Finite Group Databasebeta

← #6343705

Subgroups — #6343705

Order 512.

2675 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62831C211yesmaximal, characteristic
2#60251C211yesmaximal, characteristic, complemented
3#34394C211yesmaximal, characteristic, complemented
4#17628C214yesmaximal, complemented
5#17624C214yesmaximal, complemented
6#17612C212yesmaximal, complemented
7#17610C212yesmaximal, complemented
8#17607C212yesmaximal, complemented
9#17605C212yesmaximal, complemented
10#17602C214yesmaximal, complemented
11#17601C214yesmaximal, complemented
12#17585C211yesmaximal, characteristic, complemented
13#17581C211yesmaximal, characteristic, complemented
14#17579C211yesmaximal, characteristic, complemented
15#17560C211yesmaximal, characteristic, complemented
16#3565—22no—
17#3564—22no—
18#3557C414yescomplemented
19#3555C412yescomplemented
20#3554C412yescomplemented
21#3552—21no—
22#3544—21no—
23#3535—22no—
24#3523C2212yes—
25#3522C2212yes—
26#3520—22no—
27#3518—21no—
28#3515—21no—
29#3515—22no—
30#3510C412yescomplemented
31#3507C411yescharacteristic, complemented
32#3507C2214yes—
33#3506C411yescharacteristic, complemented
34#3504C412yescomplemented
35#3502C411yescharacteristic, complemented
36#3501C411yescharacteristic, complemented
37#3495—22no—
38#3495C2212yes—
39#3494C2212yes—
40#3444C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#529C2211yescharacteristic
43#2987—22no—
44#2985—22no—
45#2984C2214yescomplemented
46#2983C2214yescomplemented
47#2962—22no—
48#2961—21no—
49#2961—21no—
50#2924C2212yes—
51#2924C2212yes—
52#2920C2211yescharacteristic
53C2×#432C2211yescharacteristic
54#2378—22no—
55#2369—21no—
56#2365—21no—
57#2356C2212yescomplemented
58#2351C2212yescomplemented
59#2347C2212yes—
60#2346C2212yes—
61#2330—22no—
62#2323—22no—
63#2320C2214yescomplemented
64#2285C2211yescharacteristic
65#2283C2211yescharacteristic
66#1521C2214yes—
67#1521C2214yes—
68#1521C2214yescomplemented
69#1520C2211yescharacteristic
70#1520C2211yescharacteristic
71#1519C2211yescharacteristic
72#1519C2211yescharacteristic
73#1518C2212yescomplemented
74#1518C2214yescomplemented
75#1517C2214yes—
76#1517C2212yescomplemented
77#1515C2212yescomplemented
78#1515C2214yescomplemented
79#1514C2214yes—
80#1514C2212yescomplemented
81#1513C2212yes—
82#1513C2212yes—
83#1512C2212yes—
84#1512C2212yes—
85#1512C2214yes—
86#1512C2214yes—
87#1512C2212yescomplemented
88#1512C2212yescomplemented
89#1512C2214yescomplemented
90#1509C2214yes—
91#1509C2214yes—
92#1509C2214yescomplemented
93#1509C2214yescomplemented
94#1508C2212yes—
95#1507C2212yes—
96#1506C2214yescomplemented
97#1505C2214yes—
98#1503C2214yescomplemented
99#1502C2214yes—
100#1501C2212yes—
101#1501C2212yes—
102#1500C2214yes—
103#1500C2214yescomplemented
104#563—24no—
105#563—24no—
106#563—24no—
107#562—24no—
108#559C2×C414yes—
109#559C2×C412yes—
110#559C2×C414yes—
111#559C2×C414yes—
112Q82—21no—
113Q82C2×C412yes—
114#557—21no—
115#557—22no—
116#557C2×C412yes—
117#557C2×C414yes—
118#557C2×C412yes—
119#557C2×C414yes—
120#557C2×C414yes—
121#556—21no—
122#556—22no—
123#556—24no—
124#556—24no—
125#556—22no—
126#556C2×C412yes—
127#556C2×C414yes—
128#556C2×C414yes—
129#556C2×C414yes—
130#555—21no—
131#555—22no—
