Finite Group Databasebeta

← #7087043

Subgroups — #7087043

Order 512.

1477 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45174C211yesmaximal, characteristic, complemented
2#42589C211yesmaximal, characteristic
3#32247C211yesmaximal, characteristic, complemented
4#32180C211yesmaximal, characteristic, complemented
5#32180C211yesmaximal, characteristic, complemented
6#32113C211yesmaximal, characteristic, complemented
7#31823C211yesmaximal, characteristic, complemented
8#31088C211yesmaximal, characteristic, complemented
9#30547C211yesmaximal, characteristic, complemented
10#30527C211yesmaximal, characteristic, complemented
11#29569C211yesmaximal, characteristic, complemented
12#29358C211yesmaximal, characteristic, complemented
13#29051C211yesmaximal, characteristic, complemented
14#28988C211yesmaximal, characteristic, complemented
15#28024C211yesmaximal, characteristic, complemented
16#27780C211yesmaximal, characteristic, complemented
17#27523C211yesmaximal, characteristic, complemented
18#27348C211yesmaximal, characteristic, complemented
19#27264C211yesmaximal, characteristic, complemented
20#27023C211yesmaximal, characteristic, complemented
21#26913C211yesmaximal, characteristic, complemented
22#26825C211yesmaximal, characteristic, complemented
23#26716C211yesmaximal, characteristic, complemented
24#26629C211yesmaximal, characteristic, complemented
25#25288C211yesmaximal, characteristic, complemented
26#24478C211yesmaximal, characteristic, complemented
27#23690C211yesmaximal, characteristic, complemented
28#23289C211yesmaximal, characteristic, complemented
29#23229C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#22230C211yesmaximal, characteristic, complemented
32C2×#490C2211yescharacteristic
33C2×#490C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#478C2211yescharacteristic, complemented
37C2×#450C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic
41#2825—21no—
42#2788—21no—
43#2776—21no—
44#2767—21no—
45#2758—21no—
46#2703—21no—
47#2688—21no—
48#2678—21no—
49#2668—21no—
50#2641C2211yescharacteristic
51#2635—21no—
52#2617—21no—
53#2577—21no—
54#2550C2211yescharacteristic, complemented
55#2541C2211yescharacteristic
56#2541C2211yescharacteristic
57#2523—21no—
58#2514—21no—
59#2514C2211yescharacteristic, complemented
60#2514C2211yescharacteristic, complemented
61#2513C2211yescharacteristic
62#2495C2211yescharacteristic
63#2494—21no—
64#2492C2211yescharacteristic
65#2490C2211yescharacteristic
66#2489C2211yescharacteristic
67#2454C2211yescharacteristic
68#2453C2211yescharacteristic, complemented
69#2445C2211yescharacteristic
70#2442C2211yescharacteristic
71#2433C2211yescharacteristic
72#2433C2211yescharacteristic
73#2428C2211yescharacteristic
74#2424—21no—
75#2420C2211yescharacteristic
76#2401C2211yescharacteristic
77#2370C2211yescharacteristic, complemented
78#2370C2211yescharacteristic, complemented
79#2366C2211yescharacteristic
80#2360C2211yescharacteristic
81#2345C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2331C2211yescharacteristic, complemented
84#2328C2211yescharacteristic
85#2320C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2085C2211yescharacteristic, complemented
89#2077C2211yescharacteristic
90#2076C2211yescharacteristic
91#2074C2211yescharacteristic, complemented
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic, complemented
95#2067C2211yescharacteristic, complemented
96#2066C2211yescharacteristic, complemented
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic, complemented
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic, complemented
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic, complemented
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic, complemented
119#2014C2211yescharacteristic
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1982C2211yescharacteristic
131#1982C2211yescharacteristic
132#1982C2211yescharacteristic
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1961C2211yescharacteristic
140#1961C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic, complemented
151#1934C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1925C2211yescharacteristic, complemented
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1919C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1892C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1846C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1768C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×#120—21no—
230C2×#120—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239#490—24no—
240#490—42no—
241#486—24no—
242#481—42no—
243#478—42no—
244#450—24no—
245#440—42no—
246C4×SD16—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#102—42no—
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#401—21no—
305#401D411yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400D411yescharacteristic
314#400D411yescharacteristic
315#400D411yescharacteristic
316#399—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397D411yescharacteristic
327#397D411yescharacteristic
328#397D411yescharacteristic
329#396—21no—
330#396D411yescharacteristic
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#393—21no—
342#392—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—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#386—21no—
407#386—21no—
408#386—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#383—21no—
421#383—21no—
422#383—21no—
423#383—21no—
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C4⋊Q8—22no—
543C4⋊Q8—41no—
544#127—22no—
545#127—22no—
546#127—41no—
547#127—41no—
548#127—41no—
549#127—41no—
550#127—41no—
551#127—41no—
552#127—41no—
553#127—41no—
554#125—22no—
555#125—22no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—82no—
568#121—82no—
569#121—82no—
570#121—82no—
571#121—82no—
572#120—82no—
573#120—82no—
574#120—82no—
575#120—82no—
576C4×Q8—22no—
577C4×Q8—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—82no—
587C2×C4⋊C4—22no—
