Finite Group Databasebeta

← #7624720

Subgroups — #7624720

Order 512.

1181 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62490C211yesmaximal, characteristic, complemented
2#61478C211yesmaximal, characteristic, complemented
3#33954C211yesmaximal, characteristic, complemented
4#33952C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33943C211yesmaximal, characteristic, complemented
7#33917C211yesmaximal, characteristic, complemented
8#33916C211yesmaximal, characteristic, complemented
9#33915C211yesmaximal, characteristic, complemented
10#33914C211yesmaximal, characteristic, complemented
11#33909C211yesmaximal, characteristic, complemented
12#33907C211yesmaximal, characteristic, complemented
13#33888C211yesmaximal, characteristic, complemented
14#33887C211yesmaximal, characteristic, complemented
15#33880C211yesmaximal, characteristic, complemented
16#33879C211yesmaximal, characteristic, complemented
17#33868C211yesmaximal, characteristic, complemented
18#33867C211yesmaximal, characteristic, complemented
19#33829C211yesmaximal, characteristic, complemented
20#33828C211yesmaximal, characteristic, complemented
21#33814C211yesmaximal, characteristic, complemented
22#33810C211yesmaximal, characteristic, complemented
23#33809C211yesmaximal, characteristic, complemented
24#33803C211yesmaximal, characteristic, complemented
25#33681C211yesmaximal, characteristic, complemented
26#33681C211yesmaximal, characteristic, complemented
27#33671C211yesmaximal, characteristic, complemented
28#33632C211yesmaximal, characteristic, complemented
29#33632C211yesmaximal, characteristic, complemented
30#33626C211yesmaximal, characteristic, complemented
31#33506C211yesmaximal, characteristic, complemented
32#3565—21no—
33#3518—21no—
34#3393C2211yescharacteristic
35#3388—21no—
36#3383C2211yescharacteristic
37Q8×Q16C2211yescharacteristic
38#3380C2211yescharacteristic
39#3369—21no—
40#3351—21no—
41#3350—21no—
42#3348—21no—
43#3342C2211yescharacteristic
44#3342C2211yescharacteristic
45#3342C2211yescharacteristic
46#3341C2211yescharacteristic
47#3341C2211yescharacteristic
48#3339C2211yescharacteristic
49#3339C2211yescharacteristic
50#3336C2211yescharacteristic
51#3336C2211yescharacteristic
52#3329—21no—
53#3313—21no—
54#3313—21no—
55D4×Q16C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3244—21no—
59#3244—21no—
60#3240—21no—
61#3175C2211yescharacteristic
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69#3160C2211yescharacteristic
70#3121—21no—
71#3121—21no—
72#3116—21no—
73#2966C2211yescharacteristic
74#2950C2211yescharacteristic
75#2950C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2254C2211yescharacteristic
82#2252C2211yescharacteristic
83#2245C2211yescharacteristic
84#2245C2211yescharacteristic
85#2243C2211yescharacteristic
86#2243C2211yescharacteristic
87#2242C2211yescharacteristic
88#2242C2211yescharacteristic
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic
95#2237C2211yescharacteristic
96#2237C2211yescharacteristic
97#2237C2211yescharacteristic
98#2236C2211yescharacteristic
99#2235C2211yescharacteristic
100#2234C2211yescharacteristic
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic
103#2234C2211yescharacteristic
104#2234C2211yescharacteristic
105#2233C2211yescharacteristic
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic
108#2229C2211yescharacteristic
109#2229C2211yescharacteristic
110#2229C2211yescharacteristic
111#2229C2211yescharacteristic
112#2229C2211yescharacteristic
113#2229C2211yescharacteristic
114#2229C2211yescharacteristic
115#2229C2211yescharacteristic
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2227C2211yescharacteristic
120#2227C2211yescharacteristic
121#2227C2211yescharacteristic
122#2227C2211yescharacteristic
123#2227C2211yescharacteristic
124#2227C2211yescharacteristic
125#2226C2211yescharacteristic
126#2226C2211yescharacteristic
127#2225C2211yescharacteristic
128#2225C2211yescharacteristic
129#2225C2211yescharacteristic
130#2225C2211yescharacteristic
131#2225C2211yescharacteristic
132#2225C2211yescharacteristic
133#2225C2211yescharacteristic
134#2224C2211yescharacteristic
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2219C2211yescharacteristic
140#2218C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2217C2211yescharacteristic
145#2216C2211yescharacteristic
146#2216C2211yescharacteristic
147#2216C2211yescharacteristic
148#2215C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2211C2211yescharacteristic
153#2211C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2209C2211yescharacteristic