132#554—21no—
133#554—21no—
134#554—22no—
135#554—24no—
136#554—24no—
137#554—22no—
138#554C2×C414yes—
139#554C2×C412yes—
140#554C2×C414yes—
141#554C2×C414yes—
142#553—22no—
143#553—22no—
144#553—22no—
145#552—24no—
146#552—24no—
147#552—22no—
148#552—22no—
149#552—24no—
150#552—24no—
151#552—24no—
152#552—22no—
153#552—22no—
154#552—24no—
155#552—22no—
156#551—24no—
157#551—24no—
158#551—24no—
159#551—24no—
160#550C2×C412yes—
161D4×Q8—22no—
162D4×Q8—21no—
163D4×Q8C2×C412yes—
164#548—22no—
165#548—22no—
166#547—21no—
167#547—22no—
168#547—22no—
169#547—24no—
170#547—22no—
171#546—24no—
172#544—22no—
173#544—22no—
174#544—22no—
175#544—22no—
176#544C2×C412yes—
177#544C2×C412yes—
178#543—22no—
179#542—22no—
180#542—22no—
181#542—22no—
182#542—24no—
183#542—24no—
184#542—22no—
185#542—24no—
186#542C2×C414yes—
187#542C2×C414yes—
188#541—22no—
189#541—24no—
190#541—22no—
191#541—24no—
192#541C2×C414yes—
193#540C2×C414yes—
194#539—24no—
195#539—22no—
196#539—24no—
197#539—24no—
198#539—24no—
199#539—24no—
200#538—22no—
201#536—24no—
202#536—22no—
203#536C2×C412yes—
204#535C2×C412yes—
205#533—22no—
206#533—22no—
207#533C2×C411yescharacteristic
208#533C2×C411yescharacteristic
209#533C2×C411yescharacteristic
210#533C2×C411yescharacteristic
211#533C2×C412yes—
212#533C2×C412yes—
213#533C2×C412yes—
214#533D411yescharacteristic
215#533D411yescharacteristic
216#533D412yes—
217#533D412yes—
218#533D412yes—
219#533C2311yescharacteristic
220#533C2314yes—
221#532C2×C411yescharacteristic
222#532C2×C411yescharacteristic
223#532C2311yescharacteristic
224#532C2314yes—
225C2×C4⋊Q8D411yescharacteristic
226C2×C4⋊Q8D411yescharacteristic
227#529—22no—
228#529—22no—
229#529—22no—
230#529—21no—
231#529—21no—
232#529—21no—
233#529—21no—
234#529—21no—
235#529—21no—
236#529—21no—
237#529—21no—
238#529C2×C412yes—
239#529C2×C412yes—
240#529C2×C412yes—
241#529C2312yes—
242#529C2312yes—
243#529C2312yes—
244#529C2314yes—
245#529C2314yes—
246C2×#126—21no—
247C2×#125—22no—
248C2×#125C2×C411yescharacteristic
249C2×#125D412yes—
250C2×#124C2×C411yescharacteristic
251#525—21no—
252#525—21no—
253#525—22no—
254#525C2312yes—
255C2×#123—21no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8D412yes—
258C2×C22⋊Q8D412yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×#121C2311yescharacteristic
261#520—22no—
262#520—24no—
263#520C2×C412yes—
264#520C2×C412yes—
265#519—22no—
266#519C2×C412yes—
267#518C2×C412yes—
268C4×#41—21no—
269C4×#41—21no—
270C4×#41C2×C412yes—
271C2×C4×Q8—22no—
272C2×C4×Q8C2×C411yescharacteristic
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×D4—21no—
276C2×C4×D4C2×C411yescharacteristic
277C2×#117—21no—
278C2×#117—21no—
279C2×#117C2312yes—
280C22×C42C2311yescharacteristic
281#446—24no—
282#446—24no—
283#446—24no—
284#446—24no—
285#446—24no—
286#446—24no—
287#446—24no—
288C8×Q8—24no—
289#433—24no—
290#433—24no—
291#432—21no—
292#432—21no—
293#432—21no—
294#432C2312yes—
295#432C2312yes—
296#432C2312yes—
297#432C2314yes—
298#432C2314yes—
299#431—21no—
300#431C2312yes—
301#431C2314yes—
302#431C2314yes—
303#424—22no—
304#424—22no—
305#423—21no—
306C2×C4⋊C8—21no—
307#407C2312yes—
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310#405—22no—
311#405—22no—
