Finite Group Databasebeta

← #7624106

Subgroups — #7624106

Order 512.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#61485C211yesmaximal, characteristic, complemented
2#61471C211yesmaximal, characteristic, complemented
3#33970C211yesmaximal, characteristic, complemented
4#33952C211yesmaximal, characteristic, complemented
5#33942C211yesmaximal, characteristic, complemented
6#33937C211yesmaximal, characteristic, complemented
7#33913C211yesmaximal, characteristic, complemented
8#33910C211yesmaximal, characteristic, complemented
9#33901C211yesmaximal, characteristic, complemented
10#33881C211yesmaximal, characteristic, complemented
11#33876C211yesmaximal, characteristic, complemented
12#33875C211yesmaximal, characteristic, complemented
13#33873C211yesmaximal, characteristic, complemented
14#33867C211yesmaximal, characteristic, complemented
15#33861C211yesmaximal, characteristic, complemented
16#33848C211yesmaximal, characteristic, complemented
17#33834C211yesmaximal, characteristic, complemented
18#33831C211yesmaximal, characteristic, complemented
19#33746C211yesmaximal, characteristic, complemented
20#33744C211yesmaximal, characteristic, complemented
21#33739C211yesmaximal, characteristic, complemented
22#33684C211yesmaximal, characteristic, complemented
23#33684C211yesmaximal, characteristic, complemented
24#33679C211yesmaximal, characteristic, complemented
25#33678C211yesmaximal, characteristic, complemented
26#33668C211yesmaximal, characteristic, complemented
27#33660C211yesmaximal, characteristic, complemented
28#33482C211yesmaximal, characteristic, complemented
29#33459C211yesmaximal, characteristic, complemented
30#33454C211yesmaximal, characteristic, complemented
31C2×#2175C211yesmaximal, characteristic, complemented
32#3522—21no—
33#3513—21no—
34C2×#509C2211yescharacteristic
35C2×#508C2211yescharacteristic
36C22×SD32C2211yescharacteristic
37#3396C2211yescharacteristic
38#3396C2211yescharacteristic, complemented
39Q8×Q16C2211yescharacteristic, complemented
40#3380C2211yescharacteristic
41#3375—21no—
42#3370—21no—
43#3339C2211yescharacteristic
44#3338C2211yescharacteristic, complemented
45#3336C2211yescharacteristic
46#3334C2211yescharacteristic
47#3334C2211yescharacteristic
48#3334C2211yescharacteristic, complemented
49#3333—21no—
50#3322—21no—
51#3310—21no—
52#3308—21no—
53#3308—21no—
54#3306—21no—
55#3287C2211yescharacteristic, complemented
56#3285C2211yescharacteristic
57#3285C2211yescharacteristic, complemented
58#3280C2211yescharacteristic
59#3280C2211yescharacteristic
60D4×D8C2211yescharacteristic
61#3176C2211yescharacteristic
62#3175C2211yescharacteristic
63#3175C2211yescharacteristic, complemented
64#3175C2211yescharacteristic, complemented
65#3169C2211yescharacteristic, complemented
66#3168C2211yescharacteristic
67#3124—21no—
68#3124—21no—
69#3119—21no—
70#3118—21no—
71#3114—21no—
72#3112—21no—
73#2966C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic, complemented
76#2951C2211yescharacteristic, complemented
77#2948C2211yescharacteristic
78C2×C4×Q16C2211yescharacteristic, complemented
79C2×C4×D8C2211yescharacteristic
80#2255C2211yescharacteristic, complemented
81#2255C2211yescharacteristic, complemented
82#2252C2211yescharacteristic, complemented
83#2250C2211yescharacteristic
84#2250C2211yescharacteristic, complemented
85#2249C2211yescharacteristic, complemented
86#2244C2211yescharacteristic, complemented
87#2243C2211yescharacteristic, complemented
88#2243C2211yescharacteristic, complemented
89#2243C2211yescharacteristic, complemented
90#2242C2211yescharacteristic, complemented
91#2240C2211yescharacteristic
