Finite Group Databasebeta

← #7526673

Subgroups — #7526673

Order 512.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45252C211yesmaximal, characteristic, complemented
2#35713C211yesmaximal, characteristic
3#31989C211yesmaximal, characteristic, complemented
4#31605C211yesmaximal, characteristic, complemented
5#31594C211yesmaximal, characteristic, complemented
6#31376C211yesmaximal, characteristic, complemented
7#29024C211yesmaximal, characteristic, complemented
8#28853C211yesmaximal, characteristic, complemented
9#27871C211yesmaximal, characteristic, complemented
10#27712C211yesmaximal, characteristic, complemented
11#27668C211yesmaximal, characteristic, complemented
12#27534C211yesmaximal, characteristic, complemented
13#27525C211yesmaximal, characteristic, complemented
14#27323C211yesmaximal, characteristic, complemented
15#27312C211yesmaximal, characteristic, complemented
16#27162C211yesmaximal, characteristic, complemented
17#26705C211yesmaximal, characteristic, complemented
18#26118C211yesmaximal, characteristic, complemented
19#25974C211yesmaximal, characteristic, complemented
20#25958C211yesmaximal, characteristic, complemented
21#24936C211yesmaximal, characteristic, complemented
22#24618C211yesmaximal, characteristic, complemented
23#24589C211yesmaximal, characteristic, complemented
24#24033C211yesmaximal, characteristic
25#22975C211yesmaximal, characteristic, complemented
26#22913C211yesmaximal, characteristic, complemented
27#22566C211yesmaximal, characteristic, complemented
28#22562C211yesmaximal, characteristic, complemented
29#22423C211yesmaximal, characteristic
30#20876C211yesmaximal, characteristic, complemented
31#20744C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#433C2211yescharacteristic, complemented
38C2×#428C2211yescharacteristic, complemented
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2794—21no—
43#2765—21no—
44#2762—21no—
45#2750—21no—
46#2624C2211yescharacteristic
47#2622—21no—
48#2599—21no—
49#2570C2211yescharacteristic, complemented
50#2517—21no—
51#2509C2211yescharacteristic, complemented
52#2508C2211yescharacteristic, complemented
53#2500C2211yescharacteristic
54#2495C2211yescharacteristic, complemented
55#2494C2211yescharacteristic, complemented
56#2487C2211yescharacteristic
57#2485C2211yescharacteristic
58#2477—21no—
59#2445C2211yescharacteristic
60#2445C2211yescharacteristic
61#2444—21no—
62#2443—21no—
63#2440C2211yescharacteristic, complemented
64#2439C2211yescharacteristic, complemented
65#2423—21no—
66#2422C2211yescharacteristic
67#2420C2211yescharacteristic
68#2418—21no—
69#2418—21no—
70#2412—21no—
71#2405—21no—
72#2395C2211yescharacteristic
73C2×#394—21no—
74#2365C2211yescharacteristic, complemented
75#2352C2211yescharacteristic
76#2349C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2345C2211yescharacteristic, complemented
79#2344C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2317C2211yescharacteristic, complemented
84#2314C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2092C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic, complemented
103#2073C2211yescharacteristic, complemented
104#2073C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2023C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#1993C2211yescharacteristic, complemented
118#1982C2211yescharacteristic
119#1961C2211yescharacteristic
120#1949C2211yescharacteristic, complemented
121#1948C2211yescharacteristic, complemented
122#1944C2211yescharacteristic, complemented
123#1943C2211yescharacteristic, complemented
124#1943C2211yescharacteristic, complemented
125#1941C2211yescharacteristic, complemented
126#1940C2211yescharacteristic, complemented
127#1936C2211yescharacteristic, complemented
128#1936C2211yescharacteristic, complemented
129#1936C2211yescharacteristic, complemented
130#1936C2211yescharacteristic, complemented
131#1936C2211yescharacteristic, complemented
132#1934C2211yescharacteristic, complemented
133#1926C2211yescharacteristic, complemented
134#1926C2211yescharacteristic, complemented
135#1926C2211yescharacteristic, complemented
136#1926C2211yescharacteristic, complemented
137#1925C2211yescharacteristic, complemented
138#1925C2211yescharacteristic, complemented
139#1924C2211yescharacteristic, complemented
140#1923C2211yescharacteristic, complemented
141#1920C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1917C2211yescharacteristic, complemented
146#1917C2211yescharacteristic, complemented
147#1895C2211yescharacteristic
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1875C2211yescharacteristic
151#1874C2211yescharacteristic
152#1869C2211yescharacteristic
153#1864C2211yescharacteristic
154#1864C2211yescharacteristic
155#1864C2211yescharacteristic
