Finite Group Databasebeta

← #6343168

Subgroups — #6343168

Order 512.

2780 conjugacy classes of subgroups.

The subgroup lattice has 1093 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62788C211yesmaximal, characteristic
2#60295C211yesmaximal, characteristic, complemented
3#60281C211yesmaximal, characteristic, complemented
4#17525C214yesmaximal, complemented
5#17524C214yesmaximal, complemented
6#17516C214yesmaximal, complemented
7#17514C214yesmaximal, complemented
8#17506C214yesmaximal, complemented
9#17499C211yesmaximal, characteristic, complemented
10#17493C211yesmaximal, characteristic, complemented
11#17454C214yesmaximal, complemented
12#17449C211yesmaximal, characteristic, complemented
13#17449C211yesmaximal, characteristic, complemented
14#3523—21no—
15#3523C412yes—
16#3522—21no—
17#3522C412yes—
18#3516—22no—
19#3516C414yes—
20#3507—22no—
21#3507C411yescharacteristic
22#3507C411yescharacteristic
23#3502C411yescharacteristic
24#3497C411yescharacteristic
25#3492—22no—
26#3492C412yes—
27#3486C412yes—
28#3482—22no—
29#3482C2214yes—
30#3480—21no—
31#3480C2212yes—
32Q8×#41—21no—
33Q8×#41C2212yes—
34#3461—22no—
35#3461C2212yes—
36#3444—22no—
37#3444C2211yescharacteristic
38#3444C2211yescharacteristic
39C4×2−1+4C2212yes—
40C22×C4×Q8C2211yescharacteristic
41#2995—22no—
42#2995—22no—
43#2991C2212yes—
44#2990C2212yes—
45#2989C2214yes—
46#2987—21no—
47#2985—21no—
48#2981—21no—
49#2980—21no—
50#2978—22no—
51#2978—22no—
52#2969—22no—
53#2967—22no—
54#2965C2214yes—
55#2965C2214yes—
56#2925C2214yes—
57#2922C2214yes—
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60#2920C2211yescharacteristic
61#2920C2211yescharacteristic
62#1497C2212yes—
63#1497C2214yescomplemented
64#1496C2212yes—
65#1495C2214yes—
66#1495C2214yescomplemented
67#1494C2214yescomplemented
68#1493C2214yescomplemented
69#1491C2212yes—
70#1491C2212yes—
71#1491C2214yes—
72#1491C2214yescomplemented
73#1489C2214yes—
74#1489C2214yescomplemented
75#1488C2214yes—
76#1488C2214yescomplemented
77#1487C2212yes—
78#1487C2212yes—
79#1487C2214yes—
80#1487C2214yescomplemented
81#1485C2212yes—
82#1485C2214yescomplemented
83#1484C2212yes—
84#1483C2214yescomplemented
85#1482C2212yes—
86#1482C2212yes—
87#1482C2214yescomplemented
88#1481C2214yescomplemented
89#1479C2214yes—
90#1479C2212yes—
91#1479C2212yes—
92#1479C2214yescomplemented
93#1477C2214yescomplemented
94#1476C2214yescomplemented
95C2×Q8⋊C8C2214yescomplemented
96C2×2−1+4C2×C412yes—
97C23×Q8C2×C411yescharacteristic
98#559—21no—
99#559—22no—
100#559—22no—
101#559C2×C412yes—
102Q82—21no—
103Q82C2×C412yes—
104#557—21no—
105#557—21no—
106#557—22no—
107#557—22no—
108#557—22no—
109#557C2×C412yes—
110#557C2×C412yes—
111#557C2×C414yes—
112#556—21no—
113#556—24no—
114#556—22no—
115#556—22no—
116#556—22no—
117#556—24no—
118#556C2×C414yes—
119#556C2×C412yes—
120#554—21no—
121#554—22no—
122#554—24no—
123#554—22no—
124#554—24no—
125#554—22no—
126#554C2×C414yes—
127#554C2×C412yes—
128#553—24no—
129#553—22no—
130#553—24no—
131#553C2×C414yes—
132#552—24no—
133#552—22no—
134#552—24no—
135#552—22no—
136#552—24no—
137#552—24no—
138#552C2×C414yes—
139#552C2×C414yes—
140#550—21no—
141#550C2×C412yes—
142D4×Q8—21no—