92#2237C2211yescharacteristic, complemented
93#2236C2211yescharacteristic, complemented
94#2236C2211yescharacteristic, complemented
95#2235C2211yescharacteristic, complemented
96#2234C2211yescharacteristic, complemented
97#2233C2211yescharacteristic, complemented
98#2232C2211yescharacteristic
99#2232C2211yescharacteristic
100#2232C2211yescharacteristic, complemented
101#2232C2211yescharacteristic, complemented
102#2232C2211yescharacteristic, complemented
103#2232C2211yescharacteristic, complemented
104#2229C2211yescharacteristic, complemented
105#2229C2211yescharacteristic, complemented
106#2229C2211yescharacteristic, complemented
107#2228C2211yescharacteristic, complemented
108#2227C2211yescharacteristic, complemented
109#2227C2211yescharacteristic, complemented
110#2226C2211yescharacteristic
111#2224C2211yescharacteristic
112#2224C2211yescharacteristic
113#2224C2211yescharacteristic, complemented
114#2224C2211yescharacteristic, complemented
115#2224C2211yescharacteristic, complemented
116#2220C2211yescharacteristic
117#2220C2211yescharacteristic, complemented
118#2220C2211yescharacteristic, complemented
119#2218C2211yescharacteristic, complemented
120#2217C2211yescharacteristic, complemented
121#2217C2211yescharacteristic, complemented
122#2217C2211yescharacteristic, complemented
123#2216C2211yescharacteristic, complemented
124#2215C2211yescharacteristic
125#2215C2211yescharacteristic
126#2215C2211yescharacteristic
127#2215C2211yescharacteristic, complemented
128#2211C2211yescharacteristic, complemented
129#2211C2211yescharacteristic, complemented
130#2211C2211yescharacteristic, complemented
131#2211C2211yescharacteristic, complemented
132#2210C2211yescharacteristic
133#2210C2211yescharacteristic
134#2210C2211yescharacteristic, complemented
135#2210C2211yescharacteristic, complemented
136#2207C2211yescharacteristic
137#2206C2211yescharacteristic
138#2206C2211yescharacteristic
139#2206C2211yescharacteristic, complemented
140#2189C2211yescharacteristic
141#2189C2211yescharacteristic, complemented
142#2188C2211yescharacteristic, complemented
143#2187C2211yescharacteristic
144#2186C2211yescharacteristic
145#2186C2211yescharacteristic
146#2186C2211yescharacteristic, complemented
147#2186C2211yescharacteristic, complemented
148#2185C2211yescharacteristic
149#2184C2211yescharacteristic
150#2184C2211yescharacteristic
151#2184C2211yescharacteristic
152#2183C2211yescharacteristic, complemented
153#2183C2211yescharacteristic, complemented
154#2177C2211yescharacteristic
155#2177C2211yescharacteristic, complemented
156#2177C2211yescharacteristic, complemented
157#2175C2211yescharacteristic
158#2175C2211yescharacteristic
159#2175C2211yescharacteristic
160#2175C2211yescharacteristic
161#2175C2211yescharacteristic
162#2175C2211yescharacteristic, complemented
163#2175C2211yescharacteristic, complemented
164#2175C2211yescharacteristic, complemented
165#2175C2211yescharacteristic, complemented
166#2175C2211yescharacteristic, complemented
167#2175C2211yescharacteristic, complemented
168#2175C2211yescharacteristic, complemented
169#2175C2211yescharacteristic, complemented
170C4×Q32C2211yescharacteristic, complemented
171C4×Q32C2211yescharacteristic, complemented
172C4×Q32C2211yescharacteristic, complemented
173C4×SD32C2211yescharacteristic
174C4×SD32C2211yescharacteristic, complemented
175C4×SD32C2211yescharacteristic, complemented
176C4×D16C2211yescharacteristic
177C4×D16C2211yescharacteristic
178C4×D16C2211yescharacteristic
179C4×D16C2211yescharacteristic, complemented
180C4×D16C2211yescharacteristic, complemented
181C4×D16C2211yescharacteristic, complemented
