Finite Group Databasebeta

← #6473601

Subgroups — #6473601

Order 512.

1641 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35080C211yesmaximal, characteristic, complemented
2#35023C211yesmaximal, characteristic, complemented
3#33057C211yesmaximal, characteristic, complemented
4#33050C211yesmaximal, characteristic, complemented
5#32937C211yesmaximal, characteristic, complemented
6#32936C211yesmaximal, characteristic
7#30295C211yesmaximal, characteristic, complemented
8#30249C211yesmaximal, characteristic, complemented
9#29744C211yesmaximal, characteristic, complemented
10#29744C211yesmaximal, characteristic, complemented
11#28935C211yesmaximal, characteristic, complemented
12#28924C211yesmaximal, characteristic, complemented
13#28913C211yesmaximal, characteristic, complemented
14#28910C211yesmaximal, characteristic, complemented
15#28872C211yesmaximal, characteristic, complemented
16#28859C211yesmaximal, characteristic, complemented
17#28853C211yesmaximal, characteristic, complemented
18#28842C211yesmaximal, characteristic, complemented
19#28089C211yesmaximal, characteristic, complemented
20#28084C211yesmaximal, characteristic, complemented
21#28077C211yesmaximal, characteristic, complemented
22#28064C211yesmaximal, characteristic, complemented
23#26986C211yesmaximal, characteristic, complemented
24#26975C211yesmaximal, characteristic, complemented
25#26970C211yesmaximal, characteristic, complemented
26#26959C211yesmaximal, characteristic, complemented
27#22190C211yesmaximal, characteristic, complemented
28#22188C211yesmaximal, characteristic, complemented
29#21540C211yesmaximal, characteristic, complemented
30C4×#468C211yesmaximal, characteristic, complemented
31C22⋊C4×M16C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#489C2211yescharacteristic, complemented
34C2×#488C2211yescharacteristic, complemented
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#466C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×C4×SD16C2211yescharacteristic, complemented
45C2×#407C2211yescharacteristic
46C2×C4×M16C2211yescharacteristic
47C2×C4×M16C2211yescharacteristic
48#2857C2211yescharacteristic
49#2851C2211yescharacteristic
50#2850C2211yescharacteristic
51#2850C2211yescharacteristic
52#2848C2211yescharacteristic
53#2848C2211yescharacteristic
54#2847C2211yescharacteristic
55#2847C2211yescharacteristic
56#2653—21no—
57#2649—21no—
58#2643—21no—
59#2622—21no—
60#2597—21no—
61#2595—21no—
62#2578—21no—
63#2576—21no—
64#2510—21no—
65#2495C2211yescharacteristic
66#2495C2211yescharacteristic
67#2494C2211yescharacteristic
68#2494C2211yescharacteristic
69#2492C2211yescharacteristic
70#2491C2211yescharacteristic
71#2490C2211yescharacteristic
72#2489C2211yescharacteristic
73#2472—21no—
74#2450—21no—
75#2427C2211yescharacteristic
76#2427C2211yescharacteristic
77#2426C2211yescharacteristic
78#2426C2211yescharacteristic
79#2423C2211yescharacteristic
80#2422C2211yescharacteristic
81#2421C2211yescharacteristic
82#2420C2211yescharacteristic
83#2418—21no—
84#2337—21no—
85#2335—21no—
86#2321—21no—
87#2318—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C4×#121C2211yescharacteristic
91C4×#121C2211yescharacteristic
92C2×C4×C22⋊C4C2211yescharacteristic
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2092C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2059C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2058C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2015C2211yescharacteristic, complemented
118#2015C2211yescharacteristic, complemented
119#2012C2211yescharacteristic, complemented
120#2012C2211yescharacteristic, complemented
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1993C2211yescharacteristic, complemented
126#1991C2211yescharacteristic, complemented
127#1973C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1959C2211yescharacteristic, complemented
130#1958C2211yescharacteristic, complemented
131#1943C2211yescharacteristic, complemented
132#1942C2211yescharacteristic, complemented
133#1936C2211yescharacteristic, complemented
134#1936C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1879C2211yescharacteristic, complemented
170#1879C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1864C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1836C2211yescharacteristic, complemented
178#1835C2211yescharacteristic, complemented
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1807C2211yescharacteristic
186#1807C2211yescharacteristic
187#1776C2211yescharacteristic, complemented
188C4×#107C2211yescharacteristic, complemented
189#1763C2211yescharacteristic, complemented
190#1762C2211yescharacteristic, complemented
191C4×#103C2211yescharacteristic, complemented
192C4×#102C2211yescharacteristic, complemented
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1728C2211yescharacteristic
202#1728C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16—24no—
209C22×M16—42no—
210C22×M16—42no—
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C22×C22⋊C4D411yescharacteristic
247C22×C22⋊C4D411yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#489—42no—
251#488—42no—
252#470—24no—
253#470—42no—
254#469—24no—
255#469—42no—
256#468—24no—
257#468—24no—
258#467—42no—
259#466—42no—
260#440—42no—
261C4×SD16—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298#407—24no—
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C4×M16—42no—
304C4×M16—42no—
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#401—21no—
314#401—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#383—21no—
421#383—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C2×#95D411yescharacteristic
463C2×#95D411yescharacteristic
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
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—41no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—416no—
555C2×M16#4114yes—
556C2×M16#4114yes—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573#125—41no—
574#125—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—82no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#120—44no—
607#120—82no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—82no—
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⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
