Finite Group Databasebeta

← #7624322

Subgroups — #7624322

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62267C211yesmaximal, characteristic
2#61264C211yesmaximal, characteristic, complemented
3#33923C211yesmaximal, characteristic, complemented
4#33923C211yesmaximal, characteristic, complemented
5#33919C211yesmaximal, characteristic, complemented
6#33918C211yesmaximal, characteristic, complemented
7#33917C211yesmaximal, characteristic, complemented
8#33916C211yesmaximal, characteristic, complemented
9#33911C211yesmaximal, characteristic, complemented
10#33911C211yesmaximal, characteristic, complemented
11#33898C211yesmaximal, characteristic, complemented
12#33895C211yesmaximal, characteristic, complemented
13#33894C211yesmaximal, characteristic, complemented
14#33894C211yesmaximal, characteristic, complemented
15#33883C211yesmaximal, characteristic, complemented
16#33882C211yesmaximal, characteristic, complemented
17#33880C211yesmaximal, characteristic, complemented
18#33879C211yesmaximal, characteristic, complemented
19#33810C211yesmaximal, characteristic, complemented
20#33808C211yesmaximal, characteristic, complemented
21#33768C211yesmaximal, characteristic, complemented
22#33767C211yesmaximal, characteristic, complemented
23#33762C211yesmaximal, characteristic, complemented
24#33761C211yesmaximal, characteristic, complemented
25#33687C211yesmaximal, characteristic, complemented
26#33681C211yesmaximal, characteristic, complemented
27#33653C211yesmaximal, characteristic, complemented
28#33651C211yesmaximal, characteristic, complemented
29#33649C211yesmaximal, characteristic, complemented
30#33647C211yesmaximal, characteristic, complemented
31#33492C211yesmaximal, characteristic, complemented
32#3541—21no—
33#3495—21no—
34#3349—21no—
35#3349—21no—
36#3344—21no—
37#3344—21no—
38#3342C2211yescharacteristic
39#3342C2211yescharacteristic
40#3342C2211yescharacteristic
41#3339C2211yescharacteristic
42#3338C2211yescharacteristic
43#3338C2211yescharacteristic
44#3338C2211yescharacteristic
45#3336C2211yescharacteristic
46#3336C2211yescharacteristic
47#3336C2211yescharacteristic
48#3336C2211yescharacteristic
49#3336C2211yescharacteristic
50#3320—21no—
51#3316—21no—
52#3315—21no—
53#3313—21no—
54D4×Q16C2211yescharacteristic
55#3285C2211yescharacteristic
56#3285C2211yescharacteristic
57#3283C2211yescharacteristic
58#3258—21no—
59#3201—21no—
60#3196—21no—
61#3177C2211yescharacteristic
62#3175C2211yescharacteristic
63#3164C2211yescharacteristic
64#3097—21no—
65#3095—21no—
66#3082—21no—
67#3061C2211yescharacteristic
68#3059C2211yescharacteristic
69#3059C2211yescharacteristic
70#3050C2211yescharacteristic
71C2×#467C2211yescharacteristic
72C2×#467C2211yescharacteristic
73#2950C2211yescharacteristic
74#2929C2211yescharacteristic
75#2913C2211yescharacteristic
76C2×#427C2211yescharacteristic
77#2255C2211yescharacteristic, complemented
78#2255C2211yescharacteristic, complemented
79#2254C2211yescharacteristic, complemented
80#2253C2211yescharacteristic, complemented
81#2245C2211yescharacteristic, complemented
82#2243C2211yescharacteristic, complemented
83#2242C2211yescharacteristic, complemented
84#2241C2211yescharacteristic, complemented
85#2237C2211yescharacteristic
86#2237C2211yescharacteristic
87#2237C2211yescharacteristic
88#2237C2211yescharacteristic
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2237C2211yescharacteristic
94#2237C2211yescharacteristic
95#2237C2211yescharacteristic, complemented
96#2237C2211yescharacteristic, complemented
97#2237C2211yescharacteristic, complemented
98#2237C2211yescharacteristic, complemented
99#2237C2211yescharacteristic, complemented
100#2236C2211yescharacteristic
101#2236C2211yescharacteristic
102#2236C2211yescharacteristic
103#2236C2211yescharacteristic, complemented
104#2236C2211yescharacteristic, complemented
