Finite Group Databasebeta

← #6343599

Subgroups — #6343599

Order 512.

2877 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic
2#60128C211yesmaximal, characteristic, complemented
3#34195C211yesmaximal, characteristic, complemented
4#17612C214yesmaximal, complemented
5#17609C218yesmaximal, complemented
6#17608C214yesmaximal, complemented
7#17596C211yesmaximal, characteristic, complemented
8#17593C212yesmaximal, complemented
9#17586C212yesmaximal, complemented
10#17584C211yesmaximal, characteristic, complemented
11#17562C212yesmaximal, complemented
12#17560C211yesmaximal, characteristic, complemented
13#17558C211yesmaximal, characteristic, complemented
14C2×#1515C212yesmaximal, complemented
15#3523—21no—
16#3520—21no—
17#3520—22no—
18#3518—21no—
19#3515—21no—
20#3515—22no—
21#3511C412yescomplemented
22#3511C411yescharacteristic, complemented
23#3509C412yescomplemented
24#3509C411yescharacteristic, complemented
25#3503C411yescharacteristic, complemented
26#3499C411yescharacteristic, complemented
27#3495C2214yes—
28#3495C2212yes—
29#3489C2212yes—
30#3482—21no—
31#3482—21no—
32#3482—22no—
33Q8×#41—21no—
34#3475—22no—
35#3475—21no—
36#3461C414yescomplemented
37#3461C412yescomplemented
38#3444C2211yescharacteristic
39#3444C2212yes—
40C2×#533C2212yes—
41C2×#533C2211yescharacteristic
42C4×2−1+4C412yescomplemented
43C2×C4×#41C2211yescharacteristic
44#2925—22no—
45#2925—21no—
46#2924C2214yes—
47#2924C2212yes—
48#2923—22no—
49#2923—21no—
50#2920C2211yescharacteristic
51#2920C2212yes—
52C2×#432C2212yes—
53C2×#432C2211yescharacteristic
54#2906—21no—
55#2880C2212yes—
56#2875—21no—
57#2356—21no—
58#2353—22no—
59#2349—21no—
60#2347C2212yes—
61#2343C2214yes—
62#2339C2212yes—
63#2320—21no—
64#2318—22no—
65#2283C2212yes—
66#2283C2211yescharacteristic
67#2283C2211yescharacteristic
68C2×#383C2212yes—
69#2275—21no—
70#1521C2218yes—
71#1520C2214yes—
72#1518C2214yes—
73#1516C2218yes—
74#1515C2211yescharacteristic
75#1515C2212yes—
76#1515C2212yes—
77#1515C2212yes—
78#1515C2218yes—
79#1515C2211yescharacteristic
80#1515C2212yes—
81#1515C2212yes—
82#1514C2212yes—
83#1514C2211yescharacteristic
84#1514C2211yescharacteristic
85#1513C2214yes—
86#1512C2214yes—
87#1511C2218yes—
88#1509C2218yes—
89#1508C2214yes—
90#1506C2214yes—
91#1504C2218yes—
92#1503C2218yes—
93#1501C2214yes—
94#1500C2214yes—
95C2×#328C2218yes—
96C2×2−1+4C2×C412yes—
97C22×#41C2311yescharacteristic
98C2×#131—22no—
99Q82—21no—
100#557—21no—
101#557—22no—
102#557—21no—
103#557—21no—
104#557—22no—
105#556—21no—
106#556—22no—
107#556—21no—
108#556—22no—
109#556—21no—
110#556—22no—
111#556—22no—
112#556—24no—
113#555—21no—
114#555—22no—
115#554—21no—
116#554—22no—
117#554—22no—
118#554—21no—
119#554—24no—
120#554—22no—
121#553—22no—
122#553—22no—
123#553—22no—
124#552—22no—
125#552—22no—
126#552—22no—
127#552—22no—
128#552—22no—
129#552—22no—
130#552—24no—
131#552—24no—
132#552—24no—
133#552—22no—
134#552—24no—
135#552—22no—