158#2208C2211yescharacteristic
159#2189C2211yescharacteristic
160#2188C2211yescharacteristic
161#2188C2211yescharacteristic
162#2186C2211yescharacteristic
163#2185C2211yescharacteristic
164#2185C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2177C2211yescharacteristic
168#2176C2211yescharacteristic
169#2176C2211yescharacteristic
170#2176C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic
176C4×Q32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic
187#2163C2211yescharacteristic
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic
190#2158C2211yescharacteristic
191#2158C2211yescharacteristic
192#2158C2211yescharacteristic
193#2158C2211yescharacteristic
194#2151C2211yescharacteristic
195#2151C2211yescharacteristic
196C2×C4⋊C16C2211yescharacteristic
197#2141C2211yescharacteristic
198#2141C2211yescharacteristic
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic
201C2×#358C2211yescharacteristic
202C2×#358C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206#563—41no—
207#562—41no—
208Q82—21no—
209#557—21no—
210#556—21no—
211#556—21no—
212#556—21no—
213#556—21no—
214#556—41no—
215#556—41no—
216#556—41no—
217#556—41no—
218#555—21no—
219#555—21no—
220#555—41no—
221#554—21no—
222#553—21no—
223#553—21no—
224#552—21no—
225#552—21no—
226#552—41no—
227D4×Q8—21no—
228#548—21no—
229#548—21no—
230#544—21no—
231#544—21no—
232#542—21no—
233#542—21no—
234#542—21no—
235#542—21no—
236#542—41no—
237#542—41no—
238#542—41no—
239#542—41no—
240#541—41no—
241#539—41no—
242#533—21no—
243#533—21no—
244#533—41no—
245#529—21no—
246#529—41no—
247#529D411yescharacteristic
248#519—21no—
249#519—21no—
250C4×#41—21no—
251C2×Q32C2311yescharacteristic
252C2×Q32C2311yescharacteristic
253C2×Q32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×SD32C2311yescharacteristic
258C2×D16C2311yescharacteristic
259C2×M32C2311yescharacteristic
260C2×M32C2311yescharacteristic
261C22×C16C2311yescharacteristic
262C22×C16C2311yescharacteristic
263C22×C16C2311yescharacteristic
264C22×C16C2311yescharacteristic
265#501—21no—
266#501—21no—
267#501—21no—
268#501—21no—
269#500C2311yescharacteristic
270#500C2311yescharacteristic
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#500C2311yescharacteristic
274#500C2311yescharacteristic
275#500C2311yescharacteristic
276#499—21no—
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#498—21no—
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#495C2311yescharacteristic
286#494C2311yescharacteristic
287#489—21no—
288#489—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#487—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#485—21no—
301#483—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—21no—
306#482—21no—
307#482—21no—
308#482—21no—
309#481—21no—
310#481—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#478—21no—
316#478—21no—
317#478—21no—
318#478—21no—
319#477—21no—
320#477—21no—
321#477—21no—
322#476—21no—
323#476—21no—
324#476—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#475—21no—
329#468—21no—
330#468—21no—
331#468—21no—
332#468—21no—
333#467—21no—
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#466C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#465—21no—
347#464—21no—
348#464—21no—
349#464—21no—
350#464—21no—
351#462—21no—
352#461—21no—
353#452—21no—
354#452—21no—
355#451—21no—
356#451—21no—
357#448—21no—
358#448—21no—
359#446D411yescharacteristic
360C8×Q8C2311yescharacteristic
361#441—21no—
362#441—21no—
363#441—21no—
364#441—21no—
365#440—21no—
366#440—21no—
367#440—21no—
368#440—21no—
369C4×Q16—21no—
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×SD16—21no—
382C4×SD16—21no—
383C4×SD16—21no—
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389#436D411yescharacteristic
390#435D411yescharacteristic
391#435D411yescharacteristic
392C8×D4C2311yescharacteristic
393C8×D4C2311yescharacteristic
394C8×D4C2311yescharacteristic
395#433D411yescharacteristic
396#433D411yescharacteristic
397#432D411yescharacteristic
398#428—21no—
399#428—21no—
400#427—21no—
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403#427C2311yescharacteristic
404#427C2311yescharacteristic
405#427C2311yescharacteristic
406#427C2311yescharacteristic
407#427C2311yescharacteristic
408C2×#107C2311yescharacteristic
409C2×#107C2311yescharacteristic
410#419—21no—
411#419—21no—
412#416—21no—
413#405C2311yescharacteristic
414#405C2311yescharacteristic
415C2×C4×C8C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
450#358C2311yescharacteristic
451#358C2311yescharacteristic
452#358C2311yescharacteristic
453#358C2311yescharacteristic
