Finite Group Databasebeta

← #6343223

Subgroups — #6343223

Order 512.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62752C211yesmaximal, characteristic
2#60292C211yesmaximal, characteristic, complemented
3#60281C211yesmaximal, characteristic, complemented
4#17525C214yesmaximal, complemented
5#17524C214yesmaximal, complemented
6#17514C214yesmaximal, complemented
7#17513C214yesmaximal, complemented
8#17506C214yesmaximal, complemented
9#17497C211yesmaximal, characteristic, complemented
10#17491C211yesmaximal, characteristic, complemented
11#17469C214yesmaximal, complemented
12#17465C211yesmaximal, characteristic, complemented
13#17464C211yesmaximal, characteristic, complemented
14#3565—22no—
15#3564—22no—
16#3563—21no—
17#3563C412yes—
18#3561C412yes—
19#3559—21no—
20#3555C412yes—
21#3552C412yes—
22#3547C412yes—
23#3544C412yes—
24#3538C412yes—
25#3536C412yes—
26#3535—22no—
27#3531—22no—
28#3482C2214yes—
29Q8×#41C2212yes—
30#3475—22no—
31#3475C2212yes—
32#3461—22no—
33#3461C2214yes—
34#3458—21no—
35#3455—21no—
36#3444C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#529C2211yescharacteristic
39#2995—22no—
40#2995—22no—
41#2991C2212yescomplemented
42#2990C2212yescomplemented
43#2989C2212yescomplemented
44#2988C2212yescomplemented
45#2987—21no—
46#2986—21no—
47#2980—21no—
48#2979—21no—
49#2978—22no—
50#2976—22no—
51#2969—22no—
52#2966—22no—
53#2965C2214yes—
54#2965C2214yescomplemented
55#2925C2214yes—
56#2922C2214yescomplemented
57#2920C2211yescharacteristic
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60C2×#431C2211yescharacteristic
61#1497C2214yes—
62#1497C2214yescomplemented
63#1495C2212yes—
64#1495C2212yes—
65#1495C2214yescomplemented
66#1494C2214yescomplemented
67#1493C2214yescomplemented
68#1491C2212yes—
69#1491C2214yescomplemented
70#1490C2212yes—
71#1489C2214yescomplemented
72#1488C2214yescomplemented
73#1487C2212yescomplemented
74#1487C2212yescomplemented
75#1487C2214yescomplemented
76#1485C2214yes—
77#1485C2214yescomplemented
78#1485C2214yescomplemented
79#1483C2212yes—
80#1483C2212yes—
81#1483C2214yescomplemented
82#1482C2214yes—
83#1482C2214yes—
84#1482C2214yescomplemented
85#1481C2212yescomplemented
86#1481C2212yescomplemented
87#1481C2214yescomplemented
88#1479C2212yes—
89#1479C2214yescomplemented
90#1479C2214yescomplemented
91#1478C2212yes—
92#1477C2214yescomplemented
93#1476C2214yescomplemented
94C2×Q8⋊C8C2214yescomplemented
95#564—22no—
96#563—24no—
97#563—24no—
98#563—22no—
99#563—22no—
100#563—24no—
101#563—24no—
102#562—22no—
103#562—24no—
104#562—24no—
105Q82C2×C412yes—
106#557—22no—
107#557C2×C412yes—
108#557C2×C414yes—
109#556—22no—
110#556—24no—
111#556C2×C412yes—
112#556C2×C414yes—
113#555—22no—
114#555C2×C412yes—
115#554—22no—
116#554—24no—
117#554—22no—
118#554C2×C412yes—
119#554C2×C414yes—
120#554C2×C412yes—
121#553—22no—
122#553—22no—
123#553—22no—
124#552—24no—
125#552—22no—
126#552—22no—
127#552—22no—
128#552—24no—
129#552—24no—
130#552C2×C414yes—
131#552C2×C414yes—
132#552C2×C414yes—
133#551—24no—
134#551—24no—
135#551—24no—
136D4×Q8C2×C414yes—
