Finite Group Databasebeta

← #7624814

Subgroups — #7624814

Order 512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62249C211yesmaximal, characteristic, complemented
2#62247C211yesmaximal, characteristic, complemented
3#33917C211yesmaximal, characteristic, complemented
4#33916C211yesmaximal, characteristic, complemented
5#33915C211yesmaximal, characteristic, complemented
6#33914C211yesmaximal, characteristic, complemented
7#33888C211yesmaximal, characteristic, complemented
8#33886C211yesmaximal, characteristic, complemented
9#33884C211yesmaximal, characteristic, complemented
10#33882C211yesmaximal, characteristic, complemented
11#33880C211yesmaximal, characteristic, complemented
12#33878C211yesmaximal, characteristic, complemented
13#33876C211yesmaximal, characteristic, complemented
14#33874C211yesmaximal, characteristic, complemented
15#33837C211yesmaximal, characteristic, complemented
16#33835C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33814C211yesmaximal, characteristic, complemented
20#33813C211yesmaximal, characteristic, complemented
21#33757C211yesmaximal, characteristic, complemented
22#33757C211yesmaximal, characteristic, complemented
23#33756C211yesmaximal, characteristic, complemented
24#33754C211yesmaximal, characteristic, complemented
25#33747C211yesmaximal, characteristic, complemented
26#33746C211yesmaximal, characteristic, complemented
27#33606C211yesmaximal, characteristic, complemented
28#33605C211yesmaximal, characteristic, complemented
29#33600C211yesmaximal, characteristic, complemented
30#33600C211yesmaximal, characteristic, complemented
31C2×#2168C211yesmaximal, characteristic, complemented
32#3506—21no—
33#3505—21no—
34C2×#510C2211yescharacteristic, complemented
35C2×#509C2211yescharacteristic, complemented
36C2×#508C2211yescharacteristic, complemented
37C2×#508C2211yescharacteristic, complemented
38C22×M32C2211yescharacteristic
39C23×C16C2211yescharacteristic, complemented
40#3342C2211yescharacteristic
41#3342C2211yescharacteristic, complemented
42#3341C2211yescharacteristic
43#3341C2211yescharacteristic, complemented
44#3339C2211yescharacteristic
45#3339C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic
48#3304—21no—
49#3304—21no—
50#3303—21no—
51#3303—21no—
52#3301—21no—
53#3301—21no—
54#3296—21no—
55#3296—21no—
56#3287C2211yescharacteristic
57#3287C2211yescharacteristic, complemented
58#3285C2211yescharacteristic
59#3285C2211yescharacteristic
60#3283C2211yescharacteristic
61#3283C2211yescharacteristic, complemented
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3250—21no—
65#3246—21no—
66#3191—21no—
67#3191—21no—
68#3191—21no—
69#3187—21no—
70#3170C2211yescharacteristic, complemented
71#3169C2211yescharacteristic, complemented
72#3168C2211yescharacteristic
73#3168C2211yescharacteristic
74#3050C2211yescharacteristic
75#3050C2211yescharacteristic
76#3050C2211yescharacteristic
77#3050C2211yescharacteristic
78#3050C2211yescharacteristic, complemented
79#3050C2211yescharacteristic, complemented
80C2×#467C2211yescharacteristic
81C2×#466C2211yescharacteristic
82C2×C8×D4C2211yescharacteristic
83#2255C2211yescharacteristic, complemented
84#2255C2211yescharacteristic, complemented
85#2251C2211yescharacteristic, complemented
86#2250C2211yescharacteristic, complemented
87#2245C2211yescharacteristic, complemented
88#2244C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2243C2211yescharacteristic, complemented
91#2237C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2234C2211yescharacteristic, complemented
100#2234C2211yescharacteristic, complemented
101#2234C2211yescharacteristic, complemented
102#2234C2211yescharacteristic, complemented
103#2234C2211yescharacteristic, complemented
104#2234C2211yescharacteristic, complemented