136#552—24no—
137#551—24no—
138#551—24no—
139#551—24no—
140D4×Q8—22no—
141D4×Q8—21no—
142D4×Q8—21no—
143D4×Q8—22no—
144D4×Q8—21no—
145#548—22no—
146#548—22no—
147#548—22no—
148#548—22no—
149#547—22no—
150#547—24no—
151#547—22no—
152#547—21no—
153#547—22no—
154#547—21no—
155#547—21no—
156#547—22no—
157#546—22no—
158#546—24no—
159#544C2×C414yescomplemented
160#544C2×C412yescomplemented
161#542—22no—
162#542—24no—
163#542C2×C414yescomplemented
164#542C2×C414yescomplemented
165#542C2×C414yescomplemented
166#541—22no—
167#541—24no—
168#541C2×C414yescomplemented
169#541C2×C414yescomplemented
170#541C2×C414yescomplemented
171#539—24no—
172#539—24no—
173#539—24no—
174#537C2×C414yes—
175#537C2×C412yes—
176#536C2×C412yes—
177#536C2×C414yes—
178#536C2×C414yescomplemented
179#536C2×C412yescomplemented
180#533—22no—
181#533—24no—
182#533—21no—
183#533—22no—
184#533—21no—
185#533—22no—
186#533—21no—
187#533—22no—
188#533—22no—
189#533—21no—
190#533C2×C414yescomplemented
191#533C2×C412yescomplemented
192#533C2×C412yescomplemented
193#533C2×C412yescomplemented
194#533C2×C412yescomplemented
195#533C2×C411yescharacteristic, complemented
196#533C2×C412yescomplemented
197#533C2×C411yescharacteristic, complemented
198#533C2×C412yescomplemented
199#533C2311yescharacteristic
200#533C2312yes—
201#533C2314yes—
202#533C2312yes—
203#532C2×C411yescharacteristic, complemented
204#532C2×C412yescomplemented
205#532C2×C411yescharacteristic, complemented
206#532C2×C412yescomplemented
207#532C2311yescharacteristic
208C2×C4⋊Q8C2×C412yescomplemented
209C2×C4⋊Q8C2×C411yescharacteristic, complemented
210C2×C4⋊Q8C2×C412yescomplemented
211C2×C4⋊Q8C2×C411yescharacteristic, complemented
212#529—24no—
213#529—24no—
214#529—24no—
215#529—22no—
216#529—24no—
217#529—22no—
218#529—21no—
219#529—22no—
220#529—21no—
221#529—21no—
222#529—22no—
223#529—22no—
224#529—21no—
225#529C2×C412yescomplemented
226#529C2×C414yescomplemented
227#529C2312yes—
228#529C2314yes—
229C2×#125—22no—
230C2×#125—21no—
231#525—22no—
232#525—21no—
233#525—22no—
234#525—21no—
235#525C2312yes—
236#525C2314yes—
237C2×C22⋊Q8—22no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241#520—24no—
242#520—22no—
243#520C2×C412yes—
244#520C2×C414yescomplemented
245#520C2×C412yescomplemented
246#519—22no—
247#519C2×C414yescomplemented
248#519C2×C412yescomplemented
249C4×#41—24no—
250C4×#41—22no—
251C4×#41—21no—
252C4×#41—22no—
253C4×#41—21no—
254C4×#41—22no—
255C4×#41C2×C411yescharacteristic
256C4×#41C2×C412yes—
257C4×#41C2×C411yescharacteristic
258C4×#41C2×C411yescharacteristic
259C4×#41C2×C412yes—
260C4×#41C2×C411yescharacteristic
261C4×#41C2×C412yescomplemented
262C4×#41C2×C414yescomplemented
263C4×#41D411yescharacteristic
264C4×#41D411yescharacteristic
265C4×#41D412yes—
266C4×#41D411yescharacteristic
267C4×#41D412yes—
268C4×#41D411yescharacteristic
269C2×C4×Q8—22no—
270C2×C4×Q8—22no—
271C2×C4×Q8—21no—
272C2×C4×Q8C2×C414yescomplemented
