Finite Group Databasebeta

← #32861429

Subgroups — #32861429

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×#17986764C211yesmaximal, characteristic, complemented
2C2×#131×D71C211yesmaximal, characteristic, complemented
3#41×D284C211yesmaximal, characteristic
4#22597083C213yesmaximal, complemented
5#22597075C213yesmaximal, complemented
6#22597064C213yesmaximal, complemented
7#22597064C213yesmaximal, complemented
8#22597057C213yesmaximal, complemented
9#22597042C213yesmaximal, complemented
10#22597033C213yesmaximal, complemented
11C2×#17986069C213yesmaximal, complemented
12#22596787C211yesmaximal, characteristic, complemented
13#22596787C211yesmaximal, characteristic, complemented
14#22596768C211yesmaximal, characteristic, complemented
15C71×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D71C2211yescharacteristic
17C2×#41×D71C2211yescharacteristic
18#17986764—28no—
19C2×#14556136C2213yescomplemented
20C2×#14556136C2213yescomplemented
21C2×#14556135C2211yescharacteristic
22C2×#14556135C2211yescharacteristic
23C2×#14556134C2213yescomplemented
24C2×#14556134C2213yescomplemented
25#131×D71—28no—
26C22×#11765848C2213yescomplemented
27C2×M16×D71C2213yescomplemented
28C2×M16×D71C2213yescomplemented
29C22×C8×D71C2213yescomplemented
30#17986671C411yescharacteristic
31Q8×D284C411yescharacteristic
32#17986661C411yescharacteristic
33#17986661C411yescharacteristic
34#17986653C413yes—
35#17986644C413yes—
36#17986644C413yes—
37D4×D284C413yes—
38#17986549C2213yes—
39#17986511C2213yes—
40#17986511C2213yes—
41C2×C4×D284C2213yes—
42#17986076C2216yescomplemented
43#17986076C2216yescomplemented
44#17986069C2211yescharacteristic
45#17986069C2213yes—
46#17986069C2213yescomplemented
47#17986069C2213yescomplemented
48#17986069C2213yescomplemented
49#17986069C2213yescomplemented
50#17986069C2213yescomplemented
51#17986069C2213yescomplemented
52#17986069C2216yescomplemented
53#17986069C2216yescomplemented
54#17986069C2216yescomplemented
55#17986064C2216yescomplemented
56#17986064C2216yescomplemented
57#17985967C2213yescomplemented
58#17985967C2213yescomplemented
59#17985965C2213yescomplemented
60#17985965C2213yescomplemented
61#17985962C2213yescomplemented
62#17985962C2213yescomplemented
63C2×(C2×D71)⋊C8C2213yescomplemented
64C2×(C2×D71)⋊C8C2213yescomplemented
65#17985955C2213yescomplemented
66#17985955C2213yescomplemented
67C4×#11765849C2213yescomplemented
68C2×#14556039C2213yescomplemented
69C2×#131×C71C2211yescharacteristic
70C2×#131×C71C2211yescharacteristic
71C4×#41×C71C2211yescharacteristic
72#424×C71C2213yescomplemented
73#424×C71C2213yescomplemented
74#423×C71C2213yescomplemented
75C2×C4⋊C8×C71C2213yescomplemented
76C2×#11765866C2×C411yescharacteristic
77C2×#11765866C2×C411yescharacteristic
78C2×#11765865C2313yes—
79C2×#11765865C2313yes—
80C2×#11765864C2×C413yes—
81C2×#11765864C2×C413yes—
82#41×D71—24no—
83#41×D71—24no—
84#41×D71—24no—
85#41×D71—24no—
86C2×Q8×D71C2×C411yescharacteristic