312C4×M16—21no—
313C2×#97—21no—
314#391—24no—
315#391—22no—
316#389—24no—
317#389—22no—
318#389—22no—
319#389—22no—
320#389—24no—
321#388—24no—
322#388—24no—
323#387—24no—
324#387—24no—
325#387—24no—
326#384—21no—
327#383C2312yes—
328#383C2314yes—
329#382C2312yes—
330#382C2314yes—
331#382C2311yescharacteristic
332#382C2311yescharacteristic
333#381—21no—
334#380—21no—
335#380—21no—
336#380C2311yescharacteristic
337#380C2311yescharacteristic
338C4×C4⋊C4—22no—
339C4×C4⋊C4—22no—
340C4×C4⋊C4—22no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—21no—
343C4×C4⋊C4C2314yes—
344C4×C4⋊C4C2312yes—
345C4×C22⋊C4C2312yes—
346#376—21no—
347#376C2314yes—
348#328C2312yes—
349#328C2314yes—
350#328C2314yes—
351#328C2314yes—
352#328C2312yes—
353#328C2312yes—
354#328C2312yes—
355#328C2314yes—
356#328C2314yes—
357#328C2314yes—
358#327C2314yes—
359#327C2314yes—
360#327C2312yes—
361#327C2314yes—
362#327C2312yes—
363#327C2312yes—
364#327C2312yes—
365#327C2314yes—
366#327C2314yes—
367#327C2314yes—
368C2×#41—22no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—24no—
372C2×#41C22×C412yes—
373C22×Q8—22no—
374C22×Q8C22×C411yescharacteristic
375C22×Q8C2×D412yes—
376C22×Q8C2×D412yes—
377C22×D4—21no—
378C22×D4C22×C411yescharacteristic
379C23×C4—21no—
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2411yescharacteristic
383C2×M16—22no—
384C22×C8—21no—
385C22×C8—21no—
386C4⋊Q8—22no—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—24no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393C4⋊Q8—24no—
394C4⋊Q8C22⋊C412yes—
395C4⋊Q8C22⋊C412yes—
396C4⋊Q8C22⋊C412yes—
397C4⋊Q8C22⋊C412yes—
398C4⋊Q8C22⋊C411yescharacteristic
399C4⋊Q8C22⋊C411yescharacteristic
400C4⋊Q8C22⋊C411yescharacteristic
401C4⋊Q8C22⋊C411yescharacteristic
402C4⋊Q8C22⋊C412yes—
403C4⋊Q8C22⋊C412yes—
404C4⋊Q8C22×C411yescharacteristic
405C4⋊Q8C22×C414yes—
406C4⋊Q8C22×C411yescharacteristic
407C4⋊Q8C22×C411yescharacteristic
408C4⋊Q8C22×C414yes—
409C4⋊Q8C22×C414yes—
410#127C22×C411yescharacteristic
411#127C22×C414yes—
412#126—24no—
413#126—24no—
414#126—24no—
415#126—24no—
416#126—24no—
417#126—24no—
418#126—24no—
419#126—24no—
420#126—24no—
421#126—24no—
422#126—24no—
423#126—22no—
424#126—22no—
425#126—22no—
426#126—22no—
427#126—22no—
428#126—22no—
429#126—24no—
430#126—24no—
431#125—24no—
432#125—24no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125—24no—
437#125—24no—
438#125—24no—
439#125—24no—
440#125—24no—
441#125—24no—
442#125—24no—
443#125—24no—
444#125—21no—
445#125—21no—
446#125—21no—
447#125—21no—
448#125—24no—
449#125C22⋊C412yes—
450#125C22⋊C412yes—
451#125C22⋊C414yes—
452#125C22⋊C414yes—
453#125C22⋊C412yes—
454#125C22⋊C412yes—
455#125C22×C412yes—
456#125C22×C412yes—
457#125C22×C412yes—
458#125C22×C414yes—
459#125C22×C414yes—
460#124—22no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—21no—
467#124—21no—
468#124—21no—
469#124—21no—
470#124—24no—
471#124C22×C412yes—
472#124C22×C412yes—
473#124C22×C412yes—
474#124C22×C414yes—
475#124C22×C414yes—
476#123—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496#123—24no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8C22⋊C412yes—
528C22⋊Q8C22⋊C412yes—
529C22⋊Q8C22⋊C412yes—
530C22⋊Q8C22⋊C412yes—
531C22⋊Q8C22⋊C414yes—