273C2×C4×Q8C2×C412yescomplemented
274C2×C4×Q8D411yescharacteristic
275C2×C4×Q8D411yescharacteristic
276C2×C4×D4—22no—
277C2×C4×D4D412yes—
278C2×C4×D4D411yescharacteristic
279C2×C4×D4D412yes—
280C2×C4×D4D411yescharacteristic
281C2×#117—22no—
282C2×#117—21no—
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C22×C42C2312yes—
286C22×C42C2311yescharacteristic
287#433—24no—
288#433—24no—
289#433—24no—
290#432—21no—
291#432—22no—
292#432—21no—
293#432—22no—
294#432—21no—
295#432—22no—
296#432C2311yescharacteristic
297#432C2312yes—
298#432C2311yescharacteristic
299#432C2312yes—
300#432C2314yes—
301#431—21no—
302#431—22no—
303#431C2312yes—
304#431C2314yes—
305#424—24no—
306#424—22no—
307#423—22no—
308#423—21no—
309C2×C4⋊C8—22no—
310C2×C4⋊C8—21no—
311#408—24no—
312#408—22no—
313#407C2314yes—
314#407C2312yes—
315C2×C22⋊C8C2314yes—
316C2×C22⋊C8C2312yes—
317#405—24no—
318#405—22no—
319C4×M16—22no—
320C4×M16—21no—
321C2×#97—22no—
322C2×#97—21no—
323#391—22no—
324#389—22no—
325#388—24no—
326#387—24no—
327#387—24no—
328#386—24no—
329#385—24no—
330#383—22no—
331#383—22no—
332#383C2314yes—
333#383C2311yescharacteristic
334#383C2312yes—
335#383C2311yescharacteristic
336#382—22no—
337#382—21no—
338#382C2312yes—
339#381—21no—
340#381—21no—
341#381C2314yes—
342#380—21no—
343#380—22no—
344#380C2312yes—
345C4×C4⋊C4—22no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4—21no—
348C4×C4⋊C4C2314yes—
349C4×C22⋊C4—22no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—24no—
352C4×C22⋊C4C2312yes—
353#376—21no—
354#376—22no—
355#376C2312yes—
356C2×#95—22no—
357C2×#95—22no—
358C2×#95C2314yes—
359#328C2314yes—
360#328C2318yes—
361#328C2318yes—
362#328C2318yes—
363#328C2314yes—
364#328C2318yes—
365#328C2318yes—
366#327C2318yes—
367#327C2314yes—
368#327C2314yes—
3692−1+4—48no—
370C2×#41—24no—
371C2×#41—22no—
372C2×#41—21no—
373C2×#41—22no—
374C2×#41—21no—
375C2×#41—44no—
376C2×#41C22×C414yes—
377C2×#41C22×C412yes—
378C2×#41C22×C411yescharacteristic
379C2×#41C22×C412yes—
380C2×#41C22×C411yescharacteristic
381C2×#41C2×D411yescharacteristic
382C2×#41C2×D412yes—
383C2×#41C2×D411yescharacteristic
384C22×Q8—22no—
385C22×Q8—21no—
386C22×Q8—22no—
387C22×Q8C22×C412yes—
388C22×Q8C22×C414yes—
389C22×Q8C2×D411yescharacteristic
390C22×D4C2×D411yescharacteristic
391C22×D4C2×D412yes—
392C23×C4—24no—
393C23×C4C2×D412yes—
394C23×C4C2×D411yescharacteristic
395C23×C4C2×D412yes—
396C23×C4C2×D411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399#131—48no—
400C2×M16—24no—
401C2×M16—22no—
402C22×C8—24no—
403C22×C8—22no—
404C4⋊Q8—22no—
405C4⋊Q8—24no—
406C4⋊Q8—24no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—21no—
410C4⋊Q8—22no—
411C4⋊Q8—21no—
412C4⋊Q8—22no—
413C4⋊Q8—21no—
414C4⋊Q8—22no—
415C4⋊Q8—21no—
416C4⋊Q8C22×C411yescharacteristic
417C4⋊Q8C22×C412yes—
418C4⋊Q8C22×C414yes—
419C4⋊Q8C22×C412yes—
420C4⋊Q8C22×C411yescharacteristic
421C4⋊Q8C22×C412yes—
422C4⋊Q8C22×C414yes—