143D4×Q8—22no—
144D4×Q8—22no—
145D4×Q8C2×C414yes—
146D4×Q8C2×C412yes—
147D4×Q8C2×C414yes—
148#548—22no—
149#548—22no—
150#548—22no—
151#548C2×C414yes—
152#548C2×C414yes—
153#548C2×C414yes—
154#547—24no—
155#547—24no—
156#547—22no—
157#547C2×C414yes—
158#544—22no—
159#544C2×C412yes—
160#542—24no—
161#542—24no—
162#542—22no—
163#542C2×C414yes—
164#541—24no—
165#541—24no—
166#541—22no—
167#541C2×C414yes—
168#539—24no—
169#539—22no—
170#539—22no—
171#539—24no—
172#537—22no—
173#537C2×C412yes—
174#536—24no—
175#536C2×C412yes—
176#536C2×C412yes—
177#533—22no—
178#533—22no—
179#533—24no—
180#533—22no—
181#533—22no—
182#533—24no—
183#533C2×C411yescharacteristic
184#533C2×C411yescharacteristic
185#533C2×C411yescharacteristic
186#533D411yescharacteristic
187#533D411yescharacteristic
188#533C2311yescharacteristic
189#533C2314yes—
190#532—22no—
191#532—22no—
192#532—22no—
193#532C2×C411yescharacteristic
194#532C2×C411yescharacteristic
195#532C2×C411yescharacteristic
196#532D411yescharacteristic
197#532D411yescharacteristic
198#532C2311yescharacteristic
199#529—24no—
200#529—24no—
201#529—22no—
202#529—22no—
203#529—22no—
204#529—22no—
205#529—24no—
206#529—24no—
207#529—24no—
208#529—22no—
209#529—24no—
210#529—21no—
211#529—21no—
212#529—21no—
213#529—21no—
214#529C2×C412yes—
215#529C2×C412yes—
216#529C2×C412yes—
217#529D412yes—
218#529D412yes—
219#529D412yes—
220#529D412yes—
221#529C2312yes—
222#529C2314yes—
223#525—21no—
224#525—21no—
225#525—24no—
226#525—24no—
227#525C2×C412yes—
228#525C2×C412yes—
229#525D412yes—
230#525D412yes—
231#520—24no—
232#520—22no—
233#520C2×C412yes—
234#520C2×C414yes—
235#520C2×C412yes—
236#519—22no—
237#519C2×C412yes—
238#519C2×C414yes—
239C4×#41—22no—
240C4×#41—24no—
241C4×#41—22no—
242C4×#41—24no—
243C4×#41—22no—
244C4×#41—21no—
245C4×#41—21no—
246C4×#41C2312yes—
247C4×#41C2314yes—
248C4×#41C2312yes—
249C4×#41C2312yes—
250C4×#41C2312yes—
251C2×C4×Q8—22no—
252C2×C4×Q8—21no—
253C2×C4×Q8—21no—
254C2×C4×Q8—21no—
255C2×C4×Q8—21no—
256C2×C4×Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2×C411yescharacteristic
259C2×C4×Q8C2×C411yescharacteristic
260C2×C4×Q8C2×C412yes—
261C2×C4×Q8C2×C412yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C22×C4⋊C4—21no—
268C22×C4⋊C4C2×C411yescharacteristic
269C22×C42—21no—
270C22×C42C2311yescharacteristic
271#446—24no—
272#446—24no—
273#446—24no—
274#446—22no—
275C8×Q8—22no—
276#436—24no—
277#436—24no—
278#436—24no—
279#436—24no—
280#436—22no—
281#435—24no—
282#435—24no—
283#435—24no—
284#435—24no—
285#435—24no—
286#435—24no—
287#435—24no—
288C8×D4—22no—
289#433—24no—
290#433—24no—
291#433—24no—
292#433—24no—
293#432—21no—
294#432—21no—
295#432—21no—
296#432—21no—
297#432—21no—
298#432—21no—
299#432C2312yes—
300#432C2312yes—
301#432C2314yes—
302#431—21no—
303#431—21no—
304#431C2312yes—
305#431C2311yescharacteristic
306#431C2311yescharacteristic
307#431C2314yes—
308#431C2312yes—
309#431C2312yes—
310#431C2312yes—
311#431C2312yes—
312#431C2314yes—
313#431C2314yes—
314#424—24no—
315#423—21no—
316#423—21no—
317#423C2312yes—
318#423C2312yes—
319#423C2314yes—
320C2×C4⋊C8C2314yes—
321#408—24no—
322#408—24no—
323#407—21no—
324#407—21no—
325#407—21no—
326#407—21no—