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic, complemented
184#2168C2211yescharacteristic, complemented
185#2168C2211yescharacteristic, complemented
186D4×C16C2211yescharacteristic
187D4×C16C2211yescharacteristic, complemented
188#2164C2211yescharacteristic, complemented
189#2164C2211yescharacteristic, complemented
190#2162C2211yescharacteristic, complemented
191#2159C2211yescharacteristic, complemented
192C2×#366C2211yescharacteristic, complemented
193C2×#366C2211yescharacteristic, complemented
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic, complemented
196#2138C2211yescharacteristic, complemented
197C2×#358C2211yescharacteristic, complemented
198C2×#357C2211yescharacteristic
199C2×#357C2211yescharacteristic
200#2108C2211yescharacteristic, complemented
201#2108C2211yescharacteristic, complemented
202C2×#346C2211yescharacteristic, complemented
203C2×#135C2311yescharacteristic
204C2×#135C2311yescharacteristic
205C2×#135C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#559—21no—
210#559—21no—
211#559—41no—
212Q82—21no—
213#554—21no—
214#554—21no—
215#554—41no—
216#553—21no—
217#553—41no—
218#552—21no—
219#551—41no—
220#551—41no—
221#550—21no—
222#548—21no—
223#548—21no—
224#547—21no—
225#547—21no—
226#547—21no—
227#547—41no—
228#547—41no—
229#546—21no—
230#546—21no—
231#546—41no—
232D42—21no—
233#542—21no—
234#542—21no—
235#542—21no—
236#542—41no—
237#542—41no—
238#540—21no—
239#539—41no—
240#538—41no—
241#532—21no—
242#532—41no—
243#529—21no—
244#529—41no—
245#529D411yescharacteristic
246#525—41no—
247C2×#123—41no—
248#520—21no—
249#520—21no—
250#520—21no—
251#518—21no—
252C2×C4×Q8—21no—
253C2×C4×D4—21no—
254#509—24no—
255#508—24no—
256C2×Q32C2311yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×SD32—24no—
259C2×SD32C2311yescharacteristic
260C2×SD32C2311yescharacteristic
261C2×SD32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×D16C2311yescharacteristic
268C2×D16C2311yescharacteristic
269C2×D16C2311yescharacteristic
270C2×D16C2311yescharacteristic
271C2×D16C2311yescharacteristic
272C2×D16C2311yescharacteristic
273C2×M32C2311yescharacteristic
274C2×M32C2311yescharacteristic
275C22×C16C2311yescharacteristic
276C22×C16C2311yescharacteristic
277C22×C16C2311yescharacteristic
278C22×C16C2311yescharacteristic
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#499C2311yescharacteristic
284#499C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#495C2311yescharacteristic
288#495C2311yescharacteristic
289#493C2311yescharacteristic
290#493C2311yescharacteristic
291#490—21no—
292#489—21no—
293#489—21no—
294#489—21no—
295#488—21no—
296#486—21no—
297#485—21no—
298#484—21no—
299#484—21no—
300#483—21no—
301#482—21no—
302#481—21no—
303#480—21no—
304#480—21no—
305#480—21no—
306#480—21no—
307#480—21no—
308#480—21no—
309#479—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#477—21no—
314#477—21no—
315#477—21no—
316#477—21no—
317#476—21no—
318#474—21no—
319#474—21no—
320#474—21no—
321#469—21no—
322#468—21no—
323#468—21no—
324#468—21no—
325#467C2311yescharacteristic
326#467C2311yescharacteristic
327#467C2311yescharacteristic
328#467C2311yescharacteristic
329#466—21no—
330#466C2311yescharacteristic
331#466C2311yescharacteristic
332#466C2311yescharacteristic
333#466C2311yescharacteristic
334#466C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#463—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#460—21no—
348#460—21no—
349#460—21no—
350#459—21no—
351#452—21no—
352#452—21no—
353#450—21no—
354#450—21no—
355#449—21no—
356#449—21no—
357#449—21no—
358#449—21no—
359#448—21no—
360#448—21no—
361#447—21no—
