Finite Group Databasebeta

← #6343280

Subgroups — #6343280

Order 512.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62752C211yesmaximal, characteristic
2#60293C211yesmaximal, characteristic, complemented
3#60210C211yesmaximal, characteristic, complemented
4#17524C214yesmaximal, complemented
5#17519C214yesmaximal, complemented
6#17514C214yesmaximal, complemented
7#17513C214yesmaximal, complemented
8#17506C214yesmaximal, complemented
9#17502C211yesmaximal, characteristic, complemented
10#17501C211yesmaximal, characteristic, complemented
11#17484C214yesmaximal, complemented
12#17480C211yesmaximal, characteristic, complemented
13C2×#1497C211yesmaximal, 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#2990C2214yescomplemented
40#2989C2214yescomplemented
41#2987—21no—
42#2980—21no—
43#2976—22no—
44#2969—22no—
45#2968—22no—
46#2968—22no—
47#2967—22no—
48#2965C2214yes—
49#2965C2212yescomplemented
50C8×#41C2212yescomplemented
51#2962—21no—
52#2935—21no—
53#2933—22no—
54#2925C2214yes—
55#2922C2212yescomplemented
56#2920C2211yescharacteristic
57C2×#432C2211yescharacteristic
58C2×#431C2211yescharacteristic
59C4×#131C2212yescomplemented
60C2×C4×M16C2211yescharacteristic
61#1497C2214yes—
62#1497C2212yescomplemented
63#1497C2212yescomplemented
64#1497C2214yescomplemented
65#1495C2212yes—
66#1495C2212yes—
67#1495C2214yescomplemented
68#1494C2214yes—
69#1494C2214yes—
70#1494C2214yescomplemented
71#1493C2214yescomplemented
72#1493C2214yescomplemented
73#1491C2212yes—
74#1491C2212yescomplemented
75#1491C2212yescomplemented
76#1491C2214yescomplemented
77#1490C2212yes—
78#1489C2214yescomplemented
79#1488C2214yescomplemented
80#1487C2214yescomplemented
81#1485C2214yes—
82#1485C2214yescomplemented
83#1483C2212yes—
84#1483C2212yes—
85#1483C2214yescomplemented
86#1482C2214yescomplemented
87#1481C2214yescomplemented
88#1479C2212yes—
89#1479C2214yescomplemented
90#1478C2212yes—
91#1477C2214yescomplemented
92#1476C2214yescomplemented
93C2×Q8⋊C8C2214yescomplemented
94C2×Q8⋊C8C2214yescomplemented
95C2×#131—22no—
96C22×M16—21no—
97#564—22no—
98#563—24no—
99#563—24no—
100#563—22no—
101#563—22no—
102#563—24no—
103#563—24no—
104#562—22no—
105#562—24no—
106#562—24no—
107Q82C2×C412yes—
108#557—22no—
109#557C2×C412yes—
110#557C2×C414yes—
111#556—22no—
112#556—24no—
113#556C2×C412yes—
114#556C2×C414yes—
115#555—22no—
116#555C2×C412yes—
117#554—22no—
118#554—24no—
119#554—22no—
120#554C2×C412yes—
121#554C2×C414yes—
122#554C2×C412yes—
123#553—22no—
124#553—22no—
125#553—22no—
126#552—24no—
127#552—22no—
128#552—22no—
129#552—22no—
130#552—24no—
131#552—24no—
132#552C2×C414yes—
133#552C2×C414yes—
134#552C2×C414yes—
135#551—24no—
136#551—24no—
137#551—24no—
138D4×Q8C2×C414yes—
139D4×Q8C2×C412yes—
140D4×Q8C2×C414yes—
141#548C2×C414yes—
142#548C2×C414yes—
143#547—24no—
144#547—22no—
145#547C2×C412yes—
146#547C2×C414yes—
147#546—24no—
148#546C2×C414yes—
149#544—22no—
150#544—22no—
151#544—22no—
152#544—22no—
153#544—22no—
154#544—22no—
155#544—22no—
156#544C2×C414yes—
157#543—22no—
158#543—22no—
159#542—24no—
160#542—22no—
161#542—22no—
162#542—24no—
163#542—24no—
164#542C2×C414yes—
165#542C2×C414yes—
166#541—22no—
167#541—24no—
168#541—24no—
169#541—24no—
170#541C2×C414yes—
171#541C2×C414yes—
172#540—22no—
173#539—24no—
174#539—22no—
175#539—22no—
176#539—22no—
177#539—22no—
178#539—24no—
