Finite Group Databasebeta

← #6507942

Subgroups — #6507942

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37381C211yesmaximal, characteristic, complemented
2#35516C211yesmaximal, characteristic
3#29120C211yesmaximal, characteristic, complemented
4#29003C211yesmaximal, characteristic, complemented
5#29001C211yesmaximal, characteristic, complemented
6#28996C211yesmaximal, characteristic, complemented
7#28994C211yesmaximal, characteristic, complemented
8#28870C211yesmaximal, characteristic, complemented
9#28868C211yesmaximal, characteristic, complemented
10#28861C211yesmaximal, characteristic, complemented
11#28859C211yesmaximal, characteristic, complemented
12#28326C211yesmaximal, characteristic, complemented
13#27985C211yesmaximal, characteristic, complemented
14#27959C211yesmaximal, characteristic, complemented
15#26988C211yesmaximal, characteristic, complemented
16#26983C211yesmaximal, characteristic, complemented
17#26972C211yesmaximal, characteristic, complemented
18#26967C211yesmaximal, characteristic, complemented
19#25049C211yesmaximal, characteristic, complemented
20#25044C211yesmaximal, characteristic, complemented
21#25039C211yesmaximal, characteristic, complemented
22#25036C211yesmaximal, characteristic, complemented
23#24559C211yesmaximal, characteristic, complemented
24#24556C211yesmaximal, characteristic, complemented
25#24389C211yesmaximal, characteristic
26#24389C211yesmaximal, characteristic
27#22089C211yesmaximal, characteristic, complemented
28#22087C211yesmaximal, characteristic, complemented
29#21465C211yesmaximal, characteristic, complemented
30#21461C211yesmaximal, characteristic, complemented
31#20529C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#483C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#441C2211yescharacteristic, complemented
43C2×#440C2211yescharacteristic, complemented
44C2×C4×Q16C2211yescharacteristic, complemented
45C2×C4×SD16C2211yescharacteristic, complemented
46C2×#407C2211yescharacteristic
47C2×#407C2211yescharacteristic
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2788—21no—
51#2788—21no—
52#2771—21no—
53#2770—21no—
54#2770—21no—
55#2764—21no—
56#2736—21no—
57#2735—21no—
58#2628C2211yescharacteristic
59#2621C2211yescharacteristic
60#2495C2211yescharacteristic
61#2495C2211yescharacteristic
62#2492C2211yescharacteristic
63#2492C2211yescharacteristic
64#2487—21no—
65#2486—21no—
66#2485—21no—
67#2485—21no—
68#2429C2211yescharacteristic
69#2429C2211yescharacteristic
70#2423C2211yescharacteristic
71#2423C2211yescharacteristic
72#2422C2211yescharacteristic
73#2422C2211yescharacteristic
74#2421C2211yescharacteristic
75#2421C2211yescharacteristic
76#2421C2211yescharacteristic
77#2421C2211yescharacteristic
78#2420C2211yescharacteristic
79#2420C2211yescharacteristic
80#2419—21no—
81#2419—21no—
82#2418—21no—
83#2418—21no—
84#2323C2211yescharacteristic
85#2323C2211yescharacteristic
86#2317C2211yescharacteristic
87#2316C2211yescharacteristic
88#2311C2211yescharacteristic
89#2280C2211yescharacteristic
90C2×#380C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2092C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2073C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2072C2211yescharacteristic, complemented
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2024C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#2016C2211yescharacteristic, complemented
118#2013C2211yescharacteristic, complemented
119#2001C2211yescharacteristic
120#2001C2211yescharacteristic
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#1993C2211yescharacteristic, complemented
124#1990C2211yescharacteristic, complemented
125#1973C2211yescharacteristic, complemented
126#1971C2211yescharacteristic, complemented
127#1969C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1960C2211yescharacteristic, complemented
130#1956C2211yescharacteristic, complemented
131#1944C2211yescharacteristic, complemented
132#1943C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1919C2211yescharacteristic, complemented
146#1918C2211yescharacteristic, complemented
147#1895C2211yescharacteristic
148#1895C2211yescharacteristic
149#1894C2211yescharacteristic
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic
152#1894C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1878C2211yescharacteristic, complemented
156#1878C2211yescharacteristic, complemented
