Finite Group Databasebeta

← #32861433

Subgroups — #32861433

Order 18176.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986766C211yesmaximal, characteristic, complemented
2C22×#14556135C211yesmaximal, characteristic, complemented
3#22597084C213yesmaximal, complemented
4D4×#11765849C213yesmaximal, complemented
5#22597067C213yesmaximal, complemented
6#22597067C213yesmaximal, complemented
7#22597058C213yesmaximal, complemented
8#22597044C213yesmaximal, complemented
9#22597035C213yesmaximal, complemented
10C2×#17986071C213yesmaximal, complemented
11#22596908C211yesmaximal, characteristic, complemented
12#22596789C211yesmaximal, characteristic, complemented
13#22596789C211yesmaximal, characteristic, complemented
14#22596768C211yesmaximal, characteristic, complemented
15D4×#41×C71C211yesmaximal, characteristic
16#17986766—28no—
17C2×#14556135—28no—
18C2×#14556135C2211yescharacteristic
19C2×#14556135C2211yescharacteristic
20C2×#14556135C2211yescharacteristic
21C2×#14556135C2211yescharacteristic
22C2×#14556135C2213yescomplemented
23C2×#14556135C2213yescomplemented
24C2×#14556135C2213yescomplemented
25C2×#14556135C2213yescomplemented
26C22×#11765849C2213yescomplemented
27C22×#11765849C2213yescomplemented
28C22×#11765849C2213yescomplemented
29C23×C71⋊C8C2213yescomplemented
30#17986077C2216yescomplemented
31#17986077C2216yescomplemented
32#17986071C2211yescharacteristic
33#17986071C2213yes—
34#17986071C2213yescomplemented
35#17986071C2213yescomplemented
36#17986071C2213yescomplemented
37#17986071C2213yescomplemented
38#17986071C2213yescomplemented
39#17986071C2213yescomplemented
40#17986071C2216yescomplemented
41#17986071C2216yescomplemented
42#17986071C2216yescomplemented
43D4×C71⋊C8C2216yescomplemented
44D4×C71⋊C8C2216yescomplemented
45#17986026C2213yescomplemented
46#17986026C2213yescomplemented
47#17986023C2213yescomplemented
48C2×C4⋊(C71⋊C8)C2213yescomplemented
49#17985966C2213yescomplemented
50#17985966C2213yescomplemented
51#17985966C2213yescomplemented
52#17985966C2213yescomplemented
53#17985963C2213yescomplemented
54#17985963C2213yescomplemented
55C2×C22⋊(C71⋊C8)C2213yescomplemented
56C2×C22⋊(C71⋊C8)C2213yescomplemented
57#17985955C2213yescomplemented
58#17985955C2213yescomplemented
59C4×#11765849C2213yescomplemented
60C2×#14556039C2213yescomplemented
61C22×#41×C71C2211yescharacteristic
62C22×#41×C71C2211yescharacteristic
63#550×C71C411yescharacteristic
64D4×Q8×C71C411yescharacteristic
65#548×C71C411yescharacteristic
66#548×C71C411yescharacteristic
67#547×C71C413yes—
68#546×C71C413yes—
69#546×C71C413yes—
70D42×C71C413yes—
71#532×C71C2213yes—
72#525×C71C2213yes—
73#525×C71C2213yes—
74C4×#41×C71C2211yescharacteristic
