Finite Group Databasebeta

← #7624791

Subgroups — #7624791

Order 512.

1209 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62496C211yesmaximal, characteristic, complemented
2#61471C211yesmaximal, characteristic
3#33955C211yesmaximal, characteristic, complemented
4#33952C211yesmaximal, characteristic, complemented
5#33942C211yesmaximal, characteristic, complemented
6#33938C211yesmaximal, characteristic, complemented
7#33920C211yesmaximal, characteristic, complemented
8#33919C211yesmaximal, characteristic, complemented
9#33917C211yesmaximal, characteristic, complemented
10#33916C211yesmaximal, characteristic, complemented
11#33913C211yesmaximal, characteristic, complemented
12#33910C211yesmaximal, characteristic, complemented
13#33891C211yesmaximal, characteristic, complemented
14#33890C211yesmaximal, characteristic, complemented
15#33881C211yesmaximal, characteristic, complemented
16#33878C211yesmaximal, characteristic, complemented
17#33878C211yesmaximal, characteristic, complemented
18#33877C211yesmaximal, characteristic, complemented
19#33826C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33818C211yesmaximal, characteristic, complemented
22#33809C211yesmaximal, characteristic, complemented
23#33807C211yesmaximal, characteristic, complemented
24#33806C211yesmaximal, characteristic, complemented
25#33683C211yesmaximal, characteristic, complemented
26#33680C211yesmaximal, characteristic, complemented
27#33670C211yesmaximal, characteristic, complemented
28#33633C211yesmaximal, characteristic, complemented
29#33631C211yesmaximal, characteristic, complemented
30#33627C211yesmaximal, characteristic, complemented
31#33509C211yesmaximal, characteristic, complemented
32#3555—21no—
33#3513—21no—
34#3396C2211yescharacteristic
35#3387—21no—
36#3383C2211yescharacteristic, complemented
37Q8×Q16C2211yescharacteristic, complemented
38#3380C2211yescharacteristic
39#3370—21no—
40#3356—21no—
41#3349—21no—
42#3349—21no—
43#3342C2211yescharacteristic
44#3342C2211yescharacteristic, complemented
45#3342C2211yescharacteristic, complemented
46#3339C2211yescharacteristic
47#3338C2211yescharacteristic, complemented
48#3336C2211yescharacteristic
49#3336C2211yescharacteristic
50#3336C2211yescharacteristic, complemented
51#3334C2211yescharacteristic
52#3322—21no—
53#3310—21no—
54#3306—21no—
55#3280C2211yescharacteristic
56#3280C2211yescharacteristic
57D4×D8C2211yescharacteristic
58#3242—21no—
59#3242—21no—
60#3237—21no—
61#3177C2211yescharacteristic, complemented
62#3177C2211yescharacteristic, complemented
63#3176C2211yescharacteristic
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic, complemented
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic, complemented
68#3164C2211yescharacteristic, complemented
69#3160C2211yescharacteristic, complemented
70#3119—21no—
71#3118—21no—
72#3114—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2948C2211yescharacteristic
76C2×C4×D8C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2255C2211yescharacteristic, complemented
80#2255C2211yescharacteristic, complemented
81#2253C2211yescharacteristic, complemented
82#2252C2211yescharacteristic, complemented
83#2244C2211yescharacteristic
84#2243C2211yescharacteristic, complemented
85#2243C2211yescharacteristic, complemented
86#2243C2211yescharacteristic, complemented
87#2242C2211yescharacteristic, complemented
88#2240C2211yescharacteristic
89#2237C2211yescharacteristic, complemented
90#2237C2211yescharacteristic, complemented
91#2237C2211yescharacteristic, complemented
92#2237C2211yescharacteristic, complemented
93#2237C2211yescharacteristic, complemented
94#2236C2211yescharacteristic, complemented
95#2236C2211yescharacteristic, complemented
96#2236C2211yescharacteristic, complemented
97#2236C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2234C2211yescharacteristic
100#2234C2211yescharacteristic
