Finite Group Databasebeta

← #7624869

Subgroups — #7624869

Order 512.

1299 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62332C211yesmaximal, characteristic, complemented
2#62330C211yesmaximal, characteristic, complemented
3#33913C211yesmaximal, characteristic, complemented
4#33912C211yesmaximal, characteristic, complemented
5#33911C211yesmaximal, characteristic, complemented
6#33910C211yesmaximal, characteristic, complemented
7#33884C211yesmaximal, characteristic, complemented
8#33883C211yesmaximal, characteristic, complemented
9#33882C211yesmaximal, characteristic, complemented
10#33881C211yesmaximal, characteristic, complemented
11#33876C211yesmaximal, characteristic, complemented
12#33875C211yesmaximal, characteristic, complemented
13#33874C211yesmaximal, characteristic, complemented
14#33873C211yesmaximal, characteristic, complemented
15#33837C211yesmaximal, characteristic, complemented
16#33835C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33833C211yesmaximal, characteristic, complemented
19#33818C211yesmaximal, characteristic, complemented
20#33817C211yesmaximal, characteristic, complemented
21#33770C211yesmaximal, characteristic, complemented
22#33769C211yesmaximal, characteristic, complemented
23#33767C211yesmaximal, characteristic, complemented
24#33764C211yesmaximal, characteristic, complemented
25#33747C211yesmaximal, characteristic, complemented
26#33746C211yesmaximal, characteristic, complemented
27#33613C211yesmaximal, characteristic, complemented
28#33612C211yesmaximal, characteristic, complemented
29#33611C211yesmaximal, characteristic, complemented
30#33610C211yesmaximal, characteristic, complemented
31#33435C211yesmaximal, characteristic, complemented
32#3551—21no—
33#3548—21no—
34C2×#510C2211yescharacteristic, complemented
35C2×#509C2211yescharacteristic
36C2×#508C2211yescharacteristic
37C2×#508C2211yescharacteristic
38C2×#504C2211yescharacteristic
39C2×#504C2211yescharacteristic, complemented
40#3339C2211yescharacteristic
41#3339C2211yescharacteristic
42#3338C2211yescharacteristic
43#3338C2211yescharacteristic, complemented
44#3336C2211yescharacteristic
45#3336C2211yescharacteristic
46#3334C2211yescharacteristic
47#3334C2211yescharacteristic, complemented
48#3333—21no—
49#3333—21no—
50#3330—21no—
51#3330—21no—
52#3326—21no—
53#3326—21no—
54#3323—21no—
55#3323—21no—
56#3287C2211yescharacteristic
57#3287C2211yescharacteristic, complemented
58#3285C2211yescharacteristic
59#3285C2211yescharacteristic
60#3283C2211yescharacteristic
61#3283C2211yescharacteristic, complemented
62#3280C2211yescharacteristic
63#3280C2211yescharacteristic
64#3256—21no—
65#3254—21no—
66#3204—21no—
67#3203—21no—
68#3203—21no—
69#3200—21no—
70#3170C2211yescharacteristic, complemented
71#3169C2211yescharacteristic, complemented
72#3168C2211yescharacteristic
73#3168C2211yescharacteristic
74#3061C2211yescharacteristic
75#3061C2211yescharacteristic
76#3061C2211yescharacteristic
77#3061C2211yescharacteristic
78#3061C2211yescharacteristic, complemented
79#3061C2211yescharacteristic, complemented
80#3059C2211yescharacteristic
81#3058C2211yescharacteristic
82#2931C2211yescharacteristic
83#2255C2211yescharacteristic, complemented
84#2255C2211yescharacteristic, complemented
85#2251C2211yescharacteristic
