Finite Group Databasebeta

← #7624183

Subgroups — #7624183

Order 512.

1498 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62267C211yesmaximal, characteristic, complemented
2#61057C211yesmaximal, characteristic, complemented
3#33887C211yesmaximal, characteristic, complemented
4#33882C211yesmaximal, characteristic, complemented
5#33881C211yesmaximal, characteristic, complemented
6#33880C211yesmaximal, characteristic, complemented
7#33869C211yesmaximal, characteristic, complemented
8#33867C211yesmaximal, characteristic, complemented
9#33866C211yesmaximal, characteristic, complemented
10#33864C211yesmaximal, characteristic, complemented
11D4×Q32C211yesmaximal, characteristic, complemented
12#33851C211yesmaximal, characteristic, complemented
13#33849C211yesmaximal, characteristic, complemented
14#33848C211yesmaximal, characteristic, complemented
15#33836C211yesmaximal, characteristic, complemented
16#33835C211yesmaximal, characteristic, complemented
17#33835C211yesmaximal, characteristic, complemented
18#33832C211yesmaximal, characteristic, complemented
19#33791C211yesmaximal, characteristic, complemented
20#33789C211yesmaximal, characteristic, complemented
21#33769C211yesmaximal, characteristic, complemented
22#33767C211yesmaximal, characteristic, complemented
23#33756C211yesmaximal, characteristic, complemented
24#33755C211yesmaximal, characteristic, complemented
25#33684C211yesmaximal, characteristic, complemented
26#33680C211yesmaximal, characteristic, complemented
27#33527C211yesmaximal, characteristic, complemented
28#33525C211yesmaximal, characteristic, complemented
29#33516C211yesmaximal, characteristic, complemented
30C2×#2189C211yesmaximal, characteristic, complemented
31#33491C211yesmaximal, characteristic, complemented
32C2×#578C2211yescharacteristic
33C22×#135C2211yescharacteristic
34#3541—21no—
35#3489—21no—
36C2×#510C2211yescharacteristic, complemented
37C2×#510C2211yescharacteristic, complemented
38C2×#508C2211yescharacteristic
39C2×#508C2211yescharacteristic
40C2×#508C2211yescharacteristic, complemented
41C22×Q32C2211yescharacteristic
42C22×Q32C2211yescharacteristic, complemented
43C22×SD32C2211yescharacteristic
44#3342C2211yescharacteristic, complemented
45#3339C2211yescharacteristic
46#3338C2211yescharacteristic
47#3336C2211yescharacteristic, complemented
48#3320—21no—
49#3316—21no—
50#3315—21no—
51#3313—21no—
52D4×Q16C2211yescharacteristic
53D4×Q16C2211yescharacteristic
54D4×Q16C2211yescharacteristic
55#3285C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3285C2211yescharacteristic, complemented
59#3283C2211yescharacteristic
60#3283C2211yescharacteristic
61#3283C2211yescharacteristic, complemented
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3269—21no—
65#3269—21no—
66#3266—21no—
67#3266—21no—
68#3258—21no—
69#3201—21no—
70#3196—21no—
71#3177C2211yescharacteristic, complemented
72#3175C2211yescharacteristic, complemented
73#3156C2211yescharacteristic
74#3061C2211yescharacteristic
75#3061C2211yescharacteristic, complemented
76#3059C2211yescharacteristic, complemented
77#3050C2211yescharacteristic
78C2×#467C2211yescharacteristic
79C2×#467C2211yescharacteristic
80#3046—21no—
81#3013—21no—
82#3007—21no—
83#2951C2211yescharacteristic
84#2929C2211yescharacteristic
85#2251C2211yescharacteristic, complemented
86#2251C2211yescharacteristic, complemented
