Finite Group Databasebeta

← #6826536

Subgroups — #6826536

Order 512.

1353 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42859C211yesmaximal, characteristic, complemented
2#42548C211yesmaximal, characteristic
3#33215C211yesmaximal, characteristic, complemented
4#32004C211yesmaximal, characteristic
5#32000C211yesmaximal, characteristic, complemented
6#31612C211yesmaximal, characteristic, complemented
7#31602C211yesmaximal, characteristic, complemented
8#31485C211yesmaximal, characteristic, complemented
9#31478C211yesmaximal, characteristic, complemented
10#31380C211yesmaximal, characteristic, complemented
11#31376C211yesmaximal, characteristic, complemented
12#30183C211yesmaximal, characteristic, complemented
13#30177C211yesmaximal, characteristic, complemented
14#28839C211yesmaximal, characteristic, complemented
15#28235C211yesmaximal, characteristic
16#28008C211yesmaximal, characteristic, complemented
17#27852C211yesmaximal, characteristic, complemented
18#27845C211yesmaximal, characteristic, complemented
19#27666C211yesmaximal, characteristic, complemented
20#27295C211yesmaximal, characteristic, complemented
21#27294C211yesmaximal, characteristic, complemented
22#27036C211yesmaximal, characteristic, complemented
23#27033C211yesmaximal, characteristic, complemented
24#26495C211yesmaximal, characteristic, complemented
25#26065C211yesmaximal, characteristic, complemented
26#25036C211yesmaximal, characteristic, complemented
27#25031C211yesmaximal, characteristic, complemented
28#23032C211yesmaximal, characteristic, complemented
29#22671C211yesmaximal, characteristic, complemented
30#21568C211yesmaximal, characteristic, complemented
31#21543C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#468C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#440C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×C4×SD16C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C22×#107C2211yescharacteristic
40C2×#405C2211yescharacteristic
41#2838—21no—
42#2835—21no—
43#2805—21no—
44#2796—21no—
45#2782—21no—
46#2744—21no—
47#2723—21no—
48#2721—21no—
49#2720—21no—
50#2696—21no—
51#2655—21no—
52#2652—21no—
53#2636—21no—
54#2628C2211yescharacteristic
55#2628C2211yescharacteristic
56#2623—21no—
57#2571C2211yescharacteristic
58#2570C2211yescharacteristic
59#2560—21no—
60#2538C2211yescharacteristic
61#2535C2211yescharacteristic
62#2508C2211yescharacteristic
63#2506C2211yescharacteristic
64#2497C2211yescharacteristic
65#2496C2211yescharacteristic
66#2496C2211yescharacteristic
67#2494C2211yescharacteristic
68#2487C2211yescharacteristic
69#2487C2211yescharacteristic
70#2452C2211yescharacteristic
71#2451C2211yescharacteristic
72#2449—21no—
73#2440C2211yescharacteristic
74#2440C2211yescharacteristic
75#2422C2211yescharacteristic
76#2421C2211yescharacteristic
77#2421C2211yescharacteristic
78#2420C2211yescharacteristic
79#2395C2211yescharacteristic
80#2361C2211yescharacteristic
81#2360C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84#2324C2211yescharacteristic
85#2323C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2099C2211yescharacteristic
92#2088C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic
104#2076C2211yescharacteristic
105#2076C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic
108#2074C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2072C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2024C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic
127#1993C2211yescharacteristic
128#1973C2211yescharacteristic
129#1968C2211yescharacteristic
130#1949C2211yescharacteristic
131#1947C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1944C2211yescharacteristic
135#1944C2211yescharacteristic
136#1943C2211yescharacteristic
137#1942C2211yescharacteristic
138#1942C2211yescharacteristic
139#1942C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1928C2211yescharacteristic
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1874C2211yescharacteristic
159#1872C2211yescharacteristic
160#1869C2211yescharacteristic
161#1865C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1863C2211yescharacteristic
166#1863C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1850C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1846C2211yescharacteristic
179#1845C2211yescharacteristic
180#1824C2211yescharacteristic
181#1824C2211yescharacteristic
182#1818C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1805C2211yescharacteristic
191#1803C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4—21no—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232#500—42no—
233#468—24no—
234#465—24no—
235#440—42no—
236#440—42no—
237C4×SD16—24no—
238#435—42no—
239C2×#107—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281#405—42no—
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#401—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400D411yescharacteristic
305#399—21no—
306#399—21no—
307#399—21no—
308#399—21no—
309#399D411yescharacteristic
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398D411yescharacteristic
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397D411yescharacteristic
