Finite Group Databasebeta

← #7624093

Subgroups — #7624093

Order 512.

1295 conjugacy classes of subgroups.

The subgroup lattice has 1221 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61487C211yesmaximal, characteristic, complemented
2#61482C211yesmaximal, characteristic, complemented
3#33969C211yesmaximal, characteristic, complemented
4#33951C211yesmaximal, characteristic, complemented
5#33943C211yesmaximal, characteristic, complemented
6#33934C211yesmaximal, characteristic, complemented
7#33923C211yesmaximal, characteristic, complemented
8#33913C211yesmaximal, characteristic, complemented
9#33910C211yesmaximal, characteristic, complemented
10#33898C211yesmaximal, characteristic, complemented
11#33889C211yesmaximal, characteristic, complemented
12#33882C211yesmaximal, characteristic, complemented
13#33881C211yesmaximal, characteristic, complemented
14#33878C211yesmaximal, characteristic, complemented
15#33873C211yesmaximal, characteristic, complemented
16#33839C211yesmaximal, characteristic, complemented
17#33833C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33745C211yesmaximal, characteristic, complemented
20#33742C211yesmaximal, characteristic, complemented
21#33738C211yesmaximal, characteristic, complemented
22#33685C211yesmaximal, characteristic, complemented
23#33684C211yesmaximal, characteristic, complemented
24#33680C211yesmaximal, characteristic, complemented
25#33678C211yesmaximal, characteristic, complemented
26#33676C211yesmaximal, characteristic, complemented
27#33674C211yesmaximal, characteristic, complemented
28#33481C211yesmaximal, characteristic, complemented
29#33459C211yesmaximal, characteristic, complemented
30#33454C211yesmaximal, characteristic, complemented
31C4×#509C211yesmaximal, characteristic, complemented
32#3521—21no—
33#3520—21no—
34C2×#509C2211yescharacteristic
35C2×#509C2211yescharacteristic
36C2×#508C2211yescharacteristic
37#3393C2211yescharacteristic, complemented
38#3393C2211yescharacteristic, complemented
39#3380C2211yescharacteristic, complemented
40Q8×D8C2211yescharacteristic, complemented
41#3376—21no—
42#3367—21no—
43#3342C2211yescharacteristic
44#3339C2211yescharacteristic
45#3338C2211yescharacteristic
46#3338C2211yescharacteristic, complemented
47#3336C2211yescharacteristic, complemented
48#3334C2211yescharacteristic
49#3330—21no—
50#3323—21no—
51#3314—21no—
52#3314—21no—
53#3311—21no—
54#3307—21no—
55#3283C2211yescharacteristic
56#3283C2211yescharacteristic
57#3280C2211yescharacteristic
58#3280C2211yescharacteristic
59#3280C2211yescharacteristic, complemented
60#3280C2211yescharacteristic, complemented
61#3177C2211yescharacteristic, complemented
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic, complemented
64#3175C2211yescharacteristic, complemented
65#3170C2211yescharacteristic, complemented
66#3168C2211yescharacteristic
67#3125—21no—
68#3124—21no—
69#3124—21no—
70#3123—21no—
71#3111—21no—
72#3110—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic, complemented
76#2951C2211yescharacteristic, complemented
77#2948C2211yescharacteristic, complemented
78C4×#135C2211yescharacteristic
79C2×C4×D8C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2254C2211yescharacteristic, complemented
83#2251C2211yescharacteristic, complemented
84#2251C2211yescharacteristic, complemented
85#2249C2211yescharacteristic
86#2245C2211yescharacteristic, complemented
87#2243C2211yescharacteristic, complemented
88#2243C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2242C2211yescharacteristic, complemented
91#2241C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2236C2211yescharacteristic, complemented
96#2236C2211yescharacteristic, complemented
97#2235C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2235C2211yescharacteristic, complemented
100#2234C2211yescharacteristic
101#2233C2211yescharacteristic, complemented
102#2232C2211yescharacteristic
103#2232C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2228C2211yescharacteristic, complemented
106#2228C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2227C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2226C2211yescharacteristic, complemented
111#2226C2211yescharacteristic, complemented