87#2249C2211yescharacteristic, complemented
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2243C2211yescharacteristic, complemented
91#2242C2211yescharacteristic, complemented
92#2241C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2237C2211yescharacteristic, complemented
95#2237C2211yescharacteristic, complemented
96#2236C2211yescharacteristic
97#2236C2211yescharacteristic
98#2236C2211yescharacteristic, complemented
99#2236C2211yescharacteristic, complemented
100#2236C2211yescharacteristic, complemented
101#2235C2211yescharacteristic, complemented
102#2234C2211yescharacteristic, complemented
103#2232C2211yescharacteristic, complemented
104#2232C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2228C2211yescharacteristic, complemented
107#2227C2211yescharacteristic, complemented
108#2224C2211yescharacteristic, complemented
109#2220C2211yescharacteristic, complemented
110#2220C2211yescharacteristic, complemented
111#2220C2211yescharacteristic, complemented
112#2219C2211yescharacteristic, complemented
113#2217C2211yescharacteristic
114#2217C2211yescharacteristic
115#2217C2211yescharacteristic, complemented
116#2216C2211yescharacteristic
117#2216C2211yescharacteristic
118#2216C2211yescharacteristic, complemented
119#2216C2211yescharacteristic, complemented
120#2216C2211yescharacteristic, complemented
121#2216C2211yescharacteristic, complemented
122#2216C2211yescharacteristic, complemented
123#2216C2211yescharacteristic, complemented
124#2215C2211yescharacteristic, complemented
125#2211C2211yescharacteristic, complemented
126#2211C2211yescharacteristic, complemented
127#2211C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2210C2211yescharacteristic, complemented
130#2210C2211yescharacteristic, complemented
131#2209C2211yescharacteristic, complemented
132#2209C2211yescharacteristic, complemented
133#2209C2211yescharacteristic, complemented
134#2209C2211yescharacteristic, complemented
135#2208C2211yescharacteristic, complemented
136#2208C2211yescharacteristic, complemented
137#2189C2211yescharacteristic
138#2189C2211yescharacteristic
139#2189C2211yescharacteristic
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic
142#2189C2211yescharacteristic
143#2189C2211yescharacteristic
144#2189C2211yescharacteristic
145#2189C2211yescharacteristic
146#2189C2211yescharacteristic
147#2189C2211yescharacteristic, complemented
148#2189C2211yescharacteristic, complemented
149#2189C2211yescharacteristic, complemented
150#2189C2211yescharacteristic, complemented
151#2189C2211yescharacteristic, complemented
152#2189C2211yescharacteristic, complemented
153#2188C2211yescharacteristic
154#2188C2211yescharacteristic
155#2188C2211yescharacteristic
156#2188C2211yescharacteristic, complemented
157#2188C2211yescharacteristic, complemented
158#2188C2211yescharacteristic, complemented
159#2188C2211yescharacteristic, complemented
160#2188C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2188C2211yescharacteristic, complemented
163#2187C2211yescharacteristic
164#2186C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic, complemented
167#2186C2211yescharacteristic, complemented
168#2185C2211yescharacteristic
169#2185C2211yescharacteristic, complemented
170#2185C2211yescharacteristic, complemented
171#2185C2211yescharacteristic, complemented
172#2184C2211yescharacteristic
173#2176C2211yescharacteristic, complemented
