Finite Group Databasebeta

← #6345475

Subgroups — #6345475

Order 512.

1659 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60949C211yesmaximal, characteristic
2C2×#2994C211yesmaximal, characteristic, complemented
3#60236C211yesmaximal, characteristic, complemented
4#18082C214yesmaximal, complemented
5#18080C214yesmaximal, complemented
6#18020C214yesmaximal, complemented
7#18014C214yesmaximal, complemented
8#17936C211yesmaximal, characteristic, complemented
9#17935C211yesmaximal, characteristic, complemented
10#17929C211yesmaximal, characteristic, complemented
11#17928C211yesmaximal, characteristic, complemented
12#17908C211yesmaximal, characteristic, complemented
13#17907C211yesmaximal, characteristic, complemented
14#17901C211yesmaximal, characteristic, complemented
15#17900C211yesmaximal, characteristic, complemented
16#17807C211yesmaximal, characteristic, complemented
17#17487C211yesmaximal, characteristic, complemented
18C2×#1480C211yesmaximal, characteristic, complemented
19#17325C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#529C2211yescharacteristic
22#3251C412yes—
23#3251C412yes—
24#3239C412yes—
25#3234C412yes—
26#3217C412yes—
27#3213C412yes—
28#3193C412yes—
29#3192C412yes—
30#3171C2214yes—
31#3105C2214yes—
32#3103C2211yescharacteristic
33#3103C2211yescharacteristic
34#3100C2211yescharacteristic
35#3100C2211yescharacteristic
36#2994—21no—
37#2994—21no—
38#2994—21no—
39#2994—21no—
40#2994C2212yes—
41#2994C2212yes—
42#2994C2212yescomplemented
43#2994C2212yescomplemented
44#2981—21no—
45#2981—21no—
46#2979C2212yescomplemented
47#2979C2212yescomplemented
48#2975—21no—
49#2974C2212yescomplemented
50#2974C2212yescomplemented
51#2972—21no—
52C2×#446C2211yescharacteristic, complemented
53C2×C8×Q8C2211yescharacteristic, complemented
54#2935—21no—
55#2935—21no—
56#2931C2211yescharacteristic
57#2931C2211yescharacteristic
58#2931C2211yescharacteristic
59#2931C2211yescharacteristic
60C2×#436C2211yescharacteristic, complemented
61C2×#435—21no—
62C2×C8×D4—21no—
63C2×C8×D4C2211yescharacteristic, complemented
64#2920C2211yescharacteristic
65#2920C2211yescharacteristic
66C2×#433—21no—
67C2×#431C2211yescharacteristic
68C2×#431C2211yescharacteristic
69C2×#424—21no—
70C22×C4⋊C8C2211yescharacteristic
71#2880—21no—
72#2880—21no—
73#1594C2214yescomplemented
74#1592C2214yescomplemented
75#1590C2214yescomplemented
76#1589C2214yescomplemented
77#1588C2214yescomplemented
78#1586C2214yescomplemented
79#1586C2214yescomplemented
80#1585C2214yescomplemented
81#1583C2214yescomplemented
82#1582C2214yescomplemented
83#1581C2214yescomplemented
84#1581C2214yescomplemented
85#1580C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×SD16C2214yescomplemented
88C8×D8C2214yescomplemented
89#1573C2214yescomplemented
90#1571C2211yescharacteristic, complemented
91#1571C2211yescharacteristic, complemented
92#1570C2211yescharacteristic, complemented
93#1570C2211yescharacteristic, complemented
94#1565C2214yescomplemented
95#1494C2214yes—
96#1487C2211yescharacteristic, complemented
97#1487C2211yescharacteristic, complemented
98#1486C2211yescharacteristic, complemented
99#1486C2211yescharacteristic, complemented
100#1482C2214yescomplemented
101#1480C2211yescharacteristic
102#1480C2211yescharacteristic
103#1480C2211yescharacteristic
104#1480C2211yescharacteristic
105#1480C2214yescomplemented
106C2×D4⋊C8C2214yescomplemented
107#1453C2212yescomplemented
108#1453C2212yescomplemented
109#1452C2211yescharacteristic, complemented
110#1452C2211yescharacteristic, complemented
111#1452C2212yescomplemented
112#1450C2211yescharacteristic, complemented
113#1450C2211yescharacteristic, complemented
