Finite Group Databasebeta

← #7624064

Subgroups — #7624064

Order 512.

1266 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61488C211yesmaximal, characteristic, complemented
2#61473C211yesmaximal, characteristic, complemented
3#33961C211yesmaximal, characteristic, complemented
4#33950C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33938C211yesmaximal, characteristic, complemented
7#33924C211yesmaximal, characteristic, complemented
8#33918C211yesmaximal, characteristic, complemented
9#33918C211yesmaximal, characteristic, complemented
10#33888C211yesmaximal, characteristic, complemented
11#33883C211yesmaximal, characteristic, complemented
12#33879C211yesmaximal, characteristic, complemented
13#33876C211yesmaximal, characteristic, complemented
14#33868C211yesmaximal, characteristic, complemented
15#33867C211yesmaximal, characteristic, complemented
16#33844C211yesmaximal, characteristic, complemented
17#33843C211yesmaximal, characteristic, complemented
18#33843C211yesmaximal, characteristic, complemented
19#33750C211yesmaximal, characteristic, complemented
20#33743C211yesmaximal, characteristic, complemented
21#33739C211yesmaximal, characteristic, complemented
22#33687C211yesmaximal, characteristic, complemented
23#33685C211yesmaximal, characteristic, complemented
24#33681C211yesmaximal, characteristic, complemented
25#33679C211yesmaximal, characteristic, complemented
26#33668C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33483C211yesmaximal, characteristic, complemented
29#33455C211yesmaximal, characteristic, complemented
30#33455C211yesmaximal, characteristic, complemented
31C4×#510C211yesmaximal, characteristic, complemented
32#3524—21no—
33#3516—21no—
34C2×#510C2211yescharacteristic
35C2×#510C2211yescharacteristic
36C2×#510C2211yescharacteristic
37#3396C2211yescharacteristic
38#3393C2211yescharacteristic
39#3383C2211yescharacteristic
40#3383C2211yescharacteristic
41#3377—21no—
42#3371—21no—
43#3341C2211yescharacteristic
44#3339C2211yescharacteristic
45#3339C2211yescharacteristic
46#3338C2211yescharacteristic
47#3336C2211yescharacteristic
48#3336C2211yescharacteristic
49#3327—21no—
50#3326—21no—
51#3321—21no—
52#3320—21no—
53#3317—21no—
54#3316—21no—
55#3287C2211yescharacteristic
56D4×Q16C2211yescharacteristic
57#3285C2211yescharacteristic
58#3285C2211yescharacteristic
59#3285C2211yescharacteristic
60#3285C2211yescharacteristic
61#3177C2211yescharacteristic
62#3176C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic
67#3126—21no—
68#3125—21no—
69#3121—21no—
70#3120—21no—
71#3117—21no—
72#3111—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76#2950C2211yescharacteristic
77#2950C2211yescharacteristic
78C4×#135C2211yescharacteristic
79C2×C4×Q16C2211yescharacteristic
80#2253C2211yescharacteristic
81#2253C2211yescharacteristic
82#2252C2211yescharacteristic
83#2249C2211yescharacteristic
84#2249C2211yescharacteristic
85#2248C2211yescharacteristic
86#2245C2211yescharacteristic
87#2244C2211yescharacteristic
88#2243C2211yescharacteristic
89#2243C2211yescharacteristic
90#2242C2211yescharacteristic
91#2242C2211yescharacteristic
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic
95#2237C2211yescharacteristic
96#2235C2211yescharacteristic
97#2235C2211yescharacteristic
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic
100#2233C2211yescharacteristic
101#2233C2211yescharacteristic
102#2232C2211yescharacteristic
103#2232C2211yescharacteristic
104#2229C2211yescharacteristic
105#2229C2211yescharacteristic
106#2229C2211yescharacteristic
107#2229C2211yescharacteristic
108#2229C2211yescharacteristic
109#2229C2211yescharacteristic
110#2228C2211yescharacteristic
111#2228C2211yescharacteristic
112#2227C2211yescharacteristic
113#2226C2211yescharacteristic
114#2225C2211yescharacteristic
115#2225C2211yescharacteristic
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic
119#2220C2211yescharacteristic
120#2220C2211yescharacteristic
121#2220C2211yescharacteristic
122#2219C2211yescharacteristic
123#2218C2211yescharacteristic
124#2217C2211yescharacteristic
125#2217C2211yescharacteristic
126#2216C2211yescharacteristic
127#2215C2211yescharacteristic
128#2211C2211yescharacteristic
129#2211C2211yescharacteristic
130#2211C2211yescharacteristic
131#2211C2211yescharacteristic
132#2211C2211yescharacteristic
133#2211C2211yescharacteristic
134#2210C2211yescharacteristic
135#2210C2211yescharacteristic
136#2209C2211yescharacteristic
137#2209C2211yescharacteristic
138#2207C2211yescharacteristic
139#2206C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2188C2211yescharacteristic
143#2188C2211yescharacteristic
144#2188C2211yescharacteristic
145#2188C2211yescharacteristic
146#2186C2211yescharacteristic
147#2186C2211yescharacteristic
148#2186C2211yescharacteristic
149#2186C2211yescharacteristic
150#2185C2211yescharacteristic
151#2185C2211yescharacteristic
152#2183C2211yescharacteristic
153Q8×C16C2211yescharacteristic
154#2177C2211yescharacteristic
155#2176C2211yescharacteristic
156#2176C2211yescharacteristic
157#2176C2211yescharacteristic
158#2176C2211yescharacteristic
159#2176C2211yescharacteristic
160#2175C2211yescharacteristic
161#2175C2211yescharacteristic
162#2175C2211yescharacteristic
163#2175C2211yescharacteristic
164#2175C2211yescharacteristic
165#2175C2211yescharacteristic
166C4×Q32C2211yescharacteristic
167C4×Q32C2211yescharacteristic
168C4×Q32C2211yescharacteristic
169C4×Q32C2211yescharacteristic
170C4×Q32C2211yescharacteristic
171C4×Q32C2211yescharacteristic
172C4×Q32C2211yescharacteristic
173C4×SD32C2211yescharacteristic
174C4×SD32C2211yescharacteristic
175C4×SD32C2211yescharacteristic
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179C4×SD32C2211yescharacteristic
180C4×SD32C2211yescharacteristic
181C4×D16C2211yescharacteristic
182#2169C2211yescharacteristic
183#2169C2211yescharacteristic
184#2169C2211yescharacteristic
185#2168C2211yescharacteristic
186#2168C2211yescharacteristic
187D4×C16C2211yescharacteristic
188#2164C2211yescharacteristic
189#2164C2211yescharacteristic
190#2162C2211yescharacteristic
191#2159C2211yescharacteristic
192#2159C2211yescharacteristic
193#2159C2211yescharacteristic
194#2141C2211yescharacteristic
195#2139C2211yescharacteristic
196#2138C2211yescharacteristic
197#2138C2211yescharacteristic
198C2×#358C2211yescharacteristic
199C2×#358C2211yescharacteristic
200#2108C2211yescharacteristic
201#2108C2211yescharacteristic
202C4×M32C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209#559—21no—
210#559—41no—
211#557—21no—
212#557—21no—
213#556—21no—
214#556—41no—
215#555—21no—
216#555—41no—
217#554—21no—
218#554—41no—
219#553—21no—
220#553—21no—
221#553—41no—
222#553—41no—
223#552—21no—
224#552—21no—
225#552—41no—
226#552—41no—
227#550—21no—
228D4×Q8—21no—
229#548—21no—
230#548—21no—
231#548—21no—
232#548—21no—
233#542—21no—
234#542—21no—
235#542—41no—
236#542—41no—
237#541—21no—
238#541—41no—
239#540—21no—
240#540—41no—
241#529—21no—
242#529—21no—
243#529—41no—
244#529—41no—
245#529—41no—
246#529—41no—
247#529D411yescharacteristic
248#520—21no—
249#520—21no—
250#519—21no—
251#519—21no—
252C4×#41—21no—
253C2×C4×Q8—21no—
254#510—24no—
255#510—24no—
256#510—24no—
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×Q32C2311yescharacteristic
262C2×Q32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C2×M32C2311yescharacteristic
276C2×M32C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#499C2311yescharacteristic
282#499C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#494C2311yescharacteristic
290#493C2311yescharacteristic
291#491—21no—
292#490—21no—
293#489—21no—
294#489—21no—
295#488—21no—
296#488—21no—
297#485—21no—
298#485—21no—
299#484—21no—
300#484—21no—