105#2233C2211yescharacteristic, complemented
106#2232C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2228C2211yescharacteristic, complemented
110#2228C2211yescharacteristic, complemented
111#2227C2211yescharacteristic, complemented
112#2226C2211yescharacteristic, complemented
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic, complemented
115#2220C2211yescharacteristic, complemented
116#2220C2211yescharacteristic, complemented
117#2220C2211yescharacteristic, complemented
118#2220C2211yescharacteristic, complemented
119#2219C2211yescharacteristic, complemented
120#2219C2211yescharacteristic, complemented
121#2218C2211yescharacteristic, complemented
122#2218C2211yescharacteristic, complemented
123#2217C2211yescharacteristic
124#2217C2211yescharacteristic
125#2217C2211yescharacteristic
126#2217C2211yescharacteristic
127#2217C2211yescharacteristic, complemented
128#2217C2211yescharacteristic, complemented
129#2217C2211yescharacteristic, complemented
130#2217C2211yescharacteristic, complemented
131#2217C2211yescharacteristic, complemented
132#2217C2211yescharacteristic, complemented
133#2217C2211yescharacteristic, complemented
134#2217C2211yescharacteristic, complemented
135#2216C2211yescharacteristic, complemented
136#2216C2211yescharacteristic, complemented
137#2216C2211yescharacteristic, complemented
138#2216C2211yescharacteristic, complemented
139#2216C2211yescharacteristic, complemented
140#2216C2211yescharacteristic, complemented
141#2215C2211yescharacteristic
142#2215C2211yescharacteristic
143#2215C2211yescharacteristic
144#2215C2211yescharacteristic
145#2215C2211yescharacteristic, complemented
146#2215C2211yescharacteristic, complemented
147#2211C2211yescharacteristic, complemented
148#2211C2211yescharacteristic, complemented
149#2210C2211yescharacteristic, complemented
150#2210C2211yescharacteristic, complemented
151#2209C2211yescharacteristic, complemented
152#2208C2211yescharacteristic, complemented
153#2207C2211yescharacteristic, complemented
154#2206C2211yescharacteristic, complemented
155#2189C2211yescharacteristic, complemented
156#2189C2211yescharacteristic, complemented
157#2189C2211yescharacteristic, complemented
158#2189C2211yescharacteristic, complemented
159#2189C2211yescharacteristic, complemented
160#2189C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2187C2211yescharacteristic, complemented
163#2186C2211yescharacteristic, complemented
164#2186C2211yescharacteristic, complemented
165#2186C2211yescharacteristic, complemented
166#2186C2211yescharacteristic, complemented
167#2186C2211yescharacteristic, complemented
168#2186C2211yescharacteristic, complemented
169#2185C2211yescharacteristic, complemented
170#2184C2211yescharacteristic, complemented
171#2177C2211yescharacteristic, complemented
172#2177C2211yescharacteristic, complemented
173#2176C2211yescharacteristic, complemented
174#2176C2211yescharacteristic, complemented
175#2175C2211yescharacteristic, complemented
176#2175C2211yescharacteristic, complemented
177#2175C2211yescharacteristic, complemented
178#2175C2211yescharacteristic, complemented
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185#2168C2211yescharacteristic, complemented
186#2168C2211yescharacteristic, complemented
187#2159C2211yescharacteristic, complemented
188#2159C2211yescharacteristic, complemented
189#2158C2211yescharacteristic, complemented
190#2158C2211yescharacteristic, complemented
191C2×C4⋊C16C2211yescharacteristic, complemented
192#2141C2211yescharacteristic, complemented
193#2140C2211yescharacteristic, complemented
194#2139C2211yescharacteristic, complemented
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic, complemented
197#2138C2211yescharacteristic, complemented
198#2138C2211yescharacteristic, complemented
