Finite Group Databasebeta

← #7081714

Subgroups — #7081714

Order 512.

1729 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59099C211yesmaximal, characteristic
2#39476C211yesmaximal, characteristic, complemented
3#32081C211yesmaximal, characteristic, complemented
4#32049C211yesmaximal, characteristic, complemented
5#31922C211yesmaximal, characteristic, complemented
6#31582C211yesmaximal, characteristic, complemented
7#31519C211yesmaximal, characteristic, complemented
8#31286C211yesmaximal, characteristic, complemented
9#30640C211yesmaximal, characteristic, complemented
10#30606C211yesmaximal, characteristic, complemented
11#28943C211yesmaximal, characteristic, complemented
12#28408C211yesmaximal, characteristic, complemented
13#28365C211yesmaximal, characteristic, complemented
14#28087C211yesmaximal, characteristic, complemented
15#27276C211yesmaximal, characteristic, complemented
16#27064C211yesmaximal, characteristic, complemented
17#26538C211yesmaximal, characteristic, complemented
18#26361C211yesmaximal, characteristic, complemented
19#26156C211yesmaximal, characteristic, complemented
20#25976C211yesmaximal, characteristic, complemented
21#25501C211yesmaximal, characteristic, complemented
22#25102C211yesmaximal, characteristic, complemented
23#24901C211yesmaximal, characteristic, complemented
24#24795C211yesmaximal, characteristic, complemented
25#24505C211yesmaximal, characteristic, complemented
26#24452C211yesmaximal, characteristic, complemented
27#23734C211yesmaximal, characteristic, complemented
28#23035C211yesmaximal, characteristic, complemented
29#22906C211yesmaximal, characteristic, complemented
30#22427C211yesmaximal, characteristic, complemented
31#21859C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#488C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic, complemented
40C2×#464C2211yescharacteristic, complemented
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#431C2211yescharacteristic, complemented
46C2×#428C2211yescharacteristic, complemented
47C2×#428C2211yescharacteristic, complemented
48C2×#417C2211yescharacteristic
49C2×#417C2211yescharacteristic
50C2×#418C2211yescharacteristic
51#2855C2211yescharacteristic, complemented
52#2794—21no—
53#2793—21no—
54#2791—21no—
55#2721—21no—
56#2688—21no—
57#2678—21no—
58#2623—21no—
59#2570C2211yescharacteristic, complemented
60#2565C2211yescharacteristic, complemented
61#2557—21no—
62#2544C2211yescharacteristic
63#2511C2211yescharacteristic, complemented
64#2506C2211yescharacteristic, complemented
65#2499C2211yescharacteristic
66#2496C2211yescharacteristic
67#2492C2211yescharacteristic
68#2481—21no—
69#2473—21no—
70#2472—21no—
71#2457—21no—
72#2452C2211yescharacteristic
73#2447C2211yescharacteristic
74#2442C2211yescharacteristic, complemented
75#2441C2211yescharacteristic
76#2433C2211yescharacteristic
77#2431C2211yescharacteristic
78#2427C2211yescharacteristic
79#2423C2211yescharacteristic
80#2417C2211yescharacteristic
81#2414C2211yescharacteristic
82#2407—21no—
83#2404—21no—
84#2366C2211yescharacteristic
85#2363C2211yescharacteristic
86#2360C2211yescharacteristic, complemented
87#2358—21no—
88#2352C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90#2313—21no—
91C4×#123C2211yescharacteristic
92#2297C2211yescharacteristic
93C2×#384C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2095C2211yescharacteristic, complemented
97#2095C2211yescharacteristic, complemented
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic, complemented
104#2086C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2077C2211yescharacteristic
107#2074C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2066C2211yescharacteristic, complemented
113#2065C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2057C2211yescharacteristic, complemented
116#2056C2211yescharacteristic, complemented
117#2056C2211yescharacteristic, complemented
118#2055C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic, complemented
121#2042C2211yescharacteristic, complemented
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2036C2211yescharacteristic
125#2035C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2015C2211yescharacteristic
131#2014C2211yescharacteristic
132#2014C2211yescharacteristic
133#2001C2211yescharacteristic
134#1990C2211yescharacteristic, complemented
135#1990C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1982C2211yescharacteristic
138#1973C2211yescharacteristic
139#1969C2211yescharacteristic, complemented
140#1968C2211yescharacteristic
141#1968C2211yescharacteristic, complemented
