Finite Group Databasebeta

← #7014826

Subgroups — #7014826

Order 512.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59550C211yesmaximal, characteristic, complemented
2#39408C211yesmaximal, characteristic, complemented
3#32019C211yesmaximal, characteristic, complemented
4#31830C211yesmaximal, characteristic, complemented
5#31798C211yesmaximal, characteristic, complemented
6#31784C211yesmaximal, characteristic, complemented
7#31269C211yesmaximal, characteristic, complemented
8#31165C211yesmaximal, characteristic, complemented
9#31063C211yesmaximal, characteristic, complemented
10#31063C211yesmaximal, characteristic, complemented
11#29482C211yesmaximal, characteristic, complemented
12#29045C211yesmaximal, characteristic, complemented
13#28900C211yesmaximal, characteristic, complemented
14#28101C211yesmaximal, characteristic, complemented
15#27796C211yesmaximal, characteristic, complemented
16#27231C211yesmaximal, characteristic, complemented
17#27094C211yesmaximal, characteristic, complemented
18#26721C211yesmaximal, characteristic, complemented
19#26488C211yesmaximal, characteristic, complemented
20#25716C211yesmaximal, characteristic, complemented
21#25156C211yesmaximal, characteristic, complemented
22#25128C211yesmaximal, characteristic, complemented
23#24504C211yesmaximal, characteristic, complemented
24#24454C211yesmaximal, characteristic, complemented
25#24237C211yesmaximal, characteristic, complemented
26#23966C211yesmaximal, characteristic, complemented
27#23701C211yesmaximal, characteristic, complemented
28#23085C211yesmaximal, characteristic, complemented
29#22883C211yesmaximal, characteristic, complemented
30#22870C211yesmaximal, characteristic, complemented
31#22051C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#547C2211yescharacteristic, complemented
34C2×#538—21no—
35C2×#501C2211yescharacteristic, complemented
36C2×#477C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#431C2211yescharacteristic, complemented
50C2×#417C2211yescharacteristic, complemented
51C22×#102C2211yescharacteristic
52#2854C2211yescharacteristic
53#2702—21no—
54#2697—21no—
55#2693—21no—
56#2691—21no—
57#2688—21no—
58#2684—21no—
59#2630—21no—
60#2558—21no—
61#2553—21no—
62#2547C2211yescharacteristic
63#2537C2211yescharacteristic
64#2512C2211yescharacteristic
65#2496C2211yescharacteristic
66#2491C2211yescharacteristic
67#2489C2211yescharacteristic, complemented
68#2486C2211yescharacteristic
69#2485C2211yescharacteristic, complemented
70#2480—21no—
71#2473—21no—
72#2471—21no—
73#2464—21no—
74#2459—21no—
75#2454C2211yescharacteristic, complemented
76#2452C2211yescharacteristic
77#2446C2211yescharacteristic, complemented
78#2429C2211yescharacteristic
79#2417C2211yescharacteristic
80#2416C2211yescharacteristic
81#2408C2211yescharacteristic
82#2408C2211yescharacteristic
83#2407C2211yescharacteristic
84#2407C2211yescharacteristic
85#2361C2211yescharacteristic
86#2361C2211yescharacteristic
87#2352—21no—
88#2341C2211yescharacteristic, complemented
89D4×C22⋊C4C2211yescharacteristic
90C4×C22⋊Q8C2211yescharacteristic, complemented
91C4×#121C2211yescharacteristic
92C4×#121C2211yescharacteristic
93#2297C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2043C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic, complemented
130#2013C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1989C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1970C2211yescharacteristic
141#1968C2211yescharacteristic
142#1956C2211yescharacteristic, complemented
143#1955C2211yescharacteristic
144#1955C2211yescharacteristic
145#1954C2211yescharacteristic, complemented
146#1943C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic, complemented
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1893C2211yescharacteristic
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic, complemented
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1864C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic
190#1809C2211yescharacteristic, complemented
191#1802C2211yescharacteristic, complemented
192#1788C2211yescharacteristic, complemented
193#1788C2211yescharacteristic, complemented
194#1788C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1749C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#552—42no—
215#552—42no—
216#547—42no—
217#547—42no—
218#538—48no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#124—21no—
227C2×#124—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121D411yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#120—21no—
248C2×#120—21no—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117C2311yescharacteristic
262C22×C4⋊C4—21no—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#501—42no—