199#2138C2211yescharacteristic, complemented
200C2×C22⋊C16C2211yescharacteristic
201C2×C22⋊C16C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C2×#135C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#559—41no—
214#559—41no—
215#556—21no—
216#556—21no—
217#555—21no—
218#555—21no—
219#553—21no—
220#553—21no—
221#553—41no—
222#553—41no—
223#553—41no—
224#553—41no—
225#552—21no—
226#552—21no—
227#551—41no—
228#551—41no—
229#550—21no—
230#550—21no—
231#548—21no—
232#548—21no—
233#547—21no—
234#547—21no—
235#546—21no—
236#546—21no—
237#539—41no—
238#538—41no—
239#538—41no—
240#538—41no—
241#535—41no—
242#534—41no—
243#533—21no—
244#532—21no—
245#529—21no—
246#529—21no—
247#525—21no—
248#525—21no—
249#525—21no—
250#525—21no—
251#525—21no—
252#525—21no—
253C2×C22⋊Q8—21no—
254C2×#121—21no—
255#520—41no—
256#518—41no—
257C2×C4×D4D411yescharacteristic
258#510—42no—
259#509—42no—
260#508—42no—
261#508—42no—
262C2×Q32C2311yescharacteristic
263C2×Q32C2311yescharacteristic
264C2×Q32C2311yescharacteristic
265C2×Q32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×D16C2311yescharacteristic
275C2×D16C2311yescharacteristic
276C2×D16C2311yescharacteristic
277C2×D16C2311yescharacteristic
278C2×M32—42no—
279C2×M32C2311yescharacteristic
280C2×M32C2311yescharacteristic
281C2×M32C2311yescharacteristic
282C2×M32C2311yescharacteristic
283C22×C16—42no—
284C22×C16C2311yescharacteristic
285C22×C16C2311yescharacteristic
286C22×C16C2311yescharacteristic
287C22×C16C2311yescharacteristic
288C22×C16C2311yescharacteristic
289C22×C16C2311yescharacteristic
290C22×C16C2311yescharacteristic
291C22×C16C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#499C2311yescharacteristic
295#499C2311yescharacteristic
296#495C2311yescharacteristic
297#495C2311yescharacteristic
298#494C2311yescharacteristic
299#493C2311yescharacteristic
300#488—21no—
301#488—21no—
302#487—21no—
303#486—21no—
304#485—21no—
305#485—21no—
306#485—21no—
307#485—21no—
308#485—21no—
309#485—21no—
310#483—21no—
311#483—21no—
312#482—21no—
313#482—21no—
314#482—21no—
315#482—21no—
316#482—21no—
317#482—21no—
318#481—21no—
319#481—21no—
320#479—21no—
321#479—21no—
322#478—21no—
323#478—21no—
324#476—21no—
325#476—21no—
326#475—21no—
327#475—21no—
328#467—21no—
329#467—21no—
330#467—21no—
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#466—21no—
344#466—21no—
345#466—21no—
346#466C2311yescharacteristic
347#466C2311yescharacteristic
348#466C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#466C2311yescharacteristic
353#466C2311yescharacteristic
354#466C2311yescharacteristic
355#466C2311yescharacteristic
356#466C2311yescharacteristic
357#466C2311yescharacteristic
358#465—21no—
359#465—21no—
360#465—21no—
361#465—21no—
362#465—21no—
363#465—21no—
364#465—21no—
365#465—21no—
366#465—21no—
367#465—21no—
368#465—21no—
369#465—21no—
370#465—21no—
371#465—21no—
372#464—21no—
373#464—21no—
374#463—21no—
375#463—21no—
376#461—21no—
377#461—21no—
378#460—21no—
379#460—21no—
380#452—21no—
381#452—21no—
382#452—21no—
383#452—21no—
384#452—21no—
385#452—21no—
386#450—21no—
387#450—21no—
388#449—21no—
389#449—21no—
390#449—21no—
391#449—21no—
392#449—21no—
393#449—21no—
394#448—21no—
395#448—21no—
396C4×Q16—21no—
397C4×Q16C2311yescharacteristic
398C4×Q16C2311yescharacteristic
399C4×Q16C2311yescharacteristic
400C4×Q16C2311yescharacteristic
401C4×SD16—21no—
402C4×SD16—21no—
403C4×D8—21no—
404C4×D8C2311yescharacteristic
405C4×D8C2311yescharacteristic
406C4×D8C2311yescharacteristic
407C4×D8C2311yescharacteristic
408C8×D4D411yescharacteristic
409C8×D4D411yescharacteristic
410C8×D4D411yescharacteristic
411C8×D4D411yescharacteristic
412C8×D4C2311yescharacteristic
413C8×D4C2311yescharacteristic
414C8×D4C2311yescharacteristic