75C2×C4×D4×C71C2213yes—
76#14556135—212no—
77#14556135—212no—
78#14556135—212no—
79#14556135—212no—
80#14556135—24no—
81#14556135—24no—
82#14556135—24no—
83#14556135D418yescomplemented
84C2×#11765849—212no—
85C2×#11765849—212no—
86C2×#11765849—212no—
87C2×#11765849C2311yescharacteristic
88C2×#11765849C2313yes—
89C2×#11765849C2313yes—
90C2×#11765849C2313yes—
91C2×#11765849C2316yes—
92C2×#11765849C2313yes—
93C2×#11765849C2313yes—
94C2×#11765849C2313yes—
95C2×#11765849C2313yes—
96C22×C71⋊C8—212no—
97C22×C71⋊C8C2313yes—
98C22×C71⋊C8C2313yes—
99C22×C71⋊C8C2316yes—
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2313yes—
102C22×C71⋊C8C2313yes—
103C22×C71⋊C8C2313yes—
104C22×C71⋊C8C2313yes—
105C22×C71⋊C8C2313yes—
106C4⋊(C71⋊C8)C2313yes—
107C4⋊(C71⋊C8)C2316yes—
108C4⋊(C71⋊C8)C2311yescharacteristic
109C4⋊(C71⋊C8)C2313yes—
110C4⋊(C71⋊C8)C2313yes—
111C22⋊(C71⋊C8)C2313yes—
112C22⋊(C71⋊C8)C2313yes—
113C22⋊(C71⋊C8)C2316yes—
114C22⋊(C71⋊C8)C2316yes—
115C22⋊(C71⋊C8)C2311yescharacteristic
116C22⋊(C71⋊C8)C2311yescharacteristic
117C22⋊(C71⋊C8)C2313yes—
118C22⋊(C71⋊C8)C2313yes—
119C22⋊(C71⋊C8)C2313yes—
120C22⋊(C71⋊C8)C2313yes—
121#14556039C2311yescharacteristic
122#14556039C2313yes—
123#14556039C2313yes—
124#14556039C2313yes—
125C4×C71⋊C8C2316yes—
126C2×#41×C71—24no—
127C2×#41×C71—24no—
128C2×#41×C71—24no—
129C2×#41×C71—24no—
130C2×#41×C71C2×C413yes—
131C2×#41×C71C2×C413yes—
132C2×#41×C71C2×C411yescharacteristic
133C2×#41×C71C2×C411yescharacteristic
134C2×#41×C71C2313yes—
135C2×#41×C71C2313yes—
136C2×#41×C71C2311yescharacteristic
137C22×Q8×C71C2×C411yescharacteristic
138C22×Q8×C71C2×C411yescharacteristic
139C22×D4×C71C2×C413yes—
140C22×D4×C71C2×C413yes—
141C22×D4×C71C2×C413yes—
142C23×C4×C71C2313yes—
143C23×C4×C71C2313yes—
144C4⋊Q8×C71C2×C413yes—
145#127×C71C2×C413yes—
146#124×C71C2×C413yes—
147#124×C71C2×C413yes—
148#123×C71C2×C416yes—
149#123×C71C2×C416yes—
150C22⋊Q8×C71C2×C413yes—
151C22⋊Q8×C71C2×C413yes—
152C22⋊Q8×C71C2×C413yes—
153C22⋊Q8×C71C2×C413yes—
154#121×C71C2×C413yes—
155#121×C71C2×C413yes—
156#121×C71C2×C413yes—
157#121×C71C2×C413yes—
158#121×C71C2×C416yes—
159#121×C71C2×C416yes—
160#120×C71C2×C416yes—
161#120×C71C2×C416yes—
162C4×Q8×C71C2×C411yescharacteristic
163C4×Q8×C71C2×C411yescharacteristic
164C4×D4×C71C2×C413yes—
165C4×D4×C71C2×C413yes—
166C4×D4×C71C2×C413yes—
167C4×D4×C71C2×C413yes—
168C4×D4×C71C2×C413yes—
169C4×D4×C71C2×C413yes—
170C4×D4×C71C2313yes—
171C4×D4×C71C2316yes—
172C4×D4×C71C2311yescharacteristic
173C4×D4×C71C2313yes—
174C4×D4×C71C2313yes—
175#117×C71C2313yes—
176C2×C4⋊C4×C71C2×C413yes—
177C2×C22⋊C4×C71C2×C413yes—
178C2×C22⋊C4×C71C2×C413yes—
179C2×C42×C71C2313yes—
180#11765849—26no—