301#483—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—21no—
306#482—21no—
307#481—21no—
308#481—21no—
309#479—21no—
310#479—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#478—21no—
316#478—21no—
317#477—21no—
318#476—21no—
319#475—21no—
320#475—21no—
321#470—21no—
322#469—21no—
323#468—21no—
324#468—21no—
325#467C2311yescharacteristic
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#466C2311yescharacteristic
332#466C2311yescharacteristic
333#466C2311yescharacteristic
334#466C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#465—21no—
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#464—21no—
344#464—21no—
345#463—21no—
346#463—21no—
347#462—21no—
348#461—21no—
349#460—21no—
350#460—21no—
351#452—21no—
352#452—21no—
353#452—21no—
354#452—21no—
355#451—21no—
356#451—21no—
357#449—21no—
358#449—21no—
359#448—21no—
360#448—21no—
361#448—21no—
362#448—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#442—21no—
366#441—21no—
367#441—21no—
368#441—21no—
369#441—21no—
370#441—21no—
371#440—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16—21no—
378C4×Q16—21no—
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×Q16C2311yescharacteristic
384C4×Q16C2311yescharacteristic
385C4×Q16C2311yescharacteristic
386C4×Q16C2311yescharacteristic
387C4×Q16C2311yescharacteristic
388C4×Q16C2311yescharacteristic
389C4×Q16C2311yescharacteristic
390C4×Q16C2311yescharacteristic
391C4×Q16C2311yescharacteristic
392C4×Q16C2311yescharacteristic
393C4×SD16—21no—
394C4×SD16—21no—
395C4×SD16—21no—
396C4×SD16—21no—
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403#436D411yescharacteristic
404#435D411yescharacteristic
405#435D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#433D411yescharacteristic
410#433D411yescharacteristic
411#432D411yescharacteristic
412#427C2311yescharacteristic
413#427C2311yescharacteristic
414#427C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#419—21no—
419#419—21no—
420#417—21no—
421#417—21no—
422#416—21no—
423C2×#103—21no—
424#405C2311yescharacteristic
425#405C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#367C2311yescharacteristic
432#367C2311yescharacteristic
433#367C2311yescharacteristic
434#367C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
442#366C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449#358C2311yescharacteristic
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#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503#135—22no—
504#135—22no—
505#135—22no—
506#135—41no—
507#135—41no—
508#135—41no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—21no—
513C2×Q16—21no—
514C2×Q16—21no—
515C2×Q16—21no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16C2411yescharacteristic
520C2×Q16C2411yescharacteristic
521C2×Q16C2411yescharacteristic
522C2×Q16C2411yescharacteristic
523C2×Q16C2411yescharacteristic
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8C2411yescharacteristic
533C2×D8C2411yescharacteristic
534C2×D8C2411yescharacteristic
535C2×M16C2×D411yescharacteristic
536C2×M16C2×D411yescharacteristic
537C22×C8C2×D411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#127—21no—
548#127—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#126—41no—
556#126—41no—
557#126—41no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126D811yescharacteristic
562#126D811yescharacteristic
563#125—21no—
564#125—21no—
565#125—21no—
566#125—21no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125D811yescharacteristic
577#124—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124D811yescharacteristic
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123D811yescharacteristic
604#123D811yescharacteristic
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
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⋊Q8D811yescharacteristic
623#121—21no—
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#121—41no—