415C8×D4C2311yescharacteristic
416#427C2311yescharacteristic
417#427C2311yescharacteristic
418#427C2311yescharacteristic
419#427C2311yescharacteristic
420#427C2311yescharacteristic
421#427C2311yescharacteristic
422C2×#107C2311yescharacteristic
423C2×#107C2311yescharacteristic
424C2×C4⋊C8D411yescharacteristic
425#416—21no—
426#416—21no—
427#416—21no—
428#416—21no—
429#416—21no—
430#416—21no—
431C2×#103—21no—
432C2×#102—21no—
433C2×C22⋊C8D411yescharacteristic
434C2×C22⋊C8D411yescharacteristic
435C2×C4×C8C2311yescharacteristic
436#367C2311yescharacteristic
437#367C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
442#367C2311yescharacteristic
443#367C2311yescharacteristic
444#366C2311yescharacteristic
445#366C2311yescharacteristic
446#366C2311yescharacteristic
447#366C2311yescharacteristic
448#366C2311yescharacteristic
449#366C2311yescharacteristic
450#366C2311yescharacteristic
451#366C2311yescharacteristic
452C4⋊C16C2311yescharacteristic
453C4⋊C16C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
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
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488C22⋊C16C2311yescharacteristic
489C22⋊C16C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494C22⋊C16C2311yescharacteristic
495C22⋊C16C2311yescharacteristic
496#346C2311yescharacteristic
497#346C2311yescharacteristic
498#346C2311yescharacteristic
499#346C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—21no—
506C2×#41—41no—
507C22×Q8—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4D811yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517#135—41no—
518#135—41no—
519#135—41no—
520#135—41no—
521#135—41no—
522#135—41no—
523#135—41no—
524#135—41no—
525C2×Q16—21no—
526C2×Q16—21no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16C2411yescharacteristic
530C2×Q16C2411yescharacteristic
531C2×Q16C2411yescharacteristic
532C2×Q16C2411yescharacteristic
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×SD16—21no—
541C2×D8—21no—
542C2×D8—21no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8C2411yescharacteristic
546C2×D8C2411yescharacteristic
547C2×D8C2411yescharacteristic
548C2×D8C2411yescharacteristic
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2×D411yescharacteristic
554C22×C8C2×D411yescharacteristic
555C22×C8C2×D411yescharacteristic
556C22×C8C2×D411yescharacteristic
557C22×C8C2×D411yescharacteristic
558C22×C8C2×D411yescharacteristic
559C22×C8C2×D411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568#127—21no—
569#127—41no—
570#127—41no—
571#126—41no—
572#126—41no—
573#126—41no—
574#126—41no—
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#126—41no—
580#126—41no—
581#125—21no—
582#125—21no—
583#125—41no—
584#125—41no—
585#125—41no—
586#124—21no—
587#124—21no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123—41no—
604#123—41no—
605#123—41no—
606#123—41no—
607#123—41no—
608#123—41no—
609#123—41no—
610#123—41no—
611#123—41no—
612#123—41no—
613#123—41no—
614#123—41no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—21no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—41no—
645#121—41no—
646#121—41no—
647#121—41no—
648#121—41no—
649#121—41no—
650#121—41no—
651#121—41no—
652#121—41no—
653#121—41no—
654#121—41no—
655#121—41no—
656#121—41no—
657#121—41no—
658#121—41no—
659#121—41no—
660#121—41no—
661#120—41no—
662#120—41no—
663#120—41no—
664#120—41no—
665#120—41no—
666#120—41no—
667#120—41no—
668#120—41no—
669C4×Q8—21no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—21no—
673C4×Q8—41no—
674C4×Q8—41no—
675C4×Q8—41no—
676C4×D4—21no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—21no—
680C4×D4—41no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4—41no—
684C4×D4—41no—
685C4×D4—41no—
686C4×D4—41no—
687C4×D4—41no—
688C4×D4—41no—
