Finite Group Databasebeta

← #7624402

Subgroups — #7624402

Order 512.

1191 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62377C211yesmaximal, characteristic, complemented
2#61370C211yesmaximal, characteristic, complemented
3#33956C211yesmaximal, characteristic, complemented
4#33956C211yesmaximal, characteristic, complemented
5#33955C211yesmaximal, characteristic, complemented
6#33955C211yesmaximal, characteristic, complemented
7#33953C211yesmaximal, characteristic, complemented
8#33951C211yesmaximal, characteristic, complemented
9#33948C211yesmaximal, characteristic, complemented
10#33947C211yesmaximal, characteristic, complemented
11#33943C211yesmaximal, characteristic, complemented
12#33943C211yesmaximal, characteristic, complemented
13#33940C211yesmaximal, characteristic, complemented
14#33937C211yesmaximal, characteristic, complemented
15#33937C211yesmaximal, characteristic, complemented
16#33934C211yesmaximal, characteristic, complemented
17#33928C211yesmaximal, characteristic, complemented
18#33927C211yesmaximal, characteristic, complemented
19#33810C211yesmaximal, characteristic, complemented
20#33809C211yesmaximal, characteristic, complemented
21#33808C211yesmaximal, characteristic, complemented
22#33807C211yesmaximal, characteristic, complemented
23#33806C211yesmaximal, characteristic, complemented
24#33799C211yesmaximal, characteristic, complemented
25#33683C211yesmaximal, characteristic, complemented
26#33682C211yesmaximal, characteristic
27#33678C211yesmaximal, characteristic, complemented
28#33678C211yesmaximal, characteristic, complemented
29#33674C211yesmaximal, characteristic, complemented
30#33665C211yesmaximal, characteristic, complemented
31#33499C211yesmaximal, characteristic, complemented
32#3557—21no—
33#3501—21no—
34#3396C2211yescharacteristic, complemented
35#3396C2211yescharacteristic, complemented
36#3393C2211yescharacteristic, complemented
37#3393C2211yescharacteristic, complemented
38#3389—21no—
39#3389—21no—
40#3384—21no—
41#3384—21no—
42#3383C2211yescharacteristic, complemented
43#3383C2211yescharacteristic, complemented
44#3380C2211yescharacteristic
45#3380C2211yescharacteristic
46#3380C2211yescharacteristic
47#3380C2211yescharacteristic
48#3380C2211yescharacteristic
49#3380C2211yescharacteristic
50#3380C2211yescharacteristic, complemented
51#3380C2211yescharacteristic, complemented
52Q8×D8C2211yescharacteristic
53Q8×D8C2211yescharacteristic
54#3376—21no—
55#3376—21no—
56#3371—21no—
57#3371—21no—
58#3263—21no—
59#3260—21no—
60#3256—21no—
61#3177C2211yescharacteristic
62#3176C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69#3160C2211yescharacteristic
70#3081—21no—
71#3081—21no—
72#3077—21no—
73#2960C2211yescharacteristic
74#2948C2211yescharacteristic
75#2948C2211yescharacteristic
76C2×C4×D8C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2255C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2255C2211yescharacteristic, complemented
83#2254C2211yescharacteristic, complemented
84#2253C2211yescharacteristic, complemented
85#2253C2211yescharacteristic, complemented
86#2253C2211yescharacteristic, complemented
87#2253C2211yescharacteristic, complemented
88#2252C2211yescharacteristic, complemented
89#2245C2211yescharacteristic, complemented
90#2244C2211yescharacteristic, complemented
91#2243C2211yescharacteristic, complemented
92#2243C2211yescharacteristic, complemented
93#2243C2211yescharacteristic, complemented
94#2243C2211yescharacteristic, complemented
95#2242C2211yescharacteristic, complemented
96#2242C2211yescharacteristic, complemented
97#2242C2211yescharacteristic, complemented
98#2242C2211yescharacteristic, complemented
99#2241C2211yescharacteristic, complemented
100#2240C2211yescharacteristic, complemented