174#2175C2211yescharacteristic, complemented
175#2175C2211yescharacteristic, complemented
176#2175C2211yescharacteristic, complemented
177C4×Q32C2211yescharacteristic, complemented
178C4×Q32C2211yescharacteristic, complemented
179C4×SD32C2211yescharacteristic, complemented
180C4×D16C2211yescharacteristic, complemented
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185D4×C16C2211yescharacteristic
186D4×C16C2211yescharacteristic
187D4×C16C2211yescharacteristic, complemented
188D4×C16C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2164C2211yescharacteristic, complemented
191#2141C2211yescharacteristic, complemented
192#2139C2211yescharacteristic, complemented
193#2138C2211yescharacteristic
194#2138C2211yescharacteristic
195#2138C2211yescharacteristic, complemented
196C2×#358C2211yescharacteristic
197C2×#358C2211yescharacteristic, complemented
198C2×#357C2211yescharacteristic
199#2113C2211yescharacteristic, complemented
200#2113C2211yescharacteristic, complemented
201C2×C22⋊C16C2211yescharacteristic
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
223C22×Q16C2311yescharacteristic
224C22×Q16C2311yescharacteristic
225C22×Q16C2311yescharacteristic
226C22×Q16C2311yescharacteristic
227C22×Q16C2311yescharacteristic
228C22×Q16C2311yescharacteristic
229C22×SD16—21no—
230C22×D8C2311yescharacteristic
231C2×#131C2311yescharacteristic
232C23×C8C2311yescharacteristic
233#563—41no—
234#562—41no—
235#556—21no—
236#554—21no—
237#554—41no—
238#553—21no—
239#553—41no—
240#552—21no—
241D4×Q8—21no—
242D4×Q8—21no—
243D4×Q8—21no—
244#548—21no—
245#548—21no—
246#548—21no—
247#548—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#542—21no—
258#542—41no—
259#541—21no—
260#539—41no—
261#538—41no—
262#538—41no—
263#537—21no—
264#537—21no—
265#537—41no—
266#536—21no—
267#536—21no—
268#536—41no—
269#525—21no—
270#525—41no—
271#525D411yescharacteristic
272C2×C22⋊Q8—21no—
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8—41no—
275#520—21no—
276#510—42no—
277#510—42no—
278#508—42no—
279#508—42no—
280#508—42no—
281C2×Q32—42no—
282C2×Q32—42no—
283C2×Q32C2311yescharacteristic
284C2×Q32C2311yescharacteristic
285C2×Q32C2311yescharacteristic
286C2×Q32C2311yescharacteristic
287C2×Q32C2311yescharacteristic
288C2×Q32C2311yescharacteristic
289C2×Q32C2311yescharacteristic
290C2×Q32C2311yescharacteristic
291C2×Q32C2311yescharacteristic
292C2×Q32C2311yescharacteristic
293C2×Q32C2311yescharacteristic
294C2×Q32C2311yescharacteristic
295C2×SD32—42no—
296C2×SD32C2311yescharacteristic
297C2×SD32C2311yescharacteristic
298C2×SD32C2311yescharacteristic
299C2×SD32C2311yescharacteristic
300C2×SD32C2311yescharacteristic
301C2×SD32C2311yescharacteristic
302C2×SD32C2311yescharacteristic
303C2×SD32C2311yescharacteristic
304C2×SD32C2311yescharacteristic
305C2×SD32C2311yescharacteristic
306C2×D16C2311yescharacteristic
307C2×D16C2311yescharacteristic
308C2×M32C2311yescharacteristic
309C2×M32C2311yescharacteristic
310C22×C16C2311yescharacteristic
311C22×C16C2311yescharacteristic
312C22×C16C2311yescharacteristic
313C22×C16C2311yescharacteristic
314C22×C16C2311yescharacteristic
315C22×C16C2311yescharacteristic
316#500C2311yescharacteristic
317#499C2311yescharacteristic
318#497—21no—
319#497—21no—
320#495C2311yescharacteristic
321#495C2311yescharacteristic
322#495C2311yescharacteristic
323#494C2311yescharacteristic
324#494C2311yescharacteristic