689C4×D4—41no—
690C4×D4—41no—
691C4×D4—41no—
692C4×D4—41no—
693C4×D4—41no—
694C4×D4—41no—
695C4×D4—41no—
696C4×D4—41no—
697C4×D4—41no—
698C4×D4—41no—
699C4×D4—41no—
700C4×D4—41no—
701C4×D4D811yescharacteristic
702C4×D4D811yescharacteristic
703C4×D4D811yescharacteristic
704C4×D4D811yescharacteristic
705C4×D4C2×D411yescharacteristic
706C4×D4C2×D411yescharacteristic
707C4×D4C2×D411yescharacteristic
708C4×D4C2×D411yescharacteristic
709#117—21no—
710#117—21no—
711#117—21no—
712#117—21no—
713#117—21no—
714#117—21no—
715#117—41no—
716#117—41no—
717#117—41no—
718#117—41no—
719#117—41no—
720#117—41no—
721#117—41no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—41no—
725C2×C4⋊C4—41no—
726C2×C4⋊C4—41no—
727C2×C4⋊C4D811yescharacteristic
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4D811yescharacteristic
733C2×C22⋊C4D811yescharacteristic
734C2×C42C2×D411yescharacteristic
735Q32—22no—
736Q32—41no—
737Q32—41no—
738Q32—41no—
739SD32—22no—
740SD32—22no—
741SD32—41no—
742SD32—41no—
743SD32—41no—
744SD32—41no—
745SD32—41no—
746SD32—41no—
747D16—22no—
748D16—41no—
749D16—41no—
750D16—41no—
751M32—22no—
752M32—22no—
753M32—41no—
754M32—41no—
755C2×C16—22no—
756C2×C16—22no—
757C2×C16—22no—
758C2×C16—41no—
759C2×C16—41no—
760C2×C16—41no—
761C2×C16—41no—
762C2×C16—41no—
763C2×C16C2411yescharacteristic
764C2×C16C2411yescharacteristic
765C2×C16C2411yescharacteristic
766C2×C16C2411yescharacteristic
767C2×C16C2411yescharacteristic
768C2×C16C2411yescharacteristic
769C2×C16C2411yescharacteristic
770C2×C16C2411yescharacteristic
771#107—21no—
772#107—21no—
773#107—21no—
774#107—21no—
775#107C2411yescharacteristic
776#107C2411yescharacteristic
777#107C2411yescharacteristic
778#107C2411yescharacteristic
779#107C2411yescharacteristic
780#107C2411yescharacteristic
781#107C2411yescharacteristic
782#107C2411yescharacteristic
783#106—21no—
784#106—21no—
785#106—21no—
786#106—21no—
787#106—21no—
788#106—21no—
789#106—21no—
790#106—21no—
791C4⋊C8C2×D411yescharacteristic
792C4⋊C8C2×D411yescharacteristic
793C4⋊C8C2×D411yescharacteristic
794C4⋊C8C2×D411yescharacteristic
795#103—21no—
796#103—21no—
797#103—21no—
798#103—21no—
799#103—21no—
800#103—21no—
801#103—21no—
802#103—21no—
803#103—21no—
804#103—21no—
805#103—21no—
806#103—21no—
807#103—21no—
808#103—21no—
809#103—21no—
810#103—21no—
811#102—21no—
812#102—21no—
813#102—21no—
814#102—21no—
815#102—21no—
816#102—21no—
817#102—21no—
818#102—21no—
819#102—21no—
820#102—21no—
821#102—21no—
822#102—21no—
823#102—21no—
824#102—21no—
825#102—21no—
826#102—21no—
827C22⋊C8C2×D411yescharacteristic
828C22⋊C8C2×D411yescharacteristic
829C22⋊C8C2×D411yescharacteristic
830C22⋊C8C2×D411yescharacteristic
831C22⋊C8C2×D411yescharacteristic
832C22⋊C8C2×D411yescharacteristic
833C22⋊C8C2×D411yescharacteristic
834C22⋊C8C2×D411yescharacteristic
835C4×C8C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2411yescharacteristic
838C4×C8C2411yescharacteristic
839C24—41no—
840C24C2×D811yescharacteristic
841C24C2×D811yescharacteristic
842#41—84no—
843#41—81no—
844#41—81no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851#41—81no—
852#41—81no—
853#41—81no—
854#41—81no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—42no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—84no—
893C2×D4C2×D811yescharacteristic
894C2×D4C2×D811yescharacteristic
895C2×D4C2×D811yescharacteristic
896C2×D4C2×D811yescharacteristic
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4C2×D811yescharacteristic
915C22×C4C2×D811yescharacteristic
916C22×C4C2×D811yescharacteristic
917C22×C4C2×D811yescharacteristic
918C22×C4C2×D811yescharacteristic
919C22×C4C2×D811yescharacteristic
920C22×C4C2×D811yescharacteristic
921C22×C4C2×D811yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927Q16—21no—