327#405—24no—
328C4×M16—21no—
329C4×M16—21no—
330C4×M16C2312yes—
331C4×M16C2312yes—
332C4×M16C2314yes—
333C2×C4×C8C2314yes—
334Q8⋊C8C2314yes—
335Q8⋊C8C2314yes—
336Q8⋊C8C2314yes—
337Q8⋊C8C2314yes—
338Q8⋊C8C2314yes—
339Q8⋊C8C2314yes—
340Q8⋊C8C2314yes—
341Q8⋊C8C2314yes—
342Q8⋊C8C2314yes—
343Q8⋊C8C2314yes—
344Q8⋊C8C2314yes—
345Q8⋊C8C2314yes—
346D4⋊C8C2314yes—
347D4⋊C8C2314yes—
348D4⋊C8C2314yes—
349D4⋊C8C2314yes—
3502−1+4—48no—
351C2×#41—24no—
352C2×#41—22no—
353C2×#41—24no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41C22×C414yes—
357C2×#41C22×C412yes—
358C2×#41C22×C412yes—
359C2×#41C2×D412yes—
360C2×#41C2×D412yes—
361C22×Q8—22no—
362C22×Q8—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C22×Q8—44no—
366C22×Q8C22×C411yescharacteristic
367C22×Q8C22×C412yes—
368C22×Q8C22×C412yes—
369C22×Q8C22×C414yes—
370C22×Q8C22×C411yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C22×C411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—24no—
381C2×M16—24no—
382C22×C8—24no—
383C22×C8—24no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—24no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4⋊Q8—24no—
390C4⋊Q8—24no—
391C4⋊Q8—24no—
392C4⋊Q8—22no—
393C4⋊Q8C22⋊C411yescharacteristic
394C4⋊Q8C22⋊C411yescharacteristic
395C4⋊Q8C22⋊C411yescharacteristic
396C4⋊Q8C22×C411yescharacteristic
397C4⋊Q8C22×C414yes—
398C4⋊Q8C22×C411yescharacteristic
399C4⋊Q8C22×C411yescharacteristic
400C4⋊Q8C22×C414yes—
401#127—22no—
402#127C22⋊C411yescharacteristic
403#127C22×C411yescharacteristic
404#126—24no—
405#126—24no—
406#126—24no—
407#126—24no—
408#126—24no—
409#126—24no—
410#126—24no—
411#126—24no—
412#126—24no—
413#126—22no—
414#126—22no—
415#126—24no—
416#126C22⋊C414yes—
417#126C22⋊C414yes—
418#125—24no—
419#125—24no—
420#125—22no—
421#125—22no—
422#125—24no—
423#125—24no—
424#125—22no—
425#125—24no—
426#125—24no—
427#125—24no—
428#125—24no—
429#125—24no—
430#125—21no—
431#125—21no—
432#125—24no—
433#125C22⋊C412yes—
434#125C22⋊C412yes—
435#125C22⋊C412yes—
436#125C22×C412yes—
437#125C22×C414yes—
438#124—22no—
439#124—22no—
440#124—22no—
441#124—24no—
442#124—24no—
443#124—24no—
444#124—24no—
445#124—21no—
446#124—21no—
447#124C22⋊C412yes—
448#124C22⋊C412yes—
449#124C22⋊C412yes—
450#124C22×C412yes—
451#124C22×C414yes—
452#123—24no—
453#123—24no—
454#123—24no—
455#123—22no—
456#123—22no—
457#123—22no—
458#123—24no—
459#123—24no—
460#123—24no—
461#123—24no—
462#123—24no—
463#123—24no—
464#123—24no—
465#123C22⋊C414yes—
466#123C22⋊C414yes—
467#123C22⋊C414yes—
468C22⋊Q8—22no—
469C22⋊Q8—24no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—24no—
475C22⋊Q8—24no—
476C22⋊Q8—22no—
477C22⋊Q8—24no—
478C22⋊Q8—22no—
479C22⋊Q8—24no—
480C22⋊Q8—24no—
481C22⋊Q8—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8—24no—
487C22⋊Q8—24no—
488C22⋊Q8—24no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8C22⋊C412yes—
492C22⋊Q8C22⋊C412yes—
493C22⋊Q8C22⋊C412yes—
494C22⋊Q8C22⋊C412yes—
495C22⋊Q8C22⋊C412yes—
496C22⋊Q8C22⋊C412yes—
497C22⋊Q8C22×C412yes—
498C22⋊Q8C22×C412yes—
499C22⋊Q8C22×C414yes—
500C22⋊Q8C22×C414yes—
501C22⋊Q8C22×C414yes—
502#121—24no—
503#121—24no—
504#121—24no—
505#121—24no—
506#121—24no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—24no—
