Finite Group Databasebeta

← #7624167

Subgroups — #7624167

Order 512.

1500 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62276C211yesmaximal, characteristic, complemented
2#61057C211yesmaximal, characteristic, complemented
3#33890C211yesmaximal, characteristic, complemented
4#33889C211yesmaximal, characteristic, complemented
5#33887C211yesmaximal, characteristic, complemented
6#33882C211yesmaximal, characteristic, complemented
7#33879C211yesmaximal, characteristic, complemented
8#33874C211yesmaximal, characteristic, complemented
9#33868C211yesmaximal, characteristic, complemented
10#33867C211yesmaximal, characteristic, complemented
11#33850C211yesmaximal, characteristic, complemented
12#33849C211yesmaximal, characteristic, complemented
13#33844C211yesmaximal, characteristic, complemented
14#33842C211yesmaximal, characteristic, complemented
15#33837C211yesmaximal, characteristic, complemented
16#33835C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33789C211yesmaximal, characteristic, complemented
20#33787C211yesmaximal, characteristic, complemented
21#33770C211yesmaximal, characteristic, complemented
22#33769C211yesmaximal, characteristic, complemented
23#33762C211yesmaximal, characteristic, complemented
24#33756C211yesmaximal, characteristic, complemented
25#33680C211yesmaximal, characteristic, complemented
26#33679C211yesmaximal, characteristic, complemented
27#33527C211yesmaximal, characteristic, complemented
28#33527C211yesmaximal, characteristic, complemented
29#33519C211yesmaximal, characteristic, complemented
30#33516C211yesmaximal, characteristic, complemented
31#33490C211yesmaximal, characteristic, complemented
32C2×#578C2211yescharacteristic
33C22×#135C2211yescharacteristic
34#3539—21no—
35#3489—21no—
36C2×#510C2211yescharacteristic
37C2×#510C2211yescharacteristic, complemented
38C2×#510C2211yescharacteristic, complemented
39C2×#509C2211yescharacteristic
40C2×#508C2211yescharacteristic
41C2×#508C2211yescharacteristic
42C2×#508C2211yescharacteristic, complemented
43C2×#508C2211yescharacteristic, complemented
44#3339C2211yescharacteristic
45#3339C2211yescharacteristic, complemented
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3317—21no—
49#3317—21no—
50#3307—21no—
51#3307—21no—
52#3287C2211yescharacteristic
53#3287C2211yescharacteristic, complemented
54D4×Q16C2211yescharacteristic
55D4×Q16C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3283C2211yescharacteristic
59#3283C2211yescharacteristic
60#3283C2211yescharacteristic
61#3283C2211yescharacteristic, complemented
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3269—21no—
65#3269—21no—
66#3266—21no—
67#3266—21no—
68#3260—21no—
69#3204—21no—
70#3197—21no—
71#3177C2211yescharacteristic, complemented
72#3176C2211yescharacteristic, complemented
73#3156C2211yescharacteristic
74#3061C2211yescharacteristic
75#3061C2211yescharacteristic, complemented
76#3061C2211yescharacteristic, complemented
77#3050C2211yescharacteristic
78#3050C2211yescharacteristic
79C2×#467C2211yescharacteristic
80#3046—21no—
81#3013—21no—
82#3007—21no—
83#2951C2211yescharacteristic
84#2929C2211yescharacteristic
85#2251C2211yescharacteristic, complemented
86#2250C2211yescharacteristic, complemented
87#2248C2211yescharacteristic, complemented
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2245C2211yescharacteristic, complemented
91#2242C2211yescharacteristic, complemented
92#2242C2211yescharacteristic, complemented
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2236C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2235C2211yescharacteristic, complemented
101#2233C2211yescharacteristic, complemented