423C4⋊Q8C22×C412yes—
424C4⋊Q8C22×C411yescharacteristic
425#127C22×C411yescharacteristic
426#126—24no—
427#126—24no—
428#126—24no—
429#126—24no—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—22no—
437#126—24no—
438#126—22no—
439#125—24no—
440#125—24no—
441#125—24no—
442#125—24no—
443#125—22no—
444#125—24no—
445#125—24no—
446#125—24no—
447#125—24no—
448#125—22no—
449#125—22no—
450#125—22no—
451#125—22no—
452#125—22no—
453#125—21no—
454#125—21no—
455#125—22no—
456#125—22no—
457#125—24no—
458#125C22×C412yes—
459#125C22×C414yes—
460#124—22no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—22no—
466#124—21no—
467#124—21no—
468#124C22×C412yes—
469#124C22×C414yes—
470#123—24no—
471#123—24no—
472#123—24no—
473#123—22no—
474#123—24no—
475#123—24no—
476#123—22no—
477#123—24no—
478#123—22no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8—22no—
488C22⋊Q8—24no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—22no—
494C22⋊Q8—21no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—21no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—24no—
502C22⋊Q8—22no—
503C22⋊Q8—24no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—22no—
508C22⋊Q8—24no—
509C22⋊Q8—22no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8C22×C414yes—
517C22⋊Q8C22×C414yes—
518C22⋊Q8C22×C414yes—
519C22⋊Q8C22×C412yes—
520C22⋊Q8C22×C414yes—
521C22⋊Q8C2412yes—
522C22⋊Q8C2414yes—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—22no—
527#121—24no—
528#121—21no—
529#121—22no—
530#121—21no—
531#121—22no—
532#121—21no—
533#121—22no—
534#121—21no—
535#121C22×C412yes—
536#121C22×C414yes—
537#121C2412yes—
538#120—24no—
539#120—22no—
540C4×Q8—22no—
541C4×Q8—24no—
542C4×Q8—22no—
543C4×Q8—24no—
544C4×Q8—22no—
545C4×Q8—24no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—24no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—24no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—21no—
556C4×Q8—21no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8—22no—
562C4×Q8—24no—
563C4×Q8—22no—
564C4×Q8C22⋊C411yescharacteristic
565C4×Q8C22⋊C411yescharacteristic
566C4×Q8C22⋊C411yescharacteristic
567C4×Q8C22⋊C412yes—
568C4×Q8C22⋊C411yescharacteristic
569C4×Q8C22⋊C412yes—
570C4×Q8C22⋊C411yescharacteristic
571C4×Q8C22⋊C411yescharacteristic
572C4×Q8C22⋊C411yescharacteristic
573C4×Q8C22⋊C412yes—
574C4×Q8C22⋊C411yescharacteristic
575C4×Q8C22⋊C412yes—
576C4×Q8C22×C412yes—
577C4×Q8C22×C414yes—
578C4×Q8C22×C414yes—
579C4×Q8C22×C414yes—
580C4×Q8C22×C414yes—
581C4×Q8C22×C412yes—
582C4×Q8C22×C414yes—
583C4×D4—24no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4—22no—
592C4×D4—24no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—22no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—21no—
602C4×D4—22no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—22no—
606C4×D4—21no—
607C4×D4—48no—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C411yescharacteristic
610C4×D4C22⋊C412yes—
