Finite Group Databasebeta

← #6593306

Subgroups — #6593306

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37851C211yesmaximal, characteristic, complemented
2#34200C211yesmaximal, characteristic, complemented
3#33158C211yesmaximal, characteristic, complemented
4#33013C211yesmaximal, characteristic, complemented
5#32979C211yesmaximal, characteristic, complemented
6#29119C211yesmaximal, characteristic, complemented
7#28127C211yesmaximal, characteristic, complemented
8#27619C211yesmaximal, characteristic, complemented
9#27117C211yesmaximal, characteristic, complemented
10#27096C211yesmaximal, characteristic, complemented
11#27053C211yesmaximal, characteristic, complemented
12#27032C211yesmaximal, characteristic, complemented
13#26738C211yesmaximal, characteristic, complemented
14#26727C211yesmaximal, characteristic, complemented
15#26672C211yesmaximal, characteristic, complemented
16#26661C211yesmaximal, characteristic, complemented
17#26422C211yesmaximal, characteristic, complemented
18#26416C211yesmaximal, characteristic, complemented
19#25204C211yesmaximal, characteristic, complemented
20#25200C211yesmaximal, characteristic, complemented
21#24618C211yesmaximal, characteristic, complemented
22#24382C211yesmaximal, characteristic
23#24004C211yesmaximal, characteristic, complemented
24#23134C211yesmaximal, characteristic, complemented
25#23127C211yesmaximal, characteristic, complemented
26#22938C211yesmaximal, characteristic, complemented
27#22920C211yesmaximal, characteristic, complemented
28#22558C211yesmaximal, characteristic, complemented
29#21584C211yesmaximal, characteristic, complemented
30#20746C211yesmaximal, characteristic, complemented
31C2×#1823C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#466C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#433C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2847C2211yescharacteristic
45#2748—21no—
46#2743—21no—
47#2741—21no—
48#2740—21no—
49#2629C2211yescharacteristic
50#2624C2211yescharacteristic
51#2534—21no—
52#2501C2211yescharacteristic
53#2498—21no—
54#2497C2211yescharacteristic
55#2497C2211yescharacteristic
56#2490C2211yescharacteristic
57#2442C2211yescharacteristic
58#2420C2211yescharacteristic
59#2419—21no—
60#2411—21no—
61#2361C2211yescharacteristic
62#2361C2211yescharacteristic
63#2361C2211yescharacteristic
64#2361C2211yescharacteristic
65#2361C2211yescharacteristic
66#2360C2211yescharacteristic
67#2360C2211yescharacteristic
68#2360C2211yescharacteristic
69#2360C2211yescharacteristic
70#2352—21no—
71#2352—21no—
72D4×C4⋊C4—21no—
73D4×C4⋊C4—21no—
74#2344C2211yescharacteristic
75#2324C2211yescharacteristic
76#2322—21no—
77#2322—21no—
78#2317C2211yescharacteristic
79#2314C2211yescharacteristic
80#2311C2211yescharacteristic
81C4×#120—21no—
82C4×#120—21no—
83#2280C2211yescharacteristic
84C2×#380C2211yescharacteristic
85#2274C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2088C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2084C2211yescharacteristic, complemented
91#2083C2211yescharacteristic, complemented
92#2072C2211yescharacteristic, complemented
93#2071C2211yescharacteristic, complemented
94#2067C2211yescharacteristic, complemented
95#2066C2211yescharacteristic, complemented
96#2065C2211yescharacteristic, complemented
97#2065C2211yescharacteristic, complemented
98#2055C2211yescharacteristic, complemented
99#2054C2211yescharacteristic, complemented
100#2036C2211yescharacteristic
101#2036C2211yescharacteristic
102#2036C2211yescharacteristic
103#2034C2211yescharacteristic
104#2034C2211yescharacteristic
105#2034C2211yescharacteristic
106#2026C2211yescharacteristic, complemented
107#2025C2211yescharacteristic, complemented
108#2000C2211yescharacteristic
109#1999C2211yescharacteristic
110#1989C2211yescharacteristic, complemented
111#1989C2211yescharacteristic, complemented
112#1948C2211yescharacteristic, complemented
113#1947C2211yescharacteristic, complemented
114#1943C2211yescharacteristic, complemented
115#1941C2211yescharacteristic, complemented
116#1936C2211yescharacteristic, complemented
117#1936C2211yescharacteristic, complemented
118#1935C2211yescharacteristic, complemented
119#1934C2211yescharacteristic, complemented
120#1934C2211yescharacteristic, complemented
121#1933C2211yescharacteristic, complemented
122#1927C2211yescharacteristic, complemented
123#1926C2211yescharacteristic, complemented
124#1926C2211yescharacteristic, complemented
125#1925C2211yescharacteristic, complemented
126#1924C2211yescharacteristic
127#1924C2211yescharacteristic
128#1923C2211yescharacteristic
129#1923C2211yescharacteristic
130#1921C2211yescharacteristic, complemented
131#1921C2211yescharacteristic, complemented
132#1920C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1919C2211yescharacteristic, complemented
136#1919C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1918C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1893C2211yescharacteristic
141#1892C2211yescharacteristic
142#1880C2211yescharacteristic, complemented
143#1880C2211yescharacteristic, complemented
144#1879C2211yescharacteristic, complemented
145#1879C2211yescharacteristic, complemented
146#1879C2211yescharacteristic, complemented
147#1877C2211yescharacteristic, complemented
148#1875C2211yescharacteristic
149#1874C2211yescharacteristic