179#539—24no—
180#538—22no—
181#538—22no—
182#537—22no—
183#537C2×C414yes—
184#536—24no—
185#536C2×C414yes—
186#536C2×C414yes—
187#533—24no—
188#533—24no—
189#533—22no—
190#533—24no—
191#533—21no—
192#533—21no—
193#533—21no—
194#533—21no—
195#533C2×C412yes—
196#533C2×C412yes—
197#533C2×C411yescharacteristic
198#533D411yescharacteristic
199#533D411yescharacteristic
200#533C2312yes—
201#533C2312yes—
202#533C2314yes—
203#532C2×C411yescharacteristic
204#532D411yescharacteristic
205#532D411yescharacteristic
206C2×C4⋊Q8C2×C411yescharacteristic
207C2×C4⋊Q8C2×C411yescharacteristic
208#529—24no—
209#529—24no—
210#529—24no—
211#529—24no—
212#529—24no—
213#529—24no—
214#529—21no—
215#529—21no—
216#529—21no—
217#529—21no—
218#529C2×C412yes—
219#529C2×C412yes—
220#529C2×C412yes—
221#529C2×C412yes—
222#529D412yes—
223#529D412yes—
224#529D412yes—
225#529D412yes—
226#529C2312yes—
227#529C2312yes—
228#529C2314yes—
229C2×#126—21no—
230C2×#125—21no—
231C2×#125C2×C411yescharacteristic
232C2×#124C2×C411yescharacteristic
233#525—22no—
234#525C2×C412yes—
235#525D412yes—
236#525D412yes—
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2×C411yescharacteristic
240C2×C22⋊Q8C2×C412yes—
241C2×#121C2×C411yescharacteristic
242C4×#41—22no—
243C4×#41—24no—
244C4×#41C2314yes—
245C4×#41C2312yes—
246C4×#41C2312yes—
247C4×#41C2312yes—
248C2×C4×Q8—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×D4—21no—
253C2×C4×D4C2311yescharacteristic
254C2×#117—21no—
255C2×#117—22no—
256C2×#117—21no—
257C22×C42C2311yescharacteristic
258#446—24no—
259#446—22no—
260#446—24no—
261#446—24no—
262C8×Q8—22no—
263#436—24no—
264#436—22no—
265#436—24no—
266#435—24no—
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—24no—
276#433—24no—
277#433—24no—
278#433—24no—
279#432—21no—
280#432—21no—
281#432—21no—
282#432C2312yes—
283#432C2312yes—
284#432C2312yes—
285#432C2314yes—
286#431—21no—
287#431—21no—
288#431—21no—
289#431C2312yes—
290#431C2314yes—
291#431C2311yescharacteristic
292#431C2312yes—
293#431C2311yescharacteristic
294#431C2314yes—
295#431C2314yes—
296#424—22no—
297#423C2312yes—
298#423C2314yes—
299C2×C4⋊C8—21no—
300C2×C4⋊C8C2312yes—
301C2×C4⋊C8C2314yes—
302#408—22no—
303#408—24no—
304#407—21no—
305C2×C22⋊C8—21no—
306C2×C22⋊C8—21no—
307#405—22no—
308#405—24no—
309#405—24no—
310C4×M16—21no—
311C4×M16—21no—
312C4×M16—21no—
313C4×M16C2311yescharacteristic
314C4×M16C2311yescharacteristic
315C4×M16C2312yes—
316C4×M16C2314yes—
317C2×#97—21no—
318C2×#97—21no—
319C2×C4×C8C2312yes—
320C2×C4×C8C2312yes—
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
353#131—48no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—22no—
357C2×M16—24no—
358C2×M16—22no—
359C2×M16—24no—
360C2×M16—44no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—24no—
364C22×C8—22no—
365C22×C8—24no—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368C4⋊Q8—24no—
369C4⋊Q8—24no—
370C4⋊Q8—24no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—24no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C22⋊C411yescharacteristic
379C4⋊Q8C22⋊C411yescharacteristic
380C4⋊Q8C22⋊C411yescharacteristic
381C4⋊Q8C22×C412yes—
382C4⋊Q8C22×C412yes—
383C4⋊Q8C22×C414yes—
384C4⋊Q8C22×C412yes—
385C4⋊Q8C22×C412yes—
386C4⋊Q8C22×C414yes—
387#127C22⋊C411yescharacteristic
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—24no—
398#126—24no—
399#126—24no—