87C2×Q8×D71C2×C411yescharacteristic
88C22×D284C2×C413yes—
89C2×D4×D71C2×C413yes—
90C2×D4×D71C2×C413yes—
91C22×C4×D71C2313yes—
92C22×C4×D71C2313yes—
93#14556136—212no—
94#14556136—212no—
95#14556135—24no—
96#14556135D418yescomplemented
97#14556134—212no—
98#14556134—212no—
99C2×#11765849C2313yes—
100C2×#11765849C2313yes—
101C2×#11765848—212no—
102C2×#11765848C2311yescharacteristic
103C2×#11765848C2313yes—
104C2×#11765848C2313yes—
105C2×#11765848C2316yes—
106C2×#11765848C2313yes—
107M16×D71—212no—
108M16×D71—212no—
109C22×C71⋊C8C2313yes—
110C22×C71⋊C8C2313yes—
111C2×C8×D71—212no—
112C2×C8×D71C2313yes—
113C2×C8×D71C2313yes—
114C2×C8×D71C2316yes—
115C2×C8×D71C2311yescharacteristic
116C2×C8×D71C2313yes—
117#14556128C2×C413yes—
118#14556125C2×C413yes—
119#14556116C2×C413yes—
120#14556116C2×C413yes—
121#14556112C2×C416yes—
122#14556112C2×C416yes—
123#14556108C2×C413yes—
124#14556108C2×C413yes—
125#14556108C2×C413yes—
126#14556108C2×C413yes—
127#14556103C2×C413yes—
128#14556103C2×C413yes—
129#14556103C2×C413yes—
130#14556103C2×C413yes—
131#14556102C2×C416yes—
132#14556102C2×C416yes—
133#14556098C2×C416yes—
134#14556098C2×C416yes—
135C4×D284C2×C413yes—
136C4×D284C2×C413yes—
137C4×D284C2×C413yes—
138C4×D284C2×C413yes—
139C4×D284C2313yes—
140C4×D284C2316yes—
141C4×D284C2311yescharacteristic
142C4×D284C2313yes—
143C4×D284C2313yes—
144C2×C4⋊Dic71C2×C413yes—
145C2×(C2×D71)⋊C4C2×C413yes—
146C2×(C2×D71)⋊C4C2×C413yes—
147(C2×D71)⋊C8C2313yes—
148(C2×D71)⋊C8C2313yes—
149(C2×D71)⋊C8C2316yes—
150(C2×D71)⋊C8C2316yes—
151(C2×D71)⋊C8C2311yescharacteristic
152(C2×D71)⋊C8C2311yescharacteristic
153(C2×D71)⋊C8C2313yes—
154(C2×D71)⋊C8C2313yes—
155(C2×D71)⋊C8C2313yes—
156(C2×D71)⋊C8C2313yes—
157#14556039C2311yescharacteristic
158#14556039C2313yes—
159#14556039C2313yes—
160#14556039C2313yes—
161C4×C71⋊C8C2316yes—
162C2×#41×C71C2311yescharacteristic
163#131×C71—24no—
164#131×C71—24no—
165C2×M16×C71C2313yes—
166C2×M16×C71C2313yes—
167C22×C8×C71C2313yes—
168C22×C8×C71C2313yes—
169C4×Q8×C71C2×C411yescharacteristic
170C4×Q8×C71C2×C411yescharacteristic
171C4×D4×C71C2×C413yes—
172C4×D4×C71C2×C413yes—
173#117×C71C2313yes—
174C2×C42×C71C2313yes—
175C4⋊C8×C71C2313yes—
176C4⋊C8×C71C2316yes—
177C4⋊C8×C71C2311yescharacteristic
178C4⋊C8×C71C2313yes—
179C4⋊C8×C71C2313yes—
180C23×D71C22×C413yes—
181C23×D71C22×C413yes—
182#11765866—24no—
183#11765866—24no—
184#11765865—26no—
185#11765865—26no—
186#11765865—26no—
187#11765865—26no—
188#11765864—212no—
189#11765864—212no—
190C2×Dic142C22×C413yes—
191C2×Dic142C22×C413yes—
192Q8×D71—24no—
193Q8×D71—24no—
194C2×D284—46no—
195C2×D284C22×C413yes—
196C2×D284C22×C413yes—
197C2×D284C22×C411yescharacteristic
198C2×D284C22×C413yes—
199C2×D284C22×C413yes—
200C2×D284C22×C413yes—
201C2×D284C22×C416yes—
202C2×C22⋊D71C22×C416yes—
203C2×C22⋊D71C22×C416yes—
204D4×D71—212no—
205D4×D71—212no—
206C22×Dic71C22×C413yes—
207C22×Dic71C22×C413yes—
208C2×C4×D71—26no—
209C2×C4×D71—26no—
210C2×C4×D71—26no—