112#2226C2211yescharacteristic, complemented
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic, complemented
115#2224C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic
119#2219C2211yescharacteristic, complemented
120#2219C2211yescharacteristic, complemented
121#2219C2211yescharacteristic, complemented
122#2219C2211yescharacteristic, complemented
123#2218C2211yescharacteristic
124#2217C2211yescharacteristic
125#2217C2211yescharacteristic, complemented
126#2217C2211yescharacteristic, complemented
127#2216C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2210C2211yescharacteristic
131#2210C2211yescharacteristic
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic
135#2210C2211yescharacteristic
136#2209C2211yescharacteristic, complemented
137#2209C2211yescharacteristic, complemented
138#2208C2211yescharacteristic, complemented
139#2208C2211yescharacteristic, complemented
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2189C2211yescharacteristic
143#2189C2211yescharacteristic
144#2189C2211yescharacteristic, complemented
145#2189C2211yescharacteristic, complemented
146#2187C2211yescharacteristic, complemented
147#2187C2211yescharacteristic, complemented
148#2186C2211yescharacteristic
149#2186C2211yescharacteristic
150#2184C2211yescharacteristic
151#2184C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2177C2211yescharacteristic
155#2177C2211yescharacteristic
156#2177C2211yescharacteristic
157#2177C2211yescharacteristic
158#2177C2211yescharacteristic
159#2176C2211yescharacteristic, complemented
160#2176C2211yescharacteristic, complemented
161#2175C2211yescharacteristic, complemented
162#2175C2211yescharacteristic, complemented
163#2175C2211yescharacteristic, complemented
164#2175C2211yescharacteristic, complemented
165#2175C2211yescharacteristic, complemented
166#2175C2211yescharacteristic, complemented
167#2175C2211yescharacteristic, complemented
168#2175C2211yescharacteristic, complemented
169#2175C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×Q32C2211yescharacteristic, complemented
172C4×Q32C2211yescharacteristic, complemented
173C4×SD32C2211yescharacteristic, complemented
174C4×SD32C2211yescharacteristic, complemented
175C4×SD32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic, complemented
177C4×SD32C2211yescharacteristic, complemented
178C4×D16C2211yescharacteristic
179C4×D16C2211yescharacteristic
180C4×D16C2211yescharacteristic
181C4×D16C2211yescharacteristic
182#2169C2211yescharacteristic
183#2169C2211yescharacteristic, complemented
184#2168C2211yescharacteristic
185#2168C2211yescharacteristic, complemented
186#2168C2211yescharacteristic, complemented
187#2168C2211yescharacteristic, complemented
188#2164C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2163C2211yescharacteristic, complemented
191#2159C2211yescharacteristic, complemented
192#2159C2211yescharacteristic, complemented
193C2×#366C2211yescharacteristic, complemented
194#2140C2211yescharacteristic, complemented
195#2139C2211yescharacteristic
196#2139C2211yescharacteristic, complemented
197#2139C2211yescharacteristic, complemented
198#2138C2211yescharacteristic
199C2×#357C2211yescharacteristic, complemented
200#2108C2211yescharacteristic, complemented
201#2108C2211yescharacteristic, complemented
202C4×M32C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#556—21no—
210#556—21no—
211#556—21no—
212#554—21no—
213#554—21no—
214#554—21no—
215#553—21no—
216#553—41no—
217#552—21no—
218#552—41no—
219#552—41no—
220#551—41no—
221#551—41no—
222#551—41no—
223#551—41no—
224D4×Q8—21no—
225#548—41no—
226#547—21no—
227#547—21no—
228#547—21no—
229#546—21no—
230#546—21no—
231#546—21no—
232#546—21no—
233#542—21no—
234#542—21no—
235#542—21no—
236#541—21no—
237#539—41no—
238#539—41no—
239#539—41no—
240#538—41no—
241#533—21no—
242#529—21no—
243#529—41no—
244#529D411yescharacteristic
245C2×#126—41no—
246#525—41no—
247C2×C22⋊Q8—41no—
248#520—21no—
249#520—21no—
250#520—21no—
251#518—21no—
252C4×#41—21no—
253C2×C4×D4—21no—
254#509—24no—
255#509—24no—
256#508—24no—
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×D16C2311yescharacteristic