325#494C2311yescharacteristic
326#491—21no—
327#489—21no—
328#485—21no—
329#485—21no—
330#485—21no—
331#484—21no—
332#484—21no—
333#483—21no—
334#482—21no—
335#481—21no—
336#479—21no—
337#478—21no—
338#477—21no—
339#475—21no—
340#470—21no—
341#470—21no—
342#470—21no—
343#468—21no—
344#468—21no—
345#468—21no—
346#468—21no—
347#468—21no—
348#467—21no—
349#467—21no—
350#467—21no—
351#467—21no—
352#467C2311yescharacteristic
353#467C2311yescharacteristic
354#467C2311yescharacteristic
355#467C2311yescharacteristic
356#467C2311yescharacteristic
357#467C2311yescharacteristic
358#467C2311yescharacteristic
359#467C2311yescharacteristic
360#467C2311yescharacteristic
361#467C2311yescharacteristic
362#467C2311yescharacteristic
363#467C2311yescharacteristic
364#467C2311yescharacteristic
365#467C2311yescharacteristic
366#467C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#466C2311yescharacteristic
370#466C2311yescharacteristic
371#466C2311yescharacteristic
372#465—21no—
373#465—21no—
374#464—21no—
375#464—21no—
376#464—21no—
377#464—21no—
378#463—21no—
379#463—21no—
380#462—21no—
381#462—21no—
382#462—21no—
383#461—21no—
384#461—21no—
385#461—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#451—21no—
401#451—21no—
402#450—21no—
403#450—21no—
404#449—21no—
405#449—21no—
406#448—21no—
407#448—21no—
408#448—21no—
409#448—21no—
410#441—21no—
411#440—21no—
412#440—21no—
413#440—21no—
414C4×Q16C2311yescharacteristic
415C4×Q16C2311yescharacteristic
416C4×Q16C2311yescharacteristic
417C4×Q16C2311yescharacteristic
418C4×Q16C2311yescharacteristic
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#419—21no—
437#417—21no—
438#417—21no—
439#417—21no—
440#416—21no—
441C2×#103—21no—
442C2×#103—21no—
443#408D411yescharacteristic
444#407D411yescharacteristic
445#405C2311yescharacteristic
446#367C2311yescharacteristic
447#367C2311yescharacteristic
448#366C2311yescharacteristic
449#366C2311yescharacteristic
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#358C2311yescharacteristic
479#358C2311yescharacteristic
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—41no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—44no—
522C2×#41—82no—
523C2×#41C2×D411yescharacteristic
524C22×Q8—21no—
525C22×Q8—21no—
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—44no—
556#135—44no—
557C2×Q16—22no—
558C2×Q16—22no—
559C2×Q16—22no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16—21no—
564C2×Q16—21no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×Q16—21no—
569C2×Q16—41no—
570C2×Q16—41no—
571C2×Q16—41no—
572C2×Q16—41no—
573C2×Q16—41no—
574C2×Q16—41no—
575C2×Q16—41no—
576C2×Q16—41no—
577C2×Q16—41no—
578C2×Q16C2411yescharacteristic
579C2×Q16C2411yescharacteristic
580C2×Q16C2411yescharacteristic
581C2×Q16C2411yescharacteristic
582C2×Q16C2411yescharacteristic
583C2×Q16C2411yescharacteristic
584C2×Q16C2411yescharacteristic
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—21no—
595C2×SD16—21no—
596C2×SD16—44no—
597C2×D8—22no—
598C2×D8—21no—
599C2×D8—41no—
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—21no—
623C4⋊Q8—41no—
624C4⋊Q8—41no—
625C4⋊Q8—41no—
626C4⋊Q8—41no—
627#126—41no—
628#126—41no—
629#126—41no—
630#126—41no—
631#126—41no—
632#126—41no—
633#126—41no—
634#125—21no—
635#125—41no—
636#125—41no—
637#125—41no—
638#125—41no—
639#124—21no—
640#124—21no—
641#124—21no—
642#124—41no—
643#124—41no—
644#124—41no—