156#1864C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1864C2211yescharacteristic, complemented
160#1864C2211yescharacteristic, complemented
161#1862C2211yescharacteristic
162#1862C2211yescharacteristic
163#1862C2211yescharacteristic
164#1862C2211yescharacteristic
165#1862C2211yescharacteristic, complemented
166#1862C2211yescharacteristic, complemented
167#1854C2211yescharacteristic, complemented
168#1853C2211yescharacteristic, complemented
169#1851C2211yescharacteristic, complemented
170#1850C2211yescharacteristic, complemented
171#1836C2211yescharacteristic, complemented
172#1825C2211yescharacteristic, complemented
173#1825C2211yescharacteristic, complemented
174#1824C2211yescharacteristic, complemented
175#1823C2211yescharacteristic, complemented
176#1809C2211yescharacteristic, complemented
177#1808C2211yescharacteristic, complemented
178#1807C2211yescharacteristic, complemented
179#1807C2211yescharacteristic, complemented
180#1804C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic, complemented
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic, complemented
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1752C2211yescharacteristic, complemented
200#1752C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209D42—24no—
210D42—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×#121—21no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222#518—24no—
223#518—42no—
224C2×C4×Q8—21no—
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×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117—21no—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247#481—42no—
248#476—24no—
249#435—42no—
250#433—42no—
251#428—42no—
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
269#418—24no—
270C2×#102—24no—
271C2×#102—24no—
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400D411yescharacteristic
314#399—21no—
315#399—21no—
316#399D411yescharacteristic
317#398—21no—
318#398—21no—
319#398—21no—
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397D411yescharacteristic
328#397D411yescharacteristic
329#397D411yescharacteristic
330#396—21no—
331#395—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394D411yescharacteristic
344#394D411yescharacteristic
345#393—21no—
346#391—21no—
347#391—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384—21no—
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#383—21no—
417#382—21no—
418#382—21no—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437#379—21no—
438#379—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C2×#95—21no—
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
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—
491C25—21no—
492C22×Q8—21no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—44no—
511C22×D4—82no—
512C22×D4—82no—
513C22×D4C2×D411yescharacteristic
514C22×D4#4114yes—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548#127—22no—
549#127—41no—
550#123—82no—
551#123—82no—
552#123—82no—
553C22⋊Q8—82no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—41no—
558#121—44no—
559#120—44no—
560#120—44no—
561C4×Q8—82no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—44no—
579C4×D4—44no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—41no—
586#117—82no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—82no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×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—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4—82no—
667C2×C22⋊C4—82no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102#4114yes—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—41no—
738#97—41no—
739#97—41no—
740#97—41no—
741C4×C8—41no—
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#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—21no—
788C24—21no—
789C24—24no—
790C24—21no—
791C24—42no—
792C24—42no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×D4—28no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—41no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—44no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—816no—
853C2×D4C2×#4112yes—
854C2×D4C2×#4112yes—
855C2×D4C2×#4112yes—
856C2×D42−1+412yes—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C2×#4112yes—
920C22×C4H(5,𝔽2)12yes—
921C22×C4C2511yescharacteristic
922M16—44no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—82no—
947C2×C8—82no—
948C2×C8C2×#4112yes—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C2×#4112yes—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—21no—
1070C23—22no—
1071C23—21no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—48no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—84no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—84no—