86#2250C2211yescharacteristic
87#2245C2211yescharacteristic, complemented
88#2244C2211yescharacteristic, complemented
89#2243C2211yescharacteristic
90#2243C2211yescharacteristic
91#2237C2211yescharacteristic
92#2237C2211yescharacteristic, complemented
93#2236C2211yescharacteristic
94#2236C2211yescharacteristic, complemented
95#2236C2211yescharacteristic, complemented
96#2235C2211yescharacteristic
97#2235C2211yescharacteristic, complemented
98#2235C2211yescharacteristic, complemented
99#2234C2211yescharacteristic
100#2234C2211yescharacteristic, complemented
101#2233C2211yescharacteristic
102#2233C2211yescharacteristic
103#2233C2211yescharacteristic, complemented
104#2232C2211yescharacteristic
105#2232C2211yescharacteristic
106#2232C2211yescharacteristic, complemented
107#2229C2211yescharacteristic, complemented
108#2229C2211yescharacteristic, complemented
109#2228C2211yescharacteristic, complemented
110#2228C2211yescharacteristic, complemented
111#2227C2211yescharacteristic, complemented
112#2226C2211yescharacteristic
113#2225C2211yescharacteristic, complemented
114#2224C2211yescharacteristic
115#2220C2211yescharacteristic
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic
118#2220C2211yescharacteristic
119#2220C2211yescharacteristic
120#2220C2211yescharacteristic, complemented
121#2220C2211yescharacteristic, complemented
122#2220C2211yescharacteristic, complemented
123#2219C2211yescharacteristic
124#2219C2211yescharacteristic, complemented
125#2219C2211yescharacteristic, complemented
126#2219C2211yescharacteristic, complemented
127#2218C2211yescharacteristic
128#2218C2211yescharacteristic
129#2218C2211yescharacteristic
130#2218C2211yescharacteristic
131#2217C2211yescharacteristic
132#2217C2211yescharacteristic
133#2217C2211yescharacteristic
134#2217C2211yescharacteristic
135#2217C2211yescharacteristic
136#2217C2211yescharacteristic, complemented
137#2217C2211yescharacteristic, complemented
138#2217C2211yescharacteristic, complemented
139#2216C2211yescharacteristic
140#2216C2211yescharacteristic, complemented
141#2216C2211yescharacteristic, complemented
142#2216C2211yescharacteristic, complemented
143#2215C2211yescharacteristic
144#2215C2211yescharacteristic
145#2215C2211yescharacteristic
146#2215C2211yescharacteristic
147#2211C2211yescharacteristic
148#2211C2211yescharacteristic
149#2210C2211yescharacteristic
150#2210C2211yescharacteristic
151#2209C2211yescharacteristic, complemented
152#2208C2211yescharacteristic
153#2207C2211yescharacteristic, complemented
154#2206C2211yescharacteristic
155#2189C2211yescharacteristic
156#2189C2211yescharacteristic
157#2189C2211yescharacteristic
158#2189C2211yescharacteristic
159#2189C2211yescharacteristic, complemented
160#2189C2211yescharacteristic, complemented
161#2188C2211yescharacteristic, complemented
162#2187C2211yescharacteristic
163#2186C2211yescharacteristic
164#2186C2211yescharacteristic
165#2186C2211yescharacteristic
166#2186C2211yescharacteristic
167#2186C2211yescharacteristic
168#2186C2211yescharacteristic
169#2185C2211yescharacteristic, complemented
170#2184C2211yescharacteristic
171#2177C2211yescharacteristic
172#2177C2211yescharacteristic
173#2176C2211yescharacteristic, complemented
174#2176C2211yescharacteristic, complemented