928Q16—21no—
929Q16—21no—
930Q16—21no—
931Q16—21no—
932Q16—21no—
933Q16—21no—
934Q16—21no—
935Q16—81no—
936Q16—81no—
937SD16—81no—
938SD16—81no—
939SD16—81no—
940SD16—81no—
941SD16—81no—
942SD16—81no—
943SD16—81no—
944SD16—81no—
945D8—21no—
946D8—21no—
947D8—21no—
948D8—21no—
949D8—21no—
950D8—21no—
951D8—21no—
952D8—21no—
953D8—81no—
954D8—81no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—41no—
966C2×C8—41no—
967C2×C8—41no—
968C2×C8—41no—
969C2×C8—41no—
970C2×C8—41no—
971C2×C8—41no—
972C2×C8C22×D411yescharacteristic
973C2×C8C22×D411yescharacteristic
974C2×C8C22×D411yescharacteristic
975C2×C8C22×D411yescharacteristic
976C2×C8C22×D411yescharacteristic
977C2×C8C22×D411yescharacteristic
978C2×C8C22×D411yescharacteristic
979C2×C8C2511yescharacteristic
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4C2×D811yescharacteristic
1015C4⋊C4C2×D811yescharacteristic
1016C4⋊C4C2×D811yescharacteristic
1017C4⋊C4C2×D811yescharacteristic
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4C2×D811yescharacteristic
1057C22⋊C4C2×D811yescharacteristic
1058C22⋊C4C2×D811yescharacteristic
1059C22⋊C4C2×D811yescharacteristic
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C22⋊C4C2×D811yescharacteristic
1063C22⋊C4C2×D811yescharacteristic
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42C2×D811yescharacteristic
1075C42C2×D811yescharacteristic
1076C42C22×D411yescharacteristic
1077C42C22×D411yescharacteristic
1078C16—21no—
1079C16—21no—
1080C16—21no—
1081C16—21no—
1082C16—21no—
1083C16—21no—
1084C16—21no—
1085C16H(5,𝔽2)12yes—
1086C23—22no—
1087C23—22no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—82no—
1097C23—161no—
1098C23—161no—
1099C23C22×D811yescharacteristic
1100C23C22×D811yescharacteristic
1101C23C22×D811yescharacteristic
1102C23C22×D811yescharacteristic
1103C23C22×D811yescharacteristic
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—82no—
1113Q8—161no—
1114Q8—161no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—82no—
1128D4—82no—
1129D4—82no—
1130D4—82no—
1131D4—82no—
1132D4—82no—
1133D4—82no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137D4—161no—
1138D4—161no—
1139D4—161no—
1140D4—161no—
1141D4—161no—
1142D4—161no—
1143D4—161no—
1144D4—161no—
1145D4—161no—
1146D4—161no—
1147D4—161no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—82no—
1179C2×C4—82no—
1180C2×C4—82no—
1181C2×C4—161no—
1182C2×C4—161no—
1183C2×C4—161no—
1184C2×C4—161no—
1185C2×C4—161no—
1186C2×C4—161no—
1187C2×C4—161no—
1188C2×C4—161no—
1189C2×C4—161no—
1190C2×C4—161no—
1191C2×C4C22×D811yescharacteristic
1192C2×C4C22×D811yescharacteristic
1193C2×C4C22×D811yescharacteristic
1194C2×C4C22×D811yescharacteristic
1195C2×C4C22×D811yescharacteristic
1196C2×C4C22×D811yescharacteristic
1197C2×C4C22×D811yescharacteristic
1198C2×C4C22×D811yescharacteristic
1199C2×C4C22×D811yescharacteristic
1200C2×C4C23×D411yescharacteristic
1201C8—21no—
1202C8—21no—
1203C8—21no—
1204C8—21no—
1205C8—21no—
1206C8—21no—
1207C8—21no—
1208C8C2×H(5,𝔽2)11yescharacteristic
1209C8#58511yescharacteristic
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—21no—
1224C22—44no—
1225C22—82no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—322no—
1239C22#341412yes—
1240C22C23×D811yescharacteristic
1241C4—21no—
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—21no—
1247C4—21no—
1248C4—21no—
1249C4—21no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4#349611yescharacteristic
1263C4#358411yescharacteristic
1264C2—22no—
1265C2—41no—
1266C2—41no—
1267C2—41no—
1268C2—41no—
1269C2—161no—
1270C2—161no—
1271C2—161no—
1272C2—161no—
1273C2#6224511yescharacteristic
1274C2C2×#341411yescharacteristic
1275C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62249C2semidirect
2. #62247C2semidirect
