Finite Group Databasebeta

← #7624717

Subgroups — #7624717

Order 512.

1200 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62488C211yesmaximal, characteristic, complemented
2#61473C211yesmaximal, characteristic, complemented
3#33957C211yesmaximal, characteristic, complemented
4#33953C211yesmaximal, characteristic, complemented
5#33944C211yesmaximal, characteristic, complemented
6#33934C211yesmaximal, characteristic, complemented
7#33916C211yesmaximal, characteristic, complemented
8#33913C211yesmaximal, characteristic, complemented
9#33913C211yesmaximal, characteristic, complemented
10#33910C211yesmaximal, characteristic, complemented
11#33906C211yesmaximal, characteristic, complemented
12#33905C211yesmaximal, characteristic, complemented
13#33887C211yesmaximal, characteristic, complemented
14#33883C211yesmaximal, characteristic, complemented
15#33880C211yesmaximal, characteristic, complemented
16#33875C211yesmaximal, characteristic, complemented
17#33868C211yesmaximal, characteristic, complemented
18#33866C211yesmaximal, characteristic, complemented
19#33828C211yesmaximal, characteristic, complemented
20#33824C211yesmaximal, characteristic, complemented
21#33816C211yesmaximal, characteristic, complemented
22#33809C211yesmaximal, characteristic, complemented
23#33808C211yesmaximal, characteristic, complemented
24#33805C211yesmaximal, characteristic, complemented
25#33684C211yesmaximal, characteristic, complemented
26#33681C211yesmaximal, characteristic, complemented
27#33677C211yesmaximal, characteristic, complemented
28#33633C211yesmaximal, characteristic, complemented
29#33632C211yesmaximal, characteristic, complemented
30C2×#2227C211yesmaximal, characteristic, complemented
31#33506C211yesmaximal, characteristic, complemented
32#3552—21no—
33#3516—21no—
34#3393C2211yescharacteristic
35#3386—21no—
36#3383C2211yescharacteristic
37#3383C2211yescharacteristic
38Q8×D8C2211yescharacteristic
39#3377—21no—
40#3353—21no—
41#3346—21no—
42#3346—21no—
43#3342C2211yescharacteristic
44#3339C2211yescharacteristic
45#3339C2211yescharacteristic
46#3339C2211yescharacteristic
47#3338C2211yescharacteristic
48#3338C2211yescharacteristic
49#3338C2211yescharacteristic
50#3336C2211yescharacteristic
51#3334C2211yescharacteristic
52#3327—21no—
53#3320—21no—
54#3316—21no—
55D4×Q16C2211yescharacteristic
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic
58#3243—21no—
59#3243—21no—
60#3239—21no—
61#3177C2211yescharacteristic
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69C2×#500C2211yescharacteristic
70#3121—21no—
71#3120—21no—
72#3117—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2950C2211yescharacteristic
76C2×C4×Q16C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2253C2211yescharacteristic
82#2252C2211yescharacteristic
83#2245C2211yescharacteristic
84#2243C2211yescharacteristic
85#2243C2211yescharacteristic
86#2243C2211yescharacteristic
87#2242C2211yescharacteristic
88#2241C2211yescharacteristic
89#2237C2211yescharacteristic
90#2237C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic
93#2236C2211yescharacteristic
94#2236C2211yescharacteristic
95#2236C2211yescharacteristic
96#2236C2211yescharacteristic
97#2236C2211yescharacteristic
98#2236C2211yescharacteristic
99#2235C2211yescharacteristic
100#2234C2211yescharacteristic
101#2234C2211yescharacteristic
102#2233C2211yescharacteristic
103#2233C2211yescharacteristic
104#2233C2211yescharacteristic
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic
107#2229C2211yescharacteristic
108#2229C2211yescharacteristic
109#2229C2211yescharacteristic
110#2229C2211yescharacteristic
111#2229C2211yescharacteristic
112#2229C2211yescharacteristic
113#2229C2211yescharacteristic
114#2229C2211yescharacteristic
115#2228C2211yescharacteristic
116#2228C2211yescharacteristic
117#2228C2211yescharacteristic
118#2228C2211yescharacteristic
119#2227C2211yescharacteristic
120#2227C2211yescharacteristic
121#2227C2211yescharacteristic
122#2227C2211yescharacteristic
123#2227C2211yescharacteristic
124#2227C2211yescharacteristic
125#2227C2211yescharacteristic
126#2227C2211yescharacteristic
127#2227C2211yescharacteristic