268#477—42no—
269#468—42no—
270#461—42no—
271#450—42no—
272#450—42no—
273#449—24no—
274#449—24no—
275#449—42no—
276#449—42no—
277#447—24no—
278C4×SD16—42no—
279C4×D8—42no—
280#435—42no—
281#431—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#417—42no—
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×#102—42no—
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×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342#400—21no—
343#400—21no—
344#400—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—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#393—21no—
373#393—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390D411yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389D411yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388D411yescharacteristic
415#388D411yescharacteristic
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—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#386—21no—
431#386—21no—
432#386—21no—
433#386D411yescharacteristic
434#386D411yescharacteristic
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#384C2311yescharacteristic
443#382—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380D411yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C22×Q8—21no—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2×D411yescharacteristic
531C22×D4C2×D411yescharacteristic
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2×D411yescharacteristic
544C23×C4C2×D411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
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×D8—22no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8#4114yes—
566C2×M16—22no—
567C2×M16—41no—
568C2×M16—41no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8—41no—
584#126—44no—
585#126—44no—
586#126—44no—
587#125—22no—
588#125—41no—
589#125—44no—
590#124—44no—
591#124—44no—
592#123—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596#123—44no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—44no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606#121—24no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—44no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—44no—
615#121—44no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#120—44no—
621#120—44no—
622C4×Q8—22no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×D4—22no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—44no—
639C4×D4—44no—
640C4×D4—44no—
641#117—41no—
642#117—41no—
643#117—44no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
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—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—44no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
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—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—44no—
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—41no—
745C2×C42—41no—
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752#107—22no—
753#107—22no—
754#107—41no—
755#107—41no—
756#107—41no—
757#107—41no—
758#106—41no—
759#106—41no—
760#106—41no—
761#106—41no—
762C4⋊C8—22no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—22no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794C22⋊C8—22no—
795C22⋊C8—22no—
796C22⋊C8—22no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804#97—41no—
805#97—41no—
806#97—41no—
807C4×C8—22no—
808C4×C8—41no—
809C4×C8—41no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843C24—21no—
844C24—21no—
845C24—21no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—82no—
858#41—82no—
859#41—82no—
860#41—82no—
861#41—82no—
862#41—82no—
863#41—82no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—42no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8H(5,𝔽2)12yes—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
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—21no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—82no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4C2×#4112yes—
933C2×D4C2×#4112yes—
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—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—22no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C2511yescharacteristic
1004SD16—44no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008D8—44no—
1009D8—82no—
1010M16—82no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—82no—
1034C2×C8C2×#4112yes—
1035C2×C8H(5,𝔽2)12yes—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4H(5,𝔽2)12yes—
1085C22⋊C4—24no—
1086C22⋊C4—22no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4AGL(1,ℤ/8)14yes—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—41no—
1144C42—41no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—81no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—22no—
