Finite Group Databasebeta

← #6593371

Subgroups — #6593371

Order 512.

1769 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37859C211yesmaximal, characteristic, complemented
2#34200C211yesmaximal, characteristic
3#33159C211yesmaximal, characteristic, complemented
4#33017C211yesmaximal, characteristic, complemented
5#32983C211yesmaximal, characteristic, complemented
6#29120C211yesmaximal, characteristic, complemented
7#28131C211yesmaximal, characteristic, complemented
8#27619C211yesmaximal, characteristic, complemented
9#27113C211yesmaximal, characteristic, complemented
10#27100C211yesmaximal, characteristic, complemented
11#27052C211yesmaximal, characteristic, complemented
12#27033C211yesmaximal, characteristic, complemented
13#26739C211yesmaximal, characteristic, complemented
14#26726C211yesmaximal, characteristic, complemented
15#26678C211yesmaximal, characteristic, complemented
16#26659C211yesmaximal, characteristic, complemented
17#26428C211yesmaximal, characteristic, complemented
18#26426C211yesmaximal, characteristic, complemented
19#25220C211yesmaximal, characteristic, complemented
20#25216C211yesmaximal, characteristic, complemented
21#24614C211yesmaximal, characteristic, complemented
22#24389C211yesmaximal, characteristic
23#24008C211yesmaximal, characteristic
24#23139C211yesmaximal, characteristic, complemented
25#23138C211yesmaximal, characteristic, complemented
26#22946C211yesmaximal, characteristic, complemented
27#22928C211yesmaximal, characteristic, complemented
28#22559C211yesmaximal, characteristic, complemented
29#21585C211yesmaximal, characteristic, complemented
30#20746C211yesmaximal, characteristic, complemented
31#20700C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#484C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#433C2211yescharacteristic
43C2×#407C2211yescharacteristic
44#2848C2211yescharacteristic
45#2745—21no—
46#2739—21no—
47#2736—21no—
48#2735—21no—
49#2628C2211yescharacteristic
50#2625C2211yescharacteristic
51#2575—21no—
52#2574—21no—
53#2530—21no—
54#2527—21no—
55#2499C2211yescharacteristic
56#2497C2211yescharacteristic
57#2494C2211yescharacteristic
58#2492C2211yescharacteristic
59#2439C2211yescharacteristic
60#2421C2211yescharacteristic
61#2362C2211yescharacteristic
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#2346C2211yescharacteristic
75#2323C2211yescharacteristic
76#2322—21no—
77#2322—21no—
78#2317C2211yescharacteristic
79#2314C2211yescharacteristic
80#2311C2211yescharacteristic
81C4×#120—21no—
82C4×#120—21no—
83#2280C2211yescharacteristic
84#2280C2211yescharacteristic
85#2274C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2087C2211yescharacteristic, complemented
89#2086C2211yescharacteristic, complemented
90#2084C2211yescharacteristic, complemented
91#2083C2211yescharacteristic, complemented
92#2074C2211yescharacteristic, complemented
93#2073C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2068C2211yescharacteristic, complemented
96#2067C2211yescharacteristic, complemented
97#2066C2211yescharacteristic, complemented
98#2056C2211yescharacteristic, complemented
99#2055C2211yescharacteristic, complemented
100#2036C2211yescharacteristic
101#2036C2211yescharacteristic
102#2035C2211yescharacteristic
103#2034C2211yescharacteristic
104#2034C2211yescharacteristic
105#2033C2211yescharacteristic
106#2024C2211yescharacteristic, complemented
107#2023C2211yescharacteristic, complemented
108#2001C2211yescharacteristic
109#2000C2211yescharacteristic
110#1988C2211yescharacteristic, complemented
111#1987C2211yescharacteristic, complemented
112#1949C2211yescharacteristic, complemented
113#1949C2211yescharacteristic, complemented
114#1944C2211yescharacteristic, complemented
115#1942C2211yescharacteristic, complemented
116#1936C2211yescharacteristic, complemented
117#1935C2211yescharacteristic, complemented
118#1935C2211yescharacteristic, complemented
119#1934C2211yescharacteristic, complemented
120#1933C2211yescharacteristic, complemented
121#1933C2211yescharacteristic, complemented
122#1928C2211yescharacteristic, complemented
123#1928C2211yescharacteristic, complemented
124#1927C2211yescharacteristic, complemented
125#1925C2211yescharacteristic, complemented
126#1924C2211yescharacteristic
127#1924C2211yescharacteristic
128#1923C2211yescharacteristic
129#1923C2211yescharacteristic
130#1921C2211yescharacteristic, complemented
131#1921C2211yescharacteristic, complemented
132#1921C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1919C2211yescharacteristic, complemented
136#1919C2211yescharacteristic, complemented
137#1918C2211yescharacteristic, complemented