400#126—22no—
401#126—22no—
402#126—22no—
403#126—22no—
404#126—24no—
405#126C22⋊C414yes—
406#126C22⋊C414yes—
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—24no—
417#125—24no—
418#125—24no—
419#125—22no—
420#125—22no—
421#125—22no—
422#125—22no—
423#125—21no—
424#125—21no—
425#125—22no—
426#125—22no—
427#125—24no—
428#125C22⋊C412yes—
429#125C22⋊C412yes—
430#125C22⋊C412yes—
431#125C22×C412yes—
432#125C22×C412yes—
433#125C22×C414yes—
434#124—24no—
435#124—24no—
436#124—24no—
437#124—24no—
438#124—24no—
439#124—24no—
440#124—21no—
441#124—21no—
442#124C22⋊C412yes—
443#124C22⋊C412yes—
444#124C22⋊C412yes—
445#124C22×C412yes—
446#124C22×C412yes—
447#124C22×C414yes—
448#123—24no—
449#123—24no—
450#123—24no—
451#123—24no—
452#123—24no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—22no—
457#123—24no—
458#123—24no—
459#123—24no—
460#123—24no—
461#123—24no—
462#123—24no—
463#123—24no—
464#123—24no—
465#123—24no—
466#123C22⋊C414yes—
467#123C22⋊C414yes—
468#123C22⋊C414yes—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—24no—
472C22⋊Q8—24no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
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⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8C22⋊C412yes—
501C22⋊Q8C22⋊C412yes—
502C22⋊Q8C22⋊C412yes—
503C22⋊Q8C22⋊C412yes—
504C22⋊Q8C22⋊C412yes—
505C22⋊Q8C22⋊C412yes—
506C22⋊Q8C22×C412yes—
507C22⋊Q8C22×C412yes—
508C22⋊Q8C22×C414yes—
509C22⋊Q8C22×C414yes—
510C22⋊Q8C22×C414yes—
511C22⋊Q8C22×C414yes—
512C22⋊Q8C22×C414yes—
513#121—22no—
514#121—22no—
515#121—24no—
516#121—24no—
517#121—24no—
518#121—24no—
519#121—24no—
520#121—21no—
521#121—21no—
522#121—24no—
523#121C22⋊C412yes—
524#121C22⋊C412yes—
525#121C22⋊C412yes—
526#121C22⋊C412yes—
527#121C22⋊C412yes—
528#121C22⋊C412yes—
529#121C22×C412yes—
530#121C22×C412yes—
531#121C22×C414yes—
532#120—24no—
533#120C22⋊C414yes—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—24no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—21no—
542C4×Q8—24no—
543C4×Q8—22no—
544C4×Q8—21no—
545C4×Q8—22no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8C22×C412yes—
549C4×Q8C22×C414yes—
550C4×Q8C22×C414yes—
551C4×Q8C22×C414yes—
552C4×Q8C22×C414yes—
553C4×Q8C22×C412yes—
554C4×Q8C22×C412yes—
555C4×Q8C2×D412yes—
556C4×Q8C2×D412yes—
557C4×Q8C2×D412yes—
558C4×Q8C2×D412yes—
559C4×Q8C2412yes—
560C4×Q8C2414yes—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4C22×C412yes—
578C4×D4C22×C414yes—
579C4×D4C22×C414yes—
580C4×D4C22×C414yes—
581C4×D4C22×C412yes—
582C4×D4C22×C412yes—
583C4×D4C2×D414yes—
584C4×D4C2×D414yes—
585C4×D4C2×D414yes—
586C4×D4C2×D414yes—
587C4×D4C2×D412yes—
588C4×D4C2×D412yes—
589C4×D4C2×D412yes—
590C4×D4C2×D412yes—
591C4×D4C2412yes—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—24no—
597#117—22no—
598#117—22no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—22no—
604#117—22no—
605#117—24no—
606#117—22no—
607#117—22no—
608#117—24no—
609#117C22×C414yes—
610#117C22×C412yes—
611#117C22×C414yes—
612#117C2×D412yes—
613#117C2×D412yes—
614#117C2×D414yes—
615#117C2×D414yes—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4C22×C411yescharacteristic
629C2×C4⋊C4C22×C411yescharacteristic
630C2×C4⋊C4C22×C412yes—
631C2×C4⋊C4C22×C414yes—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—24no—
639C2×C42—21no—
640C2×C42—22no—
641C2×C42—24no—
642C2×C42—24no—