270C2×D16C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C2×M32C2311yescharacteristic
276C2×M32C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#494C2311yescharacteristic
290#494C2311yescharacteristic
291#491—21no—
292#489—21no—
293#489—21no—
294#489—21no—
295#488—21no—
296#487—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#484—21no—
301#484—21no—
302#484—21no—
303#484—21no—
304#483—21no—
305#482—21no—
306#481—21no—
307#480—21no—
308#480—21no—
309#479—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#477—21no—
314#477—21no—
315#476—21no—
316#475—21no—
317#474—21no—
318#474—21no—
319#474—21no—
320#474—21no—
321#470—21no—
322#468—21no—
323#468—21no—
324#468—21no—
325#467—21no—
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#466C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#463—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#461—21no—
348#461—21no—
349#461—21no—
350#461—21no—
351#452—21no—
352#452—21no—
353#452—21no—
354#452—21no—
355#450—21no—
356#450—21no—
357#450—21no—
358#450—21no—
359#449—21no—
360#449—21no—
361#449—21no—
362#449—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#442—21no—
366#442—21no—
367#441—21no—
368#440—21no—
369#440—21no—
370#440—21no—
371#440—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16—21no—
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×Q16C2311yescharacteristic
384C4×Q16C2311yescharacteristic
385C4×Q16C2311yescharacteristic
386C4×SD16—21no—
387C4×SD16—21no—
388C4×SD16—21no—
389C4×D8—21no—
390C4×D8—21no—
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
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
414C2×#107C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#418—21no—
419#417—21no—
420#417—21no—
421#417—21no—
422#416—21no—
423C2×#102—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#357C2311yescharacteristic
466#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
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
491#346C2311yescharacteristic
492#346C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—41no—
502C22×Q8—41no—
503C22×D4—21no—
504C22×D4—21no—
505C23×C4—41no—
506#135—22no—
507#135—22no—
508#135—22no—
509#135—22no—
510#135—41no—
511#135—41no—
512#135—41no—
513#135—41no—
514C2×Q16—21no—
515C2×Q16—21no—
516C2×Q16C2411yescharacteristic
517C2×Q16C2411yescharacteristic
518C2×Q16C2411yescharacteristic
519C2×Q16C2411yescharacteristic
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—21no—
523C2×SD16—21no—
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—21no—
531C2×D8—21no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8C2411yescharacteristic
535C2×D8C2411yescharacteristic
536C2×D8C2411yescharacteristic
537C2×D8C2411yescharacteristic
538C2×M16C2×D411yescharacteristic
539C2×M16C2×D411yescharacteristic
540C22×C8C2×D411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
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#126—41no—
562#126—41no—
563#126—41no—
564#126D811yescharacteristic
565#126D811yescharacteristic
566#125—21no—
567#125—21no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125D811yescharacteristic
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124D811yescharacteristic
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123D811yescharacteristic
601#123D811yescharacteristic
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8D811yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121—41no—
639#121D811yescharacteristic
640#120—41no—
641#120—41no—
642#120—41no—
643#120—41no—
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—41no—
653C4×Q8—41no—
654C4×Q8C2×D411yescharacteristic
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
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×D4C2×D411yescharacteristic
684C4×D4C2×D411yescharacteristic
685C4×D4C2×D411yescharacteristic
686#117—21no—
687#117—21no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117C2×D411yescharacteristic
698#117C2×D411yescharacteristic
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—41no—
720Q32—41no—
721Q32—41no—
722SD32—22no—
723SD32—22no—
724SD32—22no—
725SD32—22no—
726SD32—22no—
727SD32—22no—
728SD32—41no—
729SD32—41no—
730D16—22no—
731D16—22no—
732D16—41no—
733D16#4114yescomplemented