101#2234C2211yescharacteristic
102#2234C2211yescharacteristic, complemented
103#2234C2211yescharacteristic, complemented
104#2233C2211yescharacteristic, complemented
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2229C2211yescharacteristic, complemented
110#2229C2211yescharacteristic, complemented
111#2229C2211yescharacteristic, complemented
112#2229C2211yescharacteristic, complemented
113#2229C2211yescharacteristic, complemented
114#2228C2211yescharacteristic
115#2228C2211yescharacteristic
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic, complemented
119#2228C2211yescharacteristic, complemented
120#2228C2211yescharacteristic, complemented
121#2228C2211yescharacteristic, complemented
122#2228C2211yescharacteristic, complemented
123#2227C2211yescharacteristic, complemented
124#2227C2211yescharacteristic, complemented
125#2227C2211yescharacteristic, complemented
126#2226C2211yescharacteristic
127#2226C2211yescharacteristic
128#2226C2211yescharacteristic, complemented
129#2226C2211yescharacteristic, complemented
130#2225C2211yescharacteristic, complemented
131#2224C2211yescharacteristic
132#2224C2211yescharacteristic
133#2224C2211yescharacteristic
134#2224C2211yescharacteristic, complemented
135#2224C2211yescharacteristic, complemented
136#2224C2211yescharacteristic, complemented
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2220C2211yescharacteristic
140#2220C2211yescharacteristic, complemented
141#2220C2211yescharacteristic, complemented
142#2219C2211yescharacteristic, complemented
143#2219C2211yescharacteristic, complemented
144#2219C2211yescharacteristic, complemented
145#2217C2211yescharacteristic
146#2217C2211yescharacteristic, complemented
147#2217C2211yescharacteristic, complemented
148#2216C2211yescharacteristic, complemented
149#2211C2211yescharacteristic, complemented
150#2211C2211yescharacteristic, complemented
151#2211C2211yescharacteristic, complemented
152#2211C2211yescharacteristic, complemented
153#2209C2211yescharacteristic, complemented
154#2208C2211yescharacteristic
155#2208C2211yescharacteristic, complemented
156#2208C2211yescharacteristic, complemented
157#2207C2211yescharacteristic
158#2207C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic
161#2187C2211yescharacteristic
162#2187C2211yescharacteristic
163#2187C2211yescharacteristic
164#2187C2211yescharacteristic
165#2183C2211yescharacteristic, complemented
166#2183C2211yescharacteristic, complemented
167#2176C2211yescharacteristic, complemented
168#2175C2211yescharacteristic
169#2175C2211yescharacteristic
170#2175C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic, complemented
173#2175C2211yescharacteristic, complemented
174#2175C2211yescharacteristic, complemented
175C4×Q32C2211yescharacteristic, complemented
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic, complemented
179#2169C2211yescharacteristic
180#2169C2211yescharacteristic, complemented
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic, complemented
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185#2164C2211yescharacteristic, complemented
186#2164C2211yescharacteristic, complemented
187#2163C2211yescharacteristic, complemented
188#2159C2211yescharacteristic, complemented
189#2159C2211yescharacteristic, complemented
190#2159C2211yescharacteristic, complemented
191#2159C2211yescharacteristic, complemented
192#2158C2211yescharacteristic, complemented
193C2×#366C2211yescharacteristic, complemented
194#2151C2211yescharacteristic, complemented
195#2151C2211yescharacteristic, complemented
196#2150C2211yescharacteristic, complemented
197#2140C2211yescharacteristic
198#2140C2211yescharacteristic
199#2140C2211yescharacteristic
200#2139C2211yescharacteristic
201#2138C2211yescharacteristic
202C2×#357C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206#563—41no—
207#563—41no—
208#559—21no—