102#2233C2211yescharacteristic, complemented
103#2232C2211yescharacteristic, complemented
104#2232C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2228C2211yescharacteristic, complemented
109#2220C2211yescharacteristic
110#2220C2211yescharacteristic
111#2220C2211yescharacteristic, complemented
112#2220C2211yescharacteristic, complemented
113#2219C2211yescharacteristic
114#2219C2211yescharacteristic
115#2219C2211yescharacteristic, complemented
116#2218C2211yescharacteristic, complemented
117#2217C2211yescharacteristic, complemented
118#2217C2211yescharacteristic, complemented
119#2217C2211yescharacteristic, complemented
120#2217C2211yescharacteristic, complemented
121#2216C2211yescharacteristic, complemented
122#2216C2211yescharacteristic, complemented
123#2216C2211yescharacteristic, complemented
124#2215C2211yescharacteristic, complemented
125#2211C2211yescharacteristic, complemented
126#2211C2211yescharacteristic, complemented
127#2210C2211yescharacteristic, complemented
128#2210C2211yescharacteristic, complemented
129#2209C2211yescharacteristic, complemented
130#2209C2211yescharacteristic, complemented
131#2209C2211yescharacteristic, complemented
132#2208C2211yescharacteristic, complemented
133#2208C2211yescharacteristic, complemented
134#2208C2211yescharacteristic, complemented
135#2207C2211yescharacteristic, complemented
136#2206C2211yescharacteristic, complemented
137#2189C2211yescharacteristic
138#2189C2211yescharacteristic
139#2189C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2189C2211yescharacteristic
143#2189C2211yescharacteristic
144#2189C2211yescharacteristic
145#2189C2211yescharacteristic, complemented
146#2189C2211yescharacteristic, complemented
147#2189C2211yescharacteristic, complemented
148#2189C2211yescharacteristic, complemented
149#2189C2211yescharacteristic, complemented
150#2189C2211yescharacteristic, complemented
151#2188C2211yescharacteristic
152#2188C2211yescharacteristic, complemented
153#2188C2211yescharacteristic, complemented
154#2188C2211yescharacteristic, complemented
155#2188C2211yescharacteristic, complemented
156#2187C2211yescharacteristic
157#2186C2211yescharacteristic
158#2186C2211yescharacteristic
159#2186C2211yescharacteristic
160#2186C2211yescharacteristic
161#2186C2211yescharacteristic
162#2186C2211yescharacteristic
163#2186C2211yescharacteristic, complemented
164#2186C2211yescharacteristic, complemented
165#2186C2211yescharacteristic, complemented
166#2186C2211yescharacteristic, complemented
167#2185C2211yescharacteristic
168#2185C2211yescharacteristic, complemented
169#2185C2211yescharacteristic, complemented
170#2185C2211yescharacteristic, complemented
171#2185C2211yescharacteristic, complemented
172#2184C2211yescharacteristic
173#2177C2211yescharacteristic, complemented
174#2176C2211yescharacteristic, complemented
175#2175C2211yescharacteristic, complemented
176#2175C2211yescharacteristic, complemented
177C4×Q32C2211yescharacteristic, complemented
178C4×SD32C2211yescharacteristic, complemented
179C4×SD32C2211yescharacteristic, complemented
180C4×D16C2211yescharacteristic, complemented
181#2169C2211yescharacteristic
182#2169C2211yescharacteristic
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic
185#2168C2211yescharacteristic, complemented
186#2168C2211yescharacteristic, complemented
187D4×C16C2211yescharacteristic, complemented
188D4×C16C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2164C2211yescharacteristic, complemented
191#2141C2211yescharacteristic
192#2140C2211yescharacteristic
193#2139C2211yescharacteristic, complemented
194#2139C2211yescharacteristic, complemented
195#2138C2211yescharacteristic