101#2237C2211yescharacteristic
102#2237C2211yescharacteristic
103#2237C2211yescharacteristic
104#2237C2211yescharacteristic
105#2236C2211yescharacteristic
106#2235C2211yescharacteristic
107#2234C2211yescharacteristic
108#2234C2211yescharacteristic
109#2234C2211yescharacteristic
110#2234C2211yescharacteristic
111#2233C2211yescharacteristic
112#2232C2211yescharacteristic
113#2229C2211yescharacteristic, complemented
114#2229C2211yescharacteristic, complemented
115#2229C2211yescharacteristic, complemented
116#2229C2211yescharacteristic, complemented
117#2229C2211yescharacteristic, complemented
118#2229C2211yescharacteristic, complemented
119#2228C2211yescharacteristic
120#2228C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2228C2211yescharacteristic
124#2228C2211yescharacteristic
125#2228C2211yescharacteristic
126#2228C2211yescharacteristic
127#2228C2211yescharacteristic, complemented
128#2228C2211yescharacteristic, complemented
129#2228C2211yescharacteristic, complemented
130#2228C2211yescharacteristic, complemented
131#2228C2211yescharacteristic, complemented
132#2228C2211yescharacteristic, complemented
133#2227C2211yescharacteristic, complemented
134#2227C2211yescharacteristic, complemented
135#2227C2211yescharacteristic, complemented
136#2226C2211yescharacteristic
137#2226C2211yescharacteristic
138#2226C2211yescharacteristic, complemented
139#2226C2211yescharacteristic, complemented
140#2226C2211yescharacteristic, complemented
141#2225C2211yescharacteristic, complemented
142#2225C2211yescharacteristic, complemented
143#2225C2211yescharacteristic, complemented
144#2224C2211yescharacteristic
145#2224C2211yescharacteristic
146#2224C2211yescharacteristic, complemented
147#2224C2211yescharacteristic, complemented
148#2224C2211yescharacteristic, complemented
149#2210C2211yescharacteristic
150#2210C2211yescharacteristic
151#2210C2211yescharacteristic
152#2210C2211yescharacteristic
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2208C2211yescharacteristic
158#2208C2211yescharacteristic
159#2206C2211yescharacteristic
160#2206C2211yescharacteristic
161#2187C2211yescharacteristic
162#2187C2211yescharacteristic
163#2184C2211yescharacteristic
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
175#2177C2211yescharacteristic
176#2177C2211yescharacteristic
177#2177C2211yescharacteristic
178#2177C2211yescharacteristic
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic
183#2175C2211yescharacteristic
184#2175C2211yescharacteristic
185C4×SD32C2211yescharacteristic
186C4×SD32C2211yescharacteristic
187C4×SD32C2211yescharacteristic
188C4×SD32C2211yescharacteristic
189C4×SD32C2211yescharacteristic
190C4×SD32C2211yescharacteristic
191C4×D16C2211yescharacteristic
192C4×D16C2211yescharacteristic
193C4×D16C2211yescharacteristic
194C4×D16C2211yescharacteristic
195C4×D16C2211yescharacteristic
196C4×D16C2211yescharacteristic
197#2164C2211yescharacteristic
198#2164C2211yescharacteristic
199#2164C2211yescharacteristic
200#2164C2211yescharacteristic
201#2163C2211yescharacteristic
202#2162C2211yescharacteristic
203C22×D8C2311yescharacteristic
204#563—41no—
205#563—41no—
206#559—21no—
207#559—21no—
208#557—21no—
209#557—21no—
210#556—21no—
211#556—21no—
212#554—21no—
213#554—21no—
214#554—21no—
215#554—21no—
216#554—21no—
217#554—21no—
218#554—21no—
219#554—21no—
220#554—41no—
221#554—41no—
222#554—41no—
223#552—41no—
224#552—41no—
225D4×Q8—21no—
226D4×Q8—21no—
227D4×Q8—41no—
228#544—21no—
229#544—21no—
230#543—41no—
231#543—41no—
232#542—21no—
233#542—21no—
234#542—41no—
235#542—41no—
236#541—21no—
237#540—21no—
238#539—41no—
239#539—41no—
240#533—21no—
241#533D411yescharacteristic
242#529—21no—
243#529—21no—
244C2×C22⋊Q8—41no—
245C2×C22⋊Q8—41no—
246#518—21no—
