Finite Group Databasebeta

← #6599814

Subgroups — #6599814

Order 512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39058C211yesmaximal, characteristic, complemented
2#34292C211yesmaximal, characteristic
3#33090C211yesmaximal, characteristic, complemented
4#33011C211yesmaximal, characteristic, complemented
5#32914C211yesmaximal, characteristic, complemented
6#29506C211yesmaximal, characteristic, complemented
7#29480C211yesmaximal, characteristic, complemented
8#29414C211yesmaximal, characteristic, complemented
9#29382C211yesmaximal, characteristic, complemented
10#29252C211yesmaximal, characteristic, complemented
11#28588C211yesmaximal, characteristic, complemented
12#27528C211yesmaximal, characteristic, complemented
13#27312C211yesmaximal, characteristic, complemented
14#27125C211yesmaximal, characteristic, complemented
15#26941C211yesmaximal, characteristic, complemented
16#26783C211yesmaximal, characteristic, complemented
17#26614C211yesmaximal, characteristic, complemented
18#26227C211yesmaximal, characteristic, complemented
19#26182C211yesmaximal, characteristic, complemented
20#26139C211yesmaximal, characteristic, complemented
21#25166C211yesmaximal, characteristic, complemented
22#24442C211yesmaximal, characteristic
23#24426C211yesmaximal, characteristic
24#23144C211yesmaximal, characteristic, complemented
25#23030C211yesmaximal, characteristic, complemented
26#22864C211yesmaximal, characteristic, complemented
27#22854C211yesmaximal, characteristic, complemented
28#22794C211yesmaximal, characteristic, complemented
29#21457C211yesmaximal, characteristic, complemented
30#21125C211yesmaximal, characteristic, complemented
31#20879C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#470C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#441C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C2×#418C2211yescharacteristic
49C22×#102C2211yescharacteristic
50#2855C2211yescharacteristic, complemented
51#2776—21no—
52#2765—21no—
53#2750—21no—
54#2747—21no—
55#2645C2211yescharacteristic, complemented
56#2621C2211yescharacteristic
57#2590—21no—
58#2587—21no—
59#2578—21no—
60#2509C2211yescharacteristic, complemented
61#2494—21no—
62#2494C2211yescharacteristic, complemented
63#2446C2211yescharacteristic, complemented
64#2429C2211yescharacteristic, complemented
65#2417C2211yescharacteristic
66#2415C2211yescharacteristic
67#2367C2211yescharacteristic
68#2363C2211yescharacteristic
69#2362C2211yescharacteristic
70#2362C2211yescharacteristic
71#2361—21no—
72#2360C2211yescharacteristic
73#2359—21no—
74#2358—21no—
75#2354C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2342—21no—
78#2339C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2326C2211yescharacteristic
81#2325—21no—
82#2323C2211yescharacteristic
83#2321—21no—
84#2320C2211yescharacteristic, complemented
85#2316C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic, complemented
87C4×#123—21no—
88C4×#121C2211yescharacteristic
89#2290C2211yescharacteristic
90C2×#388—21no—
91#2275C2211yescharacteristic
92#2099C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2036C2211yescharacteristic, complemented
108#2035C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2016C2211yescharacteristic, complemented
112#2015C2211yescharacteristic
113#2015C2211yescharacteristic
114#2000C2211yescharacteristic
115#2000C2211yescharacteristic
116#1973C2211yescharacteristic
117#1971C2211yescharacteristic, complemented
118#1968C2211yescharacteristic
119#1943C2211yescharacteristic, complemented
120#1936C2211yescharacteristic
121#1936C2211yescharacteristic
122#1935C2211yescharacteristic, complemented
123#1933C2211yescharacteristic, complemented
124#1928C2211yescharacteristic, complemented
125#1928C2211yescharacteristic, complemented
126#1928C2211yescharacteristic, complemented
127#1928C2211yescharacteristic, complemented
128#1927C2211yescharacteristic, complemented
129#1927C2211yescharacteristic, complemented
130#1925C2211yescharacteristic
131#1925C2211yescharacteristic
132#1924C2211yescharacteristic, complemented
133#1923C2211yescharacteristic, complemented
134#1921C2211yescharacteristic, complemented
135#1921C2211yescharacteristic, complemented
136#1920C2211yescharacteristic, complemented
137#1920C2211yescharacteristic, complemented
138#1918C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1917C2211yescharacteristic, complemented
141#1917C2211yescharacteristic, complemented
142#1894C2211yescharacteristic
143#1892C2211yescharacteristic
144#1880C2211yescharacteristic
145#1880C2211yescharacteristic
146#1878C2211yescharacteristic, complemented
147#1878C2211yescharacteristic, complemented
148#1878C2211yescharacteristic, complemented
149#1878C2211yescharacteristic, complemented
150#1877C2211yescharacteristic