181#11765849—26no—
182#11765849—26no—
183#11765849—22no—
184#11765849—26no—
185#11765849—26no—
186#11765849—212no—
187#11765849—26no—
188#11765849C2×D4112yescomplemented
189C2×C71⋊C8—26no—
190C2×C71⋊C8—26no—
191C2×C71⋊C8—26no—
192C2×C71⋊C8—22no—
193C2×C71⋊C8—26no—
194C2×C71⋊C8—26no—
195C2×C71⋊C8—26no—
196C2×C71⋊C8—212no—
197C2×C71⋊C8C2×D4112yescomplemented
198C2×C71⋊C8C2413yes—
199C2×C71⋊C8C2411yescharacteristic
200C2×C71⋊C8C2411yescharacteristic
201C2×C71⋊C8C2413yes—
202C2×C71⋊C8C2413yes—
203C2×C71⋊C8C2411yescharacteristic
204C2×C71⋊C8C2413yes—
205C2×C71⋊C8C2411yescharacteristic
206C24×C71C22×C413yes—
207C24×C71C22×C413yes—
208#41×C71—24no—
209#41×C71—24no—
210#41×C71—212no—
211#41×C71—212no—
212#41×C71—26no—
213#41×C71—26no—
214#41×C71—26no—
215#41×C71—26no—
216#41×C71C2×D414yes—
217#41×C71#4114yes—
218C2×Q8×C71—24no—
219C2×Q8×C71—24no—
220C2×Q8×C71C22×C413yes—
221C2×Q8×C71C22×C413yes—
222C2×Q8×C71C22×C411yescharacteristic
223C2×D4×C71—212no—
224C2×D4×C71—212no—
225C2×D4×C71—46no—
226C2×D4×C71C22×C411yescharacteristic
227C2×D4×C71C22×C413yes—
228C2×D4×C71C22×C416yes—
229C2×D4×C71C22×C416yes—
230C2×D4×C71C22×C413yes—
231C2×D4×C71C22×C413yes—
232C2×D4×C71C22×C413yes—
233C2×D4×C71C22×C413yes—
234C2×D4×C71C22×C416yes—
235C2×D4×C71C22×C413yes—
236C22×C4×C71—26no—
237C22×C4×C71—26no—
238C22×C4×C71—26no—
239C22×C4×C71—26no—
240C22×C4×C71C22×C413yes—
241C22×C4×C71C22×C413yes—
242C22×C4×C71C22×C413yes—
243C22×C4×C71C22×C413yes—
244C22×C4×C71C22×C413yes—
245C22×C4×C71C22×C413yes—
246C22×C4×C71C22×C413yes—
247C22×C4×C71C22×C413yes—
248C22×C4×C71C2411yescharacteristic
249C22×C4×C71C2411yescharacteristic
250C22×C4×C71C2413yes—
251C22×C4×C71C2413yes—
252C22×C4×C71C2413yes—
253C4⋊C4×C71C22×C411yescharacteristic
254C4⋊C4×C71C22×C413yes—
255C4⋊C4×C71C22×C413yes—
256C4⋊C4×C71C22×C413yes—
257C4⋊C4×C71C22×C413yes—
258C4⋊C4×C71C22×C413yes—
259C4⋊C4×C71C22×C416yes—
260C22⋊C4×C71C22×C411yescharacteristic
261C22⋊C4×C71C22×C411yescharacteristic
262C22⋊C4×C71C22×C413yes—
263C22⋊C4×C71C22×C413yes—
264C22⋊C4×C71C22×C413yes—
265C22⋊C4×C71C22×C413yes—
266C22⋊C4×C71C22×C413yes—
267C22⋊C4×C71C22×C413yes—
268C22⋊C4×C71C22×C416yes—
269C22⋊C4×C71C22×C416yes—
270C22⋊C4×C71C22×C416yes—
271C42×C71C22×C413yes—
272C42×C71C22×C413yes—
273C42×C71C2411yescharacteristic
274C42×C71C2413yes—
275C23×C71—26no—
276C23×C71—26no—
277C23×C71—26no—
278C23×C71—43no—
279C23×C71—43no—
280C23×C71—43no—
281C23×C71C23×C411yescharacteristic
282C23×C71C23×C413yes—
283C23×C71C23×C413yes—
284C23×C71C23×C413yes—
285C23×C71C23×C411yescharacteristic
286Q8×C71—26no—
287Q8×C71—26no—
288Q8×C71C4×D414yes—
289D4×C71—212no—
290D4×C71—212no—
291D4×C71—22no—
292D4×C71—26no—