532C22⋊Q8C22⋊C412yes—
533C22⋊Q8C22⋊C412yes—
534C22⋊Q8C22⋊C412yes—
535C22⋊Q8C22⋊C412yes—
536C22⋊Q8C22⋊C414yes—
537C22⋊Q8C22⋊C414yes—
538C22⋊Q8C22⋊C414yes—
539C22⋊Q8C22×C412yes—
540C22⋊Q8C22×C412yes—
541C22⋊Q8C2412yes—
542C22⋊Q8C2412yes—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#121—24no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—24no—
554#121—24no—
555#121—24no—
556#121C22×C412yes—
557#121C22×C412yes—
558#121C2412yes—
559#121C2412yes—
560#120—22no—
561#120—24no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—24no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—21no—
576C4×Q8—24no—
577C4×Q8—84no—
578C4×Q8C22×C412yes—
579C4×Q8C22×C412yes—
580C4×Q8C22×C412yes—
581C4×Q8C22×C412yes—
582C4×Q8C22×C414yes—
583C4×Q8C22×C414yes—
584C4×Q8C22×C414yes—
585C4×Q8C22×C414yes—
586C4×Q8C22×C412yes—
587C4×Q8C22×C412yes—
588C4×Q8C22×C412yes—
589C4×Q8C22×C414yes—
590C4×Q8C22×C414yes—
591C4×Q8C22×C412yes—
592C4×Q8C2×D412yes—
593C4×Q8C2×D412yes—
594C4×Q8C2×D414yes—
595C4×Q8C2×D412yes—
596C4×Q8C2×D414yes—
597C4×Q8C2×D412yes—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—24no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—22no—
616C4×D4—24no—
617C4×D4—24no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—24no—
625C4×D4C22×C412yes—
626C4×D4C22×C412yes—
627C4×D4C22×C412yes—
628C4×D4C22×C412yes—
629C4×D4C22×C414yes—
630C4×D4C22×C414yes—
631C4×D4C22×C414yes—
632C4×D4C22×C414yes—
633#117—21no—
634#117—21no—
635#117—24no—
636#117—22no—
637#117—24no—
638#117—24no—
639#117—24no—
640#117—22no—
641#117—22no—
642#117—24no—
643#117—22no—
644#117—22no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—22no—
649#117—22no—
650#117—24no—
651#117—24no—
652#117—82no—
653#117C22×C412yes—
654#117C22×C412yes—
655#117C22×C412yes—
656#117C22×C414yes—
657#117C2×D414yes—
658#117C2×D412yes—
659#117C2×D412yes—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—24no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—24no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4C22×C411yescharacteristic
679C2×C4⋊C4C22×C411yescharacteristic
680C2×C4⋊C4C2×D412yes—
681C2×C4⋊C4C2×D412yes—
682C2×C4⋊C4C2×D414yes—
683C2×C4⋊C4C2×D414yes—
684C2×C4⋊C4C2×D412yes—
685C2×C4⋊C4C2×D412yes—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4C2×D414yes—
696C2×C42—21no—
697C2×C42—22no—
698C2×C42—22no—
699C2×C42—22no—
700C2×C42—24no—
701C2×C42—24no—
702C2×C42C22×C411yescharacteristic
703C2×C42C22×C411yescharacteristic
704C2×C42C22×C411yescharacteristic
705C2×C42C22×C411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—22no—
718C4⋊C8—22no—
719C4⋊C8—24no—
720C4⋊C8—24no—
721C4⋊C8—24no—
722C4⋊C8—24no—
723C22⋊C8—21no—
724C22⋊C8—21no—
725C22⋊C8—22no—
726C22⋊C8C2412yes—
727C22⋊C8C2412yes—
728C22⋊C8C2414yes—
729#97—22no—
730#97—22no—
731#97—22no—
732#97—24no—
733#97—24no—
734C4×C8—22no—
735C4×C8—24no—
736C4×C8—24no—
737#95—22no—
738#95—21no—
739#95—21no—
740#95—24no—
741#95—22no—
742#95—22no—
743#95—24no—
744#95—24no—
745#95—24no—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750C24—21no—
751C24C22×D411yescharacteristic
752#41—44no—
753#41—84no—
754#41—81no—
755#41—81no—
756#41—84no—
757#41—82no—
758#41—84no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—24no—