114#1450C2212yescomplemented
115C22×#41—21no—
116C2×#131—21no—
117C2×#131—21no—
118C2×#131—21no—
119C2×#131—21no—
120C22×M16—21no—
121C23×C8—21no—
122C23×C8—21no—
123#532—21no—
124#532—21no—
125#532—21no—
126#532—21no—
127#532C2×C412yes—
128#532C2×C411yescharacteristic
129#532C2×C411yescharacteristic
130#532C2311yescharacteristic
131#532C2311yescharacteristic
132#532C2312yes—
133C2×C4⋊Q8C2×C411yescharacteristic
134C2×#127C2×C411yescharacteristic
135#529—21no—
136#529—21no—
137#529—21no—
138#529—21no—
139#529C2×C412yes—
140#529C2×C412yes—
141#529C2312yes—
142#529C2312yes—
143C2×#126—21no—
144C2×#125C2×C411yescharacteristic
145C2×#124—21no—
146C2×#124C2×C411yescharacteristic
147C2×#123—21no—
148C2×C22⋊Q8C2×C411yescharacteristic
149C2×#121—21no—
150C2×#121C2×C411yescharacteristic
151C2×#121C2×C412yes—
152C2×C4×Q8C2311yescharacteristic
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2312yes—
157C2×#117—21no—
158C22×C42C2311yescharacteristic
159#501C2×C414yes—
160#496C2×C414yes—
161#490C2×C414yes—
162#489C2×C414yes—
163#484C2×C414yes—
164#481C2×C412yes—
165#481C2×C412yes—
166#481C2×C414yes—
167#480C2×C412yes—
168#480C2×C412yes—
169#478C2×C414yes—
170#478C2×C414yes—
171#475C2×C412yes—
172#475C2×C412yes—
173#474C2×C412yes—
174#474C2×C412yes—
175#469C2×C414yes—
176#469C2×C414yes—
177#468C2×C414yes—
178#468C2×C414yes—
179#463C2×C414yes—
180#463C2×C414yes—
181#460C2×C412yes—
182#460C2×C412yes—
183#459C2×C412yes—
184#459C2×C412yes—
185#450C2×C414yes—
186#448C2×C412yes—
187#448C2×C412yes—
188#447C2×C412yes—
189#447C2×C412yes—
190#447C2×C414yes—
191#446—21no—
192#446—21no—
193#446C2312yes—
194#446C2312yes—
195C8×Q8—21no—
196C8×Q8—21no—
197C8×Q8C2312yes—
198C8×Q8C2312yes—
199C4×SD16C2314yes—
200C4×SD16C2314yes—
201C4×D8C2314yes—
202C4×D8C2314yes—
203#436—22no—
204#436—22no—
205#436—21no—
206#436—21no—
207#436—21no—
208#436—21no—
209#436—21no—
210#436—21no—
211#436C2312yes—
212#436C2312yes—
213#436C2312yes—
214#436C2312yes—
215#436C2312yes—
216#436C2312yes—
217#435—22no—
218#435—22no—
219#435—22no—
220#435—22no—
221#435—22no—
222#435—22no—
223#435—22no—
224#435—22no—
225C8×D4—22no—
226C8×D4—22no—
227C8×D4—22no—
228C8×D4—22no—
229C8×D4—22no—
230C8×D4—22no—
231C8×D4—21no—
232C8×D4—21no—
233C8×D4—21no—
234C8×D4—21no—
235C8×D4—21no—
236C8×D4—21no—
237C8×D4C2312yes—
238C8×D4C2312yes—
239C8×D4C2312yes—
240C8×D4C2312yes—
241C8×D4C2312yes—
242C8×D4C2312yes—
243#433—22no—
244#433—22no—
245#433—22no—
246#433—22no—
247#432—21no—
248#432C2×C412yes—
249#432C2×C412yes—
250#432C2312yes—
251#431—21no—
252#431—21no—
253#431—21no—
254#431D411yescharacteristic
255#431D411yescharacteristic
256#431D411yescharacteristic
257#431D411yescharacteristic
258#431C2312yes—
259#431C2311yescharacteristic
260#431C2311yescharacteristic
261#431C2312yes—
262#431C2311yescharacteristic
263#431C2311yescharacteristic
264#431C2312yes—
265#431C2311yescharacteristic
266#431C2311yescharacteristic
267#431C2311yescharacteristic
268#431C2311yescharacteristic
269#424—22no—
270#424—22no—
271#424—22no—
272#424—22no—
273#423C2×C412yes—
274#423C2311yescharacteristic
275#423C2311yescharacteristic
276C2×C4⋊C8—21no—
277C2×C4⋊C8—21no—
278C2×C4⋊C8—21no—
279C2×C4⋊C8—21no—
280C2×C4⋊C8—21no—
281C2×C4⋊C8—21no—
282C2×C4⋊C8D411yescharacteristic
283C2×C4⋊C8D411yescharacteristic
284C2×C4⋊C8C2312yes—
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2312yes—
288#408—21no—
289#408—21no—
290#408—21no—
291#408—21no—
292#408—22no—
293#408—22no—
294#408—22no—
295#408—22no—
296#407—21no—
297#407—22no—
298#407—22no—
299#407C2×C412yes—
300C2×C22⋊C8—21no—
301C2×C22⋊C8—21no—
302C2×C22⋊C8—21no—
303C2×C22⋊C8—22no—