293D4×C71—26no—
294D4×C71—26no—
295D4×C71—43no—
296D4×C71—43no—
297D4×C71—46no—
298D4×C71C4×D4112yes—
299C2×C4×C71—26no—
300C2×C4×C71—26no—
301C2×C4×C71—26no—
302C2×C4×C71—26no—
303C2×C4×C71—26no—
304C2×C4×C71—26no—
305C2×C4×C71—21no—
306C2×C4×C71—21no—
307C2×C4×C71—23no—
308C2×C4×C71—23no—
309C2×C4×C71—21no—
310C2×C4×C71—21no—
311C2×C4×C71—23no—
312C2×C4×C71—23no—
313C2×C4×C71—43no—
314C2×C4×C71—43no—
315C2×C4×C71C23×C411yescharacteristic
316C2×C4×C71C23×C411yescharacteristic
317C2×C4×C71C23×C413yes—
318C2×C4×C71C23×C413yes—
319C2×C4×C71C23×C411yescharacteristic
320C2×C4×C71C23×C411yescharacteristic
321C2×C4×C71C23×C413yes—
322C2×C4×C71C23×C413yes—
323C2×C4×C71C23×C413yes—
324C2×C4×C71C22×D416yes—
325C2×C4×C71C2×#4116yes—
326C2×C4×C71C2511yescharacteristic
327C71⋊C8—21no—
328C71⋊C8—23no—
329C71⋊C8—21no—
330C71⋊C8—23no—
331C71⋊C8—21no—
332C71⋊C8—23no—
333C71⋊C8C22×D412yes—
334C71⋊C8C22×D416yes—
335C22×C71—21no—
336C22×C71—23no—
337C22×C71—23no—
338C22×C71—21no—
339C22×C71—21no—
340C22×C71—23no—
341C22×C71—23no—
342C22×C71—21no—
343C22×C71—23no—
344C22×C71—23no—
345C22×C71—23no—
346C22×C71—23no—
347C22×C71—21no—
348C22×C71—412no—
349C22×C71—86no—
350C22×C71C2×C4×D416yes—
351C22×C71#56812yescomplemented
352C22×C71C24×C411yescharacteristic
353C4×C71—21no—
354C4×C71—21no—
355C4×C71—23no—
356C4×C71—23no—
357C4×C71—21no—
358C4×C71—23no—
359C4×C71—21no—
360C4×C71—23no—
361C4×C71C2×C4×D416yes—
362C4×C71C23×D411yescharacteristic
363C4×C71C22×#4111yescharacteristic
364#60146—711nomaximal, Sylow
365C2×C71—22no—
366C2×C71—26no—
367C2×C71—43no—
368C2×C71—43no—
369C2×C71—41no—
370C2×C71C22×C4×D411yescharacteristic
371C2×C71C2×#56811yescharacteristic
372C2×C71#357311yescharacteristic
373C2×#568—711no—
374C22×#131—711no—
375D4×#41D7111yescharacteristic
376#2935—713no—
377D4×M16—713no—
378#2933—713no—
379#2933—713no—
380#2932—713no—
381#2930—713no—
382#2929—713no—
383C2×#435—713no—
384#2906—711no—
385#2880—711no—
386#2880—711no—
387#2875—711no—
388C71#6014611yescharacteristic, complemented, Sylow
389C22×#41C2×D7111yescharacteristic
390C22×#41C2×D7111yescharacteristic
391#568—1428no—
392C2×#131—711no—
393C2×#131—711no—
394C2×#131—711no—
395C2×#131—711no—
396C2×#131—713no—
397C2×#131—713no—
398C2×#131—713no—
399C2×#131—713no—
400C2×#131—1428no—
401C22×M16—713no—
402C22×M16—713no—
403C22×M16—713no—
404C23×C8—713no—
405#550Dic7111yescharacteristic
406D4×Q8Dic7111yescharacteristic
407#548Dic7111yescharacteristic
408#548Dic7111yescharacteristic
409#547Dic7113yes—
410#546Dic7113yes—
411#546Dic7113yes—
412D42Dic7113yes—
413#532C2×D7113yes—
414#525C2×D7113yes—
415#525C2×D7113yes—
416C4×#41C2×D7111yescharacteristic
417C2×C4×D4C2×D7113yes—
