Finite Group Databasebeta

← #7624472

Subgroups — #7624472

Order 512.

1215 conjugacy classes of subgroups.

The subgroup lattice has 1195 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62380C211yesmaximal, characteristic, complemented
2#61413C211yesmaximal, characteristic, complemented
3#33969C211yesmaximal, characteristic, complemented
4#33969C211yesmaximal, characteristic, complemented
5#33968C211yesmaximal, characteristic, complemented
6#33968C211yesmaximal, characteristic, complemented
7#33967C211yesmaximal, characteristic, complemented
8#33965C211yesmaximal, characteristic, complemented
9#33961C211yesmaximal, characteristic, complemented
10#33960C211yesmaximal, characteristic, complemented
11#33944C211yesmaximal, characteristic, complemented
12#33943C211yesmaximal, characteristic, complemented
13#33942C211yesmaximal, characteristic, complemented
14#33938C211yesmaximal, characteristic, complemented
15#33937C211yesmaximal, characteristic, complemented
16#33936C211yesmaximal, characteristic, complemented
17#33932C211yesmaximal, characteristic, complemented
18#33931C211yesmaximal, characteristic, complemented
19#33791C211yesmaximal, characteristic, complemented
20#33790C211yesmaximal, characteristic
21#33789C211yesmaximal, characteristic, complemented
22#33788C211yesmaximal, characteristic, complemented
23#33781C211yesmaximal, characteristic, complemented
24#33777C211yesmaximal, characteristic, complemented
25#33687C211yesmaximal, characteristic, complemented
26#33683C211yesmaximal, characteristic, complemented
27#33681C211yesmaximal, characteristic, complemented
28#33678C211yesmaximal, characteristic, complemented
29#33671C211yesmaximal, characteristic, complemented
30#33667C211yesmaximal, characteristic, complemented
31#33499C211yesmaximal, characteristic, complemented
32#3555—21no—
33#3510—21no—
34#3401—21no—
35#3401—21no—
36#3401—21no—
37#3401—21no—
38#3396C2211yescharacteristic
39#3396C2211yescharacteristic
40#3396C2211yescharacteristic
41#3396C2211yescharacteristic
42#3395C2211yescharacteristic, complemented
43#3393C2211yescharacteristic
44#3393C2211yescharacteristic
45#3393C2211yescharacteristic
46#3393C2211yescharacteristic
47#3393C2211yescharacteristic, complemented
48#3393C2211yescharacteristic, complemented
49#3393C2211yescharacteristic, complemented
50#3383C2211yescharacteristic, complemented
51#3383C2211yescharacteristic, complemented
52Q8×Q16C2211yescharacteristic, complemented
53#3380C2211yescharacteristic, complemented
54#3377—21no—
55#3377—21no—
56#3372—21no—
57#3369—21no—
58#3258—21no—
59#3258—21no—
60#3252—21no—
61#3177C2211yescharacteristic
62#3177C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic
66#3168C2211yescharacteristic
67#3156C2211yescharacteristic
68#3155C2211yescharacteristic
69C2×#495C2211yescharacteristic
70#3043—21no—
71#3042—21no—
72#3040—21no—
73#2960C2211yescharacteristic
74#2950C2211yescharacteristic
75#2948C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2251C2211yescharacteristic
78#2251C2211yescharacteristic
79#2251C2211yescharacteristic
80#2251C2211yescharacteristic, complemented
81#2251C2211yescharacteristic, complemented
82#2250C2211yescharacteristic
83#2249C2211yescharacteristic
84#2249C2211yescharacteristic
85#2249C2211yescharacteristic
86#2249C2211yescharacteristic, complemented
87#2248C2211yescharacteristic
88#2247C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2244C2211yescharacteristic