175#2175C2211yescharacteristic
176#2175C2211yescharacteristic
177#2175C2211yescharacteristic, complemented
178#2175C2211yescharacteristic, complemented
179#2168C2211yescharacteristic
180#2168C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185#2168C2211yescharacteristic, complemented
186#2168C2211yescharacteristic, complemented
187#2159C2211yescharacteristic
188#2159C2211yescharacteristic, complemented
189C2×#367C2211yescharacteristic, complemented
190C2×#366C2211yescharacteristic, complemented
191#2150C2211yescharacteristic, complemented
192#2139C2211yescharacteristic
193#2139C2211yescharacteristic
194#2139C2211yescharacteristic, complemented
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic
197#2138C2211yescharacteristic, complemented
198C2×#358C2211yescharacteristic, complemented
199C2×#357C2211yescharacteristic
200#2113C2211yescharacteristic
201#2113C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C2×#135C2311yescharacteristic
208C2×#135C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C2×#131C2311yescharacteristic
212C2×#131C2311yescharacteristic
213#563—41no—
214#562—41no—
215#562—41no—
216#560—41no—
217#555—41no—
218#554—21no—
219#554—21no—
220#554—41no—
221#553—21no—
222#553—21no—
223#552—21no—
224#552—21no—
225#551—41no—
226#550—21no—
227#550—21no—
228#550—41no—
229#548—21no—
230#548—21no—
231#547—21no—
232#547—21no—
233#547—21no—
234#547—21no—
235#546—21no—
236#546—21no—
237#540—41no—
238#540—41no—
239#540—41no—
240#540—41no—
241#538—41no—
242#538—41no—
243#537—21no—
244#537—21no—
245#537—21no—
246#537—21no—
247#537—21no—
248#537—21no—
249#537—41no—
250#537—41no—
251#536—21no—
252#535—21no—
253#533—21no—
254#532—21no—
255#532D411yescharacteristic
256#529—21no—
257#529—21no—
258#510—42no—
259#509—42no—
260#508—42no—
261#508—42no—
262C2×Q32C2311yescharacteristic
263C2×Q32C2311yescharacteristic
264C2×Q32C2311yescharacteristic
265C2×Q32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×SD32C2311yescharacteristic
269C2×SD32C2311yescharacteristic
270C2×SD32C2311yescharacteristic
271C2×SD32C2311yescharacteristic
272C2×SD32C2311yescharacteristic
273C2×SD32C2311yescharacteristic
274C2×D16C2311yescharacteristic
275C2×D16C2311yescharacteristic
276C2×D16C2311yescharacteristic
277C2×D16C2311yescharacteristic
278#504—42no—
279#504—42no—
280C2×M32C2311yescharacteristic
281C2×M32C2311yescharacteristic
282C2×M32C2311yescharacteristic
283C2×M32C2311yescharacteristic
284C2×M32C2311yescharacteristic
285C2×M32C2311yescharacteristic
286C22×C16C2311yescharacteristic
287C22×C16C2311yescharacteristic
288C22×C16C2311yescharacteristic
289C22×C16C2311yescharacteristic
290C22×C16C2311yescharacteristic
291C22×C16C2311yescharacteristic
292#500C2311yescharacteristic
293#500C2311yescharacteristic
294#499C2311yescharacteristic
295#499C2311yescharacteristic
296#495C2311yescharacteristic
297#495C2311yescharacteristic
298#494C2311yescharacteristic
299#493C2311yescharacteristic
300#488—21no—
301#488—21no—
302#487—21no—
303#486—21no—
304#485—21no—
305#485—21no—
306#484—21no—
307#484—21no—
308#484—21no—
309#484—21no—
310#483—21no—
311#483—21no—
312#482—21no—
313#482—21no—
314#481—21no—
315#481—21no—
316#480—21no—
317#480—21no—
318#480—21no—
319#480—21no—
320#479—21no—
321#479—21no—