142#1961C2211yescharacteristic
143#1958C2211yescharacteristic
144#1957C2211yescharacteristic
145#1957C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1940C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic
160#1920C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic, complemented
166#1894C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic, complemented
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic, complemented
174#1874C2211yescharacteristic, complemented
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic, complemented
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1804C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1788C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#546—24no—
214#546—42no—
215#532—24no—
216#532—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4—21no—
251C22×C4⋊C4—21no—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257#488—42no—
258#482—42no—
259#478—42no—
260#468—24no—
261#468—42no—
262#468—42no—
263#464—42no—
264#452—42no—
265#450—42no—
266C4×SD16—42no—
267#436—42no—
268#431—42no—
269#428—42no—
270#428—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#418—42no—
289#417—42no—
290#417—42no—
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#393—21no—
363#393—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
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#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386D411yescharacteristic
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385D411yescharacteristic
441#384—21no—
442#384—21no—
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#381—21no—
450#381—21no—
451#381D411yescharacteristic
452#380—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—44no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—82no—
508C2×#41—82no—
509C22×Q8—21no—
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573#127—22no—
574#127—22no—
575#127—41no—
576#127—41no—
577#126—82no—
578#125—41no—
579#125—41no—
580#125—82no—
581#124—22no—
582#124—44no—
583#124—41no—
584#124—41no—
585#124—41no—
586#123—42no—
587#123—44no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—82no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—44no—
599#121—44no—
600#121—41no—
601#121—41no—
602#121#4114yes—
603#120—44no—
604#120—44no—
605#120—82no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—44no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—82no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
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—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—82no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
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×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—22no—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
727#107—22no—
728#107—22no—
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—22no—
734#106—22no—
735#106—41no—
736#106—41no—
737#106—41no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
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—22no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780#97—41no—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—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#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840#41—44no—
841#41—44no—
842#41—82no—
843#41—82no—
844#41—816no—
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—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×D4—22no—
861C2×D4—24no—
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—21no—
878C2×D4—41no—
879C2×D4—41no—
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—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4C2×#4112yes—
911C2×D42−1+412yes—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—22no—
920C22×C4—21no—
921C22×C4—22no—
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—41no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C2×#4112yes—
975C22×C4H(5,𝔽2)12yes—
976C22×C4C2511yescharacteristic
977Q16—82no—
978SD16—44no—
979SD16—82no—
980SD16—82no—
981M16—44no—
982M16—44no—
983M16—82no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8H(5,𝔽2)12yes—
1007C2×C8H(5,𝔽2)12yes—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—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⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4C2×#4112yes—
1060C22⋊C4—22no—
1061C22⋊C4—24no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—42no—
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—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