611C4×D4C22⋊C411yescharacteristic
612C4×D4C22⋊C411yescharacteristic
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22⋊C412yes—
619C4×D4C22⋊C412yes—
620C4×D4C22⋊C411yescharacteristic
621C4×D4C22⋊C412yes—
622C4×D4C22⋊C412yes—
623C4×D4C22⋊C411yescharacteristic
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C411yescharacteristic
626C4×D4C22⋊C411yescharacteristic
627C4×D4C22⋊C412yes—
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C412yes—
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C412yes—
633C4×D4C22⋊C412yes—
634C4×D4C22⋊C411yescharacteristic
635C4×D4C22⋊C412yes—
636C4×D4C22×C412yes—
637C4×D4C22×C412yes—
638C4×D4C22×C414yes—
639#117—22no—
640#117—24no—
641#117—22no—
642#117—22no—
643#117—22no—
644#117—21no—
645#117—22no—
646#117—21no—
647#117—22no—
648#117—24no—
649#117—22no—
650#117—24no—
651#117—22no—
652#117—24no—
653#117—24no—
654#117—24no—
655#117—22no—
656#117—24no—
657#117—24no—
658#117—22no—
659#117—22no—
660#117—24no—
661#117C22×C412yes—
662#117C22×C414yes—
663#117C22×C412yes—
664#117C22×C411yescharacteristic
665#117C22×C412yes—
666#117C22×C411yescharacteristic
667#117C22×C412yes—
668#117C22×C412yes—
669#117C22×C412yes—
670#117C2×D412yes—
671#117C2×D411yescharacteristic
672#117C2×D412yes—
673#117C2×D412yes—
674#117C2×D412yes—
675#117C2×D411yescharacteristic
676#117C2×D412yes—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—24no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—24no—
692C2×C4⋊C4C22×C414yes—
693C2×C4⋊C4C22×C412yes—
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D412yes—
696C2×C4⋊C4C2×D412yes—
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C22⋊C4—24no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4C2×D412yes—
704C2×C22⋊C4C2×D412yes—
705C2×C22⋊C4C2×D412yes—
706C2×C42—22no—
707C2×C42—24no—
708C2×C42—24no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—24no—
712C2×C42—22no—
713C2×C42C22×C412yes—
714C2×C42C22×C411yescharacteristic
715C2×C42C22×C412yes—
716C2×C42C22×C411yescharacteristic
717C2×C42C22×C412yes—
718C2×C42C22×C411yescharacteristic
719C2×C42C22×C412yes—
720C2×C42C22×C411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D412yes—
723C2×C42C2×D412yes—
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D412yes—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D412yes—
729C2×C42C2×D412yes—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2411yescharacteristic
736C4⋊C8—21no—
737C4⋊C8—22no—
738C4⋊C8—21no—
739C4⋊C8—24no—
740C4⋊C8—22no—
741C4⋊C8—24no—
742C4⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—24no—
745C22⋊C8—22no—
746C22⋊C8—24no—
747C22⋊C8C2412yes—
748C22⋊C8C2414yes—
749C22⋊C8C2412yes—
750#97—21no—
751#97—22no—
752#97—21no—
753#97—22no—
754#97—24no—
755C4×C8—22no—
756C4×C8—24no—
757#95—21no—
758#95—21no—
759#95—22no—
760#95—22no—
761#95—24no—
762#95—24no—
763#95—24no—
764#95—21no—
765#95—21no—
766#95—22no—
767#95—24no—
768#95—22no—
769#95C2412yes—
770#95C2414yes—