454#358C2311yescharacteristic
455#358C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#358C2311yescharacteristic
470#358C2311yescharacteristic
471#358C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487C22⋊C16C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497#135—22no—
498#135—41no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—21no—
502C2×Q16—21no—
503C2×Q16—21no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×Q16C2411yescharacteristic
507C2×Q16C2411yescharacteristic
508C2×Q16C2411yescharacteristic
509C2×Q16C2411yescharacteristic
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×D8C2411yescharacteristic
515C2×D8C2411yescharacteristic
516C2×M16C2×D411yescharacteristic
517C2×M16C2×D411yescharacteristic
518C22×C8C2×D411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537#126—41no—
538#126—41no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#126—41no—
544#126—41no—
545#126—41no—
546#126—41no—
547#126—41no—
548#126—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126D811yescharacteristic
555#126D811yescharacteristic
556#125—21no—
557#125—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125D811yescharacteristic
569#124—21no—
570#124—21no—
571#124—21no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124D811yescharacteristic
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123D811yescharacteristic
596#123D811yescharacteristic
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8D811yescharacteristic
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121D811yescharacteristic
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—21no—
640C4×Q8—21no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×Q8—41no—
659C4×Q8C2×D411yescharacteristic
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4C2×D411yescharacteristic
674C4×D4C2×D411yescharacteristic
675C4×D4C2×D411yescharacteristic
676#117—21no—
677#117—21no—
678#117—21no—
679#117—21no—
680#117—21no—
681#117—21no—
682#117—21no—
683#117—41no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117C2×D411yescharacteristic
696#117C2×D411yescharacteristic
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—41no—
700C2×C42—41no—
701C2×C42C2×D411yescharacteristic
702Q32—22no—
703Q32—41no—
704Q32—41no—
705SD32—22no—
706SD32—41no—
707SD32—41no—
708SD32—41no—
709D16—41no—
710M32—41no—
711M32—41no—
712C2×C16—41no—
713C2×C16—41no—
714C2×C16—41no—
715C2×C16—41no—
716C2×C16C2411yescharacteristic
717C2×C16C2411yescharacteristic
718C2×C16C2411yescharacteristic
719C2×C16C2411yescharacteristic
720C2×C16C2411yescharacteristic
721C2×C16C2411yescharacteristic
722C2×C16C2411yescharacteristic
723C2×C16C2411yescharacteristic
724#107—21no—
725#107—21no—
726#107—21no—
727#107—21no—
728#107—21no—
729#107—21no—
730#107—21no—
731#107—21no—
732#107—21no—
733#107C2411yescharacteristic
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#107C2411yescharacteristic
743#106—21no—
744#106—21no—
745#106—21no—
746#106—21no—
747#106—21no—
748#106—21no—
749#106—21no—
750#106—21no—
751#106—21no—
752#106—21no—
753#106—21no—
754#106—21no—
755C4⋊C8C2×D411yescharacteristic
756C4⋊C8C2×D411yescharacteristic
757C4⋊C8C2×D411yescharacteristic
758C4⋊C8C2×D411yescharacteristic
759C4⋊C8C2×D411yescharacteristic
760C4⋊C8C2×D411yescharacteristic
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#103—21no—
768#103—21no—
769#103—21no—
770#103—21no—
771#103—21no—
772#103—21no—
773#103—21no—
774#103—21no—
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#102—21no—
780#102—21no—
781#102—21no—
782#102—21no—
783#102—21no—
784#102—21no—
785#102—21no—
786#102—21no—
787#102—21no—
788#102—21no—
789C22⋊C8C2×D411yescharacteristic
790C22⋊C8C2×D411yescharacteristic
791C22⋊C8C2×D411yescharacteristic
792C22⋊C8C2×D411yescharacteristic
793C22⋊C8C2×D411yescharacteristic
794C22⋊C8C2×D411yescharacteristic
795#97C2×D411yescharacteristic
796#97C2×D411yescharacteristic
797#97C2×D411yescharacteristic
798#97C2×D411yescharacteristic
799C4×C8C2×D411yescharacteristic
800C4×C8C2×D411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805#41—42no—
806#41—81no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—41no—
814C2×Q8—41no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—41no—
821C2×Q8—41no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8C2×D811yescharacteristic
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4C2×D811yescharacteristic
834C2×D4C2×D811yescharacteristic
835C2×D4C2×D811yescharacteristic
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4C2×D811yescharacteristic