326#397D411yescharacteristic
327#397D411yescharacteristic
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#394D411yescharacteristic
340#394D411yescharacteristic
341#393—21no—
342#393—21no—
343#393—21no—
344#392—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—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#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—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#384C2311yescharacteristic
417#384C2311yescharacteristic
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16#4114yes—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—22no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#126—82no—
526#126—82no—
527#125—82no—
528#123—82no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533C22⋊Q8—82no—
534C22⋊Q8—82no—
535C22⋊Q8—82no—
536#121—22no—
537#121—22no—
538#121—41no—
539#121—41no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×D4—22no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—82no—
555#117—41no—
556#117—41no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
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—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—82no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#107—22no—
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#106—22no—
674#106—22no—
675#106—22no—
676#106—41no—
677#106—41no—
678C4⋊C8—22no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—41no—
693#102—41no—
694#102—41no—
695C22⋊C8—22no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700#97—22no—
701#97—22no—
702#97—22no—
703#97—41no—
704C4×C8—22no—
705C4×C8—22no—
706C4×C8—41no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
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#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759C24—21no—
760C24C22×D411yescharacteristic
761C24C22×D411yescharacteristic
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8C2×#4112yes—
774C2×D4—22no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—81no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4C2×#4112yes—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C2511yescharacteristic
844SD16—28no—
845M16—44no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—44no—
867C2×C8—44no—
868C2×C8C2×#4112yes—
869C2×C8H(5,𝔽2)12yes—
870C2×C82−1+412yes—
871C2×C82−1+412yes—
872C4⋊C4—22no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—42no—
982C42—42no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23#57812yes—
1009C23C23×D411yescharacteristic
1010Q8—22no—
1011Q8—22no—
1012Q8—41no—
1013Q8—41no—
1014Q8—162no—
1015Q8—162no—
1016D4—22no—
1017D4—22no—
1018D4—41no—
1019D4—41no—
1020D4—82no—
1021D4—84no—
1022D4—162no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—84no—
1112C2×C4—162no—
1113C2×C4—162no—
1114C2×C4—162no—
1115C2×C4—162no—
1116C2×C4#57612yes—
1117C2×C4C22×#4111yescharacteristic
1118C2×C4C2×H(5,𝔽2)11yescharacteristic
1119C2×C4C2×2−1+411yescharacteristic
1120C2×C4C2×2−1+411yescharacteristic
1121C2×C4#58511yescharacteristic
1122C2×C4#58511yescharacteristic
1123C8—22no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8#53914yes—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—42no—
1141C22—41no—
1142C22—42no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—42no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22D4×#4111yescharacteristic
1153C22#349611yescharacteristic
1154C22#349911yescharacteristic
1155C22C2×#57611yescharacteristic
1156C22C2×#57811yescharacteristic
1157C22#358511yescharacteristic
1158C22#358611yescharacteristic
1159C4—22no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4C2×#53911yescharacteristic
1187C4#351511yescharacteristic
1188C4#354111yescharacteristic
1189C4#356511yescharacteristic
1190C2—42no—
1191C2—81no—
1192C2—82no—
1193C2#3940011yescharacteristic
1194C2#6152311yescharacteristic
1195C2#6152411yescharacteristic
1196C2#6231711yescharacteristic
1197C2#6234911yescharacteristic
1198C2#6248811yescharacteristic
1199C2#6249911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2535C22
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. #42859C2semidirect
3. #33215C2semidirect
5. #32000C2semidirect
6. #31612C2semidirect
7. #31602C2semidirect
8. #31485C2semidirect
9. #31478C2semidirect
10. #31380C2semidirect
11. #31376C2semidirect
12. #30183C2semidirect
13. #30177C2semidirect
14. #28839C2semidirect
16. #28008C2semidirect
17. #27852C2semidirect
18. #27845C2semidirect
19. #27666C2semidirect
20. #27295C2semidirect
21. #27294C2semidirect
22. #27036C2semidirect
23. #27033C2semidirect
24. #26495C2semidirect
25. #26065C2semidirect
26. #25036C2semidirect
27. #25031C2semidirect
28. #23032C2semidirect
29. #22671C2semidirect
30. #21568C2semidirect
31. #21543C2semidirect

Maximal subgroups

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

subgroupindex
#428592
#425482
#332152
#320042
#320002
#316122
#316022
#314852
#314782
#313802
#313762
#301832
#301772
#288392
#282352
#280082
#278522
#278452
#276662
#272952
#272942
#270362
#270332
#264952
#260652
#250362
#250312
#230322
#226712
#215682
#215432