Finite Group Databasebeta

← #7595039

Subgroups — #7595039

Order 512.

1699 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C211yesmaximal, characteristic, complemented
2#59807C211yesmaximal, characteristic
3#31908C211yesmaximal, characteristic, complemented
4#31878C211yesmaximal, characteristic, complemented
5#31785C211yesmaximal, characteristic, complemented
6#31018C211yesmaximal, characteristic, complemented
7#29241C211yesmaximal, characteristic, complemented
8#29084C211yesmaximal, characteristic, complemented
9#29018C211yesmaximal, characteristic, complemented
10#28570C211yesmaximal, characteristic, complemented
11#28120C211yesmaximal, characteristic, complemented
12#28111C211yesmaximal, characteristic, complemented
13#28072C211yesmaximal, characteristic, complemented
14#27529C211yesmaximal, characteristic, complemented
15#27393C211yesmaximal, characteristic, complemented
16#26973C211yesmaximal, characteristic, complemented
17#26727C211yesmaximal, characteristic, complemented
18#26671C211yesmaximal, characteristic, complemented
19#25541C211yesmaximal, characteristic, complemented
20#25254C211yesmaximal, characteristic, complemented
21#25128C211yesmaximal, characteristic, complemented
22#24933C211yesmaximal, characteristic, complemented
23#24861C211yesmaximal, characteristic, complemented
24#24426C211yesmaximal, characteristic, complemented
25#22941C211yesmaximal, characteristic, complemented
26#22879C211yesmaximal, characteristic, complemented
27#22491C211yesmaximal, characteristic, complemented
28#22419C211yesmaximal, characteristic, complemented
29C4×#467C211yesmaximal, characteristic, complemented
30#21487C211yesmaximal, characteristic, complemented
31C2×#1934C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic, complemented
41C2×#436C2211yescharacteristic, complemented
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×C4×C8C2211yescharacteristic
48#2802—21no—
49#2780—21no—
50#2714—21no—
51#2694—21no—
52#2587—21no—
53#2579—21no—
54#2569—21no—
55#2554—21no—
56#2539—21no—
57#2522—21no—
58#2511C2211yescharacteristic, complemented
59#2507C2211yescharacteristic, complemented
60#2497C2211yescharacteristic, complemented
61#2490—21no—
62#2490C2211yescharacteristic
63#2487—21no—
64#2487C2211yescharacteristic, complemented
65#2486C2211yescharacteristic
66#2454C2211yescharacteristic
67#2448C2211yescharacteristic
68#2426C2211yescharacteristic
69#2423C2211yescharacteristic, complemented
70#2417C2211yescharacteristic
71#2417C2211yescharacteristic
72#2417C2211yescharacteristic, complemented
73#2414C2211yescharacteristic
74#2412—21no—
75#2411—21no—
76#2408C2211yescharacteristic
77#2407C2211yescharacteristic
78#2364—21no—
79#2363C2211yescharacteristic
80#2360C2211yescharacteristic, complemented
81D4×C4⋊C4C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2345C2211yescharacteristic, complemented
84#2342—21no—
85#2341C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C4×#121C2211yescharacteristic
89C2×#390C2211yescharacteristic
90C2×#389C2211yescharacteristic
91#2099C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2042C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic, complemented
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2026C2211yescharacteristic, complemented
119#2015C2211yescharacteristic
120#2001C2211yescharacteristic, complemented
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#1992C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1973C2211yescharacteristic
127#1969C2211yescharacteristic, complemented
128#1959C2211yescharacteristic
129#1954C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1942C2211yescharacteristic, complemented
132#1939C2211yescharacteristic, complemented
133#1936C2211yescharacteristic
134#1935C2211yescharacteristic, complemented
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1921C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1894C2211yescharacteristic, complemented
158#1894C2211yescharacteristic, complemented
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1878C2211yescharacteristic, complemented
164#1877C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1872C2211yescharacteristic, complemented
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic, complemented
181#1825C2211yescharacteristic, complemented
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185#1808C2211yescharacteristic
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1797C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192C4×#107C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#552—24no—
213#552—42no—
214#546—24no—
215#546—42no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C22×C4⋊C4—21no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#483—42no—
257#480—24no—
258#468—42no—
259#467—24no—
260#452—24no—
261#450—42no—
262C4×Q16—42no—
263#436—42no—
264#435—42no—
265#435—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#417—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102—24no—
293C2×#102—42no—
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8—42no—
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390D411yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
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#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386D411yescharacteristic
418#386D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#381—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380D411yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C2×#95—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—41no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562#126—44no—
563#125—22no—
564#125—41no—
565#125—44no—
566#124—22no—
567#124—41no—
568#123—44no—
569#123—44no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8#4114yes—
581#121—24no—
