Finite Group Databasebeta

← #131×C22⋊D67 #31719795

Subgroups — #131×C22⋊D67 #31719795

Order 17152.

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×D67C211yesmaximal, characteristic, complemented
2#41×C22⋊D67C211yesmaximal, characteristic
3#22568951C213yesmaximal, complemented
4M16×C22⋊D67C213yesmaximal, complemented
5#22568934C213yesmaximal, complemented
6#22568931C213yesmaximal, complemented
7#22568919C213yesmaximal, complemented
8#22568903C213yesmaximal, complemented
9#22568901C213yesmaximal, complemented
10C2×C8×C22⋊D67C213yesmaximal, complemented
11#22568775C211yesmaximal, characteristic, complemented
12#22568658C211yesmaximal, characteristic, complemented
13#22568656C211yesmaximal, characteristic, complemented
14#131×Dic67C211yesmaximal, characteristic, complemented
15C22×#131×C67C211yesmaximal, characteristic, complemented
16C2×#41×D67C2211yescharacteristic
17C2×#14524051C2213yescomplemented
18C2×#14524050C2211yescharacteristic
19C2×#14524050C2211yescharacteristic
20C2×#14524049C2213yescomplemented
21#131×D67—28no—
22C2×M16×D67C2213yescomplemented
23C22×C8×D67C2213yescomplemented
24#16864065C411yescharacteristic
25Q8×C22⋊D67C411yescharacteristic
26#16864057C411yescharacteristic
27#16864053C411yescharacteristic
28#16864045C413yes—
29#16864040C413yes—
30#16864034C413yes—
31D4×C22⋊D67C413yes—
32#16863942C2213yes—
33#16863907C2213yes—
34#16863903C2213yes—
35#41×Dic67C2211yescharacteristic
36C2×C4×C22⋊D67C2213yes—
37#16863472C2216yescomplemented
38#16863472C2216yescomplemented
39#16863467C2216yescomplemented
40#16863467C2216yescomplemented
41#16863465C2216yescomplemented
42#16863465C2216yescomplemented
43C8×C22⋊D67C2211yescharacteristic
44C8×C22⋊D67C2213yes—
45C8×C22⋊D67C2213yescomplemented
46C8×C22⋊D67C2213yescomplemented
47C8×C22⋊D67C2213yescomplemented
48C8×C22⋊D67C2213yescomplemented
49C8×C22⋊D67C2213yescomplemented
50C8×C22⋊D67C2213yescomplemented
51C8×C22⋊D67C2216yescomplemented
52#16863424C2213yescomplemented
53#16863422C2213yescomplemented
54#16863419C2213yescomplemented
55C2×Dic67⋊C8C2213yescomplemented
56#16863364C2213yescomplemented
57#16863363C2213yescomplemented
58#16863363C2213yescomplemented
59#16863362C2213yescomplemented
60#16863360C2213yescomplemented
61#16863359C2213yescomplemented
62C2×C22⋊(C67⋊C8)C2213yescomplemented
63C2×(C2×D67)⋊C8C2213yescomplemented
64#16863354C2213yescomplemented
65#16863351C2213yescomplemented
66M16×Dic67C2213yescomplemented
67C2×C8×Dic67C2213yescomplemented
68C22×#41×C67C2211yescharacteristic
69C2×#131×C67—28no—
70C2×#131×C67C2211yescharacteristic
71C2×#131×C67C2211yescharacteristic
72C2×#131×C67C2213yescomplemented
73C2×#131×C67C2213yescomplemented
74C22×M16×C67C2213yescomplemented