137D4×Q8C2×C412yes—
138D4×Q8C2×C414yes—
139#548C2×C414yes—
140#548C2×C414yes—
141#547—24no—
142#547—22no—
143#547C2×C412yes—
144#547C2×C414yes—
145#546—24no—
146#546C2×C414yes—
147#544—22no—
148#544—22no—
149#544—22no—
150#544—22no—
151#544—22no—
152#544—22no—
153#544—22no—
154#544C2×C414yes—
155#543—22no—
156#543—22no—
157#542—24no—
158#542—22no—
159#542—22no—
160#542—24no—
161#542—24no—
162#542C2×C414yes—
163#542C2×C414yes—
164#541—22no—
165#541—24no—
166#541—24no—
167#541—24no—
168#541C2×C414yes—
169#541C2×C414yes—
170#540—22no—
171#539—24no—
172#539—22no—
173#539—22no—
174#539—22no—
175#539—22no—
176#539—24no—
177#539—24no—
178#538—22no—
179#538—22no—
180#537—22no—
181#537C2×C414yes—
182#536—24no—
183#536C2×C414yes—
184#536C2×C414yes—
185#533—24no—
186#533—24no—
187#533—22no—
188#533—24no—
189#533—21no—
190#533—21no—
191#533—21no—
192#533—21no—
193#533C2×C412yes—
194#533C2×C412yes—
195#533C2×C411yescharacteristic
196#533D411yescharacteristic
197#533D411yescharacteristic
198#533C2312yes—
199#533C2312yes—
200#533C2314yes—
201#532C2×C411yescharacteristic
202#532D411yescharacteristic
203#532D411yescharacteristic
204C2×C4⋊Q8C2×C411yescharacteristic
205C2×C4⋊Q8C2×C411yescharacteristic
206#529—24no—
207#529—24no—
208#529—24no—
209#529—24no—
210#529—24no—
211#529—24no—
212#529—21no—
213#529—21no—
214#529—21no—
215#529—21no—
216#529C2×C412yes—
217#529C2×C412yes—
218#529C2×C412yes—
219#529C2×C412yes—
220#529D412yes—
221#529D412yes—
222#529D412yes—
223#529D412yes—
224#529C2312yes—
225#529C2312yes—
226#529C2314yes—
227C2×#126—21no—
228C2×#125—21no—
229C2×#125C2×C411yescharacteristic
230C2×#124C2×C411yescharacteristic
231#525—22no—
232#525C2×C412yes—
233#525D412yes—
234#525D412yes—
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C2×C411yescharacteristic
238C2×C22⋊Q8C2×C412yes—
239C2×#121C2×C411yescharacteristic
240C4×#41—22no—
241C4×#41—24no—
242C4×#41C2314yes—
243C4×#41C2312yes—
244C4×#41C2312yes—
245C4×#41C2312yes—
246C2×C4×Q8—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—22no—
254C2×#117—21no—
255C22×C42C2311yescharacteristic
256#446—24no—
257#446—24no—
258#446—22no—
259#446—22no—
260C8×Q8—22no—
261C8×Q8—22no—
262#436—24no—
263#436—24no—
264#436—22no—
265#436—24no—
266#436—22no—
267#435—24no—
268#435—24no—
269#435—24no—
270#435—24no—
271#435—24no—
272#435—24no—
273C8×D4—24no—
274C8×D4—22no—
275C8×D4—22no—
276#433—24no—
277#433—24no—
278#433—24no—
279#433—24no—
280#432—21no—
281#432—21no—
282#432—21no—
283#432—21no—
284#432—21no—
285#432C2312yes—
286#432C2314yes—
287#431—21no—
288#431—21no—
289#431—21no—
290#431C2312yes—
291#431C2312yes—
292#431C2312yes—
293#431C2314yes—
294#431C2312yes—
295#431C2312yes—
296#431C2312yes—
297#431C2312yes—
298#431C2314yes—
299#431C2314yes—
300#424—24no—
301#423—21no—
302#423—21no—
303#423C2311yescharacteristic
304#423C2311yescharacteristic
305#423C2314yes—
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2314yes—
309#408—24no—
310#408—24no—
311#407—21no—
312#407—21no—
313#407—21no—
314C2×C22⋊C8—21no—
315#405—24no—
316C4×M16—21no—
317C4×M16C2312yes—
318C4×M16C2312yes—