771#95C2412yes—
772C24C22×D412yes—
773C24C22×D411yescharacteristic
774#41—24no—
775#41—24no—
776#41—44no—
777#41—44no—
778#41—42no—
779#41—42no—
780#41—44no—
781#41—48no—
782#41—44no—
783#41—416no—
784#41—48no—
785#41—82no—
786#41—84no—
787C2×Q8—21no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—22no—
791C2×Q8—21no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—42no—
795C2×Q8—44no—
796C2×Q8—48no—
797C2×Q8—48no—
798C2×Q8—84no—
799C2×Q8—82no—
800C2×Q8C2×C22⋊C411yescharacteristic
801C2×Q8C2×C22⋊C411yescharacteristic
802C2×Q8C2×C22⋊C412yes—
803C2×Q8C23×C414yes—
804C2×Q8C23×C412yes—
805C2×D4—24no—
806C2×D4—22no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—44no—
814C2×D4C2×C22⋊C412yes—
815C2×D4C2×C22⋊C412yes—
816C2×D4C2×C22⋊C412yes—
817C2×D4C2×C22⋊C411yescharacteristic
818C2×D4C2×C22⋊C412yes—
819C2×D4C2×C22⋊C412yes—
820C2×D4C2×C22⋊C411yescharacteristic
821C2×D4C23×C412yes—
822C22×C4—22no—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—24no—
831C22×C4—22no—
832C22×C4—24no—
833C22×C4—22no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—81no—
840C22×C4—82no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4C2×C22⋊C411yescharacteristic
844C22×C4C2×C22⋊C412yes—
845C22×C4C2×C22⋊C411yescharacteristic
846C22×C4C2×C22⋊C412yes—
847C22×C4C2×C22⋊C411yescharacteristic
848C22×C4C2×C22⋊C412yes—
849C22×C4C2×C22⋊C411yescharacteristic
850C22×C4C2×C22⋊C412yes—
851C22×C4C2×C22⋊C411yescharacteristic
852C22×C4C2×C22⋊C412yes—
853C22×C4C2×C22⋊C411yescharacteristic
854C22×C4C2×C22⋊C412yes—
855C22×C4C2×C22⋊C411yescharacteristic
856C22×C4C2×C22⋊C412yes—
857C22×C4C2×C22⋊C411yescharacteristic
858C22×C4C2×C22⋊C412yes—
859C22×C4C23×C412yes—
860C22×C4C23×C411yescharacteristic
861C22×C4C23×C412yes—
862C22×C4C23×C411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D412yes—
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D412yes—
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D412yes—
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D412yes—
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D412yes—
875C22×C4C2511yescharacteristic
876M16—48no—
877M16—44no—
878C2×C8—24no—
879C2×C8—22no—
880C2×C8—22no—
881C2×C8—48no—
882C2×C8—44no—
883C4⋊C4—22no—
884C4⋊C4—21no—
885C4⋊C4—22no—
886C4⋊C4—21no—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—21no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—44no—
917C4⋊C4—82no—
918C4⋊C4—84no—
919C4⋊C4C2×C22⋊C412yes—
920C4⋊C4C2×C22⋊C411yescharacteristic
921C4⋊C4C2×C22⋊C412yes—
922C4⋊C4C2×C22⋊C411yescharacteristic
923C4⋊C4C2×C22⋊C412yes—
924C4⋊C4C2×C22⋊C412yes—
925C4⋊C4C2×C22⋊C412yes—
926C4⋊C4C2×C22⋊C412yes—
927C4⋊C4C2×C22⋊C411yescharacteristic
928C4⋊C4C2×C22⋊C412yes—
929C4⋊C4C2×C22⋊C411yescharacteristic
930C4⋊C4C2×C22⋊C412yes—
931C4⋊C4C2×C22⋊C412yes—
932C4⋊C4C2×C22⋊C412yes—
933C4⋊C4C23×C412yes—
934C4⋊C4C23×C414yes—
935C4⋊C4C23×C412yes—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—22no—