211C2×C4×D71—26no—
212C2×C4×D71C22×C413yes—
213C2×C4×D71C22×C413yes—
214C2×C4×D71C22×C413yes—
215C2×C4×D71C22×C413yes—
216C2×C4×D71C2411yescharacteristic
217C2×C4×D71C2411yescharacteristic
218C2×C4×D71C2413yes—
219C2×C4×D71C2413yes—
220#11765849—26no—
221#11765849C2×D4112yescomplemented
222#11765848—26no—
223#11765848—212no—
224#11765848—22no—
225#11765848—26no—
226#11765848—26no—
227C2×C71⋊C8—26no—
228C2×C71⋊C8C2×D4112yescomplemented
229C2×C71⋊C8C2413yes—
230C2×C71⋊C8C2411yescharacteristic
231C2×C71⋊C8C2413yes—
232C2×C71⋊C8C2411yescharacteristic
233C8×D71—22no—
234C8×D71—26no—
235C8×D71—26no—
236C8×D71—26no—
237C8×D71—212no—
238C4⋊Dic71C22×C411yescharacteristic
239C4⋊Dic71C22×C413yes—
240C4⋊Dic71C22×C413yes—
241C4⋊Dic71C22×C413yes—
242C4⋊Dic71C22×C416yes—
243(C2×D71)⋊C4C22×C411yescharacteristic
244(C2×D71)⋊C4C22×C411yescharacteristic
245(C2×D71)⋊C4C22×C413yes—
246(C2×D71)⋊C4C22×C413yes—
247(C2×D71)⋊C4C22×C413yes—
248(C2×D71)⋊C4C22×C413yes—
249(C2×D71)⋊C4C22×C413yes—
250(C2×D71)⋊C4C22×C413yes—
251(C2×D71)⋊C4C22×C416yes—
252(C2×D71)⋊C4C22×C416yes—
253#41×C71C2×D414yes—
254#41×C71#4114yes—
255C2×Q8×C71C22×C411yescharacteristic
256C2×D4×C71C22×C413yes—
257C22×C4×C71C22×C413yes—
258C22×C4×C71C22×C413yes—
259C22×C4×C71C2413yes—
260M16×C71—26no—
261M16×C71—26no—
262C2×C8×C71—26no—
263C2×C8×C71—26no—
264C2×C8×C71C2411yescharacteristic
265C2×C8×C71C2411yescharacteristic
266C2×C8×C71C2413yes—
267C2×C8×C71C2413yes—
268C4⋊C4×C71C22×C413yes—
269C4⋊C4×C71C22×C413yes—
270C22⋊C4×C71C22×C416yes—
271C42×C71C22×C413yes—
272C42×C71C22×C413yes—
273C42×C71C2411yescharacteristic
274C42×C71C2413yes—
275C23×C71C23×C413yes—
276C22×D71—26no—
277C22×D71—26no—
278C22×D71—26no—
279C22×D71—43no—
280C22×D71—43no—
281C22×D71—43no—
282C22×D71C23×C411yescharacteristic
283C22×D71C23×C413yes—
284C22×D71C23×C413yes—
285C22×D71C23×C411yescharacteristic
286Q8×C71C4×D414yes—
287D4×C71C4×D4112yes—
288C2×C4×C71—43no—
289C2×C4×C71—43no—
290C2×C4×C71C23×C411yescharacteristic
291C2×C4×C71C23×C411yescharacteristic
292C2×C4×C71C23×C413yes—
293C2×C4×C71C23×C413yes—
294C2×C4×C71C23×C413yes—
295C2×C4×C71C22×D416yes—
296C2×C4×C71C2×#4116yes—
297C2×C4×C71C2511yescharacteristic
298C22⋊D71—212no—
299C22⋊D71—212no—
300C2×Dic71—26no—
301C2×Dic71—26no—
302C2×Dic71C23×C411yescharacteristic
303C2×Dic71C23×C411yescharacteristic
304C2×Dic71C23×C413yes—
305C2×Dic71C23×C413yes—
306D284—22no—
307D284—26no—
308D284—26no—
309D284—26no—
310D284—43no—
311D284—43no—
312D284—46no—
313C4×D71—26no—
314C4×D71—26no—
315C4×D71—26no—
316C4×D71—26no—
317C4×D71—21no—
318C4×D71—23no—
319C4×D71—23no—
320C4×D71—21no—
321C4×D71—21no—
322C4×D71—21no—
323C4×D71—23no—
324C4×D71—23no—
325Dic142—26no—
326Dic142—26no—
327C8×C71—21no—
328C8×C71—21no—
329C8×C71—23no—
330C8×C71—23no—
331C71⋊C8—21no—
332C71⋊C8—23no—
333C71⋊C8C22×D412yes—
334C71⋊C8C22×D416yes—
335C22×C71—23no—
336C22×C71—23no—
337C22×C71C2×C4×D416yes—
338C22×C71C24×C411yescharacteristic
339C2×D71—21no—