322#478—21no—
323#478—21no—
324#477—21no—
325#477—21no—
326#474—21no—
327#474—21no—
328#470—21no—
329#470—21no—
330#469—21no—
331#469—21no—
332#468—21no—
333#468—21no—
334#468—21no—
335#468—21no—
336#468—21no—
337#468—21no—
338#468—21no—
339#468—21no—
340#468—21no—
341#468—21no—
342#468—21no—
343#468—21no—
344#467—21no—
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#467C2311yescharacteristic
349#467C2311yescharacteristic
350#467C2311yescharacteristic
351#467C2311yescharacteristic
352#467C2311yescharacteristic
353#467C2311yescharacteristic
354#467C2311yescharacteristic
355#467C2311yescharacteristic
356#467C2311yescharacteristic
357#466—21no—
358#466C2311yescharacteristic
359#466C2311yescharacteristic
360#466C2311yescharacteristic
361#466C2311yescharacteristic
362#466C2311yescharacteristic
363#466C2311yescharacteristic
364#466C2311yescharacteristic
365#466C2311yescharacteristic
366#466C2311yescharacteristic
367#466C2311yescharacteristic
368#466C2311yescharacteristic
369#466C2311yescharacteristic
370#465—21no—
371#465—21no—
372#464—21no—
373#464—21no—
374#463—21no—
375#463—21no—
376#461—21no—
377#461—21no—
378#460—21no—
379#460—21no—
380#452—21no—
381#452—21no—
382#452—21no—
383#452—21no—
384#452—21no—
385#452—21no—
386#450—21no—
387#450—21no—
388#449—21no—
389#449—21no—
390#449—21no—
391#449—21no—
392#449—21no—
393#449—21no—
394#448—21no—
395#448—21no—
396C4×Q16—21no—
397C4×Q16C2311yescharacteristic
398C4×Q16C2311yescharacteristic
399C4×Q16C2311yescharacteristic
400C4×Q16C2311yescharacteristic
401C4×SD16—21no—
402C4×SD16—21no—
403C4×D8—21no—
404C4×D8C2311yescharacteristic
405C4×D8C2311yescharacteristic
406C4×D8C2311yescharacteristic
407C4×D8C2311yescharacteristic
408#436D411yescharacteristic
409#436D411yescharacteristic
410#436D411yescharacteristic
411#436D411yescharacteristic
412C8×D4C2311yescharacteristic
413C8×D4C2311yescharacteristic
414C8×D4C2311yescharacteristic
415C8×D4C2311yescharacteristic
416#427C2311yescharacteristic
417#427C2311yescharacteristic
418C2×#107C2311yescharacteristic
419C2×#107C2311yescharacteristic
420C2×#107C2311yescharacteristic
421C2×#107C2311yescharacteristic
422C2×#107C2311yescharacteristic
423C2×#107C2311yescharacteristic
424#423D411yescharacteristic
425#419—21no—
426#418—21no—
427#417—21no—
428#417—21no—
429#417—21no—
430#417—21no—
431#417—21no—
432#417—21no—
433#408D411yescharacteristic
434#408D411yescharacteristic
435C2×C4×C8C2311yescharacteristic
436#367C2311yescharacteristic
437#367C2311yescharacteristic
438#367C2311yescharacteristic
439#367C2311yescharacteristic
440#367C2311yescharacteristic
441#367C2311yescharacteristic
442#367C2311yescharacteristic
443#367C2311yescharacteristic
444#366C2311yescharacteristic
445#366C2311yescharacteristic
446#366C2311yescharacteristic
447#366C2311yescharacteristic
448#366C2311yescharacteristic
449#366C2311yescharacteristic
450#366C2311yescharacteristic
451#366C2311yescharacteristic
452C4⋊C16C2311yescharacteristic
453C4⋊C16C2311yescharacteristic
454C4⋊C16C2311yescharacteristic
455C4⋊C16C2311yescharacteristic
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
482#357C2311yescharacteristic
483#357C2311yescharacteristic
484#357C2311yescharacteristic
485#357C2311yescharacteristic
486#357C2311yescharacteristic