91#2243C2211yescharacteristic
92#2243C2211yescharacteristic
93#2243C2211yescharacteristic
94#2243C2211yescharacteristic, complemented
95#2242C2211yescharacteristic
96#2242C2211yescharacteristic
97#2242C2211yescharacteristic
98#2242C2211yescharacteristic, complemented
99#2241C2211yescharacteristic, complemented
100#2240C2211yescharacteristic
101#2237C2211yescharacteristic
102#2237C2211yescharacteristic
103#2237C2211yescharacteristic
104#2234C2211yescharacteristic
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2228C2211yescharacteristic
109#2228C2211yescharacteristic
110#2228C2211yescharacteristic, complemented
111#2227C2211yescharacteristic, complemented
112#2226C2211yescharacteristic
113#2225C2211yescharacteristic, complemented
114#2225C2211yescharacteristic, complemented
115#2224C2211yescharacteristic
116#2224C2211yescharacteristic, complemented
117#2211C2211yescharacteristic
118#2211C2211yescharacteristic
119#2211C2211yescharacteristic
120#2211C2211yescharacteristic
121#2211C2211yescharacteristic
122#2211C2211yescharacteristic
123#2211C2211yescharacteristic
124#2211C2211yescharacteristic
125#2211C2211yescharacteristic
126#2211C2211yescharacteristic, complemented
127#2211C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2211C2211yescharacteristic, complemented
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic
135#2210C2211yescharacteristic
136#2210C2211yescharacteristic
137#2210C2211yescharacteristic, complemented
138#2210C2211yescharacteristic, complemented
139#2209C2211yescharacteristic, complemented
140#2209C2211yescharacteristic, complemented
141#2209C2211yescharacteristic, complemented
142#2209C2211yescharacteristic, complemented
143#2209C2211yescharacteristic, complemented
144#2209C2211yescharacteristic, complemented
145#2208C2211yescharacteristic
146#2208C2211yescharacteristic
147#2208C2211yescharacteristic, complemented
148#2208C2211yescharacteristic, complemented
149#2207C2211yescharacteristic
150#2207C2211yescharacteristic
151#2207C2211yescharacteristic
152#2206C2211yescharacteristic
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2189C2211yescharacteristic
156#2188C2211yescharacteristic
157#2188C2211yescharacteristic
158#2188C2211yescharacteristic
159#2187C2211yescharacteristic
160#2187C2211yescharacteristic
161#2187C2211yescharacteristic
162#2186C2211yescharacteristic
163#2185C2211yescharacteristic
164#2184C2211yescharacteristic
165#2183C2211yescharacteristic, complemented
166#2183C2211yescharacteristic, complemented
167#2183C2211yescharacteristic, complemented
168#2183C2211yescharacteristic, complemented
169#2183C2211yescharacteristic, complemented
170#2183C2211yescharacteristic, complemented
171Q8×C16C2211yescharacteristic, complemented
172Q8×C16C2211yescharacteristic, complemented
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic, complemented
175#2176C2211yescharacteristic, complemented
176#2176C2211yescharacteristic, complemented
177#2176C2211yescharacteristic, complemented
178#2176C2211yescharacteristic, complemented
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic, complemented
183#2175C2211yescharacteristic, complemented
184#2175C2211yescharacteristic, complemented
185C4×Q32C2211yescharacteristic, complemented
186C4×Q32C2211yescharacteristic, complemented
187C4×Q32C2211yescharacteristic, complemented
188C4×Q32C2211yescharacteristic, complemented
189C4×Q32C2211yescharacteristic, complemented
190C4×SD32C2211yescharacteristic