247#518—21no—
248C2×C4×D4—21no—
249C2×SD32C2311yescharacteristic
250C2×SD32C2311yescharacteristic
251C2×SD32C2311yescharacteristic
252C2×SD32C2311yescharacteristic
253C2×D16C2311yescharacteristic
254C2×D16C2311yescharacteristic
255C2×D16C2311yescharacteristic
256C2×D16C2311yescharacteristic
257#501—21no—
258#501—21no—
259#501—21no—
260#501—21no—
261#500C2311yescharacteristic
262#500C2311yescharacteristic
263#500C2311yescharacteristic
264#500C2311yescharacteristic
265#500C2311yescharacteristic
266#500C2311yescharacteristic
267#500C2311yescharacteristic
268#500C2311yescharacteristic
269#499—21no—
270#499C2311yescharacteristic
271#499C2311yescharacteristic
272#499C2311yescharacteristic
273#499C2311yescharacteristic
274#499C2311yescharacteristic
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#498—21no—
281#495C2311yescharacteristic
282#495C2311yescharacteristic
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#494C2311yescharacteristic
286#493C2311yescharacteristic
287#491—21no—
288#490—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#488—21no—
293#479—21no—
294#479—21no—
295#479—21no—
296#479—21no—
297#478—21no—
298#478—21no—
299#478—21no—
300#478—21no—
301#478—21no—
302#478—21no—
303#478—21no—
304#478—21no—
305#478—21no—
306#478—21no—
307#478—21no—
308#478—21no—
309#478—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#476—21no—
314#476—21no—
315#476—21no—
316#476—21no—
317#476—21no—
318#476—21no—
319#476—21no—
320#476—21no—
321#475—21no—
322#475—21no—
323#474—21no—
324#474—21no—
325#474—21no—
326#474—21no—
327#474—21no—
328#474—21no—
329#470—21no—
330#469—21no—
331#468—21no—
332#468—21no—
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#465—21no—
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#460—21no—
350#460—21no—
351#446D411yescharacteristic
352#446D411yescharacteristic
353#446D411yescharacteristic
354#446D411yescharacteristic
355C8×Q8C2311yescharacteristic
356C8×Q8C2311yescharacteristic
357C8×Q8C2311yescharacteristic
358C8×Q8C2311yescharacteristic
359#442—21no—
360#442—21no—
361#442—21no—
362#442—21no—
363#442—21no—
364#441—21no—
365#440—21no—
366#440—21no—
367C4×Q16C2311yescharacteristic
368C4×Q16C2311yescharacteristic
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×SD16—21no—
374C4×SD16—21no—
375C4×D8—21no—
376C4×D8—21no—
377C4×D8C2311yescharacteristic
378C4×D8C2311yescharacteristic
379C4×D8C2311yescharacteristic
380C4×D8C2311yescharacteristic
381C4×D8C2311yescharacteristic
382C4×D8C2311yescharacteristic
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389C4×D8C2311yescharacteristic
390C4×D8C2311yescharacteristic
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395#428—21no—
396#428—21no—
397#427—21no—
398#427C2311yescharacteristic
399#427C2311yescharacteristic
400C2×#107C2311yescharacteristic
401#424D411yescharacteristic
402#424D411yescharacteristic
403#423D411yescharacteristic
404#418—21no—
405#418—21no—
406C2×#102—21no—
407#405C2311yescharacteristic
408#405C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410#367C2311yescharacteristic
411#367C2311yescharacteristic
412#367C2311yescharacteristic
413#367C2311yescharacteristic
414#367C2311yescharacteristic
415#367C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#366C2311yescharacteristic
423#366C2311yescharacteristic
424#366C2311yescharacteristic
425#366C2311yescharacteristic
426#366C2311yescharacteristic
427#366C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
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#357C2311yescharacteristic
459#357C2311yescharacteristic
460#357C2311yescharacteristic
461#357C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
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
494C22×Q8—41no—
495C22×Q8—41no—