196#2138C2211yescharacteristic
197C2×#358C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199#2113C2211yescharacteristic, complemented
200#2113C2211yescharacteristic, complemented
201#2112C2211yescharacteristic
202C2×C22⋊C16C2211yescharacteristic
203C2×2−1+4—21no—
204C22×#41—21no—
205#578—42no—
206#578—42no—
207C2×#137—21no—
208C2×#137—21no—
209C2×#137—21no—
210C2×#137—21no—
211C2×#135—21no—
212C2×#135—21no—
213C2×#135—42no—
214C2×#135—42no—
215C2×#135C2311yescharacteristic
216C2×#135C2311yescharacteristic
217C2×#135C2311yescharacteristic
218C2×#135C2311yescharacteristic
219C2×#135C2311yescharacteristic
220C2×#135C2311yescharacteristic
221C2×#135C2311yescharacteristic
222C2×#135C2311yescharacteristic
223C2×#135C2311yescharacteristic
224C2×#135C2311yescharacteristic
225C22×Q16C2311yescharacteristic
226C22×Q16C2311yescharacteristic
227C22×Q16C2311yescharacteristic
228C22×Q16C2311yescharacteristic
229C22×SD16—21no—
230C22×D8C2311yescharacteristic
231C2×#131C2311yescharacteristic
232C23×C8C2311yescharacteristic
233#560—41no—
234#560—41no—
235#553—21no—
236#553—21no—
237#553—41no—
238#553—41no—
239#552—21no—
240#552—21no—
241#550—21no—
242#550—21no—
243D4×Q8—21no—
244D4×Q8—21no—
245#548—21no—
246#548—21no—
247#547—21no—
248#547—21no—
249#547—21no—
250#547—21no—
251#547—41no—
252#547—41no—
253#546—21no—
254#546—21no—
255#546—41no—
256#546—41no—
257#541—21no—
258#540—21no—
259#540—41no—
260#540—41no—
261#539—41no—
262#539—41no—
263#537—21no—
264#537—21no—
265#537—21no—
266#537—41no—
267#536—21no—
268#536—41no—
269#525—21no—
270#525—21no—
271#525—41no—
272#525D411yescharacteristic
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8—41no—
275#520—21no—
276#510—42no—
277#510—42no—
278#510—42no—
279#509—42no—
280#508—42no—
281#508—42no—
282#508—42no—
283#508—42no—
284C2×Q32C2311yescharacteristic
285C2×Q32C2311yescharacteristic
286C2×Q32C2311yescharacteristic
287C2×Q32C2311yescharacteristic
288C2×Q32C2311yescharacteristic
289C2×Q32C2311yescharacteristic
290C2×Q32C2311yescharacteristic
291C2×Q32C2311yescharacteristic
292C2×SD32C2311yescharacteristic
293C2×SD32C2311yescharacteristic
294C2×SD32C2311yescharacteristic
295C2×SD32C2311yescharacteristic
296C2×SD32C2311yescharacteristic
297C2×SD32C2311yescharacteristic
298C2×SD32C2311yescharacteristic
299C2×SD32C2311yescharacteristic
300C2×SD32C2311yescharacteristic
301C2×SD32C2311yescharacteristic
302C2×SD32C2311yescharacteristic
303C2×SD32C2311yescharacteristic
304C2×D16C2311yescharacteristic
305C2×D16C2311yescharacteristic
306C2×D16C2311yescharacteristic
307C2×D16C2311yescharacteristic
308C2×M32C2311yescharacteristic
309C2×M32C2311yescharacteristic
310C2×M32C2311yescharacteristic
311C2×M32C2311yescharacteristic
312C22×C16C2311yescharacteristic
313C22×C16C2311yescharacteristic
314C22×C16C2311yescharacteristic
315C22×C16C2311yescharacteristic
316#499C2311yescharacteristic
317#499C2311yescharacteristic
318#497—21no—
319#497—21no—
320#495C2311yescharacteristic
321#495C2311yescharacteristic
322#494C2311yescharacteristic
323#494C2311yescharacteristic
324#494C2311yescharacteristic
325#493C2311yescharacteristic
326#491—21no—
327#490—21no—
328#485—21no—
329#485—21no—
330#483—21no—
331#483—21no—
332#482—21no—
333#482—21no—
334#481—21no—
335#481—21no—
336#479—21no—
337#479—21no—
338#478—21no—
339#478—21no—
340#470—21no—
341#469—21no—
342#468—21no—
343#468—21no—
344#468—21no—
345#468—21no—
346#468—21no—
347#468—21no—
348#467—21no—
349#467—21no—
350#467C2311yescharacteristic
351#467C2311yescharacteristic
352#467C2311yescharacteristic
353#467C2311yescharacteristic
354#467C2311yescharacteristic
355#467C2311yescharacteristic
356#467C2311yescharacteristic
