Finite Group Databasebeta

← #7624699

Subgroups — #7624699

Order 512.

1219 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62475C211yesmaximal, characteristic, complemented
2#61430C211yesmaximal, characteristic, complemented
3#33957C211yesmaximal, characteristic, complemented
4#33955C211yesmaximal, characteristic, complemented
5#33938C211yesmaximal, characteristic, complemented
6#33937C211yesmaximal, characteristic, complemented
7#33917C211yesmaximal, characteristic, complemented
8#33916C211yesmaximal, characteristic, complemented
9#33913C211yesmaximal, characteristic, complemented
10#33912C211yesmaximal, characteristic, complemented
11#33906C211yesmaximal, characteristic, complemented
12#33904C211yesmaximal, characteristic, complemented
13#33884C211yesmaximal, characteristic, complemented
14#33883C211yesmaximal, characteristic, complemented
15#33876C211yesmaximal, characteristic, complemented
16#33875C211yesmaximal, characteristic, complemented
17#33868C211yesmaximal, characteristic, complemented
18#33867C211yesmaximal, characteristic, complemented
19#33822C211yesmaximal, characteristic, complemented
20#33816C211yesmaximal, characteristic, complemented
21#33813C211yesmaximal, characteristic, complemented
22#33806C211yesmaximal, characteristic, complemented
23#33800C211yesmaximal, characteristic, complemented
24#33798C211yesmaximal, characteristic, complemented
25#33677C211yesmaximal, characteristic, complemented
26#33671C211yesmaximal, characteristic, complemented
27#33662C211yesmaximal, characteristic, complemented
28#33630C211yesmaximal, characteristic, complemented
29#33626C211yesmaximal, characteristic, complemented
30C2×#2229C211yesmaximal, characteristic, complemented
31#33504C211yesmaximal, characteristic, complemented
32#3515—21no—
33#3480—21no—
34#3396C2211yescharacteristic
35#3383C2211yescharacteristic
36#3383C2211yescharacteristic
37#3381—21no—
38#3380C2211yescharacteristic
39#3365—21no—
40#3342C2211yescharacteristic
41#3339C2211yescharacteristic
42#3339C2211yescharacteristic
43#3339C2211yescharacteristic
44#3339C2211yescharacteristic
45#3338C2211yescharacteristic
46#3337—21no—
47#3337—21no—
48#3336C2211yescharacteristic
49#3336C2211yescharacteristic
50#3335—21no—
51#3334C2211yescharacteristic
52#3304—21no—
53#3301—21no—
54#3301—21no—
55#3287C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3233—21no—
59#3232—21no—
60#3232—21no—
61#3169C2211yescharacteristic
62#3168C2211yescharacteristic
63#3168C2211yescharacteristic
64#3168C2211yescharacteristic
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic
67#3160C2211yescharacteristic
68C2×#499C2211yescharacteristic
69C2×#499C2211yescharacteristic
70#3103—21no—
71#3102—21no—
72#3102—21no—
73C8×#41C2211yescharacteristic
74C4×#135C2211yescharacteristic
75C4×#135C2211yescharacteristic
76C2×C4×Q16C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2253C2211yescharacteristic
82#2253C2211yescharacteristic
83#2244C2211yescharacteristic
84#2244C2211yescharacteristic
85#2243C2211yescharacteristic
86#2243C2211yescharacteristic
87#2242C2211yescharacteristic
88#2242C2211yescharacteristic
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2236C2211yescharacteristic
94#2236C2211yescharacteristic
95#2235C2211yescharacteristic
96#2234C2211yescharacteristic
97#2234C2211yescharacteristic
98#2234C2211yescharacteristic
99#2234C2211yescharacteristic
100#2233C2211yescharacteristic
101#2233C2211yescharacteristic
102#2233C2211yescharacteristic
103#2233C2211yescharacteristic
104#2232C2211yescharacteristic
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic
108#2229C2211yescharacteristic
109#2229C2211yescharacteristic
110#2229C2211yescharacteristic
111#2229C2211yescharacteristic
112#2229C2211yescharacteristic
113#2229C2211yescharacteristic
114#2229C2211yescharacteristic
115#2229C2211yescharacteristic
116#2229C2211yescharacteristic
117#2229C2211yescharacteristic
118#2229C2211yescharacteristic
119#2229C2211yescharacteristic
120#2229C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2228C2211yescharacteristic
124#2228C2211yescharacteristic
125#2228C2211yescharacteristic
126#2228C2211yescharacteristic
127#2228C2211yescharacteristic
128#2228C2211yescharacteristic