643C2×C42C22×C411yescharacteristic
644C2×C42C22×C411yescharacteristic
645C2×C42C22×C411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2414yes—
655C2×C42C2411yescharacteristic
656C4⋊C8—21no—
657C4⋊C8—22no—
658C4⋊C8—21no—
659C4⋊C8—22no—
660C4⋊C8—24no—
661C4⋊C8—22no—
662C4⋊C8—24no—
663C4⋊C8—24no—
664C4⋊C8—24no—
665C4⋊C8C2414yes—
666C4⋊C8C2414yes—
667C22⋊C8—22no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8—22no—
671C22⋊C8—22no—
672C22⋊C8—22no—
673C22⋊C8—22no—
674C22⋊C8—24no—
675C22⋊C8—24no—
676C22⋊C8—24no—
677C22⋊C8—24no—
678#97—21no—
679#97—21no—
680#97—22no—
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×C8C2412yes—
692C4×C8C2412yes—
693C4×C8C2412yes—
694C4×C8C2412yes—
695C24—21no—
696C24C2×C22⋊C411yescharacteristic
697#41—44no—
698#41—42no—
699#41—42no—
700#41—44no—
701#41—48no—
702#41—88no—
703C2×Q8—21no—
704C2×Q8—24no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—22no—
708C2×Q8—24no—
709C2×Q8—42no—
710C2×Q8—44no—
711C2×Q8—48no—
712C2×Q8—82no—
713C2×Q8C2×C22⋊C412yes—
714C2×Q8C2×C22⋊C412yes—
715C2×Q8C2×C22⋊C412yes—
716C2×Q8C23×C412yes—
717C2×Q8C23×C414yes—
718C2×D4—22no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—22no—
722C2×D4—21no—
723C2×D4—42no—
724C2×D4—82no—
725C2×D4C2×C22⋊C414yes—
726C2×D4C2×C22⋊C414yes—
727C2×D4C2×C22⋊C412yes—
728C2×D4C2×C22⋊C412yes—
729C2×D4C2×C22⋊C414yes—
730C2×D4C2×C22⋊C412yes—
731C2×D4C23×C412yes—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—44no—
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×D411yescharacteristic
763C22×C4C22×D414yes—
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D414yes—
768M16—24no—
769M16—44no—
770M16—48no—
771M16—42no—
772M16—84no—
773M16—82no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—24no—
779C2×C8—24no—
780C2×C8—44no—
781C2×C8—48no—
782C2×C8—44no—
783C2×C8—82no—
784C2×C8—84no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—24no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—24no—
795C4⋊C4—22no—
796C4⋊C4—22no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—24no—
818C4⋊C4C2×C22⋊C412yes—
819C4⋊C4C2×C22⋊C412yes—
820C4⋊C4C2×C22⋊C414yes—
821C4⋊C4C2×C22⋊C412yes—
822C4⋊C4C2×C22⋊C412yes—
823C4⋊C4C2×C22⋊C414yes—
824C4⋊C4C2×C22⋊C414yes—
825C4⋊C4C2×C22⋊C412yes—
826C4⋊C4C2×C22⋊C414yes—
827C4⋊C4C2×C22⋊C414yes—
828C4⋊C4C2×C22⋊C412yes—
829C4⋊C4C2×C22⋊C414yes—
830C4⋊C4C23×C412yes—
831C4⋊C4C23×C414yes—
832C4⋊C4C23×C412yes—
833C22⋊C4—24no—
834C22⋊C4—22no—
835C22⋊C4—24no—
836C22⋊C4—22no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—22no—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—22no—
849C22⋊C4—22no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—22no—
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—
861C22⋊C4C2×C22⋊C414yes—
862C42—24no—
863C42—24no—
864C42—22no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—22no—
869C42—24no—
870C42C2×C22⋊C411yescharacteristic
871C42C2×C22⋊C411yescharacteristic
872C42C2×C22⋊C411yescharacteristic
873C42C2×C22⋊C411yescharacteristic
874C42C2×C22⋊C411yescharacteristic
875C42C2×C22⋊C411yescharacteristic
876C42C23×C411yescharacteristic
877C42C23×C411yescharacteristic
878C42C23×C411yescharacteristic
879C42C23×C414yes—
880C42C22×D411yescharacteristic
881C42C22×D411yescharacteristic
882C42C22×D414yes—
883C42C22×D411yescharacteristic
884C42C22×D411yescharacteristic
885C42C22×D414yes—