940C22⋊C4—24no—
941C22⋊C4—22no—
942C22⋊C4—24no—
943C22⋊C4—22no—
944C22⋊C4—24no—
945C22⋊C4—22no—
946C22⋊C4—24no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—24no—
954C22⋊C4—22no—
955C22⋊C4—48no—
956C22⋊C4—82no—
957C22⋊C4—82no—
958C22⋊C4C2×C22⋊C412yes—
959C22⋊C4C2×C22⋊C412yes—
960C22⋊C4C2×C22⋊C412yes—
961C22⋊C4C2×C22⋊C412yes—
962C22⋊C4C2×C22⋊C412yes—
963C22⋊C4C2×C22⋊C412yes—
964C22⋊C4C2×C22⋊C412yes—
965C22⋊C4C2×C22⋊C412yes—
966C22⋊C4C2×C22⋊C412yes—
967C22⋊C4C2×C22⋊C412yes—
968C22⋊C4C2×C22⋊C412yes—
969C22⋊C4C2×C22⋊C412yes—
970C42—24no—
971C42—22no—
972C42—22no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—22no—
979C42—44no—
980C42—84no—
981C42—82no—
982C42C2×C22⋊C412yes—
983C42C2×C22⋊C411yescharacteristic
984C42C2×C22⋊C411yescharacteristic
985C42C2×C22⋊C412yes—
986C42C2×C22⋊C412yes—
987C42C2×C22⋊C411yescharacteristic
988C42C2×C22⋊C411yescharacteristic
989C42C2×C22⋊C412yes—
990C42C2×C22⋊C412yes—
991C42C2×C22⋊C412yes—
992C42C2×C22⋊C411yescharacteristic
993C42C2×C22⋊C411yescharacteristic
994C42C2×C22⋊C412yes—
995C42C2×C22⋊C411yescharacteristic
996C42C2×C22⋊C412yes—
997C42C2×C22⋊C411yescharacteristic
998C42C23×C411yescharacteristic
999C42C23×C411yescharacteristic
1000C42C23×C411yescharacteristic
1001C42C23×C412yes—
1002C42C23×C411yescharacteristic
1003C42C23×C412yes—
1004C42C22×D411yescharacteristic
1005C42C22×D412yes—
1006C42C22×D411yescharacteristic
1007C42C22×D411yescharacteristic
1008C42C22×D412yes—
1009C42C22×D411yescharacteristic
1010C23—24no—
1011C23—24no—
1012C23—22no—
1013C23—22no—
1014C23—42no—
1015C23—41no—
1016C23—41no—
1017C23C22×C22⋊C411yescharacteristic
1018C23C22×C22⋊C412yes—
1019C23C22×C22⋊C411yescharacteristic
1020C23C22×C22⋊C412yes—
1021C23C23×D411yescharacteristic
1022Q8—22no—
1023Q8—22no—
1024Q8—42no—
1025Q8—44no—
1026Q8—42no—
1027Q8—48no—
1028Q8—42no—
1029Q8—44no—
1030Q8—42no—
1031Q8—44no—
1032Q8—82no—
1033Q8—84no—
1034D4—24no—
1035D4—24no—
1036D4—24no—
1037D4—22no—
1038D4—42no—
1039D4—42no—
1040D4—42no—
1041D4—42no—
1042D4—42no—
1043D4—44no—
1044D4—44no—
1045D4—48no—
1046D4—84no—
1047D4—82no—
1048D4#41014yes—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—41no—
1063C2×C4—42no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—42no—
1068C2×C4—41no—
1069C2×C4—42no—
1070C2×C4—41no—
1071C2×C4—42no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—42no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—42no—
1087C2×C4—48no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—48no—
1091C2×C4—44no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—44no—
1100C2×C4—42no—
1101C2×C4—82no—
1102C2×C4—84no—
1103C2×C4—84no—
1104C2×C4—82no—
1105C2×C4—168no—
1106C2×C4C22×C22⋊C411yescharacteristic
1107C2×C4C22×C22⋊C412yes—
1108C2×C4C22×C22⋊C411yescharacteristic
1109C2×C4C22×C22⋊C412yes—
1110C2×C4C22×C22⋊C411yescharacteristic
1111C2×C4C22×C22⋊C412yes—
1112C2×C4C22×C22⋊C411yescharacteristic
1113C2×C4C22×C22⋊C411yescharacteristic
