Finite Group Databasebeta

← #7090832

Subgroups — #7090832

Order 512.

1721 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59945C211yesmaximal, characteristic
2#59413C211yesmaximal, characteristic, complemented
3#32658C211yesmaximal, characteristic, complemented
4#32555C211yesmaximal, characteristic, complemented
5#32000C211yesmaximal, characteristic, complemented
6#31611C211yesmaximal, characteristic, complemented
7#31556C211yesmaximal, characteristic, complemented
8#31316C211yesmaximal, characteristic, complemented
9#31002C211yesmaximal, characteristic, complemented
10#30404C211yesmaximal, characteristic
11#29369C211yesmaximal, characteristic, complemented
12#29368C211yesmaximal, characteristic, complemented
13#29049C211yesmaximal, characteristic, complemented
14#27538C211yesmaximal, characteristic, complemented
15#26974C211yesmaximal, characteristic, complemented
16#26945C211yesmaximal, characteristic, complemented
17#26571C211yesmaximal, characteristic, complemented
18#25176C211yesmaximal, characteristic, complemented
19#25078C211yesmaximal, characteristic, complemented
20#24921C211yesmaximal, characteristic, complemented
21#24914C211yesmaximal, characteristic, complemented
22#24358C211yesmaximal, characteristic, complemented
23#24199C211yesmaximal, characteristic, complemented
24#24199C211yesmaximal, characteristic, complemented
25#24042C211yesmaximal, characteristic, complemented
26#23855C211yesmaximal, characteristic
27#23683C211yesmaximal, characteristic, complemented
28#22855C211yesmaximal, characteristic, complemented
29#22437C211yesmaximal, characteristic, complemented
30#22395C211yesmaximal, characteristic, complemented
31#22152C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#557C2211yescharacteristic, complemented
34C2×D4×Q8C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#465C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#448C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C22×#103C2211yescharacteristic, complemented
49#2782—21no—
50#2704—21no—
51#2704—21no—
52#2684—21no—
53#2598—21no—
54#2598—21no—
55#2582C2211yescharacteristic, complemented
56#2580C2211yescharacteristic
57#2580C2211yescharacteristic
58#2572—21no—
59#2556—21no—
60#2556—21no—
61#2550—21no—
62#2538C2211yescharacteristic
63#2495C2211yescharacteristic
64#2495C2211yescharacteristic
65#2487C2211yescharacteristic
66#2482—21no—
67#2482—21no—
68#2454—21no—
69#2451—21no—
70#2434C2211yescharacteristic
71#2434C2211yescharacteristic, complemented
72#2429C2211yescharacteristic
73#2429C2211yescharacteristic, complemented
74#2423C2211yescharacteristic
75#2423C2211yescharacteristic, complemented
76#2420C2211yescharacteristic
77#2420C2211yescharacteristic
78#2408C2211yescharacteristic
79#2367—21no—
80#2361C2211yescharacteristic
81#2361C2211yescharacteristic
82#2358—21no—
83Q8×C22⋊C4C2211yescharacteristic
84Q8×C22⋊C4C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87C4×C4⋊Q8C2211yescharacteristic, complemented
88C4×C4⋊Q8C2211yescharacteristic, complemented
89C4×#124C2211yescharacteristic
90#2293C2211yescharacteristic
91#2293C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2093C2211yescharacteristic
98#2086C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2043C2211yescharacteristic, complemented
117#2043C2211yescharacteristic, complemented
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic, complemented
122#2035C2211yescharacteristic
123#2034C2211yescharacteristic
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#2013C2211yescharacteristic
127#2013C2211yescharacteristic
128#2013C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1985C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1981C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1960C2211yescharacteristic, complemented
139#1960C2211yescharacteristic, complemented
140#1947C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1924C2211yescharacteristic, complemented
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic, complemented
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1872C2211yescharacteristic, complemented
173#1869C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1852C2211yescharacteristic, complemented
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1839C2211yescharacteristic, complemented
189#1808C2211yescharacteristic
190#1805C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1767C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202#1752C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#557—42no—
220#557—42no—
221D4×Q8—42no—
222D4×Q8—42no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#125—21no—
229C2×#125—21no—
230C2×#125—21no—
231C2×#124D411yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262#484—42no—
263#465—42no—
264#461—24no—
265#461—42no—
266#461—42no—
267#450—42no—
268#450—42no—
269#448—24no—
270#448—42no—
271#440—42no—
272#440—42no—
273#440—42no—
274#440—42no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×#103—42no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#395—21no—
354#395—21no—
355#395—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#393—21no—
360#393—21no—
361#392—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391D411yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390D411yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388D411yescharacteristic
411#388D411yescharacteristic
412#388D411yescharacteristic
413#388D411yescharacteristic
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#383—21no—
439#383—21no—
440#382D411yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C43C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
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#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8C2×D411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—416no—
564C2×SD16#4114yes—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C4⋊Q8—22no—
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—44no—
588#125—44no—
589#125—44no—
590#125—44no—
591#124—24no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—44no—
597C22⋊Q8—44no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—41no—
606#120—44no—
607C4×Q8—22no—