513#121C22⋊C412yes—
514#121C22⋊C412yes—
515#121C22⋊C412yes—
516#121C22⋊C412yes—
517#121C22⋊C412yes—
518#121C22⋊C412yes—
519#121C22×C412yes—
520#121C22×C412yes—
521#121C22×C414yes—
522#120—22no—
523#120C22⋊C414yes—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×Q8—22no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×Q8—22no—
531C4×Q8—24no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—21no—
537C4×Q8—21no—
538C4×Q8—21no—
539C4×Q8—22no—
540C4×Q8—21no—
541C4×Q8—22no—
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—21no—
556C4×Q8—24no—
557C4×Q8C22×C412yes—
558C4×Q8C22×C412yes—
559C4×Q8C22×C412yes—
560C4×Q8C22×C412yes—
561C4×Q8C22×C412yes—
562C4×Q8C22×C412yes—
563C4×Q8C22×C414yes—
564C4×Q8C22×C414yes—
565C4×Q8C22×C412yes—
566C4×Q8C22×C414yes—
567C4×Q8C22×C412yes—
568C4×Q8C22×C412yes—
569C4×Q8C2×D412yes—
570C4×Q8C2×D412yes—
571C4×Q8C2×D412yes—
572C4×Q8C2×D412yes—
573C4×Q8C2412yes—
574C4×Q8C2412yes—
575C4×Q8C2412yes—
576C4×D4—24no—
577C4×D4—22no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4C22×C412yes—
606C4×D4C22×C414yes—
607C4×D4C22×C414yes—
608C4×D4C22×C414yes—
609C4×D4C22×C412yes—
610C4×D4C22×C412yes—
611C4×D4C2×D414yes—
612C4×D4C2×D414yes—
613C4×D4C2×D412yes—
614C4×D4C2×D414yes—
615C4×D4C2×D412yes—
616C4×D4C2×D414yes—
617C4×D4C2×D412yes—
618C4×D4C2×D412yes—
619C4×D4C2412yes—
620#117—21no—
621#117—21no—
622#117—24no—
623#117—24no—
624#117—22no—
625#117—24no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—24no—
630#117—24no—
631#117—22no—
632#117—22no—
633#117—24no—
634#117—22no—
635#117—24no—
636#117C22×C412yes—
637#117C22×C414yes—
638#117C22×C412yes—
639#117C22×C414yes—
640#117C2×D412yes—
641#117C2×D412yes—
642#117C2×D414yes—
643#117C2×D414yes—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—24no—
656C2×C4⋊C4—24no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C22×C411yescharacteristic
659C2×C4⋊C4C22×C411yescharacteristic
660C2×C4⋊C4C22×C412yes—
661C2×C4⋊C4C22×C412yes—
662C2×C4⋊C4C22×C414yes—
663C2×C42—22no—
664C2×C42—21no—
665C2×C42—22no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—22no—
669C2×C42—22no—
670C2×C42—21no—
671C2×C42—24no—
672C2×C42—22no—
673C2×C42—24no—
674C2×C42C22×C411yescharacteristic
675C2×C42C22×C411yescharacteristic
676C2×C42C22×C411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2414yes—
687C4⋊C8—24no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—22no—
691C4⋊C8—22no—
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—24no—
695C4⋊C8—24no—
696C4⋊C8—24no—
697C4⋊C8C2412yes—
698C4⋊C8C2414yes—
699C4⋊C8C2412yes—
700C22⋊C8—22no—
701C22⋊C8—22no—
702C22⋊C8—22no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—21no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—21no—
709C22⋊C8—24no—
710C22⋊C8—24no—
711C22⋊C8—24no—
712C22⋊C8—24no—
713#97—22no—
714#97—22no—
715#97—22no—
716#97—22no—
717#97—24no—
718#97—24no—
719C4×C8—24no—
720C4×C8—22no—
721C4×C8—21no—
722C4×C8—21no—
723C4×C8—24no—
724C4×C8C2414yes—
725C4×C8C2414yes—
726C24C2×C22⋊C411yescharacteristic
727#41—28no—
728#41—44no—
729#41—44no—
730#41—44no—
731#41—44no—
732#41—44no—
733#41—416no—
734#41—48no—
735#41—82no—
736#41—82no—
737#41—88no—