150#1874C2211yescharacteristic
151#1874C2211yescharacteristic
152#1874C2211yescharacteristic
153#1874C2211yescharacteristic
154#1872C2211yescharacteristic
155#1865C2211yescharacteristic, complemented
156#1865C2211yescharacteristic, complemented
157#1864C2211yescharacteristic, complemented
158#1864C2211yescharacteristic, complemented
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1853C2211yescharacteristic
163#1853C2211yescharacteristic
164#1853C2211yescharacteristic
165#1853C2211yescharacteristic
166#1850C2211yescharacteristic
167#1850C2211yescharacteristic
168#1824C2211yescharacteristic
169#1824C2211yescharacteristic
170#1823C2211yescharacteristic
171#1823C2211yescharacteristic
172#1823C2211yescharacteristic
173#1823C2211yescharacteristic
174#1823C2211yescharacteristic
175#1823C2211yescharacteristic
176#1823C2211yescharacteristic
177#1823C2211yescharacteristic
178#1818C2211yescharacteristic
179#1805C2211yescharacteristic, complemented
180#1804C2211yescharacteristic, complemented
181#1803C2211yescharacteristic, complemented
182#1802C2211yescharacteristic, complemented
183#1798C2211yescharacteristic
184#1788C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1779C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189C4×#106C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1762C2211yescharacteristic, complemented
192#1762C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196#1752C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198#1750C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4—21no—
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211#525—24no—
212#525—24no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×#120—21no—
225#520—24no—
226#520—42no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
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×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4—24no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4—21no—
250C22×C4⋊C4—21no—
251C22×C4⋊C4—42no—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261#483—24no—
262#481—24no—
263#481—42no—
264#480—24no—
265#466—24no—
266#465—24no—
267#449—42no—
268#433—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8—42no—
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#384—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#382—21no—
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#381D411yescharacteristic
414#381D411yescharacteristic
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380D411yescharacteristic
421#380D411yescharacteristic
422#380D411yescharacteristic
423#380D411yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379D411yescharacteristic
432#379D411yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C2×#95—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
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#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25C2×D411yescharacteristic
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—41no—
526C23×C4—41no—
527C23×C4—44no—
528C23×C4—82no—
529C23×C4—82no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×D8—22no—
540C2×D8—41no—
541C2×D8—41no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556#125—41no—
557#125—41no—
558#123—28no—
559#123—82no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8#4114yes—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—41no—
573#121—41no—
574#121#4114yes—
575#120—28no—
576#120—82no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—82no—
592C4×D4—82no—
593C4×D4—82no—
594C4×D4—82no—
595C4×D4—82no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—41no—
601#117—41no—
602#117—44no—
603#117—82no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
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—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—44no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—44no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4#4114yes—
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×C4⋊C4C2411yescharacteristic
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—82no—
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×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
718C2×C42—21no—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—22no—
726#106—22no—
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—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—41no—
768#97—41no—
769C4×C8—41no—
770C4×C8—41no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
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#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—22no—
809C24—22no—
810C24—22no—
811C24—22no—
812C24—22no—
813C24—21no—
814C24—21no—
815C24—41no—
816C24—41no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—44no—
822#41—44no—
823#41—44no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8C2×#4112yes—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4C2×#4112yes—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—24no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
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—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
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—816no—
938C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
950C22×C4C2×#4112yes—
951C22×C4C2×#4112yes—