105#2235C2211yescharacteristic
106#2235C2211yescharacteristic
107#2235C2211yescharacteristic
108#2235C2211yescharacteristic
109#2235C2211yescharacteristic
110#2235C2211yescharacteristic
111#2235C2211yescharacteristic, complemented
112#2235C2211yescharacteristic, complemented
113#2235C2211yescharacteristic, complemented
114#2234C2211yescharacteristic
115#2234C2211yescharacteristic
116#2234C2211yescharacteristic
117#2234C2211yescharacteristic
118#2234C2211yescharacteristic, complemented
119#2233C2211yescharacteristic
120#2233C2211yescharacteristic, complemented
121#2229C2211yescharacteristic, complemented
122#2229C2211yescharacteristic, complemented
123#2229C2211yescharacteristic, complemented
124#2229C2211yescharacteristic, complemented
125#2229C2211yescharacteristic, complemented
126#2228C2211yescharacteristic, complemented
127#2227C2211yescharacteristic, complemented
128#2227C2211yescharacteristic, complemented
129#2226C2211yescharacteristic, complemented
130#2225C2211yescharacteristic, complemented
131#2225C2211yescharacteristic, complemented
132#2225C2211yescharacteristic, complemented
133#2220C2211yescharacteristic
134#2220C2211yescharacteristic
135#2220C2211yescharacteristic, complemented
136#2219C2211yescharacteristic
137#2219C2211yescharacteristic
138#2219C2211yescharacteristic
139#2219C2211yescharacteristic
140#2219C2211yescharacteristic
141#2219C2211yescharacteristic
142#2219C2211yescharacteristic, complemented
143#2219C2211yescharacteristic, complemented
144#2219C2211yescharacteristic, complemented
145#2217C2211yescharacteristic, complemented
146#2216C2211yescharacteristic, complemented
147#2216C2211yescharacteristic, complemented
148#2216C2211yescharacteristic, complemented
149#2211C2211yescharacteristic, complemented
150#2211C2211yescharacteristic, complemented
151#2209C2211yescharacteristic, complemented
152#2209C2211yescharacteristic, complemented
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2189C2211yescharacteristic, complemented
156#2189C2211yescharacteristic, complemented
157#2188C2211yescharacteristic
158#2188C2211yescharacteristic
159#2188C2211yescharacteristic
160#2188C2211yescharacteristic
161#2188C2211yescharacteristic
162#2188C2211yescharacteristic, complemented
163#2188C2211yescharacteristic, complemented
164#2185C2211yescharacteristic
165#2176C2211yescharacteristic, complemented
166#2176C2211yescharacteristic, complemented
167#2176C2211yescharacteristic, complemented
168#2175C2211yescharacteristic, complemented
169C4×Q32C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×Q32C2211yescharacteristic, complemented
172C4×SD32C2211yescharacteristic, complemented
173#2169C2211yescharacteristic
174#2169C2211yescharacteristic
175#2169C2211yescharacteristic
176#2169C2211yescharacteristic
177#2168C2211yescharacteristic
178#2168C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2164C2211yescharacteristic
182#2164C2211yescharacteristic
183#2159C2211yescharacteristic
184#2159C2211yescharacteristic
185#2159C2211yescharacteristic
186#2159C2211yescharacteristic
187#2159C2211yescharacteristic, complemented
188#2159C2211yescharacteristic, complemented
189#2158C2211yescharacteristic, complemented
190C2×#367C2211yescharacteristic, complemented
191#2141C2211yescharacteristic
192#2141C2211yescharacteristic
193#2141C2211yescharacteristic, complemented
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic
196#2139C2211yescharacteristic, complemented
197#2138C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199#2113C2211yescharacteristic
200#2113C2211yescharacteristic
201#2112C2211yescharacteristic
202#2112C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C2×#131C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#563—41no—
211#562—41no—
212#556—21no—
213#556—21no—
214#556—21no—
215#554—21no—
216#554—21no—
217#554—21no—