418#436—716no—
419#436—716no—
420#435—711no—
421#435—713no—
422#435—713no—
423#435—713no—
424#435—713no—
425#435—713no—
426#435—713no—
427#435—713no—
428#435—716no—
429#435—716no—
430#435—716no—
431C8×D4—716no—
432C8×D4—716no—
433#424—713no—
434#424—713no—
435#423—713no—
436C2×C4⋊C8—713no—
437#408—713no—
438#408—713no—
439#408—713no—
440#408—713no—
441#407—713no—
442#407—713no—
443C2×C22⋊C8—713no—
444C2×C22⋊C8—713no—
445#405—713no—
446#405—713no—
447C4×M16—713no—
448C2×#97—713no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic7113yes—
454C2×#41C2×Dic7113yes—
455C2×#41C2×Dic7111yescharacteristic
456C2×#41C2×Dic7111yescharacteristic
457C2×#41C22×D7113yes—
458C2×#41C22×D7113yes—
459C2×#41C22×D7111yescharacteristic
460C22×Q8C2×Dic7111yescharacteristic
461C22×Q8C2×Dic7111yescharacteristic
462C22×D4C2×Dic7113yes—
463C22×D4C2×Dic7113yes—
464C22×D4C2×Dic7113yes—
465C23×C4C22×D7113yes—
466C23×C4C22×D7113yes—
467#131—718no—
468#131—14212no—
469#131—14212no—
470#131—14212no—
471#131—14212no—
472#131—1424no—
473#131—1424no—
474#131—1424no—
475C2×M16—713no—
476C2×M16—711no—
477C2×M16—713no—
478C2×M16—713no—
479C2×M16—713no—
480C2×M16—713no—
481C2×M16—713no—
482C2×M16—716no—
483C2×M16—713no—
484C2×M16—14212no—
485C2×M16—14212no—
486C2×M16—14212no—
487C22×C8—713no—
488C22×C8—711no—
489C22×C8—713no—
490C22×C8—713no—
491C22×C8—713no—
492C22×C8—713no—
493C22×C8—713no—
494C22×C8—716no—
495C22×C8—713no—
496C22×C8—14212no—
497C4⋊Q8C2×Dic7113yes—
498#127C2×Dic7113yes—
499#124C2×Dic7113yes—
500#124C2×Dic7113yes—
501#123C2×Dic7116yes—
502#123C2×Dic7116yes—
503C22⋊Q8C2×Dic7113yes—
504C22⋊Q8C2×Dic7113yes—
505C22⋊Q8C2×Dic7113yes—
506C22⋊Q8C2×Dic7113yes—
507#121C2×Dic7113yes—
508#121C2×Dic7113yes—
509#121C2×Dic7113yes—
510#121C2×Dic7113yes—
511#121C2×Dic7116yes—
512#121C2×Dic7116yes—
513#120C2×Dic7116yes—
514#120C2×Dic7116yes—
515C4×Q8C2×Dic7111yescharacteristic
516C4×Q8C2×Dic7111yescharacteristic
517C4×D4C2×Dic7113yes—
518C4×D4C2×Dic7113yes—
519C4×D4C2×Dic7113yes—
520C4×D4C2×Dic7113yes—
521C4×D4C2×Dic7113yes—
522C4×D4C2×Dic7113yes—
523C4×D4C22×D7111yescharacteristic
524C4×D4C22×D7113yes—
525C4×D4C22×D7113yes—
526C4×D4C22×D7113yes—
527C4×D4C22×D7116yes—
528#117C22×D7113yes—
529C2×C4⋊C4C2×Dic7113yes—
530C2×C22⋊C4C2×Dic7113yes—
531C2×C22⋊C4C2×Dic7113yes—
532C2×C42C22×D7113yes—
533C4⋊C8—711no—
534C4⋊C8—713no—
535C4⋊C8—713no—
536C4⋊C8—713no—
537C4⋊C8—716no—
538C22⋊C8—711no—
539C22⋊C8—711no—
540C22⋊C8—713no—
541C22⋊C8—713no—
542C22⋊C8—713no—
543C22⋊C8—713no—
544C22⋊C8—713no—
545C22⋊C8—713no—
546C22⋊C8—716no—
547C22⋊C8—716no—
548#97—711no—
549#97—713no—
550#97—713no—
551#97—713no—
552C4×C8—716no—
553C24C22×Dic7113yes—
554C24C22×Dic7113yes—