357#467C2311yescharacteristic
358#467C2311yescharacteristic
359#467C2311yescharacteristic
360#467C2311yescharacteristic
361#467C2311yescharacteristic
362#466C2311yescharacteristic
363#466C2311yescharacteristic
364#466C2311yescharacteristic
365#466C2311yescharacteristic
366#466C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#466C2311yescharacteristic
370#465—21no—
371#465—21no—
372#465—21no—
373#465—21no—
374#464—21no—
375#464—21no—
376#463—21no—
377#463—21no—
378#462—21no—
379#462—21no—
380#461—21no—
381#461—21no—
382#461—21no—
383#461—21no—
384#460—21no—
385#460—21no—
386#452—21no—
387#452—21no—
388#452—21no—
389#452—21no—
390#452—21no—
391#452—21no—
392#452—21no—
393#452—21no—
394#452—21no—
395#452—21no—
396#451—21no—
397#451—21no—
398#451—21no—
399#451—21no—
400#450—21no—
401#450—21no—
402#449—21no—
403#449—21no—
404#449—21no—
405#449—21no—
406#449—21no—
407#449—21no—
408#448—21no—
409#448—21no—
410#442—21no—
411#441—21no—
412#440—21no—
413#440—21no—
414C4×Q16C2311yescharacteristic
415C4×Q16C2311yescharacteristic
416C4×Q16C2311yescharacteristic
417C4×Q16C2311yescharacteristic
418C4×D8C2311yescharacteristic
419C4×D8C2311yescharacteristic
420C4×D8C2311yescharacteristic
421C4×D8C2311yescharacteristic
422#435D411yescharacteristic
423#435D411yescharacteristic
424#435D411yescharacteristic
425#435D411yescharacteristic
426C8×D4C2311yescharacteristic
427C8×D4C2311yescharacteristic
428C8×D4C2311yescharacteristic
429C8×D4C2311yescharacteristic
430#427C2311yescharacteristic
431#427C2311yescharacteristic
432C2×#107C2311yescharacteristic
433C2×#107C2311yescharacteristic
434C2×#107C2311yescharacteristic
435#424D411yescharacteristic
436#417—21no—
437#417—21no—
438#417—21no—
439#417—21no—
440#416—21no—
441#416—21no—
442C2×#103—21no—
443#408D411yescharacteristic
444#407D411yescharacteristic
445#405C2311yescharacteristic
446#367C2311yescharacteristic
447#367C2311yescharacteristic
448#367C2311yescharacteristic
449#367C2311yescharacteristic
450#366C2311yescharacteristic
451#366C2311yescharacteristic
452#366C2311yescharacteristic
453#366C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
456C4⋊C16C2311yescharacteristic
457C4⋊C16C2311yescharacteristic
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#358C2311yescharacteristic
473#358C2311yescharacteristic
474#358C2311yescharacteristic
475#358C2311yescharacteristic
476#358C2311yescharacteristic
477#358C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488#357C2311yescharacteristic
489#357C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494C22⋊C16C2311yescharacteristic
495C22⋊C16C2311yescharacteristic
496C22⋊C16C2311yescharacteristic
497C22⋊C16C2311yescharacteristic
498C22⋊C16C2311yescharacteristic
499C22⋊C16C2311yescharacteristic
500C22⋊C16C2311yescharacteristic
501C22⋊C16C2311yescharacteristic
502#346C2311yescharacteristic
503#346C2311yescharacteristic
504C4×C16C2311yescharacteristic
505C4×C16C2311yescharacteristic
5062−1+4—44no—
5072−1+4—82no—
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—21no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41—21no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—44no—
524C2×#41—82no—
525C2×#41C2×D411yescharacteristic
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—41no—
531C22×D4—21no—
532C22×D4—41no—
533C23×C4—41no—
534C23×C4C2×D411yescharacteristic
535#137—44no—
536#137—44no—
537#137—44no—
538#137—82no—
539#135—22no—
540#135—22no—
541#135—22no—
542#135—22no—
543#135—22no—
544#135—22no—
545#135—41no—
546#135—41no—
547#135—41no—
548#135—41no—
549#135—41no—
550#135—41no—
551#135—41no—
552#135—41no—
553#135—41no—
554#135—41no—
555#135—41no—
556#135—41no—
557#135—41no—