75C23×C8×C67C2213yescomplemented
76C2×#11761629C2×C411yescharacteristic
77C2×#11761628C2313yes—
78C2×#11761627C2×C413yes—
79#41×D67—24no—
80#41×D67—24no—
81C2×Q8×D67C2×C411yescharacteristic
82C22×C22⋊D67C2×C413yes—
83C2×D4×D67C2×C413yes—
84C22×C4×D67C2313yes—
85#14524051—212no—
86#14524050—24no—
87#14524050—24no—
88#14524049—212no—
89C2×#11761612C2313yes—
90C2×#11761612C2313yes—
91C2×#11761611C2316yes—
92M16×D67—212no—
93C22×C67⋊C8C2313yes—
94C22×C67⋊C8C2313yes—
95C2×C8×D67—212no—
96C2×C8×D67C2311yescharacteristic
97C2×C8×D67C2313yes—
98C2×C8×D67C2313yes—
99C2×C8×D67C2313yes—
100#14524041C2×C413yes—
101#14524039C2×C413yes—
102#14524032C2×C413yes—
103#14524030C2×C413yes—
104#14524026C2×C416yes—
105#14524024C2×C416yes—
106#14524022C2×C413yes—
107#14524022C2×C413yes—
108#14524019C2×C413yes—
109#14524019C2×C413yes—
110#14524017C2×C413yes—
111#14524017C2×C413yes—
112#14524015C2×C416yes—
113#14524015C2×C416yes—
114#14524014C2×C413yes—
115#14524014C2×C413yes—
116#14524012C2×C416yes—
117#14524011C2×C416yes—
118Q8×Dic67C2×C411yescharacteristic
119Q8×Dic67C2×C411yescharacteristic
120D4×Dic67C2×C413yes—
121D4×Dic67C2×C413yes—
122C4×C22⋊D67C2×C413yes—
123C4×C22⋊D67C2×C413yes—
124C4×C22⋊D67C2×C413yes—
125C4×C22⋊D67C2×C413yes—
126C4×C22⋊D67C2311yescharacteristic
127C4×C22⋊D67C2313yes—
128C4×C22⋊D67C2313yes—
129C4×C22⋊D67C2313yes—
130C4×C22⋊D67C2316yes—
131#14524002C2313yes—
132C2×Dic67⋊C4C2×C413yes—
133C2×C22⋊Dic67C2×C413yes—
134C2×(C2×D67)⋊C4C2×C413yes—
135C2×C4×Dic67C2313yes—
136Dic67⋊C8C2311yescharacteristic
137Dic67⋊C8C2313yes—
138Dic67⋊C8C2313yes—
139Dic67⋊C8C2313yes—
140Dic67⋊C8C2316yes—
141C22⋊(C67⋊C8)C2311yescharacteristic
142C22⋊(C67⋊C8)C2313yes—
143C22⋊(C67⋊C8)C2313yes—
144C22⋊(C67⋊C8)C2313yes—
145C22⋊(C67⋊C8)C2316yes—
146(C2×D67)⋊C8C2311yescharacteristic
147(C2×D67)⋊C8C2313yes—
148(C2×D67)⋊C8C2313yes—
149(C2×D67)⋊C8C2313yes—
150(C2×D67)⋊C8C2316yes—
151#14523953C2316yes—
152C8×Dic67C2311yescharacteristic
153C8×Dic67C2313yes—
154C8×Dic67C2313yes—
155C8×Dic67C2313yes—
156C2×#41×C67—24no—
157C2×#41×C67—24no—
158C2×#41×C67C2×C413yes—
159C2×#41×C67C2×C411yescharacteristic
160C2×#41×C67C2313yes—
161C2×#41×C67C2311yescharacteristic
162C22×Q8×C67C2×C411yescharacteristic
163C22×D4×C67C2×C413yes—
164C23×C4×C67C2313yes—
165#131×C67—24no—
166#131×C67—212no—
167#131×C67—212no—
168#131×C67D418yescomplemented
169C2×M16×C67—212no—
170C2×M16×C67C2313yes—
171C2×M16×C67C2316yes—
172C2×M16×C67C2313yes—
173C22×C8×C67—212no—
174C22×C8×C67C2311yescharacteristic
175C22×C8×C67C2313yes—
176C22×C8×C67C2313yes—
177C22×C8×C67C2313yes—
178C22×C8×C67C2313yes—
179C22×C8×C67C2313yes—
180C23×D67C22×C413yes—
181#11761629—24no—
182#11761628—26no—
183#11761628—26no—
184#11761627—212no—