209Q82—21no—
210#557—21no—
211#557—41no—
212#556—21no—
213#556—21no—
214#556—21no—
215#556—41no—
216#554—21no—
217#554—21no—
218#553—21no—
219#553—41no—
220#552—21no—
221#552—21no—
222#552—21no—
223#551—41no—
224#551—41no—
225#547—21no—
226#546—21no—
227#546—21no—
228#546—41no—
229D42—21no—
230#544—21no—
231#544—21no—
232#542—21no—
233#542—41no—
234#541—21no—
235#541—21no—
236#541—41no—
237#541—41no—
238#541—41no—
239#540—21no—
240#539—41no—
241#538—41no—
242#533—21no—
243#533—21no—
244#529—21no—
245#529D411yescharacteristic
246#525—41no—
247C2×#123—41no—
248#520—21no—
249#518—21no—
250C2×C4×D4—21no—
251C2×Q32C2311yescharacteristic
252C2×Q32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×SD32C2311yescharacteristic
258C2×SD32C2311yescharacteristic
259C2×M32C2311yescharacteristic
260C2×M32C2311yescharacteristic
261C2×M32C2311yescharacteristic
262C2×M32C2311yescharacteristic
263C22×C16C2311yescharacteristic
264C22×C16C2311yescharacteristic
265#501—21no—
266#501—21no—
267#501—21no—
268#501—21no—
269#500C2311yescharacteristic
270#500C2311yescharacteristic
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#500C2311yescharacteristic
274#500C2311yescharacteristic
275#499—21no—
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#498—21no—
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#494C2311yescharacteristic
286#493C2311yescharacteristic
287#491—21no—
288#491—21no—
289#490—21no—
290#489—21no—
291#488—21no—
292#487—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#485—21no—
298#485—21no—
299#485—21no—
300#485—21no—
301#485—21no—
302#484—21no—
303#484—21no—
304#483—21no—
305#483—21no—
306#483—21no—
307#482—21no—
308#481—21no—
309#480—21no—
310#480—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#479—21no—
316#478—21no—
317#478—21no—
318#478—21no—
319#477—21no—
320#477—21no—
321#477—21no—
322#477—21no—
323#476—21no—
324#475—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#474—21no—
329#470—21no—
330#470—21no—
331#469—21no—
332#468—21no—
333#467—21no—
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#466C2311yescharacteristic
346#465—21no—
347#463—21no—
348#463—21no—
349#463—21no—
350#463—21no—
351#460—21no—
352#459—21no—
353#450—21no—
354#450—21no—
355#449—21no—
356#449—21no—
357#447—21no—
358#447—21no—
359#446D411yescharacteristic
360C8×Q8C2311yescharacteristic
361#442—21no—
362#442—21no—
363#442—21no—
364#441—21no—
365#441—21no—
366#440—21no—
367#440—21no—
368#440—21no—
369C4×Q16—21no—
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×SD16—21no—
379C4×D8—21no—
380C4×D8—21no—
381C4×D8C2311yescharacteristic
382C4×D8C2311yescharacteristic
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389#436D411yescharacteristic
390#435D411yescharacteristic
391#435D411yescharacteristic
392C8×D4C2311yescharacteristic
393C8×D4C2311yescharacteristic
394C8×D4C2311yescharacteristic
395#433D411yescharacteristic
396#433D411yescharacteristic
397#432D411yescharacteristic
398#428—21no—
399#428—21no—
400#427—21no—
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403#427C2311yescharacteristic
404#427C2311yescharacteristic
405#427C2311yescharacteristic
406C2×#107C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#107C2311yescharacteristic
409C2×#107C2311yescharacteristic
410#418—21no—
411#417—21no—
412C2×#102—21no—
413#405C2311yescharacteristic
414#405C2311yescharacteristic
415C2×C4×C8C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#366C2311yescharacteristic
427#366C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
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
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487C22⋊C16C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—41no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C23×C4—41no—
500#135—22no—
501#135—41no—
502C2×Q16—21no—
503C2×Q16C2411yescharacteristic
504C2×Q16C2411yescharacteristic