129#2228C2211yescharacteristic
130#2228C2211yescharacteristic
131#2227C2211yescharacteristic
132#2227C2211yescharacteristic
133#2226C2211yescharacteristic
134#2226C2211yescharacteristic
135#2225C2211yescharacteristic
136#2224C2211yescharacteristic
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2219C2211yescharacteristic
140#2218C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2217C2211yescharacteristic
145#2216C2211yescharacteristic
146#2215C2211yescharacteristic
147#2215C2211yescharacteristic
148#2215C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2211C2211yescharacteristic
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2207C2211yescharacteristic
158#2206C2211yescharacteristic
159#2189C2211yescharacteristic
160#2189C2211yescharacteristic
161#2188C2211yescharacteristic
162#2186C2211yescharacteristic
163#2186C2211yescharacteristic
164#2185C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2177C2211yescharacteristic
168#2176C2211yescharacteristic
169#2176C2211yescharacteristic
170#2176C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic
176C4×SD32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×D16C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic
185#2163C2211yescharacteristic
186#2163C2211yescharacteristic
187#2162C2211yescharacteristic
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic
190#2158C2211yescharacteristic
191#2158C2211yescharacteristic
192C2×#367C2211yescharacteristic
193C2×#366C2211yescharacteristic
194#2150C2211yescharacteristic
195C2×C4⋊C16C2211yescharacteristic
196C2×C4⋊C16C2211yescharacteristic
197#2139C2211yescharacteristic
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200#2138C2211yescharacteristic
201C2×#358C2211yescharacteristic
202C2×#358C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206#559—21no—
207#559—41no—
208#557—21no—
209#557—21no—
210#556—21no—
211#556—41no—
212#554—21no—
213#554—21no—
214#553—21no—
215#553—21no—
216#553—21no—
217#553—21no—
218#553—41no—
219#553—41no—
220#552—21no—
221#552—21no—
222#552—41no—
223#552—41no—
224#552—41no—
225#550—21no—
226#548—21no—
227#548—21no—
228#547—21no—
229#547—41no—
230#541—41no—
231#539—41no—
232#539—41no—
233#533—21no—
234#532—21no—
235#532—41no—
236#529—21no—
237#529—21no—
238#529—21no—
239#529—21no—
240#529—21no—
241#529—41no—
242#529—41no—
243C2×#125—21no—
244C2×#125—21no—
245#520—41no—
246C4×#41—21no—
247C4×#41—21no—
248C4×#41—41no—
249C4×#41D411yescharacteristic
250C2×C4×Q8—21no—
251C2×Q32C2311yescharacteristic
252C2×Q32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×D16C2311yescharacteristic
258C2×D16C2311yescharacteristic
259C2×M32C2311yescharacteristic
260C2×M32C2311yescharacteristic
261C22×C16C2311yescharacteristic
262C22×C16C2311yescharacteristic
263C22×C16C2311yescharacteristic
264C22×C16C2311yescharacteristic
265#500C2311yescharacteristic
266#500C2311yescharacteristic
267#500C2311yescharacteristic
268#499—21no—
269#499—21no—
270#499—21no—
271#499—21no—
272#499—21no—
273#499C2311yescharacteristic
274#499C2311yescharacteristic
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#498—21no—
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#495C2311yescharacteristic
286#493C2311yescharacteristic
287#488—21no—
288#488—21no—
289#488—21no—
290#488—21no—
291#488—21no—
292#486—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#485—21no—
297#484—21no—
298#484—21no—
299#483—21no—
300#483—21no—
301#482—21no—
302#482—21no—
303#482—21no—
304#482—21no—
305#481—21no—
306#481—21no—
307#481—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#479—21no—
317#478—21no—
318#478—21no—
319#478—21no—
320#478—21no—
321#478—21no—
322#478—21no—
323#477—21no—
324#476—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#474—21no—
329#467C2311yescharacteristic
330#467C2311yescharacteristic
331#467C2311yescharacteristic
332#467C2311yescharacteristic
333#467C2311yescharacteristic
334#466—21no—
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#466C2311yescharacteristic
339#466C2311yescharacteristic
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#465—21no—
343#465—21no—
344#465—21no—
345#465—21no—
346#465—21no—
347#464—21no—
348#464—21no—
349#463—21no—
350#463—21no—
351#460—21no—
352#460—21no—
