Finite Group Databasebeta

← #6477904

Subgroups — #6477904

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37380C211yesmaximal, characteristic, complemented
2#34200C211yesmaximal, characteristic
3#32983C211yesmaximal, characteristic, complemented
4#32982C211yesmaximal, characteristic, complemented
5#32968C211yesmaximal, characteristic, complemented
6#32916C211yesmaximal, characteristic, complemented
7#29979C211yesmaximal, characteristic, complemented
8#29766C211yesmaximal, characteristic, complemented
9#29601C211yesmaximal, characteristic
10#29601C211yesmaximal, characteristic
11#27116C211yesmaximal, characteristic, complemented
12#27112C211yesmaximal, characteristic, complemented
13#27101C211yesmaximal, characteristic, complemented
14#27097C211yesmaximal, characteristic, complemented
15#26949C211yesmaximal, characteristic, complemented
16#26945C211yesmaximal, characteristic, complemented
17#26932C211yesmaximal, characteristic, complemented
18#26928C211yesmaximal, characteristic, complemented
19#26804C211yesmaximal, characteristic, complemented
20#26800C211yesmaximal, characteristic, complemented
21#26789C211yesmaximal, characteristic, complemented
22#26785C211yesmaximal, characteristic, complemented
23#26679C211yesmaximal, characteristic, complemented
24#26675C211yesmaximal, characteristic, complemented
25#26662C211yesmaximal, characteristic, complemented
26#26658C211yesmaximal, characteristic, complemented
27#22059C211yesmaximal, characteristic, complemented
28#22057C211yesmaximal, characteristic, complemented
29#21910C211yesmaximal, characteristic, complemented
30#21591C211yesmaximal, characteristic, complemented
31#21589C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#483C2211yescharacteristic
40C2×#483C2211yescharacteristic
41C2×#479C2211yescharacteristic, complemented
42C2×#478C2211yescharacteristic, complemented
43C2×#462C2211yescharacteristic, complemented
44C2×#461C2211yescharacteristic, complemented
45C2×#452C2211yescharacteristic
46C2×#452C2211yescharacteristic
47#2848C2211yescharacteristic
48#2848C2211yescharacteristic
49#2787—21no—
50#2787—21no—
51#2768—21no—
52#2768—21no—
53#2765—21no—
54#2765—21no—
55#2735—21no—
56#2735—21no—
57#2629C2211yescharacteristic
58#2621C2211yescharacteristic
59#2494C2211yescharacteristic
60#2494C2211yescharacteristic
61#2489C2211yescharacteristic
62#2489C2211yescharacteristic
63#2429C2211yescharacteristic
64#2429C2211yescharacteristic
65#2423C2211yescharacteristic
66#2423C2211yescharacteristic
67#2361C2211yescharacteristic
68#2361C2211yescharacteristic
69#2361C2211yescharacteristic
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic
74#2360C2211yescharacteristic
75#2352—21no—
76#2352—21no—
77D4×C4⋊C4—21no—
78D4×C4⋊C4—21no—
79#2323C2211yescharacteristic
80#2323C2211yescharacteristic
81#2322—21no—
82#2322—21no—
83#2317C2211yescharacteristic
84#2311C2211yescharacteristic
85C4×#120—21no—
86C4×#120—21no—
87#2280C2211yescharacteristic
88#2274C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2059C2211yescharacteristic, complemented
103#2043C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2001C2211yescharacteristic
114#2001C2211yescharacteristic
115#2001C2211yescharacteristic
116#2001C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#1973C2211yescharacteristic, complemented
122#1971C2211yescharacteristic, complemented
123#1969C2211yescharacteristic, complemented
124#1968C2211yescharacteristic, complemented
125#1936C2211yescharacteristic, complemented
126#1935C2211yescharacteristic, complemented
127#1934C2211yescharacteristic, complemented
128#1933C2211yescharacteristic, complemented
129#1928C2211yescharacteristic, complemented
130#1928C2211yescharacteristic, complemented
131#1928C2211yescharacteristic, complemented
132#1927C2211yescharacteristic, complemented
133#1927C2211yescharacteristic, complemented
134#1927C2211yescharacteristic, complemented
135#1926C2211yescharacteristic, complemented
136#1925C2211yescharacteristic, complemented
137#1924C2211yescharacteristic
138#1924C2211yescharacteristic
139#1924C2211yescharacteristic
140#1924C2211yescharacteristic
141#1923C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1880C2211yescharacteristic, complemented
150#1880C2211yescharacteristic, complemented
151#1878C2211yescharacteristic, complemented
152#1878C2211yescharacteristic, complemented
153#1878C2211yescharacteristic, complemented