157#1877C2211yescharacteristic, complemented
158#1877C2211yescharacteristic, complemented
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1865C2211yescharacteristic, complemented
164#1865C2211yescharacteristic, complemented
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1847C2211yescharacteristic, complemented
176#1846C2211yescharacteristic, complemented
177#1836C2211yescharacteristic, complemented
178#1835C2211yescharacteristic, complemented
179#1824C2211yescharacteristic
180#1823C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1763C2211yescharacteristic, complemented
188#1762C2211yescharacteristic, complemented
189C4×#103C2211yescharacteristic, complemented
190C4×#102C2211yescharacteristic, complemented
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215#525—42no—
216#525—42no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231#520—42no—
232#520—42no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251#484—24no—
252#483—24no—
253#470—42no—
254#470—42no—
255#468—42no—
256#468—42no—
257#452—24no—
258#452—24no—
259#441—42no—
260#440—42no—
261C4×Q16—42no—
262C4×SD16—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299#407—24no—
300#407—24no—
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#391—21no—
358#391—21no—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—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#384C2311yescharacteristic
422#384C2311yescharacteristic
423#383—21no—
424#383—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#381D411yescharacteristic
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380D411yescharacteristic
440#380D411yescharacteristic
441#380D411yescharacteristic
442#380D411yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379D411yescharacteristic
456#379D411yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C2×#95—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#123—44no—
565#123—82no—
566#123—82no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583#121—22no—
584#121—22no—
585#121—41no—
586#121—41no—
587#120—44no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—44no—
603C4×D4—44no—
604#117—41no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—41no—
609#117—41no—
610#117—44no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
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—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—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—44no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
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⋊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—82no—
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#107—22no—
713#107—22no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—22no—
719#106—22no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754C22⋊C8#4114yes—
755C22⋊C8#4114yes—
756#97—41no—
757#97—41no—
758#97—41no—
759#97—41no—
760C4×C8—41no—
761C4×C8—41no—
762C4×C8—41no—
763C4×C8—41no—
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#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#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812C24—21no—
813C24—22no—
814C24—41no—
815C24—41no—
816C24—41no—
817C24—41no—
818C24—41no—
819C24—41no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823#41—44no—
824#41—44no—
825#41—44no—
826#41—44no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8H(5,𝔽2)12yes—
848C2×D4—24no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4H(5,𝔽2)12yes—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—24no—
868C22×C4—21no—
869C22×C4—22no—
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—22no—
883C22×C4—22no—
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—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—82no—
911C22×C4—82no—
912C22×C4—82no—
913C22×C4—82no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2×#4112yes—
934C22×C4C2×#4112yes—
935C22×C4C2511yescharacteristic
936Q16—44no—
937Q16—44no—
938SD16—44no—
939SD16—44no—
940M16—82no—
941M16—82no—
942M16—82no—
943M16—82no—
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—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8C2×#4112yes—
965C2×C8C2×#4112yes—
966C2×C8C2×#4112yes—
967C2×C8C2×#4112yes—
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—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