319C4×M16C2314yes—
320C2×C4×C8—21no—
321C2×C4×C8C2314yes—
322Q8⋊C8C2314yes—
323Q8⋊C8C2314yes—
324Q8⋊C8C2314yes—
325Q8⋊C8C2314yes—
326Q8⋊C8C2314yes—
327Q8⋊C8C2314yes—
328Q8⋊C8C2314yes—
329Q8⋊C8C2314yes—
330Q8⋊C8C2314yes—
331Q8⋊C8C2314yes—
332Q8⋊C8C2314yes—
333Q8⋊C8C2314yes—
334D4⋊C8C2314yes—
335D4⋊C8C2314yes—
336D4⋊C8C2314yes—
337D4⋊C8C2314yes—
338C2×#41—24no—
339C2×#41C22×C414yes—
340C2×#41C22×C412yes—
341C2×#41C2×D412yes—
342C2×#41C2×D412yes—
343C22×Q8—21no—
344C22×Q8C22×C411yescharacteristic
345C22×Q8C22×C412yes—
346C22×Q8C22×C414yes—
347C22×D4—21no—
348C22×D4C22×C411yescharacteristic
349C23×C4—21no—
350C23×C4C22×C411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—24no—
358C2×M16—24no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—24no—
362C22×C8—24no—
363C4⋊Q8—24no—
364C4⋊Q8—24no—
365C4⋊Q8—24no—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—24no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C22⋊C411yescharacteristic
376C4⋊Q8C22⋊C411yescharacteristic
377C4⋊Q8C22⋊C411yescharacteristic
378C4⋊Q8C22×C412yes—
379C4⋊Q8C22×C412yes—
380C4⋊Q8C22×C414yes—
381C4⋊Q8C22×C412yes—
382C4⋊Q8C22×C412yes—
383C4⋊Q8C22×C414yes—
384#127C22⋊C411yescharacteristic
385#126—24no—
386#126—24no—
387#126—24no—
388#126—24no—
389#126—24no—
390#126—24no—
391#126—24no—
392#126—24no—
393#126—24no—
394#126—24no—
395#126—24no—
396#126—24no—
397#126—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#126—24no—
402#126C22⋊C414yes—
403#126C22⋊C414yes—
404#125—24no—
405#125—24no—
406#125—24no—
407#125—24no—
408#125—24no—
409#125—24no—
410#125—24no—
411#125—24no—
412#125—24no—
413#125—24no—
414#125—24no—
415#125—24no—
416#125—22no—
417#125—22no—
418#125—22no—
419#125—22no—
420#125—21no—
421#125—21no—
422#125—22no—
423#125—22no—
424#125—24no—
425#125C22⋊C412yes—
426#125C22⋊C412yes—
427#125C22⋊C412yes—
428#125C22×C412yes—
429#125C22×C412yes—
430#125C22×C414yes—
431#124—24no—
432#124—24no—
433#124—24no—
434#124—24no—
435#124—24no—
436#124—24no—
437#124—21no—
438#124—21no—
439#124C22⋊C412yes—
440#124C22⋊C412yes—
441#124C22⋊C412yes—
442#124C22×C412yes—
443#124C22×C412yes—
444#124C22×C414yes—
445#123—24no—
446#123—24no—
447#123—24no—
448#123—24no—
449#123—24no—
450#123—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454#123—24no—
455#123—24no—
456#123—24no—
457#123—24no—
458#123—24no—
459#123—24no—
460#123—24no—
461#123—24no—
462#123—24no—
463#123C22⋊C414yes—
464#123C22⋊C414yes—
465#123C22⋊C414yes—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—24no—
469C22⋊Q8—24no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—24no—
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⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495C22⋊Q8—24no—
496C22⋊Q8—24no—
497C22⋊Q8C22⋊C412yes—
498C22⋊Q8C22⋊C412yes—
499C22⋊Q8C22⋊C412yes—
500C22⋊Q8C22⋊C412yes—
501C22⋊Q8C22⋊C412yes—
502C22⋊Q8C22⋊C412yes—
503C22⋊Q8C22×C412yes—
504C22⋊Q8C22×C412yes—
505C22⋊Q8C22×C414yes—
506C22⋊Q8C22×C414yes—
507C22⋊Q8C22×C414yes—
508C22⋊Q8C22×C414yes—
509C22⋊Q8C22×C414yes—
510#121—22no—
511#121—22no—
512#121—24no—
513#121—24no—
514#121—24no—