362#447—21no—
363#446D411yescharacteristic
364C8×Q8C2311yescharacteristic
365#442—21no—
366#442—21no—
367#442—21no—
368#440—21no—
369#440—21no—
370#440—21no—
371#440—21no—
372#440—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377C4×Q16—21no—
378C4×Q16—21no—
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×Q16C2311yescharacteristic
384C4×Q16C2311yescharacteristic
385C4×Q16C2311yescharacteristic
386C4×Q16C2311yescharacteristic
387C4×SD16—21no—
388C4×D8—21no—
389C4×D8—21no—
390C4×D8—21no—
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399C4×D8C2311yescharacteristic
400C4×D8C2311yescharacteristic
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403#436D411yescharacteristic
404#435D411yescharacteristic
405#435D411yescharacteristic
406C8×D4C2311yescharacteristic
407C8×D4C2311yescharacteristic
408C8×D4C2311yescharacteristic
409#433D411yescharacteristic
410#433D411yescharacteristic
411#432D411yescharacteristic
412#427C2311yescharacteristic
413C2×#107C2311yescharacteristic
414C2×#107C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417C2×#107C2311yescharacteristic
418#418—21no—
419#417—21no—
420#417—21no—
421#417—21no—
422C2×#103—21no—
423C2×#102—21no—
424#405C2311yescharacteristic
425#405C2311yescharacteristic
426C2×C4×C8C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#367C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438#366C2311yescharacteristic
439#366C2311yescharacteristic
440#366C2311yescharacteristic
441#366C2311yescharacteristic
442#366C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
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#357C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
464#357C2311yescharacteristic
465#357C2311yescharacteristic
466#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
469#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484C22⋊C16C2311yescharacteristic
485C22⋊C16C2311yescharacteristic
486C22⋊C16C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490#346C2311yescharacteristic
491#346C2311yescharacteristic
492#346C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C4×C16C2311yescharacteristic
495C4×C16C2311yescharacteristic
496C4×C16C2311yescharacteristic
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C22×Q8—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C23×C4—41no—
509#135—22no—
510#135—22no—
511#135—22no—
512#135—41no—
513#135—41no—
514#135—41no—
515C2×Q16—22no—
516C2×Q16—21no—
517C2×Q16—41no—
518C2×Q16C2411yescharacteristic
519C2×Q16C2411yescharacteristic
520C2×Q16C2411yescharacteristic
521C2×SD16—21no—
522C2×SD16—21no—
523C2×SD16—21no—
524C2×SD16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8C2411yescharacteristic
537C2×D8C2411yescharacteristic
538C2×D8C2411yescharacteristic
539C2×D8C2411yescharacteristic
540C2×D8C2411yescharacteristic
541C2×M16C2×D411yescharacteristic
542C2×M16C2×D411yescharacteristic
543C22×C8C2×D411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#127—21no—
555#127—21no—
556#127—41no—
557#126—41no—
558#126—41no—
559#126—41no—
560#126—41no—
561#126—41no—
562#126—41no—
563#126D811yescharacteristic
564#126D811yescharacteristic
565#125—21no—
566#125—21no—
567#125—41no—
568#125—41no—
569#125D811yescharacteristic
570#124—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124D811yescharacteristic
583#123—41no—
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123D811yescharacteristic
604#123D811yescharacteristic
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8D811yescharacteristic
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121—41no—
639#121—41no—
640#121—41no—
641#121—41no—