558#135—41no—
559#135—44no—
560#135—44no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—22no—
564C2×Q16—21no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16—21no—
571C2×Q16—41no—
572C2×Q16—41no—
573C2×Q16—41no—
574C2×Q16—41no—
575C2×Q16—41no—
576C2×Q16C2411yescharacteristic
577C2×Q16C2411yescharacteristic
578C2×Q16C2411yescharacteristic
579C2×Q16C2411yescharacteristic
580C2×Q16C2411yescharacteristic
581C2×Q16C2411yescharacteristic
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—21no—
585C2×SD16—21no—
586C2×SD16—21no—
587C2×SD16—21no—
588C2×SD16—21no—
589C2×SD16—21no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—44no—
595C2×D8—22no—
596C2×D8—21no—
597C2×D8—21no—
598C2×D8—41no—
599C2×D8C2411yescharacteristic
600C2×D8C2411yescharacteristic
601C2×D8C2411yescharacteristic
602C2×D8C2411yescharacteristic
603#131—41no—
604#131—41no—
605C2×M16C2×D411yescharacteristic
606C2×M16C2×D411yescharacteristic
607C2×M16C2×D411yescharacteristic
608C2×M16C2×D411yescharacteristic
609C22×C8—41no—
610C22×C8—41no—
611C22×C8C2×D411yescharacteristic
612C22×C8C2×D411yescharacteristic
613C22×C8C2×D411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C4⋊Q8—21no—
620C4⋊Q8—21no—
621C4⋊Q8—21no—
622C4⋊Q8—41no—
623C4⋊Q8—41no—
624#127—21no—
625#127—41no—
626#127—41no—
627#126—41no—
628#126—41no—
629#126—41no—
630#126—41no—
631#126—41no—
632#126—41no—
633#125—21no—
634#125—21no—
635#125—41no—
636#125—41no—
637#125—41no—
638#125—41no—
639#124—21no—
640#124—21no—
641#124—41no—
642#124—41no—
643#123—41no—
644#123—41no—
645#123—41no—
646#123—41no—
647#123—41no—
648#123—41no—
649#123—41no—
650#123—41no—
651#123—41no—
652#123—41no—
653#123—41no—
654#123—41no—
655#123—41no—
656#123—41no—
657#123—41no—
658#123—41no—
659#123—41no—
660#123—41no—
661#123—41no—
662#123—41no—
663#123D811yescharacteristic
664#123D811yescharacteristic
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8—21no—
673C22⋊Q8—21no—
674C22⋊Q8—21no—
675C22⋊Q8—21no—
676C22⋊Q8—21no—
677C22⋊Q8—41no—
678C22⋊Q8—41no—
679C22⋊Q8—41no—
680C22⋊Q8—41no—
681C22⋊Q8—41no—
682C22⋊Q8—41no—
683C22⋊Q8—41no—
684C22⋊Q8—41no—
685C22⋊Q8—41no—
686C22⋊Q8—41no—
687C22⋊Q8—41no—
688C22⋊Q8—41no—
689C22⋊Q8—41no—
690C22⋊Q8D811yescharacteristic
691C22⋊Q8D811yescharacteristic
692#121—21no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121—41no—
701#121—41no—
702#121—41no—
703#121—41no—
704#121—41no—
705#121—41no—
706#121—41no—
707#121—41no—
708#121—41no—
709#121—41no—
710#121—41no—
711#121—41no—
712#121—41no—
713#121—41no—
714#121—41no—
715#121—41no—
716#121—41no—
717#121—41no—
718#121—41no—
719#121—41no—
720#121—41no—
721#121—41no—
722#121—41no—
723#121—41no—
724#121—41no—
725#121D811yescharacteristic
726#121D811yescharacteristic
727#120—41no—
728#120—41no—
729#120—41no—
730#120—41no—
731#120D811yescharacteristic
732#120D811yescharacteristic
733C4×Q8—21no—
734C4×Q8—21no—
735C4×Q8—21no—
736C4×Q8—21no—
737C4×D4—21no—
738C4×D4—21no—
739C4×D4—21no—
740C4×D4—21no—
741C4×D4—41no—
742C4×D4—41no—
743C4×D4—41no—
744C4×D4—41no—
745C4×D4—41no—
746C4×D4—41no—
747C4×D4—41no—
748C4×D4—41no—
749C4×D4—41no—
750C4×D4—41no—
751C4×D4—41no—
752C4×D4—41no—
753C4×D4—41no—
754C4×D4—41no—
755C4×D4C2×D411yescharacteristic
756C4×D4C2×D411yescharacteristic
757C4×D4C2×D411yescharacteristic
758C4×D4C2×D411yescharacteristic
759#117—21no—
760#117—21no—
761#117—41no—
762#117—41no—
763#117—41no—
764#117C2×D411yescharacteristic
765C2×C4⋊C4—21no—
766C2×C4⋊C4—21no—
767C2×C4⋊C4—21no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777Q32—22no—
778Q32—22no—
779Q32—41no—
780Q32—41no—
781Q32—41no—
782Q32—41no—
783Q32—41no—
784Q32—41no—
785SD32—22no—
786SD32—22no—
787SD32—22no—