847C22×C4C2×D811yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851Q16—21no—
852Q16—21no—
853Q16—21no—
854Q16—21no—
855Q16—21no—
856Q16—21no—
857Q16—21no—
858Q16—42no—
859Q16—42no—
860Q16—81no—
861Q162−1+412yes—
862SD16—42no—
863SD16—42no—
864SD16—81no—
865SD16—81no—
866D8—21no—
867D8—21no—
868D8—21no—
869D8—21no—
870M16—41no—
871M16—41no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—41no—
879C2×C8C22×D411yescharacteristic
880C2×C8C22×D411yescharacteristic
881C2×C8C22×D411yescharacteristic
882C2×C8C22×D411yescharacteristic
883C2×C8C22×D411yescharacteristic
884C2×C8C22×D411yescharacteristic
885C2×C8C22×D411yescharacteristic
886C2×C8C2511yescharacteristic
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4C2×D811yescharacteristic
937C4⋊C4C2×D811yescharacteristic
938C4⋊C4C2×D811yescharacteristic
939C4⋊C4C2×D811yescharacteristic
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C4⋊C4C2×D811yescharacteristic
944C4⋊C4C2×D811yescharacteristic
945C4⋊C4C2×D811yescharacteristic
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4C2×D811yescharacteristic
977C22⋊C4C2×D811yescharacteristic
978C22⋊C4C2×D811yescharacteristic
979C22⋊C4C2×D811yescharacteristic
980C22⋊C4C2×D811yescharacteristic
981C22⋊C4C2×D811yescharacteristic
982C22⋊C4C2×D811yescharacteristic
983C22⋊C4C2×D811yescharacteristic
984C22⋊C4C2×D811yescharacteristic
985C22⋊C4C2×D811yescharacteristic
986C42—41no—
987C42—41no—
988C42—41no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42C2×D811yescharacteristic
1005C42C2×D811yescharacteristic
1006C42C22×D411yescharacteristic
1007C42C22×D411yescharacteristic
1008C42C22×D411yescharacteristic
1009C42C22×D411yescharacteristic
1010C16—21no—
1011C16—21no—
1012C16—21no—
1013C16—21no—
1014C16—21no—
1015C16—21no—
1016C16—21no—
1017C16—21no—
1018C23—41no—
1019C23—41no—
1020C23C22×D811yescharacteristic
1021C23C22×D811yescharacteristic
1022C23C22×D811yescharacteristic
1023Q8—22no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—82no—
1033Q8—82no—
1034Q8—161no—
1035Q8—161no—
1036Q8—161no—
1037Q8—161no—
1038Q8—161no—
1039Q8—161no—
1040Q8—161no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—82no—
1049D4—161no—
1050D4—161no—
1051D4—161no—
1052D4—161no—
1053D4—161no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—82no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—82no—
1080C2×C4—161no—
1081C2×C4—161no—
1082C2×C4—161no—
1083C2×C4—161no—
1084C2×C4—161no—
1085C2×C4—161no—
1086C2×C4C22×D811yescharacteristic
1087C2×C4C22×D811yescharacteristic
1088C2×C4C22×D811yescharacteristic
1089C2×C4C22×D811yescharacteristic
1090C2×C4C22×D811yescharacteristic
1091C2×C4C22×D811yescharacteristic
1092C2×C4C22×D811yescharacteristic
1093C2×C4C22×D811yescharacteristic
1094C2×C4C22×D811yescharacteristic
1095C2×C4C22×D811yescharacteristic
1096C2×C4C22×D811yescharacteristic
1097C2×C4C23×D411yescharacteristic
1098C8—21no—
1099C8—21no—
1100C8—21no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—21no—
1105C8C2×2−1+411yescharacteristic
1106C8#58511yescharacteristic
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C23×D811yescharacteristic
1123C4—21no—
1124C4—21no—
1125C4—21no—
1126C4—21no—
1127C4—21no—
1128C4—21no—
1129C4—21no—
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—21no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4#348911yescharacteristic
1149C4#358611yescharacteristic
1150C2—41no—
1151C2—41no—
1152C2—41no—
1153C2—161no—
1154C2—161no—
1155C2#6209511yescharacteristic
1156C2#6263511yescharacteristic
1157C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62490C2semidirect
2. #61478C2semidirect
3. #33954C2semidirect
4. #33952C2semidirect
5. #33944C2semidirect
6. #33943C2semidirect
7. #33917C2semidirect
8. #33916C2semidirect
9. #33915C2semidirect
10. #33914C2semidirect
11. #33909C2semidirect
12. #33907C2semidirect
13. #33888C2semidirect
14. #33887C2semidirect
15. #33880C2semidirect
16. #33879C2semidirect
17. #33868C2semidirect
18. #33867C2semidirect
19. #33829C2semidirect
20. #33828C2semidirect
21. #33814C2semidirect
22. #33810C2semidirect
23. #33809C2semidirect
24. #33803C2semidirect
25. #33681C2semidirect
26. #33681C2semidirect
27. #33671C2semidirect
28. #33632C2semidirect
29. #33632C2semidirect
30. #33626C2semidirect
31. #33506C2semidirect

Maximal subgroups

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

subgroupindex
#624902
#614782
#339542
#339522
#339442
#339432
#339172
#339162
#339152
#339142
#339092
#339072
#338882
#338872
#338802
#338792
#338682
#338672
#338292
#338282
#338142
#338102
#338092
#338032
#336812
#336712
#336322
#336262
#335062