515#121—24no—
516#121—24no—
517#121—21no—
518#121—21no—
519#121—24no—
520#121C22⋊C412yes—
521#121C22⋊C412yes—
522#121C22⋊C412yes—
523#121C22⋊C412yes—
524#121C22⋊C412yes—
525#121C22⋊C412yes—
526#121C22×C412yes—
527#121C22×C412yes—
528#121C22×C414yes—
529#120—24no—
530#120C22⋊C414yes—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—24no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—21no—
539C4×Q8—22no—
540C4×Q8—24no—
541C4×Q8—21no—
542C4×Q8—22no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8C22×C412yes—
546C4×Q8C22×C414yes—
547C4×Q8C22×C414yes—
548C4×Q8C22×C414yes—
549C4×Q8C22×C414yes—
550C4×Q8C22×C412yes—
551C4×Q8C22×C412yes—
552C4×Q8C2×D412yes—
553C4×Q8C2×D412yes—
554C4×Q8C2×D412yes—
555C4×Q8C2×D412yes—
556C4×Q8C2412yes—
557C4×Q8C2414yes—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4C22×C412yes—
575C4×D4C22×C414yes—
576C4×D4C22×C414yes—
577C4×D4C22×C414yes—
578C4×D4C22×C412yes—
579C4×D4C22×C412yes—
580C4×D4C2×D414yes—
581C4×D4C2×D414yes—
582C4×D4C2×D414yes—
583C4×D4C2×D414yes—
584C4×D4C2×D412yes—
585C4×D4C2×D412yes—
586C4×D4C2×D412yes—
587C4×D4C2×D412yes—
588C4×D4C2412yes—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—24no—
594#117—22no—
595#117—22no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—24no—
605#117—24no—
606#117C22×C414yes—
607#117C22×C412yes—
608#117C22×C414yes—
609#117C2×D412yes—
610#117C2×D412yes—
611#117C2×D414yes—
612#117C2×D414yes—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4C22×C411yescharacteristic
626C2×C4⋊C4C22×C411yescharacteristic
627C2×C4⋊C4C22×C412yes—
628C2×C4⋊C4C22×C414yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—24no—
636C2×C42—21no—
637C2×C42—22no—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42C22×C411yescharacteristic
641C2×C42C22×C411yescharacteristic
642C2×C42C22×C411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2414yes—
652C2×C42C2411yescharacteristic
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—24no—
656C4⋊C8—22no—
657C4⋊C8—22no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—21no—
661C4⋊C8—21no—
662C4⋊C8—24no—
663C4⋊C8—24no—
664C4⋊C8—24no—
665C4⋊C8C2412yes—
666C4⋊C8C2412yes—
667C4⋊C8C2412yes—
668C4⋊C8C2412yes—
669C22⋊C8—22no—
670C22⋊C8—22no—
671C22⋊C8—22no—
672C22⋊C8—22no—
673C22⋊C8—22no—
674C22⋊C8—22no—
675C22⋊C8—22no—
676C22⋊C8—22no—
677C22⋊C8—24no—
678C22⋊C8—24no—
679C22⋊C8—24no—
680C22⋊C8—24no—
681#97—22no—
682#97—22no—
683#97—22no—
684#97—24no—
685#97—24no—
686C4×C8—22no—
687C4×C8—22no—
688C4×C8—24no—
689C4×C8—22no—
690C4×C8—24no—
691C4×C8C2414yes—
692C4×C8C2414yes—
693C24—21no—
694C24C2×C22⋊C411yescharacteristic
695#41—44no—
696#41—42no—
697#41—42no—
698#41—48no—
699#41—82no—
700#41—88no—
701C2×Q8—21no—
702C2×Q8—24no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—24no—
707C2×Q8—42no—
708C2×Q8—44no—
709C2×Q8—48no—
710C2×Q8—82no—
711C2×Q8C2×C22⋊C412yes—
712C2×Q8C2×C22⋊C412yes—
713C2×Q8C2×C22⋊C412yes—
714C2×Q8C23×C412yes—
715C2×Q8C23×C414yes—
716C2×D4—22no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—42no—
722C2×D4—82no—
723C2×D4C2×C22⋊C414yes—
724C2×D4C2×C22⋊C412yes—
