Finite Group Databasebeta

← #7207616

Subgroups — #7207616

Order 512.

1481 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53067C211yesmaximal, characteristic, complemented
2#35976C211yesmaximal, characteristic
3#32968C211yesmaximal, characteristic, complemented
4#32968C211yesmaximal, characteristic, complemented
5#32756C211yesmaximal, characteristic, complemented
6#32754C211yesmaximal, characteristic, complemented
7#32463C211yesmaximal, characteristic, complemented
8#32298C211yesmaximal, characteristic, complemented
9#32294C211yesmaximal, characteristic, complemented
10#32275C211yesmaximal, characteristic, complemented
11#31992C211yesmaximal, characteristic, complemented
12#31988C211yesmaximal, characteristic, complemented
13#31624C211yesmaximal, characteristic, complemented
14#31620C211yesmaximal, characteristic, complemented
15#31109C211yesmaximal, characteristic, complemented
16#31101C211yesmaximal, characteristic, complemented
17#30818C211yesmaximal, characteristic, complemented
18#30810C211yesmaximal, characteristic, complemented
19#27544C211yesmaximal, characteristic, complemented
20#27542C211yesmaximal, characteristic, complemented
21#27541C211yesmaximal, characteristic, complemented
22#27539C211yesmaximal, characteristic, complemented
23#27309C211yesmaximal, characteristic, complemented
24#27307C211yesmaximal, characteristic, complemented
25#26059C211yesmaximal, characteristic, complemented
26#26059C211yesmaximal, characteristic, complemented
27#25976C211yesmaximal, characteristic, complemented
28#25968C211yesmaximal, characteristic, complemented
29#25890C211yesmaximal, characteristic
30#24050C211yesmaximal, characteristic
31#23325C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#418C2211yescharacteristic
42#2839—21no—
43#2837—21no—
44#2836—21no—
45#2823—21no—
46#2793—21no—
47#2791—21no—
48#2725—21no—
49#2721—21no—
50#2629C2211yescharacteristic, complemented
51#2629C2211yescharacteristic, complemented
52#2624C2211yescharacteristic
53#2623—21no—
54#2562C2211yescharacteristic
55#2552C2211yescharacteristic, complemented
56#2552C2211yescharacteristic, complemented
57#2507C2211yescharacteristic, complemented
58#2506C2211yescharacteristic, complemented
59#2504C2211yescharacteristic
60#2498—21no—
61#2497C2211yescharacteristic
62#2497C2211yescharacteristic, complemented
63#2496C2211yescharacteristic
64#2496C2211yescharacteristic, complemented
65#2486C2211yescharacteristic
66#2485C2211yescharacteristic
67#2482—21no—
68#2448C2211yescharacteristic
69#2448C2211yescharacteristic
70#2444—21no—
71#2444—21no—
72#2441C2211yescharacteristic
73#2441C2211yescharacteristic
74#2421C2211yescharacteristic
75#2421C2211yescharacteristic
76#2418—21no—
77#2418—21no—
78#2395C2211yescharacteristic
79C2×#397—21no—
80#2349C2211yescharacteristic
81#2349C2211yescharacteristic
82#2339C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic, complemented
106#2075C2211yescharacteristic, complemented
107#2072C2211yescharacteristic, complemented
108#2072C2211yescharacteristic, complemented
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic
111#2068C2211yescharacteristic, complemented
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2066C2211yescharacteristic, complemented
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2059C2211yescharacteristic, complemented
120#2059C2211yescharacteristic, complemented
121#2059C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2036C2211yescharacteristic
126#2035C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2025C2211yescharacteristic
132#2025C2211yescharacteristic
133#1983C2211yescharacteristic
134#1954C2211yescharacteristic
135#1949C2211yescharacteristic, complemented
136#1949C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic, complemented
152#1924C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1894C2211yescharacteristic
158#1870C2211yescharacteristic
159#1865C2211yescharacteristic, complemented
160#1865C2211yescharacteristic, complemented
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1863C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic, complemented
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1852C2211yescharacteristic, complemented
179#1851C2211yescharacteristic
180#1851C2211yescharacteristic
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1803C2211yescharacteristic, complemented
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic, complemented
192#1798C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206#546—42no—
207#546—42no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221#520—42no—
222#520—42no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4—21no—
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241#488—42no—
242#485—42no—
243#479—42no—
244#479—42no—
245#478—42no—
246#478—42no—
247#478—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#418—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400D411yescharacteristic
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#399D411yescharacteristic
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398D411yescharacteristic
334#397—21no—
335#397—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#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
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#394D411yescharacteristic
361#394D411yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
389#388—21no—
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#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384—21no—
422#384—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C2×#95—21no—
454C2×#95—21no—
455C2×#95—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530#126—82no—
531#126—82no—
532#125—41no—
533#125—41no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—82no—
539#124—22no—
540#124—41no—
541#123—44no—
542#123—82no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—41no—
546#121—41no—
547#121—44no—
548#120—44no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—44no—