734M32—22no—
735M32—22no—
736M32—41no—
737M32—41no—
738C2×C16—22no—
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#107—21no—
754#107—21no—
755#107—21no—
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#107C2411yescharacteristic
763#107C2411yescharacteristic
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#102—21no—
791#102—21no—
792#102—21no—
793#102—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
822C24—41no—
823C24—41no—
824#41—42no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—81no—
829#41—81no—
830#41—81no—
831#41—81no—
832#41—162no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—162no—
842C2×Q8C2×D811yescharacteristic
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—42no—
848C2×D4—42no—
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×D4—81no—
860C2×D4—81no—
861C2×D4C2×D811yescharacteristic
862C2×D4C2×D811yescharacteristic
863C2×D4C2×D811yescharacteristic
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×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—162no—
885C22×C4C2×D811yescharacteristic
886C22×C4C2×D811yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890Q16—21no—
891Q16—21no—
892Q16—21no—
893Q16—21no—
894Q16—21no—
895Q16—21no—
896Q16—21no—
897Q16—21no—
898Q16—81no—
899Q16—81no—
900SD16—42no—
901SD16—42no—
902SD16—42no—
903SD16—42no—
904SD16—81no—
905SD16—81no—
906SD16—81no—
907SD16—81no—
908D8—21no—
909D8—21no—
910D8—21no—
911D8—21no—
912D8—21no—
913D8—21no—
914D8—42no—
915D8—42no—
916D8C2×#4112yes—
917D8C2×#4112yes—
918M16—41no—
919M16—41no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—41no—
927C2×C8C22×D411yescharacteristic
928C2×C8C22×D411yescharacteristic
929C2×C8C22×D411yescharacteristic
930C2×C8C22×D411yescharacteristic
931C2×C8C22×D411yescharacteristic
932C2×C8C22×D411yescharacteristic
933C2×C8C22×D411yescharacteristic
934C2×C8C2511yescharacteristic
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
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⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C4⋊C4C2×D811yescharacteristic
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4C2×D811yescharacteristic
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C22⋊C4C2×D811yescharacteristic
1024C22⋊C4C2×D811yescharacteristic
1025C22⋊C4C2×D811yescharacteristic
1026C22⋊C4C2×D811yescharacteristic
1027C22⋊C4C2×D811yescharacteristic
1028C22⋊C4C2×D811yescharacteristic
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42C2×D811yescharacteristic
1040C42C2×D811yescharacteristic
1041C42C22×D411yescharacteristic
1042C42C22×D411yescharacteristic
1043C42C22×D411yescharacteristic
1044C42C22×D411yescharacteristic
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16—21no—
1050C16—21no—
1051C16—21no—
1052C16C2×#4112yes—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—82no—
1058C23—82no—
1059C23—82no—
1060C23—161no—
1061C23—161no—
1062C23—161no—
1063C23C22×D811yescharacteristic
1064C23C22×D811yescharacteristic
1065C23C22×D811yescharacteristic
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—82no—
1076Q8—161no—
1077Q8—161no—
1078Q8—161no—
1079D4—22no—
1080D4—22no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—82no—
1091D4—82no—
1092D4—82no—
1093D4—82no—
1094D4—82no—
1095D4—82no—
1096D4—161no—
1097D4—161no—
1098D4—161no—
1099D4—161no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—82no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—161no—
1127C2×C4—161no—
1128C2×C4—161no—
1129C2×C4—161no—
1130C2×C4—161no—
1131C2×C4—161no—
1132C2×C4—161no—
1133C2×C4—161no—
1134C2×C4—161no—
1135C2×C4—161no—
1136C2×C4—161no—
1137C2×C4—161no—
1138C2×C4—161no—
1139C2×C4—161no—
1140C2×C4C22×D811yescharacteristic
1141C2×C4C22×D811yescharacteristic
1142C2×C4C22×D811yescharacteristic
1143C2×C4C22×D811yescharacteristic
1144C2×C4C22×D811yescharacteristic
1145C2×C4C22×D811yescharacteristic
1146C2×C4C22×D811yescharacteristic
1147C2×C4C22×D811yescharacteristic
1148C2×C4C22×D811yescharacteristic
1149C2×C4C22×D811yescharacteristic
1150C2×C4C22×D811yescharacteristic
1151C2×C4C23×D411yescharacteristic
1152C8—21no—
1153C8—21no—
1154C8—21no—
1155C8—21no—
1156C8—21no—
1157C8—21no—
1158C8—21no—
1159C8C22×#4111yescharacteristic