582#121—22no—
583#121—22no—
584#121—44no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#120—44no—
590#120—82no—
591C4×Q8—22no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—82no—
606C4×D4—82no—
607#117—22no—
608#117—44no—
609#117—41no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
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—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—82no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—82no—
702C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—22no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
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#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102#4114yes—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#97—41no—
776#97—41no—
777C4×C8—22no—
778C4×C8—22no—
779C4×C8—41no—
780C4×C8—41no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
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#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829#41—44no—
830#41—82no—
831#41—82no—
832#41—82no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8C2×#4112yes—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4C2×#4112yes—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4#13714yes—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2×#4112yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956Q16—44no—
957SD16—82no—
958SD16—82no—
959M16—82no—
960M16—82no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—44no—
984C2×C8—44no—
985C2×C8C2×#4112yes—
986C2×C8H(5,𝔽2)12yes—
987C4⋊C4—24no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4C2×#4112yes—
1044C4⋊C4C2×#4112yes—
1045C22⋊C4—24no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—41no—
1096C42—41no—
1097C42—42no—
1098C42—42no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—84no—
1138C23—84no—
1139C23—84no—
1140C23—84no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23#54612yes—
1145C23C2×#13712yes—
1146C23#57612yes—
1147C23C23×D411yescharacteristic
1148Q8—22no—
1149Q8—22no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156D4—22no—
1157D4—22no—
1158D4—44no—
1159D4—44no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—82no—
1167D4—84no—
1168D4—84no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4#54612yes—
1266C2×C4C2×#13712yes—
1267C2×C4C2×#13712yes—
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—22no—
1275C8—22no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—168no—
1317C22#333314yes—
1318C22C2×#54611yescharacteristic
1319C22D4×#4111yescharacteristic
1320C22#349611yescharacteristic
1321C22C22×#13711yescharacteristic
1322C22C2×#57611yescharacteristic
1323C22#358411yescharacteristic
1324C22#358411yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—42no—
1331C4—42no—
1332C4—41no—
1333C4—41no—
1334C4—42no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4#348111yescharacteristic
1351C4#349411yescharacteristic
1352C4#352111yescharacteristic
1353C4#353411yescharacteristic
1354C2—24no—
1355C2—81no—
1356C2—81no—
1357C2—82no—
1358C2—161no—
1359C2#5940611yescharacteristic
1360C2C2×#333311yescharacteristic
1361C2#6121611yescharacteristic
1362C2#6143811yescharacteristic
1363C2#6147111yescharacteristic
1364C2#6225411yescharacteristic
1365C2#6227811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59807C2
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. #59856C2semidirect
3. #31908C2semidirect
4. #31878C2semidirect
5. #31785C2semidirect
6. #31018C2semidirect
7. #29241C2semidirect
8. #29084C2semidirect
9. #29018C2semidirect
10. #28570C2semidirect
11. #28120C2semidirect
12. #28111C2semidirect
13. #28072C2semidirect
14. #27529C2semidirect
15. #27393C2semidirect
16. #26973C2semidirect
17. #26727C2semidirect
18. #26671C2semidirect
19. #25541C2semidirect
20. #25254C2semidirect
21. #25128C2semidirect
22. #24933C2semidirect
23. #24861C2semidirect
24. #24426C2semidirect
25. #22941C2semidirect
26. #22879C2semidirect
27. #22491C2semidirect
28. #22419C2semidirect
29. C4×#467C2semidirect
30. #21487C2semidirect
31. C2×#1934C2semidirect
40. C2×C4×Q16C22semidirect
41. C2×#436C22semidirect
58. #2511C22semidirect
59. #2507C22semidirect
60. #2497C22semidirect
64. #2487C22semidirect
69. #2423C22semidirect
72. #2417C22semidirect
80. #2360C22semidirect
83. #2345C22semidirect
91. #2099C22semidirect
93. #2088C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2083C22semidirect
97. #2077C22semidirect
98. #2075C22semidirect
99. #2075C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
107. #2059C22semidirect
112. #2036C22semidirect
113. #2035C22semidirect
118. #2026C22semidirect
120. #2001C22semidirect
123. #1992C22semidirect
124. #1989C22semidirect
127. #1969C22semidirect
129. #1954C22semidirect
130. #1943C22semidirect
131. #1942C22semidirect
132. #1939C22semidirect
134. #1935C22semidirect
143. #1933C22semidirect
144. #1933C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1921C22semidirect
152. #1921C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
157. #1894C22semidirect
158. #1894C22semidirect
163. #1878C22semidirect
167. #1873C22semidirect
170. #1872C22semidirect
173. #1865C22semidirect
174. #1863C22semidirect
175. #1863C22semidirect
177. #1854C22semidirect
180. #1852C22semidirect
181. #1825C22semidirect
183. #1823C22semidirect
184. #1809C22semidirect
186. #1803C22semidirect
192. C4×#107C22semidirect
193. #1770C22semidirect
194. #1763C22semidirect
196. C4×#103C22semidirect
197. C4×#103C22semidirect
198. #1753C22semidirect
199. #1753C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#598562
#598072
#319082
#318782
#317852
#310182
#292412
#290842
#290182
#285702
#281202
#281112
#280722
#275292
#273932
#269732
#267272
#266712
#255412
#252542
#251282
#249332
#248612
#244262
#229412
#228792
#224912
#224192
C4×#4672
#214872
C2×#19342