191C4×SD32C2211yescharacteristic
192C4×SD32C2211yescharacteristic
193C4×SD32C2211yescharacteristic, complemented
194C4×SD32C2211yescharacteristic, complemented
195C4×SD32C2211yescharacteristic, complemented
196C4×D16C2211yescharacteristic
197#2164C2211yescharacteristic
198#2164C2211yescharacteristic
199#2164C2211yescharacteristic
200#2164C2211yescharacteristic
201#2163C2211yescharacteristic
202#2162C2211yescharacteristic
203C2×#137—21no—
204C2×AGL(1,ℤ/8)—21no—
205C2×#135C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16—21no—
208C22×D8C2311yescharacteristic
209#563—41no—
210#563—41no—
211#559—21no—
212#559—21no—
213#559—21no—
214#559—21no—
215Q82—21no—
216#557—21no—
217#557—21no—
218#557—21no—
219#556—21no—
220#556—21no—
221#556—21no—
222#556—21no—
223#556—21no—
224#556—21no—
225#556—21no—
226#556—41no—
227#554—21no—
228#552—41no—
229#551—41no—
230#551—41no—
231#551—41no—
232#551—41no—
233#544—41no—
234#542—21no—
235#542—21no—
236#542—41no—
237#542—41no—
238#541—21no—
239#541—21no—
240#541—41no—
241#541—41no—
242#541—41no—
243#536—21no—
244#535—21no—
245#533—21no—
246#533D411yescharacteristic
247#529—21no—
248#529—41no—
249#529—41no—
250C2×#124—21no—
251#519—21no—
252#518—21no—
253C4×#41—21no—
254C2×Q32C2311yescharacteristic
255C2×Q32C2311yescharacteristic
256C2×Q32C2311yescharacteristic
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×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×SD32C2311yescharacteristic
275C2×D16C2311yescharacteristic
276C2×D16C2311yescharacteristic
277C2×D16C2311yescharacteristic
278#500C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#499C2311yescharacteristic
282#499C2311yescharacteristic
283#499C2311yescharacteristic
284#497—21no—
285#497—21no—
286#496—21no—
287#496—21no—
288#495—21no—
289#495—21no—
290#495C2311yescharacteristic
291#495C2311yescharacteristic
292#495C2311yescharacteristic
293#495C2311yescharacteristic
294#495C2311yescharacteristic
295#495C2311yescharacteristic
296#495C2311yescharacteristic
297#495C2311yescharacteristic
298#495C2311yescharacteristic
299#495C2311yescharacteristic
300#495C2311yescharacteristic
301#494C2311yescharacteristic
302#494C2311yescharacteristic
303#494C2311yescharacteristic
304#494C2311yescharacteristic
305#494C2311yescharacteristic
306#493C2311yescharacteristic
307#493C2311yescharacteristic
308#491—21no—
309#491—21no—
310#489—21no—
311#489—21no—
312#488—21no—
313#487—21no—
314#479—21no—
315#479—21no—
316#479—21no—
317#479—21no—
318#478—21no—
319#478—21no—
320#477—21no—
321#477—21no—
322#477—21no—
323#476—21no—
324#475—21no—
325#475—21no—
326#470—21no—
327#470—21no—
328#468—21no—
329#468—21no—
330#467—21no—
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#466C2311yescharacteristic
335#465—21no—
336#464—21no—
337#464—21no—
338#464—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#464—21no—
344#464—21no—
345#464—21no—
346#464—21no—
347#464—21no—
348#464—21no—
349#464—21no—
350#463—21no—
351#463—21no—
352#463—21no—
353#463—21no—
354#463—21no—
355#463—21no—
356#463—21no—
357#463—21no—
358#462—21no—
359#462—21no—
360#462—21no—
361#461—21no—
362#461—21no—
363#461—21no—
364#461—21no—
365#461—21no—
366#461—21no—
367#461—21no—
368#460—21no—
369#460—21no—
370#460—21no—
371#460—21no—
372#446D411yescharacteristic
373#446D411yescharacteristic
374#446D411yescharacteristic
375#446D411yescharacteristic
376C8×Q8C2311yescharacteristic
377C8×Q8C2311yescharacteristic