340C2×D71—21no—
341C2×D71—21no—
342C2×D71—23no—
343C2×D71—23no—
344C2×D71—21no—
345C2×D71—23no—
346C2×D71—23no—
347C2×D71—23no—
348C2×D71—23no—
349C2×D71—21no—
350C2×D71—412no—
351C2×D71—86no—
352C2×D71#56812yescomplemented
353C4×C71—21no—
354C4×C71—23no—
355C4×C71—23no—
356C4×C71—21no—
357C4×C71C2×C4×D416yes—
358C4×C71C23×D411yescharacteristic
359C4×C71C22×#4111yescharacteristic
360Dic71—23no—
361Dic71—23no—
362Dic71—21no—
363Dic71—21no—
364#60146—711nomaximal, Sylow
365C2×C71—26no—
366C2×C71C22×C4×D411yescharacteristic
367C2×C71C2×#56811yescharacteristic
368C2×C71#357311yescharacteristic
369D71—22no—
370D71—43no—
371D71—43no—
372D71—41no—
373C2×#568—711no—
374C22×#131—711no—
375D4×#41—711no—
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#2906D7111yescharacteristic, complemented
385#2880—711no—
386#2880—711no—
387#2875—711no—
388C71#6014611yescharacteristic, complemented, Sylow
389C22×#41—711no—
390C22×#41—711no—
391#568—1428no—
392C2×#131—711no—
393C2×#131—711no—
394C2×#131—713no—
395C2×#131—713no—
396C2×#131—713no—
397C2×#131—713no—
398C2×#131—1428no—
399C2×#131C2×D7111yescharacteristic
400C2×#131C2×D7111yescharacteristic
401C22×M16—713no—
402C22×M16—713no—
403C22×M16—713no—
404C23×C8—713no—
405#550—711no—
406D4×Q8—711no—
407#548—711no—
408#548—711no—
409#547—713no—
410#546—713no—
411#546—713no—
412D42—713no—
413#532—713no—
414#525—713no—
415#525—713no—
416C4×#41C2×D7111yescharacteristic
417C2×C4×D4—713no—
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#424C2×D7113yescomplemented
434#424C2×D7113yescomplemented
435#423C2×D7113yescomplemented
436C2×C4⋊C8C2×D7113yescomplemented
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—711no—
450C2×#41—711no—
451C2×#41—713no—
452C2×#41—713no—
453C2×#41—713no—
454C2×#41—713no—
455C2×#41—1424no—
456C2×#41—1424no—
457C2×#41—1424no—
458C2×#41—1424no—
459C2×#41C22×D7111yescharacteristic
460C22×Q8—711no—
461C22×Q8—711no—
462C22×D4—713no—
463C22×D4—713no—
464C22×D4—713no—
465C23×C4—713no—
466C23×C4—713no—
467#131—24no—
468#131—24no—
469#131—718no—
470#131—14212no—
471#131—14212no—
472#131—14212no—
473#131—14212no—
474#131—1424no—
475C2×M16—713no—
476C2×M16—713no—
477C2×M16—711no—
478C2×M16—713no—
479C2×M16—713no—
480C2×M16—716no—
481C2×M16—713no—
482C2×M16—14212no—
483C2×M16—14212no—
484C2×M16—14212no—
485C2×M16C22×D7113yes—
486C2×M16C22×D7113yes—
487C22×C8—713no—
488C22×C8—713no—
489C22×C8—711no—
490C22×C8—713no—
491C22×C8—713no—
492C22×C8—713no—
493C22×C8—716no—
494C22×C8—14212no—
495C22×C8C22×D7113yes—
496C22×C8C22×D7113yes—
497C4⋊Q8—713no—
498#127—713no—
499#124—713no—
500#124—713no—
501#123—716no—
502#123—716no—
503C22⋊Q8—713no—
504C22⋊Q8—713no—
505C22⋊Q8—713no—
506C22⋊Q8—713no—
507#121—716no—
508#121—716no—
509#121—713no—
510#121—713no—
511#121—713no—
512#121—713no—
513#120—716no—
514#120—716no—
515C4×Q8C4×D7111yescharacteristic
516C4×Q8C4×D7111yescharacteristic
517C4×D4—713no—
518C4×D4—713no—
519C4×D4—713no—
520C4×D4—713no—