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—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—41no—
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×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⋊C4—21no—
655C2×C22⋊C4—82no—
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×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—22no—
677#107—41no—
678#107—41no—
679#107—41no—
680#106—22no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
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#4114yes—
721C22⋊C8—22no—
722C22⋊C8—41no—
723C22⋊C8—41no—
724#97—22no—
725#97—41no—
726#97—41no—
727#97—41no—
728#97—41no—
729C4×C8—22no—
730C4×C8—41no—
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#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#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
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
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—42no—
801C2×Q8—81no—
802C2×Q8—81no—
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—21no—
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—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—44no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4C2×#4112yes—
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—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
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×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
917SD16—44no—
918SD16—44no—
919SD16—82no—
920SD16—82no—
921C2×C8—21no—
922C2×C8—21no—
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—82no—
945C2×C8C2×#4112yes—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
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—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4C2×#4112yes—
992C4⋊C4H(5,𝔽2)12yes—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
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—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—42no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—84no—
1084C23—84no—
1085C23—162no—
1086C23—162no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23#57712yes—
1091C23C23×D411yescharacteristic
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—162no—
1097D4—22no—
1098D4—22no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—84no—
1114D4—84no—
1115D4—162no—
1116D4—162no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120D4—162no—
1121D4—162no—
1122D4—162no—
1123D4—162no—
1124D4—162no—
1125D4—162no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
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—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
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—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4C22×#4111yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C8—22no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—168no—
1260C22D4×#4111yescharacteristic
1261C22#348811yescharacteristic
1262C22#350011yescharacteristic
1263C22C2×#57711yescharacteristic
1264C22#358511yescharacteristic
1265C22#358511yescharacteristic
1266C22#358511yescharacteristic
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4#350611yescharacteristic
1293C4#352111yescharacteristic
1294C4#354011yescharacteristic
1295C4#356811yescharacteristic
1296C2—42no—
1297C2—82no—
1298C2—161no—
1299C2—161no—
1300C2—161no—
1301C2#4418211yescharacteristic
1302C2#6150611yescharacteristic
1303C2#6152111yescharacteristic
1304C2#6200911yescharacteristic
1305C2#6207911yescharacteristic
1306C2#6256411yescharacteristic
1307C2#6259611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42589C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45174C2semidirect
3. #32247C2semidirect
4. #32180C2semidirect
5. #32180C2semidirect
6. #32113C2semidirect
7. #31823C2semidirect
8. #31088C2semidirect
9. #30547C2semidirect
10. #30527C2semidirect
11. #29569C2semidirect
12. #29358C2semidirect
13. #29051C2semidirect
14. #28988C2semidirect
15. #28024C2semidirect
16. #27780C2semidirect
17. #27523C2semidirect
18. #27348C2semidirect
19. #27264C2semidirect
20. #27023C2semidirect
21. #26913C2semidirect
22. #26825C2semidirect
23. #26716C2semidirect
24. #26629C2semidirect
25. #25288C2semidirect
26. #24478C2semidirect
27. #23690C2semidirect
28. #23289C2semidirect
29. #23229C2semidirect
30. #22854C2semidirect
31. #22230C2semidirect
36. C2×#478C22semidirect
39. C2×C4×SD16C22semidirect
54. #2550C22semidirect
59. #2514C22semidirect
60. #2514C22semidirect
68. #2453C22semidirect
77. #2370C22semidirect
78. #2370C22semidirect
83. #2331C22semidirect
85. #2320C22semidirect
86. #2101C22semidirect
87. #2088C22semidirect
88. #2085C22semidirect
91. #2074C22semidirect
94. #2073C22semidirect
95. #2067C22semidirect
96. #2066C22semidirect
100. #2059C22semidirect
101. #2059C22semidirect
104. #2055C22semidirect
105. #2055C22semidirect
110. #2041C22semidirect
113. #2026C22semidirect
116. #2025C22semidirect
118. #2023C22semidirect
123. #2014C22semidirect
126. #1993C22semidirect
127. #1989C22semidirect
128. #1989C22semidirect
129. #1989C22semidirect
134. #1982C22semidirect
137. #1973C22semidirect
140. #1961C22semidirect
141. #1943C22semidirect
142. #1940C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1935C22semidirect
150. #1934C22semidirect
151. #1934C22semidirect
152. #1927C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
161. #1925C22semidirect
162. #1925C22semidirect
166. #1919C22semidirect
167. #1918C22semidirect
168. #1918C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
176. #1880C22semidirect
178. #1877C22semidirect
181. #1864C22semidirect
184. #1862C22semidirect
185. #1862C22semidirect
188. #1846C22semidirect
192. #1776C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
195. #1768C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#451742
#425892
#322472
#321802
#321132
#318232
#310882
#305472
#305272
#295692
#293582
#290512
#289882
#280242
#277802
#275232
#273482
#272642
#270232
#269132
#268252
#267162
#266292
#252882
#244782
#236902
#232892
#232292
#228542
#222302