353#452—21no—
354#452—21no—
355#449—21no—
356#449—21no—
357#448—21no—
358#448—21no—
359C8×Q8D411yescharacteristic
360C8×Q8C2311yescharacteristic
361C4×Q16—21no—
362C4×Q16—21no—
363C4×Q16C2311yescharacteristic
364C4×Q16C2311yescharacteristic
365C4×Q16C2311yescharacteristic
366C4×Q16C2311yescharacteristic
367C4×Q16C2311yescharacteristic
368C4×Q16C2311yescharacteristic
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×SD16—21no—
373C4×SD16—21no—
374C4×SD16—21no—
375C4×SD16—21no—
376C4×SD16—21no—
377C4×SD16—21no—
378C4×SD16—21no—
379C4×SD16—21no—
380C4×SD16—21no—
381C4×D8—21no—
382C4×D8C2311yescharacteristic
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389C8×D4D411yescharacteristic
390C8×D4D411yescharacteristic
391C8×D4D411yescharacteristic
392C8×D4C2311yescharacteristic
393C8×D4C2311yescharacteristic
394C8×D4C2311yescharacteristic
395#431D411yescharacteristic
396#431D411yescharacteristic
397#431D411yescharacteristic
398#427—21no—
399#427C2311yescharacteristic
400#427C2311yescharacteristic
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403C2×#107C2311yescharacteristic
404C2×#107C2311yescharacteristic
405C2×#107C2311yescharacteristic
406C2×#107C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#106—21no—
409C2×#106—21no—
410#416—21no—
411#416—21no—
412C2×#103—21no—
413C2×C4×C8C2311yescharacteristic
414C2×C4×C8C2311yescharacteristic
415C2×C4×C8C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
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#358C2311yescharacteristic
465#358C2311yescharacteristic
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—21no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41D811yescharacteristic
499C22×Q8—21no—
500#135—22no—
501#135—22no—
502#135—41no—
503#135—41no—
504C2×Q16—22no—
505C2×Q16—21no—
506C2×Q16—41no—
507C2×Q16C2411yescharacteristic
508C2×Q16C2411yescharacteristic
509C2×Q16C2411yescharacteristic
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×D8—21no—
516C2×D8C2411yescharacteristic
517C2×D8C2411yescharacteristic
518C2×D8C2411yescharacteristic
519C22×C8C2×D411yescharacteristic
520C22×C8C2×D411yescharacteristic
521C22×C8C2×D411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#127—21no—
531#127—41no—
532#126—41no—
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#126—41no—
544#126—41no—
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—21no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#124—21no—
566#124—21no—
567#124—21no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—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—
581#123—41no—
582#123—41no—
583#123—41no—
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
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—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—41no—
619C4×Q8—21no—
620C4×Q8—21no—
621C4×Q8—21no—
622C4×Q8—21no—
623C4×Q8—21no—
624C4×Q8—21no—
625C4×Q8—21no—
626C4×Q8—21no—
627C4×Q8—21no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×Q8—41no—
635C4×Q8D811yescharacteristic
636C4×Q8C2×D411yescharacteristic
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4D811yescharacteristic
664C4×D4D811yescharacteristic
665C4×D4D811yescharacteristic
666C4×D4C2×D411yescharacteristic
667C4×D4C2×D411yescharacteristic
668C4×D4C2×D411yescharacteristic
669#117—21no—
670#117—21no—
671#117—21no—
672#117—21no—
673#117—41no—
674#117—41no—
675#117—41no—
676#117—41no—
677#117—41no—
678#117—41no—
679#117—41no—
680#117—41no—
681#117—41no—
682#117D811yescharacteristic
683#117D811yescharacteristic
684#117D811yescharacteristic
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702Q32—22no—
703Q32—41no—
704SD32—22no—
705SD32—41no—
706SD32—41no—
707SD32—41no—
708D16—41no—
709D16—41no—
710M32—41no—
711M32—41no—
712C2×C16—41no—
713C2×C16—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#107C2411yescharacteristic
733#107C2411yescharacteristic
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#106—21no—
743#106—21no—
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#102—21no—
776#102—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
795C4×C8C2×D411yescharacteristic
796C4×C8C2×D411yescharacteristic
797C4×C8C2×D411yescharacteristic
798C4×C8C2×D411yescharacteristic