138#1918C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1895C2211yescharacteristic
141#1894C2211yescharacteristic
142#1880C2211yescharacteristic, complemented
143#1878C2211yescharacteristic, complemented
144#1878C2211yescharacteristic, complemented
145#1878C2211yescharacteristic, complemented
146#1877C2211yescharacteristic, complemented
147#1877C2211yescharacteristic, complemented
148#1875C2211yescharacteristic
149#1873C2211yescharacteristic
150#1873C2211yescharacteristic
151#1872C2211yescharacteristic
152#1872C2211yescharacteristic
153#1872C2211yescharacteristic
154#1872C2211yescharacteristic
155#1863C2211yescharacteristic, complemented
156#1863C2211yescharacteristic, complemented
157#1862C2211yescharacteristic, complemented
158#1862C2211yescharacteristic, complemented
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1852C2211yescharacteristic
163#1852C2211yescharacteristic
164#1852C2211yescharacteristic
165#1852C2211yescharacteristic
166#1851C2211yescharacteristic
167#1851C2211yescharacteristic
168#1824C2211yescharacteristic
169#1824C2211yescharacteristic
170#1824C2211yescharacteristic
171#1824C2211yescharacteristic
172#1824C2211yescharacteristic
173#1824C2211yescharacteristic
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×#107C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1762C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1750C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4—21no—
205C24×C4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211#525—24no—
212#525—24no—
213C2×#123—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222#520—24no—
223#520—42no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
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×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4—24no—
244C22×C4⋊C4—21no—
245C22×C4⋊C4—21no—
246C22×C4⋊C4—21no—
247C22×C4⋊C4—21no—
248C22×C4⋊C4—42no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255#485—24no—
256#484—24no—
257#484—42no—
258#482—24no—
259#470—24no—
260#468—24no—
261#452—42no—
262#433—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
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
297#407—42no—
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#401—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
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#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#385—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#384—21no—
405#384C2311yescharacteristic
406#382—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381D411yescharacteristic
412#381D411yescharacteristic
413#380—21no—
414#380—21no—
415#380D411yescharacteristic
416#380D411yescharacteristic
417#380D411yescharacteristic
418#380D411yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428#379D411yescharacteristic
429#379D411yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
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
452#376—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×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—44no—
523C23×C4—82no—
524C23×C4—82no—
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553#123—28no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8#4114yes—
564#121—22no—
565#121—22no—
566#121—22no—
567#121#4114yes—
568#120—28no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—82no—
584C4×D4—82no—
585C4×D4—82no—
586C4×D4—82no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—41no—
594#117—41no—
595#117—44no—
596#117—41no—
597#117—41no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4—44no—
638C2×C4⋊C4—44no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4#4114yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—22no—
710#107—22no—
711#107—22no—
712#107—22no—
713#107—22no—
714#107—41no—
715#107—41no—
716#106—22no—
717#106—22no—
718#106—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754#97—41no—
755C4×C8—41no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
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#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—22no—
803C24—22no—
804C24—22no—
805C24—21no—
806C24—41no—
807C24—41no—
808C24—41no—
809C24—41no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813#41—44no—
814#41—44no—
815#41—44no—
816#41—44no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8C2×#4112yes—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4C2×#4112yes—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—24no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—816no—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2×#4112yes—