1114C2×C4C22×C22⋊C411yescharacteristic
1115C2×C4C22×C22⋊C411yescharacteristic
1116C2×C4C22×C22⋊C412yes—
1117C2×C4C22×C22⋊C411yescharacteristic
1118C2×C4C22×C22⋊C412yes—
1119C2×C4C22×C22⋊C412yes—
1120C2×C4C22×C22⋊C411yescharacteristic
1121C2×C4C22×C22⋊C411yescharacteristic
1122C2×C4C24×C411yescharacteristic
1123C2×C4C23×D411yescharacteristic
1124C8—42no—
1125C8—44no—
1126C8—42no—
1127C22—21no—
1128C22—22no—
1129C22—21no—
1130C22—22no—
1131C22—21no—
1132C22—21no—
1133C22—22no—
1134C22—22no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—22no—
1139C22—21no—
1140C22—48no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—82no—
1145C22C2×#41014yes—
1146C22C23×C22⋊C411yescharacteristic
1147C22#358612yes—
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—21no—
1152C4—22no—
1153C4—21no—
1154C4—21no—
1155C4—22no—
1156C4—22no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—21no—
1162C4—22no—
1163C4—21no—
1164C4—22no—
1165C4—44no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—44no—
1170C4—82no—
1171C4—84no—
1172C4—82no—
1173C4C2×#41012yes—
1174C2—22no—
1175C2—24no—
1176C2—42no—
1177C2—41no—
1178C2—41no—
1179C2—82no—
1180C2C22×#41011yescharacteristic
1181C2#6008811yescharacteristic
1182C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62805C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60128C2semidirect
3. #34195C2semidirect
4. #17612C2semidirect
5. #17609C2semidirect
6. #17608C2semidirect
7. #17596C2semidirect
8. #17593C2semidirect
9. #17586C2semidirect
10. #17584C2semidirect
11. #17562C2semidirect
12. #17560C2semidirect
13. #17558C2semidirect
14. C2×#1515C2semidirect
21. #3511C4semidirect
22. #3511C4semidirect
23. #3509C4semidirect
24. #3509C4semidirect
25. #3503C4semidirect
26. #3499C4semidirect
36. #3461C4semidirect
37. #3461C4semidirect
42. C4×2−1+4C4semidirect
159. #544C2×C4semidirect
160. #544C2×C4semidirect
163. #542C2×C4semidirect
164. #542C2×C4semidirect
165. #542C2×C4semidirect
168. #541C2×C4semidirect
169. #541C2×C4semidirect
170. #541C2×C4semidirect
178. #536C2×C4semidirect
179. #536C2×C4semidirect
190. #533C2×C4semidirect
191. #533C2×C4semidirect
192. #533C2×C4semidirect
193. #533C2×C4semidirect
194. #533C2×C4semidirect
195. #533C2×C4semidirect
196. #533C2×C4semidirect
197. #533C2×C4semidirect
198. #533C2×C4semidirect
203. #532C2×C4semidirect
204. #532C2×C4semidirect
205. #532C2×C4semidirect
206. #532C2×C4semidirect
208. C2×C4⋊Q8C2×C4semidirect
209. C2×C4⋊Q8C2×C4semidirect
210. C2×C4⋊Q8C2×C4semidirect
211. C2×C4⋊Q8C2×C4semidirect
225. #529C2×C4semidirect
226. #529C2×C4semidirect
244. #520C2×C4semidirect
245. #520C2×C4semidirect
247. #519C2×C4semidirect
248. #519C2×C4semidirect
261. C4×#41C2×C4semidirect
262. C4×#41C2×C4semidirect
272. C2×C4×Q8C2×C4semidirect
273. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628052
#601282
#341952
#176122
#176092
#176082
#175962
#175932
#175862
#175842
#175622
#175602
#175582
C2×#15152