1160C8#58511yescharacteristic
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—42no—
1171C22—42no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—164no—
1183C22—322no—
1184C22C23×D811yescharacteristic
1185C4—21no—
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—21no—
1190C4—21no—
1191C4—21no—
1192C4—21no—
1193C4—21no—
1194C4—21no—
1195C4—21no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4D4×#4111yescharacteristic
1209C4#358411yescharacteristic
1210C2—41no—
1211C2—41no—
1212C2—41no—
1213C2—82no—
1214C2—82no—
1215C2—161no—
1216C2—161no—
1217C2D8×#4111yescharacteristic
1218C2#6263611yescharacteristic
1219C2#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. #61487C2semidirect
2. #61482C2semidirect
3. #33969C2semidirect
4. #33951C2semidirect
5. #33943C2semidirect
6. #33934C2semidirect
7. #33923C2semidirect
8. #33913C2semidirect
9. #33910C2semidirect
10. #33898C2semidirect
11. #33889C2semidirect
12. #33882C2semidirect
13. #33881C2semidirect
14. #33878C2semidirect
15. #33873C2semidirect
16. #33839C2semidirect
17. #33833C2semidirect
18. #33833C2semidirect
19. #33745C2semidirect
20. #33742C2semidirect
21. #33738C2semidirect
22. #33685C2semidirect
23. #33684C2semidirect
24. #33680C2semidirect
25. #33678C2semidirect
26. #33676C2semidirect
27. #33674C2semidirect
28. #33481C2semidirect
29. #33459C2semidirect
30. #33454C2semidirect
31. C4×#509C2semidirect
37. #3393C22semidirect
38. #3393C22semidirect
39. #3380C22semidirect
40. Q8×D8C22semidirect
46. #3338C22semidirect
47. #3336C22semidirect
59. #3280C22semidirect
60. #3280C22semidirect
61. #3177C22semidirect
63. #3175C22semidirect
64. #3175C22semidirect
65. #3170C22semidirect
75. #2951C22semidirect
76. #2951C22semidirect
77. #2948C22semidirect
79. C2×C4×D8C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2254C22semidirect
83. #2251C22semidirect
84. #2251C22semidirect
86. #2245C22semidirect
87. #2243C22semidirect
88. #2243C22semidirect
89. #2243C22semidirect
90. #2242C22semidirect
91. #2241C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2236C22semidirect
96. #2236C22semidirect
97. #2235C22semidirect
98. #2235C22semidirect
99. #2235C22semidirect
101. #2233C22semidirect
103. #2232C22semidirect
104. #2229C22semidirect
105. #2228C22semidirect
106. #2228C22semidirect
107. #2228C22semidirect
108. #2227C22semidirect
109. #2227C22semidirect
110. #2226C22semidirect
111. #2226C22semidirect
112. #2226C22semidirect
113. #2225C22semidirect
114. #2224C22semidirect
115. #2224C22semidirect
119. #2219C22semidirect
120. #2219C22semidirect
121. #2219C22semidirect
122. #2219C22semidirect
125. #2217C22semidirect
126. #2217C22semidirect
127. #2216C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
136. #2209C22semidirect
137. #2209C22semidirect
138. #2208C22semidirect
139. #2208C22semidirect
144. #2189C22semidirect
145. #2189C22semidirect
146. #2187C22semidirect
147. #2187C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
159. #2176C22semidirect
160. #2176C22semidirect
161. #2175C22semidirect
162. #2175C22semidirect
163. #2175C22semidirect
164. #2175C22semidirect
165. #2175C22semidirect
166. #2175C22semidirect
167. #2175C22semidirect
168. #2175C22semidirect
169. #2175C22semidirect
170. C4×Q32C22semidirect
171. C4×Q32C22semidirect
172. C4×Q32C22semidirect
173. C4×SD32C22semidirect
174. C4×SD32C22semidirect
175. C4×SD32C22semidirect
176. C4×SD32C22semidirect
177. C4×SD32C22semidirect
183. #2169C22semidirect
185. #2168C22semidirect
186. #2168C22semidirect
187. #2168C22semidirect
188. #2164C22semidirect
189. #2164C22semidirect
190. #2163C22semidirect
191. #2159C22semidirect
192. #2159C22semidirect
193. C2×#366C22semidirect
194. #2140C22semidirect
196. #2139C22semidirect
197. #2139C22semidirect
199. C2×#357C22semidirect
200. #2108C22semidirect
201. #2108C22semidirect
202. C4×M32C22semidirect
733. D16#41semidirect

Maximal subgroups

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

subgroupindex
#614872
#614822
#339692
#339512
#339432
#339342
#339232
#339132
#339102
#338982
#338892
#338822
#338812
#338782
#338732
#338392
#338332
#337452
#337422
#337382
#336852
#336842
#336802
#336782
#336762
#336742
#334812
#334592
#334542
C4×#5092