154#1878C2211yescharacteristic, complemented
155#1877C2211yescharacteristic, complemented
156#1877C2211yescharacteristic, complemented
157#1872C2211yescharacteristic
158#1872C2211yescharacteristic
159#1872C2211yescharacteristic
160#1872C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1872C2211yescharacteristic
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1862C2211yescharacteristic, complemented
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1852C2211yescharacteristic
174#1852C2211yescharacteristic
175#1852C2211yescharacteristic
176#1852C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1805C2211yescharacteristic, complemented
184#1804C2211yescharacteristic, complemented
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic, complemented
187#1798C2211yescharacteristic
188#1798C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1779C2211yescharacteristic
192#1779C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4—21no—
205C24×C4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2311yescharacteristic
212#525—24no—
213#525—24no—
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226#520—42no—
227#520—42no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4—21no—
250C22×C4⋊C4—42no—
251C22×C4⋊C4—42no—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258#485—24no—
259#485—24no—
260#484—42no—
261#484—42no—
262#483—42no—
263#483—42no—
264#479—42no—
265#478—42no—
266#462—42no—
267#461—42no—
268#452—24no—
269#452—24no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#401—21no—
327#401—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#399—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
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#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384—21no—
423#384C2311yescharacteristic
424#382—21no—
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#381D411yescharacteristic
429#381D411yescharacteristic
430#380—21no—
431#380—21no—
432#380D411yescharacteristic
433#380D411yescharacteristic
434#380D411yescharacteristic
435#380D411yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379D411yescharacteristic
445#379D411yescharacteristic
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
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
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41#4114yes—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4—41no—
525C23×C4—44no—
526C23×C4—82no—
527C23×C4—82no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#125—41no—
557#125—41no—
558#123—28no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#120—28no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595C4×D4—44no—
596C4×D4—82no—
597C4×D4—82no—
598C4×D4—82no—
599C4×D4—82no—
600#117—22no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—44no—
606#117#4114yes—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
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—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—44no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—44no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
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—21no—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—22no—
723#107—22no—
724#107—22no—
725#107—41no—
726#107—41no—
727#106—22no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
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—22no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773#97—41no—
774#97—41no—
775C4×C8—41no—
776C4×C8—41no—
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#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819C24—22no—
820C24—22no—
821C24—22no—
822C24—21no—
823C24—41no—
824C24—41no—
825C24—41no—
826C24—41no—
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830#41—44no—
831#41—44no—
832#41—44no—
833#41—44no—
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×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8C2×#4112yes—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4C2×#4112yes—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
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—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—42no—
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—816no—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
951C22×C4C2×#4112yes—
952C22×C4C2511yescharacteristic
953Q16—82no—
954Q16—82no—
955SD16—82no—
956SD16—82no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