151#1877C2211yescharacteristic
152#1877C2211yescharacteristic
153#1877C2211yescharacteristic
154#1877C2211yescharacteristic
155#1877C2211yescharacteristic
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic, complemented
162#1872C2211yescharacteristic
163#1870C2211yescharacteristic
164#1869C2211yescharacteristic
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1863C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1840C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1817C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1798C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1749C2211yescharacteristic, complemented
200#1746C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#546—24no—
214#546—24no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226#518—42no—
227#518—42no—
228C4×#41—42no—
229C4×#41—42no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C42—21no—
259C22×C42C2311yescharacteristic
260#485—42no—
261#470—24no—
262#467—24no—
263#461—42no—
264#461—42no—
265#452—24no—
266#452—42no—
267#450—24no—
268#450—24no—
269#441—42no—
270#440—24no—
271#440—42no—
272#427—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#418—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#401—21no—
326#401—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—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#397—21no—
342#396—21no—
343#396—21no—
344#394—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388D411yescharacteristic
392#388D411yescharacteristic
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387D411yescharacteristic
407#387D411yescharacteristic
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386D411yescharacteristic
416#386D411yescharacteristic
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382—21no—
430#382C2311yescharacteristic
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376C2311yescharacteristic
463C2×#95—21no—
464C2×#95—21no—
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#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
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—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4#4114yes—
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×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×M16—22no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#124—22no—
569#124—22no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8#4114yes—
581#121—28no—
582#121—22no—
583#121—22no—
584#120—28no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—44no—
610C4×D4—44no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4—82no—
614#117—22no—
615#117—22no—
616#117—41no—
617#117—41no—
618#117—44no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
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—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×C22⋊C4—28no—
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—44no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—82no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42—44no—
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#106—22no—
733#106—22no—
734#106—41no—
735#106—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738#103—22no—
739#103—22no—
740#103—22no—
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#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—41no—
764#102—41no—
765#102#4114yes—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772#97—22no—
773#97—41no—
774#97—41no—
775C4×C8—41no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
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#95—21no—
812#95—21no—
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823C24—21no—
824C24—21no—
825C24—24no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—44no—
835#41—44no—
836#41—44no—
837#41—44no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8C2×#4112yes—
856C2×D4—28no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—24no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C2×D4C2×#4112yes—
882C2×D4C2×#4112yes—
883C2×D4H(5,𝔽2)12yes—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—24no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—24no—
894C22×C4—24no—
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—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
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×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
955C22×C4C2511yescharacteristic
956Q16—44no—
957Q16—82no—
958SD16—44no—
959SD16—44no—
960SD16—82no—
961SD16—82no—
962M16—82no—
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—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—44no—
987C2×C8C2×#4112yes—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—21no—