378C8×Q8C2311yescharacteristic
379C8×Q8C2311yescharacteristic
380#442—21no—
381#442—21no—
382#441—21no—
383#441—21no—
384#441—21no—
385#441—21no—
386#440—21no—
387#440—21no—
388C4×Q16—21no—
389C4×Q16C2311yescharacteristic
390C4×Q16C2311yescharacteristic
391C4×Q16C2311yescharacteristic
392C4×Q16C2311yescharacteristic
393C4×Q16C2311yescharacteristic
394C4×Q16C2311yescharacteristic
395C4×Q16C2311yescharacteristic
396C4×Q16C2311yescharacteristic
397C4×Q16C2311yescharacteristic
398C4×Q16C2311yescharacteristic
399C4×Q16C2311yescharacteristic
400C4×Q16C2311yescharacteristic
401C4×Q16C2311yescharacteristic
402C4×Q16C2311yescharacteristic
403C4×Q16C2311yescharacteristic
404C4×SD16—21no—
405C4×SD16—21no—
406C4×SD16—21no—
407C4×D8C2311yescharacteristic
408C4×D8C2311yescharacteristic
409C4×D8C2311yescharacteristic
410C4×D8C2311yescharacteristic
411C4×D8C2311yescharacteristic
412C4×D8C2311yescharacteristic
413C4×D8C2311yescharacteristic
414C4×D8C2311yescharacteristic
415C4×D8C2311yescharacteristic
416#427C2311yescharacteristic
417#424D411yescharacteristic
418#424D411yescharacteristic
419#423D411yescharacteristic
420#419—21no—
421#418—21no—
422#416—21no—
423#405C2311yescharacteristic
424#405C2311yescharacteristic
425C2×C4×C8C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434C4⋊C16C2311yescharacteristic
435C4⋊C16C2311yescharacteristic
436C4⋊C16C2311yescharacteristic
437C4⋊C16C2311yescharacteristic
438C4⋊C16C2311yescharacteristic
439C4⋊C16C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446#358C2311yescharacteristic
447#358C2311yescharacteristic
448#358C2311yescharacteristic
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#357C2311yescharacteristic
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
478C22⋊C16C2311yescharacteristic
479C22⋊C16C2311yescharacteristic
480C22⋊C16C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482#346C2311yescharacteristic
483#346C2311yescharacteristic
484#346C2311yescharacteristic
485#346C2311yescharacteristic
486#346C2311yescharacteristic
487#346C2311yescharacteristic
488C4×C16C2311yescharacteristic
489C4×C16C2311yescharacteristic
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C22×Q8—21no—
496C22×D4—21no—
497#137—82no—
498AGL(1,ℤ/8)—82no—
499#135—41no—
500#135—41no—
501C2×Q16—21no—
502C2×Q16—21no—
503C2×Q16—21no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16C2411yescharacteristic
510C2×Q16C2411yescharacteristic
511C2×Q16C2411yescharacteristic
512C2×Q16C2411yescharacteristic
513C2×Q16C2411yescharacteristic
514C2×Q16C2411yescharacteristic
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—21no—
523C2×SD16—21no—
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—82no—
528C2×D8—21no—
529C2×D8—21no—
530C2×D8—21no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8C2411yescharacteristic
534C2×D8C2411yescharacteristic
535C2×D8C2411yescharacteristic
536C2×D8C2411yescharacteristic
537C2×M16C2×D411yescharacteristic
538C2×M16C2×D411yescharacteristic
539C22×C8C2×D411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8D811yescharacteristic
555C4⋊Q8D811yescharacteristic
556#127—21no—
557#127—21no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#126—41no—
564#126—41no—
565#126—41no—
566#126—41no—
567#126—41no—
568#126—41no—
569#126—41no—
570#126—41no—
571#126—41no—
572#126—41no—
573#126—41no—
574#126—41no—
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#125—21no—
580#125—21no—
581#125—21no—
582#125—41no—
583#125—41no—