185C2×Dic134C22×C413yes—
186Q8×D67—24no—
187C2×D268C22×C413yes—
188C2×C22⋊D67—212no—
189C2×C22⋊D67C22×C413yes—
190C2×C22⋊D67C22×C413yes—
191C2×C22⋊D67C22×C413yes—
192C2×C22⋊D67C22×C416yes—
193C2×C22⋊D67C22×C416yes—
194C2×C22⋊D67C22×C411yescharacteristic
195D4×D67—212no—
196C22×Dic67C22×C413yes—
197C22×Dic67C22×C413yes—
198C22×Dic67C22×C413yes—
199C2×C4×D67—26no—
200C2×C4×D67—26no—
201C2×C4×D67C22×C413yes—
202C2×C4×D67C22×C413yes—
203C2×C4×D67C2411yescharacteristic
204C2×C4×D67C2413yes—
205#11761612—26no—
206#11761612—26no—
207#11761611—212no—
208C2×C67⋊C8—26no—
209C2×C67⋊C8—26no—
210C2×C67⋊C8C2411yescharacteristic
211C2×C67⋊C8C2413yes—
212C2×C67⋊C8C2411yescharacteristic
213C2×C67⋊C8C2413yes—
214C8×D67—22no—
215C8×D67—26no—
216C8×D67—26no—
217C8×D67—26no—
218C4⋊Dic67C22×C413yes—
219C4⋊Dic67C22×C413yes—
220Dic67⋊C4C22×C411yescharacteristic
221Dic67⋊C4C22×C413yes—
222Dic67⋊C4C22×C413yes—
223Dic67⋊C4C22×C413yes—
224Dic67⋊C4C22×C416yes—
225C22⋊Dic67C22×C411yescharacteristic
226C22⋊Dic67C22×C413yes—
227C22⋊Dic67C22×C413yes—
228C22⋊Dic67C22×C413yes—
229C22⋊Dic67C22×C416yes—
230C22⋊Dic67C22×C416yes—
231(C2×D67)⋊C4C22×C411yescharacteristic
232(C2×D67)⋊C4C22×C413yes—
233(C2×D67)⋊C4C22×C413yes—
234(C2×D67)⋊C4C22×C413yes—
235(C2×D67)⋊C4C22×C416yes—
236C4×Dic67C22×C413yes—
237C4×Dic67C22×C413yes—
238C4×Dic67C2411yescharacteristic
239C4×Dic67C2413yes—
240C24×C67C22×C413yes—
241#41×C67—24no—
242#41×C67—212no—
243#41×C67—26no—
244#41×C67—26no—
245#41×C67C2×D414yes—
246#41×C67#4114yes—
247C2×Q8×C67—24no—
248C2×Q8×C67C22×C413yes—
249C2×Q8×C67C22×C411yescharacteristic
250C2×D4×C67—212no—
251C2×D4×C67C22×C416yes—
252C2×D4×C67C22×C413yes—
253C2×D4×C67C22×C413yes—
254C22×C4×C67—26no—
255C22×C4×C67—26no—
256C22×C4×C67C22×C413yes—
257C22×C4×C67C22×C413yes—
258C22×C4×C67C22×C413yes—
259C22×C4×C67C2411yescharacteristic
260C22×C4×C67C2413yes—
261C22×C4×C67C2413yes—
262M16×C67—26no—
263M16×C67—212no—
264M16×C67C2×D4112yescomplemented
265C2×C8×C67—26no—
266C2×C8×C67—22no—
267C2×C8×C67—26no—
268C2×C8×C67—26no—
269C2×C8×C67—26no—
270C2×C8×C67C2×D4112yescomplemented
271C2×C8×C67C2411yescharacteristic
272C2×C8×C67C2413yes—
273C2×C8×C67C2413yes—
274C2×C8×C67C2411yescharacteristic
275C23×C67—26no—
276C23×C67—26no—
277C23×C67—43no—
278C23×C67C23×C413yes—
279C23×C67C23×C413yes—
280C23×C67C23×C411yescharacteristic
281C22×D67—26no—
282C22×D67—26no—
283C22×D67—43no—
284C22×D67C23×C413yes—
285C22×D67C23×C411yescharacteristic
286Q8×C67—26no—
287Q8×C67C4×D414yes—
288D4×C67—212no—
289D4×C67—26no—
290D4×C67C4×D4112yes—
291C2×C4×C67—26no—
292C2×C4×C67—26no—
293C2×C4×C67—26no—
294C2×C4×C67—21no—
295C2×C4×C67—23no—
296C2×C4×C67—21no—
297C2×C4×C67—23no—
298C2×C4×C67C23×C411yescharacteristic
