Finite Group Databasebeta

← #7307580

Subgroups — #7307580

Order 512.

1715 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59099C211yesmaximal, characteristic, complemented
2#40052C211yesmaximal, characteristic, complemented
3#32204C211yesmaximal, characteristic, complemented
4#32088C211yesmaximal, characteristic, complemented
5#31891C211yesmaximal, characteristic, complemented
6#31785C211yesmaximal, characteristic, complemented
7#31582C211yesmaximal, characteristic, complemented
8#31310C211yesmaximal, characteristic, complemented
9#31303C211yesmaximal, characteristic, complemented
10#31170C211yesmaximal, characteristic, complemented
11#31138C211yesmaximal, characteristic, complemented
12#31001C211yesmaximal, characteristic, complemented
13#30595C211yesmaximal, characteristic, complemented
14#30560C211yesmaximal, characteristic, complemented
15#29954C211yesmaximal, characteristic, complemented
16#29687C211yesmaximal, characteristic, complemented
17#28119C211yesmaximal, characteristic, complemented
18#27124C211yesmaximal, characteristic, complemented
19#26889C211yesmaximal, characteristic, complemented
20#26803C211yesmaximal, characteristic, complemented
21#26565C211yesmaximal, characteristic, complemented
22#26538C211yesmaximal, characteristic, complemented
23#26368C211yesmaximal, characteristic, complemented
24#25950C211yesmaximal, characteristic, complemented
25#25076C211yesmaximal, characteristic, complemented
26#24913C211yesmaximal, characteristic, complemented
27#24738C211yesmaximal, characteristic, complemented
28#24245C211yesmaximal, characteristic, complemented
29#24150C211yesmaximal, characteristic, complemented
30#24039C211yesmaximal, characteristic, complemented
31#23322C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#474C2211yescharacteristic
37C2×#474C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic, complemented
39C2×#466C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic, complemented
42C2×#459C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2857C2211yescharacteristic, complemented
49#2746—21no—
50#2745—21no—
51#2728—21no—
52#2693—21no—
53#2688—21no—
54#2678—21no—
55#2652—21no—
56#2570C2211yescharacteristic, complemented
57#2557—21no—
58#2544C2211yescharacteristic
59#2535C2211yescharacteristic
60#2509C2211yescharacteristic, complemented
61#2497C2211yescharacteristic, complemented
62#2494C2211yescharacteristic
63#2492C2211yescharacteristic
64#2487C2211yescharacteristic
65#2472—21no—
66#2463—21no—
67#2457—21no—
68#2452C2211yescharacteristic
69#2452C2211yescharacteristic, complemented
70#2449—21no—
71#2447C2211yescharacteristic
72#2440C2211yescharacteristic
73#2433C2211yescharacteristic
74#2431C2211yescharacteristic
75#2427C2211yescharacteristic
76#2422C2211yescharacteristic
77#2420C2211yescharacteristic, complemented
78#2414C2211yescharacteristic
79#2407—21no—
80#2404—21no—
81#2366C2211yescharacteristic
82#2363C2211yescharacteristic
83#2361C2211yescharacteristic
84#2358—21no—
85D4×C4⋊C4C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2322—21no—
88C4×#123C2211yescharacteristic
89C4×#121C2211yescharacteristic, complemented
90#2297C2211yescharacteristic
91#2095C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2074C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2057C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2036C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic, complemented
131#2033C2211yescharacteristic, complemented
132#2033C2211yescharacteristic, complemented
133#2024C2211yescharacteristic, complemented
134#2023C2211yescharacteristic
135#2011C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic, complemented
139#1988C2211yescharacteristic, complemented
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1973C2211yescharacteristic, complemented
143#1961C2211yescharacteristic
144#1959C2211yescharacteristic, complemented
145#1958C2211yescharacteristic
146#1954C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1943C2211yescharacteristic, complemented
149#1942C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1940C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1924C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1892C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic, complemented
172#1879C2211yescharacteristic, complemented
173#1877C2211yescharacteristic, complemented
174#1874C2211yescharacteristic
175#1869C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1808C2211yescharacteristic
191#1804C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1797C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202#1776C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#546—42no—
212#546—42no—
213#532—42no—
214#532—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123D411yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4—21no—
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#484—42no—
259#482—42no—
260#474—42no—
261#474—42no—
262#474—42no—
263#466—42no—
264#463—42no—
265#463—42no—
266#459—42no—
267#449—42no—
268#447—42no—
269#442—42no—
270C4×D8—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102—42no—
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#401—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388D411yescharacteristic
404#388D411yescharacteristic
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#386—21no—
413#386—21no—
414#386—21no—
415#386—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#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386D411yescharacteristic
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385D411yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381—21no—
446#381—21no—
447#381D411yescharacteristic
448#380—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—44no—
504C2×#41—82no—
505C2×#41—82no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
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×C4—21no—
539C23×C4—21no—
540C23×C4C2×D411yescharacteristic
541C23×C4C2×D411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#127—22no—
572#127—22no—
573#127—41no—
574#127—41no—
575#124—22no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—44no—
580#123—42no—
