Finite Group Databasebeta

← #131×C22⋊D71 #32861416

Subgroups — #131×C22⋊D71 #32861416

Order 18176.

2814 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×#131×D71C211yesmaximal, characteristic, complemented
2#41×C22⋊D71C211yesmaximal, characteristic
3#22597082C213yesmaximal, complemented
4M16×C22⋊D71C213yesmaximal, complemented
5#22597065C213yesmaximal, complemented
6#22597062C213yesmaximal, complemented
7#22597050C213yesmaximal, complemented
8#22597034C213yesmaximal, complemented
9#22597032C213yesmaximal, complemented
10C2×C8×C22⋊D71C213yesmaximal, complemented
11#22596906C211yesmaximal, characteristic, complemented
12#22596789C211yesmaximal, characteristic, complemented
13#22596787C211yesmaximal, characteristic, complemented
14#131×Dic71C211yesmaximal, characteristic, complemented
15C22×#131×C71C211yesmaximal, characteristic, complemented
16C2×#41×D71C2211yescharacteristic
17C2×#14556136C2213yescomplemented
18C2×#14556135C2211yescharacteristic
19C2×#14556135C2211yescharacteristic
20C2×#14556134C2213yescomplemented
21#131×D71—28no—
22C2×M16×D71C2213yescomplemented
23C22×C8×D71C2213yescomplemented
24#17986668C411yescharacteristic
25Q8×C22⋊D71C411yescharacteristic
26#17986660C411yescharacteristic
27#17986656C411yescharacteristic
28#17986648C413yes—
29#17986643C413yes—
30#17986637C413yes—
31D4×C22⋊D71C413yes—
32#17986545C2213yes—
33#17986510C2213yes—
34#17986506C2213yes—
35#41×Dic71C2211yescharacteristic
36C2×C4×C22⋊D71C2213yes—
37#17986075C2216yescomplemented
38#17986075C2216yescomplemented
39#17986070C2216yescomplemented
40#17986070C2216yescomplemented
41#17986068C2216yescomplemented
42#17986068C2216yescomplemented
43C8×C22⋊D71C2211yescharacteristic
44C8×C22⋊D71C2213yes—
45C8×C22⋊D71C2213yescomplemented
46C8×C22⋊D71C2213yescomplemented
47C8×C22⋊D71C2213yescomplemented
48C8×C22⋊D71C2213yescomplemented
49C8×C22⋊D71C2213yescomplemented
50C8×C22⋊D71C2213yescomplemented
51C8×C22⋊D71C2216yescomplemented
52#17986027C2213yescomplemented
53#17986025C2213yescomplemented
54#17986022C2213yescomplemented
55C2×Dic71⋊C8C2213yescomplemented
56#17985967C2213yescomplemented
57#17985966C2213yescomplemented
58#17985966C2213yescomplemented
59#17985965C2213yescomplemented
60#17985963C2213yescomplemented
61#17985962C2213yescomplemented
62C2×C22⋊(C71⋊C8)C2213yescomplemented
63C2×(C2×D71)⋊C8C2213yescomplemented
64#17985957C2213yescomplemented
65#17985954C2213yescomplemented
66M16×Dic71C2213yescomplemented
67C2×C8×Dic71C2213yescomplemented
68C22×#41×C71C2211yescharacteristic
69C2×#131×C71—28no—
70C2×#131×C71C2211yescharacteristic
71C2×#131×C71C2211yescharacteristic