299C2×C4×C67C23×C413yes—
300C2×C4×C67C23×C413yes—
301C2×C4×C67C22×D416yes—
302C2×C4×C67C2×#4116yes—
303C2×C4×C67C2511yescharacteristic
304C22⋊D67—212no—
305C22⋊D67—26no—
306C22⋊D67—26no—
307C22⋊D67—26no—
308C22⋊D67—46no—
309C22⋊D67#13114yesdirect product factor
310C2×Dic67—26no—
311C2×Dic67—26no—
312C2×Dic67—43no—
313C2×Dic67C23×C411yescharacteristic
314C2×Dic67C23×C413yes—
315C2×Dic67C23×C413yes—
316C2×Dic67C23×C411yescharacteristic
317C2×Dic67C23×C413yes—
318C2×Dic67C23×C411yescharacteristic
319D268—26no—
320C4×D67—26no—
321C4×D67—26no—
322C4×D67—21no—
323C4×D67—23no—
324C4×D67—21no—
325C4×D67—23no—
326Dic134—26no—
327C8×C67—21no—
328C8×C67—23no—
329C8×C67C22×D412yes—
330C8×C67C22×D416yes—
331C67⋊C8—21no—
332C67⋊C8—23no—
333C67⋊C8—21no—
334C67⋊C8—23no—
335C22×C67—21no—
336C22×C67—23no—
337C22×C67—23no—
338C22×C67—21no—
339C22×C67—23no—
340C22×C67—23no—
341C22×C67—23no—
342C22×C67—412no—
343C22×C67C2×C4×D416yes—
344C22×C67C2×#13112yescomplemented
345C22×C67C24×C411yescharacteristic
346C2×D67—21no—
347C2×D67—21no—
348C2×D67—23no—
349C2×D67—23no—
350C2×D67—23no—
351C2×D67—412no—
352C2×D67C2×#13112yescomplemented
353C4×C67—21no—
354C4×C67—23no—
355C4×C67C2×C4×D416yes—
356C4×C67C23×D411yescharacteristic
357C4×C67C22×#4111yescharacteristic
358Dic67—23no—
359Dic67—21no—
360Dic67—23no—
361Dic67—21no—
362Dic67—23no—
363Dic67C2×#13112yescomplemented
364D4×#131—671nomaximal, Sylow
365C2×C67—26no—
366C2×C67—22no—
367C2×C67—43no—
368C2×C67C22×C4×D411yescharacteristic
369C2×C67C22×#13111yescharacteristic
370C2×C67#357311yescharacteristic
371D67—22no—
372D67—43no—
373C22×#131—671no—
374C22×#131D6711yescharacteristic, complemented
375D4×#41—671no—
376#2935—673no—
377D4×M16—673no—
378#2933—673no—
379#2933—673no—
380#2931—673no—
381#2929—673no—
382#2929—673no—
383C2×C8×D4—673no—
384#2906—671no—
385#2880—671no—
386#2880—671no—
387C4×#131—671no—
388C67D4×#13111yescharacteristic, complemented, Sylow
389C22×#41—671no—
390C22×#41C2×D6711yescharacteristic
391C2×#131—28no—
392C2×#131—671no—
393C2×#131—671no—
394C2×#131—673no—
395C2×#131—673no—
396C2×#131—1348no—
397C2×#131C2×D6711yescharacteristic
398C2×#131C2×D6711yescharacteristic
399C2×#131C2×D6713yescomplemented
400C2×#131C2×D6713yescomplemented
401C22×M16—673no—
402C22×M16C2×D6713yescomplemented
403C23×C8—673no—
404C23×C8C2×D6713yescomplemented
405#550—671no—
406D4×Q8—671no—
407#548—671no—
408#548—671no—
409#547—673no—
410#546—673no—
411#546—673no—
412D42—673no—
413#532—673no—
414#525—673no—
415#525—673no—
416C4×#41—671no—
417C2×C4×D4—673no—
418#436—676no—
419#436—676no—
420#435—676no—
421#435—676no—
422#435—676no—
423#435—676no—
424C8×D4—671no—
425C8×D4—673no—
426C8×D4—673no—
427C8×D4—673no—
428C8×D4—673no—
