Finite Group Databasebeta

← #7337213

Subgroups — #7337213

Order 512.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53008C211yesmaximal, characteristic, complemented
2#45108C211yesmaximal, characteristic
3#32171C211yesmaximal, characteristic, complemented
4#31921C211yesmaximal, characteristic, complemented
5#31035C211yesmaximal, characteristic, complemented
6#30996C211yesmaximal, characteristic, complemented
7#30878C211yesmaximal, characteristic, complemented
8#30757C211yesmaximal, characteristic, complemented
9#30707C211yesmaximal, characteristic, complemented
10#30604C211yesmaximal, characteristic, complemented
11#30530C211yesmaximal, characteristic, complemented
12#30467C211yesmaximal, characteristic, complemented
13#30450C211yesmaximal, characteristic, complemented
14#30449C211yesmaximal, characteristic, complemented
15#29726C211yesmaximal, characteristic, complemented
16#29672C211yesmaximal, characteristic, complemented
17#29083C211yesmaximal, characteristic, complemented
18#28986C211yesmaximal, characteristic, complemented
19#28471C211yesmaximal, characteristic, complemented
20#28326C211yesmaximal, characteristic, complemented
21#27087C211yesmaximal, characteristic, complemented
22#26945C211yesmaximal, characteristic, complemented
23#26624C211yesmaximal, characteristic, complemented
24#25784C211yesmaximal, characteristic, complemented
25#25769C211yesmaximal, characteristic
26#25613C211yesmaximal, characteristic, complemented
27#25382C211yesmaximal, characteristic, complemented
28#24905C211yesmaximal, characteristic, complemented
29#24358C211yesmaximal, characteristic, complemented
30#23852C211yesmaximal, characteristic
31#22372C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#497C2211yescharacteristic
37C2×#497C2211yescharacteristic
38C2×#494C2211yescharacteristic, complemented
39C2×#487C2211yescharacteristic, complemented
40C2×#484C2211yescharacteristic, complemented
41C2×#483C2211yescharacteristic, complemented
42C2×#467C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#462C2211yescharacteristic, complemented
45C2×#462C2211yescharacteristic, complemented
46C2×#461C2211yescharacteristic
47C2×#461C2211yescharacteristic
48C2×#461C2211yescharacteristic
49C2×#452C2211yescharacteristic
50C2×#452C2211yescharacteristic
51C2×#452C2211yescharacteristic
52C2×#452C2211yescharacteristic
53C2×#451C2211yescharacteristic
54C2×#451C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×C4×SD16C2211yescharacteristic
58#2843—21no—
59#2838—21no—
60#2838—21no—
61#2834—21no—
62#2807—21no—
63#2792—21no—
64#2757—21no—
65#2757—21no—
66#2708—21no—
67#2695—21no—
68#2687—21no—
69#2684—21no—
70#2621C2211yescharacteristic, complemented
71#2621C2211yescharacteristic, complemented
72#2547C2211yescharacteristic
73#2546C2211yescharacteristic, complemented
74#2546C2211yescharacteristic, complemented
75#2542C2211yescharacteristic
76#2534—21no—
77#2514C2211yescharacteristic, complemented
78#2514C2211yescharacteristic, complemented
79#2492C2211yescharacteristic
80#2480—21no—
81#2452C2211yescharacteristic
82#2447C2211yescharacteristic
83#2437—21no—
84#2435C2211yescharacteristic
85#2434C2211yescharacteristic
86#2434C2211yescharacteristic
87#2432C2211yescharacteristic
88#2429C2211yescharacteristic
89#2429C2211yescharacteristic, complemented
90#2429C2211yescharacteristic, complemented
91#2427—21no—
92#2421C2211yescharacteristic
93#2421C2211yescharacteristic
94#2417C2211yescharacteristic
95#2409C2211yescharacteristic
96#2395C2211yescharacteristic
97#2367C2211yescharacteristic
98#2361C2211yescharacteristic
99D4×C22⋊C4C2211yescharacteristic
100#2311C2211yescharacteristic
101#2097C2211yescharacteristic, complemented
102#2092C2211yescharacteristic
103#2086C2211yescharacteristic, complemented
104#2077C2211yescharacteristic
105#2074C2211yescharacteristic, complemented
106#2073C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2056C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2043C2211yescharacteristic, complemented
117#2043C2211yescharacteristic, complemented
118#2043C2211yescharacteristic, complemented
119#2042C2211yescharacteristic
120#2036C2211yescharacteristic
121#2035C2211yescharacteristic
122#2024C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2016C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2016C2211yescharacteristic, complemented
128#2016C2211yescharacteristic, complemented