218#554—41no—
219#553—21no—
220#553—41no—
221#552—21no—
222#552—21no—
223#552—21no—
224#552—21no—
225#552—21no—
226#552—41no—
227#552—41no—
228#551—41no—
229#551—41no—
230D4×Q8—21no—
231#548—21no—
232#548—21no—
233#547—21no—
234#544—21no—
235#542—21no—
236#542—41no—
237#542—41no—
238#541—21no—
239#541—41no—
240#539—41no—
241#538—41no—
242#538—41no—
243#537—21no—
244#536—21no—
245#536—21no—
246#533—41no—
247#529—41no—
248#525—21no—
249#525D411yescharacteristic
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8—21no—
252#520—21no—
253#519—21no—
254C2×#117—21no—
255C2×Q32C2311yescharacteristic
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×M32C2311yescharacteristic
264C2×M32C2311yescharacteristic
265C2×M32C2311yescharacteristic
266C2×M32C2311yescharacteristic
267C2×M32C2311yescharacteristic
268C2×M32C2311yescharacteristic
269C22×C16C2311yescharacteristic
270C22×C16C2311yescharacteristic
271#501—21no—
272#501—21no—
273#500C2311yescharacteristic
274#500C2311yescharacteristic
275#500C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#495C2311yescharacteristic
280#494C2311yescharacteristic
281#491—21no—
282#489—21no—
283#485—21no—
284#485—21no—
285#485—21no—
286#485—21no—
287#485—21no—
288#485—21no—
289#485—21no—
290#485—21no—
291#485—21no—
292#485—21no—
293#485—21no—
294#484—21no—
295#484—21no—
296#484—21no—
297#484—21no—
298#484—21no—
299#484—21no—
300#483—21no—
301#483—21no—
302#483—21no—
303#483—21no—
304#483—21no—
305#482—21no—
306#481—21no—
307#479—21no—
308#479—21no—
309#479—21no—
310#479—21no—
311#479—21no—
312#478—21no—
313#477—21no—
314#477—21no—
315#477—21no—
316#475—21no—
317#475—21no—
318#475—21no—
319#470—21no—
320#470—21no—
321#470—21no—
322#470—21no—
323#470—21no—
324#468—21no—
325#468—21no—
326#468—21no—
327#467—21no—
328#467—21no—
329#467—21no—
330#467—21no—
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#467C2311yescharacteristic
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#466C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#465—21no—
352#465—21no—
353#464—21no—
354#464—21no—
355#462—21no—
356#461—21no—
357#452—21no—
358#452—21no—
359#452—21no—
360#452—21no—
361#451—21no—
362#451—21no—
363#448—21no—
364#448—21no—
365#441—21no—
366#441—21no—
367#441—21no—
368#440—21no—
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×D8C2311yescharacteristic
377#435D411yescharacteristic
378#435D411yescharacteristic
379#435D411yescharacteristic
380#435D411yescharacteristic
381C8×D4C2311yescharacteristic
382C8×D4C2311yescharacteristic
383C8×D4C2311yescharacteristic
384C8×D4C2311yescharacteristic
385#428—21no—
386#428—21no—
387#428—21no—
388#428—21no—
389#427—21no—
390#427—21no—
391#427C2311yescharacteristic
392#427C2311yescharacteristic
393#427C2311yescharacteristic
394#427C2311yescharacteristic
395#427C2311yescharacteristic
396#427C2311yescharacteristic
397#427C2311yescharacteristic
398#427C2311yescharacteristic
399C2×#107C2311yescharacteristic
400C2×#107C2311yescharacteristic
401C2×#107C2311yescharacteristic
402C2×#107C2311yescharacteristic
403C2×#107C2311yescharacteristic
404C2×#107C2311yescharacteristic
405C2×#107C2311yescharacteristic
406C2×#106—21no—
407#424D411yescharacteristic
408#419—21no—
409#419—21no—
410#419—21no—
411#417—21no—
412#416—21no—
413C2×#103—21no—
414C2×#103—21no—
415#408D411yescharacteristic
416#407D411yescharacteristic
417#405C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#367C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
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#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#358C2311yescharacteristic
470#358C2311yescharacteristic
471#358C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478C22⋊C16C2311yescharacteristic
479C22⋊C16C2311yescharacteristic
480C22⋊C16C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487C22⋊C16C2311yescharacteristic