128#2227C2211yescharacteristic
129#2227C2211yescharacteristic
130#2225C2211yescharacteristic
131#2225C2211yescharacteristic
132#2225C2211yescharacteristic
133#2224C2211yescharacteristic
134#2224C2211yescharacteristic
135#2224C2211yescharacteristic
136#2224C2211yescharacteristic
137#2220C2211yescharacteristic
138#2220C2211yescharacteristic
139#2220C2211yescharacteristic
140#2219C2211yescharacteristic
141#2217C2211yescharacteristic
142#2217C2211yescharacteristic
143#2217C2211yescharacteristic
144#2216C2211yescharacteristic
145#2216C2211yescharacteristic
146#2216C2211yescharacteristic
147#2215C2211yescharacteristic
148#2215C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2211C2211yescharacteristic
153#2211C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2209C2211yescharacteristic
158#2208C2211yescharacteristic
159#2189C2211yescharacteristic
160#2188C2211yescharacteristic
161#2188C2211yescharacteristic
162#2186C2211yescharacteristic
163#2185C2211yescharacteristic
164#2185C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2176C2211yescharacteristic
168#2176C2211yescharacteristic
169#2176C2211yescharacteristic
170#2175C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic
176C4×Q32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×D16C2211yescharacteristic
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183D4×C16C2211yescharacteristic
184D4×C16C2211yescharacteristic
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic
187#2163C2211yescharacteristic
188#2159C2211yescharacteristic
189#2159C2211yescharacteristic
190#2158C2211yescharacteristic
191C2×#366C2211yescharacteristic
192C2×#366C2211yescharacteristic
193C2×#366C2211yescharacteristic
194#2151C2211yescharacteristic
195#2151C2211yescharacteristic
196C2×C4⋊C16C2211yescharacteristic
197#2141C2211yescharacteristic
198#2139C2211yescharacteristic
199#2138C2211yescharacteristic
200C2×#358C2211yescharacteristic
201C2×#358C2211yescharacteristic
202C2×#358C2211yescharacteristic
203C2×#135C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206#563—41no—
207#563—41no—
208#557—21no—
209#557—21no—
210#556—21no—
211#556—21no—
212#556—41no—
213#554—21no—
214#554—21no—
215#554—21no—
216#554—41no—
217#553—21no—
218#553—21no—
219#553—21no—
220#553—41no—
221#552—21no—
222#552—41no—
223D4×Q8—21no—
224D4×Q8—21no—
225D4×Q8—41no—
226#548—21no—
227#548—21no—
228#548—41no—
229#547—21no—
230#544—21no—
231#544—21no—
232#542—21no—
233#542—21no—
234#542—21no—
235#542—41no—
236#541—21no—
237#541—41no—
238#541—41no—
239#539—41no—
240#539—41no—
241#536—41no—
242C2×C4⋊Q8—21no—
243#529—21no—
244#529—21no—
245#529—41no—
246#529—41no—
247#529D411yescharacteristic
248#520—21no—
249#519—21no—
250C2×C4×Q8—21no—
251C2×Q32C2311yescharacteristic
252C2×Q32C2311yescharacteristic
253C2×Q32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×SD32C2311yescharacteristic
258C2×D16C2311yescharacteristic
259C2×M32C2311yescharacteristic
260C2×M32C2311yescharacteristic
261C22×C16C2311yescharacteristic
262C22×C16C2311yescharacteristic
263C22×C16C2311yescharacteristic
264C22×C16C2311yescharacteristic
265#501—21no—
266#501—21no—
267#501—21no—
268#501—21no—
269#500—21no—
270#500—21no—
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#500C2311yescharacteristic
274#500C2311yescharacteristic
275#500C2311yescharacteristic
276#500C2311yescharacteristic
277#500C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#499C2311yescharacteristic
282#499C2311yescharacteristic
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#495C2311yescharacteristic
286#494C2311yescharacteristic
287#491—21no—
288#489—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#488—21no—
293#485—21no—
294#485—21no—
295#485—21no—
296#484—21no—
297#484—21no—
298#484—21no—
299#484—21no—
300#484—21no—
301#484—21no—
302#483—21no—
303#482—21no—
304#482—21no—
305#482—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#478—21no—
317#478—21no—
318#478—21no—
319#477—21no—
320#477—21no—
321#477—21no—
322#475—21no—
323#475—21no—
324#475—21no—
325#474—21no—
326#474—21no—
327#474—21no—
328#474—21no—
329#470—21no—
330#468—21no—
331#468—21no—