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×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—44no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—44no—
633C4×D4—82no—
634C4×D4—82no—
635#117—82no—
636#117—82no—
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—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
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—82no—
713C2×C22⋊C4—82no—
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#107—41no—
742#107—41no—
743#107—41no—
744#107—41no—
745#107—41no—
746#107—41no—
747#106—41no—
748#106—41no—
749C4⋊C8—22no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791#97—41no—
792#97—41no—
793#97—41no—
794#97—41no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
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#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835C24—21no—
836C24—21no—
837C24—42no—
838C24—42no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846C2×Q8—22no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
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—21no—
868C2×Q8—41no—
869C2×Q8—41no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—82no—
879C2×Q8—82no—
880C2×Q8—82no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×Q8—82no—
884C2×Q8C2×#4112yes—
885C2×Q8H(5,𝔽2)12yes—
886C2×Q8H(5,𝔽2)12yes—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—44no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4#13714yes—
913C2×D4C2×#4112yes—
914C2×D4H(5,𝔽2)12yes—
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—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C2511yescharacteristic
975SD16—28no—
976SD16—44no—
977SD16—44no—
978SD16—44no—
979SD16—44no—
980SD16—44no—
981SD16—82no—
982SD16—82no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
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—44no—
1007C2×C8—82no—
1008C2×C8C2×#4112yes—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
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—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
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—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
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—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C42—22no—
1103C42—22no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—41no—
1115C42—41no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C42—81no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—22no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—84no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23C2×#13712yes—
1158C23C2×#13712yes—
1159C23C23×D411yescharacteristic
1160Q8—22no—
1161Q8—22no—
1162Q8—22no—
1163Q8—22no—
1164Q8—22no—
1165Q8—22no—
1166Q8—44no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—84no—
1178Q8—84no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—44no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
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—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4C2×#13712yes—
1283C2×C4#57712yes—
1284C2×C4C22×#4111yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4C2×H(5,𝔽2)11yescharacteristic
1288C2×C4#58511yescharacteristic
1289C2×C4#58511yescharacteristic
1290C8—22no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—168no—
1327C22D4×#4111yescharacteristic
1328C22#348411yescharacteristic
1329C22#348811yescharacteristic
1330C22C22×#13711yescharacteristic
1331C22C2×#57711yescharacteristic
1332C22#358511yescharacteristic
1333C22#358611yescharacteristic
1334C4—22no—
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4#349011yescharacteristic
1361C4#351311yescharacteristic
1362C4#353411yescharacteristic
1363C4#356011yescharacteristic
1364C2—42no—
1365C2—42no—
1366C2—82no—
1367C2—82no—
1368C2#4423111yescharacteristic
1369C2#6145311yescharacteristic
1370C2#6152011yescharacteristic
1371C2#6157411yescharacteristic
1372C2#6168211yescharacteristic
1373C2#6198011yescharacteristic
1374C2#6208411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59413C2semidirect
3. #32658C2semidirect
4. #32555C2semidirect
5. #32000C2semidirect
6. #31611C2semidirect
7. #31556C2semidirect
8. #31316C2semidirect
9. #31002C2semidirect
11. #29369C2semidirect
12. #29368C2semidirect
13. #29049C2semidirect
14. #27538C2semidirect
15. #26974C2semidirect
16. #26945C2semidirect
17. #26571C2semidirect
18. #25176C2semidirect
19. #25078C2semidirect
20. #24921C2semidirect
21. #24914C2semidirect
22. #24358C2semidirect
23. #24199C2semidirect
24. #24199C2semidirect
25. #24042C2semidirect
27. #23683C2semidirect
28. #22855C2semidirect
29. #22437C2semidirect
30. #22395C2semidirect
31. #22152C2semidirect
33. C2×#557C22semidirect
35. C2×#484C22semidirect
48. C22×#103C22semidirect
55. #2582C22semidirect
71. #2434C22semidirect
73. #2429C22semidirect
75. #2423C22semidirect
84. Q8×C22⋊C4C22semidirect
87. C4×C4⋊Q8C22semidirect
88. C4×C4⋊Q8C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2099C22semidirect
95. #2097C22semidirect
98. #2086C22semidirect
99. #2085C22semidirect
100. #2083C22semidirect
103. #2076C22semidirect
104. #2074C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
109. #2066C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2043C22semidirect
116. #2043C22semidirect
117. #2043C22semidirect
121. #2036C22semidirect
132. #1985C22semidirect
133. #1985C22semidirect
134. #1981C22semidirect
138. #1960C22semidirect
139. #1960C22semidirect
140. #1947C22semidirect
141. #1944C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
148. #1927C22semidirect
149. #1927C22semidirect
152. #1924C22semidirect
153. #1924C22semidirect
157. #1892C22semidirect
172. #1872C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
185. #1852C22semidirect
187. #1850C22semidirect
188. #1839C22semidirect
190. #1805C22semidirect
191. #1805C22semidirect
196. #1787C22semidirect
198. #1767C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect
202. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#599452
#594132
#326582
#325552
#320002
#316112
#315562
#313162
#310022
#304042
#293692
#293682
#290492
#275382
#269742
#269452
#265712
#251762
#250782
#249212
#249142
#243582
#241992
#240422
#238552
#236832
#228552
#224372
#223952
#221522