488C22⋊C16C2311yescharacteristic
489C22⋊C16C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—21no—
496C2×#41C2×D411yescharacteristic
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C23×C4C2×D411yescharacteristic
501#135—41no—
502#135—41no—
503#135—41no—
504#135—41no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×Q16—21no—
508C2×Q16—21no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16C2411yescharacteristic
516C2×Q16C2411yescharacteristic
517C2×Q16C2411yescharacteristic
518C2×Q16C2411yescharacteristic
519C2×Q16C2411yescharacteristic
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—21no—
523C2×D8C2411yescharacteristic
524#131—41no—
525#131—41no—
526C2×M16C2×D411yescharacteristic
527C2×M16C2×D411yescharacteristic
528C2×M16C2×D411yescharacteristic
529C2×M16C2×D411yescharacteristic
530C22×C8—41no—
531C22×C8—41no—
532C22×C8C2×D411yescharacteristic
533C22×C8C2×D411yescharacteristic
534C22×C8C2×D411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—21no—
541C4⋊Q8—21no—
542C4⋊Q8—21no—
543C4⋊Q8—21no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#126—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#126—41no—
556#126—41no—
557#126—41no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#125—21no—
564#125—21no—
565#125—21no—
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#125—41no—
577#124—21no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123D811yescharacteristic
601#123D811yescharacteristic
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—41no—
632C22⋊Q8—41no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8D811yescharacteristic
638C22⋊Q8D811yescharacteristic
639#121—21no—
640#121—21no—
641#121—21no—
642#121—41no—
643#121—41no—
644#121—41no—
645#121—41no—
646#121—41no—
647#121—41no—
648#121—41no—
649#121D811yescharacteristic
650#121D811yescharacteristic
651#120—41no—
652#120D811yescharacteristic
653#120D811yescharacteristic
654C4×Q8—21no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—21no—
658C4×Q8—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×Q8—41no—
664C4×Q8—41no—
665C4×Q8—41no—
666C4×Q8—41no—
667C4×D4—21no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4—41no—
677C4×D4—41no—
678C4×D4—41no—
679C4×D4—41no—
680C4×D4C2×D411yescharacteristic
681C4×D4C2×D411yescharacteristic
682C4×D4C2×D411yescharacteristic
683C4×D4C2×D411yescharacteristic
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—21no—
692#117—41no—
693#117—41no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117—41no—
698#117—41no—
699#117—41no—
700#117—41no—
701#117C2×D411yescharacteristic
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C42—41no—
716Q32—41no—
717Q32—41no—
718Q32—41no—
719Q32—41no—
720Q32—41no—
721Q32—41no—
722SD32—41no—
723SD32—41no—
724M32—41no—
725M32—41no—
726M32—41no—
727M32—41no—
728M32—41no—
729M32—41no—
730C2×C16—41no—
731C2×C16—41no—
732C2×C16C2411yescharacteristic
733C2×C16C2411yescharacteristic
734C2×C16C2411yescharacteristic
735C2×C16C2411yescharacteristic
736C2×C16C2411yescharacteristic
737C2×C16C2411yescharacteristic
738C2×C16C2411yescharacteristic
739C2×C16C2411yescharacteristic
740#107—21no—
741#107—21no—
742#107—21no—
743#107—21no—
744#107—21no—
745#107—21no—
746#107—21no—
747#107—21no—
748#107—21no—
749#107—21no—
750#107C2411yescharacteristic
751#107C2411yescharacteristic
752#107C2411yescharacteristic
753#107C2411yescharacteristic
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#106—21no—
761#106—21no—
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768#106—21no—
769#106—21no—
770#106—21no—
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774C4⋊C8C2×D411yescharacteristic
775#103—21no—
776#103—21no—
777#103—21no—
778#103—21no—
779#103—21no—
780#103—21no—
781#103—21no—
782#103—21no—
783#103—21no—
784#103—21no—
785#103—21no—