1164C23—22no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—84no—
1193C23—84no—
1194C23—162no—
1195C23—162no—
1196C23—162no—
1197C23—162no—
1198C23—162no—
1199C23C2×AGL(1,ℤ/8)12yes—
1200C23C23×D411yescharacteristic
1201Q8—22no—
1202Q8—22no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—162no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—82no—
1223D4—82no—
1224D4—82no—
1225D4—84no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—162no—
1232D4—162no—
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—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—44no—
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—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—82no—
1317C2×C4—84no—
1318C2×C4—84no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4C2×AGL(1,ℤ/8)12yes—
1325C2×C4C2×AGL(1,ℤ/8)12yes—
1326C2×C4C22×#4111yescharacteristic
1327C2×C4C2×H(5,𝔽2)11yescharacteristic
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4C2×H(5,𝔽2)11yescharacteristic
1330C2×C4#58511yescharacteristic
1331C2×C4#58511yescharacteristic
1332C8—22no—
1333C8—22no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C8—41no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—42no—
1358C22—42no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—42no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—168no—
1383C22D4×#4111yescharacteristic
1384C22#348411yescharacteristic
1385C22#349611yescharacteristic
1386C22C22×AGL(1,ℤ/8)11yescharacteristic
1387C22#358411yescharacteristic
1388C22#358411yescharacteristic
1389C22#358611yescharacteristic
1390C4—22no—
1391C4—22no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—42no—
1396C4—41no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—42no—
1401C4—41no—
1402C4—41no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4—81no—
1414C4#350511yescharacteristic
1415C4#351911yescharacteristic
1416C4#354511yescharacteristic
1417C4#355811yescharacteristic
1418C2—42no—
1419C2—81no—
1420C2—81no—
1421C2—82no—
1422C2—82no—
1423C2—161no—
1424C2#4303811yescharacteristic
1425C2#6143711yescharacteristic
1426C2#6153211yescharacteristic
1427C2#6159811yescharacteristic
1428C2#6168111yescharacteristic
1429C2#6228211yescharacteristic
1430C2#6229511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59550C2semidirect
2. #39408C2semidirect
3. #32019C2semidirect
4. #31830C2semidirect
5. #31798C2semidirect
6. #31784C2semidirect
7. #31269C2semidirect
8. #31165C2semidirect
9. #31063C2semidirect
10. #31063C2semidirect
11. #29482C2semidirect
12. #29045C2semidirect
13. #28900C2semidirect
14. #28101C2semidirect
15. #27796C2semidirect
16. #27231C2semidirect
17. #27094C2semidirect
18. #26721C2semidirect
19. #26488C2semidirect
20. #25716C2semidirect
21. #25156C2semidirect
22. #25128C2semidirect
23. #24504C2semidirect
24. #24454C2semidirect
25. #24237C2semidirect
26. #23966C2semidirect
27. #23701C2semidirect
28. #23085C2semidirect
29. #22883C2semidirect
30. #22870C2semidirect
31. #22051C2semidirect
33. C2×#547C22semidirect
35. C2×#501C22semidirect
36. C2×#477C22semidirect
49. C2×#431C22semidirect
50. C2×#417C22semidirect
67. #2489C22semidirect
69. #2485C22semidirect
75. #2454C22semidirect
77. #2446C22semidirect
88. #2341C22semidirect
90. C4×C22⋊Q8C22semidirect
93. #2297C22semidirect
94. #2099C22semidirect
95. #2088C22semidirect
96. #2086C22semidirect
97. #2083C22semidirect
98. #2077C22semidirect
99. #2076C22semidirect
100. #2076C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
105. #2065C22semidirect
111. #2043C22semidirect
112. #2036C22semidirect
113. #2036C22semidirect
114. #2036C22semidirect
128. #2024C22semidirect
129. #2023C22semidirect
134. #1989C22semidirect
142. #1956C22semidirect
145. #1954C22semidirect
146. #1943C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
150. #1936C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
157. #1927C22semidirect
158. #1926C22semidirect
160. #1925C22semidirect
162. #1923C22semidirect
163. #1918C22semidirect
176. #1872C22semidirect
177. #1870C22semidirect
179. #1865C22semidirect
182. #1862C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
185. #1853C22semidirect
188. #1824C22semidirect
190. #1809C22semidirect
191. #1802C22semidirect
192. #1788C22semidirect
193. #1788C22semidirect
194. #1788C22semidirect
195. C4×#107C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. C4×#103C22semidirect
200. #1753C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#595502
#394082
#320192
#318302
#317982
#317842
#312692
#311652
#310632
#294822
#290452
#289002
#281012
#277962
#272312
#270942
#267212
#264882
#257162
#251562
#251282
#245042
#244542
#242372
#239662
#237012
#230852
#228832
#228702
#220512