429C8×D4—673no—
430C8×D4—673no—
431C8×D4—673no—
432C8×D4—676no—
433#424—673no—
434#424—673no—
435#423—673no—
436C2×C4⋊C8—673no—
437#408—673no—
438#408—673no—
439#408—673no—
440#408—673no—
441#407—673no—
442#407—673no—
443C2×C22⋊C8—673no—
444C2×C22⋊C8—673no—
445#405—673no—
446#405—673no—
447C4×M16—673no—
448C2×C4×C8—673no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—671no—
452C2×#41—673no—
453C2×#41—673no—
454C2×#41—1344no—
455C2×#41—1344no—
456C2×#41C4×D6713yes—
457C2×#41C4×D6711yescharacteristic
458C2×#41C22×D6713yes—
459C2×#41C22×D6711yescharacteristic
460C22×Q8—671no—
461C22×Q8C4×D6711yescharacteristic
462C22×D4—673no—
463C22×D4—673no—
464C22×D4C4×D6713yes—
465C23×C4—673no—
466C23×C4C22×D6713yes—
467#131—24no—
468#131—212no—
469#131—212no—
470#131—1344no—
471#131—1344no—
472#131—13412no—
473#131—13412no—
474#131C22⋊D6718yesdirect product factor
475C2×M16—212no—
476C2×M16—673no—
477C2×M16—673no—
478C2×M16—676no—
479C2×M16—13412no—
480C2×M16C22×D6713yes—
481C2×M16C22×D6716yes—
482C2×M16C22×D6713yes—
483C22×C8—212no—
484C22×C8—673no—
485C22×C8—673no—
486C22×C8—673no—
487C22×C8—673no—
488C22×C8—671no—
489C22×C8—673no—
490C22×C8—13412no—
491C22×C8C22×D6713yes—
492C22×C8C22×D6713yes—
493C22×C8C22×D6713yes—
494C22×C8C22×D6711yescharacteristic
495C22×C8C22×D6713yes—
496C22×C8C22×D6713yes—
497C4⋊Q8—673no—
498#127—673no—
499#124—673no—
500#124—673no—
501#123—676no—
502#123—676no—
503C22⋊Q8—673no—
504C22⋊Q8—673no—
505C22⋊Q8—673no—
506C22⋊Q8—673no—
507#121—673no—
508#121—673no—
509#121—676no—
510#121—676no—
511#121—673no—
512#121—673no—
513#120—676no—
514#120—676no—
515C4×Q8—671no—
516C4×Q8—671no—
517C4×D4—673no—
518C4×D4—673no—
519C4×D4—673no—
520C4×D4—673no—
521C4×D4—673no—
522C4×D4—673no—
523C4×D4—671no—
524C4×D4—673no—
525C4×D4—673no—
526C4×D4—673no—
527C4×D4—676no—
528#117—673no—
529C2×C4⋊C4—673no—
530C2×C22⋊C4—673no—
531C2×C22⋊C4—673no—
532C2×C42—673no—
533C4⋊C8—671no—
534C4⋊C8—673no—
535C4⋊C8—673no—
536C4⋊C8—673no—
537C4⋊C8—676no—
538C22⋊C8—671no—
539C22⋊C8—673no—
540C22⋊C8—673no—
541C22⋊C8—673no—
542C22⋊C8—676no—
543C22⋊C8—671no—
544C22⋊C8—673no—
545C22⋊C8—673no—
546C22⋊C8—673no—
547C22⋊C8—676no—
548#97—676no—
549C4×C8—673no—
550C4×C8—673no—
551C4×C8—671no—
552C4×C8—673no—
553C24—673no—
554C24C2×C4×D6713yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1344no—
560#41—13412no—
561#41—1346no—
562#41—1346no—
563#41C2×C22⋊D6714yes—
564#41#1176162814yes—
565C2×Q8—24no—
566C2×Q8—673no—
567C2×Q8—1344no—
568C2×Q8C2×C4×D6713yes—
569C2×Q8C2×C4×D6711yescharacteristic
570C2×D4—212no—
571C2×D4—676no—
572C2×D4—671no—
573C2×D4—673no—
574C2×D4—673no—
575C2×D4—673no—
576C2×D4—676no—
577C2×D4—673no—
578C2×D4—13412no—
579C2×D4—13412no—
580C2×D4C2×C4×D6716yes—