738C2×Q8—24no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—22no—
742C2×Q8—22no—
743C2×Q8—21no—
744C2×Q8—24no—
745C2×Q8—21no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—28no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—42no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—48no—
758C2×Q8C2×C22⋊C412yes—
759C2×Q8C2×C22⋊C412yes—
760C2×Q8C2×C22⋊C412yes—
761C2×Q8C23×C412yes—
762C2×Q8C23×C412yes—
763C2×Q8C23×C412yes—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—22no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4C2×C22⋊C414yes—
772C2×D4C2×C22⋊C412yes—
773C2×D4C2×C22⋊C414yes—
774C2×D4C2×C22⋊C414yes—
775C2×D4C2×C22⋊C412yes—
776C2×D4C2×C22⋊C412yes—
777C2×D4C23×C412yes—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—24no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—81no—
797C22×C4—82no—
798C22×C4C2×C22⋊C411yescharacteristic
799C22×C4C2×C22⋊C411yescharacteristic
800C22×C4C2×C22⋊C411yescharacteristic
801C22×C4C2×C22⋊C411yescharacteristic
802C22×C4C2×C22⋊C411yescharacteristic
803C22×C4C2×C22⋊C411yescharacteristic
804C22×C4C2×C22⋊C411yescharacteristic
805C22×C4C2×C22⋊C411yescharacteristic
806C22×C4C2×C22⋊C411yescharacteristic
807C22×C4C23×C411yescharacteristic
808C22×C4C23×C411yescharacteristic
809C22×C4C23×C411yescharacteristic
810C22×C4C23×C414yes—
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D414yes—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D414yes—
819M16—82no—
820M16—82no—
821M16—84no—
822M16—84no—
823M16—82no—
824M16—82no—
825C2×C8—24no—
826C2×C8—24no—
827C2×C8—22no—
828C2×C8—24no—
829C2×C8—22no—
830C2×C8—84no—
831C2×C8—84no—
832C4⋊C4—22no—
833C4⋊C4—21no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—24no—
852C4⋊C4—21no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4C2×C22⋊C412yes—
867C4⋊C4C2×C22⋊C414yes—
868C4⋊C4C2×C22⋊C412yes—
869C4⋊C4C2×C22⋊C414yes—
870C4⋊C4C2×C22⋊C414yes—
871C4⋊C4C2×C22⋊C412yes—
872C4⋊C4C2×C22⋊C412yes—
873C4⋊C4C2×C22⋊C412yes—
874C4⋊C4C2×C22⋊C414yes—
875C4⋊C4C2×C22⋊C414yes—
876C4⋊C4C2×C22⋊C412yes—
877C4⋊C4C2×C22⋊C414yes—
878C4⋊C4C23×C412yes—
879C4⋊C4C23×C412yes—
880C4⋊C4C23×C412yes—
881C4⋊C4C23×C412yes—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—24no—
885C22⋊C4—22no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—22no—
890C22⋊C4—24no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4C2×C22⋊C414yes—
900C22⋊C4C2×C22⋊C414yes—
901C22⋊C4C2×C22⋊C414yes—
902C22⋊C4C2×C22⋊C414yes—
903C22⋊C4C2×C22⋊C414yes—
904C22⋊C4C2×C22⋊C414yes—
905C22⋊C4C2×C22⋊C414yes—
906C22⋊C4C2×C22⋊C414yes—
907C22⋊C4C2×C22⋊C414yes—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—22no—
914C42—24no—
915C42—22no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—22no—
920C42—22no—
921C42—22no—
922C42—22no—
923C42C2×C22⋊C411yescharacteristic
924C42C2×C22⋊C411yescharacteristic
925C42C2×C22⋊C411yescharacteristic
926C42C2×C22⋊C411yescharacteristic
927C42C2×C22⋊C411yescharacteristic
928C42C2×C22⋊C411yescharacteristic
929C42C23×C411yescharacteristic
930C42C23×C411yescharacteristic
931C42C23×C411yescharacteristic
932C42C23×C414yes—
933C42C22×D414yes—
934C42C22×D411yescharacteristic
935C42C22×D411yescharacteristic
936C42C22×D411yescharacteristic