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—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
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⋊C4C2×#4112yes—
1037C4⋊C4C2×#4112yes—
1038C4⋊C4H(5,𝔽2)12yes—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—22no—
1045C22⋊C4—24no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
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—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—41no—
1084C42—41no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—22no—
1102C23—22no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—48no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23#52512yes—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145D4—22no—
1146D4—22no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—48no—
1151D4—48no—
1152D4—41no—
1153D4—41no—
1154D4—82no—
1155D4—84no—
1156D4#55314yes—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
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—48no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
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—84no—
1244C2×C4—84no—
1245C2×C4—82no—
1246C2×C4—82no—
1247C2×C4—84no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4—162no—
1253C2×C4#52512yes—
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C22×#4111yescharacteristic
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—22no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—24no—
1270C22—22no—
1271C22—22no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—42no—
1286C22—41no—
1287C22—42no—
1288C22—41no—
1289C22—42no—
1290C22—41no—
1291C22—41no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—168no—
1297C22C2×#52511yescharacteristic
1298C22D4×#4111yescharacteristic
1299C22#348411yescharacteristic
1300C22#358411yescharacteristic
1301C22#358511yescharacteristic
1302C22#358611yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4C2×#55311yescharacteristic
1331C4#348111yescharacteristic
1332C4#350511yescharacteristic
1333C4#351311yescharacteristic
1334C2—42no—
1335C2—44no—
1336C2—81no—
1337C2—82no—
1338C2#3622111yescharacteristic
1339C2#6057511yescharacteristic
1340C2#6058111yescharacteristic
1341C2#6151411yescharacteristic
1342C2#6152911yescharacteristic
1343C2#6161311yescharacteristic
1344C2#6165411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39058C2semidirect
3. #33090C2semidirect
4. #33011C2semidirect
5. #32914C2semidirect
6. #29506C2semidirect
7. #29480C2semidirect
8. #29414C2semidirect
9. #29382C2semidirect
10. #29252C2semidirect
11. #28588C2semidirect
12. #27528C2semidirect
13. #27312C2semidirect
14. #27125C2semidirect
15. #26941C2semidirect
16. #26783C2semidirect
17. #26614C2semidirect
18. #26227C2semidirect
19. #26182C2semidirect
20. #26139C2semidirect
21. #25166C2semidirect
24. #23144C2semidirect
25. #23030C2semidirect
26. #22864C2semidirect
27. #22854C2semidirect
28. #22794C2semidirect
29. #21457C2semidirect
30. #21125C2semidirect
31. #20879C2semidirect
35. C2×#485C22semidirect
44. C2×#441C22semidirect
50. #2855C22semidirect
55. #2645C22semidirect
60. #2509C22semidirect
62. #2494C22semidirect
63. #2446C22semidirect
64. #2429C22semidirect
84. #2320C22semidirect
86. C4×C22⋊Q8C22semidirect
92. #2099C22semidirect
93. #2095C22semidirect
94. #2088C22semidirect
95. #2086C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2076C22semidirect
99. #2075C22semidirect
100. #2074C22semidirect
101. #2072C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2043C22semidirect
107. #2036C22semidirect
108. #2035C22semidirect
111. #2016C22semidirect
117. #1971C22semidirect
119. #1943C22semidirect
122. #1935C22semidirect
123. #1933C22semidirect
124. #1928C22semidirect
125. #1928C22semidirect
126. #1928C22semidirect
127. #1928C22semidirect
128. #1927C22semidirect
129. #1927C22semidirect
132. #1924C22semidirect
133. #1923C22semidirect
134. #1921C22semidirect
135. #1921C22semidirect
136. #1920C22semidirect
137. #1920C22semidirect
138. #1918C22semidirect
139. #1918C22semidirect
140. #1917C22semidirect
141. #1917C22semidirect
146. #1878C22semidirect
147. #1878C22semidirect
148. #1878C22semidirect
149. #1878C22semidirect
161. #1873C22semidirect
165. #1865C22semidirect
172. #1863C22semidirect
173. #1863C22semidirect
174. #1863C22semidirect
182. #1854C22semidirect
184. #1840C22semidirect
185. #1825C22semidirect
186. #1817C22semidirect
192. #1776C22semidirect
193. #1763C22semidirect
195. C4×#103C22semidirect
199. #1749C22semidirect
200. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#390582
#342922
#330902
#330112
#329142
#295062
#294802
#294142
#293822
#292522
#285882
#275282
#273122
#271252
#269412
#267832
#266142
#262272
#261822
#261392
#251662
#244422
#244262
#231442
#230302
#228642
#228542
#227942
#214572
#211252
#208792