Finite Group Databasebeta

← #7324883

Subgroups — #7324883

Order 512.

1551 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59019C211yesmaximal, characteristic
2#45624C211yesmaximal, characteristic, complemented
3#32299C211yesmaximal, characteristic, complemented
4#32023C211yesmaximal, characteristic, complemented
5#31837C211yesmaximal, characteristic, complemented
6#31565C211yesmaximal, characteristic, complemented
7#31433C211yesmaximal, characteristic, complemented
8#31403C211yesmaximal, characteristic, complemented
9#31191C211yesmaximal, characteristic, complemented
10#31119C211yesmaximal, characteristic, complemented
11#31038C211yesmaximal, characteristic, complemented
12#30723C211yesmaximal, characteristic, complemented
13#30678C211yesmaximal, characteristic, complemented
14#30425C211yesmaximal, characteristic, complemented
15#29897C211yesmaximal, characteristic, complemented
16#29601C211yesmaximal, characteristic, complemented
17#29006C211yesmaximal, characteristic, complemented
18#27530C211yesmaximal, characteristic, complemented
19#27043C211yesmaximal, characteristic, complemented
20#26952C211yesmaximal, characteristic, complemented
21#26222C211yesmaximal, characteristic, complemented
22#25557C211yesmaximal, characteristic, complemented
23#25394C211yesmaximal, characteristic, complemented
24#25263C211yesmaximal, characteristic, complemented
25#25151C211yesmaximal, characteristic, complemented
26#25039C211yesmaximal, characteristic, complemented
27#25028C211yesmaximal, characteristic, complemented
28#24561C211yesmaximal, characteristic, complemented
29#24389C211yesmaximal, characteristic, complemented
30#24127C211yesmaximal, characteristic, complemented
31#22038C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#484C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic, complemented
38C2×#479C2211yescharacteristic, complemented
39C2×#470C2211yescharacteristic
40C2×#470C2211yescharacteristic, complemented
41C2×#468C2211yescharacteristic
42C2×#462C2211yescharacteristic, complemented
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic, complemented
46C2×#436C2211yescharacteristic
47C2×#407C2211yescharacteristic
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2827—21no—
51#2807—21no—
52#2796—21no—
53#2790—21no—
54#2757—21no—
55#2735—21no—
56#2685—21no—
57#2685—21no—
58#2678—21no—
59#2558—21no—
60#2542C2211yescharacteristic
61#2538C2211yescharacteristic
62#2538C2211yescharacteristic
63#2536C2211yescharacteristic
64#2500C2211yescharacteristic
65#2496C2211yescharacteristic
66#2495C2211yescharacteristic
67#2490C2211yescharacteristic
68#2485C2211yescharacteristic
69#2471—21no—
70#2466—21no—
71#2460—21no—
72#2457—21no—
73#2441C2211yescharacteristic
74#2429C2211yescharacteristic
75#2429C2211yescharacteristic
76#2423C2211yescharacteristic
77#2421C2211yescharacteristic
78#2421C2211yescharacteristic
79#2416C2211yescharacteristic
80#2415C2211yescharacteristic
81#2415C2211yescharacteristic
82#2414C2211yescharacteristic
83#2407C2211yescharacteristic
84#2383—21no—
85#2363—21no—
86#2362C2211yescharacteristic
87#2352C2211yescharacteristic
88#2341C2211yescharacteristic
89C4×#120C2211yescharacteristic
90#2280C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2094C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2067C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2013C2211yescharacteristic, complemented
130#2001C2211yescharacteristic
131#2001C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#2000C2211yescharacteristic, complemented
139#1991C2211yescharacteristic, complemented
140#1971C2211yescharacteristic, complemented
141#1968C2211yescharacteristic, complemented
142#1956C2211yescharacteristic, complemented
143#1955C2211yescharacteristic
144#1954C2211yescharacteristic
145#1948C2211yescharacteristic, complemented
146#1947C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1941C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1920C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic, complemented
174#1872C2211yescharacteristic, complemented
175#1870C2211yescharacteristic
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1852C2211yescharacteristic, complemented
188#1851C2211yescharacteristic
189#1847C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1825C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1805C2211yescharacteristic, complemented
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1779C2211yescharacteristic
199#1763C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212#552—42no—
213#552—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219#525—42no—
220#525—42no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120D411yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255#485—42no—
256#485—42no—
257#484—42no—
258#482—42no—
259#479—42no—
260#470—42no—
261#470—42no—
262#468—42no—
263#462—42no—
264#452—42no—
265#452—42no—
266C4×Q16—42no—
267#436—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307#407—42no—
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#392—21no—
363#392—21no—
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—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#386—21no—
417#386—21no—
418#386—21no—
419#386D411yescharacteristic
420#386D411yescharacteristic
421#386D411yescharacteristic
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#385D411yescharacteristic
432#384—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#383—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454#379—21no—
455#379D411yescharacteristic
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—41no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#126—44no—
561#126—44no—
562#125—22no—
563#125—41no—
564#125—44no—
565#123—44no—
566#123—44no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—44no—
594#121—41no—
595#121—41no—
596#120—42no—
597#120—44no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—44no—
613C4×D4—44no—