72C2×#131×C71C2213yescomplemented
73C2×#131×C71C2213yescomplemented
74C22×M16×C71C2213yescomplemented
75C23×C8×C71C2213yescomplemented
76C2×#11765866C2×C411yescharacteristic
77C2×#11765865C2313yes—
78C2×#11765864C2×C413yes—
79#41×D71—24no—
80#41×D71—24no—
81C2×Q8×D71C2×C411yescharacteristic
82C22×C22⋊D71C2×C413yes—
83C2×D4×D71C2×C413yes—
84C22×C4×D71C2313yes—
85#14556136—212no—
86#14556135—24no—
87#14556135—24no—
88#14556134—212no—
89C2×#11765849C2313yes—
90C2×#11765849C2313yes—
91C2×#11765848C2316yes—
92M16×D71—212no—
93C22×C71⋊C8C2313yes—
94C22×C71⋊C8C2313yes—
95C2×C8×D71—212no—
96C2×C8×D71C2311yescharacteristic
97C2×C8×D71C2313yes—
98C2×C8×D71C2313yes—
99C2×C8×D71C2313yes—
100#14556126C2×C413yes—
101#14556124C2×C413yes—
102#14556117C2×C413yes—
103#14556115C2×C413yes—
104#14556111C2×C416yes—
105#14556109C2×C416yes—
106#14556107C2×C413yes—
107#14556107C2×C413yes—
108#14556104C2×C413yes—
109#14556104C2×C413yes—
110#14556102C2×C413yes—
111#14556102C2×C413yes—
112#14556100C2×C416yes—
113#14556100C2×C416yes—
114#14556099C2×C413yes—
115#14556099C2×C413yes—
116#14556097C2×C416yes—
117#14556096C2×C416yes—
118Q8×Dic71C2×C411yescharacteristic
119Q8×Dic71C2×C411yescharacteristic
120D4×Dic71C2×C413yes—
121D4×Dic71C2×C413yes—
122C4×C22⋊D71C2×C413yes—
123C4×C22⋊D71C2×C413yes—
124C4×C22⋊D71C2×C413yes—
125C4×C22⋊D71C2×C413yes—
126C4×C22⋊D71C2311yescharacteristic
127C4×C22⋊D71C2313yes—
128C4×C22⋊D71C2313yes—
129C4×C22⋊D71C2313yes—
130C4×C22⋊D71C2316yes—
131#14556087C2313yes—
132C2×Dic71⋊C4C2×C413yes—
133C2×C22⋊Dic71C2×C413yes—
134C2×(C2×D71)⋊C4C2×C413yes—
135C2×C4×Dic71C2313yes—
136Dic71⋊C8C2311yescharacteristic
137Dic71⋊C8C2313yes—
138Dic71⋊C8C2313yes—
139Dic71⋊C8C2313yes—
140Dic71⋊C8C2316yes—
141C22⋊(C71⋊C8)C2311yescharacteristic
142C22⋊(C71⋊C8)C2313yes—
143C22⋊(C71⋊C8)C2313yes—
144C22⋊(C71⋊C8)C2313yes—
145C22⋊(C71⋊C8)C2316yes—
146(C2×D71)⋊C8C2311yescharacteristic
147(C2×D71)⋊C8C2313yes—
148(C2×D71)⋊C8C2313yes—
149(C2×D71)⋊C8C2313yes—
150(C2×D71)⋊C8C2316yes—
151#14556038C2316yes—
152C8×Dic71C2311yescharacteristic
153C8×Dic71C2313yes—
154C8×Dic71C2313yes—
155C8×Dic71C2313yes—
156C2×#41×C71—24no—
157C2×#41×C71—24no—
158C2×#41×C71C2×C413yes—
159C2×#41×C71C2×C411yescharacteristic
160C2×#41×C71C2313yes—
161C2×#41×C71C2311yescharacteristic
162C22×Q8×C71C2×C411yescharacteristic
163C22×D4×C71C2×C413yes—
164C23×C4×C71C2313yes—
165#131×C71—24no—
166#131×C71—212no—
167#131×C71—212no—
168#131×C71D418yescomplemented
169C2×M16×C71—212no—
170C2×M16×C71C2316yes—
171C2×M16×C71C2313yes—
172C2×M16×C71C2313yes—
173C22×C8×C71—212no—
174C22×C8×C71C2311yescharacteristic
175C22×C8×C71C2313yes—