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⋊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—42no—
690C2×C22⋊C4—42no—
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×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—41no—
706C2×C42—41no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—22no—
718#107—22no—
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#106—22no—
724#106—22no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757#97—22no—
758#97—22no—
759#97—41no—
760#97—41no—
761C4×C8—22no—
762C4×C8—22no—
763C4×C8—41no—
764C4×C8—41no—
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#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—22no—
812C24—22no—
813C24—21no—
814C24—21no—
815C24—41no—
816C24—41no—
817C24—41no—
818C24—41no—
819C24—41no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
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—42no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
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×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
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—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2×#4112yes—
941C22×C4C2×#4112yes—
942C22×C4C2511yescharacteristic
943Q16—82no—
944SD16—44no—
945SD16—44no—
946D8—82no—
947M16—28no—
948M16—44no—
949M16—44no—
950M16—44no—
951M16—44no—
952M16—44no—
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×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—44no—
972C2×C8—44no—
973C2×C8C2×#4112yes—
974C2×C8C2×#4112yes—
975C2×C8C2×#4112yes—
976C2×C8C2×#4112yes—
977C2×C8H(5,𝔽2)12yes—
978C2×C8H(5,𝔽2)12yes—
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—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—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
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—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
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—81no—
1049C22⋊C4—81no—
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—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—41no—
1079C42—41no—
1080C42—41no—
1081C42—41no—
1082C42—42no—
1083C42—42no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—44no—
1108C23—44no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—82no—
1124C23—82no—
1125C23—82no—
1126C23—82no—
1127C23—82no—
1128C23#53212yes—
1129C23#57512yes—
1130C23C23×D411yescharacteristic
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—162no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—44no—
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—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—82no—
1243C2×C4—82no—
1244C2×C4—82no—
1245C2×C4—82no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4#53212yes—
1249C2×C4#57512yes—
1250C2×C4C22×#4111yescharacteristic
1251C2×C4C22×#4111yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4C2×H(5,𝔽2)11yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C8—22no—
1257C8—22no—
1258C8—22no—
1259C8—22no—
1260C8—22no—
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—88no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22C2×#53211yescharacteristic
1301C22#349611yescharacteristic
1302C22#349611yescharacteristic
1303C22C2×#57511yescharacteristic
1304C22C2×#57511yescharacteristic
1305C22#358511yescharacteristic
1306C22#358611yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#345911yescharacteristic
1333C4#346011yescharacteristic
1334C4#349011yescharacteristic
1335C4#349311yescharacteristic
1336C2—42no—
1337C2—42no—
1338C2—81no—
1339C2—161no—
1340C2—161no—
1341C2#3500311yescharacteristic
1342C2#6070211yescharacteristic
1343C2#6070311yescharacteristic
1344C2#6229711yescharacteristic
1345C2#6230111yescharacteristic
1346C2#6230211yescharacteristic
1347C2#6230411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32936C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35080C2semidirect
2. #35023C2semidirect
3. #33057C2semidirect
4. #33050C2semidirect
5. #32937C2semidirect
7. #30295C2semidirect
8. #30249C2semidirect
9. #29744C2semidirect
10. #29744C2semidirect
11. #28935C2semidirect
12. #28924C2semidirect
13. #28913C2semidirect
14. #28910C2semidirect
15. #28872C2semidirect
16. #28859C2semidirect
17. #28853C2semidirect
18. #28842C2semidirect
19. #28089C2semidirect
20. #28084C2semidirect
21. #28077C2semidirect
22. #28064C2semidirect
23. #26986C2semidirect
24. #26975C2semidirect
25. #26970C2semidirect
26. #26959C2semidirect
27. #22190C2semidirect
28. #22188C2semidirect
29. #21540C2semidirect
30. C4×#468C2semidirect
31. C22⋊C4×M16C2semidirect
33. C2×#489C22semidirect
34. C2×#488C22semidirect
43. C2×#440C22semidirect
44. C2×C4×SD16C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2092C22semidirect
96. #2092C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
105. #2059C22semidirect
106. #2059C22semidirect
107. #2058C22semidirect
108. #2057C22semidirect
117. #2015C22semidirect
118. #2015C22semidirect
119. #2012C22semidirect
120. #2012C22semidirect
125. #1993C22semidirect
126. #1991C22semidirect
127. #1973C22semidirect
128. #1968C22semidirect
129. #1959C22semidirect
130. #1958C22semidirect
131. #1943C22semidirect
132. #1942C22semidirect
133. #1936C22semidirect
134. #1936C22semidirect
135. #1936C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
139. #1934C22semidirect
140. #1934C22semidirect
141. #1934C22semidirect
142. #1933C22semidirect
143. #1933C22semidirect
144. #1933C22semidirect
145. #1927C22semidirect
146. #1927C22semidirect
147. #1925C22semidirect
148. #1925C22semidirect
149. #1920C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1920C22semidirect
169. #1879C22semidirect
170. #1879C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
173. #1864C22semidirect
174. #1864C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
177. #1836C22semidirect
178. #1835C22semidirect
187. #1776C22semidirect
188. C4×#107C22semidirect
189. #1763C22semidirect
190. #1762C22semidirect
191. C4×#103C22semidirect
192. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#350802
#350232
#330572
#330502
#329372
#329362
#302952
#302492
#297442
#289352
#289242
#289132
#289102
#288722
#288592
#288532
#288422
#280892
#280842
#280772
#280642
#269862
#269752
#269702
#269592
#221902
#221882
#215402
C4×#4682
C22⋊C4×M162