886C42C22×D411yescharacteristic
887C42C22×D411yescharacteristic
888C42C2511yescharacteristic
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—42no—
894C23—81no—
895C23—81no—
896C23C22×C22⋊C411yescharacteristic
897C23C22×C22⋊C414yes—
898C23C22×C22⋊C411yescharacteristic
899C23C22×C22⋊C411yescharacteristic
900Q8—24no—
901Q8—28no—
902Q8—42no—
903Q8—42no—
904Q8—42no—
905Q8—81no—
906Q8—82no—
907Q8—84no—
908Q8—82no—
909Q8—82no—
910Q8—84no—
911D4—28no—
912D4—24no—
913D4—42no—
914D4—44no—
915D4—42no—
916D4—44no—
917D4—42no—
918D4—44no—
919D4—81no—
920D4—82no—
921D4—84no—
922D4—84no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—22no—
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—41no—
940C2×C4—44no—
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—44no—
951C2×C4—42no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—84no—
955C2×C4—84no—
956C2×C4—81no—
957C2×C4—82no—
958C2×C4—84no—
959C2×C4—81no—
960C2×C4—84no—
961C2×C4C22×C22⋊C411yescharacteristic
962C2×C4C22×C22⋊C411yescharacteristic
963C2×C4C22×C22⋊C414yes—
964C2×C4C22×C22⋊C414yes—
965C2×C4C22×C22⋊C414yes—
966C2×C4C22×C22⋊C411yescharacteristic
967C2×C4C22×C22⋊C411yescharacteristic
968C2×C4C22×C22⋊C411yescharacteristic
969C2×C4C22×C22⋊C411yescharacteristic
970C2×C4C22×C22⋊C411yescharacteristic
971C2×C4C22×C22⋊C411yescharacteristic
972C2×C4C22×C22⋊C411yescharacteristic
973C2×C4C24×C411yescharacteristic
974C2×C4C23×D411yescharacteristic
975C2×C4C23×D411yescharacteristic
976C8—24no—
977C8—42no—
978C8—42no—
979C8—42no—
980C8—44no—
981C8—44no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—24no—
987C22—21no—
988C22—21no—
989C22—24no—
990C22—21no—
991C22—21no—
992C22—24no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—82no—
997C22—162no—
998C22#290112yes—
999C22C23×C22⋊C411yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—24no—
1004C4—21no—
1005C4—21no—
1006C4—21no—
1007C4—24no—
1008C4—21no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—24no—
1013C4—44no—
1014C4—42no—
1015C4—42no—
1016C4—44no—
1017C4—42no—
1018C4#357312yes—
1019C4#358612yes—
1020C2—22no—
1021C2—44no—
1022C2—41no—
1023C2—41no—
1024C2—82no—
1025C2#6006511yescharacteristic
1026C2#6008811yescharacteristic
1027C2C2×#290111yescharacteristic
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. #60293C2semidirect
3. #60210C2semidirect
4. #17524C2semidirect
5. #17519C2semidirect
6. #17514C2semidirect
7. #17513C2semidirect
8. #17506C2semidirect
9. #17502C2semidirect
10. #17501C2semidirect
11. #17484C2semidirect
12. #17480C2semidirect
13. C2×#1497C2semidirect
39. #2990C22semidirect
40. #2989C22semidirect
49. #2965C22semidirect
50. C8×#41C22semidirect
55. #2922C22semidirect
59. C4×#131C22semidirect
62. #1497C22semidirect
63. #1497C22semidirect
64. #1497C22semidirect
67. #1495C22semidirect
70. #1494C22semidirect
71. #1493C22semidirect
72. #1493C22semidirect
74. #1491C22semidirect
75. #1491C22semidirect
76. #1491C22semidirect
78. #1489C22semidirect
79. #1488C22semidirect
80. #1487C22semidirect
82. #1485C22semidirect
85. #1483C22semidirect
86. #1482C22semidirect
87. #1481C22semidirect
89. #1479C22semidirect
91. #1477C22semidirect
92. #1476C22semidirect
93. C2×Q8⋊C8C22semidirect
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
#602932
#602102
#175242
#175192
#175142
#175132
#175062
#175022
#175012
#174842
#174802
C2×#14972