176C22×C8×C71C2313yes—
177C22×C8×C71C2313yes—
178C22×C8×C71C2313yes—
179C22×C8×C71C2313yes—
180C23×D71C22×C413yes—
181#11765866—24no—
182#11765865—26no—
183#11765865—26no—
184#11765864—212no—
185C2×Dic142C22×C413yes—
186Q8×D71—24no—
187C2×D284C22×C413yes—
188C2×C22⋊D71—212no—
189C2×C22⋊D71C22×C416yes—
190C2×C22⋊D71C22×C413yes—
191C2×C22⋊D71C22×C413yes—
192C2×C22⋊D71C22×C413yes—
193C2×C22⋊D71C22×C416yes—
194C2×C22⋊D71C22×C411yescharacteristic
195D4×D71—212no—
196C22×Dic71C22×C413yes—
197C22×Dic71C22×C413yes—
198C22×Dic71C22×C413yes—
199C2×C4×D71—26no—
200C2×C4×D71—26no—
201C2×C4×D71C22×C413yes—
202C2×C4×D71C22×C413yes—
203C2×C4×D71C2411yescharacteristic
204C2×C4×D71C2413yes—
205#11765849—26no—
206#11765849—26no—
207#11765848—212no—
208C2×C71⋊C8—26no—
209C2×C71⋊C8—26no—
210C2×C71⋊C8C2411yescharacteristic
211C2×C71⋊C8C2413yes—
212C2×C71⋊C8C2411yescharacteristic
213C2×C71⋊C8C2413yes—
214C8×D71—22no—
215C8×D71—26no—
216C8×D71—26no—
217C8×D71—26no—
218C4⋊Dic71C22×C413yes—
219C4⋊Dic71C22×C413yes—
220Dic71⋊C4C22×C411yescharacteristic
221Dic71⋊C4C22×C413yes—
222Dic71⋊C4C22×C413yes—
223Dic71⋊C4C22×C413yes—
224Dic71⋊C4C22×C416yes—
225C22⋊Dic71C22×C411yescharacteristic
226C22⋊Dic71C22×C413yes—
227C22⋊Dic71C22×C413yes—
228C22⋊Dic71C22×C413yes—
229C22⋊Dic71C22×C416yes—
230C22⋊Dic71C22×C416yes—
231(C2×D71)⋊C4C22×C411yescharacteristic
232(C2×D71)⋊C4C22×C413yes—
233(C2×D71)⋊C4C22×C413yes—
234(C2×D71)⋊C4C22×C413yes—
235(C2×D71)⋊C4C22×C416yes—
236C4×Dic71C22×C413yes—
237C4×Dic71C22×C413yes—
238C4×Dic71C2411yescharacteristic
239C4×Dic71C2413yes—
240C24×C71C22×C413yes—
241#41×C71—24no—
242#41×C71—212no—
243#41×C71—26no—
244#41×C71—26no—
245#41×C71C2×D414yes—
246#41×C71#4114yes—
247C2×Q8×C71—24no—
248C2×Q8×C71C22×C413yes—
249C2×Q8×C71C22×C411yescharacteristic
250C2×D4×C71—212no—
251C2×D4×C71C22×C416yes—
252C2×D4×C71C22×C413yes—
253C2×D4×C71C22×C413yes—
254C22×C4×C71—26no—
255C22×C4×C71—26no—
256C22×C4×C71C22×C413yes—
257C22×C4×C71C22×C413yes—
258C22×C4×C71C22×C413yes—
259C22×C4×C71C2411yescharacteristic
260C22×C4×C71C2413yes—
261C22×C4×C71C2413yes—
262M16×C71—26no—
263M16×C71—212no—
264M16×C71C2×D4112yescomplemented
265C2×C8×C71—26no—
266C2×C8×C71—22no—
267C2×C8×C71—26no—
268C2×C8×C71—26no—
269C2×C8×C71—26no—
270C2×C8×C71C2×D4112yescomplemented
271C2×C8×C71C2411yescharacteristic
272C2×C8×C71C2413yes—
273C2×C8×C71C2413yes—
274C2×C8×C71C2411yescharacteristic
275C23×C71—26no—
276C23×C71—26no—
277C23×C71—43no—
278C23×C71C23×C413yes—
279C23×C71C23×C413yes—
280C23×C71C23×C411yescharacteristic
281C22×D71—26no—
282C22×D71—26no—
283C22×D71—43no—
284C22×D71C23×C413yes—