762C2×Q8—21no—
763C2×Q8—24no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—82no—
768C2×Q8—84no—
769C2×Q8C2×C22⋊C412yes—
770C2×Q8C2×C22⋊C412yes—
771C2×Q8C2×C22⋊C412yes—
772C2×Q8C2×C22⋊C414yes—
773C2×Q8C2×C22⋊C414yes—
774C2×Q8C2×C22⋊C412yes—
775C2×Q8C23×C412yes—
776C2×Q8C23×C412yes—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4C23×C412yes—
791C2×D4C23×C412yes—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—42no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—81no—
812C22×C4—82no—
813C22×C4C2×C22⋊C411yescharacteristic
814C22×C4C2×C22⋊C411yescharacteristic
815C22×C4C2×C22⋊C411yescharacteristic
816C22×C4C2×C22⋊C411yescharacteristic
817C22×C4C2×C22⋊C411yescharacteristic
818C22×C4C2×C22⋊C411yescharacteristic
819C22×C4C2×C22⋊C411yescharacteristic
820C22×C4C2×C22⋊C411yescharacteristic
821C22×C4C23×C411yescharacteristic
822C22×C4C23×C411yescharacteristic
823C22×C4C22×D414yes—
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D414yes—
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C2511yescharacteristic
833M16—44no—
834C2×C8—24no—
835C2×C8—22no—
836C2×C8—22no—
837C2×C8—42no—
838C2×C8—42no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—24no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—82no—
876C4⋊C4—84no—
877C4⋊C4—84no—
878C4⋊C4—82no—
879C4⋊C4C2×C22⋊C414yes—
880C4⋊C4C2×C22⋊C414yes—
881C4⋊C4C2×C22⋊C412yes—
882C4⋊C4C2×C22⋊C412yes—
883C4⋊C4C2×C22⋊C412yes—
884C4⋊C4C2×C22⋊C414yes—
885C4⋊C4C2×C22⋊C412yes—
886C4⋊C4C2×C22⋊C412yes—
887C4⋊C4C2×C22⋊C412yes—
888C4⋊C4C2×C22⋊C414yes—
889C4⋊C4C2×C22⋊C414yes—
890C4⋊C4C2×C22⋊C414yes—
891C4⋊C4C2×C22⋊C414yes—
892C4⋊C4C2×C22⋊C414yes—
893C4⋊C4C2×C22⋊C414yes—
894C4⋊C4C2×C22⋊C414yes—
895C4⋊C4C2×C22⋊C412yes—
896C4⋊C4C2×C22⋊C414yes—
897C4⋊C4C2×C22⋊C414yes—
898C4⋊C4C2×C22⋊C412yes—
899C4⋊C4C23×C412yes—
900C4⋊C4C23×C412yes—
901C4⋊C4C23×C412yes—
902C4⋊C4C23×C412yes—
903C22⋊C4—22no—
904C22⋊C4—22no—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—22no—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—22no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—82no—
933C22⋊C4C2×C22⋊C414yes—
934C22⋊C4C2×C22⋊C414yes—
935C22⋊C4C2×C22⋊C414yes—
936C22⋊C4C2×C22⋊C414yes—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—44no—
947C42—44no—
948C42—84no—
949C42—84no—
950C42C2×C22⋊C411yescharacteristic
951C42C2×C22⋊C411yescharacteristic
952C42C2×C22⋊C411yescharacteristic
953C42C2×C22⋊C411yescharacteristic
954C42C2×C22⋊C411yescharacteristic
955C42C2×C22⋊C411yescharacteristic
956C42C2×C22⋊C411yescharacteristic
957C42C2×C22⋊C411yescharacteristic
958C42C23×C411yescharacteristic
959C42C23×C411yescharacteristic
960C42C23×C411yescharacteristic
961C42C23×C411yescharacteristic
962C42C23×C414yes—
963C42C23×C414yes—
964C42C22×D411yescharacteristic
965C42C22×D414yes—
966C42C22×D414yes—
967C42C22×D411yescharacteristic
968C42C22×D411yescharacteristic
969C42C22×D411yescharacteristic
970C23—21no—
971C23—21no—
972C23—22no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—81no—
978C23—81no—
979C23C22×C22⋊C411yescharacteristic
980C23C22×C22⋊C411yescharacteristic
981C23C23×D411yescharacteristic
982Q8—42no—
983Q8—44no—
984Q8—42no—
985Q8—42no—
986Q8—44no—
987Q8—42no—
988Q8—42no—