581C2×D4C2×C4×D6713yes—
582C2×D4C2×C4×D6713yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—673no—
586C22×C4—673no—
587C22×C4—673no—
588C22×C4—673no—
589C22×C4—673no—
590C22×C4—671no—
591C22×C4—673no—
592C22×C4—1346no—
593C22×C4—1346no—
594C22×C4C2×C4×D6713yes—
595C22×C4C2×C4×D6713yes—
596C22×C4C2×C4×D6713yes—
597C22×C4C23×D6711yescharacteristic
598C22×C4C23×D6713yes—
599C22×C4C23×D6713yes—
600M16—26no—
601M16—212no—
602M16—1346no—
603M16—1346no—
604M16—13412no—
605M16C2×C22⋊D67112yescomplemented
606C2×C8—26no—
607C2×C8—22no—
608C2×C8—26no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—671no—
612C2×C8—673no—
613C2×C8—671no—
614C2×C8—673no—
615C2×C8—1346no—
616C2×C8—1346no—
617C2×C8—1342no—
618C2×C8—1346no—
619C2×C8—1346no—
620C2×C8—1346no—
621C2×C8C2×C22⋊D67112yescomplemented
622C2×C8C23×D6711yescharacteristic
623C2×C8C23×D6713yes—
624C2×C8C23×D6713yes—
625C2×C8C23×D6711yescharacteristic
626C4⋊C4—671no—
627C4⋊C4—673no—
628C4⋊C4—673no—
629C4⋊C4—673no—
630C4⋊C4—673no—
631C4⋊C4—673no—
632C4⋊C4—676no—
633C22⋊C4—671no—
634C22⋊C4—673no—
635C22⋊C4—673no—
636C22⋊C4—673no—
637C22⋊C4—676no—
638C22⋊C4—676no—
639C22⋊C4—671no—
640C22⋊C4—673no—
641C22⋊C4—673no—
642C22⋊C4—673no—
643C22⋊C4—676no—
644C42—673no—
645C42—673no—
646C42—671no—
647C42—673no—
648C23—26no—
649C23—26no—
650C23—43no—
651C23—2683no—
652C23—671no—
653C23—673no—
654C23—1346no—
655C23—1346no—
656C23C22×C4×D6713yes—
657C23C22×C4×D6713yes—
658C23C22×C4×D6711yescharacteristic
659Q8—26no—
660Q8—1346no—
661Q8C4×C22⋊D6714yes—
662D4—212no—
663D4—26no—
664D4—2686no—
665D4—674no—
666D4—1346no—
667D4—1346no—
668D4—13412no—
669D4—1346no—
670D4—1346no—
671D4C4×C22⋊D67112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—21no—
676C2×C4—23no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—2683no—
680C2×C4—671no—
681C2×C4—671no—
682C2×C4—673no—
683C2×C4—673no—
684C2×C4—671no—
685C2×C4—673no—
686C2×C4—1346no—
687C2×C4—1346no—
688C2×C4—1346no—
689C2×C4—1346no—
690C2×C4—1341no—
691C2×C4—1343no—
692C2×C4—1341no—
693C2×C4—1343no—
694C2×C4C22×C4×D6711yescharacteristic
695C2×C4C22×C4×D6713yes—
696C2×C4C22×C4×D6713yes—
697C2×C4C22×C22⋊D6716yes—
698C2×C4C2×#1176162816yes—
699C2×C4C24×D6711yescharacteristic
700C8—21no—
701C8—23no—
702C8—1341no—
703C8—1343no—
704C8—1341no—
705C8—1343no—
706C8C22×C22⋊D6712yes—
707C8C22×C22⋊D6716yes—
708C22—23no—
709C22—21no—
710C22—23no—
711C22—21no—
712C22—23no—
713C22—23no—
714C22—23no—
715C22—412no—
716C22—26812no—
717C22—672no—
718C22—1343no—
719C22—1343no—
720C22—1343no—
721C22—1341no—
722C22—1341no—
723C22C2×C4×C22⋊D6716yes—
724C22#131×D6712yescomplemented
725C22C23×C4×D6711yescharacteristic
726C4—21no—
727C4—23no—
728C4—672no—
729C4—1343no—