929C22×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4H(5,𝔽2)12yes—
932C22×C4C2511yescharacteristic
933Q16—82no—
934SD16—82no—
935M16—82no—
936M16—82no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4C2×#4112yes—
1014C4⋊C4C2×#4112yes—
1015C4⋊C4C2×#4112yes—
1016C4⋊C4C2×#4112yes—
1017C22⋊C4—24no—
1018C22⋊C4—24no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—24no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C42—24no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—22no—
1092C23—44no—
1093C23—44no—
1094C23—44no—
1095C23—44no—
1096C23—44no—
1097C23—44no—
1098C23—44no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23#52512yes—
1106C23#54612yes—
1107C23#57812yes—
1108C23C23×D411yescharacteristic
1109Q8—22no—
1110Q8—22no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—162no—
1118D4—22no—
1119D4—22no—
1120D4—48no—
1121D4—48no—
1122D4—48no—
1123D4—41no—
1124D4—41no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
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—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—84no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4#52512yes—
1226C2×C4#54612yes—
1227C2×C4C22×#4111yescharacteristic
1228C2×C4C22×#4111yescharacteristic
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—416no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#52511yescharacteristic
1271C22C2×#54611yescharacteristic
1272C22#348511yescharacteristic
1273C22C2×#57811yescharacteristic
1274C22#358511yescharacteristic
1275C22#358511yescharacteristic
1276C22#358611yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—42no—
1285C4—41no—
1286C4—41no—
1287C4—42no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4#347511yescharacteristic
1304C4#347511yescharacteristic
1305C4#351311yescharacteristic
1306C4#351311yescharacteristic
1307C2—42no—
1308C2—42no—
1309C2—42no—
1310C2—82no—
1311C2#3615911yescharacteristic
1312C2#6056511yescharacteristic
1313C2#6058911yescharacteristic
1314C2#6117511yescharacteristic
1315C2#6118611yescharacteristic
1316C2#6174711yescharacteristic
1317C2#6177511yescharacteristic
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. #37859C2semidirect
3. #33159C2semidirect
4. #33017C2semidirect
5. #32983C2semidirect
6. #29120C2semidirect
7. #28131C2semidirect
8. #27619C2semidirect
9. #27113C2semidirect
10. #27100C2semidirect
11. #27052C2semidirect
12. #27033C2semidirect
13. #26739C2semidirect
14. #26726C2semidirect
15. #26678C2semidirect
16. #26659C2semidirect
17. #26428C2semidirect
18. #26426C2semidirect
19. #25220C2semidirect
20. #25216C2semidirect
21. #24614C2semidirect
24. #23139C2semidirect
25. #23138C2semidirect
26. #22946C2semidirect
27. #22928C2semidirect
28. #22559C2semidirect
29. #21585C2semidirect
30. #20746C2semidirect
31. #20700C2semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2087C22semidirect
89. #2086C22semidirect
90. #2084C22semidirect
91. #2083C22semidirect
92. #2074C22semidirect
93. #2073C22semidirect
94. #2068C22semidirect
95. #2068C22semidirect
96. #2067C22semidirect
97. #2066C22semidirect
98. #2056C22semidirect
99. #2055C22semidirect
106. #2024C22semidirect
107. #2023C22semidirect
110. #1988C22semidirect
111. #1987C22semidirect
112. #1949C22semidirect
113. #1949C22semidirect
114. #1944C22semidirect
115. #1942C22semidirect
116. #1936C22semidirect
117. #1935C22semidirect
118. #1935C22semidirect
119. #1934C22semidirect
120. #1933C22semidirect
121. #1933C22semidirect
122. #1928C22semidirect
123. #1928C22semidirect
124. #1927C22semidirect
125. #1925C22semidirect
130. #1921C22semidirect
131. #1921C22semidirect
132. #1921C22semidirect
133. #1920C22semidirect
134. #1920C22semidirect
135. #1919C22semidirect
136. #1919C22semidirect
137. #1918C22semidirect
138. #1918C22semidirect
139. #1918C22semidirect
142. #1880C22semidirect
143. #1878C22semidirect
144. #1878C22semidirect
145. #1878C22semidirect
146. #1877C22semidirect
147. #1877C22semidirect
155. #1863C22semidirect
156. #1863C22semidirect
157. #1862C22semidirect
158. #1862C22semidirect
179. #1805C22semidirect
180. #1804C22semidirect
181. #1803C22semidirect
182. #1802C22semidirect
188. #1776C22semidirect
189. C4×#107C22semidirect
190. #1763C22semidirect
191. #1763C22semidirect
192. #1762C22semidirect
193. C4×#103C22semidirect
194. C4×#103C22semidirect
195. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#378592
#342002
#331592
#330172
#329832
#291202
#281312
#276192
#271132
#271002
#270522
#270332
#267392
#267262
#266782
#266592
#264282
#264262
#252202
#252162
#246142
#243892
#240082
#231392
#231382
#229462
#229282
#225592
#215852
#207462
#207002