642#121D811yescharacteristic
643#120—41no—
644#120—41no—
645#120—41no—
646#120—41no—
647C4×Q8—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8—21no—
652C4×Q8—21no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—41no—
656C4×Q8—41no—
657C4×Q8—41no—
658C4×Q8C2×D411yescharacteristic
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
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×D4—41no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4—41no—
684C4×D4—41no—
685C4×D4—41no—
686C4×D4—41no—
687C4×D4—41no—
688C4×D4—41no—
689C4×D4—41no—
690C4×D4C2×D411yescharacteristic
691C4×D4C2×D411yescharacteristic
692C4×D4C2×D411yescharacteristic
693#117—21no—
694#117—41no—
695#117—41no—
696#117—41no—
697#117—41no—
698#117—41no—
699#117C2×D411yescharacteristic
700#117C2×D411yescharacteristic
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718Q32—22no—
719Q32—41no—
720SD32—22no—
721SD32—22no—
722SD32—22no—
723SD32—22no—
724SD32—22no—
725SD32—41no—
726SD32—41no—
727SD32#4114yescomplemented
728D16—22no—
729D16—22no—
730D16—22no—
731D16—41no—
732D16—41no—
733D16—41no—
734M32—22no—
735M32—41no—
736C2×C16—22no—
737C2×C16—22no—
738C2×C16—41no—
739C2×C16—41no—
740C2×C16C2411yescharacteristic
741C2×C16C2411yescharacteristic
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748#107—21no—
749#107—21no—
750#107—21no—
751#107—21no—
752#107—21no—
753#107—21no—
754#107—21no—
755#107—21no—
756#107—21no—
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#107C2411yescharacteristic
763#107C2411yescharacteristic
764#107C2411yescharacteristic
765#106—21no—
766#106—21no—
767#106—21no—
768C4⋊C8C2×D411yescharacteristic
769C4⋊C8C2×D411yescharacteristic
770C4⋊C8C2×D411yescharacteristic
771C4⋊C8C2×D411yescharacteristic
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774#103—21no—
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#102—21no—
787#102—21no—
788#102—21no—
789#102—21no—
790#102—21no—
791#102—21no—
792#102—21no—
793#102—21no—
794#102—21no—
795#102—21no—
796#102—21no—
797#102—21no—
798#102—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802#102—21no—
803#102—21no—
804#102—21no—
805#102—21no—
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808C22⋊C8C2×D411yescharacteristic
809C22⋊C8C2×D411yescharacteristic
810C22⋊C8C2×D411yescharacteristic
811C22⋊C8C2×D411yescharacteristic
812#97C2×D411yescharacteristic
813#97C2×D411yescharacteristic
814#97C2×D411yescharacteristic
815#97C2×D411yescharacteristic
816C4×C8C2×D411yescharacteristic
817C4×C8C2×D411yescharacteristic
818C4×C8C2411yescharacteristic
819C4×C8C2411yescharacteristic
820C4×C8C2411yescharacteristic
821C4×C8C2411yescharacteristic
822C24—41no—
823C24—41no—
824#41—42no—
825#41—42no—
826#41—42no—
827#41—81no—
828#41—81no—
829#41—81no—
830#41—162no—
831#41—162no—
832#41—162no—
833#41—162no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—42no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—41no—
842C2×Q8—41no—
843C2×Q8—81no—
844C2×Q8C2×D811yescharacteristic
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—162no—
872C2×D4C2×D811yescharacteristic
873C2×D4C2×D811yescharacteristic
874C2×D4C2×D811yescharacteristic
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—162no—
897C22×C4C2×D811yescharacteristic
898C22×C4C2×D811yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902Q16—21no—
903Q16—21no—
904Q16—21no—
905Q16—21no—
906Q16—21no—
907Q16—42no—
908Q16C2×#4112yes—
909SD16—42no—
910SD16—42no—
911SD16—42no—
912SD16—81no—
913SD16—81no—
914SD16—81no—
915SD16—81no—
916D8—21no—
917D8—21no—
918D8—21no—
919D8—21no—
920D8—21no—
921D8—21no—
922D8—21no—
923D8—21no—
924D8—21no—
925D8—42no—