332#468—21no—
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#467C2311yescharacteristic
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#465—21no—
346#465—21no—
347#464—21no—
348#464—21no—
349#464—21no—
350#464—21no—
351#462—21no—
352#461—21no—
353#452—21no—
354#452—21no—
355#451—21no—
356#451—21no—
357#448—21no—
358#448—21no—
359#446D411yescharacteristic
360C8×Q8C2311yescharacteristic
361#441—21no—
362#441—21no—
363#441—21no—
364#440—21no—
365#440—21no—
366#440—21no—
367#440—21no—
368#440—21no—
369C4×Q16—21no—
370C4×Q16—21no—
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×SD16—21no—
383C4×SD16—21no—
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#427C2311yescharacteristic
401#427C2311yescharacteristic
402#427C2311yescharacteristic
403C2×#107—21no—
404C2×#107C2311yescharacteristic
405C2×#107C2311yescharacteristic
406C2×#107C2311yescharacteristic
407C2×#107C2311yescharacteristic
408C2×#107C2311yescharacteristic
409C2×#107C2311yescharacteristic
410#419—21no—
411#417—21no—
412C2×#103—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#366C2311yescharacteristic
425#366C2311yescharacteristic
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#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
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×Q8—21no—
497C22×Q8—21no—
498C22×Q8—41no—
499C22×Q8—41no—
500#135—22no—
501#135—41no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×Q16—21no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16C2411yescharacteristic
510C2×Q16C2411yescharacteristic
511C2×Q16C2411yescharacteristic
512C2×Q16C2411yescharacteristic
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×SD16—21no—
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—21no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—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—41no—
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#125D811yescharacteristic
575#124—21no—
576#124—21no—
577#124—21no—
578#124—41no—
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#123D811yescharacteristic
597#123D811yescharacteristic
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
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⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8D811yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121D811yescharacteristic
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—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8C2×D411yescharacteristic
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—
673C4×D4—41no—
674C4×D4—41no—
675C4×D4—41no—
676C4×D4C2×D411yescharacteristic
677C4×D4C2×D411yescharacteristic
678C4×D4C2×D411yescharacteristic
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#117—41no—
689#117C2×D411yescharacteristic
690#117C2×D411yescharacteristic
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C42—41no—
701C2×C42C2×D411yescharacteristic
702Q32—22no—
703Q32—41no—
704Q32—41no—
705SD32—22no—
706SD32—41no—
707SD32—41no—
708SD32—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#107—21no—
733#107—21no—
734#107—21no—
735#107—21no—
736#107—21no—
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#107C2411yescharacteristic
743#107C2411yescharacteristic
744#107C2411yescharacteristic
745#107C2411yescharacteristic
746#107C2411yescharacteristic
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#103—21no—
778#103—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
805#41—42no—
806#41—81no—
807#41—162no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—41no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—41no—
821C2×Q8—41no—
822C2×Q8—41no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—162no—
826C2×Q8—162no—
827C2×Q8C2×D811yescharacteristic
828C2×D4—21no—
829C2×D4—21no—
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×C4C2×D811yescharacteristic
854C22×C4C2×D811yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858Q16—21no—
859Q16—21no—
860Q16—21no—
861Q16—21no—
862Q16—21no—
863Q16—21no—
864Q16—21no—
865Q16—42no—
866Q16—42no—
867Q16—81no—
868Q162−1+412yes—
869SD16—42no—
870SD16—42no—
871SD16—81no—
872SD16—81no—
873D8—21no—