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#2015C2211yescharacteristic
133#2015C2211yescharacteristic
134#2013C2211yescharacteristic
135#2013C2211yescharacteristic
136#2013C2211yescharacteristic
137#2013C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic, complemented
142#2001C2211yescharacteristic, complemented
143#2001C2211yescharacteristic, complemented
144#2001C2211yescharacteristic, complemented
145#2000C2211yescharacteristic
146#2000C2211yescharacteristic
147#2000C2211yescharacteristic
148#2000C2211yescharacteristic
149#1993C2211yescharacteristic, complemented
150#1983C2211yescharacteristic
151#1981C2211yescharacteristic, complemented
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic, complemented
155#1971C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1968C2211yescharacteristic
158#1958C2211yescharacteristic
159#1955C2211yescharacteristic
160#1940C2211yescharacteristic, complemented
161#1935C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1934C2211yescharacteristic
164#1933C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1928C2211yescharacteristic, complemented
167#1924C2211yescharacteristic, complemented
168#1923C2211yescharacteristic
169#1923C2211yescharacteristic
170#1923C2211yescharacteristic, complemented
171#1921C2211yescharacteristic, complemented
172#1920C2211yescharacteristic, complemented
173#1917C2211yescharacteristic, complemented
174#1916C2211yescharacteristic, complemented
175#1892C2211yescharacteristic
176#1892C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1878C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1877C2211yescharacteristic
187#1872C2211yescharacteristic, complemented
188#1872C2211yescharacteristic, complemented
189#1869C2211yescharacteristic
190#1865C2211yescharacteristic, complemented
191#1862C2211yescharacteristic
192#1850C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1798C2211yescharacteristic, complemented
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1770C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1752C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16—42no—
215C22×SD16—42no—
216C22×SD16—42no—
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×SD16C2311yescharacteristic
225C23×C8C2311yescharacteristic
226#546—42no—
227#546—42no—
228#542—42no—
229#542—42no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×#126—21no—
238C2×#124—21no—
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×#123—21no—
243C2×#123—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×#121—21no—
256C2×#121C2311yescharacteristic
257C2×#120—21no—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C22⋊C4—21no—
269C22×C22⋊C4—21no—
270#497—42no—
271#497—42no—
272#497—42no—
273#494—42no—
274#487—42no—
275#484—42no—
276#483—42no—
277#467—42no—
278#464—42no—
279#462—42no—
280#462—42no—
281#461—42no—
282#461—42no—
283#461—42no—
284#452—42no—
285#452—42no—
286#452—42no—
287#452—42no—
288#451—42no—
289#451—42no—
290#450—42no—
291#450—42no—
292C4×SD16—42no—
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×C22⋊C8C2311yescharacteristic
339C2×C22⋊C8C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346#401—21no—
347#401—21no—
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#400—21no—
353#400D411yescharacteristic
354#399—21no—
355#399—21no—
356#399D411yescharacteristic
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398D411yescharacteristic
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397D411yescharacteristic
381#397D411yescharacteristic
382#397D411yescharacteristic
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396—21no—
388#395—21no—
389#395—21no—
390#395—21no—
391#395—21no—
392#395—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#394D411yescharacteristic
398#394D411yescharacteristic
399#393—21no—
400#393—21no—
401#393—21no—
402#391—21no—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#390—21no—
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#384—21no—
463#383—21no—
464#383—21no—
465#382C2311yescharacteristic
466#382C2311yescharacteristic
467#381—21no—
468#380—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473#380C2311yescharacteristic
474#380C2311yescharacteristic
475#379—21no—
476#379—21no—
477#379—21no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508C25—21no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8—41no—
522C22×Q8—41no—
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4C2×D411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×Q16—41no—