636#121—41no—
637#121—41no—
638#121—41no—
639#121—41no—
640#121D811yescharacteristic
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8—21no—
652C4×Q8—21no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×Q8C2×D411yescharacteristic
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4—41no—
677C4×D4—41no—
678C4×D4—41no—
679C4×D4—41no—
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×D4C2×D411yescharacteristic
689C4×D4C2×D411yescharacteristic
690C4×D4C2×D411yescharacteristic
691#117—21no—
692#117—21no—
693#117—21no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117—41no—
698#117—41no—
699#117—41no—
700#117—41no—
701#117—41no—
702#117—41no—
703#117—41no—
704#117—41no—
705#117—41no—
706#117—41no—
707#117C2×D411yescharacteristic
708#117C2×D411yescharacteristic
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4—41no—
714C2×C4⋊C4—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—22no—
720Q32—22no—
721Q32—41no—
722Q32—41no—
723Q32#4114yes—
724SD32—22no—
725SD32—22no—
726SD32—22no—
727SD32—22no—
728SD32—22no—
729SD32—22no—
730SD32—41no—
731SD32—41no—
732D16—41no—
733D16—41no—
734M32—22no—
735M32—22no—
736M32—22no—
737M32—41no—
738C2×C16—41no—
739C2×C16—41no—
740C2×C16C2411yescharacteristic
741C2×C16C2411yescharacteristic
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748#107—21no—
749#107—21no—
750#107—21no—
751#107—21no—
752#107—21no—
753#107C2411yescharacteristic
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#106—21no—
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768C4⋊C8C2×D411yescharacteristic
769C4⋊C8C2×D411yescharacteristic
770C4⋊C8C2×D411yescharacteristic
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774#103—21no—
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#103—21no—
780#103—21no—
781#103—21no—
782#103—21no—
783#103—21no—
784#103—21no—
785#103—21no—
786#103—21no—
787#103—21no—
788#103—21no—
789#103—21no—
790#103—21no—
791#103—21no—
792#103—21no—
793#103—21no—
794#102—21no—
795#102—21no—
796#102—21no—
797#102—21no—
798#102—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802#102—21no—
803#102—21no—
804#102—21no—
805#102—21no—
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808C22⋊C8C2×D411yescharacteristic
809C22⋊C8C2×D411yescharacteristic
810C22⋊C8C2×D411yescharacteristic
811C22⋊C8C2×D411yescharacteristic
812#97C2×D411yescharacteristic
813#97C2×D411yescharacteristic
814#97C2×D411yescharacteristic
815#97C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822#41—42no—
823#41—42no—
824#41—42no—
825#41—81no—
826#41—81no—
827#41—81no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8C2×D811yescharacteristic
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4C2×D811yescharacteristic
860C2×D4C2×D811yescharacteristic
861C2×D4C2×D811yescharacteristic
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4C2×D811yescharacteristic
878C22×C4C2×D811yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882Q16—21no—
883Q16—21no—
884Q16—21no—
885Q16—21no—
886Q16—21no—
887Q16—21no—
888Q16—21no—
889Q16—21no—
890Q16—42no—
891Q16—42no—
892Q16—42no—
893Q16—81no—
894Q16C2×#4112yes—
895Q16C2×#4112yes—
896SD16—42no—
897SD16—42no—
898SD16—42no—
899SD16—81no—
900SD16—81no—
901SD16—81no—
902SD16—81no—
903D8—21no—
904D8—21no—
905D8—21no—
906D8—21no—
907D8—21no—
908D8—21no—
909D8—81no—
910M16—41no—
911M16—41no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—41no—
919C2×C8C22×D411yescharacteristic
920C2×C8C22×D411yescharacteristic
921C2×C8C22×D411yescharacteristic
922C2×C8C22×D411yescharacteristic
923C2×C8C22×D411yescharacteristic
924C2×C8C22×D411yescharacteristic
925C2×C8C22×D411yescharacteristic
926C2×C8C2511yescharacteristic
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4C2×D811yescharacteristic
971C4⋊C4C2×D811yescharacteristic
972C4⋊C4C2×D811yescharacteristic
973C4⋊C4C2×D811yescharacteristic