304C2×C22⋊C8—22no—
305C2×C22⋊C8D411yescharacteristic
306C2×C22⋊C8D411yescharacteristic
307C4×M16—21no—
308C4×M16C2312yes—
309C2×#97—21no—
310C2×C4×C8—21no—
311C2×C4×C8C2312yes—
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#335C2314yes—
315#335C2314yes—
316#334C2314yes—
317#334C2314yes—
318Q8⋊C8C2314yes—
319Q8⋊C8C2314yes—
320D4⋊C8C2314yes—
321D4⋊C8C2314yes—
322D4⋊C8C2314yes—
323D4⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yes—
326#322C2312yes—
327#322C2312yes—
328#322C2312yes—
329#322C2312yes—
330#322C2312yes—
331#322C2312yes—
332C82C2312yes—
333C82C2312yes—
334C2×#41—22no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—82no—
341C2×#41—82no—
342C22×Q8—21no—
343C22×Q8C22×C411yescharacteristic
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4C22×C411yescharacteristic
349C22×D4C22×C412yes—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4C22×C411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4#4111yescharacteristic
355C2×SD16C22×C414yes—
356C2×SD16C22×C414yes—
357C2×D8C22×C414yes—
358C2×D8C22×C414yes—
359#131—82no—
360#131—82no—
361#131—82no—
362#131—82no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—82no—
372C2×M16C22×C414yes—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—22no—
384C22×C8—82no—
385C22×C8—82no—
386C22×C8C2×D411yescharacteristic
387C22×C8C2×D411yescharacteristic
388C22×C8C2×D411yescharacteristic
389C22×C8C2×D411yescharacteristic
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C22×C411yescharacteristic
393C4⋊Q8C22×C411yescharacteristic
394C4⋊Q8C22×C412yes—
395#127—21no—
396#127—21no—
397#127C22×C411yescharacteristic
398#127C22×C411yescharacteristic
399#127C22×C412yes—
400#126—22no—
401#126—22no—
402#126—22no—
403#126—22no—
404#125—21no—
405#125—21no—
406#125C22×C412yes—
407#125C22×C412yes—
408#124—21no—
409#124—21no—
410#124—22no—
411#124—21no—
412#124—21no—
413#124—21no—
414#124—21no—
415#124—22no—
416#124C22×C412yes—
417#124C22×C412yes—
418#123—22no—
419#123—22no—
420#123—22no—
421#123—22no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8C22×C412yes—
425C22⋊Q8C22×C412yes—
426#121—22no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—22no—
432#121—22no—
433#121—21no—
434#121—21no—
435#121—22no—
436#121C22×C412yes—
437#121C22×C412yes—
438#121C22×C412yes—
439#121C22×C412yes—
440#121C22×C412yes—
441#121C22×C412yes—
442C4×Q8—21no—
443C4×Q8—21no—
444C4×Q8C22×C412yes—
445C4×Q8C2412yes—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—22no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—22no—
458C4×D4—21no—
459C4×D4—22no—
460C4×D4C22×C412yes—
461C4×D4C22×C412yes—
462C4×D4C22×C412yes—
463C4×D4C2412yes—
464C4×D4C2412yes—
465C4×D4C2412yes—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4C22×C412yes—
476C2×C4⋊C4C22×C411yescharacteristic
477C2×C4⋊C4C22×C411yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—21no—
485C2×C42—21no—
486C2×C42C22×C411yescharacteristic
487C2×C42C22×C411yescharacteristic
488C2×C42C22×C411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42#4111yescharacteristic
493C2×C42#4111yescharacteristic
494C2×C42#4111yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498#107C22×C414yes—
499#107C22×C414yes—
500#106C22×C414yes—
501#106C22×C414yes—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—22no—
515C4⋊C8C22×C412yes—
516C4⋊C8C22×C412yes—
517C4⋊C8C22×C414yes—
518C4⋊C8C2×D411yescharacteristic
519C4⋊C8C2×D411yescharacteristic
520C4⋊C8C2×D411yescharacteristic
521C4⋊C8C2×D411yescharacteristic
522C4⋊C8C2×D411yescharacteristic
523C4⋊C8C2×D411yescharacteristic
524C4⋊C8C2×D411yescharacteristic
525C4⋊C8C2×D411yescharacteristic
526C4⋊C8C2412yes—