285C22×D71C23×C411yescharacteristic
286Q8×C71—26no—
287Q8×C71C4×D414yes—
288D4×C71—212no—
289D4×C71—26no—
290D4×C71C4×D4112yes—
291C2×C4×C71—26no—
292C2×C4×C71—26no—
293C2×C4×C71—26no—
294C2×C4×C71—21no—
295C2×C4×C71—23no—
296C2×C4×C71—21no—
297C2×C4×C71—23no—
298C2×C4×C71C23×C411yescharacteristic
299C2×C4×C71C23×C413yes—
300C2×C4×C71C23×C413yes—
301C2×C4×C71C22×D416yes—
302C2×C4×C71C2×#4116yes—
303C2×C4×C71C2511yescharacteristic
304C22⋊D71—212no—
305C22⋊D71—26no—
306C22⋊D71—26no—
307C22⋊D71—26no—
308C22⋊D71—46no—
309C22⋊D71#13114yesdirect product factor
310C2×Dic71—26no—
311C2×Dic71—26no—
312C2×Dic71—43no—
313C2×Dic71C23×C411yescharacteristic
314C2×Dic71C23×C413yes—
315C2×Dic71C23×C413yes—
316C2×Dic71C23×C411yescharacteristic
317C2×Dic71C23×C413yes—
318C2×Dic71C23×C411yescharacteristic
319D284—26no—
320C4×D71—26no—
321C4×D71—26no—
322C4×D71—21no—
323C4×D71—23no—
324C4×D71—21no—
325C4×D71—23no—
326Dic142—26no—
327C8×C71—21no—
328C8×C71—23no—
329C8×C71C22×D412yes—
330C8×C71C22×D416yes—
331C71⋊C8—21no—
332C71⋊C8—23no—
333C71⋊C8—21no—
334C71⋊C8—23no—
335C22×C71—21no—
336C22×C71—23no—
337C22×C71—23no—
338C22×C71—21no—
339C22×C71—23no—
340C22×C71—23no—
341C22×C71—23no—
342C22×C71—412no—
343C22×C71C2×C4×D416yes—
344C22×C71C2×#13112yescomplemented
345C22×C71C24×C411yescharacteristic
346C2×D71—21no—
347C2×D71—21no—
348C2×D71—23no—
349C2×D71—23no—
350C2×D71—23no—
351C2×D71—412no—
352C2×D71C2×#13112yescomplemented
353C4×C71—21no—
354C4×C71—23no—
355C4×C71C2×C4×D416yes—
356C4×C71C23×D411yescharacteristic
357C4×C71C22×#4111yescharacteristic
358Dic71—23no—
359Dic71—21no—
360Dic71—23no—
361Dic71—21no—
362Dic71—23no—
363Dic71C2×#13112yescomplemented
364D4×#131—711nomaximal, Sylow
365C2×C71—26no—
366C2×C71—22no—
367C2×C71—43no—
368C2×C71C22×C4×D411yescharacteristic
369C2×C71C22×#13111yescharacteristic
370C2×C71#357311yescharacteristic
371D71—22no—
372D71—43no—
373C22×#131—711no—
374C22×#131D7111yescharacteristic, complemented
375D4×#41—711no—
376#2935—713no—
377D4×M16—713no—
378#2933—713no—
379#2933—713no—
380#2931—713no—
381#2929—713no—
382#2929—713no—
383C2×C8×D4—713no—
384#2906—711no—
385#2880—711no—
386#2880—711no—
387C4×#131—711no—
388C71D4×#13111yescharacteristic, complemented, Sylow
389C22×#41—711no—
390C22×#41C2×D7111yescharacteristic
391C2×#131—28no—
392C2×#131—711no—
393C2×#131—711no—
394C2×#131—713no—
395C2×#131—713no—
396C2×#131—1428no—
397C2×#131C2×D7111yescharacteristic
398C2×#131C2×D7111yescharacteristic
399C2×#131C2×D7113yescomplemented
400C2×#131C2×D7113yescomplemented
401C22×M16—713no—
402C22×M16C2×D7113yescomplemented
403C23×C8—713no—
404C23×C8C2×D7113yescomplemented
