Finite Group Databasebeta

← #7126623

Subgroups — #7126623

Order 512.

1422 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C211yesmaximal, characteristic, complemented
2#39002C211yesmaximal, characteristic, complemented
3#32640C211yesmaximal, characteristic, complemented
4#32593C211yesmaximal, characteristic, complemented
5#32120C211yesmaximal, characteristic, complemented
6#31791C211yesmaximal, characteristic, complemented
7#31207C211yesmaximal, characteristic, complemented
8#31123C211yesmaximal, characteristic, complemented
9#30791C211yesmaximal, characteristic, complemented
10#30593C211yesmaximal, characteristic, complemented
11#29444C211yesmaximal, characteristic, complemented
12#29444C211yesmaximal, characteristic, complemented
13#29064C211yesmaximal, characteristic, complemented
14#28686C211yesmaximal, characteristic, complemented
15#28562C211yesmaximal, characteristic, complemented
16#27798C211yesmaximal, characteristic, complemented
17#27480C211yesmaximal, characteristic, complemented
18#27350C211yesmaximal, characteristic, complemented
19#27166C211yesmaximal, characteristic, complemented
20#26943C211yesmaximal, characteristic, complemented
21#26815C211yesmaximal, characteristic, complemented
22#26747C211yesmaximal, characteristic, complemented
23#26439C211yesmaximal, characteristic, complemented
24#26001C211yesmaximal, characteristic, complemented
25#25300C211yesmaximal, characteristic, complemented
26#25246C211yesmaximal, characteristic, complemented
27#23784C211yesmaximal, characteristic, complemented
28#23207C211yesmaximal, characteristic, complemented
29#22935C211yesmaximal, characteristic, complemented
30#22924C211yesmaximal, characteristic, complemented
31#22120C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#459C2211yescharacteristic
39C2×#446C2211yescharacteristic
40C2×#435C2211yescharacteristic
41#2860C2211yescharacteristic
42#2785—21no—
43#2779—21no—
44#2761—21no—
45#2733—21no—
46#2705—21no—
47#2698—21no—
48#2651—21no—
49#2610—21no—
50#2610—21no—
51#2584C2211yescharacteristic
52#2567C2211yescharacteristic
53#2555—21no—
54#2548C2211yescharacteristic
55#2538C2211yescharacteristic
56#2529—21no—
57#2500—21no—
58#2500—21no—
59#2497C2211yescharacteristic
60#2491C2211yescharacteristic
61#2491C2211yescharacteristic
62#2490C2211yescharacteristic
63#2490C2211yescharacteristic
64#2486C2211yescharacteristic
65#2461—21no—
66#2442C2211yescharacteristic
67#2441C2211yescharacteristic
68#2428C2211yescharacteristic
69#2428C2211yescharacteristic
70#2420C2211yescharacteristic
71#2414C2211yescharacteristic
72#2414C2211yescharacteristic
73#2414C2211yescharacteristic
74#2372—21no—
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2361C2211yescharacteristic
78#2346C2211yescharacteristic
79#2346C2211yescharacteristic
80#2346C2211yescharacteristic
81#2319—21no—
82C4×#125C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2293C2211yescharacteristic
85#2293C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2086C2211yescharacteristic
95#2083C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2075C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2023C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1985C2211yescharacteristic
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic
132#1972C2211yescharacteristic
133#1957C2211yescharacteristic
134#1955C2211yescharacteristic
135#1949C2211yescharacteristic
136#1948C2211yescharacteristic
137#1944C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1941C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1895C2211yescharacteristic
169#1895C2211yescharacteristic
170#1895C2211yescharacteristic
171#1893C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1874C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1853C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1825C2211yescharacteristic
189#1807C2211yescharacteristic
190#1804C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1767C2211yescharacteristic
195#1767C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124—21no—
213C2×#124—21no—
214C2×#124—21no—
215C2×#124D411yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238#501—42no—
239#482—24no—
240#482—24no—
241#481—42no—
242#478—24no—
243#466—42no—
244#459—42no—
245#446—42no—
246#435—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#399—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#393—21no—
329#393—21no—
330#392—21no—
331#392—21no—
332#392—21no—
333#392—21no—
334#392—21no—
335#391—21no—
336#391D411yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390D411yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
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#388—21no—
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#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
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#388D411yescharacteristic
398#388D411yescharacteristic
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#385—21no—
412#385—21no—
413#384—21no—
414#384C2311yescharacteristic
415#382—21no—
416#382—21no—
417#382—21no—