527C4⋊C8C2412yes—
528C4⋊C8C2412yes—
529C4⋊C8C2412yes—
530#103C22×C414yes—
531#103C22×C414yes—
532#102C22×C414yes—
533#102C22×C414yes—
534#102C22×C414yes—
535#102C22×C414yes—
536#102C22×C414yes—
537#102C22×C414yes—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8C22×C412yes—
556C22⋊C8C22×C412yes—
557C22⋊C8C22×C414yes—
558C22⋊C8C2×D411yescharacteristic
559C22⋊C8C2×D411yescharacteristic
560C22⋊C8C2×D411yescharacteristic
561C22⋊C8C2×D411yescharacteristic
562C22⋊C8C2×D411yescharacteristic
563C22⋊C8C2×D411yescharacteristic
564C22⋊C8C2×D411yescharacteristic
565C22⋊C8C2×D411yescharacteristic
566#97—22no—
567#97—22no—
568#97—22no—
569#97C22×C414yes—
570C4×C8—22no—
571C4×C8—22no—
572C4×C8—22no—
573C4×C8—22no—
574C4×C8C2×D411yescharacteristic
575C4×C8C2×D411yescharacteristic
576C4×C8C2×D411yescharacteristic
577C4×C8C2×D411yescharacteristic
578C4×C8C2412yes—
579C4×C8C2412yes—
580C4×C8C2412yes—
581C4×C8C2412yes—
582C4×C8C2411yescharacteristic
583C4×C8C2411yescharacteristic
584C4×C8C2411yescharacteristic
585C4×C8C2411yescharacteristic
586C24—21no—
587C24—22no—
588C24C4×D411yescharacteristic
589#41—42no—
590#41—42no—
591#41—42no—
592#41—42no—
593#41—82no—
594#41—82no—
595#41—84no—
596#41—82no—
597#41—82no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—42no—
603C2×Q8—82no—
604C2×Q8C23×C412yes—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—42no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—82no—
624C2×D4—84no—
625C2×D4C23×C412yes—
626C2×D4C23×C412yes—
627C2×D4C23×C412yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—82no—
645C22×C4—82no—
646C22×C4C4×D411yescharacteristic
647C22×C4C4×D411yescharacteristic
648C22×C4C4×D411yescharacteristic
649C22×C4C4×D411yescharacteristic
650C22×C4C4×D411yescharacteristic
651C22×C4C4×D411yescharacteristic
652C22×C4C4×D411yescharacteristic
653C22×C4C4×D411yescharacteristic
654C22×C4C4×D411yescharacteristic
655C22×C4C23×C411yescharacteristic
656C22×C4C23×C411yescharacteristic
657C22×C4C23×C411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C2×#4111yescharacteristic
662C22×C4C2×#4111yescharacteristic
663C22×C4C2×#4111yescharacteristic
664SD16—44no—
665SD16—44no—
666D8—44no—
667D8—44no—
668M16—44no—
669M16—42no—
670M16—42no—
671M16—82no—
672M16—82no—
673M16—82no—
674M16—82no—
675M16—82no—
676M16—82no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—44no—
688C2×C8—42no—
689C2×C8—42no—
690C2×C8—82no—
691C2×C8—82no—
692C2×C8—82no—
693C2×C8—82no—
694C2×C8—82no—
695C2×C8—82no—
696C2×C8—82no—
697C2×C8—82no—
698C2×C8C23×C414yes—
699C2×C8C23×C414yes—
700C2×C8C22×D411yescharacteristic
701C2×C8C22×D411yescharacteristic
702C2×C8C22×D411yescharacteristic
703C2×C8C22×D411yescharacteristic
704C2×C8C22×D411yescharacteristic
705C2×C8C22×D411yescharacteristic
706C2×C8C22×D411yescharacteristic
707C2×C8C22×D411yescharacteristic
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—22no—
722C4⋊C4C23×C412yes—
723C4⋊C4C23×C412yes—
724C4⋊C4C23×C412yes—
725C4⋊C4C23×C412yes—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C42—22no—
745C42—22no—
746C42C4×D411yescharacteristic
747C42C4×D411yescharacteristic
748C42C4×D411yescharacteristic
749C42C4×D411yescharacteristic
750C42C4×D411yescharacteristic
751C42C4×D411yescharacteristic
752C42C23×C411yescharacteristic
753C42C23×C411yescharacteristic
754C42C23×C411yescharacteristic
755C42C22×D411yescharacteristic
756C42C22×D411yescharacteristic
757C42C22×D411yescharacteristic
758C42C2×#4111yescharacteristic
759C42C2×#4111yescharacteristic
760C42C2×#4111yescharacteristic
761C42C2511yescharacteristic
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—41no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—44no—
