Finite Group Databasebeta

← #7230787

Subgroups — #7230787

Order 512.

1423 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53117C211yesmaximal, characteristic
2#35867C211yesmaximal, characteristic, complemented
3#33039C211yesmaximal, characteristic, complemented
4#33039C211yesmaximal, characteristic, complemented
5#32831C211yesmaximal, characteristic, complemented
6#32827C211yesmaximal, characteristic, complemented
7#31248C211yesmaximal, characteristic, complemented
8#31243C211yesmaximal, characteristic, complemented
9#31235C211yesmaximal, characteristic, complemented
10#31235C211yesmaximal, characteristic, complemented
11#30892C211yesmaximal, characteristic, complemented
12#30876C211yesmaximal, characteristic, complemented
13#30876C211yesmaximal, characteristic, complemented
14#30876C211yesmaximal, characteristic, complemented
15#30825C211yesmaximal, characteristic, complemented
16#30813C211yesmaximal, characteristic, complemented
17#30807C211yesmaximal, characteristic, complemented
18#30805C211yesmaximal, characteristic, complemented
19#27207C211yesmaximal, characteristic, complemented
20#27203C211yesmaximal, characteristic, complemented
21#27203C211yesmaximal, characteristic, complemented
22#27194C211yesmaximal, characteristic, complemented
23#27014C211yesmaximal, characteristic, complemented
24#27006C211yesmaximal, characteristic, complemented
25#27003C211yesmaximal, characteristic, complemented
26#26999C211yesmaximal, characteristic, complemented
27#25288C211yesmaximal, characteristic, complemented
28#25274C211yesmaximal, characteristic, complemented
29#25272C211yesmaximal, characteristic, complemented
30#25272C211yesmaximal, characteristic, complemented
31#23373C211yesmaximal, characteristic, complemented
32C2×#490C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#460C2211yescharacteristic
44#2813—21no—
45#2813—21no—
46#2813—21no—
47#2813—21no—
48#2671—21no—
49#2671—21no—
50#2671—21no—
51#2671—21no—
52#2666—21no—
53#2647C2211yescharacteristic
54#2641C2211yescharacteristic
55#2641C2211yescharacteristic
56#2612—21no—
57#2605—21no—
58#2590—21no—
59#2588—21no—
60#2551C2211yescharacteristic
61#2550C2211yescharacteristic
62#2541C2211yescharacteristic
63#2541C2211yescharacteristic
64#2541C2211yescharacteristic
65#2541C2211yescharacteristic
66#2454C2211yescharacteristic
67#2454C2211yescharacteristic
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2453C2211yescharacteristic
71#2451—21no—
72#2451C2211yescharacteristic
73#2451C2211yescharacteristic
74#2451C2211yescharacteristic
75#2446—21no—
76#2445C2211yescharacteristic
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic
79#2445C2211yescharacteristic
80#2402C2211yescharacteristic
81#2399—21no—
82#2370C2211yescharacteristic
83#2369C2211yescharacteristic
84#2365C2211yescharacteristic
85#2365C2211yescharacteristic
86#2356C2211yescharacteristic
87#2355C2211yescharacteristic
88#2276C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2057C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#2041C2211yescharacteristic
127#2041C2211yescharacteristic
128#2041C2211yescharacteristic
129#2025C2211yescharacteristic
130#2023C2211yescharacteristic
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic
133#2014C2211yescharacteristic
134#2014C2211yescharacteristic
135#2014C2211yescharacteristic
136#2014C2211yescharacteristic
137#1989C2211yescharacteristic
138#1989C2211yescharacteristic
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1982C2211yescharacteristic
143#1982C2211yescharacteristic
144#1982C2211yescharacteristic
145#1973C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1968C2211yescharacteristic
149#1944C2211yescharacteristic
150#1942C2211yescharacteristic
151#1942C2211yescharacteristic
152#1941C2211yescharacteristic
153#1940C2211yescharacteristic
154#1939C2211yescharacteristic
155#1939C2211yescharacteristic
156#1939C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1921C2211yescharacteristic
170#1920C2211yescharacteristic
171#1920C2211yescharacteristic
172#1919C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1916C2211yescharacteristic
178#1916C2211yescharacteristic
179#1916C2211yescharacteristic
180#1916C2211yescharacteristic
181#1880C2211yescharacteristic
182#1880C2211yescharacteristic
183#1880C2211yescharacteristic
184#1880C2211yescharacteristic
185#1880C2211yescharacteristic
186#1880C2211yescharacteristic
187#1880C2211yescharacteristic
188#1880C2211yescharacteristic
189#1877C2211yescharacteristic
190#1877C2211yescharacteristic
191#1877C2211yescharacteristic
192#1877C2211yescharacteristic
193#1864C2211yescharacteristic
194#1864C2211yescharacteristic