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—
1098C42—22no—
1099C42—22no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C42—81no—
1115C42—81no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—22no—
1124C23—21no—
1125C23—21no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—84no—
1153C23—162no—
1154C23—162no—
1155C23—162no—
1156C23—162no—
1157C23#54612yes—
1158C23C23×D411yescharacteristic
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—84no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—84no—
1182D4—82no—
1183D4—84no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
1189D4—162no—
1190C2×C4—28no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
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—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—44no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4#54612yes—
1279C2×C4#57512yes—
1280C2×C4#57612yes—
1281C2×C4#57712yes—
1282C2×C4C22×#4111yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×2−1+411yescharacteristic
1287C2×C4#58511yescharacteristic
1288C8—22no—
1289C8—22no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—42no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—42no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—168no—
1332C22C2×#54611yescharacteristic
1333C22#348911yescharacteristic
1334C22#349811yescharacteristic
1335C22C2×#57511yescharacteristic
1336C22C2×#57611yescharacteristic
1337C22C2×#57711yescharacteristic
1338C22#358611yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#351311yescharacteristic
1365C4#352011yescharacteristic
1366C4#353411yescharacteristic
1367C4#353611yescharacteristic
1368C2—42no—
1369C2—81no—
1370C2—82no—
1371C2—82no—
1372C2—161no—
1373C2#4402211yescharacteristic
1374C2#6116311yescharacteristic
1375C2#6116711yescharacteristic
1376C2#6214411yescharacteristic
1377C2#6218011yescharacteristic
1378C2#6242611yescharacteristic
1379C2#6246611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59099C2
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
2. #39476C2semidirect
3. #32081C2semidirect
4. #32049C2semidirect
5. #31922C2semidirect
6. #31582C2semidirect
7. #31519C2semidirect
8. #31286C2semidirect
9. #30640C2semidirect
10. #30606C2semidirect
11. #28943C2semidirect
12. #28408C2semidirect
13. #28365C2semidirect
14. #28087C2semidirect
15. #27276C2semidirect
16. #27064C2semidirect
17. #26538C2semidirect
18. #26361C2semidirect
19. #26156C2semidirect
20. #25976C2semidirect
21. #25501C2semidirect
22. #25102C2semidirect
23. #24901C2semidirect
24. #24795C2semidirect
25. #24505C2semidirect
26. #24452C2semidirect
27. #23734C2semidirect
28. #23035C2semidirect
29. #22906C2semidirect
30. #22427C2semidirect
31. #21859C2semidirect
34. C2×#488C22semidirect
39. C2×#468C22semidirect
40. C2×#464C22semidirect
45. C2×#431C22semidirect
46. C2×#428C22semidirect
47. C2×#428C22semidirect
51. #2855C22semidirect
59. #2570C22semidirect
60. #2565C22semidirect
63. #2511C22semidirect
64. #2506C22semidirect
74. #2442C22semidirect
86. #2360C22semidirect
93. C2×#384C22semidirect
94. #2096C22semidirect
95. #2096C22semidirect
96. #2095C22semidirect
97. #2095C22semidirect
103. #2092C22semidirect
104. #2086C22semidirect
105. #2085C22semidirect
107. #2074C22semidirect
108. #2068C22semidirect
112. #2066C22semidirect
113. #2065C22semidirect
114. #2059C22semidirect
115. #2057C22semidirect
116. #2056C22semidirect
117. #2056C22semidirect
120. #2042C22semidirect
121. #2042C22semidirect
129. #2024C22semidirect
134. #1990C22semidirect
135. #1990C22semidirect
139. #1969C22semidirect
141. #1968C22semidirect
146. #1949C22semidirect
147. #1942C22semidirect
148. #1942C22semidirect
149. #1940C22semidirect
150. #1935C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
155. #1927C22semidirect
156. #1926C22semidirect
160. #1920C22semidirect
161. #1918C22semidirect
162. #1916C22semidirect
163. #1916C22semidirect
165. #1895C22semidirect
170. #1877C22semidirect
173. #1874C22semidirect
174. #1874C22semidirect
176. #1873C22semidirect
180. #1863C22semidirect
183. #1862C22semidirect
185. #1854C22semidirect
187. #1851C22semidirect
192. #1802C22semidirect
193. #1802C22semidirect
197. #1776C22semidirect
198. C8×C4⋊C4C22semidirect
201. #1753C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#590992
#394762
#320812
#320492
#319222
#315822
#315192
#312862
#306402
#306062
#289432
#284082
#283652
#280872
#272762
#270642
#265382
#263612
#261562
#259762
#255012
#251022
#249012
#247952
#245052
#244522
#237342
#230352
#229062
#224272
#218592