no—
632Q8—2842no—
633Q8—2842no—
634Q8—1422no—
635Q8—1422no—
636Q8—1422no—
637Q8—1422no—
638D4—2844no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—2848no—
650C2×C4—2842no—
651C2×C4—2842no—
652C2×C4—2842no—
653C2×C4—2842no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—1422no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1424no—
667C2×C4—1424no—
668C2×C4C2×D4×D7112yes—
669C2×C4C2×D4×D7112yes—
670C2×C4C2×D4×D7111yescharacteristic
671C2×C4C2×#1176586612yes—
672C2×C4#1455617612yes—
673C2×C4C24×D7111yescharacteristic
674C8—22no—
675C8—1422no—
676C8—1422no—
677C8C2×#1176586614yes—
678C22—2844no—
679C22—2844no—
680C22—1422no—
681C22—1422no—
682C22—1422no—
683C22—1422no—
684C22—1422no—
685C22—1422no—
686C22#1798665212yes—
687C22#1798679512yes—
688C22#1798681512yes—
689C22C22×D4×D7111yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—2842no—
697C4—2842no—
698C4—2842no—
699C4—2842no—
700C4—1422no—
701C4—1422no—
702C4#1798665212yes—
703C4C22×#1176586611yescharacteristic
704C4C2×#1455617611yescharacteristic
705C2—2842no—
706C2—2842no—
707C2#2260086914yesdirect product factor
708C2C2×#1798665211yescharacteristic
709C2C2×#1798679511yescharacteristic
710C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#501×C71C2
socleC23×C71C22×D4
prime radicalC22×D284D4
hypercenterC2×#501D71
hypocenterC71C2×#3349
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #22600869C2direct (N × H)
4. C2×#17986336C2semidirect
5. C2×#17986343C2semidirect
6. C2×#17986343C2semidirect
7. C2×#17986342C2semidirect
8. C2×#17986303C2semidirect
9. C2×#17986291C2semidirect
10. C2×#17986258C2semidirect
11. C2×#17986241C2semidirect
12. C2×#17986107C2semidirect
14. C2×#17986040C2semidirect
15. C2×#17986034C2semidirect
16. C2×#501×C71C2semidirect
43. #17986343C22semidirect
44. #17986343C22semidirect
45. #17986342C22semidirect
46. #17986336C22semidirect
47. #17986303C22semidirect
48. #17986291C22semidirect
49. #17986258C22semidirect
50. #17986241C22semidirect
51. #17986107C22semidirect
53. #17986040C22semidirect
54. #17986034C22semidirect
71. #501×C71C22semidirect
350. C2×C71#3349semidirect
359. C2×#501D71semidirect
372. C71C2×#3349semidirect
401. #501C2×D71semidirect
707. C2#22600869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867232
C2×#179866872
#226008692
C2×#179863362
C2×#179863432
C2×#179863422
C2×#179863032
C2×#179862912
C2×#179862582
C2×#179862412
C2×#179861072
C2×#179860722
C2×#179860402
C2×#179860342
C2×#501×C712
C2×#334971