788SD32—22no—
789SD32—41no—
790SD32—41no—
791SD32—41no—
792SD32—41no—
793SD32—41no—
794SD32—41no—
795SD32—41no—
796SD32—41no—
797D16—22no—
798D16—22no—
799D16—41no—
800D16—41no—
801M32—41no—
802M32—41no—
803M32—41no—
804M32—41no—
805C2×C16—41no—
806C2×C16—41no—
807C2×C16—41no—
808C2×C16—41no—
809C2×C16C2411yescharacteristic
810C2×C16C2411yescharacteristic
811C2×C16C2411yescharacteristic
812C2×C16C2411yescharacteristic
813C2×C16C2411yescharacteristic
814C2×C16C2411yescharacteristic
815C2×C16C2411yescharacteristic
816C2×C16C2411yescharacteristic
817#107—21no—
818#107—21no—
819#107—21no—
820#107C2411yescharacteristic
821#107C2411yescharacteristic
822#107C2411yescharacteristic
823#107C2411yescharacteristic
824#107C2411yescharacteristic
825#107C2411yescharacteristic
826#106—21no—
827#106—21no—
828#106—21no—
829#106—21no—
830C4⋊C8C2×D411yescharacteristic
831C4⋊C8C2×D411yescharacteristic
832C4⋊C8C2×D411yescharacteristic
833C4⋊C8C2×D411yescharacteristic
834#103—21no—
835#103—21no—
836#103—21no—
837#103—21no—
838#103—21no—
839#103—21no—
840#103—21no—
841#103—21no—
842#103—21no—
843#103—21no—
844#103—21no—
845#103—21no—
846#103—21no—
847#103—21no—
848#103—21no—
849#103—21no—
850#102—21no—
851#102—21no—
852#102—21no—
853#102—21no—
854#102—21no—
855#102—21no—
856#102—21no—
857#102—21no—
858#102—21no—
859#102—21no—
860#102—21no—
861#102—21no—
862C22⋊C8C2×D411yescharacteristic
863C22⋊C8C2×D411yescharacteristic
864C22⋊C8C2×D411yescharacteristic
865C22⋊C8C2×D411yescharacteristic
866C22⋊C8C2×D411yescharacteristic
867C22⋊C8C2×D411yescharacteristic
868C22⋊C8C2×D411yescharacteristic
869C22⋊C8C2×D411yescharacteristic
870#97C2×D411yescharacteristic
871#97C2×D411yescharacteristic
872C4×C8C2411yescharacteristic
873C4×C8C2411yescharacteristic
874C24—41no—
875C24C2×D811yescharacteristic
876#41—24no—
877#41—41no—
878#41—41no—
879#41—42no—
880#41—42no—
881#41—42no—
882#41—42no—
883#41—42no—
884#41—42no—
885#41—42no—
886#41—81no—
887#41—81no—
888#41—81no—
889#41—81no—
890#41—81no—
891#41—81no—
892#41—81no—
893#41—81no—
894#41—81no—
895#41—81no—
896#41—81no—
897#41—81no—
898#41—84no—
899#41—84no—
900#41—84no—
901#41—84no—
902#41—84no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—81no—
919C2×Q8—81no—
920C2×Q8—81no—
921C2×Q8—84no—
922C2×Q8C2×D811yescharacteristic
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—42no—
928C2×D4—41no—
929C2×D4—41no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—41no—
933C2×D4—41no—
934C2×D4—41no—
935C2×D4—41no—
936C2×D4—41no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—41no—
940C2×D4—41no—
941C2×D4—41no—
942C2×D4—41no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—81no—
950C2×D4—84no—
951C2×D4C2×D811yescharacteristic
952C2×D4C2×D811yescharacteristic
953C2×D4C2×D811yescharacteristic
954C2×D4C2×D811yescharacteristic
955C2×D4C2×D811yescharacteristic
956C2×D4C2×D811yescharacteristic
957C2×D4C2×D811yescharacteristic
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×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—84no—
982C22×C4C2×D811yescharacteristic
983C22×C4C2×D811yescharacteristic
984C22×C4C2×D811yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990Q16—21no—
991Q16—21no—
992Q16—21no—
993Q16—21no—
994Q16—21no—
995Q16—21no—
996Q16—21no—
997Q16—21no—
998Q16—21no—
999Q16—21no—
1000Q16—21no—
1001Q16—42no—
1002Q16—42no—
1003Q16—42no—
1004Q16—42no—
1005Q16—81no—
1006Q16—81no—
1007Q16—81no—
1008Q16H(5,𝔽2)12yes—
1009SD16—24no—
1010SD16—42no—
1011SD16—42no—
1012SD16—42no—
1013SD16—42no—
1014SD16—42no—
1015SD16—81no—
1016SD16—81no—
1017SD16—81no—
1018SD16—81no—
1019SD16—81no—
1020SD16—81no—
1021D8—21no—
1022D8—21no—
1023D8—21no—
1024D8—21no—