418#382D411yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#376—21no—
448#376—21no—
449#376—21no—
450C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—22no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529#127—41no—
530#127—41no—
531#126—82no—
532#125—22no—
533#125—41no—
534#125—41no—
535#125—41no—
536#124—42no—
537#124—44no—
538#124—82no—
539#124—82no—
540#123—82no—
541C22⋊Q8—82no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—41no—
546#121—41no—
547#121—41no—
548#121—41no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—82no—
555#121—82no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—44no—
567#117—22no—
568#117—22no—
569#117—22no—
570#117—41no—
571#117—41no—
572#117—41no—
573#117—82no—
574#117—82no—
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—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—22no—
686#107—22no—
687#107—22no—
688#107—41no—
689#106—22no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106#4114yes—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729#97—22no—
730#97—41no—
731#97—41no—
732#97—41no—
733#97—41no—
734C4×C8—41no—
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#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#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772C24—21no—
773C24—21no—
774C24—21no—
775C24C22×D411yescharacteristic
776C24C22×D411yescharacteristic
777C2×Q8—22no—
778C2×Q8—41no—
779C2×Q8—41no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
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—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C2511yescharacteristic
878D8—82no—
879D8—82no—
880M16—82no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
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—82no—
904C2×C8C2×#4112yes—
905C2×C8H(5,𝔽2)12yes—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—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—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4C2×#4112yes—
956C4⋊C4C2×#4112yes—
957C4⋊C42−1+412yes—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—41no—
1017C42—41no—
1018C42—41no—
1019C42—41no—
1020C42—42no—
1021C42—42no—
1022C42—42no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—81no—
1028C42—81no—
1029C42—81no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23C23×D411yescharacteristic
1066Q8—82no—
1067Q8—162no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—82no—
1081D4—84no—
1082D4—162no—
1083D4—162no—
1084D4—162no—
1085D4—162no—
1086D4—162no—
1087D4—162no—
1088D4—162no—
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—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
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—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
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—84no—
1172C2×C4—84no—
1173C2×C4—162no—
1174C2×C4—162no—
1175C2×C4#57512yes—
1176C2×C4C22×#4111yescharacteristic
1177C2×C4C2×H(5,𝔽2)11yescharacteristic
1178C2×C4C2×2−1+411yescharacteristic
1179C2×C4#58511yescharacteristic
1180C2×C4#58511yescharacteristic
1181C2×C4#58511yescharacteristic
1182C8—22no—
1183C8—22no—
1184C8—41no—
1185C8—41no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22D4×#4111yescharacteristic
1226C22#348911yescharacteristic
1227C22#349611yescharacteristic
1228C22C2×#57511yescharacteristic
1229C22#358511yescharacteristic
1230C22#358511yescharacteristic
1231C22#358511yescharacteristic
1232C4—22no—
1233C4—41no—
1234C4—42no—
1235C4—41no—
1236C4—42no—
1237C4—41no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4#351111yescharacteristic
1258C4#352411yescharacteristic
1259C4#354511yescharacteristic
1260C4#356511yescharacteristic
1261C2—81no—
1262C2—81no—
1263C2—161no—
1264C2—161no—
1265C2—161no—
1266C2#4476211yescharacteristic
1267C2#6145911yescharacteristic
1268C2#6150711yescharacteristic
1269C2#6212311yescharacteristic
1270C2#6223111yescharacteristic
1271C2#6230111yescharacteristic
1272C2#6233611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59952C2semidirect
2. #39002C2semidirect
3. #32640C2semidirect
4. #32593C2semidirect
5. #32120C2semidirect
6. #31791C2semidirect
7. #31207C2semidirect
8. #31123C2semidirect
9. #30791C2semidirect
10. #30593C2semidirect
11. #29444C2semidirect
12. #29444C2semidirect
13. #29064C2semidirect
14. #28686C2semidirect
15. #28562C2semidirect
16. #27798C2semidirect
17. #27480C2semidirect
18. #27350C2semidirect
19. #27166C2semidirect
20. #26943C2semidirect
21. #26815C2semidirect
22. #26747C2semidirect
23. #26439C2semidirect
24. #26001C2semidirect
25. #25300C2semidirect
26. #25246C2semidirect
27. #23784C2semidirect
28. #23207C2semidirect
29. #22935C2semidirect
30. #22924C2semidirect
31. #22120C2semidirect

Maximal subgroups

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

subgroupindex
#599522
#390022
#326402
#325932
#321202
#317912
#312072
#311232
#307912
#305932
#294442
#290642
#286862
#285622
#277982
#274802
#273502
#271662
#269432
#268152
#267472
#264392
#260012
#253002
#252462
#237842
#232072
#229352
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