487#357C2311yescharacteristic
488C22⋊C16C2311yescharacteristic
489C22⋊C16C2311yescharacteristic
490C22⋊C16C2311yescharacteristic
491C22⋊C16C2311yescharacteristic
492C22⋊C16C2311yescharacteristic
493C22⋊C16C2311yescharacteristic
494C22⋊C16C2311yescharacteristic
495C22⋊C16C2311yescharacteristic
496#346C2311yescharacteristic
497#346C2311yescharacteristic
498#346C2311yescharacteristic
499#346C2311yescharacteristic
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—21no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×D411yescharacteristic
510C2×#41C2×D411yescharacteristic
511C22×Q8—21no—
512C22×D4—21no—
513#135—41no—
514#135—41no—
515#135—41no—
516#135—41no—
517#135—41no—
518#135—41no—
519#135—41no—
520#135—41no—
521#135—41no—
522#135—41no—
523#135—41no—
524#135—41no—
525C2×Q16—21no—
526C2×Q16—21no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16C2411yescharacteristic
530C2×Q16C2411yescharacteristic
531C2×Q16C2411yescharacteristic
532C2×Q16C2411yescharacteristic
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C2×SD16—21no—
540C2×SD16—21no—
541C2×D8—21no—
542C2×D8—21no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8C2411yescharacteristic
546C2×D8C2411yescharacteristic
547C2×D8C2411yescharacteristic
548C2×D8C2411yescharacteristic
549#131—41no—
550#131—41no—
551#131—41no—
552#131—41no—
553C2×M16C2×D411yescharacteristic
554C2×M16C2×D411yescharacteristic
555C2×M16C2×D411yescharacteristic
556C2×M16C2×D411yescharacteristic
557C2×M16C2×D411yescharacteristic
558C2×M16C2×D411yescharacteristic
559C22×C8C2×D411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567C4⋊Q8—21no—
568C4⋊Q8—41no—
569C4⋊Q8D811yescharacteristic
570#127—21no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127D811yescharacteristic
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#126—41no—
580#126—41no—
581#125—21no—
582#125—21no—
583#125—41no—
584#125—41no—
585#125—41no—
586#125—41no—
587#125—41no—
588#124—21no—
589#124—21no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—41no—
595#124D811yescharacteristic
596#124D811yescharacteristic
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123—41no—
604#123—41no—
605#123—41no—
606#123—41no—
607#123—41no—
608#123—41no—
609#123—41no—
610#123—41no—
611#123—41no—
612#123—41no—
613#123—41no—
614#123—41no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—21no—
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⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—41no—
655#121—41no—
656#121—41no—
657#121—41no—
658#121—41no—
659#121—41no—
660#121—41no—
661#121—41no—
662#121—41no—
663#121—41no—
664#121—41no—
665#121—41no—
666#121—41no—
667#121—41no—
668#121—41no—
669#121—41no—
670#121—41no—
671#121—41no—
672#121—41no—
673#121—41no—
674#121—41no—
675#121—41no—
676#121—41no—
677#121—41no—
678#121—41no—
679#121—41no—
680#121—41no—
681#121—41no—
682#121—41no—
683#121—41no—
684#121—41no—
685#121D811yescharacteristic
686#121D811yescharacteristic
687#121D811yescharacteristic
688#121D811yescharacteristic
689#120—41no—
690#120—41no—
691#120—41no—
692#120—41no—
693C4×Q8—21no—
694C4×Q8—21no—
695C4×Q8—21no—
696C4×Q8—21no—
697C4×Q8—41no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—41no—
703C4×D4—41no—
704C4×D4—41no—
705C4×D4—41no—
706C4×D4—41no—
707C4×D4—41no—