569C2×Q16—41no—
570C2×Q16—41no—
571C2×Q16—41no—
572C2×Q16—41no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—22no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16—41no—
594C2×SD16—41no—
595C2×SD16—41no—
596C2×SD16—41no—
597C2×SD16—416no—
598C22×C8—22no—
599C22×C8—41no—
600C22×C8—41no—
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C4⋊Q8—22no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612C4⋊Q8—41no—
613C4⋊Q8—41no—
614C4⋊Q8—41no—
615C4⋊Q8—41no—
616C4⋊Q8—41no—
617C4⋊Q8—41no—
618C4⋊Q8—41no—
619C4⋊Q8—41no—
620C4⋊Q8—41no—
621C4⋊Q8—41no—
622C4⋊Q8—41no—
623#126—44no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—41no—
628#124—41no—
629#124—41no—
630#124—44no—
631#123—44no—
632#123—44no—
633C22⋊Q8—22no—
634C22⋊Q8—44no—
635C22⋊Q8—41no—
636C22⋊Q8—41no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647C22⋊Q8—41no—
648C22⋊Q8—41no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—82no—
653#121—22no—
654#121—22no—
655#121—44no—
656#120—44no—
657C4×Q8—22no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8—41no—
662C4×Q8—41no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—82no—
672#117—41no—
673#117—41no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2×D411yescharacteristic
709C2×C4⋊C4C2×D411yescharacteristic
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2×D411yescharacteristic
712C2×C4⋊C4C2×D411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—44no—
751C2×C22⋊C4—82no—
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C22⋊C4C2×D411yescharacteristic
757C2×C22⋊C4C2×D411yescharacteristic
758C2×C22⋊C4C2×D411yescharacteristic
759C2×C22⋊C4C2×D411yescharacteristic
760C2×C22⋊C4C2×D411yescharacteristic
761C2×C22⋊C4C2×D411yescharacteristic
762C2×C42—21no—
763C2×C42—21no—
764C2×C42—21no—
765C2×C42—21no—
766C2×C42—21no—
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772#107—22no—
773#107—41no—
774#106—22no—
775#106—41no—
776C4⋊C8—22no—
777C4⋊C8—41no—
778C4⋊C8—41no—
779C4⋊C8—41no—
780C4⋊C8—41no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103—41no—
800#103—41no—
801#103—41no—
802#103—41no—
803#103—41no—
804#103—41no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102—41no—
813C22⋊C8—22no—
814C22⋊C8—22no—
815C22⋊C8—22no—
816C22⋊C8—41no—
817C22⋊C8—41no—
818C22⋊C8—41no—
819C22⋊C8—41no—
820#97—41no—
821#97—41no—
822#97—41no—
823C4×C8—22no—
824C4×C8—41no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95—21no—
857#95—21no—
858#95—21no—
859#95—21no—
860#95—21no—
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864#95C2×D411yescharacteristic
865#95C2×D411yescharacteristic
866#95C2×D411yescharacteristic
867#95C2×D411yescharacteristic
868#95C2×D411yescharacteristic
869#95C2×D411yescharacteristic
870#95C2×D411yescharacteristic
871C24—21no—
872C24—21no—
873C24—42no—
874C24—42no—
875C24—42no—
876C24—81no—
877C24—81no—
878C24—81no—
879C24—81no—
880C24C22×D411yescharacteristic
881C24C22×D411yescharacteristic
882#41—82no—
883#41—82no—
884#41—82no—
885#41—82no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—21no—
917C2×Q8—21no—
918C2×Q8—21no—
919C2×Q8—21no—
920C2×Q8—21no—
921C2×Q8—21no—
922C2×Q8—42no—
923C2×Q8—44no—
924C2×Q8—81no—
925C2×Q8—81no—
926C2×Q8—81no—
927C2×Q8—81no—
928C2×Q8—81no—
929C2×Q8—82no—
930C2×Q8—82no—
931C2×Q8—82no—
932C2×D4—24no—
933C2×D4—22no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—81no—
952C2×D4—82no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4—81no—
958C2×D4H(5,𝔽2)12yes—
959C2×D4H(5,𝔽2)12yes—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
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×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C2511yescharacteristic
1017Q16—82no—
1018Q16—82no—
1019Q16—82no—
1020Q16—82no—
1021Q16—82no—
1022Q16—82no—
1023Q16—82no—
1024Q16—82no—
1025SD16—44no—
1026SD16—44no—
1027SD16—44no—
1028SD16—44no—
1029SD16—44no—
1030SD16—82no—
1031SD16—82no—
1032SD16—82no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—44no—
1056C2×C8H(5,𝔽2)12yes—
1057C2×C8H(5,𝔽2)12yes—
1058C4⋊C4—22no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C4⋊C4—81no—
1099C4⋊C4—81no—
1100C4⋊C4—81no—
1101C4⋊C4—81no—
1102C4⋊C4—81no—
1103C4⋊C4—81no—
1104C4⋊C4—81no—
1105C4⋊C4—81no—
1106C4⋊C4—81no—
1107C4⋊C4—81no—
1108C4⋊C4—81no—
1109C4⋊C4—81no—
1110C4⋊C4H(5,𝔽2)12yes—
1111C22⋊C4—24no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—42no—
1161C42—42no—
1162C42—81no—