614#117—22no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—44no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
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—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—41no—
734#107—41no—
735#107—41no—
736#107—41no—
737#106—22no—
738#106—41no—
739#106—41no—
740#106—41no—
741#106—41no—
742#106—41no—
743C4⋊C8—22no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—41no—
784C4×C8—41no—
785C4×C8—41no—
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#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—41no—
824C24—41no—
825C24—41no—
826C24—41no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24C22×D411yescharacteristic
831C24C22×D411yescharacteristic
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—82no—
835#41—82no—
836#41—82no—
837#41—82no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8H(5,𝔽2)12yes—
856C2×D4—22no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
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—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—82no—
937C22×C4—82no—
938C22×C4—82no—
939C22×C4—82no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2511yescharacteristic
952Q16—44no—
953Q16—82no—
954SD16—82no—
955SD16—82no—
956M16—82no—
957M16—82no—
958M16—82no—
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—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8H(5,𝔽2)12yes—
983C4⋊C4—24no—
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—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
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—42no—
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⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4H(5,𝔽2)12yes—
1040C22⋊C4—24no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
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—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—82no—
1140C23—82no—
1141C23—82no—
1142C23—82no—
1143C23—82no—
1144C23—82no—
1145C23—82no—
1146C23C23×D411yescharacteristic
1147Q8—22no—
1148Q8—22no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—82no—
1164D4—82no—
1165D4—82no—
1166D4—84no—
1167D4—84no—
1168D4—84no—
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—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
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—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—82no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4#57512yes—
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4#58511yescharacteristic
1270C2×C4#58511yescharacteristic
1271C2×C4#58511yescharacteristic
1272C8—22no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—88no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22#348411yescharacteristic
1317C22#348511yescharacteristic
1318C22#349611yescharacteristic
1319C22C2×#57511yescharacteristic
1320C22#358411yescharacteristic
1321C22#358611yescharacteristic
1322C22#358611yescharacteristic
1323C4—22no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—42no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4#353411yescharacteristic
1349C4#354611yescharacteristic
1350C4#356011yescharacteristic
1351C4#356211yescharacteristic
1352C2—81no—
1353C2—81no—
1354C2—81no—
1355C2—81no—
1356C2—161no—
1357C2#4792711yescharacteristic
1358C2#6159911yescharacteristic
1359C2#6165211yescharacteristic
1360C2#6172411yescharacteristic
1361C2#6174811yescharacteristic
1362C2#6230211yescharacteristic
1363C2#6231411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59019C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45624C2semidirect
3. #32299C2semidirect
4. #32023C2semidirect
5. #31837C2semidirect
6. #31565C2semidirect
7. #31433C2semidirect
8. #31403C2semidirect
9. #31191C2semidirect
10. #31119C2semidirect
11. #31038C2semidirect
12. #30723C2semidirect
13. #30678C2semidirect
14. #30425C2semidirect
15. #29897C2semidirect
16. #29601C2semidirect
17. #29006C2semidirect
18. #27530C2semidirect
19. #27043C2semidirect
20. #26952C2semidirect
21. #26222C2semidirect
22. #25557C2semidirect
23. #25394C2semidirect
24. #25263C2semidirect
25. #25151C2semidirect
26. #25039C2semidirect
27. #25028C2semidirect
28. #24561C2semidirect
29. #24389C2semidirect
30. #24127C2semidirect
31. #22038C2semidirect
34. C2×#484C22semidirect
37. C2×#482C22semidirect
38. C2×#479C22semidirect
40. C2×#470C22semidirect
42. C2×#462C22semidirect
45. C2×C4×Q16C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2094C22semidirect
95. #2088C22semidirect
96. #2084C22semidirect
100. #2077C22semidirect
104. #2074C22semidirect
105. #2073C22semidirect
106. #2072C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
109. #2067C22semidirect
110. #2067C22semidirect
111. #2059C22semidirect
112. #2055C22semidirect
113. #2043C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
128. #2026C22semidirect
129. #2013C22semidirect
133. #2001C22semidirect
137. #2000C22semidirect
138. #2000C22semidirect
139. #1991C22semidirect
140. #1971C22semidirect
141. #1968C22semidirect
142. #1956C22semidirect
145. #1948C22semidirect
146. #1947C22semidirect
147. #1942C22semidirect
148. #1941C22semidirect
149. #1936C22semidirect
150. #1934C22semidirect
151. #1928C22semidirect
152. #1925C22semidirect
157. #1920C22semidirect
158. #1918C22semidirect
160. #1895C22semidirect
164. #1894C22semidirect
165. #1880C22semidirect
166. #1880C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
173. #1873C22semidirect
174. #1872C22semidirect
178. #1865C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
186. #1854C22semidirect
187. #1852C22semidirect
189. #1847C22semidirect
194. #1805C22semidirect
195. #1805C22semidirect
199. #1763C22semidirect
200. C4×#103C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#590192
#456242
#322992
#320232
#318372
#315652
#314332
#314032
#311912
#311192
#310382
#307232
#306782
#304252
#298972
#296012
#290062
#275302
#270432
#269522
#262222
#255572
#253942
#252632
#251512
#250392
#250282
#245612
#243892
#241272
#220382