505C2×Q16C2411yescharacteristic
506C2×SD16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—21no—
512C2×D8—21no—
513C2×D8—21no—
514C2×D8—41no—
515C2×D8—41no—
516C2×D8C2411yescharacteristic
517C2×D8C2411yescharacteristic
518C2×D8C2411yescharacteristic
519C2×M16C2×D411yescharacteristic
520C2×M16C2×D411yescharacteristic
521C22×C8C2×D411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529C4⋊Q8—21no—
530C4⋊Q8—21no—
531C4⋊Q8—21no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538#127—21no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#126—41no—
544#126—41no—
545#126—41no—
546#126—41no—
547#126—41no—
548#126—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#126D811yescharacteristic
556#126D811yescharacteristic
557#125—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—21no—
562#125—21no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125D811yescharacteristic
577#124—21no—
578#124—21no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124D811yescharacteristic
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123D811yescharacteristic
600#123D811yescharacteristic
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
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
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—41no—
629#121—41no—
630#121—41no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121D811yescharacteristic
635#120—41no—
636#120—41no—
637#120—41no—
638#120—41no—
639C4×Q8—21no—
640C4×Q8—21no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8C2×D411yescharacteristic
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—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—
673C4×D4—41no—
674C4×D4C2×D411yescharacteristic
675C4×D4C2×D411yescharacteristic
676C4×D4C2×D411yescharacteristic
677#117—21no—
678#117—21no—
679#117—21no—
680#117—21no—
681#117—21no—
682#117—41no—
683#117—41no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688#117C2×D411yescharacteristic
689#117C2×D411yescharacteristic
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C42C2×D411yescharacteristic
702Q32—41no—
703Q32—41no—
704SD32—22no—
705SD32—22no—
706SD32—41no—
707SD32—41no—
708SD32—41no—
709SD32—41no—
710M32—41no—
711M32—41no—
712M32—41no—
713M32—41no—
714C2×C16—41no—
715C2×C16—41no—
716C2×C16C2411yescharacteristic
717C2×C16C2411yescharacteristic
718C2×C16C2411yescharacteristic
719C2×C16C2411yescharacteristic
720C2×C16C2411yescharacteristic
721C2×C16C2411yescharacteristic
722C2×C16C2411yescharacteristic
723C2×C16C2411yescharacteristic
724#107—21no—
725#107—21no—
726#107—21no—
727#107—21no—
728#107—21no—
729#107—21no—
730#107—21no—
731#107—21no—
732#107—21no—
733#107—21no—
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#107C2411yescharacteristic
743#107C2411yescharacteristic
744#106—21no—
745#106—21no—
746#106—21no—
747#106—21no—
748#106—21no—
749#106—21no—
750#106—21no—
751#106—21no—
752#106—21no—
753#106—21no—
754#106—21no—
755C4⋊C8C2×D411yescharacteristic
756C4⋊C8C2×D411yescharacteristic
757C4⋊C8C2×D411yescharacteristic
758C4⋊C8C2×D411yescharacteristic
759C4⋊C8C2×D411yescharacteristic
760C4⋊C8C2×D411yescharacteristic
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#103—21no—
768#103—21no—
769#103—21no—
770#103—21no—
771#103—21no—
772#103—21no—
773#103—21no—
774#103—21no—
775#103—21no—
776#103—21no—
777#102—21no—
778#102—21no—
779#102—21no—
780#102—21no—
781#102—21no—
782#102—21no—
783#102—21no—
784#102—21no—
785#102—21no—
786#102—21no—
787#102—21no—
788#102—21no—
789C22⋊C8C2×D411yescharacteristic
790C22⋊C8C2×D411yescharacteristic
791C22⋊C8C2×D411yescharacteristic
792C22⋊C8C2×D411yescharacteristic
793C22⋊C8C2×D411yescharacteristic
794C22⋊C8C2×D411yescharacteristic
795#97C2×D411yescharacteristic
796#97C2×D411yescharacteristic
797#97C2×D411yescharacteristic
798#97C2×D411yescharacteristic
799C4×C8C2×D411yescharacteristic