725C2×D4C2×C22⋊C414yes—
726C2×D4C2×C22⋊C412yes—
727C2×D4C2×C22⋊C414yes—
728C2×D4C2×C22⋊C412yes—
729C2×D4C23×C412yes—
730C22×C4—22no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—42no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—81no—
747C22×C4C2×C22⋊C411yescharacteristic
748C22×C4C2×C22⋊C411yescharacteristic
749C22×C4C2×C22⋊C411yescharacteristic
750C22×C4C2×C22⋊C411yescharacteristic
751C22×C4C2×C22⋊C411yescharacteristic
752C22×C4C2×C22⋊C411yescharacteristic
753C22×C4C2×C22⋊C411yescharacteristic
754C22×C4C2×C22⋊C411yescharacteristic
755C22×C4C2×C22⋊C411yescharacteristic
756C22×C4C23×C411yescharacteristic
757C22×C4C23×C411yescharacteristic
758C22×C4C23×C411yescharacteristic
759C22×C4C23×C414yes—
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D414yes—
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D414yes—
768M16—81no—
769M16—84no—
770M16—81no—
771M16—84no—
772M16—82no—
773M16—82no—
774C2×C8—24no—
775C2×C8—24no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—22no—
779C2×C8—22no—
780C2×C8—81no—
781C2×C8—84no—
782C2×C8—81no—
783C2×C8—84no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—24no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—24no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—22no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4C2×C22⋊C412yes—
818C4⋊C4C2×C22⋊C412yes—
819C4⋊C4C2×C22⋊C414yes—
820C4⋊C4C2×C22⋊C412yes—
821C4⋊C4C2×C22⋊C412yes—
822C4⋊C4C2×C22⋊C414yes—
823C4⋊C4C2×C22⋊C414yes—
824C4⋊C4C2×C22⋊C412yes—
825C4⋊C4C2×C22⋊C414yes—
826C4⋊C4C2×C22⋊C414yes—
827C4⋊C4C2×C22⋊C412yes—
828C4⋊C4C2×C22⋊C414yes—
829C4⋊C4C23×C412yes—
830C4⋊C4C23×C414yes—
831C4⋊C4C23×C412yes—
832C22⋊C4—24no—
833C22⋊C4—22no—
834C22⋊C4—24no—
835C22⋊C4—22no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—22no—
841C22⋊C4—22no—
842C22⋊C4—22no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—22no—
852C22⋊C4C2×C22⋊C414yes—
853C22⋊C4C2×C22⋊C414yes—
854C22⋊C4C2×C22⋊C414yes—
855C22⋊C4C2×C22⋊C414yes—
856C22⋊C4C2×C22⋊C414yes—
857C22⋊C4C2×C22⋊C414yes—
858C22⋊C4C2×C22⋊C414yes—
859C22⋊C4C2×C22⋊C414yes—
860C22⋊C4C2×C22⋊C414yes—
861C42—24no—
862C42—24no—
863C42—22no—
864C42—24no—
865C42—24no—
866C42—24no—
867C42—22no—
868C42—24no—
869C42C2×C22⋊C411yescharacteristic
870C42C2×C22⋊C411yescharacteristic
871C42C2×C22⋊C411yescharacteristic
872C42C2×C22⋊C411yescharacteristic
873C42C2×C22⋊C411yescharacteristic
874C42C2×C22⋊C411yescharacteristic
875C42C23×C411yescharacteristic
876C42C23×C411yescharacteristic
877C42C23×C411yescharacteristic
878C42C23×C414yes—
879C42C22×D414yes—
880C42C22×D411yescharacteristic
881C42C22×D411yescharacteristic
882C42C22×D411yescharacteristic
883C42C22×D411yescharacteristic
884C42C22×D411yescharacteristic
885C42C22×D411yescharacteristic
886C42C22×D414yes—
887C42C2511yescharacteristic
888C23—22no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—42no—
893C23—81no—
894C23—81no—
895C23C22×C22⋊C411yescharacteristic
896C23C22×C22⋊C414yes—
897C23C22×C22⋊C411yescharacteristic
898C23C22×C22⋊C411yescharacteristic
899Q8—24no—
900Q8—28no—
901Q8—42no—