584#125—41no—
585#125—41no—
586#125—41no—
587#125—41no—
588#125—41no—
589#125—41no—
590#125—41no—
591#125—41no—
592#125—41no—
593#125—41no—
594#125D811yescharacteristic
595#125D811yescharacteristic
596#124—21no—
597#124—21no—
598#124—21no—
599#124—21no—
600#124—21no—
601#124—21no—
602#124—21no—
603#124—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#123—41no—
616#123—41no—
617#123—41no—
618#123—41no—
619#123—41no—
620#123—41no—
621#123—41no—
622#123—41no—
623#123—41no—
624#123—41no—
625#123—41no—
626#123—41no—
627#123—41no—
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8D811yescharacteristic
647C22⋊Q8D811yescharacteristic
648C22⋊Q8D811yescharacteristic
649C22⋊Q8D811yescharacteristic
650#121—21no—
651#121—41no—
652#121—41no—
653#120—41no—
654#120—41no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—21no—
658C4×Q8—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—21no—
664C4×Q8—21no—
665C4×Q8—21no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—41no—
671C4×Q8—41no—
672C4×Q8—41no—
673C4×Q8—41no—
674C4×Q8—41no—
675C4×Q8—41no—
676C4×Q8—41no—
677C4×Q8C2×D411yescharacteristic
678C4×Q8C2×D411yescharacteristic
679C4×Q8C2×D411yescharacteristic
680C4×Q8C2×D411yescharacteristic
681C4×D4—21no—
682C4×D4—21no—
683C4×D4—21no—
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—41no—
691C4×D4—41no—
692C4×D4—41no—
693C4×D4—41no—
694C4×D4—41no—
695C4×D4—41no—
696C4×D4—41no—
697C4×D4—41no—
698C4×D4—41no—
699#117—21no—
700#117—41no—
701#117—41no—
702#117—41no—
703#117—41no—
704#117—41no—
705#117—41no—
706#117—41no—
707#117—41no—
708#117—41no—
709#117—41no—
710#117—41no—
711#117—41no—
712#117C2×D411yescharacteristic
713#117C2×D411yescharacteristic
714C2×C4⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C42—41no—
720C2×C42C2×D411yescharacteristic
721Q32—41no—
722Q32—41no—
723Q32—41no—
724Q32—41no—
725Q32—41no—
726Q32—41no—
727Q32—41no—
728Q32—41no—
729Q32—41no—
730SD32—41no—
731SD32—41no—
732SD32—41no—
733SD32—41no—
734SD32—41no—
735SD32—41no—
736SD32—41no—
737SD32—41no—
738SD32—41no—
739SD32—41no—
740SD32—41no—
741SD32—41no—
742D16—41no—
743D16—41no—
744D16—41no—
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748C2×C16C2411yescharacteristic
749C2×C16C2411yescharacteristic
750C2×C16C2411yescharacteristic
751C2×C16C2411yescharacteristic
752C2×C16C2411yescharacteristic
753#107—21no—
754#107—21no—
755#107—21no—
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766C4⋊C8C2×D411yescharacteristic
767C4⋊C8C2×D411yescharacteristic
768C4⋊C8C2×D411yescharacteristic
769C4⋊C8C2×D411yescharacteristic
770C4⋊C8C2×D411yescharacteristic
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774C4⋊C8C2×D411yescharacteristic
775C4⋊C8C2×D411yescharacteristic
776C4⋊C8C2×D411yescharacteristic
777C4⋊C8C2×D411yescharacteristic
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#103—21no—
795#103—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—
806#97C2×D411yescharacteristic
807#97C2×D411yescharacteristic
808#97C2×D411yescharacteristic
809#97C2×D411yescharacteristic
810C4×C8C2×D411yescharacteristic
811C4×C8C2×D411yescharacteristic
812C4×C8C2411yescharacteristic
813C4×C8C2411yescharacteristic
814C4×C8C2411yescharacteristic
815C4×C8C2411yescharacteristic
816C4×C8C2411yescharacteristic
817C4×C8C2411yescharacteristic
818C24—41no—
819#41—42no—
820#41—42no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—41no—
830C2×Q8—41no—
831C2×Q8—41no—
832C2×Q8—41no—