800C4×C8C2×D411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805C24—41no—
806C24—41no—
807#41—42no—
808#41—81no—
809#41—162no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—41no—
814C2×Q8—41no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8C2×D811yescharacteristic
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—162no—
837C2×D4C2×D811yescharacteristic
838C2×D4C2×D811yescharacteristic
839C2×D4C2×D811yescharacteristic
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—162no—
854C22×C4C2×D811yescharacteristic
855C22×C4C2×D811yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859Q16—21no—
860Q16—21no—
861Q16—21no—
862Q16—21no—
863Q16—21no—
864Q16—21no—
865Q16—42no—
866SD16—42no—
867SD16—81no—
868SD16—81no—
869D8—21no—
870D8—21no—
871D8—21no—
872D8—21no—
873D8—21no—
874D8—42no—
875D8—42no—
876D8—81no—
877D82−1+412yes—
878M16—41no—
879M16—41no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—41no—
887C2×C8C22×D411yescharacteristic
888C2×C8C22×D411yescharacteristic
889C2×C8C22×D411yescharacteristic
890C2×C8C22×D411yescharacteristic
891C2×C8C22×D411yescharacteristic
892C2×C8C22×D411yescharacteristic
893C2×C8C22×D411yescharacteristic
894C2×C8C2511yescharacteristic
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
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⋊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⋊C4C2×D811yescharacteristic
946C4⋊C4C2×D811yescharacteristic
947C4⋊C4C2×D811yescharacteristic
948C4⋊C4C2×D811yescharacteristic
949C4⋊C4C2×D811yescharacteristic
950C4⋊C4C2×D811yescharacteristic
951C4⋊C4C2×D811yescharacteristic
952C4⋊C4C2×D811yescharacteristic
953C4⋊C4C2×D811yescharacteristic
954C4⋊C4C2×D811yescharacteristic
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—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4C2×D811yescharacteristic
985C22⋊C4C2×D811yescharacteristic
986C22⋊C4C2×D811yescharacteristic
987C22⋊C4C2×D811yescharacteristic
988C22⋊C4C2×D811yescharacteristic
989C22⋊C4C2×D811yescharacteristic
990C22⋊C4C2×D811yescharacteristic
991C22⋊C4C2×D811yescharacteristic
992C22⋊C4C2×D811yescharacteristic
993C22⋊C4C2×D811yescharacteristic
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42C2×D811yescharacteristic
1008C42C2×D811yescharacteristic
1009C42C22×D411yescharacteristic
1010C42C22×D411yescharacteristic
1011C42C22×D411yescharacteristic
1012C42C22×D411yescharacteristic
1013C16—21no—
1014C16—21no—
1015C16—21no—
1016C16—21no—
1017C16—21no—
1018C16—21no—
1019C16—21no—
1020C16—21no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—82no—
1025C23—82no—
1026C23—82no—
1027C23—161no—
1028C23—161no—
1029C23—161no—
1030C23C22×D811yescharacteristic
1031C23C22×D811yescharacteristic
1032C23C22×D811yescharacteristic
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—82no—
1041Q8—161no—
1042Q8—161no—
1043Q8—161no—
1044Q8—161no—
1045Q8—161no—
1046D4—22no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—82no—
1056D4—82no—
1057D4—82no—
1058D4—82no—
1059D4—161no—
1060D4—161no—
1061D4—161no—
1062D4—161no—
1063D4—161no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—161no—
1088C2×C4—161no—
1089C2×C4—161no—
1090C2×C4—161no—
1091C2×C4—161no—
1092C2×C4—161no—
1093C2×C4—161no—
1094C2×C4—161no—
1095C2×C4—161no—
1096C2×C4—161no—
1097C2×C4—161no—
1098C2×C4C22×D811yescharacteristic
1099C2×C4C22×D811yescharacteristic
1100C2×C4C22×D811yescharacteristic
1101C2×C4C22×D811yescharacteristic
1102C2×C4C22×D811yescharacteristic
1103C2×C4C22×D811yescharacteristic
1104C2×C4C22×D811yescharacteristic
1105C2×C4C22×D811yescharacteristic
1106C2×C4C22×D811yescharacteristic
1107C2×C4C22×D811yescharacteristic
1108C2×C4C22×D811yescharacteristic
1109C2×C4C23×D411yescharacteristic
1110C8—21no—
1111C8—21no—
1112C8—21no—
1113C8—21no—
1114C8—21no—
1115C8—21no—
1116C8—21no—
1117C8C2×2−1+411yescharacteristic
1118C8#58511yescharacteristic