496C22×D4—21no—
497C23×C4—41no—
498C2×Q16—21no—
499C2×Q16C2411yescharacteristic
500C2×Q16C2411yescharacteristic
501C2×SD16—21no—
502C2×SD16—21no—
503C2×SD16—21no—
504C2×SD16—21no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—21no—
508C2×D8—21no—
509C2×D8C2411yescharacteristic
510C2×D8C2411yescharacteristic
511C2×D8C2411yescharacteristic
512C2×D8C2411yescharacteristic
513C2×M16C2×D411yescharacteristic
514C2×M16C2×D411yescharacteristic
515C22×C8C2×D411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8D811yescharacteristic
531C4⋊Q8D811yescharacteristic
532#127—21no—
533#126—41no—
534#126—41no—
535#126—41no—
536#126—41no—
537#126—41no—
538#126—41no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125—21no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—41no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—41no—
561#125D811yescharacteristic
562#125D811yescharacteristic
563#124—21no—
564#124—21no—
565#124—21no—
566#124—21no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#123—41no—
572#123—41no—
573#123—41no—
574#123—41no—
575#123—41no—
576#123—41no—
577#123—41no—
578#123—41no—
579#123—41no—
580#123—41no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
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⋊Q8D811yescharacteristic
624C22⋊Q8D811yescharacteristic
625C22⋊Q8D811yescharacteristic
626C22⋊Q8D811yescharacteristic
627#121—21no—
628#121—21no—
629#121—41no—
630#121—41no—
631C4×Q8—21no—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—21no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8C2×D411yescharacteristic
642C4×Q8C2×D411yescharacteristic
643C4×Q8C2×D411yescharacteristic
644C4×Q8C2×D411yescharacteristic
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
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—41no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673#117—21no—
674#117—21no—
675#117—41no—
676#117—41no—
677#117—41no—
678#117—41no—
679#117C2×D411yescharacteristic
680#117C2×D411yescharacteristic
681C2×C4⋊C4—21no—
682C2×C4⋊C4—41no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C42C2×D411yescharacteristic
696SD32—22no—
697SD32—22no—
698SD32—22no—
699SD32—22no—
700D16—22no—
701D16—22no—
702D16—22no—
703D16—22no—
704C2×C16C2411yescharacteristic
705C2×C16C2411yescharacteristic
706C2×C16C2411yescharacteristic
707C2×C16C2411yescharacteristic
708C2×C16C2411yescharacteristic
709C2×C16C2411yescharacteristic
710C2×C16C2411yescharacteristic
711C2×C16C2411yescharacteristic
712#107—21no—
713#107—21no—
714#107—21no—
715#107—21no—
716#107—21no—
717#107—21no—
718#107—21no—
719#107—21no—
720#107—21no—
721#107C2411yescharacteristic
722#107C2411yescharacteristic
723#107C2411yescharacteristic
724#107C2411yescharacteristic
725#107C2411yescharacteristic
726#107C2411yescharacteristic
727#107C2411yescharacteristic
728#107C2411yescharacteristic
729#107C2411yescharacteristic
730#107C2411yescharacteristic
731#106—21no—
732#106—21no—
733#106—21no—
734#106—21no—
735#106—21no—
736#106—21no—
737#106—21no—
738#106—21no—
739#106—21no—
740#106—21no—
741#106—21no—
742#106—21no—
743C4⋊C8C2×D411yescharacteristic
744C4⋊C8C2×D411yescharacteristic
745C4⋊C8C2×D411yescharacteristic
746C4⋊C8C2×D411yescharacteristic
747C4⋊C8C2×D411yescharacteristic
748C4⋊C8C2×D411yescharacteristic
749C4⋊C8C2×D411yescharacteristic
750C4⋊C8C2×D411yescharacteristic
751C4⋊C8C2×D411yescharacteristic
752C4⋊C8C2×D411yescharacteristic
753C4⋊C8C2×D411yescharacteristic
754C4⋊C8C2×D411yescharacteristic
755#103—21no—
756#103—21no—
757#103—21no—
758#103—21no—
759#103—21no—
760#103—21no—
761#103—21no—
762#103—21no—
763#102—21no—
764#102—21no—
765#102—21no—
766#102—21no—
767#102—21no—
768#102—21no—
769#102—21no—
770#102—21no—
771#102—21no—
772#102—21no—
773#102—21no—