989Q8—42no—
990Q8—42no—
991Q8—42no—
992Q8—84no—
993Q8—81no—
994Q8—84no—
995D4—42no—
996D4—42no—
997D4—42no—
998D4—44no—
999D4—42no—
1000D4—42no—
1001D4—42no—
1002D4—42no—
1003D4—42no—
1004D4—81no—
1005D4—84no—
1006D4—84no—
1007D4—82no—
1008D4—82no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—44no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—44no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—82no—
1054C2×C4—84no—
1055C2×C4—82no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—82no—
1059C2×C4—84no—
1060C2×C4—81no—
1061C2×C4—81no—
1062C2×C4C22×C22⋊C411yescharacteristic
1063C2×C4C22×C22⋊C411yescharacteristic
1064C2×C4C22×C22⋊C411yescharacteristic
1065C2×C4C22×C22⋊C411yescharacteristic
1066C2×C4C22×C22⋊C414yes—
1067C2×C4C22×C22⋊C414yes—
1068C2×C4C22×C22⋊C414yes—
1069C2×C4C22×C22⋊C411yescharacteristic
1070C2×C4C22×C22⋊C411yescharacteristic
1071C2×C4C22×C22⋊C411yescharacteristic
1072C2×C4C22×C22⋊C411yescharacteristic
1073C2×C4C22×C22⋊C411yescharacteristic
1074C2×C4C22×C22⋊C414yes—
1075C2×C4C22×C22⋊C411yescharacteristic
1076C2×C4C24×C411yescharacteristic
1077C2×C4C23×D411yescharacteristic
1078C8—42no—
1079C8—42no—
1080C8—44no—
1081C22—21no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—21no—
1087C22—21no—
1088C22—21no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—81no—
1096C22—81no—
1097C22—162no—
1098C22C23×C22⋊C411yescharacteristic
1099C22#358511yescharacteristic
1100C22#358611yescharacteristic
1101C4—21no—
1102C4—21no—
1103C4—21no—
1104C4—21no—
1105C4—21no—
1106C4—21no—
1107C4—21no—
1108C4—24no—
1109C4—24no—
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—24no—
1115C4—24no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—82no—
1123C4—82no—
1124C4—82no—
1125C4—82no—
1126C4#288412yes—
1127C2—21no—
1128C2—21no—
1129C2—41no—
1130C2—41no—
1131C2—82no—
1132C2—82no—
1133C2C2×#288411yescharacteristic
1134C2#6008911yescharacteristic
1135C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62831C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60251C2semidirect
3. #34394C2semidirect
4. #17628C2semidirect
5. #17624C2semidirect
6. #17612C2semidirect
7. #17610C2semidirect
8. #17607C2semidirect
9. #17605C2semidirect
10. #17602C2semidirect
11. #17601C2semidirect
12. #17585C2semidirect
13. #17581C2semidirect
14. #17579C2semidirect
15. #17560C2semidirect
18. #3557C4semidirect
19. #3555C4semidirect
20. #3554C4semidirect
30. #3510C4semidirect
31. #3507C4semidirect
33. #3506C4semidirect
34. #3504C4semidirect
35. #3502C4semidirect
36. #3501C4semidirect
45. #2984C22semidirect
46. #2983C22semidirect
57. #2356C22semidirect
58. #2351C22semidirect
63. #2320C22semidirect
68. #1521C22semidirect
73. #1518C22semidirect
74. #1518C22semidirect
76. #1517C22semidirect
77. #1515C22semidirect
78. #1515C22semidirect
80. #1514C22semidirect
87. #1512C22semidirect
88. #1512C22semidirect
89. #1512C22semidirect
92. #1509C22semidirect
93. #1509C22semidirect
96. #1506C22semidirect
98. #1503C22semidirect
103. #1500C22semidirect

Maximal subgroups

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

subgroupindex
#628312
#602512
#343942
#176282
#176242
#176122
#176102
#176072
#176052
#176022
#176012
#175852
#175812
#175792
#175602