555#41—24no—
556#41—24no—
557#41—212no—
558#41—212no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41—26no—
563#41D4×D7114yes—
564#41#1176586414yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic7113yes—
568C2×Q8C22×Dic7113yes—
569C2×Q8C22×Dic7111yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic7111yescharacteristic
574C2×D4C22×Dic7113yes—
575C2×D4C22×Dic7116yes—
576C2×D4C22×Dic7116yes—
577C2×D4C22×Dic7113yes—
578C2×D4C22×Dic7113yes—
579C2×D4C22×Dic7113yes—
580C2×D4C22×Dic7113yes—
581C2×D4C22×Dic7116yes—
582C2×D4C22×Dic7113yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic7113yes—
588C22×C4C22×Dic7113yes—
589C22×C4C22×Dic7113yes—
590C22×C4C22×Dic7113yes—
591C22×C4C22×Dic7113yes—
592C22×C4C22×Dic7113yes—
593C22×C4C22×Dic7113yes—
594C22×C4C22×Dic7113yes—
595C22×C4C23×D7111yescharacteristic
596C22×C4C23×D7113yes—
597C22×C4C23×D7113yes—
598C22×C4C23×D7111yescharacteristic
599C22×C4C23×D7113yes—
600M16—7112no—
601M16—1422no—
602M16—1426no—
603M16—1426no—
604M16—1426no—
605M16—14212no—
606M16—1426no—
607M16—1426no—
608M16—1426no—
609C2×C8—7112no—
610C2×C8—713no—
611C2×C8—711no—
612C2×C8—713no—
613C2×C8—711no—
614C2×C8—711no—
615C2×C8—711no—
616C2×C8—713no—
617C2×C8—713no—
618C2×C8—1422no—
619C2×C8—1426no—
620C2×C8—1426no—
621C2×C8—1426no—
622C2×C8—14212no—
623C2×C8—1426no—
624C2×C8—1426no—
625C2×C8—1426no—
626C4⋊C4C22×Dic7111yescharacteristic
627C4⋊C4C22×Dic7113yes—
628C4⋊C4C22×Dic7113yes—
629C4⋊C4C22×Dic7113yes—
630C4⋊C4C22×Dic7113yes—
631C4⋊C4C22×Dic7113yes—
632C4⋊C4C22×Dic7116yes—
633C22⋊C4C22×Dic7111yescharacteristic
634C22⋊C4C22×Dic7111yescharacteristic
635C22⋊C4C22×Dic7113yes—
636C22⋊C4C22×Dic7113yes—
637C22⋊C4C22×Dic7113yes—
638C22⋊C4C22×Dic7113yes—
639C22⋊C4C22×Dic7113yes—
640C22⋊C4C22×Dic7113yes—
641C22⋊C4C22×Dic7116yes—
642C22⋊C4C22×Dic7116yes—
643C22⋊C4C22×Dic7116yes—
644C42C22×Dic7113yes—
645C42C22×Dic7113yes—
646C42C23×D7113yes—
647C42C23×D7111yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic7111yescharacteristic
655C23C23×Dic7113yes—
656C23C23×Dic7113yes—
657C23C23×Dic7113yes—
658C23C23×Dic7111yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic7114yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic71112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—21no—
675C2×C4—23no—
676C2×C4—23no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—23no—
681C2×C4—23no—
682C2×C4—26no—
683C2×C4—26no—
684C2×C4—26no—
685C2×C4—26no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×Dic7111yescharacteristic
689C2×C4C23×Dic7111yescharacteristic
690C2×C4C23×Dic7113yes—
691C2×C4C23×Dic7113yes—
692C2×C4C23×Dic7111yescharacteristic
693C2×C4C23×Dic7111yescharacteristic
