Finite Group Databasebeta

← #7326701

Subgroups — #7326701

Order 512.

1589 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53045C211yesmaximal, characteristic, complemented
2#45105C211yesmaximal, characteristic
3#32283C211yesmaximal, characteristic, complemented
4#31852C211yesmaximal, characteristic, complemented
5#31726C211yesmaximal, characteristic, complemented
6#31676C211yesmaximal, characteristic, complemented
7#31609C211yesmaximal, characteristic, complemented
8#31393C211yesmaximal, characteristic, complemented
9#31365C211yesmaximal, characteristic, complemented
10#31083C211yesmaximal, characteristic, complemented
11#30920C211yesmaximal, characteristic, complemented
12#30585C211yesmaximal, characteristic, complemented
13#30561C211yesmaximal, characteristic, complemented
14#30510C211yesmaximal, characteristic, complemented
15#29901C211yesmaximal, characteristic, complemented
16#29604C211yesmaximal, characteristic, complemented
17#28569C211yesmaximal, characteristic, complemented
18#28230C211yesmaximal, characteristic, complemented
19#28089C211yesmaximal, characteristic, complemented
20#27113C211yesmaximal, characteristic, complemented
21#26967C211yesmaximal, characteristic, complemented
22#26624C211yesmaximal, characteristic, complemented
23#26247C211yesmaximal, characteristic, complemented
24#25551C211yesmaximal, characteristic, complemented
25#24959C211yesmaximal, characteristic, complemented
26#24905C211yesmaximal, characteristic, complemented
27#24901C211yesmaximal, characteristic, complemented
28#24566C211yesmaximal, characteristic, complemented
29#24394C211yesmaximal, characteristic, complemented
30#24126C211yesmaximal, characteristic, complemented
31#22039C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#483C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×#436C2211yescharacteristic, complemented
47C2×#408C2211yescharacteristic
48#2838—21no—
49#2837—21no—
50#2829—21no—
51#2829—21no—
52#2803—21no—
53#2801—21no—
54#2795—21no—
55#2792—21no—
56#2715—21no—
57#2709—21no—
58#2685—21no—
59#2668—21no—
60#2616C2211yescharacteristic
61#2616C2211yescharacteristic
62#2542C2211yescharacteristic
63#2538C2211yescharacteristic, complemented
64#2537C2211yescharacteristic
65#2536C2211yescharacteristic, complemented
66#2534—21no—
67#2500C2211yescharacteristic
68#2497C2211yescharacteristic, complemented
69#2494C2211yescharacteristic, complemented
70#2490C2211yescharacteristic
71#2485C2211yescharacteristic
72#2459—21no—
73#2441C2211yescharacteristic
74#2429C2211yescharacteristic, complemented
75#2429C2211yescharacteristic, complemented
76#2428—21no—
77#2424—21no—
78#2423C2211yescharacteristic
79#2421C2211yescharacteristic
80#2420C2211yescharacteristic
81#2416C2211yescharacteristic
82#2416C2211yescharacteristic
83#2415C2211yescharacteristic, complemented
84#2415C2211yescharacteristic, complemented
85#2408C2211yescharacteristic
86#2388C2211yescharacteristic
87#2361C2211yescharacteristic
88#2352C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90#2311C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2092C2211yescharacteristic
95#2086C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2075C2211yescharacteristic
105#2075C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic, complemented
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2013C2211yescharacteristic
130#2013C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#1991C2211yescharacteristic, complemented
140#1981C2211yescharacteristic, complemented
141#1960C2211yescharacteristic, complemented
142#1955C2211yescharacteristic
143#1954C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1893C2211yescharacteristic
162#1892C2211yescharacteristic, complemented
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic
170#1873C2211yescharacteristic, complemented
171#1873C2211yescharacteristic, complemented
172#1872C2211yescharacteristic, complemented
173#1872C2211yescharacteristic, complemented
174#1870C2211yescharacteristic
175#1870C2211yescharacteristic, complemented
176#1869C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1853C2211yescharacteristic, complemented
185#1852C2211yescharacteristic, complemented
186#1850C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1824C2211yescharacteristic, complemented
191#1809C2211yescharacteristic, complemented
192#1809C2211yescharacteristic, complemented
193#1807C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1803C2211yescharacteristic, complemented
196#1802C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1780C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#553—42no—
213#553—42no—
214#535—42no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#485—42no—
259#483—42no—
260#483—42no—
261#479—42no—
262#468—42no—
263#468—42no—
264#468—42no—
265#465—42no—
266#450—42no—
267#450—42no—
268C4×SD16—42no—
269C4×SD16—42no—
270#436—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310#408—42no—
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#395—21no—
355#395D411yescharacteristic
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394D411yescharacteristic
376#394D411yescharacteristic
377#394D411yescharacteristic
378#393D411yescharacteristic
379#392—21no—
380#392D411yescharacteristic
381#392D411yescharacteristic
382#392D411yescharacteristic
383#391—21no—
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#384—21no—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#127—44no—
567#126—44no—
568#125—22no—
569#125—41no—
570#124—44no—
571#123—44no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—44no—
599#121—41no—
600#121—41no—
601#121—82no—
602#121—82no—
603#121—82no—
604#120—44no—
605#120—44no—
606#120—82no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—44no—
622C4×D4—82no—
623#117—22no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629C2×C4⋊C4—22no—