708C4×D4—41no—
709C4×D4—41no—
710C4×D4—41no—
711C4×D4—41no—
712C4×D4—41no—
713C4×D4C2×D411yescharacteristic
714C4×D4C2×D411yescharacteristic
715C4×D4C2×D411yescharacteristic
716C4×D4C2×D411yescharacteristic
717#117—21no—
718#117—21no—
719#117—41no—
720#117—41no—
721#117—41no—
722#117—41no—
723#117—41no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—41no—
731C2×C4⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C42C2×D411yescharacteristic
735Q32—22no—
736Q32—41no—
737Q32—41no—
738Q32—41no—
739SD32—22no—
740SD32—22no—
741SD32—41no—
742SD32—41no—
743SD32—41no—
744SD32—41no—
745SD32—41no—
746SD32—41no—
747D16—22no—
748D16—41no—
749D16—41no—
750D16—41no—
751M32—22no—
752M32—22no—
753M32—41no—
754M32—41no—
755M32—41no—
756M32—41no—
757C2×C16—22no—
758C2×C16—22no—
759C2×C16—22no—
760C2×C16—41no—
761C2×C16—41no—
762C2×C16—41no—
763C2×C16C2411yescharacteristic
764C2×C16C2411yescharacteristic
765C2×C16C2411yescharacteristic
766C2×C16C2411yescharacteristic
767C2×C16C2411yescharacteristic
768C2×C16C2411yescharacteristic
769C2×C16C2411yescharacteristic
770C2×C16C2411yescharacteristic
771#107—21no—
772#107—21no—
773#107—21no—
774#107—21no—
775#107—21no—
776#107—21no—
777#107—21no—
778#107—21no—
779#107C2411yescharacteristic
780#107C2411yescharacteristic
781#107C2411yescharacteristic
782#107C2411yescharacteristic
783#107C2411yescharacteristic
784#107C2411yescharacteristic
785#107C2411yescharacteristic
786#107C2411yescharacteristic
787#106—21no—
788#106—21no—
789#106—21no—
790#106—21no—
791C4⋊C8C2×D411yescharacteristic
792C4⋊C8C2×D411yescharacteristic
793C4⋊C8C2×D411yescharacteristic
794C4⋊C8C2×D411yescharacteristic
795#103—21no—
796#103—21no—
797#103—21no—
798#103—21no—
799#103—21no—
800#103—21no—
801#103—21no—
802#103—21no—
803#103—21no—
804#103—21no—
805#103—21no—
806#103—21no—
807#103—21no—
808#103—21no—
809#103—21no—
810#103—21no—
811#102—21no—
812#102—21no—
813#102—21no—
814#102—21no—
815#102—21no—
816#102—21no—
817#102—21no—
818#102—21no—
819#102—21no—
820#102—21no—
821#102—21no—
822#102—21no—
823#102—21no—
824#102—21no—
825#102—21no—
826#102—21no—
827C22⋊C8C2×D411yescharacteristic
828C22⋊C8C2×D411yescharacteristic
829C22⋊C8C2×D411yescharacteristic
830C22⋊C8C2×D411yescharacteristic
831C22⋊C8C2×D411yescharacteristic
832C22⋊C8C2×D411yescharacteristic
833C22⋊C8C2×D411yescharacteristic
834C22⋊C8C2×D411yescharacteristic
835C4×C8C2×D411yescharacteristic
836C4×C8C2×D411yescharacteristic
837C4×C8C2411yescharacteristic
838C4×C8C2411yescharacteristic
839C24—41no—
840#41—41no—
841#41—41no—
842#41—41no—
843#41—41no—
844#41—81no—
845#41—81no—
846#41—81no—
847#41—81no—
848#41—81no—
849#41—81no—
850#41—81no—
851#41—81no—
852#41—81no—
853#41—81no—
854#41—81no—
855#41—81no—
856#41—162no—
857#41—162no—
858#41—162no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—41no—
864C2×Q8—41no—
865C2×Q8—41no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8C2×D811yescharacteristic
869C2×Q8C2×D811yescharacteristic
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4C2×D811yescharacteristic
898C2×D4C2×D811yescharacteristic
899C2×D4C2×D811yescharacteristic
900C2×D4C2×D811yescharacteristic
901C2×D4C2×D811yescharacteristic
902C2×D4C2×D811yescharacteristic
903C2×D4C2×D811yescharacteristic
904C2×D4C2×D811yescharacteristic