195#1864C2211yescharacteristic
196#1862C2211yescharacteristic
197#1832C2211yescharacteristic
198#1832C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241#490—42no—
242#486—42no—
243#486—42no—
244#486—42no—
245#479—42no—
246#479—42no—
247#478—42no—
248#476—42no—
249#474—42no—
250#474—42no—
251#460—42no—
252#460—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#400—21no—
312#400D411yescharacteristic
313#400D411yescharacteristic
314#400D411yescharacteristic
315#400D411yescharacteristic
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398D411yescharacteristic
328#398D411yescharacteristic
329#398D411yescharacteristic
330#398D411yescharacteristic
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#392—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#383—21no—
430#382—21no—
431#382C2311yescharacteristic
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455#376—21no—
456#376—21no—
457#376C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—82no—
541#127—41no—
542#127—41no—
543#127—41no—
544#127—41no—
545#127—41no—
546#127—41no—
547#127—41no—
548#127—41no—
549#127—41no—
550#127—41no—
551#127—41no—
552#127—41no—
553#125—22no—
554#125—41no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#123—82no—
560#123—82no—
561#123—82no—
562#123—82no—
563#121—82no—
564#121—82no—
565#121—82no—
566#121—82no—
567#121—82no—
568#121—82no—
569#121—82no—
570#121—82no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—82no—
578C4×Q8—82no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681#107—22no—
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—41no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#97—41no—
734C4×C8—41no—
735C4×C8—41no—
736C4×C8—41no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q82−1+412yes—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C2511yescharacteristic
900SD16—82no—
901SD16—82no—
902SD16—82no—
903SD16—82no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C4⋊C4—24no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
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—21no—
956C4⋊C4—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4H(5,𝔽2)12yes—
986C4⋊C4H(5,𝔽2)12yes—
987C4⋊C42−1+412yes—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C42—24no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23C23×D411yescharacteristic
1069Q8—22no—
1070Q8—22no—
1071Q8—41no—
1072Q8—41no—
1073Q8—84no—
1074Q8—84no—
1075Q8—162no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—162no—
1093D4—162no—
1094D4—162no—
1095D4—162no—
1096D4—162no—
1097D4—162no—
1098D4—162no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4#57612yes—
1184C2×C4#57712yes—
1185C2×C4#57712yes—
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4C2×2−1+411yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4#58511yescharacteristic
1191C2×C4#58511yescharacteristic
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22#348611yescharacteristic
1229C22#348811yescharacteristic
1230C22#348811yescharacteristic
1231C22C2×#57611yescharacteristic
1232C22C2×#57711yescharacteristic
1233C22C2×#57711yescharacteristic
1234C22#358511yescharacteristic
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4#353111yescharacteristic
1262C4#354811yescharacteristic
1263C4#356111yescharacteristic
1264C4#356111yescharacteristic
1265C2—161no—
1266C2—161no—
1267C2—161no—
1268C2—161no—
1269C2#4622611yescharacteristic
1270C2#6185111yescharacteristic
1271C2#6186811yescharacteristic
1272C2#6200711yescharacteristic
1273C2#6203511yescharacteristic
1274C2#6205311yescharacteristic
1275C2#6205511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#53117C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35867C2semidirect
3. #33039C2semidirect
4. #33039C2semidirect
5. #32831C2semidirect
6. #32827C2semidirect
7. #31248C2semidirect
8. #31243C2semidirect
9. #31235C2semidirect
10. #31235C2semidirect
11. #30892C2semidirect
12. #30876C2semidirect
13. #30876C2semidirect
14. #30876C2semidirect
15. #30825C2semidirect
16. #30813C2semidirect
17. #30807C2semidirect
18. #30805C2semidirect
19. #27207C2semidirect
20. #27203C2semidirect
21. #27203C2semidirect
22. #27194C2semidirect
23. #27014C2semidirect
24. #27006C2semidirect
25. #27003C2semidirect
26. #26999C2semidirect
27. #25288C2semidirect
28. #25274C2semidirect
29. #25272C2semidirect
30. #25272C2semidirect
31. #23373C2semidirect

Maximal subgroups

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

subgroupindex
#531172
#358672
#330392
#328312
#328272
#312482
#312432
#312352
#308922
#308762
#308252
#308132
#308072
#308052
#272072
#272032
#271942
#270142
#270062
#270032
#269992
#252882
#252742
#252722
#233732