974C4⋊C4C2×D811yescharacteristic
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C4⋊C4C2×D811yescharacteristic
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4C2×D811yescharacteristic
1010C22⋊C4C2×D811yescharacteristic
1011C22⋊C4C2×D811yescharacteristic
1012C22⋊C4C2×D811yescharacteristic
1013C22⋊C4C2×D811yescharacteristic
1014C22⋊C4C2×D811yescharacteristic
1015C22⋊C4C2×D811yescharacteristic
1016C22⋊C4C2×D811yescharacteristic
1017C22⋊C4C2×D811yescharacteristic
1018C22⋊C4C2×D811yescharacteristic
1019C42—41no—
1020C42—41no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42C2×D811yescharacteristic
1037C42C2×D811yescharacteristic
1038C42C22×D411yescharacteristic
1039C42C22×D411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D411yescharacteristic
1042C16—21no—
1043C16—21no—
1044C16—21no—
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16C2×#4112yes—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23C22×D811yescharacteristic
1054C23C22×D811yescharacteristic
1055C23C22×D811yescharacteristic
1056Q8—22no—
1057Q8—22no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—82no—
1068Q8—82no—
1069Q8—82no—
1070Q8—161no—
1071Q8—161no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—82no—
1082D4—82no—
1083D4—82no—
1084D4—82no—
1085D4—161no—
1086D4—161no—
1087D4—161no—
1088D4—161no—
1089D4—161no—
1090D4—161no—
1091D4—161no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—82no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—161no—
1120C2×C4—161no—
1121C2×C4—161no—
1122C2×C4—161no—
1123C2×C4—161no—
1124C2×C4—161no—
1125C2×C4—161no—
1126C2×C4—161no—
1127C2×C4—161no—
1128C2×C4C22×D811yescharacteristic
1129C2×C4C22×D811yescharacteristic
1130C2×C4C22×D811yescharacteristic
1131C2×C4C22×D811yescharacteristic
1132C2×C4C22×D811yescharacteristic
1133C2×C4C22×D811yescharacteristic
1134C2×C4C22×D811yescharacteristic
1135C2×C4C22×D811yescharacteristic
1136C2×C4C22×D811yescharacteristic
1137C2×C4C22×D811yescharacteristic
1138C2×C4C22×D811yescharacteristic
1139C2×C4C23×D411yescharacteristic
1140C8—21no—
1141C8—21no—
1142C8—21no—
1143C8—21no—
1144C8—21no—
1145C8—21no—
1146C8—21no—
1147C8C22×#4111yescharacteristic
1148C8#58511yescharacteristic
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—21no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22C23×D811yescharacteristic
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—21no—
1173C4—21no—
1174C4—21no—
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—21no—
1179C4—42no—
1180C4—42no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4D4×#4111yescharacteristic
1193C4#358411yescharacteristic
1194C2—41no—
1195C2—41no—
1196C2—41no—
1197C2—161no—
1198C2—161no—
1199C2—161no—
1200C2D8×#4111yescharacteristic
1201C2#6263511yescharacteristic
1202C2#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. #61488C2semidirect
2. #61473C2semidirect
3. #33961C2semidirect
4. #33950C2semidirect
5. #33944C2semidirect
6. #33938C2semidirect
7. #33924C2semidirect
8. #33918C2semidirect
9. #33918C2semidirect
10. #33888C2semidirect
11. #33883C2semidirect
12. #33879C2semidirect
13. #33876C2semidirect
14. #33868C2semidirect
15. #33867C2semidirect
16. #33844C2semidirect
17. #33843C2semidirect
18. #33843C2semidirect
19. #33750C2semidirect
20. #33743C2semidirect
21. #33739C2semidirect
22. #33687C2semidirect
23. #33685C2semidirect
24. #33681C2semidirect
25. #33679C2semidirect
26. #33668C2semidirect
27. #33662C2semidirect
28. #33483C2semidirect
29. #33455C2semidirect
30. #33455C2semidirect
31. C4×#510C2semidirect

Maximal subgroups

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

subgroupindex
#614882
#614732
#339612
#339502
#339442
#339382
#339242
#339182
#338882
#338832
#338792
#338762
#338682
#338672
#338442
#338432
#337502
#337432
#337392
#336872
#336852
#336812
#336792
#336682
#336622
#334832
#334552
C4×#5102