905C2×D4C2×D811yescharacteristic
906C2×D4C2×D811yescharacteristic
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4C2×D811yescharacteristic
925C22×C4C2×D811yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931Q16—21no—
932Q16—21no—
933Q16—21no—
934Q16—21no—
935Q16—21no—
936Q16—21no—
937Q16—21no—
938Q16—21no—
939Q16—81no—
940Q16—81no—
941SD16—81no—
942SD16—81no—
943SD16—81no—
944SD16—81no—
945SD16—81no—
946SD16—81no—
947SD16—81no—
948SD16—81no—
949D8—21no—
950D8—21no—
951D8—21no—
952D8—21no—
953D8—21no—
954D8—21no—
955D8—21no—
956D8—21no—
957D8—81no—
958D8—81no—
959M16—41no—
960M16—41no—
961M16—41no—
962M16—41no—
963M16—41no—
964M16—41no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—41no—
976C2×C8C22×D411yescharacteristic
977C2×C8C22×D411yescharacteristic
978C2×C8C22×D411yescharacteristic
979C2×C8C22×D411yescharacteristic
980C2×C8C22×D411yescharacteristic
981C2×C8C22×D411yescharacteristic
982C2×C8C22×D411yescharacteristic
983C2×C8C2511yescharacteristic
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4C2×D811yescharacteristic
1023C4⋊C4C2×D811yescharacteristic
1024C4⋊C4C2×D811yescharacteristic
1025C4⋊C4C2×D811yescharacteristic
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4C2×D811yescharacteristic
1061C22⋊C4C2×D811yescharacteristic
1062C22⋊C4C2×D811yescharacteristic
1063C22⋊C4C2×D811yescharacteristic
1064C22⋊C4C2×D811yescharacteristic
1065C22⋊C4C2×D811yescharacteristic
1066C22⋊C4C2×D811yescharacteristic
1067C22⋊C4C2×D811yescharacteristic
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42C2×D811yescharacteristic
1075C42C2×D811yescharacteristic
1076C42C22×D411yescharacteristic
1077C42C22×D411yescharacteristic
1078C16—21no—
1079C16—21no—
1080C16—21no—
1081C16—21no—
1082C16—21no—
1083C16—21no—
1084C16—21no—
1085C16H(5,𝔽2)12yes—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—161no—
1091C23—161no—
1092C23—161no—
1093C23C22×D811yescharacteristic
1094C23C22×D811yescharacteristic
1095C23C22×D811yescharacteristic
1096C23C22×D811yescharacteristic
1097C23C22×D811yescharacteristic
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—82no—
1109Q8—161no—
1110Q8—161no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—82no—
1130D4—161no—
1131D4—161no—
1132D4—161no—
1133D4—161no—
1134D4—161no—
1135D4—161no—
1136D4—161no—
1137D4—161no—
1138D4—161no—
1139D4—161no—
1140D4—161no—
1141D4—161no—
1142D4—161no—
1143D4—161no—
1144D4—161no—
1145D4—161no—
1146D4—161no—
1147D4—161no—
1148D4—161no—
1149D4—161no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—82no—
1175C2×C4—82no—
1176C2×C4—161no—
1177C2×C4—161no—
1178C2×C4—161no—
1179C2×C4—161no—
1180C2×C4—161no—
1181C2×C4—161no—
1182C2×C4—161no—
1183C2×C4—161no—
1184C2×C4—161no—
1185C2×C4—161no—
1186C2×C4—161no—
1187C2×C4—161no—
1188C2×C4—161no—
1189C2×C4—161no—
1190C2×C4—161no—
1191C2×C4C22×D811yescharacteristic
1192C2×C4C22×D811yescharacteristic
1193C2×C4C22×D811yescharacteristic
1194C2×C4C22×D811yescharacteristic
1195C2×C4C22×D811yescharacteristic
1196C2×C4C22×D811yescharacteristic
1197C2×C4C22×D811yescharacteristic
1198C2×C4C22×D811yescharacteristic
1199C2×C4C22×D811yescharacteristic
1200C2×C4C23×D411yescharacteristic
1201C8—21no—
1202C8—21no—
1203C8—21no—
1204C8—21no—
1205C8—21no—
1206C8—21no—
1207C8—21no—