694C2×C4C23×Dic7113yes—
695C2×C4C23×Dic7113yes—
696C2×C4C23×Dic7113yes—
697C2×C4C2×D4×D7116yes—
698C2×C4C2×#1176586416yes—
699C2×C4C24×D7111yescharacteristic
700C8—712no—
701C8—716no—
702C8—1421no—
703C8—1423no—
704C8—1423no—
705C8—1421no—
706C8—1421no—
707C8—1423no—
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic7116yes—
724C22#1798676612yescomplemented
725C22C24×Dic7111yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic7116yes—
735C4C22×D4×D7111yescharacteristic
736C4C22×#1176586411yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic7111yescharacteristic
743C2C2×#1798676611yescharacteristic
744C2#2260305211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
Fitting, prime radicalD4×#41×C71C2
cosocleC2×C4×C71C25
hypercenterD4×#41D71
hypocenterC71#60146
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#17986766C2semidirect
2. C22×#14556135C2semidirect
3. #22597084C2semidirect
4. D4×#11765849C2semidirect
5. #22597067C2semidirect
6. #22597067C2semidirect
7. #22597058C2semidirect
8. #22597044C2semidirect
9. #22597035C2semidirect
10. C2×#17986071C2semidirect
11. #22596908C2semidirect
12. #22596789C2semidirect
13. #22596789C2semidirect
14. #22596768C2semidirect
22. C2×#14556135C22semidirect
23. C2×#14556135C22semidirect
24. C2×#14556135C22semidirect
25. C2×#14556135C22semidirect
26. C22×#11765849C22semidirect
27. C22×#11765849C22semidirect
28. C22×#11765849C22semidirect
29. C23×C71⋊C8C22semidirect
30. #17986077C22semidirect
31. #17986077C22semidirect
34. #17986071C22semidirect
35. #17986071C22semidirect
36. #17986071C22semidirect
37. #17986071C22semidirect
38. #17986071C22semidirect
39. #17986071C22semidirect
40. #17986071C22semidirect
41. #17986071C22semidirect
42. #17986071C22semidirect
43. D4×C71⋊C8C22semidirect
44. D4×C71⋊C8C22semidirect
45. #17986026C22semidirect
46. #17986026C22semidirect
47. #17986023C22semidirect
48. C2×C4⋊(C71⋊C8)C22semidirect
49. #17985966C22semidirect
50. #17985966C22semidirect
51. #17985966C22semidirect
52. #17985966C22semidirect
53. #17985963C22semidirect
54. #17985963C22semidirect
55. C2×C22⋊(C71⋊C8)C22semidirect
56. C2×C22⋊(C71⋊C8)C22semidirect
57. #17985955C22semidirect
58. #17985955C22semidirect
59. C4×#11765849C22semidirect
60. C2×#14556039C22semidirect
83. #14556135D4semidirect
188. #11765849C2×D4semidirect
197. C2×C71⋊C8C2×D4semidirect
351. C22×C71#568semidirect
388. C71#60146semidirect
724. C22#17986766semidirect

Maximal subgroups

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

subgroupindex
C2×#179867662
C22×#145561352
#225970842
D4×#117658492
#225970672
#225970582
#225970442
#225970352
C2×#179860712
#225969082
#225967892
#225967682
D4×#41×C712
#6014671