833C2×Q8C2×D811yescharacteristic
834C2×Q8C2×D811yescharacteristic
835C2×Q8C2×D811yescharacteristic
836C2×Q8C2×D811yescharacteristic
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4C2×D811yescharacteristic
862C22×C4C2×D811yescharacteristic
863C22×C4C22×D411yescharacteristic
864Q16—21no—
865Q16—21no—
866Q16—21no—
867Q16—21no—
868Q16—21no—
869Q16—21no—
870Q16—21no—
871Q16—21no—
872Q16—21no—
873Q16—21no—
874Q16—21no—
875Q16—21no—
876Q16—42no—
877Q16—81no—
878Q16—81no—
879Q16—81no—
880Q16—81no—
881Q16—81no—
882SD16—42no—
883SD16—81no—
884SD16—81no—
885SD16—81no—
886SD16—81no—
887SD16—81no—
888SD16—81no—
889SD16—81no—
890SD16—81no—
891SD16—81no—
892SD16—81no—
893SD16—81no—
894D8—21no—
895D8—21no—
896D8—21no—
897D8—21no—
898D8—21no—
899D8—21no—
900D8—21no—
901D8—21no—
902D8—42no—
903D8—81no—
904D8—81no—
905M16—41no—
906M16—41no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—41no—
910C2×C8C22×D411yescharacteristic
911C2×C8C22×D411yescharacteristic
912C2×C8C22×D411yescharacteristic
913C2×C8C22×D411yescharacteristic
914C2×C8C22×D411yescharacteristic
915C2×C8C22×D411yescharacteristic
916C2×C8C22×D411yescharacteristic
917C2×C8C2511yescharacteristic
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
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⋊C4C2×D811yescharacteristic
962C4⋊C4C2×D811yescharacteristic
963C4⋊C4C2×D811yescharacteristic
964C4⋊C4C2×D811yescharacteristic
965C4⋊C4C2×D811yescharacteristic
966C4⋊C4C2×D811yescharacteristic
967C4⋊C4C2×D811yescharacteristic
968C4⋊C4C2×D811yescharacteristic
969C4⋊C4C2×D811yescharacteristic
970C4⋊C4C2×D811yescharacteristic
971C4⋊C4C2×D811yescharacteristic
972C4⋊C4C2×D811yescharacteristic
973C4⋊C4C2×D811yescharacteristic
974C4⋊C4C2×D811yescharacteristic
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
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⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4C2×D811yescharacteristic
1014C22⋊C4C2×D811yescharacteristic
1015C22⋊C4C2×D811yescharacteristic
1016C22⋊C4C2×D811yescharacteristic
1017C42—41no—
1018C42—41no—
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—
1033C42C2×D811yescharacteristic
1034C42C2×D811yescharacteristic
1035C42C22×D411yescharacteristic
1036C42C22×D411yescharacteristic
1037C42C22×D411yescharacteristic
1038C42C22×D411yescharacteristic
1039C42C22×D411yescharacteristic
1040C42C22×D411yescharacteristic
1041C16—21no—
1042C16—21no—
1043C16—21no—
1044C16—21no—
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—82no—
1054C23—161no—
1055C23—161no—
1056C23C22×D811yescharacteristic
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—82no—
1074Q8—161no—
1075Q8—161no—
1076Q8—161no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—82no—
1086D4—82no—
1087D4—161no—
1088D4—161no—
1089D4—161no—
1090D4—161no—
1091D4—161no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
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—82no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—161no—
1112C2×C4—161no—
1113C2×C4—161no—
1114C2×C4—161no—
1115C2×C4—161no—
1116C2×C4—161no—
1117C2×C4—161no—
1118C2×C4—161no—
1119C2×C4C22×D811yescharacteristic
1120C2×C4C22×D811yescharacteristic
1121C2×C4C22×D811yescharacteristic
1122C2×C4C22×D811yescharacteristic
1123C2×C4C22×D811yescharacteristic
1124C2×C4C22×D811yescharacteristic
1125C2×C4C22×D811yescharacteristic
1126C2×C4C22×D811yescharacteristic
1127C2×C4C22×D811yescharacteristic
1128C2×C4C22×D811yescharacteristic
