Finite Group Databasebeta

← #7073273

Subgroups — #7073273

Order 512.

1673 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59650C211yesmaximal, characteristic
2#39664C211yesmaximal, characteristic, complemented
3#32014C211yesmaximal, characteristic, complemented
4#31882C211yesmaximal, characteristic, complemented
5#31794C211yesmaximal, characteristic, complemented
6#31734C211yesmaximal, characteristic, complemented
7#31667C211yesmaximal, characteristic, complemented
8#31226C211yesmaximal, characteristic, complemented
9#31041C211yesmaximal, characteristic, complemented
10#30500C211yesmaximal, characteristic, complemented
11#29479C211yesmaximal, characteristic, complemented
12#29029C211yesmaximal, characteristic, complemented
13#28927C211yesmaximal, characteristic, complemented
14#27343C211yesmaximal, characteristic, complemented
15#26980C211yesmaximal, characteristic, complemented
16#26948C211yesmaximal, characteristic, complemented
17#26836C211yesmaximal, characteristic, complemented
18#26675C211yesmaximal, characteristic, complemented
19#25573C211yesmaximal, characteristic, complemented
20#25171C211yesmaximal, characteristic, complemented
21#25121C211yesmaximal, characteristic, complemented
22#24787C211yesmaximal, characteristic, complemented
23#24507C211yesmaximal, characteristic, complemented
24#24452C211yesmaximal, characteristic, complemented
25#24259C211yesmaximal, characteristic, complemented
26#24098C211yesmaximal, characteristic, complemented
27#23709C211yesmaximal, characteristic, complemented
28#23086C211yesmaximal, characteristic, complemented
29#23032C211yesmaximal, characteristic, complemented
30#22579C211yesmaximal, characteristic, complemented
31#22049C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#462C2211yescharacteristic, complemented
41C2×#452C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#441C2211yescharacteristic, complemented
46C2×#440C2211yescharacteristic
47C2×#435C2211yescharacteristic, complemented
48C2×#432C2211yescharacteristic
49C22×#107C2211yescharacteristic, complemented
50C2×#417C2211yescharacteristic
51#2855C2211yescharacteristic
52#2791—21no—
53#2780—21no—
54#2748—21no—
55#2748—21no—
56#2711—21no—
57#2696—21no—
58#2667—21no—
59#2558—21no—
60#2542C2211yescharacteristic
61#2540—21no—
62#2538C2211yescharacteristic
63#2522—21no—
64#2507C2211yescharacteristic, complemented
65#2497—21no—
66#2491C2211yescharacteristic
67#2487C2211yescharacteristic
68#2487C2211yescharacteristic
69#2472—21no—
70#2452C2211yescharacteristic
71#2448C2211yescharacteristic
72#2446C2211yescharacteristic, complemented
73#2437—21no—
74#2429C2211yescharacteristic, complemented
75#2426C2211yescharacteristic
76#2424—21no—
77#2423C2211yescharacteristic, complemented
78#2417C2211yescharacteristic
79#2417C2211yescharacteristic, complemented
80#2417C2211yescharacteristic, complemented
81#2416C2211yescharacteristic
82#2408C2211yescharacteristic
83#2407C2211yescharacteristic
84#2361C2211yescharacteristic
85#2360C2211yescharacteristic, complemented
86#2358—21no—
87#2345C2211yescharacteristic, complemented
88#2341C2211yescharacteristic
89#2333—21no—
90C4×C22⋊Q8C2211yescharacteristic
91C4×C22⋊Q8C2211yescharacteristic
92C4×#121C2211yescharacteristic
93C2×#390C2211yescharacteristic
94#2099C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2057C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2015C2211yescharacteristic
125#2013C2211yescharacteristic
126#2013C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic, complemented
130#2001C2211yescharacteristic, complemented
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1987C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1971C2211yescharacteristic, complemented
140#1959C2211yescharacteristic
141#1955C2211yescharacteristic
142#1955C2211yescharacteristic, complemented
143#1954C2211yescharacteristic
144#1944C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1940C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic, complemented
162#1924C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1894C2211yescharacteristic, complemented
165#1892C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1853C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#554—42no—
214#554—42no—
215#546—42no—
216#546—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121—21no—
236C2×#121D411yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C42C2311yescharacteristic
260#487—42no—
261#484—42no—
262#468—42no—
263#465—24no—
264#465—42no—
265#464—42no—
266#462—42no—
267#452—42no—
268#452—42no—
269#450—24no—
270#450—42no—
271#441—42no—
272#440—42no—
273#435—42no—
274#432—42no—
275C2×#107—42no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#417—24no—
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#393—21no—
368#393—21no—
369#392—21no—
370#392—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390D411yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389D411yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388D411yescharacteristic
412#388D411yescharacteristic
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386D411yescharacteristic
433#386D411yescharacteristic
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#384—21no—
444#384C2311yescharacteristic
445#381—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380D411yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—41no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573#125—44no—
574#124—22no—
575#124—41no—
576#124—82no—
577#123—44no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—44no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—82no—
597#121—24no—
598#121—22no—
599#121—22no—
600#121—41no—
601#121—41no—
602#121—44no—
603#121—41no—
604#121—41no—