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—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
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—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×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×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#107—41no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747#106—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—41no—
789C4×C8—22no—
790C4×C8—41no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
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#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—82no—
839#41—82no—
840#41—82no—
841#41—82no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—81no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4H(5,𝔽2)12yes—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
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—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
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×C4C2511yescharacteristic
973SD16—44no—
974SD16—44no—
975SD16—82no—
976SD16—82no—
977M16—82no—
978M16—82no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
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—82no—
1003C2×C8H(5,𝔽2)12yes—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
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—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1057C22⋊C4—24no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
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—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—42no—
1115C42—42no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—84no—
1164C23—84no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23—162no—
1170C23C23×D411yescharacteristic
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—82no—
1180D4—22no—
1181D4—22no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—82no—
1189D4—84no—
1190D4—82no—
1191D4—82no—
1192D4—82no—
1193D4—82no—
1194D4—82no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
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—21no—
1214C2×C4—21no—
1215C2×C4—22no—
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—21no—
1229C2×C4—21no—
1230C2×C4—21no—
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—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—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4#57712yes—
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4#58511yescharacteristic
1297C2×C4#58511yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—22no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—42no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—168no—
1350C22#348411yescharacteristic
1351C22#348511yescharacteristic
1352C22#349611yescharacteristic
1353C22C2×#57711yescharacteristic
1354C22#358411yescharacteristic
1355C22#358511yescharacteristic
1356C22#358611yescharacteristic
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4#353311yescharacteristic
1382C4#353411yescharacteristic
1383C4#354611yescharacteristic
1384C4#355111yescharacteristic
1385C2—81no—
1386C2—81no—
1387C2—81no—
1388C2—81no—
1389C2—82no—
1390C2—161no—
1391C2#4793111yescharacteristic
1392C2#6162811yescharacteristic
1393C2#6168011yescharacteristic
1394C2#6178211yescharacteristic
1395C2#6178511yescharacteristic
1396C2#6230811yescharacteristic
1397C2#6234811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45105C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53045C2semidirect
3. #32283C2semidirect
4. #31852C2semidirect
5. #31726C2semidirect
6. #31676C2semidirect
7. #31609C2semidirect
8. #31393C2semidirect
9. #31365C2semidirect
10. #31083C2semidirect
11. #30920C2semidirect
12. #30585C2semidirect
13. #30561C2semidirect
14. #30510C2semidirect
15. #29901C2semidirect
16. #29604C2semidirect
17. #28569C2semidirect
18. #28230C2semidirect
19. #28089C2semidirect
20. #27113C2semidirect
21. #26967C2semidirect
22. #26624C2semidirect
23. #26247C2semidirect
24. #25551C2semidirect
25. #24959C2semidirect
26. #24905C2semidirect
27. #24901C2semidirect
28. #24566C2semidirect
29. #24394C2semidirect
30. #24126C2semidirect
31. #22039C2semidirect
35. C2×#483C22semidirect
36. C2×#483C22semidirect
37. C2×#479C22semidirect
46. C2×#436C22semidirect
63. #2538C22semidirect
65. #2536C22semidirect
68. #2497C22semidirect
69. #2494C22semidirect
74. #2429C22semidirect
75. #2429C22semidirect
83. #2415C22semidirect
84. #2415C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
95. #2086C22semidirect
96. #2086C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
103. #2076C22semidirect
105. #2075C22semidirect
106. #2072C22semidirect
109. #2059C22semidirect
115. #2036C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
119. #2035C22semidirect
128. #2026C22semidirect
139. #1991C22semidirect
140. #1981C22semidirect
141. #1960C22semidirect
143. #1954C22semidirect
144. #1949C22semidirect
149. #1933C22semidirect
150. #1933C22semidirect
153. #1924C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
160. #1894C22semidirect
162. #1892C22semidirect
170. #1873C22semidirect
171. #1873C22semidirect
172. #1872C22semidirect
173. #1872C22semidirect
175. #1870C22semidirect
176. #1869C22semidirect
177. #1865C22semidirect
179. #1863C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
184. #1853C22semidirect
185. #1852C22semidirect
186. #1850C22semidirect
187. #1845C22semidirect
189. #1825C22semidirect
190. #1824C22semidirect
191. #1809C22semidirect
192. #1809C22semidirect
193. #1807C22semidirect
195. #1803C22semidirect
200. #1776C22semidirect
201. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#530452
#451052
#322832
#318522
#317262
#316762
#316092
#313932
#313652
#310832
#309202
#305852
#305612
#305102
#299012
#296042
#285692
#282302
#280892
#271132
#269672
#266242
#262472
#255512
#249592
#249052
#249012
#245662
#243942
#241262
#220392