926D8—42no—
927D8—81no—
928D8—81no—
929D8C2×#4112yes—
930M16—41no—
931M16—41no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—41no—
939C2×C8C22×D411yescharacteristic
940C2×C8C22×D411yescharacteristic
941C2×C8C22×D411yescharacteristic
942C2×C8C22×D411yescharacteristic
943C2×C8C22×D411yescharacteristic
944C2×C8C22×D411yescharacteristic
945C2×C8C22×D411yescharacteristic
946C2×C8C2511yescharacteristic
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
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⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
985C4⋊C4C2×D811yescharacteristic
986C4⋊C4C2×D811yescharacteristic
987C4⋊C4C2×D811yescharacteristic
988C4⋊C4C2×D811yescharacteristic
989C4⋊C4C2×D811yescharacteristic
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⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4C2×D811yescharacteristic
1024C22⋊C4C2×D811yescharacteristic
1025C22⋊C4C2×D811yescharacteristic
1026C22⋊C4C2×D811yescharacteristic
1027C22⋊C4C2×D811yescharacteristic
1028C22⋊C4C2×D811yescharacteristic
1029C22⋊C4C2×D811yescharacteristic
1030C22⋊C4C2×D811yescharacteristic
1031C22⋊C4C2×D811yescharacteristic
1032C22⋊C4C2×D811yescharacteristic
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42—41no—
1040C42—41no—
1041C42—41no—
1042C42C2×D811yescharacteristic
1043C42C2×D811yescharacteristic
1044C42C22×D411yescharacteristic
1045C42C22×D411yescharacteristic
1046C42C22×D411yescharacteristic
1047C42C22×D411yescharacteristic
1048C16—21no—
1049C16—21no—
1050C16—21no—
1051C16—21no—
1052C16—21no—
1053C16—21no—
1054C16—21no—
1055C16C2×#4112yes—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—82no—
1062C23—82no—
1063C23—82no—
1064C23—161no—
1065C23—161no—
1066C23—161no—
1067C23C22×D811yescharacteristic
1068C23C22×D811yescharacteristic
1069C23C22×D811yescharacteristic
1070Q8—22no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—82no—
1078Q8—161no—
1079Q8—161no—
1080Q8—161no—
1081Q8—161no—
1082D4—22no—
1083D4—22no—
1084D4—22no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—82no—
1096D4—82no—
1097D4—82no—
1098D4—82no—
1099D4—82no—
1100D4—82no—
1101D4—82no—
1102D4—82no—
1103D4—82no—
1104D4—161no—
1105D4—161no—
1106D4—161no—
1107D4—161no—
1108D4—161no—
1109D4—161no—
1110D4—161no—
1111D4—161no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4—82no—
1136C2×C4—82no—
1137C2×C4—161no—
1138C2×C4—161no—
1139C2×C4—161no—
1140C2×C4—161no—
1141C2×C4—161no—
1142C2×C4—161no—
1143C2×C4—161no—
1144C2×C4—161no—
1145C2×C4—161no—
1146C2×C4—161no—
1147C2×C4—161no—
1148C2×C4—161no—
1149C2×C4—161no—
1150C2×C4—161no—
1151C2×C4—161no—
1152C2×C4C22×D811yescharacteristic
1153C2×C4C22×D811yescharacteristic
1154C2×C4C22×D811yescharacteristic
1155C2×C4C22×D811yescharacteristic
1156C2×C4C22×D811yescharacteristic
1157C2×C4C22×D811yescharacteristic
1158C2×C4C22×D811yescharacteristic
1159C2×C4C22×D811yescharacteristic
1160C2×C4C22×D811yescharacteristic
1161C2×C4C22×D811yescharacteristic
1162C2×C4C22×D811yescharacteristic
1163C2×C4C23×D411yescharacteristic
1164C8—21no—
1165C8—21no—
1166C8—21no—
1167C8—21no—
1168C8—21no—
1169C8—21no—
1170C8—21no—
1171C8C22×#4111yescharacteristic
1172C8#58511yescharacteristic
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—42no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—164no—
1197C22—322no—
1198C22#341512yes—
1199C22C23×D811yescharacteristic
1200C4—21no—
1201C4—21no—
1202C4—21no—
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—21no—
1210C4—21no—
1211C4—42no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4D4×#4111yescharacteristic
1223C4#358411yescharacteristic
1224C2—22no—