521C4×D4—711no—
522C4×D4—713no—
523C4×D4—713no—
524C4×D4—713no—
525C4×D4—716no—
526C4×D4C4×D7113yes—
527C4×D4C4×D7113yes—
528#117C22×D7113yes—
529C2×C4⋊C4—713no—
530C2×C22⋊C4—713no—
531C2×C22⋊C4—713no—
532C2×C42C22×D7113yes—
533C4⋊C8C22×D7111yescharacteristic
534C4⋊C8C22×D7113yes—
535C4⋊C8C22×D7113yes—
536C4⋊C8C22×D7113yes—
537C4⋊C8C22×D7116yes—
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—
553C24—713no—
554C24—713no—
555#41—1424no—
556#41—1424no—
557#41—14212no—
558#41—14212no—
559#41—1426no—
560#41—1426no—
561#41—1426no—
562#41—1426no—
563#41D4×D7114yes—
564#41#1176586614yes—
565C2×Q8—713no—
566C2×Q8—713no—
567C2×Q8—1424no—
568C2×Q8—1424no—
569C2×Q8C2×C4×D7111yescharacteristic
570C2×D4—2846no—
571C2×D4—716no—
572C2×D4—716no—
573C2×D4—713no—
574C2×D4—713no—
575C2×D4—716no—
576C2×D4—711no—
577C2×D4—713no—
578C2×D4—713no—
579C2×D4—713no—
580C2×D4—14212no—
581C2×D4—14212no—
582C2×D4C2×C4×D7113yes—
583C22×C4—713no—
584C22×C4—713no—
585C22×C4—713no—
586C22×C4—713no—
587C22×C4—713no—
588C22×C4—713no—
589C22×C4—711no—
590C22×C4—713no—
591C22×C4—713no—
592C22×C4—711no—
593C22×C4—1426no—
594C22×C4—1426no—
595C22×C4—1426no—
596C22×C4—1426no—
597C22×C4C2×C4×D7113yes—
598C22×C4C2×C4×D7113yes—
599C22×C4C23×D7113yes—
600M16—26no—
601M16—26no—
602M16—7112no—
603M16—1422no—
604M16—1426no—
605M16—1426no—
606M16—1426no—
607M16—14212no—
608M16—1426no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—7112no—
612C2×C8—713no—
613C2×C8—711no—
614C2×C8—713no—
615C2×C8—711no—
616C2×C8—1422no—
617C2×C8—1426no—
618C2×C8—1426no—
619C2×C8—1426no—
620C2×C8—14212no—
621C2×C8—1426no—
622C2×C8C23×D7111yescharacteristic
623C2×C8C23×D7113yes—
624C2×C8C23×D7113yes—
625C2×C8C23×D7111yescharacteristic
626C4⋊C4—711no—
627C4⋊C4—713no—
628C4⋊C4—713no—
629C4⋊C4—713no—
630C4⋊C4—716no—
631C4⋊C4C2×C4×D7113yes—
632C4⋊C4C2×C4×D7113yes—
633C22⋊C4—711no—
634C22⋊C4—711no—
635C22⋊C4—713no—
636C22⋊C4—713no—
637C22⋊C4—713no—
638C22⋊C4—713no—
639C22⋊C4—713no—
640C22⋊C4—713no—
641C22⋊C4—716no—
642C22⋊C4—716no—
643C22⋊C4C2×C4×D7116yes—
644C42C2×C4×D7113yes—
645C42C2×C4×D7113yes—
646C42C23×D7113yes—
647C42C23×D7111yescharacteristic
648C23—2843no—
649C23—2843no—
650C23—2843no—
651C23—711no—
652C23—711no—
653C23—713no—
654C23—713no—
655C23—1426no—
656C23—1426no—
657C23—1426no—
658C23C22×C4×D7113yes—
659Q8—1426no—
660Q8—1426no—
661Q8#1455609014yes—
662D4—2843no—
663D4—2843no—
664D4—2846no—
665D4—1422no—
666D4—1426no—
667D4—14212no—
668D4—14212no—
669D4—1426no—
670D4—1426no—
671D4#14556090112yes—
672C2×C4—43no—
673C2×C4—43no—
674C2×C4—711no—
675C2×C4—711no—
676C2×C4—713no—
677C2×C4—713no—
678C2×C4—1426no—
679C2×C4—1426no—
680C2×C4—1421no—
681C2×C4—1423no—
682C2×C4—1423no—
683C2×C4—1421no—
684C2×C4—1421no—
685C2×C4—1421no—
686C2×C4—1423no—
687C2×C4—1423no—
688C2×C4—1426no—
689C2×C4—1426no—
690C2×C4—1426no—
691C2×C4—1426no—
692C2×C4C22×C4×D7111yescharacteristic
693C2×C4C22×C4×D7111yescharacteristic
694C2×C4C22×C4×D7113yes—