605#121—82no—
606#120—44no—
607#120—44no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—44no—
625C4×D4—82no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—82no—
715C2×C22⋊C4—82no—
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#107—22no—
742#107—22no—
743#107—41no—
744#107—41no—
745#107—41no—
746#107—41no—
747#106—22no—
748#106—41no—
749#106—41no—
750#106—41no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102#4114yes—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793#97—22no—
794#97—41no—
795#97—41no—
796#97—41no—
797#97—41no—
798C4×C8—41no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846#41—44no—
847#41—82no—
848#41—82no—
849#41—82no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8H(5,𝔽2)12yes—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—81no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4#13714yes—
910C2×D4C2×#4112yes—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—81no—
956C22×C4—81no—
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×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C2511yescharacteristic
979Q16—44no—
980Q16—82no—
981SD16—44no—
982SD16—82no—
983SD16—82no—
984SD16—82no—
985M16—82no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—44no—
1009C2×C8C2×#4112yes—
1010C2×C8H(5,𝔽2)12yes—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4C2×#4112yes—
1067C4⋊C4H(5,𝔽2)12yes—
1068C22⋊C4—24no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—41no—
1120C42—41no—
1121C42—42no—
1122C42—42no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C42—81no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—84no—
1162C23—84no—
1163C23—84no—
1164C23—84no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23C2×#13712yes—
1169C23C2×#13712yes—
1170C23C23×D411yescharacteristic
1171Q8—22no—
1172Q8—22no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—162no—
1184D4—22no—
1185D4—22no—
1186D4—44no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—82no—
1194D4—82no—
1195D4—84no—
1196D4—84no—
1197D4—84no—
1198D4—162no—
1199D4—162no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—82no—
1287C2×C4—82no—
1288C2×C4—84no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4C2×#13712yes—
1295C2×C4C22×#4111yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×H(5,𝔽2)11yescharacteristic
1298C2×C4C2×H(5,𝔽2)11yescharacteristic
1299C2×C4#58511yescharacteristic
1300C2×C4#58511yescharacteristic
1301C8—22no—
1302C8—22no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—42no—
1332C22—41no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—168no—
1345C22D4×#4111yescharacteristic
1346C22#348411yescharacteristic
1347C22#349611yescharacteristic
1348C22C22×#13711yescharacteristic
1349C22#358511yescharacteristic
1350C22#358511yescharacteristic
1351C22#358611yescharacteristic
1352C4—22no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—41no—
1364C4—41no—
1365C4—42no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4#349411yescharacteristic
1378C4#351911yescharacteristic
1379C4#354211yescharacteristic
1380C4#356211yescharacteristic
1381C2—42no—
1382C2—42no—
1383C2—81no—
1384C2—82no—
1385C2—161no—
1386C2#4392311yescharacteristic
1387C2#6145311yescharacteristic
1388C2#6151011yescharacteristic
1389C2#6157311yescharacteristic
1390C2#6167511yescharacteristic
1391C2#6228811yescharacteristic
1392C2#6229611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59650C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39664C2semidirect
3. #32014C2semidirect
4. #31882C2semidirect
5. #31794C2semidirect
6. #31734C2semidirect
7. #31667C2semidirect
8. #31226C2semidirect
9. #31041C2semidirect
10. #30500C2semidirect
11. #29479C2semidirect
12. #29029C2semidirect
13. #28927C2semidirect
14. #27343C2semidirect
15. #26980C2semidirect
16. #26948C2semidirect
17. #26836C2semidirect
18. #26675C2semidirect
19. #25573C2semidirect
20. #25171C2semidirect
21. #25121C2semidirect
22. #24787C2semidirect
23. #24507C2semidirect
24. #24452C2semidirect
25. #24259C2semidirect
26. #24098C2semidirect
27. #23709C2semidirect
28. #23086C2semidirect
29. #23032C2semidirect
30. #22579C2semidirect
31. #22049C2semidirect
34. C2×#487C22semidirect
35. C2×#484C22semidirect
40. C2×#462C22semidirect
45. C2×#441C22semidirect
47. C2×#435C22semidirect
49. C22×#107C22semidirect
64. #2507C22semidirect
72. #2446C22semidirect
74. #2429C22semidirect
77. #2423C22semidirect
79. #2417C22semidirect
80. #2417C22semidirect
85. #2360C22semidirect
87. #2345C22semidirect
94. #2099C22semidirect
95. #2088C22semidirect
96. #2086C22semidirect
97. #2084C22semidirect
100. #2075C22semidirect
101. #2068C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
108. #2057C22semidirect
109. #2057C22semidirect
110. #2056C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
120. #2035C22semidirect
129. #2001C22semidirect
130. #2001C22semidirect
134. #1987C22semidirect
139. #1971C22semidirect
142. #1955C22semidirect
144. #1944C22semidirect
145. #1943C22semidirect
146. #1940C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
156. #1928C22semidirect
161. #1924C22semidirect
162. #1924C22semidirect
163. #1919C22semidirect
164. #1894C22semidirect
165. #1892C22semidirect
168. #1878C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
185. #1853C22semidirect
188. #1824C22semidirect
189. #1823C22semidirect
190. #1809C22semidirect
195. #1776C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
199. C4×#103C22semidirect
200. #1753C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#596502
#396642
#320142
#318822
#317942
#317342
#316672
#312262
#310412
#305002
#294792
#290292
#289272
#273432
#269802
#269482
#268362
#266752
#255732
#251712
#251212
#247872
#245072
#244522
#242592
#240982
#237092
#230862
#230322
#225792
#220492