Finite Group Databasebeta

← #7308973

Subgroups — #7308973

Order 512.

1567 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45238C211yesmaximal, characteristic, complemented
2#42616C211yesmaximal, characteristic
3#32257C211yesmaximal, characteristic, complemented
4#32070C211yesmaximal, characteristic, complemented
5#31900C211yesmaximal, characteristic, complemented
6#31838C211yesmaximal, characteristic, complemented
7#31757C211yesmaximal, characteristic, complemented
8#31619C211yesmaximal, characteristic, complemented
9#31537C211yesmaximal, characteristic, complemented
10#31164C211yesmaximal, characteristic, complemented
11#31044C211yesmaximal, characteristic, complemented
12#30988C211yesmaximal, characteristic, complemented
13#30924C211yesmaximal, characteristic, complemented
14#30582C211yesmaximal, characteristic, complemented
15#29765C211yesmaximal, characteristic, complemented
16#29671C211yesmaximal, characteristic, complemented
17#29247C211yesmaximal, characteristic, complemented
18#27104C211yesmaximal, characteristic, complemented
19#26794C211yesmaximal, characteristic, complemented
20#26647C211yesmaximal, characteristic, complemented
21#26603C211yesmaximal, characteristic, complemented
22#26463C211yesmaximal, characteristic, complemented
23#26179C211yesmaximal, characteristic, complemented
24#25968C211yesmaximal, characteristic, complemented
25#25176C211yesmaximal, characteristic, complemented
26#25093C211yesmaximal, characteristic, complemented
27#24824C211yesmaximal, characteristic, complemented
28#24163C211yesmaximal, characteristic, complemented
29#24137C211yesmaximal, characteristic, complemented
30#23982C211yesmaximal, characteristic, complemented
31#23321C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#541C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic, complemented
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#461C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48#2825—21no—
49#2778—21no—
50#2721—21no—
51#2719—21no—
52#2718—21no—
53#2718—21no—
54#2714—21no—
55#2685—21no—
56#2678—21no—
57#2630—21no—
58#2622—21no—
59#2619C2211yescharacteristic
60#2566C2211yescharacteristic
61#2552—21no—
62#2552C2211yescharacteristic, complemented
63#2537C2211yescharacteristic
64#2519—21no—
65#2512C2211yescharacteristic
66#2502C2211yescharacteristic, complemented
67#2494C2211yescharacteristic
68#2490C2211yescharacteristic
69#2490C2211yescharacteristic
70#2478—21no—
71#2478—21no—
72#2453C2211yescharacteristic, complemented
73#2446C2211yescharacteristic, complemented
74#2445C2211yescharacteristic
75#2441C2211yescharacteristic
76#2433C2211yescharacteristic
77#2429C2211yescharacteristic
78#2428C2211yescharacteristic
79#2424—21no—
80#2423C2211yescharacteristic
81#2415C2211yescharacteristic
82#2408C2211yescharacteristic
83#2395C2211yescharacteristic
84#2366C2211yescharacteristic
85#2362C2211yescharacteristic
86#2362C2211yescharacteristic, complemented
87Q8×C4⋊C4C2211yescharacteristic, complemented
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2317C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2075C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic, complemented
128#2014C2211yescharacteristic
129#2014C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic, complemented
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#2000C2211yescharacteristic, complemented
139#1992C2211yescharacteristic, complemented
140#1992C2211yescharacteristic, complemented
141#1989C2211yescharacteristic, complemented
142#1982C2211yescharacteristic
143#1981C2211yescharacteristic, complemented
144#1973C2211yescharacteristic
145#1973C2211yescharacteristic
146#1968C2211yescharacteristic
147#1957C2211yescharacteristic
148#1955C2211yescharacteristic
149#1947C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1874C2211yescharacteristic, complemented
181#1870C2211yescharacteristic
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic, complemented
190#1852C2211yescharacteristic, complemented
191#1851C2211yescharacteristic
192#1851C2211yescharacteristic
193#1825C2211yescharacteristic
194#1809C2211yescharacteristic
195#1805C2211yescharacteristic, complemented
196#1805C2211yescharacteristic, complemented
197#1803C2211yescharacteristic, complemented
198#1802C2211yescharacteristic
199#1798C2211yescharacteristic, complemented
200#1798C2211yescharacteristic, complemented
201#1786C2211yescharacteristic
202C4×#106C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#552—42no—
212#552—42no—
213#541—42no—
214#541—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#482—42no—
259#482—42no—
260#479—42no—
261#478—42no—
262#478—42no—
263#468—42no—
264#461—42no—
265#460—42no—
266#460—42no—
267#450—42no—
268#450—42no—
269#440—42no—
270#440—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#418—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#400D411yescharacteristic
331#399—21no—
332#399—21no—
333#399D411yescharacteristic
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397D411yescharacteristic
349#397D411yescharacteristic
350#397D411yescharacteristic
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394D411yescharacteristic
368#394D411yescharacteristic
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#384—21no—
441#384—21no—
442#384—21no—
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#382—21no—
447#382C2311yescharacteristic
448#380—21no—
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555#127—22no—
556#127—41no—
557#127—41no—
558#127—41no—