937C42C22×D411yescharacteristic
938C42C22×D411yescharacteristic
939C42C22×D414yes—
940C42C22×D411yescharacteristic
941C42C2511yescharacteristic
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23C22×C22⋊C414yes—
947C23C22×C22⋊C411yescharacteristic
948C23C22×C22⋊C411yescharacteristic
949C23C22×C22⋊C411yescharacteristic
950Q8—24no—
951Q8—22no—
952Q8—22no—
953Q8—22no—
954Q8—24no—
955Q8—42no—
956Q8—42no—
957Q8—42no—
958Q8—44no—
959Q8—44no—
960Q8—48no—
961Q8—42no—
962Q8—42no—
963Q8—81no—
964Q8—84no—
965Q8#56814yes—
966D4—24no—
967D4—42no—
968D4—44no—
969D4—42no—
970D4—44no—
971D4—42no—
972D4—44no—
973D4—48no—
974D4—42no—
975D4—44no—
976D4—44no—
977D4—44no—
978D4—81no—
979D4—84no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—44no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—48no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—42no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—82no—
1020C2×C4—84no—
1021C2×C4—81no—
1022C2×C4—82no—
1023C2×C4—81no—
1024C2×C4—84no—
1025C2×C4C22×C22⋊C411yescharacteristic
1026C2×C4C22×C22⋊C411yescharacteristic
1027C2×C4C22×C22⋊C411yescharacteristic
1028C2×C4C22×C22⋊C411yescharacteristic
1029C2×C4C22×C22⋊C411yescharacteristic
1030C2×C4C22×C22⋊C414yes—
1031C2×C4C22×C22⋊C414yes—
1032C2×C4C22×C22⋊C414yes—
1033C2×C4C22×C22⋊C411yescharacteristic
1034C2×C4C22×C22⋊C411yescharacteristic
1035C2×C4C22×C22⋊C411yescharacteristic
1036C2×C4C22×C22⋊C411yescharacteristic
1037C2×C4C24×C411yescharacteristic
1038C2×C4C23×D411yescharacteristic
1039C2×C4C23×D411yescharacteristic
1040C8—44no—
1041C8—44no—
1042C8—42no—
1043C8—44no—
1044C8—42no—
1045C22—21no—
1046C22—21no—
1047C22—21no—
1048C22—24no—
1049C22—21no—
1050C22—21no—
1051C22—21no—
1052C22—24no—
1053C22—21no—
1054C22—21no—
1055C22—21no—
1056C22—24no—
1057C22—44no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22C23×C22⋊C411yescharacteristic
1062C4—24no—
1063C4—21no—
1064C4—24no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—24no—
1071C4—21no—
1072C4—21no—
1073C4—21no—
1074C4—21no—
1075C4—24no—
1076C4—42no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C4—42no—
1081C4—42no—
1082C4C2×#56812yes—
1083C4#358612yes—
1084C2—44no—
1085C2—41no—
1086C2—41no—
1087C2—41no—
1088C2—82no—
1089C2#6006411yescharacteristic
1090C2#6008811yescharacteristic
1091C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62788C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60295C2semidirect
3. #60281C2semidirect
4. #17525C2semidirect
5. #17524C2semidirect
6. #17516C2semidirect
7. #17514C2semidirect
8. #17506C2semidirect
9. #17499C2semidirect
10. #17493C2semidirect
11. #17454C2semidirect
12. #17449C2semidirect
13. #17449C2semidirect
63. #1497C22semidirect
66. #1495C22semidirect
67. #1494C22semidirect
68. #1493C22semidirect
72. #1491C22semidirect
74. #1489C22semidirect
76. #1488C22semidirect
80. #1487C22semidirect
82. #1485C22semidirect
84. #1483C22semidirect
87. #1482C22semidirect
88. #1481C22semidirect
92. #1479C22semidirect
93. #1477C22semidirect
94. #1476C22semidirect
95. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627882
#602952
#602812
#175252
#175242
#175162
#175142
#175062
#174992
#174932
#174542
#174492