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—42no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—164no—
1138C22—322no—
1139C22C23×D811yescharacteristic
1140C4—21no—
1141C4—21no—
1142C4—21no—
1143C4—21no—
1144C4—21no—
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4#348911yescharacteristic
1165C4#358611yescharacteristic
1166C2—41no—
1167C2—41no—
1168C2—41no—
1169C2—82no—
1170C2—161no—
1171C2—161no—
1172C2#6209511yescharacteristic
1173C2#6263611yescharacteristic
1174C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#61471C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62496C2semidirect
3. #33955C2semidirect
4. #33952C2semidirect
5. #33942C2semidirect
6. #33938C2semidirect
7. #33920C2semidirect
8. #33919C2semidirect
9. #33917C2semidirect
10. #33916C2semidirect
11. #33913C2semidirect
12. #33910C2semidirect
13. #33891C2semidirect
14. #33890C2semidirect
15. #33881C2semidirect
16. #33878C2semidirect
17. #33878C2semidirect
18. #33877C2semidirect
19. #33826C2semidirect
20. #33824C2semidirect
21. #33818C2semidirect
22. #33809C2semidirect
23. #33807C2semidirect
24. #33806C2semidirect
25. #33683C2semidirect
26. #33680C2semidirect
27. #33670C2semidirect
28. #33633C2semidirect
29. #33631C2semidirect
30. #33627C2semidirect
31. #33509C2semidirect
36. #3383C22semidirect
37. Q8×Q16C22semidirect
44. #3342C22semidirect
45. #3342C22semidirect
47. #3338C22semidirect
50. #3336C22semidirect
61. #3177C22semidirect
62. #3177C22semidirect
65. #3170C22semidirect
67. #3164C22semidirect
68. #3164C22semidirect
69. #3160C22semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2255C22semidirect
80. #2255C22semidirect
81. #2253C22semidirect
82. #2252C22semidirect
84. #2243C22semidirect
85. #2243C22semidirect
86. #2243C22semidirect
87. #2242C22semidirect
89. #2237C22semidirect
90. #2237C22semidirect
91. #2237C22semidirect
92. #2237C22semidirect
93. #2237C22semidirect
94. #2236C22semidirect
95. #2236C22semidirect
96. #2236C22semidirect
97. #2236C22semidirect
98. #2235C22semidirect
102. #2234C22semidirect
103. #2234C22semidirect
104. #2233C22semidirect
106. #2232C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2229C22semidirect
110. #2229C22semidirect
111. #2229C22semidirect
112. #2229C22semidirect
113. #2229C22semidirect
118. #2228C22semidirect
119. #2228C22semidirect
120. #2228C22semidirect
121. #2228C22semidirect
122. #2228C22semidirect
123. #2227C22semidirect
124. #2227C22semidirect
125. #2227C22semidirect
128. #2226C22semidirect
129. #2226C22semidirect
130. #2225C22semidirect
134. #2224C22semidirect
135. #2224C22semidirect
136. #2224C22semidirect
140. #2220C22semidirect
141. #2220C22semidirect
142. #2219C22semidirect
143. #2219C22semidirect
144. #2219C22semidirect
146. #2217C22semidirect
147. #2217C22semidirect
148. #2216C22semidirect
149. #2211C22semidirect
150. #2211C22semidirect
151. #2211C22semidirect
152. #2211C22semidirect
153. #2209C22semidirect
155. #2208C22semidirect
156. #2208C22semidirect
165. #2183C22semidirect
166. #2183C22semidirect
167. #2176C22semidirect
172. #2175C22semidirect
173. #2175C22semidirect
174. #2175C22semidirect
175. C4×Q32C22semidirect
178. C4×SD32C22semidirect
180. #2169C22semidirect
182. #2168C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
185. #2164C22semidirect
186. #2164C22semidirect
187. #2163C22semidirect
188. #2159C22semidirect
189. #2159C22semidirect
190. #2159C22semidirect
191. #2159C22semidirect
192. #2158C22semidirect
193. C2×#366C22semidirect
194. #2151C22semidirect
195. #2151C22semidirect
196. #2150C22semidirect

Maximal subgroups

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

subgroupindex
#624962
#614712
#339552
#339522
#339422
#339382
#339202
#339192
#339172
#339162
#339132
#339102
#338912
#338902
#338812
#338782
#338772
#338262
#338242
#338182
#338092
#338072
#338062
#336832
#336802
#336702
#336332
#336312
#336272
#335092