799C4×C8C2×D411yescharacteristic
800C4×C8C2×D411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805#41—42no—
806#41—42no—
807#41—42no—
808#41—81no—
809#41—81no—
810#41—84no—
811#41—84no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—42no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—81no—
821C2×Q8C2×D811yescharacteristic
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
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—41no—
835C2×D4—41no—
836C2×D4C2×D811yescharacteristic
837C2×D4C2×D811yescharacteristic
838C2×D4C2×D811yescharacteristic
839C22×C4—41no—
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—41no—
854C22×C4C2×D811yescharacteristic
855C22×C4C2×D811yescharacteristic
856C22×C4C2×D811yescharacteristic
857C22×C4C2×D811yescharacteristic
858C22×C4C2×D811yescharacteristic
859C22×C4C2×D811yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863Q16—21no—
864Q16—21no—
865Q16—21no—
866Q16—21no—
867Q16—21no—
868Q16—42no—
869Q162−1+412yes—
870SD16—42no—
871SD16—42no—
872SD16—42no—
873SD16—81no—
874SD16—81no—
875D8—21no—
876D8—21no—
877D8—21no—
878D8—21no—
879D8—21no—
880D8—21no—
881D8—81no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—41no—
889C2×C8—41no—
890C2×C8—41no—
891C2×C8C22×D411yescharacteristic
892C2×C8C22×D411yescharacteristic
893C2×C8C22×D411yescharacteristic
894C2×C8C22×D411yescharacteristic
895C2×C8C22×D411yescharacteristic
896C2×C8C22×D411yescharacteristic
897C2×C8C22×D411yescharacteristic
898C2×C8C2511yescharacteristic
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
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⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
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
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42C2×D811yescharacteristic
1004C42C2×D811yescharacteristic
1005C42C2×D811yescharacteristic
1006C42C2×D811yescharacteristic
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—
1024C23C22×D811yescharacteristic
1025C23C22×D811yescharacteristic
1026C23C22×D811yescharacteristic
1027Q8—22no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—82no—
1035Q8—82no—
1036Q8—82no—
1037Q8—161no—
1038D4—22no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—82no—
1048D4—82no—
1049D4—82no—
1050D4—82no—
1051D4—82no—
1052D4—82no—
1053D4—82no—
1054D4—161no—
1055D4—161no—
1056D4—161no—
1057D4—161no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
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—82no—
1084C2×C4—82no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
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—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22#341412yes—
1137C22C23×D811yescharacteristic
1138C4—21no—
1139C4—21no—
1140C4—21no—
1141C4—21no—
1142C4—21no—
1143C4—21no—
1144C4—21no—
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—42no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4#348911yescharacteristic
1163C4#358611yescharacteristic
1164C2—22no—
1165C2—41no—
1166C2—41no—
1167C2—161no—
1168C2—161no—
1169C2—161no—
1170C2#6209511yescharacteristic
1171C2C2×#341411yescharacteristic
1172C2#6263511yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62475C2semidirect
2. #61430C2semidirect
3. #33957C2semidirect
4. #33955C2semidirect
5. #33938C2semidirect
6. #33937C2semidirect
7. #33917C2semidirect
8. #33916C2semidirect
9. #33913C2semidirect
10. #33912C2semidirect
11. #33906C2semidirect
12. #33904C2semidirect
13. #33884C2semidirect
14. #33883C2semidirect
15. #33876C2semidirect
16. #33875C2semidirect
17. #33868C2semidirect
18. #33867C2semidirect
19. #33822C2semidirect
20. #33816C2semidirect
21. #33813C2semidirect
22. #33806C2semidirect
23. #33800C2semidirect
24. #33798C2semidirect
25. #33677C2semidirect
26. #33671C2semidirect
27. #33662C2semidirect
28. #33630C2semidirect
29. #33626C2semidirect
30. C2×#2229C2semidirect
31. #33504C2semidirect

Maximal subgroups

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

subgroupindex
#624752
#614302
#339572
#339552
#339382
#339372
#339172
#339162
#339132
#339122
#339062
#339042
#338842
#338832
#338762
#338752
#338682
#338672
#338222
#338162
#338132
#338062
#338002
#337982
#336772
#336712
#336622
#336302
#336262
C2×#22292
#335042