1100C23—84no—
1101C23—162no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23—162no—
1107C23—162no—
1108C23#54612yes—
1109C23#57712yes—
1110C23C23×D411yescharacteristic
1111Q8—84no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—22no—
1116D4—22no—
1117D4—48no—
1118D4—44no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—84no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—162no—
1130D4#55214yes—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
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—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4#54612yes—
1223C2×C4C22×#4111yescharacteristic
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4C2×2−1+411yescharacteristic
1227C2×C4#58511yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—22no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—24no—
1243C22—22no—
1244C22—42no—
1245C22—42no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—168no—
1273C22—168no—
1274C22C2×#54611yescharacteristic
1275C22D4×#4111yescharacteristic
1276C22#348911yescharacteristic
1277C22C2×#57711yescharacteristic
1278C22#358511yescharacteristic
1279C22#358511yescharacteristic
1280C22#358511yescharacteristic
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4C2×#55211yescharacteristic
1307C4#349111yescharacteristic
1308C4#351311yescharacteristic
1309C4#353511yescharacteristic
1310C2—42no—
1311C2—42no—
1312C2—44no—
1313C2—82no—
1314C2—161no—
1315C2#5901211yescharacteristic
1316C2#6118411yescharacteristic
1317C2#6121811yescharacteristic
1318C2#6150511yescharacteristic
1319C2#6152111yescharacteristic
1320C2#6215611yescharacteristic
1321C2#6222311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
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. #45252C2semidirect
3. #31989C2semidirect
4. #31605C2semidirect
5. #31594C2semidirect
6. #31376C2semidirect
7. #29024C2semidirect
8. #28853C2semidirect
9. #27871C2semidirect
10. #27712C2semidirect
11. #27668C2semidirect
12. #27534C2semidirect
13. #27525C2semidirect
14. #27323C2semidirect
15. #27312C2semidirect
16. #27162C2semidirect
17. #26705C2semidirect
18. #26118C2semidirect
19. #25974C2semidirect
20. #25958C2semidirect
21. #24936C2semidirect
22. #24618C2semidirect
23. #24589C2semidirect
25. #22975C2semidirect
26. #22913C2semidirect
27. #22566C2semidirect
28. #22562C2semidirect
30. #20876C2semidirect
31. #20744C2semidirect
37. C2×#433C22semidirect
38. C2×#428C22semidirect
49. #2570C22semidirect
51. #2509C22semidirect
52. #2508C22semidirect
54. #2495C22semidirect
55. #2494C22semidirect
63. #2440C22semidirect
64. #2439C22semidirect
74. #2365C22semidirect
78. #2345C22semidirect
79. #2344C22semidirect
83. #2317C22semidirect
84. #2314C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2099C22semidirect
88. #2099C22semidirect
89. #2094C22semidirect
90. #2092C22semidirect
91. #2088C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2076C22semidirect
102. #2075C22semidirect
103. #2073C22semidirect
104. #2073C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2065C22semidirect
109. #2065C22semidirect
110. #2065C22semidirect
115. #2023C22semidirect
116. #2023C22semidirect
117. #1993C22semidirect
120. #1949C22semidirect
121. #1948C22semidirect
122. #1944C22semidirect
123. #1943C22semidirect
124. #1943C22semidirect
125. #1941C22semidirect
126. #1940C22semidirect
127. #1936C22semidirect
128. #1936C22semidirect
129. #1936C22semidirect
130. #1936C22semidirect
131. #1936C22semidirect
132. #1934C22semidirect
133. #1926C22semidirect
134. #1926C22semidirect
135. #1926C22semidirect
136. #1926C22semidirect
137. #1925C22semidirect
138. #1925C22semidirect
139. #1924C22semidirect
140. #1923C22semidirect
141. #1920C22semidirect
142. #1920C22semidirect
143. #1919C22semidirect
144. #1919C22semidirect
145. #1917C22semidirect
146. #1917C22semidirect
159. #1864C22semidirect
160. #1864C22semidirect
165. #1862C22semidirect
166. #1862C22semidirect
167. #1854C22semidirect
168. #1853C22semidirect
169. #1851C22semidirect
170. #1850C22semidirect
171. #1836C22semidirect
172. #1825C22semidirect
173. #1825C22semidirect
174. #1824C22semidirect
175. #1823C22semidirect
176. #1809C22semidirect
177. #1808C22semidirect
178. #1807C22semidirect
179. #1807C22semidirect
183. #1804C22semidirect
185. #1802C22semidirect
191. #1771C22semidirect
196. #1762C22semidirect
198. C4×#102C22semidirect
199. #1752C22semidirect
200. #1752C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#452522
#357132
#319892
#316052
#315942
#313762
#290242
#288532
#278712
#277122
#276682
#275342
#275252
#273232
#273122
#271622
#267052
#261182
#259742
#259582
#249362
#246182
#245892
#240332
#229752
#229132
#225662
#225622
#224232
#208762
#207442