730C4—1341no—
731C4—1343no—
732C4—1341no—
733C4—1343no—
734C4C2×C4×C22⋊D6716yes—
735C4C23×C22⋊D6711yescharacteristic
736C4C22×#1176162811yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—2683no—
741C2—1342no—
742C2C22×C4×C22⋊D6711yescharacteristic
743C2C2×#131×D6711yescharacteristic
744C2#2257492011yescharacteristic
subgroupG/H
centerC2×C8C23×D67
commutator, socleC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×#131×C67C2
prime radical#41×C22⋊D67C2
cosocleC2×C4×C67C25
hypercenterC22×#131D67
hypocenterC67D4×#131
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C2×#131×D67C2semidirect
3. #22568951C2semidirect
4. M16×C22⋊D67C2semidirect
5. #22568934C2semidirect
6. #22568931C2semidirect
7. #22568919C2semidirect
8. #22568903C2semidirect
9. #22568901C2semidirect
10. C2×C8×C22⋊D67C2semidirect
11. #22568775C2semidirect
12. #22568658C2semidirect
13. #22568656C2semidirect
14. #131×Dic67C2semidirect
15. C22×#131×C67C2semidirect
17. C2×#14524051C22semidirect
20. C2×#14524049C22semidirect
22. C2×M16×D67C22semidirect
23. C22×C8×D67C22semidirect
37. #16863472C22semidirect
38. #16863472C22semidirect
39. #16863467C22semidirect
40. #16863467C22semidirect
41. #16863465C22semidirect
42. #16863465C22semidirect
45. C8×C22⋊D67C22semidirect
46. C8×C22⋊D67C22semidirect
47. C8×C22⋊D67C22semidirect
48. C8×C22⋊D67C22semidirect
49. C8×C22⋊D67C22semidirect
50. C8×C22⋊D67C22semidirect
51. C8×C22⋊D67C22semidirect
52. #16863424C22semidirect
53. #16863422C22semidirect
54. #16863419C22semidirect
55. C2×Dic67⋊C8C22semidirect
56. #16863364C22semidirect
57. #16863363C22semidirect
58. #16863363C22semidirect
59. #16863362C22semidirect
60. #16863360C22semidirect
61. #16863359C22semidirect
62. C2×C22⋊(C67⋊C8)C22semidirect
63. C2×(C2×D67)⋊C8C22semidirect
64. #16863354C22semidirect
65. #16863351C22semidirect
66. M16×Dic67C22semidirect
67. C2×C8×Dic67C22semidirect
72. C2×#131×C67C22semidirect
73. C2×#131×C67C22semidirect
74. C22×M16×C67C22semidirect
75. C23×C8×C67C22semidirect
168. #131×C67D4semidirect
264. M16×C67C2×D4semidirect
270. C2×C8×C67C2×D4semidirect
309. C22⋊D67#131direct (N × H)
344. C22×C67C2×#131semidirect
352. C2×D67C2×#131semidirect
363. Dic67C2×#131semidirect
374. C22×#131D67semidirect
388. C67D4×#131semidirect
399. C2×#131C2×D67semidirect
400. C2×#131C2×D67semidirect
402. C22×M16C2×D67semidirect
404. C23×C8C2×D67semidirect
474. #131C22⋊D67direct (N × H)
605. M16C2×C22⋊D67semidirect
621. C2×C8C2×C22⋊D67semidirect
724. C22#131×D67semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D672
#41×C22⋊D672
#225689512
M16×C22⋊D672
#225689342
#225689312
#225689192
#225689032
#225689012
C2×C8×C22⋊D672
#225687752
#225686582
#225686562
#131×Dic672
C22×#131×C672
D4×#13167