1163C42—81no—
1164C42—81no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—22no—
1174C23—21no—
1175C23—22no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—84no—
1193C23—84no—
1194C23—84no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23#57812yes—
1200C23C23×D411yescharacteristic
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—84no—
1226Q8—162no—
1227D4—22no—
1228D4—22no—
1229D4—22no—
1230D4—22no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—82no—
1236D4—84no—
1237D4—84no—
1238D4—84no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
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—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—162no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4—162no—
1330C2×C4#57712yes—
1331C2×C4C2×H(5,𝔽2)11yescharacteristic
1332C2×C4C2×H(5,𝔽2)11yescharacteristic
1333C2×C4C2×H(5,𝔽2)11yescharacteristic
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4#58511yescharacteristic
1337C8—22no—
1338C8—22no—
1339C8—41no—
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—41no—
1356C22—42no—
1357C22—41no—
1358C22—42no—
1359C22—41no—
1360C22—42no—
1361C22—42no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—168no—
1374C22#348411yescharacteristic
1375C22#348811yescharacteristic
1376C22#349811yescharacteristic
1377C22C2×#57711yescharacteristic
1378C22C2×#57811yescharacteristic
1379C22#358611yescharacteristic
1380C22#358611yescharacteristic
1381C4—22no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—41no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4#353211yescharacteristic
1408C4#353411yescharacteristic
1409C4#354311yescharacteristic
1410C4#354611yescharacteristic
1411C2—42no—
1412C2—81no—
1413C2—82no—
1414C2—82no—
1415C2#4795211yescharacteristic
1416C2#6162211yescharacteristic
1417C2#6168011yescharacteristic
1418C2#6205411yescharacteristic
1419C2#6208011yescharacteristic
1420C2#6245811yescharacteristic
1421C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53008C2semidirect
3. #32171C2semidirect
4. #31921C2semidirect
5. #31035C2semidirect
6. #30996C2semidirect
7. #30878C2semidirect
8. #30757C2semidirect
9. #30707C2semidirect
10. #30604C2semidirect
11. #30530C2semidirect
12. #30467C2semidirect
13. #30450C2semidirect
14. #30449C2semidirect
15. #29726C2semidirect
16. #29672C2semidirect
17. #29083C2semidirect
18. #28986C2semidirect
19. #28471C2semidirect
20. #28326C2semidirect
21. #27087C2semidirect
22. #26945C2semidirect
23. #26624C2semidirect
24. #25784C2semidirect
26. #25613C2semidirect
27. #25382C2semidirect
28. #24905C2semidirect
29. #24358C2semidirect
31. #22372C2semidirect
38. C2×#494C22semidirect
39. C2×#487C22semidirect
40. C2×#484C22semidirect
41. C2×#483C22semidirect
44. C2×#462C22semidirect
45. C2×#462C22semidirect
70. #2621C22semidirect
71. #2621C22semidirect
73. #2546C22semidirect
74. #2546C22semidirect
77. #2514C22semidirect
78. #2514C22semidirect
89. #2429C22semidirect
90. #2429C22semidirect
101. #2097C22semidirect
103. #2086C22semidirect
105. #2074C22semidirect
107. #2066C22semidirect
109. #2056C22semidirect
110. #2056C22semidirect
111. #2056C22semidirect
112. #2056C22semidirect
116. #2043C22semidirect
117. #2043C22semidirect
118. #2043C22semidirect
122. #2024C22semidirect
123. #2024C22semidirect
124. #2016C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
127. #2016C22semidirect
128. #2016C22semidirect
141. #2001C22semidirect
142. #2001C22semidirect
143. #2001C22semidirect
144. #2001C22semidirect
149. #1993C22semidirect
151. #1981C22semidirect
154. #1971C22semidirect
155. #1971C22semidirect
156. #1969C22semidirect
160. #1940C22semidirect
161. #1935C22semidirect
162. #1935C22semidirect
164. #1933C22semidirect
165. #1928C22semidirect
166. #1928C22semidirect
167. #1924C22semidirect
170. #1923C22semidirect
171. #1921C22semidirect
172. #1920C22semidirect
173. #1917C22semidirect
174. #1916C22semidirect
179. #1878C22semidirect
180. #1878C22semidirect
181. #1878C22semidirect
187. #1872C22semidirect
188. #1872C22semidirect
190. #1865C22semidirect
193. #1805C22semidirect
195. #1798C22semidirect
198. #1770C22semidirect
199. #1763C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#530082
#451082
#321712
#319212
#310352
#309962
#308782
#307572
#307072
#306042
#305302
#304672
#304502
#304492
#297262
#296722
#290832
#289862
#284712
#283262
#270872
#269452
#266242
#257842
#257692
#256132
#253822
#249052
#243582
#238522
#223722