1025D8—21no—
1026D8—21no—
1027D8—21no—
1028D8—42no—
1029D8—81no—
1030D8H(5,𝔽2)12yes—
1031M16—41no—
1032M16—41no—
1033M16—41no—
1034M16—41no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—41no—
1046C2×C8—41no—
1047C2×C8—41no—
1048C2×C8C22×D411yescharacteristic
1049C2×C8C22×D411yescharacteristic
1050C2×C8C22×D411yescharacteristic
1051C2×C8C22×D411yescharacteristic
1052C2×C8C22×D411yescharacteristic
1053C2×C8C22×D411yescharacteristic
1054C2×C8C22×D411yescharacteristic
1055C2×C8C2511yescharacteristic
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4C2×D811yescharacteristic
1092C4⋊C4C2×D811yescharacteristic
1093C4⋊C4C2×D811yescharacteristic
1094C4⋊C4C2×D811yescharacteristic
1095C4⋊C4C2×D811yescharacteristic
1096C4⋊C4C2×D811yescharacteristic
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4C2×D811yescharacteristic
1128C22⋊C4C2×D811yescharacteristic
1129C22⋊C4C2×D811yescharacteristic
1130C22⋊C4C2×D811yescharacteristic
1131C22⋊C4C2×D811yescharacteristic
1132C22⋊C4C2×D811yescharacteristic
1133C22⋊C4C2×D811yescharacteristic
1134C22⋊C4C2×D811yescharacteristic
1135C22⋊C4C2×D811yescharacteristic
1136C22⋊C4C2×D811yescharacteristic
1137C42—41no—
1138C42—41no—
1139C42—41no—
1140C42—41no—
1141C42—41no—
1142C42—41no—
1143C42C22×D411yescharacteristic
1144C42C22×D411yescharacteristic
1145C16—21no—
1146C16—21no—
1147C16—21no—
1148C16—21no—
1149C16—21no—
1150C16—21no—
1151C16—21no—
1152C16—21no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—82no—
1161C23—82no—
1162C23—161no—
1163C23C22×D811yescharacteristic
1164C23C22×D811yescharacteristic
1165C23C22×D811yescharacteristic
1166C23C22×D811yescharacteristic
1167C23C22×D811yescharacteristic
1168Q8—22no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—82no—
1182Q8—82no—
1183Q8—82no—
1184Q8—82no—
1185D4—22no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—44no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—82no—
1202D4—82no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—161no—
1208D4—161no—
1209D4—161no—
1210D4—161no—
1211D4—161no—
1212D4—161no—
1213D4—161no—
1214D4—161no—
1215D4—161no—
1216D4—161no—
1217D4—161no—
1218D4—161no—
1219D4—161no—
1220D4—161no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—44no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—82no—
1248C2×C4—82no—
1249C2×C4—82no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—82no—
1253C2×C4—82no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4—161no—
1257C2×C4—161no—
1258C2×C4—161no—
1259C2×C4—161no—
1260C2×C4—161no—
1261C2×C4—161no—
1262C2×C4—161no—
1263C2×C4—161no—
1264C2×C4—161no—
1265C2×C4—161no—
1266C2×C4—161no—
1267C2×C4C22×D811yescharacteristic
1268C2×C4C22×D811yescharacteristic
1269C2×C4C22×D811yescharacteristic
1270C2×C4C22×D811yescharacteristic
1271C2×C4C22×D811yescharacteristic
1272C2×C4C22×D811yescharacteristic
1273C2×C4C22×D811yescharacteristic
1274C2×C4C22×D811yescharacteristic
1275C2×C4C22×D811yescharacteristic
1276C2×C4C23×D411yescharacteristic
1277C8—21no—
1278C8—21no—
1279C8—21no—
1280C8—21no—
1281C8—21no—
1282C8—21no—
1283C8—21no—
1284C8C2×H(5,𝔽2)11yescharacteristic
1285C8C2×H(5,𝔽2)11yescharacteristic
1286C22—21no—
1287C22—21no—
1288C22—21no—
1289C22—21no—
1290C22—21no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—21no—
1297C22—21no—
1298C22—21no—
1299C22—21no—
1300C22—21no—
1301C22—42no—
1302C22—82no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—164no—
1315C22C23×D811yescharacteristic
1316C4—21no—
1317C4—21no—
1318C4—21no—
1319C4—21no—
1320C4—21no—
1321C4—21no—
1322C4—21no—
1323C4—21no—
1324C4—21no—
1325C4—42no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4#348411yescharacteristic