902Q8—42no—
903Q8—42no—
904Q8—81no—
905Q8—82no—
906Q8—84no—
907Q8—82no—
908Q8—82no—
909Q8—84no—
910D4—24no—
911D4—42no—
912D4—44no—
913D4—42no—
914D4—44no—
915D4—42no—
916D4—44no—
917D4—44no—
918D4—81no—
919D4—82no—
920D4—84no—
921D4—84no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—24no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—44no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—44no—
953C2×C4—42no—
954C2×C4—44no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—84no—
958C2×C4—84no—
959C2×C4—81no—
960C2×C4—82no—
961C2×C4—84no—
962C2×C4—81no—
963C2×C4—84no—
964C2×C4C22×C22⋊C411yescharacteristic
965C2×C4C22×C22⋊C411yescharacteristic
966C2×C4C22×C22⋊C414yes—
967C2×C4C22×C22⋊C414yes—
968C2×C4C22×C22⋊C414yes—
969C2×C4C22×C22⋊C411yescharacteristic
970C2×C4C22×C22⋊C411yescharacteristic
971C2×C4C22×C22⋊C411yescharacteristic
972C2×C4C22×C22⋊C411yescharacteristic
973C2×C4C22×C22⋊C411yescharacteristic
974C2×C4C22×C22⋊C411yescharacteristic
975C2×C4C22×C22⋊C411yescharacteristic
976C2×C4C24×C411yescharacteristic
977C2×C4C23×D411yescharacteristic
978C2×C4C23×D411yescharacteristic
979C8—44no—
980C8—44no—
981C8—42no—
982C8—42no—
983C8—42no—
984C8—42no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—24no—
989C22—21no—
990C22—21no—
991C22—21no—
992C22—24no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—24no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—82no—
1001C22—162no—
1002C22C23×C22⋊C411yescharacteristic
1003C4—21no—
1004C4—21no—
1005C4—21no—
1006C4—24no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—24no—
1011C4—21no—
1012C4—21no—
1013C4—21no—
1014C4—21no—
1015C4—24no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4#357312yes—
1022C4#358611yescharacteristic
1023C4#358611yescharacteristic
1024C2—44no—
1025C2—41no—
1026C2—41no—
1027C2—41no—
1028C2—82no—
1029C2#6006511yescharacteristic
1030C2#6008811yescharacteristic
1031C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62752C2
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. #60292C2semidirect
3. #60281C2semidirect
4. #17525C2semidirect
5. #17524C2semidirect
6. #17514C2semidirect
7. #17513C2semidirect
8. #17506C2semidirect
9. #17497C2semidirect
10. #17491C2semidirect
11. #17469C2semidirect
12. #17465C2semidirect
13. #17464C2semidirect
41. #2991C22semidirect
42. #2990C22semidirect
43. #2989C22semidirect
44. #2988C22semidirect
54. #2965C22semidirect
56. #2922C22semidirect
62. #1497C22semidirect
65. #1495C22semidirect
66. #1494C22semidirect
67. #1493C22semidirect
69. #1491C22semidirect
71. #1489C22semidirect
72. #1488C22semidirect
73. #1487C22semidirect
74. #1487C22semidirect
75. #1487C22semidirect
77. #1485C22semidirect
78. #1485C22semidirect
81. #1483C22semidirect
84. #1482C22semidirect
85. #1481C22semidirect
86. #1481C22semidirect
87. #1481C22semidirect
89. #1479C22semidirect
90. #1479C22semidirect
92. #1477C22semidirect
93. #1476C22semidirect
94. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627522
#602922
#602812
#175252
#175242
#175142
#175132
#175062
#174972
#174912
#174692
#174652
#174642