3. #33917C2semidirect
4. #33916C2semidirect
5. #33915C2semidirect
6. #33914C2semidirect
7. #33888C2semidirect
8. #33886C2semidirect
9. #33884C2semidirect
10. #33882C2semidirect
11. #33880C2semidirect
12. #33878C2semidirect
13. #33876C2semidirect
14. #33874C2semidirect
15. #33837C2semidirect
16. #33835C2semidirect
17. #33834C2semidirect
18. #33833C2semidirect
19. #33814C2semidirect
20. #33813C2semidirect
21. #33757C2semidirect
22. #33757C2semidirect
23. #33756C2semidirect
24. #33754C2semidirect
25. #33747C2semidirect
26. #33746C2semidirect
27. #33606C2semidirect
28. #33605C2semidirect
29. #33600C2semidirect
30. #33600C2semidirect
31. C2×#2168C2semidirect
34. C2×#510C22semidirect
35. C2×#509C22semidirect
36. C2×#508C22semidirect
37. C2×#508C22semidirect
39. C23×C16C22semidirect
41. #3342C22semidirect
43. #3341C22semidirect
57. #3287C22semidirect
61. #3283C22semidirect
70. #3170C22semidirect
71. #3169C22semidirect
78. #3050C22semidirect
79. #3050C22semidirect
83. #2255C22semidirect
84. #2255C22semidirect
85. #2251C22semidirect
86. #2250C22semidirect
87. #2245C22semidirect
88. #2244C22semidirect
89. #2243C22semidirect
90. #2243C22semidirect
91. #2237C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2236C22semidirect
98. #2235C22semidirect
99. #2234C22semidirect
100. #2234C22semidirect
101. #2234C22semidirect
102. #2234C22semidirect
103. #2234C22semidirect
104. #2234C22semidirect
105. #2233C22semidirect
106. #2232C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2228C22semidirect
110. #2228C22semidirect
111. #2227C22semidirect
112. #2226C22semidirect
113. #2225C22semidirect
114. #2224C22semidirect
115. #2220C22semidirect
116. #2220C22semidirect
117. #2220C22semidirect
118. #2220C22semidirect
119. #2219C22semidirect
120. #2219C22semidirect
121. #2218C22semidirect
122. #2218C22semidirect
127. #2217C22semidirect
128. #2217C22semidirect
129. #2217C22semidirect
130. #2217C22semidirect
131. #2217C22semidirect
132. #2217C22semidirect
133. #2217C22semidirect
134. #2217C22semidirect
135. #2216C22semidirect
136. #2216C22semidirect
137. #2216C22semidirect
138. #2216C22semidirect
139. #2216C22semidirect
140. #2216C22semidirect
145. #2215C22semidirect
146. #2215C22semidirect
147. #2211C22semidirect
148. #2211C22semidirect
149. #2210C22semidirect
150. #2210C22semidirect
151. #2209C22semidirect
152. #2208C22semidirect
153. #2207C22semidirect
154. #2206C22semidirect
155. #2189C22semidirect
156. #2189C22semidirect
157. #2189C22semidirect
158. #2189C22semidirect
159. #2189C22semidirect
160. #2189C22semidirect
161. #2188C22semidirect
162. #2187C22semidirect
163. #2186C22semidirect
164. #2186C22semidirect
165. #2186C22semidirect
166. #2186C22semidirect
167. #2186C22semidirect
168. #2186C22semidirect
169. #2185C22semidirect
170. #2184C22semidirect
171. #2177C22semidirect
172. #2177C22semidirect
173. #2176C22semidirect
174. #2176C22semidirect
175. #2175C22semidirect
176. #2175C22semidirect
177. #2175C22semidirect
178. #2175C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
185. #2168C22semidirect
186. #2168C22semidirect
187. #2159C22semidirect
188. #2159C22semidirect
189. #2158C22semidirect
190. #2158C22semidirect
191. C2×C4⋊C16C22semidirect
192. #2141C22semidirect
193. #2140C22semidirect
194. #2139C22semidirect
195. #2139C22semidirect
196. #2138C22semidirect
197. #2138C22semidirect
198. #2138C22semidirect
199. #2138C22semidirect
201. C2×C22⋊C16C22semidirect
202. C2×#346C22semidirect

Maximal subgroups

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

subgroupindex
#622492
#622472
#339172
#339162
#339152
#339142
#338882
#338862
#338842
#338822
#338802
#338782
#338762
#338742
#338372
#338352
#338342
#338332
#338142
#338132
#337572
#337562
#337542
#337472
#337462
#336062
#336052
#336002
C2×#21682