581#123—44no—
582#123—44no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587C22⋊Q8—82no—
588C22⋊Q8—82no—
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—44no—
598#121—44no—
599#121—41no—
600#121—41no—
601#120—44no—
602#120—44no—
603#120—82no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
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—44no—
621C4×D4—82no—
622C4×D4—82no—
623C4×D4—82no—
624#117—41no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—82no—
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
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—44no—
702C2×C22⋊C4—82no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—22no—
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
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—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782#97—41no—
783#97—41no—
784C4×C8—41no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
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#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837#41—82no—
838#41—82no—
839#41—82no—
840#41—82no—
841#41—816no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
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—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4H(5,𝔽2)12yes—
916C2×D4H(5,𝔽2)12yes—
917C2×D42−1+412yes—
918C22×C4—21no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C2511yescharacteristic
988SD16—82no—
989D8—44no—
990D8—44no—
991D8—82no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—82no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1062C22⋊C4—24no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
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—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—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—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—41no—
1119C42—41no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—21no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—84no—
1166C23—84no—
1167C23—84no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23—162no—
1172C23#57512yes—
1173C23C23×D411yescharacteristic
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—84no—
1179Q8—162no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—84no—
1197D4—82no—
1198D4—84no—
1199D4—84no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—162no—
1207D4—162no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
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—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—44no—
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—84no—
1288C2×C4—84no—
1289C2×C4—82no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4#57612yes—
1298C2×C4#57612yes—
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×2−1+411yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—42no—
1330C22—41no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—41no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—168no—
1356C22#348411yescharacteristic
1357C22#348811yescharacteristic
1358C22#348911yescharacteristic
1359C22C2×#57511yescharacteristic
1360C22C2×#57611yescharacteristic
1361C22C2×#57611yescharacteristic
1362C22#358611yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4#353411yescharacteristic
1388C4#353511yescharacteristic
1389C4#353611yescharacteristic
1390C4#356211yescharacteristic
1391C2—42no—
1392C2—81no—
1393C2—82no—
1394C2—82no—
1395C2—82no—
1396C2—161no—
1397C2#4784311yescharacteristic
1398C2#6158011yescharacteristic
1399C2#6163011yescharacteristic
1400C2#6197711yescharacteristic
1401C2#6204111yescharacteristic
1402C2#6212511yescharacteristic
1403C2#6218011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59099C2semidirect
2. #40052C2semidirect
3. #32204C2semidirect
4. #32088C2semidirect
5. #31891C2semidirect
6. #31785C2semidirect
7. #31582C2semidirect
8. #31310C2semidirect
9. #31303C2semidirect
10. #31170C2semidirect
11. #31138C2semidirect
12. #31001C2semidirect
13. #30595C2semidirect
14. #30560C2semidirect
15. #29954C2semidirect
16. #29687C2semidirect
17. #28119C2semidirect
18. #27124C2semidirect
19. #26889C2semidirect
20. #26803C2semidirect
21. #26565C2semidirect
22. #26538C2semidirect
23. #26368C2semidirect
24. #25950C2semidirect
25. #25076C2semidirect
26. #24913C2semidirect
27. #24738C2semidirect
28. #24245C2semidirect
29. #24150C2semidirect
30. #24039C2semidirect
31. #23322C2semidirect
35. C2×#482C22semidirect
37. C2×#474C22semidirect
38. C2×#474C22semidirect
41. C2×#463C22semidirect
48. #2857C22semidirect
56. #2570C22semidirect
60. #2509C22semidirect
61. #2497C22semidirect
69. #2452C22semidirect
77. #2420C22semidirect
85. D4×C4⋊C4C22semidirect
89. C4×#121C22semidirect
91. #2095C22semidirect
95. #2092C22semidirect
96. #2087C22semidirect
97. #2087C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
101. #2074C22semidirect
102. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2057C22semidirect
112. #2057C22semidirect
113. #2055C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
130. #2033C22semidirect
131. #2033C22semidirect
132. #2033C22semidirect
133. #2024C22semidirect
138. #1999C22semidirect
139. #1988C22semidirect
142. #1973C22semidirect
144. #1959C22semidirect
147. #1949C22semidirect
148. #1943C22semidirect
149. #1942C22semidirect
150. #1940C22semidirect
151. #1940C22semidirect
154. #1934C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
159. #1925C22semidirect
162. #1924C22semidirect
163. #1924C22semidirect
164. #1918C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
171. #1879C22semidirect
172. #1879C22semidirect
173. #1877C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
183. #1862C22semidirect
184. #1854C22semidirect
185. #1854C22semidirect
189. #1825C22semidirect
194. #1802C22semidirect
195. #1797C22semidirect
196. #1797C22semidirect
202. #1776C22semidirect

Maximal subgroups

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

subgroupindex
#590992
#400522
#322042
#320882
#318912
#317852
#315822
#313102
#313032
#311702
#311382
#310012
#305952
#305602
#299542
#296872
#281192
#271242
#268892
#268032
#265652
#265382
#263682
#259502
#250762
#249132
#247382
#242452
#241502
#240392
#233222