786#103—21no—
787#103—21no—
788#103—21no—
789#103—21no—
790#103—21no—
791#103—21no—
792#103—21no—
793#103—21no—
794#103—21no—
795#103—21no—
796#103—21no—
797#103—21no—
798#103—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802#102—21no—
803C22⋊C8C2×D411yescharacteristic
804C22⋊C8C2×D411yescharacteristic
805C22⋊C8C2×D411yescharacteristic
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808C22⋊C8C2×D411yescharacteristic
809C22⋊C8C2×D411yescharacteristic
810C22⋊C8C2×D411yescharacteristic
811#97C2×D411yescharacteristic
812#97C2×D411yescharacteristic
813C4×C8C2411yescharacteristic
814C4×C8C2411yescharacteristic
815C24C2×D811yescharacteristic
816#41—41no—
817#41—41no—
818#41—81no—
819#41—81no—
820#41—81no—
821#41—81no—
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×Q8—41no—
834C2×Q8—41no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8C2×D811yescharacteristic
840C2×D4—21no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4C2×D811yescharacteristic
847C2×D4C2×D811yescharacteristic
848C2×D4C2×D811yescharacteristic
849C2×D4C2×D811yescharacteristic
850C2×D4C2×D811yescharacteristic
851C2×D4C2×D811yescharacteristic
852C2×D4C2×D811yescharacteristic
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×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4C2×D811yescharacteristic
869C22×C4C2×D811yescharacteristic
870C22×C4C2×D811yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876Q16—21no—
877Q16—21no—
878Q16—21no—
879Q16—21no—
880Q16—21no—
881Q16—21no—
882Q16—21no—
883Q16—21no—
884Q16—21no—
885Q16—21no—
886Q16—42no—
887Q16—81no—
888Q16—81no—
889Q16—81no—
890SD16—81no—
891SD16—81no—
892SD16—81no—
893D8—21no—
894D8—21no—
895M16—41no—
896M16—41no—
897M16—41no—
898M16—41no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—41no—
910C2×C8—41no—
911C2×C8—41no—
912C2×C8C22×D411yescharacteristic
913C2×C8C22×D411yescharacteristic
914C2×C8C22×D411yescharacteristic
915C2×C8C22×D411yescharacteristic
916C2×C8C22×D411yescharacteristic
917C2×C8C22×D411yescharacteristic
918C2×C8C22×D411yescharacteristic
919C2×C8C2511yescharacteristic
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
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⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4C2×D811yescharacteristic
973C4⋊C4C2×D811yescharacteristic
974C4⋊C4C2×D811yescharacteristic
975C4⋊C4C2×D811yescharacteristic
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
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⋊C4C2×D811yescharacteristic
1010C22⋊C4C2×D811yescharacteristic
1011C22⋊C4C2×D811yescharacteristic
1012C22⋊C4C2×D811yescharacteristic
1013C22⋊C4C2×D811yescharacteristic
1014C22⋊C4C2×D811yescharacteristic
1015C22⋊C4C2×D811yescharacteristic
1016C22⋊C4C2×D811yescharacteristic
1017C22⋊C4C2×D811yescharacteristic
1018C22⋊C4C2×D811yescharacteristic
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—
1033C42—41no—
1034C42C22×D411yescharacteristic
1035C42C22×D411yescharacteristic
1036C16—21no—
1037C16—21no—
1038C16—21no—
1039C16—21no—
1040C16—21no—
1041C16—21no—
1042C16—21no—
1043C16—21no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23C22×D811yescharacteristic
1049C23C22×D811yescharacteristic
1050C23C22×D811yescharacteristic
1051C23C22×D811yescharacteristic
1052C23C22×D811yescharacteristic
1053Q8—41no—
1054Q8—41no—
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—82no—
1065Q8—161no—
1066Q8—161no—
1067Q8—161no—
1068Q8—161no—
1069Q8—161no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—82no—
1080D4—161no—
1081D4—161no—
1082D4—161no—
1083D4—161no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
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—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—82no—
1113C2×C4—82no—
1114C2×C4—161no—
1115C2×C4—161no—
1116C2×C4—161no—
1117C2×C4—161no—
1118C2×C4—161no—
1119C2×C4—161no—