1129C2×C4C22×D811yescharacteristic
1130C2×C4C22×D811yescharacteristic
1131C2×C4C22×D811yescharacteristic
1132C2×C4C23×D411yescharacteristic
1133C8—21no—
1134C8—21no—
1135C8—21no—
1136C8—21no—
1137C8—21no—
1138C8—21no—
1139C8—21no—
1140C8#58511yescharacteristic
1141C8#58511yescharacteristic
1142C22—21no—
1143C22—21no—
1144C22—21no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—322no—
1158C22C23×D811yescharacteristic
1159C4—21no—
1160C4—21no—
1161C4—21no—
1162C4—21no—
1163C4—21no—
1164C4—21no—
1165C4—21no—
1166C4—21no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4#348711yescharacteristic
1185C4#358511yescharacteristic
1186C2—41no—
1187C2—161no—
1188C2—161no—
1189C2—161no—
1190C2—161no—
1191C2#6188011yescharacteristic
1192C2#6263511yescharacteristic
1193C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#33790C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ #2960 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62380C2semidirect
2. #61413C2semidirect
3. #33969C2semidirect
4. #33969C2semidirect
5. #33968C2semidirect
6. #33968C2semidirect
7. #33967C2semidirect
8. #33965C2semidirect
9. #33961C2semidirect
10. #33960C2semidirect
11. #33944C2semidirect
12. #33943C2semidirect
13. #33942C2semidirect
14. #33938C2semidirect
15. #33937C2semidirect
16. #33936C2semidirect
17. #33932C2semidirect
18. #33931C2semidirect
19. #33791C2semidirect
21. #33789C2semidirect
22. #33788C2semidirect
23. #33781C2semidirect
24. #33777C2semidirect
25. #33687C2semidirect
26. #33683C2semidirect
27. #33681C2semidirect
28. #33678C2semidirect
29. #33671C2semidirect
30. #33667C2semidirect
31. #33499C2semidirect
42. #3395C22semidirect
47. #3393C22semidirect
48. #3393C22semidirect
49. #3393C22semidirect
50. #3383C22semidirect
51. #3383C22semidirect
52. Q8×Q16C22semidirect
53. #3380C22semidirect
80. #2251C22semidirect
81. #2251C22semidirect
86. #2249C22semidirect
88. #2247C22semidirect
89. #2245C22semidirect
94. #2243C22semidirect
98. #2242C22semidirect
99. #2241C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
107. #2229C22semidirect
110. #2228C22semidirect
111. #2227C22semidirect
113. #2225C22semidirect
114. #2225C22semidirect
116. #2224C22semidirect
126. #2211C22semidirect
127. #2211C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
131. #2211C22semidirect
137. #2210C22semidirect
138. #2210C22semidirect
139. #2209C22semidirect
140. #2209C22semidirect
141. #2209C22semidirect
142. #2209C22semidirect
143. #2209C22semidirect
144. #2209C22semidirect
147. #2208C22semidirect
148. #2208C22semidirect
165. #2183C22semidirect
166. #2183C22semidirect
167. #2183C22semidirect
168. #2183C22semidirect
169. #2183C22semidirect
170. #2183C22semidirect
171. Q8×C16C22semidirect
172. Q8×C16C22semidirect
174. #2177C22semidirect
175. #2176C22semidirect
176. #2176C22semidirect
177. #2176C22semidirect
178. #2176C22semidirect
182. #2175C22semidirect
183. #2175C22semidirect
184. #2175C22semidirect
185. C4×Q32C22semidirect
186. C4×Q32C22semidirect
187. C4×Q32C22semidirect
188. C4×Q32C22semidirect
189. C4×Q32C22semidirect
193. C4×SD32C22semidirect
194. C4×SD32C22semidirect
195. C4×SD32C22semidirect

Maximal subgroups

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

subgroupindex
#623802
#614132
#339692
#339682
#339672
#339652
#339612
#339602
#339442
#339432
#339422
#339382
#339372
#339362
#339322
#339312
#337912
#337902
#337892
#337882
#337812
#337772
#336872
#336832
#336812
#336782
#336712
#336672
#334992