774#102—21no—
775#102—21no—
776#102—21no—
777#102—21no—
778#102—21no—
779#102—21no—
780#102—21no—
781#102—21no—
782#102—21no—
783#97C2×D411yescharacteristic
784#97C2×D411yescharacteristic
785#97C2×D411yescharacteristic
786#97C2×D411yescharacteristic
787C4×C8C2×D411yescharacteristic
788C4×C8C2×D411yescharacteristic
789C4×C8C2411yescharacteristic
790C4×C8C2411yescharacteristic
791C4×C8C2411yescharacteristic
792C4×C8C2411yescharacteristic
793C4×C8C2411yescharacteristic
794C4×C8C2411yescharacteristic
795C24—41no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—41no—
799C2×Q8—41no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—41no—
804C2×Q8—41no—
805C2×Q8—41no—
806C2×Q8—162no—
807C2×Q8—162no—
808C2×Q8C2×D811yescharacteristic
809C2×Q8C2×D811yescharacteristic
810C2×Q8C2×D811yescharacteristic
811C2×Q8C2×D811yescharacteristic
812C2×D4—24no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—42no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—162no—
843C22×C4C2×D811yescharacteristic
844C22×C4C2×D811yescharacteristic
845C22×C4C22×D411yescharacteristic
846Q16—21no—
847Q16—21no—
848Q16—21no—
849Q16—21no—
850Q16—81no—
851SD16—81no—
852SD16—81no—
853SD16—81no—
854SD16—81no—
855D8—24no—
856D8—21no—
857D8—21no—
858D8—21no—
859D8—21no—
860D8—21no—
861D8—21no—
862D8—81no—
863D82−1+412yes—
864D82−1+412yes—
865M16—41no—
866M16—41no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—41no—
870C2×C8C22×D411yescharacteristic
871C2×C8C22×D411yescharacteristic
872C2×C8C22×D411yescharacteristic
873C2×C8C22×D411yescharacteristic
874C2×C8C22×D411yescharacteristic
875C2×C8C22×D411yescharacteristic
876C2×C8C22×D411yescharacteristic
877C2×C8C2511yescharacteristic
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4C2×D811yescharacteristic
928C4⋊C4C2×D811yescharacteristic
929C4⋊C4C2×D811yescharacteristic
930C4⋊C4C2×D811yescharacteristic
931C4⋊C4C2×D811yescharacteristic
932C4⋊C4C2×D811yescharacteristic
933C4⋊C4C2×D811yescharacteristic
934C4⋊C4C2×D811yescharacteristic
935C4⋊C4C2×D811yescharacteristic
936C4⋊C4C2×D811yescharacteristic
937C4⋊C4C2×D811yescharacteristic
938C4⋊C4C2×D811yescharacteristic
939C4⋊C4C2×D811yescharacteristic
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C22⋊C4—41no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
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⋊C4C2×D811yescharacteristic
976C22⋊C4C2×D811yescharacteristic
977C22⋊C4C2×D811yescharacteristic
978C22⋊C4C2×D811yescharacteristic
979C42—41no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42C2×D811yescharacteristic
988C42C2×D811yescharacteristic
989C42C22×D411yescharacteristic
990C42C22×D411yescharacteristic
991C42C22×D411yescharacteristic
992C42C22×D411yescharacteristic
993C42C22×D411yescharacteristic
994C42C22×D411yescharacteristic
995C16—21no—
996C16—21no—
997C16—21no—
998C16—21no—
999C16—21no—
1000C16—21no—
1001C16—21no—
1002C16—21no—
1003C23—44no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—161no—
1009C23—161no—
1010C23C22×D811yescharacteristic
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—82no—
1020Q8—161no—
1021Q8—161no—
1022Q8—161no—
1023Q8—161no—
1024Q8—161no—
1025Q8—161no—
1026Q8—161no—
1027D4—22no—
1028D4—22no—
1029D4—44no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—161no—
1037D4—161no—
1038D4—161no—
1039D4—161no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—161no—
1059C2×C4—161no—
1060C2×C4—161no—
1061C2×C4—161no—
1062C2×C4—161no—
1063C2×C4—161no—
1064C2×C4—161no—
1065C2×C4—161no—
1066C2×C4—161no—
1067C2×C4—161no—
1068C2×C4—161no—
1069C2×C4—161no—
1070C2×C4—161no—
1071C2×C4—161no—
1072C2×C4—161no—
1073C2×C4—161no—
1074C2×C4—161no—
1075C2×C4C22×D811yescharacteristic
1076C2×C4C22×D811yescharacteristic
1077C2×C4C22×D811yescharacteristic