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×#41—711no—
417C2×C4×D4—713no—
418#436—716no—
419#436—716no—
420#435—716no—
421#435—716no—
422#435—716no—
423#435—716no—
424C8×D4—711no—
425C8×D4—713no—
426C8×D4—713no—
427C8×D4—713no—
428C8×D4—713no—
429C8×D4—713no—
430C8×D4—713no—
431C8×D4—713no—
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×C4×C8—713no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—711no—
452C2×#41—713no—
453C2×#41—713no—
454C2×#41—1424no—
455C2×#41—1424no—
456C2×#41C4×D7113yes—
457C2×#41C4×D7111yescharacteristic
458C2×#41C22×D7113yes—
459C2×#41C22×D7111yescharacteristic
460C22×Q8—711no—
461C22×Q8C4×D7111yescharacteristic
462C22×D4—713no—
463C22×D4—713no—
464C22×D4C4×D7113yes—
465C23×C4—713no—
466C23×C4C22×D7113yes—
467#131—24no—
468#131—212no—
469#131—212no—
470#131—1424no—
471#131—1424no—
472#131—14212no—
473#131—14212no—
474#131C22⋊D7118yesdirect product factor
475C2×M16—212no—
476C2×M16—713no—
477C2×M16—713no—
478C2×M16—716no—
479C2×M16—14212no—
480C2×M16C22×D7113yes—
481C2×M16C22×D7116yes—
482C2×M16C22×D7113yes—
483C22×C8—212no—
484C22×C8—713no—
485C22×C8—713no—
486C22×C8—713no—
487C22×C8—713no—
488C22×C8—711no—
489C22×C8—713no—
490C22×C8—14212no—
491C22×C8C22×D7113yes—
492C22×C8C22×D7113yes—
493C22×C8C22×D7113yes—
494C22×C8C22×D7111yescharacteristic
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—713no—
508#121—713no—
509#121—716no—
510#121—716no—
511#121—713no—
512#121—713no—
513#120—716no—
514#120—716no—
515C4×Q8—711no—
516C4×Q8—711no—
517C4×D4—713no—
518C4×D4—713no—
519C4×D4—713no—
520C4×D4—713no—
521C4×D4—713no—
522C4×D4—713no—
523C4×D4—711no—
524C4×D4—713no—
525C4×D4—713no—
526C4×D4—713no—
527C4×D4—716no—
528#117—713no—
529C2×C4⋊C4—713no—
530C2×C22⋊C4—713no—
531C2×C22⋊C4—713no—
532C2×C42—713no—
533C4⋊C8—711no—
534C4⋊C8—713no—
535C4⋊C8—713no—
536C4⋊C8—713no—
537C4⋊C8—716no—
538C22⋊C8—711no—
539C22⋊C8—713no—
540C22⋊C8—713no—
541C22⋊C8—713no—
542C22⋊C8—716no—
543C22⋊C8—711no—
544C22⋊C8—713no—
545C22⋊C8—713no—
546C22⋊C8—713no—
547C22⋊C8—716no—
548#97—716no—
549C4×C8—713no—
550C4×C8—713no—
551C4×C8—711no—
552C4×C8—713no—
553C24—713no—
554C24C2×C4×D7113yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1424no—
560#41—14212no—
561#41—1426no—
562#41—1426no—
563#41C2×C22⋊D7114yes—
564#41#1176586514yes—
565C2×Q8—24no—
566C2×Q8—713no—
567C2×Q8—1424no—
568C2×Q8C2×C4×D7113yes—
569C2×Q8C2×C4×D7111yescharacteristic
570C2×D4—212no—
571C2×D4—716no—
572C2×D4—711no—
573C2×D4—713no—
574C2×D4—713no—
575C2×D4—713no—
576C2×D4—716no—
577C2×D4—713no—
578C2×D4—14212no—
579C2×D4—14212no—
580C2×D4C2×C4×D7116yes—
581C2×D4C2×C4×D7113yes—