559#126—44no—
560#126—44no—
561#126—44no—
562#126—82no—
563#125—22no—
564#125—22no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—44no—
570#125—44no—
571#125—44no—
572#123—44no—
573#123—82no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582#121—22no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—82no—
591#121—82no—
592#120—82no—
593#120—82no—
594#120—82no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—82no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—44no—
617#117—41no—
618#117—41no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—22no—
736#106—41no—
737#106—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780#97—41no—
781#97—41no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8H(5,𝔽2)12yes—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—44no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D42−1+412yes—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2511yescharacteristic
944SD16—44no—
945SD16—44no—
946SD16—82no—
947SD16—82no—
948SD16—82no—
949SD16—82no—
950M16—82no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
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—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
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—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4H(5,𝔽2)12yes—
1034C4⋊C4H(5,𝔽2)12yes—
1035C22⋊C4—24no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
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—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—22no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—84no—
1133C23—84no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23—162no—
1138C23—162no—
1139C23C23×D411yescharacteristic
1140Q8—22no—
1141Q8—22no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148D4—22no—
1149D4—22no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—84no—
1161D4—82no—
1162D4—84no—
1163D4—162no—
1164D4—162no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—84no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4#57712yes—
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4C2×2−1+411yescharacteristic
1261C2×C4#58511yescharacteristic
1262C2×C4#58511yescharacteristic
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—168no—
1307C22#348411yescharacteristic
1308C22#348811yescharacteristic
1309C22#348911yescharacteristic
1310C22C2×#57711yescharacteristic
1311C22#358511yescharacteristic
1312C22#358511yescharacteristic
1313C22#358611yescharacteristic
1314C4—22no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4#353311yescharacteristic
1340C4#353611yescharacteristic
1341C4#354111yescharacteristic
1342C4#354611yescharacteristic
1343C2—81no—
1344C2—81no—
1345C2—82no—
1346C2—161no—
1347C2—161no—
1348C2#4784511yescharacteristic
1349C2#6165111yescharacteristic
1350C2#6169211yescharacteristic
1351C2#6203311yescharacteristic
1352C2#6208511yescharacteristic
1353C2#6216411yescharacteristic
1354C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42616C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45238C2semidirect
3. #32257C2semidirect
4. #32070C2semidirect
5. #31900C2semidirect
6. #31838C2semidirect
7. #31757C2semidirect
8. #31619C2semidirect
9. #31537C2semidirect
10. #31164C2semidirect
11. #31044C2semidirect
12. #30988C2semidirect
13. #30924C2semidirect
14. #30582C2semidirect
15. #29765C2semidirect
16. #29671C2semidirect
17. #29247C2semidirect
18. #27104C2semidirect
19. #26794C2semidirect
20. #26647C2semidirect
21. #26603C2semidirect
22. #26463C2semidirect
23. #26179C2semidirect
24. #25968C2semidirect
25. #25176C2semidirect
26. #25093C2semidirect
27. #24824C2semidirect
28. #24163C2semidirect
29. #24137C2semidirect
30. #23982C2semidirect
31. #23321C2semidirect
33. C2×#541C22semidirect
35. C2×#482C22semidirect
36. C2×#479C22semidirect
38. C2×#478C22semidirect
46. C2×#440C22semidirect
62. #2552C22semidirect
66. #2502C22semidirect
72. #2453C22semidirect
73. #2446C22semidirect
86. #2362C22semidirect
87. Q8×C4⋊C4C22semidirect
90. #2317C22semidirect
91. #2100C22semidirect
92. #2096C22semidirect
94. #2087C22semidirect
95. #2086C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2083C22semidirect
101. #2071C22semidirect
104. #2067C22semidirect
105. #2066C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
114. #2055C22semidirect
119. #2036C22semidirect
121. #2035C22semidirect
123. #2026C22semidirect
127. #2025C22semidirect
131. #2013C22semidirect
137. #2000C22semidirect
138. #2000C22semidirect
139. #1992C22semidirect
140. #1992C22semidirect
141. #1989C22semidirect
143. #1981C22semidirect
149. #1947C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
153. #1936C22semidirect
154. #1933C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
159. #1924C22semidirect
161. #1923C22semidirect
162. #1921C22semidirect
163. #1920C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
173. #1880C22semidirect
175. #1877C22semidirect
180. #1874C22semidirect
182. #1865C22semidirect
184. #1863C22semidirect
187. #1862C22semidirect
189. #1854C22semidirect
190. #1852C22semidirect
195. #1805C22semidirect
196. #1805C22semidirect
197. #1803C22semidirect
199. #1798C22semidirect
200. #1798C22semidirect
202. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
#452382
#426162
#322572
#320702
#319002
#318382
#317572
#316192
#315372
#311642
#310442
#309882
#309242
#305822
#297652
#296712
#292472
#271042
#267942
#266472
#266032
#264632
#261792
#259682
#251762
#250932
#248242
#241632
#241372
#239822
#233212