1078C2×C4C22×D811yescharacteristic
1079C2×C4C22×D811yescharacteristic
1080C2×C4C22×D811yescharacteristic
1081C2×C4C22×D811yescharacteristic
1082C2×C4C22×D811yescharacteristic
1083C2×C4C22×D811yescharacteristic
1084C2×C4C22×D811yescharacteristic
1085C2×C4C22×D811yescharacteristic
1086C2×C4C22×D811yescharacteristic
1087C2×C4C22×D811yescharacteristic
1088C2×C4C23×D411yescharacteristic
1089C8—21no—
1090C8—21no—
1091C8—21no—
1092C8—21no—
1093C8—21no—
1094C8—21no—
1095C8—21no—
1096C8C2×2−1+411yescharacteristic
1097C8C2×2−1+411yescharacteristic
1098C22—21no—
1099C22—21no—
1100C22—21no—
1101C22—42no—
1102C22—42no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—164no—
1114C22C23×D811yescharacteristic
1115C4—21no—
1116C4—21no—
1117C4—21no—
1118C4—21no—
1119C4—21no—
1120C4—21no—
1121C4—21no—
1122C4—21no—
1123C4—21no—
1124C4—21no—
1125C4—21no—
1126C4—21no—
1127C4—21no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4#348611yescharacteristic
1141C4#358611yescharacteristic
1142C2—41no—
1143C2—82no—
1144C2—82no—
1145C2—161no—
1146C2—161no—
1147C2#6181711yescharacteristic
1148C2#6263511yescharacteristic
1149C2#6263611yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#33682C2
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. #62377C2semidirect
2. #61370C2semidirect
3. #33956C2semidirect
4. #33956C2semidirect
5. #33955C2semidirect
6. #33955C2semidirect
7. #33953C2semidirect
8. #33951C2semidirect
9. #33948C2semidirect
10. #33947C2semidirect
11. #33943C2semidirect
12. #33943C2semidirect
13. #33940C2semidirect
14. #33937C2semidirect
15. #33937C2semidirect
16. #33934C2semidirect
17. #33928C2semidirect
18. #33927C2semidirect
19. #33810C2semidirect
20. #33809C2semidirect
21. #33808C2semidirect
22. #33807C2semidirect
23. #33806C2semidirect
24. #33799C2semidirect
25. #33683C2semidirect
27. #33678C2semidirect
28. #33678C2semidirect
29. #33674C2semidirect
30. #33665C2semidirect
31. #33499C2semidirect
34. #3396C22semidirect
35. #3396C22semidirect
36. #3393C22semidirect
37. #3393C22semidirect
42. #3383C22semidirect
43. #3383C22semidirect
50. #3380C22semidirect
51. #3380C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2255C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2255C22semidirect
83. #2254C22semidirect
84. #2253C22semidirect
85. #2253C22semidirect
86. #2253C22semidirect
87. #2253C22semidirect
88. #2252C22semidirect
89. #2245C22semidirect
90. #2244C22semidirect
91. #2243C22semidirect
92. #2243C22semidirect
93. #2243C22semidirect
94. #2243C22semidirect
95. #2242C22semidirect
96. #2242C22semidirect
97. #2242C22semidirect
98. #2242C22semidirect
99. #2241C22semidirect
100. #2240C22semidirect
113. #2229C22semidirect
114. #2229C22semidirect
115. #2229C22semidirect
116. #2229C22semidirect
117. #2229C22semidirect
118. #2229C22semidirect
127. #2228C22semidirect
128. #2228C22semidirect
129. #2228C22semidirect
130. #2228C22semidirect
131. #2228C22semidirect
132. #2228C22semidirect
133. #2227C22semidirect
134. #2227C22semidirect
135. #2227C22semidirect
138. #2226C22semidirect
139. #2226C22semidirect
140. #2226C22semidirect
141. #2225C22semidirect
142. #2225C22semidirect
143. #2225C22semidirect
146. #2224C22semidirect
147. #2224C22semidirect
148. #2224C22semidirect
165. #2183C22semidirect
166. #2183C22semidirect
167. #2183C22semidirect
168. #2183C22semidirect
169. #2183C22semidirect
170. #2183C22semidirect
171. Q8×C16C22semidirect
172. Q8×C16C22semidirect

Maximal subgroups

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

subgroupindex
#623772
#613702
#339562
#339552
#339532
#339512
#339482
#339472
#339432
#339402
#339372
#339342
#339282
#339272
#338102
#338092
#338082
#338072
#338062
#337992
#336832
#336822
#336782
#336742
#336652
#334992