874D8—21no—
875D8—21no—
876D8—21no—
877M16—41no—
878M16—41no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—41no—
886C2×C8C22×D411yescharacteristic
887C2×C8C22×D411yescharacteristic
888C2×C8C22×D411yescharacteristic
889C2×C8C22×D411yescharacteristic
890C2×C8C22×D411yescharacteristic
891C2×C8C22×D411yescharacteristic
892C2×C8C22×D411yescharacteristic
893C2×C8C2511yescharacteristic
894C4⋊C4—21no—
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—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⋊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⋊C4C2×D811yescharacteristic
948C4⋊C4C2×D811yescharacteristic
949C4⋊C4C2×D811yescharacteristic
950C4⋊C4C2×D811yescharacteristic
951C4⋊C4C2×D811yescharacteristic
952C4⋊C4C2×D811yescharacteristic
953C4⋊C4C2×D811yescharacteristic
954C4⋊C4C2×D811yescharacteristic
955C4⋊C4C2×D811yescharacteristic
956C4⋊C4C2×D811yescharacteristic
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⋊C4C2×D811yescharacteristic
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
993C42—41no—
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—
1023C23C22×D811yescharacteristic
1024C23C22×D811yescharacteristic
1025C23C22×D811yescharacteristic
1026Q8—22no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—82no—
1036Q8—82no—
1037Q8—82no—
1038Q8—82no—
1039Q8—161no—
1040Q8—161no—
1041Q8—161no—
1042Q8—161no—
1043Q8—161no—
1044D4—22no—
1045D4—22no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—82no—
1052D4—82no—
1053D4—82no—
1054D4—161no—
1055D4—161no—
1056D4—161no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—41no—
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—82no—
1080C2×C4—82no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4—161no—
1084C2×C4—161no—
1085C2×C4—161no—
1086C2×C4—161no—
1087C2×C4—161no—
1088C2×C4—161no—
1089C2×C4—161no—
1090C2×C4—161no—
1091C2×C4—161no—
1092C2×C4—161no—
1093C2×C4C22×D811yescharacteristic
1094C2×C4C22×D811yescharacteristic
1095C2×C4C22×D811yescharacteristic
1096C2×C4C22×D811yescharacteristic
1097C2×C4C22×D811yescharacteristic
1098C2×C4C22×D811yescharacteristic
1099C2×C4C22×D811yescharacteristic
1100C2×C4C22×D811yescharacteristic
1101C2×C4C22×D811yescharacteristic
1102C2×C4C22×D811yescharacteristic
1103C2×C4C22×D811yescharacteristic
1104C2×C4C23×D411yescharacteristic
1105C8—21no—
1106C8—21no—
1107C8—21no—
1108C8—21no—
1109C8—21no—
1110C8—21no—
1111C8—21no—
1112C8C2×2−1+411yescharacteristic
1113C8#58511yescharacteristic
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22#341712yes—
1129C22C23×D811yescharacteristic
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—21no—
1134C4—21no—
1135C4—21no—
1136C4—21no—
1137C4—21no—
1138C4—21no—
1139C4—21no—
1140C4—21no—
1141C4—42no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4#348911yescharacteristic
1156C4#358611yescharacteristic
1157C2—22no—
1158C2—41no—
1159C2—41no—
1160C2—161no—
1161C2—161no—
1162C2#6209511yescharacteristic
1163C2C2×#341711yescharacteristic
1164C2#6263611yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
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. #62488C2semidirect
2. #61473C2semidirect
3. #33957C2semidirect
4. #33953C2semidirect
5. #33944C2semidirect
6. #33934C2semidirect
7. #33916C2semidirect
8. #33913C2semidirect
9. #33913C2semidirect
10. #33910C2semidirect
11. #33906C2semidirect
12. #33905C2semidirect
13. #33887C2semidirect
14. #33883C2semidirect
15. #33880C2semidirect
16. #33875C2semidirect
17. #33868C2semidirect
18. #33866C2semidirect
19. #33828C2semidirect
20. #33824C2semidirect
21. #33816C2semidirect
22. #33809C2semidirect
23. #33808C2semidirect
24. #33805C2semidirect
25. #33684C2semidirect
26. #33681C2semidirect
27. #33677C2semidirect
28. #33633C2semidirect
29. #33632C2semidirect
30. C2×#2227C2semidirect
31. #33506C2semidirect

Maximal subgroups

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

subgroupindex
#624882
#614732
#339572
#339532
#339442
#339342
#339162
#339132
#339102
#339062
#339052
#338872
#338832
#338802
#338752
#338682
#338662
#338282
#338242
#338162
#338092
#338082
#338052
#336842
#336812
#336772
#336332
#336322
C2×#22272
#335062