645#124—41no—
646#124—41no—
647#124—41no—
648#124—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#123—41no—
664#123—41no—
665#123D811yescharacteristic
666#123D811yescharacteristic
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—21no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8—21no—
681C22⋊Q8—21no—
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⋊Q8—41no—
691C22⋊Q8—41no—
692C22⋊Q8—41no—
693C22⋊Q8—41no—
694C22⋊Q8—41no—
695C22⋊Q8—41no—
696C22⋊Q8—41no—
697C22⋊Q8—41no—
698C22⋊Q8—41no—
699C22⋊Q8—41no—
700C22⋊Q8—41no—
701C22⋊Q8—41no—
702C22⋊Q8—41no—
703C22⋊Q8D811yescharacteristic
704C22⋊Q8D811yescharacteristic
705#121—21no—
706#121—21no—
707#121—21no—
708#121—21no—
709#121—21no—
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#121—41no—
726#121D811yescharacteristic
727#121D811yescharacteristic
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×Q8—21no—
738C4×Q8—41no—
739C4×D4—21no—
740C4×D4—21no—
741C4×D4—21no—
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#117C2×D411yescharacteristic
764C2×C4⋊C4—21no—
765C2×C4⋊C4—21no—
766C2×C4⋊C4—21no—
767C2×C4⋊C4—41no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777Q32—22no—
778Q32—22no—
779Q32—22no—
780Q32—41no—
781Q32—41no—
782Q32—41no—
783Q32—41no—
784Q32—41no—
785Q32—41no—
786Q32—41no—
787Q32—41no—
788Q32—41no—
789SD32—22no—
790SD32—22no—
791SD32—22no—
792SD32—22no—
793SD32—41no—
794SD32—41no—
795SD32—41no—
796SD32—41no—
797SD32—41no—
798SD32—41no—
799D16—22no—
800D16—41no—
801M32—41no—
802M32—41no—
803C2×C16—41no—
804C2×C16—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#107—21no—
821#107C2411yescharacteristic
822#107C2411yescharacteristic
823#107C2411yescharacteristic
824#107C2411yescharacteristic
825#107C2411yescharacteristic
826#107C2411yescharacteristic
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#103—21no—
851#103—21no—
852#103—21no—
853#103—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—84no—
895#41—84no—
896#41—84no—
897#41—84no—
898#41—84no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—41no—
912C2×Q8—41no—
913C2×Q8—41no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—81no—
919C2×Q8—81no—
920C2×Q8—81no—
921C2×Q8—81no—
922C2×Q8—81no—
923C2×Q8—81no—
924C2×Q8—81no—
925C2×Q8—84no—
926C2×Q8C2×D811yescharacteristic
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—42no—
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—81no—
946C2×D4—84no—
947C2×D4C2×D811yescharacteristic
948C2×D4C2×D811yescharacteristic
949C2×D4C2×D811yescharacteristic
950C2×D4C2×D811yescharacteristic
951C2×D4C2×D811yescharacteristic
952C2×D4C2×D811yescharacteristic
953C2×D4C2×D811yescharacteristic
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—84no—
977C22×C4C2×D811yescharacteristic
978C22×C4C2×D811yescharacteristic
979C22×C4C2×D811yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985Q16—21no—
986Q16—21no—
987Q16—21no—
988Q16—21no—
989Q16—21no—
990Q16—21no—
991Q16—21no—
992Q16—21no—
993Q16—21no—
994Q16—21no—
995Q16—21no—
996Q16—21no—
997Q16—21no—
998Q16—42no—
999Q16—42no—
1000Q16—42no—
1001Q16—42no—
1002Q16—81no—
1003Q16—81no—
1004Q16—81no—
1005Q16—81no—
1006Q16—81no—
1007Q16H(5,𝔽2)12yes—
1008SD16—24no—
1009SD16—42no—
1010SD16—42no—
1011SD16—42no—
1012SD16—42no—
1013SD16—42no—
1014SD16—81no—
1015SD16—81no—
1016SD16—81no—
1017SD16—81no—
1018SD16—81no—
1019D8—21no—
1020D8—21no—
1021D8—21no—
1022D8—21no—