1208C8C2×H(5,𝔽2)11yescharacteristic
1209C8#58511yescharacteristic
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—322no—
1238C22C23×D811yescharacteristic
1239C4—21no—
1240C4—21no—
1241C4—21no—
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—21no—
1247C4—21no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4#349611yescharacteristic
1261C4#358411yescharacteristic
1262C2—41no—
1263C2—41no—
1264C2—41no—
1265C2—41no—
1266C2—41no—
1267C2—161no—
1268C2—161no—
1269C2—161no—
1270C2—161no—
1271C2#6224511yescharacteristic
1272C2#6263611yescharacteristic
1273C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ #2931 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62332C2semidirect
2. #62330C2semidirect
3. #33913C2semidirect
4. #33912C2semidirect
5. #33911C2semidirect
6. #33910C2semidirect
7. #33884C2semidirect
8. #33883C2semidirect
9. #33882C2semidirect
10. #33881C2semidirect
11. #33876C2semidirect
12. #33875C2semidirect
13. #33874C2semidirect
14. #33873C2semidirect
15. #33837C2semidirect
16. #33835C2semidirect
17. #33834C2semidirect
18. #33833C2semidirect
19. #33818C2semidirect
20. #33817C2semidirect
21. #33770C2semidirect
22. #33769C2semidirect
23. #33767C2semidirect
24. #33764C2semidirect
25. #33747C2semidirect
26. #33746C2semidirect
27. #33613C2semidirect
28. #33612C2semidirect
29. #33611C2semidirect
30. #33610C2semidirect
31. #33435C2semidirect
34. C2×#510C22semidirect
39. C2×#504C22semidirect
43. #3338C22semidirect
47. #3334C22semidirect
57. #3287C22semidirect
61. #3283C22semidirect
70. #3170C22semidirect
71. #3169C22semidirect
78. #3061C22semidirect
79. #3061C22semidirect
83. #2255C22semidirect
84. #2255C22semidirect
87. #2245C22semidirect
88. #2244C22semidirect
92. #2237C22semidirect
94. #2236C22semidirect
95. #2236C22semidirect
97. #2235C22semidirect
98. #2235C22semidirect
100. #2234C22semidirect
103. #2233C22semidirect
106. #2232C22semidirect
107. #2229C22semidirect
108. #2229C22semidirect
109. #2228C22semidirect
110. #2228C22semidirect
111. #2227C22semidirect
113. #2225C22semidirect
120. #2220C22semidirect
121. #2220C22semidirect
122. #2220C22semidirect
124. #2219C22semidirect
125. #2219C22semidirect
126. #2219C22semidirect
136. #2217C22semidirect
137. #2217C22semidirect
138. #2217C22semidirect
140. #2216C22semidirect
141. #2216C22semidirect
142. #2216C22semidirect
151. #2209C22semidirect
153. #2207C22semidirect
159. #2189C22semidirect
160. #2189C22semidirect
161. #2188C22semidirect
169. #2185C22semidirect
173. #2176C22semidirect
174. #2176C22semidirect
177. #2175C22semidirect
178. #2175C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
185. #2168C22semidirect
186. #2168C22semidirect
188. #2159C22semidirect
189. C2×#367C22semidirect
190. C2×#366C22semidirect
191. #2150C22semidirect
194. #2139C22semidirect
195. #2139C22semidirect
197. #2138C22semidirect
198. C2×#358C22semidirect
201. #2113C22semidirect
202. C2×#346C22semidirect

Maximal subgroups

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

subgroupindex
#623322
#623302
#339132
#339122
#339112
#339102
#338842
#338832
#338822
#338812
#338762
#338752
#338742
#338732
#338372
#338352
#338342
#338332
#338182
#338172
#337702
#337692
#337672
#337642
#337472
#337462
#336132
#336122
#336112
#336102
#334352