1120C2×C4—161no—
1121C2×C4—161no—
1122C2×C4—161no—
1123C2×C4—161no—
1124C2×C4—161no—
1125C2×C4C22×D811yescharacteristic
1126C2×C4C22×D811yescharacteristic
1127C2×C4C22×D811yescharacteristic
1128C2×C4C22×D811yescharacteristic
1129C2×C4C22×D811yescharacteristic
1130C2×C4C22×D811yescharacteristic
1131C2×C4C22×D811yescharacteristic
1132C2×C4C22×D811yescharacteristic
1133C2×C4C22×D811yescharacteristic
1134C2×C4C23×D411yescharacteristic
1135C8—21no—
1136C8—21no—
1137C8—21no—
1138C8—21no—
1139C8—21no—
1140C8—21no—
1141C8—21no—
1142C8#58511yescharacteristic
1143C8#58511yescharacteristic
1144C22—21no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—21no—
1155C22—21no—
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—82no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22C23×D811yescharacteristic
1164C4—21no—
1165C4—21no—
1166C4—21no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—21no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4#348511yescharacteristic
1189C4#358611yescharacteristic
1190C2—41no—
1191C2—41no—
1192C2—41no—
1193C2—41no—
1194C2—41no—
1195C2—161no—
1196C2#6169411yescharacteristic
1197C2#6263711yescharacteristic
1198C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#62267C2
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
2. #61264C2semidirect
3. #33923C2semidirect
4. #33923C2semidirect
5. #33919C2semidirect
6. #33918C2semidirect
7. #33917C2semidirect
8. #33916C2semidirect
9. #33911C2semidirect
10. #33911C2semidirect
11. #33898C2semidirect
12. #33895C2semidirect
13. #33894C2semidirect
14. #33894C2semidirect
15. #33883C2semidirect
16. #33882C2semidirect
17. #33880C2semidirect
18. #33879C2semidirect
19. #33810C2semidirect
20. #33808C2semidirect
21. #33768C2semidirect
22. #33767C2semidirect
23. #33762C2semidirect
24. #33761C2semidirect
25. #33687C2semidirect
26. #33681C2semidirect
27. #33653C2semidirect
28. #33651C2semidirect
29. #33649C2semidirect
30. #33647C2semidirect
31. #33492C2semidirect
77. #2255C22semidirect
78. #2255C22semidirect
79. #2254C22semidirect
80. #2253C22semidirect
81. #2245C22semidirect
82. #2243C22semidirect
83. #2242C22semidirect
84. #2241C22semidirect
95. #2237C22semidirect
96. #2237C22semidirect
97. #2237C22semidirect
98. #2237C22semidirect
99. #2237C22semidirect
103. #2236C22semidirect
104. #2236C22semidirect
111. #2235C22semidirect
112. #2235C22semidirect
113. #2235C22semidirect
118. #2234C22semidirect
120. #2233C22semidirect
121. #2229C22semidirect
122. #2229C22semidirect
123. #2229C22semidirect
124. #2229C22semidirect
125. #2229C22semidirect
126. #2228C22semidirect
127. #2227C22semidirect
128. #2227C22semidirect
129. #2226C22semidirect
130. #2225C22semidirect
131. #2225C22semidirect
132. #2225C22semidirect
135. #2220C22semidirect
142. #2219C22semidirect
143. #2219C22semidirect
144. #2219C22semidirect
145. #2217C22semidirect
146. #2216C22semidirect
147. #2216C22semidirect
148. #2216C22semidirect
149. #2211C22semidirect
150. #2211C22semidirect
151. #2209C22semidirect
152. #2209C22semidirect
155. #2189C22semidirect
156. #2189C22semidirect
162. #2188C22semidirect
163. #2188C22semidirect
165. #2176C22semidirect
166. #2176C22semidirect
167. #2176C22semidirect
168. #2175C22semidirect
169. C4×Q32C22semidirect
170. C4×Q32C22semidirect
171. C4×Q32C22semidirect
172. C4×SD32C22semidirect
187. #2159C22semidirect
188. #2159C22semidirect
189. #2158C22semidirect
190. C2×#367C22semidirect
193. #2141C22semidirect
196. #2139C22semidirect
197. #2138C22semidirect
198. C2×#358C22semidirect

Maximal subgroups

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

subgroupindex
#622672
#612642
#339232
#339192
#339182
#339172
#339162
#339112
#338982
#338952
#338942
#338832
#338822
#338802
#338792
#338102
#338082
#337682
#337672
#337622
#337612
#336872
#336812
#336532
#336512
#336492
#336472
#334922