582C2×D4C2×C4×D7113yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—713no—
586C22×C4—713no—
587C22×C4—713no—
588C22×C4—713no—
589C22×C4—713no—
590C22×C4—711no—
591C22×C4—713no—
592C22×C4—1426no—
593C22×C4—1426no—
594C22×C4C2×C4×D7113yes—
595C22×C4C2×C4×D7113yes—
596C22×C4C2×C4×D7113yes—
597C22×C4C23×D7111yescharacteristic
598C22×C4C23×D7113yes—
599C22×C4C23×D7113yes—
600M16—26no—
601M16—212no—
602M16—1426no—
603M16—1426no—
604M16—14212no—
605M16C2×C22⋊D71112yescomplemented
606C2×C8—26no—
607C2×C8—22no—
608C2×C8—26no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—711no—
612C2×C8—713no—
613C2×C8—711no—
614C2×C8—713no—
615C2×C8—1426no—
616C2×C8—1426no—
617C2×C8—1422no—
618C2×C8—1426no—
619C2×C8—1426no—
620C2×C8—1426no—
621C2×C8C2×C22⋊D71112yescomplemented
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⋊C4—713no—
632C4⋊C4—713no—
633C22⋊C4—711no—
634C22⋊C4—713no—
635C22⋊C4—713no—
636C22⋊C4—713no—
637C22⋊C4—716no—
638C22⋊C4—716no—
639C22⋊C4—711no—
640C22⋊C4—713no—
641C22⋊C4—713no—
642C22⋊C4—713no—
643C22⋊C4—716no—
644C42—713no—
645C42—713no—
646C42—711no—
647C42—713no—
648C23—26no—
649C23—26no—
650C23—43no—
651C23—2843no—
652C23—711no—
653C23—713no—
654C23—1426no—
655C23—1426no—
656C23C22×C4×D7113yes—
657C23C22×C4×D7113yes—
658C23C22×C4×D7111yescharacteristic
659Q8—26no—
660Q8—1426no—
661Q8C4×C22⋊D7114yes—
662D4—212no—
663D4—26no—
664D4—2846no—
665D4—714no—
666D4—1426no—
667D4—1426no—
668D4—14212no—
669D4—1426no—
670D4—1426no—
671D4C4×C22⋊D71112yes—
672C2×C4—26no—
673C2×C4—21no—
674C2×C4—23no—
675C2×C4—21no—
676C2×C4—23no—
677C2×C4—26no—
678C2×C4—26no—
679C2×C4—2843no—
680C2×C4—711no—
681C2×C4—711no—
682C2×C4—713no—
683C2×C4—713no—
684C2×C4—711no—
685C2×C4—713no—
686C2×C4—1426no—
687C2×C4—1426no—
688C2×C4—1421no—
689C2×C4—1423no—
690C2×C4—1421no—
691C2×C4—1423no—
692C2×C4—1426no—
693C2×C4—1426no—
694C2×C4C22×C4×D7111yescharacteristic
695C2×C4C22×C4×D7113yes—
696C2×C4C22×C4×D7113yes—
697C2×C4C22×C22⋊D7116yes—
698C2×C4C2×#1176586516yes—
699C2×C4C24×D7111yescharacteristic
700C8—21no—
701C8—23no—
702C8—1421no—
703C8—1423no—
704C8—1421no—
705C8—1423no—
706C8C22×C22⋊D7112yes—
707C8C22×C22⋊D7116yes—
708C22—23no—
709C22—21no—
710C22—23no—
711C22—21no—
712C22—23no—
713C22—23no—
714C22—23no—
715C22—412no—
716C22—28412no—
717C22—712no—
718C22—1423no—
719C22—1423no—
720C22—1423no—
721C22—1421no—
722C22—1421no—
723C22C2×C4×C22⋊D7116yes—
724C22#131×D7112yescomplemented
725C22C23×C4×D7111yescharacteristic
726C4—21no—
727C4—23no—
728C4—712no—
729C4—1423no—
730C4—1421no—
731C4—1423no—
732C4—1421no—
733C4—1423no—
734C4C2×C4×C22⋊D7116yes—