1225C2—41no—
1226C2—41no—
1227C2—82no—
1228C2—161no—
1229C2—161no—
1230C2—161no—
1231C2—161no—
1232C2D8×#4111yescharacteristic
1233C2C2×#341511yescharacteristic
1234C2#6263711yescharacteristic
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. #61485C2semidirect
2. #61471C2semidirect
3. #33970C2semidirect
4. #33952C2semidirect
5. #33942C2semidirect
6. #33937C2semidirect
7. #33913C2semidirect
8. #33910C2semidirect
9. #33901C2semidirect
10. #33881C2semidirect
11. #33876C2semidirect
12. #33875C2semidirect
13. #33873C2semidirect
14. #33867C2semidirect
15. #33861C2semidirect
16. #33848C2semidirect
17. #33834C2semidirect
18. #33831C2semidirect
19. #33746C2semidirect
20. #33744C2semidirect
21. #33739C2semidirect
22. #33684C2semidirect
23. #33684C2semidirect
24. #33679C2semidirect
25. #33678C2semidirect
26. #33668C2semidirect
27. #33660C2semidirect
28. #33482C2semidirect
29. #33459C2semidirect
30. #33454C2semidirect
31. C2×#2175C2semidirect
38. #3396C22semidirect
39. Q8×Q16C22semidirect
44. #3338C22semidirect
48. #3334C22semidirect
55. #3287C22semidirect
57. #3285C22semidirect
63. #3175C22semidirect
64. #3175C22semidirect
65. #3169C22semidirect
75. #2951C22semidirect
76. #2951C22semidirect
78. C2×C4×Q16C22semidirect
80. #2255C22semidirect
81. #2255C22semidirect
82. #2252C22semidirect
84. #2250C22semidirect
85. #2249C22semidirect
86. #2244C22semidirect
87. #2243C22semidirect
88. #2243C22semidirect
89. #2243C22semidirect
90. #2242C22semidirect
92. #2237C22semidirect
93. #2236C22semidirect
94. #2236C22semidirect
95. #2235C22semidirect
96. #2234C22semidirect
97. #2233C22semidirect
100. #2232C22semidirect
101. #2232C22semidirect
102. #2232C22semidirect
103. #2232C22semidirect
104. #2229C22semidirect
105. #2229C22semidirect
106. #2229C22semidirect
107. #2228C22semidirect
108. #2227C22semidirect
109. #2227C22semidirect
113. #2224C22semidirect
114. #2224C22semidirect
115. #2224C22semidirect
117. #2220C22semidirect
118. #2220C22semidirect
119. #2218C22semidirect
120. #2217C22semidirect
121. #2217C22semidirect
122. #2217C22semidirect
123. #2216C22semidirect
127. #2215C22semidirect
128. #2211C22semidirect
129. #2211C22semidirect
130. #2211C22semidirect
131. #2211C22semidirect
134. #2210C22semidirect
135. #2210C22semidirect
139. #2206C22semidirect
141. #2189C22semidirect
142. #2188C22semidirect
146. #2186C22semidirect
147. #2186C22semidirect
152. #2183C22semidirect
153. #2183C22semidirect
155. #2177C22semidirect
156. #2177C22semidirect
162. #2175C22semidirect
163. #2175C22semidirect
164. #2175C22semidirect
165. #2175C22semidirect
166. #2175C22semidirect
167. #2175C22semidirect
168. #2175C22semidirect
169. #2175C22semidirect
170. C4×Q32C22semidirect
171. C4×Q32C22semidirect
172. C4×Q32C22semidirect
174. C4×SD32C22semidirect
175. C4×SD32C22semidirect
179. C4×D16C22semidirect
180. C4×D16C22semidirect
181. C4×D16C22semidirect
183. #2168C22semidirect
184. #2168C22semidirect
185. #2168C22semidirect
187. D4×C16C22semidirect
188. #2164C22semidirect
189. #2164C22semidirect
190. #2162C22semidirect
191. #2159C22semidirect
192. C2×#366C22semidirect
193. C2×#366C22semidirect
195. #2139C22semidirect
196. #2138C22semidirect
197. C2×#358C22semidirect
200. #2108C22semidirect
201. #2108C22semidirect
202. C2×#346C22semidirect
727. SD32#41semidirect

Maximal subgroups

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

subgroupindex
#614852
#614712
#339702
#339522
#339422
#339372
#339132
#339102
#339012
#338812
#338762
#338752
#338732
#338672
#338612
#338482
#338342
#338312
#337462
#337442
#337392
#336842
#336792
#336782
#336682
#336602
#334822
#334592
#334542
C2×#21752