1338C4#358511yescharacteristic
1339C2—41no—
1340C2—41no—
1341C2—41no—
1342C2—41no—
1343C2—41no—
1344C2—82no—
1345C2—161no—
1346C2—161no—
1347C2—161no—
1348C2#6155911yescharacteristic
1349C2#6263511yescharacteristic
1350C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ #2929 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62276C2semidirect
2. #61057C2semidirect
3. #33890C2semidirect
4. #33889C2semidirect
5. #33887C2semidirect
6. #33882C2semidirect
7. #33879C2semidirect
8. #33874C2semidirect
9. #33868C2semidirect
10. #33867C2semidirect
11. #33850C2semidirect
12. #33849C2semidirect
13. #33844C2semidirect
14. #33842C2semidirect
15. #33837C2semidirect
16. #33835C2semidirect
17. #33834C2semidirect
18. #33833C2semidirect
19. #33789C2semidirect
20. #33787C2semidirect
21. #33770C2semidirect
22. #33769C2semidirect
23. #33762C2semidirect
24. #33756C2semidirect
25. #33680C2semidirect
26. #33679C2semidirect
27. #33527C2semidirect
28. #33527C2semidirect
29. #33519C2semidirect
30. #33516C2semidirect
31. #33490C2semidirect
37. C2×#510C22semidirect
38. C2×#510C22semidirect
42. C2×#508C22semidirect
43. C2×#508C22semidirect
45. #3339C22semidirect
47. #3336C22semidirect
53. #3287C22semidirect
61. #3283C22semidirect
71. #3177C22semidirect
72. #3176C22semidirect
75. #3061C22semidirect
76. #3061C22semidirect
85. #2251C22semidirect
86. #2250C22semidirect
87. #2248C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
90. #2245C22semidirect
91. #2242C22semidirect
92. #2242C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2236C22semidirect
98. #2236C22semidirect
99. #2235C22semidirect
100. #2235C22semidirect
101. #2233C22semidirect
102. #2233C22semidirect
103. #2232C22semidirect
104. #2232C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
107. #2228C22semidirect
108. #2228C22semidirect
111. #2220C22semidirect
112. #2220C22semidirect
115. #2219C22semidirect
116. #2218C22semidirect
117. #2217C22semidirect
118. #2217C22semidirect
119. #2217C22semidirect
120. #2217C22semidirect
121. #2216C22semidirect
122. #2216C22semidirect
123. #2216C22semidirect
124. #2215C22semidirect
125. #2211C22semidirect
126. #2211C22semidirect
127. #2210C22semidirect
128. #2210C22semidirect
129. #2209C22semidirect
130. #2209C22semidirect
131. #2209C22semidirect
132. #2208C22semidirect
133. #2208C22semidirect
134. #2208C22semidirect
135. #2207C22semidirect
136. #2206C22semidirect
145. #2189C22semidirect
146. #2189C22semidirect
147. #2189C22semidirect
148. #2189C22semidirect
149. #2189C22semidirect
150. #2189C22semidirect
152. #2188C22semidirect
153. #2188C22semidirect
154. #2188C22semidirect
155. #2188C22semidirect
163. #2186C22semidirect
164. #2186C22semidirect
165. #2186C22semidirect
166. #2186C22semidirect
168. #2185C22semidirect
169. #2185C22semidirect
170. #2185C22semidirect
171. #2185C22semidirect
173. #2177C22semidirect
174. #2176C22semidirect
175. #2175C22semidirect
176. #2175C22semidirect
177. C4×Q32C22semidirect
178. C4×SD32C22semidirect
179. C4×SD32C22semidirect
180. C4×D16C22semidirect
185. #2168C22semidirect
186. #2168C22semidirect
187. D4×C16C22semidirect
188. D4×C16C22semidirect
189. #2164C22semidirect
190. #2164C22semidirect
193. #2139C22semidirect
194. #2139C22semidirect
197. C2×#358C22semidirect
198. C2×#358C22semidirect
199. #2113C22semidirect
200. #2113C22semidirect

Maximal subgroups

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

subgroupindex
#622762
#610572
#338902
#338892
#338872
#338822
#338792
#338742
#338682
#338672
#338502
#338492
#338442
#338422
#338372
#338352
#338342
#338332
#337892
#337872
#337702
#337692
#337622
#337562
#336802
#336792
#335272
#335192
#335162
#334902