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—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
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—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
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⋊C4—81no—
1037C4⋊C4C2×#4112yes—
1038C4⋊C4C2×#4112yes—
1039C4⋊C4H(5,𝔽2)12yes—
1040C4⋊C4H(5,𝔽2)12yes—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C42—24no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—22no—
1114C23—44no—
1115C23—44no—
1116C23—44no—
1117C23—44no—
1118C23—44no—
1119C23—44no—
1120C23—44no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23#52512yes—
1128C23#57712yes—
1129C23#57812yes—
1130C23C23×D411yescharacteristic
1131Q8—22no—
1132Q8—22no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143D4—22no—
1144D4—22no—
1145D4—48no—
1146D4—48no—
1147D4—48no—
1148D4—41no—
1149D4—41no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
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—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—48no—
1194C2×C4—44no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
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—84no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4#52512yes—
1252C2×C4C22×#4111yescharacteristic
1253C2×C4C22×#4111yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4#58511yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—416no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22C2×#52511yescharacteristic
1296C22#348411yescharacteristic
1297C22#348511yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22C2×#57811yescharacteristic
1300C22#358511yescharacteristic
1301C22#358611yescharacteristic
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4#346011yescharacteristic
1329C4#346011yescharacteristic
1330C4#350511yescharacteristic
1331C4#350511yescharacteristic
1332C2—42no—
1333C2—42no—
1334C2—42no—
1335C2—82no—
1336C2#3509111yescharacteristic
1337C2#6058511yescharacteristic
1338C2#6058911yescharacteristic
1339C2#6161011yescharacteristic
1340C2#6161211yescharacteristic
1341C2#6176711yescharacteristic
1342C2#6177411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37380C2semidirect
3. #32983C2semidirect
4. #32982C2semidirect
5. #32968C2semidirect
6. #32916C2semidirect
7. #29979C2semidirect
8. #29766C2semidirect
11. #27116C2semidirect
12. #27112C2semidirect
13. #27101C2semidirect
14. #27097C2semidirect
15. #26949C2semidirect
16. #26945C2semidirect
17. #26932C2semidirect
18. #26928C2semidirect
19. #26804C2semidirect
20. #26800C2semidirect
21. #26789C2semidirect
22. #26785C2semidirect
23. #26679C2semidirect
24. #26675C2semidirect
25. #26662C2semidirect
26. #26658C2semidirect
27. #22059C2semidirect
28. #22057C2semidirect
29. #21910C2semidirect
30. #21591C2semidirect
31. #21589C2semidirect
41. C2×#479C22semidirect
42. C2×#478C22semidirect
43. C2×#462C22semidirect
44. C2×#461C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2088C22semidirect
92. #2088C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2068C22semidirect
98. #2068C22semidirect
99. #2066C22semidirect
100. #2066C22semidirect
101. #2059C22semidirect
102. #2059C22semidirect
103. #2043C22semidirect
104. #2043C22semidirect
121. #1973C22semidirect
122. #1971C22semidirect
123. #1969C22semidirect
124. #1968C22semidirect
125. #1936C22semidirect
126. #1935C22semidirect
127. #1934C22semidirect
128. #1933C22semidirect
129. #1928C22semidirect
130. #1928C22semidirect
131. #1928C22semidirect
132. #1927C22semidirect
133. #1927C22semidirect
134. #1927C22semidirect
135. #1926C22semidirect
136. #1925C22semidirect
145. #1921C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1880C22semidirect
150. #1880C22semidirect
151. #1878C22semidirect
152. #1878C22semidirect
153. #1878C22semidirect
154. #1878C22semidirect
155. #1877C22semidirect
156. #1877C22semidirect
165. #1865C22semidirect
166. #1864C22semidirect
167. #1863C22semidirect
168. #1862C22semidirect
183. #1805C22semidirect
184. #1804C22semidirect
185. #1803C22semidirect
186. #1802C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect
196. C4×#106C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#373802
#342002
#329832
#329822
#329682
#329162
#299792
#297662
#296012
#271162
#271122
#271012
#270972
#269492
#269452
#269322
#269282
#268042
#268002
#267892
#267852
#266792
#266752
#266622
#266582
#220592
#220572
#219102
#215912
#215892