566C4×D4—44no—
567#117—41no—
568#117—41no—
569#117—44no—
570#117—41no—
571#117—41no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
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—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
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—44no—
656C2×C22⋊C4—82no—
657C2×C22⋊C4—82no—
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
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
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—41no—
688#106—41no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733#97—41no—
734#97—41no—
735C4×C8—41no—
736#95—21no—
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#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
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
781C24—21no—
782C24—21no—
783C24—42no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792#41—44no—
793#41—44no—
794#41—44no—
795#41—44no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8H(5,𝔽2)12yes—
802C2×D4—24no—
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—41no—
813C2×D4—41no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—82no—
823C2×D4—82no—
824C2×D4—82no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4H(5,𝔽2)12yes—
828C2×D42−1+412yes—
829C2×D42−1+412yes—
830C22×C4—24no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C2511yescharacteristic
890M16—82no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
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—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
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—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
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—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—42no—
1029C42—42no—
1030C42—42no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—84no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—162no—
1067C23—162no—
1068C23—162no—
1069C23C23×D411yescharacteristic
1070Q8—22no—
1071Q8—22no—
1072Q8—41no—
1073Q8—41no—
1074D4—22no—
1075D4—22no—
1076D4—22no—
1077D4—48no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—84no—
1083D4—82no—
1084D4—162no—
1085D4#56314yes—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
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—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—48no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
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—162no—
1174C2×C4—162no—
1175C2×C4—162no—
1176C2×C4—162no—
1177C2×C4—162no—
1178C2×C4—162no—
1179C2×C4C2×H(5,𝔽2)11yescharacteristic
1180C2×C4C2×H(5,𝔽2)11yescharacteristic
1181C2×C4C2×2−1+411yescharacteristic
1182C2×C4C2×2−1+411yescharacteristic
1183C2×C4#58511yescharacteristic
1184C2×C4#58511yescharacteristic
1185C8—41no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—168no—
1222C22#348411yescharacteristic
1223C22#348911yescharacteristic
1224C22#348911yescharacteristic
1225C22#358411yescharacteristic
1226C22#358511yescharacteristic
1227C22#358511yescharacteristic
1228C22#358611yescharacteristic
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—42no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4C2×#56311yescharacteristic
1256C4#353311yescharacteristic
1257C4#353511yescharacteristic
1258C4#353511yescharacteristic
1259C2—44no—
1260C2—81no—
1261C2—81no—
1262C2—161no—
1263C2#4545611yescharacteristic
1264C2#6162811yescharacteristic
1265C2#6167711yescharacteristic
1266C2#6219511yescharacteristic
1267C2#6219611yescharacteristic
1268C2#6223111yescharacteristic
1269C2#6223211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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. #53067C2semidirect
3. #32968C2semidirect
4. #32968C2semidirect
5. #32756C2semidirect
6. #32754C2semidirect
7. #32463C2semidirect
8. #32298C2semidirect
9. #32294C2semidirect
10. #32275C2semidirect
11. #31992C2semidirect
12. #31988C2semidirect
13. #31624C2semidirect
14. #31620C2semidirect
15. #31109C2semidirect
16. #31101C2semidirect
17. #30818C2semidirect
18. #30810C2semidirect
19. #27544C2semidirect
20. #27542C2semidirect
21. #27541C2semidirect
22. #27539C2semidirect
23. #27309C2semidirect
24. #27307C2semidirect
25. #26059C2semidirect
26. #26059C2semidirect
27. #25976C2semidirect
28. #25968C2semidirect
31. #23325C2semidirect
36. C2×#479C22semidirect
37. C2×#479C22semidirect
50. #2629C22semidirect
51. #2629C22semidirect
55. #2552C22semidirect
56. #2552C22semidirect
57. #2507C22semidirect
58. #2506C22semidirect
62. #2497C22semidirect
64. #2496C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2087C22semidirect
93. #2086C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2083C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
105. #2076C22semidirect
106. #2075C22semidirect
107. #2072C22semidirect
108. #2072C22semidirect
111. #2068C22semidirect
115. #2066C22semidirect
119. #2059C22semidirect
120. #2059C22semidirect
121. #2059C22semidirect
122. #2059C22semidirect
135. #1949C22semidirect
136. #1949C22semidirect
137. #1942C22semidirect
138. #1941C22semidirect
139. #1940C22semidirect
140. #1940C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
151. #1924C22semidirect
152. #1924C22semidirect
153. #1921C22semidirect
154. #1920C22semidirect
155. #1916C22semidirect
156. #1916C22semidirect
159. #1865C22semidirect
160. #1865C22semidirect
166. #1863C22semidirect
167. #1863C22semidirect
175. #1853C22semidirect
176. #1853C22semidirect
177. #1852C22semidirect
178. #1852C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
185. #1803C22semidirect
186. #1803C22semidirect
191. #1798C22semidirect
192. #1798C22semidirect

Maximal subgroups

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

subgroupindex
#530672
#359762
#329682
#327562
#327542
#324632
#322982
#322942
#322752
#319922
#319882
#316242
#316202
#311092
#311012
#308182
#308102
#275442
#275422
#275412
#275392
#273092
#273072
#260592
#259762
#259682
#258902
#240502
#233252