1023D8—21no—
1024D8—42no—
1025D8H(5,𝔽2)12yes—
1026M16—41no—
1027M16—41no—
1028M16—41no—
1029M16—41no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—41no—
1041C2×C8—41no—
1042C2×C8—41no—
1043C2×C8C22×D411yescharacteristic
1044C2×C8C22×D411yescharacteristic
1045C2×C8C22×D411yescharacteristic
1046C2×C8C22×D411yescharacteristic
1047C2×C8C22×D411yescharacteristic
1048C2×C8C22×D411yescharacteristic
1049C2×C8C22×D411yescharacteristic
1050C2×C8C2511yescharacteristic
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
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⋊C4C2×D811yescharacteristic
1090C4⋊C4C2×D811yescharacteristic
1091C4⋊C4C2×D811yescharacteristic
1092C4⋊C4C2×D811yescharacteristic
1093C4⋊C4C2×D811yescharacteristic
1094C4⋊C4C2×D811yescharacteristic
1095C22⋊C4—41no—
1096C22⋊C4—41no—
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⋊C4C2×D811yescharacteristic
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
1136C42—41no—
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—22no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—82no—
1160C23—82no—
1161C23—161no—
1162C23C22×D811yescharacteristic
1163C23C22×D811yescharacteristic
1164C23C22×D811yescharacteristic
1165C23C22×D811yescharacteristic
1166C23C22×D811yescharacteristic
1167Q8—22no—
1168Q8—41no—
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—41no—
1182Q8—82no—
1183Q8—82no—
1184Q8—82no—
1185Q8—82no—
1186Q8—161no—
1187Q8—161no—
1188Q8—161no—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—44no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—82no—
1207D4—82no—
1208D4—82no—
1209D4—82no—
1210D4—161no—
1211D4—161no—
1212D4—161no—
1213D4—161no—
1214D4—161no—
1215D4—161no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—44no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
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—82no—
1244C2×C4—82no—
1245C2×C4—82no—
1246C2×C4—82no—
1247C2×C4—82no—
1248C2×C4—82no—
1249C2×C4—82no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—161no—
1253C2×C4—161no—
1254C2×C4—161no—
1255C2×C4—161no—
1256C2×C4—161no—
1257C2×C4—161no—
1258C2×C4—161no—
1259C2×C4—161no—
1260C2×C4—161no—
1261C2×C4—161no—
1262C2×C4C22×D811yescharacteristic
1263C2×C4C22×D811yescharacteristic
1264C2×C4C22×D811yescharacteristic
1265C2×C4C22×D811yescharacteristic
1266C2×C4C22×D811yescharacteristic
1267C2×C4C22×D811yescharacteristic
1268C2×C4C22×D811yescharacteristic
1269C2×C4C22×D811yescharacteristic
1270C2×C4C22×D811yescharacteristic
1271C2×C4C23×D411yescharacteristic
1272C8—21no—
1273C8—21no—
1274C8—21no—
1275C8—21no—
1276C8—21no—
1277C8—21no—
1278C8—21no—
1279C8C2×H(5,𝔽2)11yescharacteristic
1280C8C2×H(5,𝔽2)11yescharacteristic
1281C22—21no—
1282C22—21no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—21no—
1287C22—21no—
1288C22—21no—
1289C22—21no—
1290C22—21no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—21no—
1295C22—42no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—164no—
1306C22#341712yes—
1307C22C23×D811yescharacteristic
1308C4—21no—
1309C4—21no—
1310C4—21no—
1311C4—21no—
1312C4—21no—
1313C4—21no—
1314C4—21no—
1315C4—21no—
1316C4—21no—
1317C4—42no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4#348411yescharacteristic
1331C4#358511yescharacteristic
1332C2—22no—
1333C2—41no—
1334C2—41no—
1335C2—41no—
1336C2—41no—
1337C2—82no—
1338C2—161no—
1339C2—161no—