695C2×C4C22×C4×D7113yes—
696C2×C4C22×C4×D7113yes—
697C2×C4C2×D4×D7116yes—
698C2×C4C2×#1176586616yes—
699C2×C4C24×D7111yescharacteristic
700C8—21no—
701C8—21no—
702C8—23no—
703C8—23no—
704C8—712no—
705C8—716no—
706C8—1421no—
707C8—1423no—
708C22—23no—
709C22—23no—
710C22—28412no—
711C22—5686no—
712C22—712no—
713C22—1421no—
714C22—1423no—
715C22—1423no—
716C22—1421no—
717C22—1423no—
718C22—1423no—
719C22—1423no—
720C22—1423no—
721C22—1421no—
722C22—1421no—
723C22—1421no—
724C22C2×#1455609016yes—
725C22C23×C4×D7111yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—1421no—
731C4—1421no—
732C4—1423no—
733C4—1423no—
734C4C2×#1455609016yes—
735C4C22×D4×D7111yescharacteristic
736C4C22×#1176586611yescharacteristic
737C2—26no—
738C2—2843no—
739C2—2841no—
740C2—2843no—
741C2—1422no—
742C2C22×#1455609011yescharacteristic
743C2#568×D7111yescharacteristic
744C2#2260305111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC71×#2906C2
prime radical#41×D284C2
cosocleC2×C4×C71C25
hypercenter#2906D71
hypocenterC71#60146
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
1. C2×#17986764C2semidirect
2. C2×#131×D71C2semidirect
4. #22597083C2semidirect
5. #22597075C2semidirect
6. #22597064C2semidirect
7. #22597064C2semidirect
8. #22597057C2semidirect
9. #22597042C2semidirect
10. #22597033C2semidirect
11. C2×#17986069C2semidirect
12. #22596787C2semidirect
13. #22596787C2semidirect
14. #22596768C2semidirect
15. C71×#2906C2semidirect
19. C2×#14556136C22semidirect
20. C2×#14556136C22semidirect
23. C2×#14556134C22semidirect
24. C2×#14556134C22semidirect
26. C22×#11765848C22semidirect
27. C2×M16×D71C22semidirect
28. C2×M16×D71C22semidirect
29. C22×C8×D71C22semidirect
42. #17986076C22semidirect
43. #17986076C22semidirect
46. #17986069C22semidirect
47. #17986069C22semidirect
48. #17986069C22semidirect
49. #17986069C22semidirect
50. #17986069C22semidirect
51. #17986069C22semidirect
52. #17986069C22semidirect
53. #17986069C22semidirect
54. #17986069C22semidirect
55. #17986064C22semidirect
56. #17986064C22semidirect
57. #17985967C22semidirect
58. #17985967C22semidirect
59. #17985965C22semidirect
60. #17985965C22semidirect
61. #17985962C22semidirect
62. #17985962C22semidirect
63. C2×(C2×D71)⋊C8C22semidirect
64. C2×(C2×D71)⋊C8C22semidirect
65. #17985955C22semidirect
66. #17985955C22semidirect
67. C4×#11765849C22semidirect
68. C2×#14556039C22semidirect
72. #424×C71C22semidirect
73. #424×C71C22semidirect
74. #423×C71C22semidirect
75. C2×C4⋊C8×C71C22semidirect
96. #14556135D4semidirect
221. #11765849C2×D4semidirect
228. C2×C71⋊C8C2×D4semidirect
352. C2×D71#568semidirect
384. #2906D71semidirect
388. C71#60146semidirect
433. #424C2×D71semidirect
434. #424C2×D71semidirect
435. #423C2×D71semidirect
436. C2×C4⋊C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179867642
C2×#131×D712
#41×D2842
#225970832
#225970752
#225970642
#225970572
#225970422
#225970332
C2×#179860692
#225967872
#225967682
C71×#29062
#6014671