952C22×C4H(5,𝔽2)12yes—
953C22×C4C2511yescharacteristic
954SD16—82no—
955D8—82no—
956C2×C8—21no—
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—82no—
981C2×C8—82no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
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—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
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⋊C4C2×#4112yes—
1036C4⋊C4C2×#4112yes—
1037C4⋊C4C2×#4112yes—
1038C4⋊C4C2×#4112yes—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—24no—
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—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
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—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C42—24no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
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—28no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
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—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23#52512yes—
1135C23#54612yes—
1136C23#57612yes—
1137C23#57712yes—
1138C23#57712yes—
1139C23C23×D411yescharacteristic
1140Q8—22no—
1141Q8—22no—
1142Q8—41no—
1143Q8—41no—
1144D4—22no—
1145D4—22no—
1146D4—48no—
1147D4—48no—
1148D4—48no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—84no—
1156D4—162no—
1157D4—162no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
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—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—44no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—48no—
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—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4#52512yes—
1259C2×C4#54612yes—
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C22×#4111yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—416no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22#311914yes—
1310C22C2×#52511yescharacteristic
1311C22C2×#54611yescharacteristic
1312C22#348511yescharacteristic
1313C22C2×#57611yescharacteristic
1314C22C2×#57711yescharacteristic
1315C22C2×#57711yescharacteristic
1316C22#358611yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—42no—
1325C4—41no—
1326C4—41no—
1327C4—42no—
1328C4—42no—
1329C4—41no—
1330C4—41no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4#347511yescharacteristic
1343C4#347511yescharacteristic
1344C4#351311yescharacteristic
1345C4#351311yescharacteristic
1346C2—24no—
1347C2—42no—
1348C2—42no—
1349C2—82no—
1350C2—161no—
1351C2#3615911yescharacteristic
1352C2C2×#311911yescharacteristic
1353C2#6058511yescharacteristic
1354C2#6116711yescharacteristic
1355C2#6118511yescharacteristic
1356C2#6174411yescharacteristic
1357C2#6176511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24382C2
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. #37851C2semidirect
2. #34200C2semidirect
3. #33158C2semidirect
4. #33013C2semidirect
5. #32979C2semidirect
6. #29119C2semidirect
7. #28127C2semidirect
8. #27619C2semidirect
9. #27117C2semidirect
10. #27096C2semidirect
11. #27053C2semidirect
12. #27032C2semidirect
13. #26738C2semidirect
14. #26727C2semidirect
15. #26672C2semidirect
16. #26661C2semidirect
17. #26422C2semidirect
18. #26416C2semidirect
19. #25204C2semidirect
20. #25200C2semidirect
21. #24618C2semidirect
23. #24004C2semidirect
24. #23134C2semidirect
25. #23127C2semidirect
26. #22938C2semidirect
27. #22920C2semidirect
28. #22558C2semidirect
29. #21584C2semidirect
30. #20746C2semidirect
31. C2×#1823C2semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2088C22semidirect
89. #2088C22semidirect
90. #2084C22semidirect
91. #2083C22semidirect
92. #2072C22semidirect
93. #2071C22semidirect
94. #2067C22semidirect
95. #2066C22semidirect
96. #2065C22semidirect
97. #2065C22semidirect
98. #2055C22semidirect
99. #2054C22semidirect
106. #2026C22semidirect
107. #2025C22semidirect
110. #1989C22semidirect
111. #1989C22semidirect
112. #1948C22semidirect
113. #1947C22semidirect
114. #1943C22semidirect
115. #1941C22semidirect
116. #1936C22semidirect
117. #1936C22semidirect
118. #1935C22semidirect
119. #1934C22semidirect
120. #1934C22semidirect
121. #1933C22semidirect
122. #1927C22semidirect
123. #1926C22semidirect
124. #1926C22semidirect
125. #1925C22semidirect
130. #1921C22semidirect
131. #1921C22semidirect
132. #1920C22semidirect
133. #1920C22semidirect
134. #1920C22semidirect
135. #1919C22semidirect
136. #1919C22semidirect
137. #1919C22semidirect
138. #1918C22semidirect
139. #1918C22semidirect
142. #1880C22semidirect
143. #1880C22semidirect
144. #1879C22semidirect
145. #1879C22semidirect
146. #1879C22semidirect
147. #1877C22semidirect
155. #1865C22semidirect
156. #1865C22semidirect
157. #1864C22semidirect
158. #1864C22semidirect
179. #1805C22semidirect
180. #1804C22semidirect
181. #1803C22semidirect
182. #1802C22semidirect
188. #1776C22semidirect
189. C4×#106C22semidirect
190. #1763C22semidirect
191. #1762C22semidirect
192. #1762C22semidirect
193. C4×#103C22semidirect
194. C4×#102C22semidirect
195. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#378512
#342002
#331582
#330132
#329792
#291192
#281272
#276192
#271172
#270962
#270532
#270322
#267382
#267272
#266722
#266612
#264222
#264162
#252042
#252002
#246182
#243822
#240042
#231342
#231272
#229382
#229202
#225582
#215842
#207462
C2×#18232