735C4C23×C22⋊D7111yescharacteristic
736C4C22×#1176586511yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—2843no—
741C2—1422no—
742C2C22×C4×C22⋊D7111yescharacteristic
743C2C2×#131×D7111yescharacteristic
744C2#2260305111yescharacteristic
subgroupG/H
centerC2×C8C23×D71
commutator, socleC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC22×#131×C71C2
prime radical#41×C22⋊D71C2
cosocleC2×C4×C71C25
hypercenterC22×#131D71
hypocenterC71D4×#131
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C2×#131×D71C2semidirect
3. #22597082C2semidirect
4. M16×C22⋊D71C2semidirect
5. #22597065C2semidirect
6. #22597062C2semidirect
7. #22597050C2semidirect
8. #22597034C2semidirect
9. #22597032C2semidirect
10. C2×C8×C22⋊D71C2semidirect
11. #22596906C2semidirect
12. #22596789C2semidirect
13. #22596787C2semidirect
14. #131×Dic71C2semidirect
15. C22×#131×C71C2semidirect
17. C2×#14556136C22semidirect
20. C2×#14556134C22semidirect
22. C2×M16×D71C22semidirect
23. C22×C8×D71C22semidirect
37. #17986075C22semidirect
38. #17986075C22semidirect
39. #17986070C22semidirect
40. #17986070C22semidirect
41. #17986068C22semidirect
42. #17986068C22semidirect
45. C8×C22⋊D71C22semidirect
46. C8×C22⋊D71C22semidirect
47. C8×C22⋊D71C22semidirect
48. C8×C22⋊D71C22semidirect
49. C8×C22⋊D71C22semidirect
50. C8×C22⋊D71C22semidirect
51. C8×C22⋊D71C22semidirect
52. #17986027C22semidirect
53. #17986025C22semidirect
54. #17986022C22semidirect
55. C2×Dic71⋊C8C22semidirect
56. #17985967C22semidirect
57. #17985966C22semidirect
58. #17985966C22semidirect
59. #17985965C22semidirect
60. #17985963C22semidirect
61. #17985962C22semidirect
62. C2×C22⋊(C71⋊C8)C22semidirect
63. C2×(C2×D71)⋊C8C22semidirect
64. #17985957C22semidirect
65. #17985954C22semidirect
66. M16×Dic71C22semidirect
67. C2×C8×Dic71C22semidirect
72. C2×#131×C71C22semidirect
73. C2×#131×C71C22semidirect
74. C22×M16×C71C22semidirect
75. C23×C8×C71C22semidirect
168. #131×C71D4semidirect
264. M16×C71C2×D4semidirect
270. C2×C8×C71C2×D4semidirect
309. C22⋊D71#131direct (N × H)
344. C22×C71C2×#131semidirect
352. C2×D71C2×#131semidirect
363. Dic71C2×#131semidirect
374. C22×#131D71semidirect
388. C71D4×#131semidirect
399. C2×#131C2×D71semidirect
400. C2×#131C2×D71semidirect
402. C22×M16C2×D71semidirect
404. C23×C8C2×D71semidirect
474. #131C22⋊D71direct (N × H)
605. M16C2×C22⋊D71semidirect
621. C2×C8C2×C22⋊D71semidirect
724. C22#131×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D712
#41×C22⋊D712
#225970822
M16×C22⋊D712
#225970652
#225970622
#225970502
#225970342
#225970322
C2×C8×C22⋊D712
#225969062
#225967892
#225967872
#131×Dic712
C22×#131×C712
D4×#13171