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⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C22⋊C4—41no—
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—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
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—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—44no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—82no—
1108C23—82no—
1109C23—82no—
1110C23—82no—
1111C23—82no—
1112C23—82no—
1113C23#53212yes—
1114C23C23×D411yescharacteristic
1115Q8—22no—
1116Q8—22no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—162no—
1128D4—22no—
1129D4—22no—
1130D4—48no—
1131D4—41no—
1132D4—41no—
1133D4—84no—
1134D4—84no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
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—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—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—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—82no—
1226C2×C4—82no—
1227C2×C4—82no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4#53212yes—
1233C2×C4C22×#4111yescharacteristic
1234C2×C4C22×#4111yescharacteristic
1235C2×C4C2×H(5,𝔽2)11yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—41no—
1271C22—88no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×#53211yescharacteristic
1277C22#348411yescharacteristic
1278C22#348511yescharacteristic
1279C22#358511yescharacteristic
1280C22#358611yescharacteristic
1281C22#358611yescharacteristic
1282C22#358611yescharacteristic
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4#351311yescharacteristic
1310C4#351311yescharacteristic
1311C4#351311yescharacteristic
1312C4#351311yescharacteristic
1313C2—42no—
1314C2—81no—
1315C2—81no—
1316C2—82no—
1317C2#3539411yescharacteristic
1318C2#6070911yescharacteristic
1319C2#6071111yescharacteristic
1320C2#6165411yescharacteristic
1321C2#6165511yescharacteristic
1322C2#6177511yescharacteristic
1323C2#6177911yescharacteristic
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. #37381C2semidirect
3. #29120C2semidirect
4. #29003C2semidirect
5. #29001C2semidirect
6. #28996C2semidirect
7. #28994C2semidirect
8. #28870C2semidirect
9. #28868C2semidirect
10. #28861C2semidirect
11. #28859C2semidirect
12. #28326C2semidirect
13. #27985C2semidirect
14. #27959C2semidirect
15. #26988C2semidirect
16. #26983C2semidirect
17. #26972C2semidirect
18. #26967C2semidirect
19. #25049C2semidirect
20. #25044C2semidirect
21. #25039C2semidirect
22. #25036C2semidirect
23. #24559C2semidirect
24. #24556C2semidirect
27. #22089C2semidirect
28. #22087C2semidirect
29. #21465C2semidirect
30. #21461C2semidirect
31. #20529C2semidirect
42. C2×#441C22semidirect
43. C2×#440C22semidirect
44. C2×C4×Q16C22semidirect
45. C2×C4×SD16C22semidirect
91. #2097C22semidirect
92. #2092C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
95. #2084C22semidirect
96. #2083C22semidirect
101. #2074C22semidirect
102. #2074C22semidirect
103. #2074C22semidirect
104. #2073C22semidirect
105. #2072C22semidirect
106. #2072C22semidirect
115. #2024C22semidirect
116. #2023C22semidirect
117. #2016C22semidirect
118. #2013C22semidirect
123. #1993C22semidirect
124. #1990C22semidirect
125. #1973C22semidirect
126. #1971C22semidirect
127. #1969C22semidirect
128. #1968C22semidirect
129. #1960C22semidirect
130. #1956C22semidirect
131. #1944C22semidirect
132. #1943C22semidirect
133. #1942C22semidirect
134. #1941C22semidirect
135. #1936C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
139. #1934C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1921C22semidirect
144. #1920C22semidirect
145. #1919C22semidirect
146. #1918C22semidirect
155. #1878C22semidirect
156. #1878C22semidirect
157. #1877C22semidirect
158. #1877C22semidirect
163. #1865C22semidirect
164. #1865C22semidirect
165. #1865C22semidirect
166. #1864C22semidirect
167. #1863C22semidirect
168. #1863C22semidirect
169. #1863C22semidirect
170. #1862C22semidirect
175. #1847C22semidirect
176. #1846C22semidirect
177. #1836C22semidirect
178. #1835C22semidirect
187. #1763C22semidirect
188. #1762C22semidirect
189. C4×#103C22semidirect
190. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#373812
#355162
#291202
#290032
#290012
#289962
#289942
#288702
#288682
#288612
#288592
#283262
#279852
#279592
#269882
#269832
#269722
#269672
#250492
#250442
#250392
#250362
#245592
#245562
#243892
#220892
#220872
#214652
#214612
#205292