772C23—82no—
773C23—82no—
774C23C2×C4×D411yescharacteristic
775C23C2×C4×D411yescharacteristic
776C23C2×C4×D411yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780Q8—42no—
781Q8—42no—
782Q8—82no—
783D4—22no—
784D4—22no—
785D4—24no—
786D4—24no—
787D4—42no—
788D4—42no—
789D4—44no—
790D4—42no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—44no—
795D4—42no—
796D4—42no—
797D4—82no—
798D4—82no—
799D4—82no—
800D4—82no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4C2×C4×D411yescharacteristic
839C2×C4C2×C4×D411yescharacteristic
840C2×C4C2×C4×D411yescharacteristic
841C2×C4C2×C4×D411yescharacteristic
842C2×C4C2×C4×D411yescharacteristic
843C2×C4C2×C4×D411yescharacteristic
844C2×C4C2×C4×D411yescharacteristic
845C2×C4C2×C4×D411yescharacteristic
846C2×C4C2×C4×D411yescharacteristic
847C2×C4#57612yes—
848C2×C4#57712yes—
849C2×C4C24×C411yescharacteristic
850C2×C4C23×D411yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C8—24no—
853C8—24no—
854C8—21no—
855C8—21no—
856C8—21no—
857C8—21no—
858C8—21no—
859C8—21no—
860C8—21no—
861C8—21no—
862C8—42no—
863C8—42no—
864C8—42no—
865C8—42no—
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—84no—
886C22—164no—
887C22#294612yes—
888C22#295512yes—
889C22C22×C4×D411yescharacteristic
890C4—21no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—21no—
895C4—21no—
896C4—21no—
897C4—21no—
898C4—21no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4#294612yes—
905C4#357312yes—
906C4C2×#57611yescharacteristic
907C4C2×#57711yescharacteristic
908C2—22no—
909C2—22no—
910C2—41no—
911C2—82no—
912C2—82no—
913C2—82no—
914C2#6014211yescharacteristic
915C2C2×#294611yescharacteristic
916C2C2×#295511yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60949C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#431 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2994C2semidirect
3. #60236C2semidirect
4. #18082C2semidirect
5. #18080C2semidirect
6. #18020C2semidirect
7. #18014C2semidirect
8. #17936C2semidirect
9. #17935C2semidirect
10. #17929C2semidirect
11. #17928C2semidirect
12. #17908C2semidirect
13. #17907C2semidirect
14. #17901C2semidirect
15. #17900C2semidirect
16. #17807C2semidirect
17. #17487C2semidirect
18. C2×#1480C2semidirect
19. #17325C2semidirect
42. #2994C22semidirect
43. #2994C22semidirect
46. #2979C22semidirect
47. #2979C22semidirect
49. #2974C22semidirect
50. #2974C22semidirect
52. C2×#446C22semidirect
53. C2×C8×Q8C22semidirect
60. C2×#436C22semidirect
63. C2×C8×D4C22semidirect
73. #1594C22semidirect
74. #1592C22semidirect
75. #1590C22semidirect
76. #1589C22semidirect
77. #1588C22semidirect
78. #1586C22semidirect
79. #1586C22semidirect
80. #1585C22semidirect
81. #1583C22semidirect
82. #1582C22semidirect
83. #1581C22semidirect
84. #1581C22semidirect
85. #1580C22semidirect
86. SD16⋊C8C22semidirect
87. C8×SD16C22semidirect
88. C8×D8C22semidirect
89. #1573C22semidirect
90. #1571C22semidirect
91. #1571C22semidirect
92. #1570C22semidirect
93. #1570C22semidirect
94. #1565C22semidirect
96. #1487C22semidirect
97. #1487C22semidirect
98. #1486C22semidirect
99. #1486C22semidirect
100. #1482C22semidirect
105. #1480C22semidirect
106. C2×D4⋊C8C22semidirect
107. #1453C22semidirect
108. #1453C22semidirect
109. #1452C22semidirect
110. #1452C22semidirect
111. #1452C22semidirect
112. #1450C22semidirect
113. #1450C22semidirect
114. #1450C22semidirect

Maximal subgroups

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

subgroupindex
#609492
C2×#29942
#602362
#180822
#180802
#180202
#180142
#179362
#179352
#179292
#179282
#179082
#179072
#179012
#179002
#178072
#174872
C2×#14802
#173252