1340C2#6155911yescharacteristic
1341C2C2×#341711yescharacteristic
1342C2#6263511yescharacteristic
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. #62267C2semidirect
2. #61057C2semidirect
3. #33887C2semidirect
4. #33882C2semidirect
5. #33881C2semidirect
6. #33880C2semidirect
7. #33869C2semidirect
8. #33867C2semidirect
9. #33866C2semidirect
10. #33864C2semidirect
11. D4×Q32C2semidirect
12. #33851C2semidirect
13. #33849C2semidirect
14. #33848C2semidirect
15. #33836C2semidirect
16. #33835C2semidirect
17. #33835C2semidirect
18. #33832C2semidirect
19. #33791C2semidirect
20. #33789C2semidirect
21. #33769C2semidirect
22. #33767C2semidirect
23. #33756C2semidirect
24. #33755C2semidirect
25. #33684C2semidirect
26. #33680C2semidirect
27. #33527C2semidirect
28. #33525C2semidirect
29. #33516C2semidirect
30. C2×#2189C2semidirect
31. #33491C2semidirect
36. C2×#510C22semidirect
37. C2×#510C22semidirect
40. C2×#508C22semidirect
42. C22×Q32C22semidirect
44. #3342C22semidirect
47. #3336C22semidirect
58. #3285C22semidirect
61. #3283C22semidirect
71. #3177C22semidirect
72. #3175C22semidirect
75. #3061C22semidirect
76. #3059C22semidirect
85. #2251C22semidirect
86. #2251C22semidirect
87. #2249C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
90. #2243C22semidirect
91. #2242C22semidirect
92. #2241C22semidirect
93. #2237C22semidirect
94. #2237C22semidirect
95. #2237C22semidirect
98. #2236C22semidirect
99. #2236C22semidirect
100. #2236C22semidirect
101. #2235C22semidirect
102. #2234C22semidirect
103. #2232C22semidirect
104. #2232C22semidirect
105. #2229C22semidirect
106. #2228C22semidirect
107. #2227C22semidirect
108. #2224C22semidirect
109. #2220C22semidirect
110. #2220C22semidirect
111. #2220C22semidirect
112. #2219C22semidirect
115. #2217C22semidirect
118. #2216C22semidirect
119. #2216C22semidirect
120. #2216C22semidirect
121. #2216C22semidirect
122. #2216C22semidirect
123. #2216C22semidirect
124. #2215C22semidirect
125. #2211C22semidirect
126. #2211C22semidirect
127. #2211C22semidirect
128. #2211C22semidirect
129. #2210C22semidirect
130. #2210C22semidirect
131. #2209C22semidirect
132. #2209C22semidirect
133. #2209C22semidirect
134. #2209C22semidirect
135. #2208C22semidirect
136. #2208C22semidirect
147. #2189C22semidirect
148. #2189C22semidirect
149. #2189C22semidirect
150. #2189C22semidirect
151. #2189C22semidirect
152. #2189C22semidirect
156. #2188C22semidirect
157. #2188C22semidirect
158. #2188C22semidirect
159. #2188C22semidirect
160. #2188C22semidirect
161. #2188C22semidirect
162. #2188C22semidirect
166. #2186C22semidirect
167. #2186C22semidirect
169. #2185C22semidirect
170. #2185C22semidirect
171. #2185C22semidirect
173. #2176C22semidirect
174. #2175C22semidirect
175. #2175C22semidirect
176. #2175C22semidirect
177. C4×Q32C22semidirect
178. C4×Q32C22semidirect
179. C4×SD32C22semidirect
180. C4×D16C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
187. D4×C16C22semidirect
188. D4×C16C22semidirect
189. #2164C22semidirect
190. #2164C22semidirect
191. #2141C22semidirect
192. #2139C22semidirect
195. #2138C22semidirect
197. 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
#622672
#610572
#338872
#338822
#338812
#338802
#338692
#338672
#338662
#338642
D4×Q322
#338512
#338492
#338482
#338362
#338352
#338322
#337912
#337892
#337692
#337672
#337562
#337552
#336842
#336802
#335272
#335252
#335162
C2×#21892
#334912