Finite Group Databasebeta

← #7207930

Subgroups — #7207930

Order 512.

1559 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45646C211yesmaximal, characteristic, complemented
2#45508C211yesmaximal, characteristic, complemented
3#32937C211yesmaximal, characteristic, complemented
4#32936C211yesmaximal, characteristic, complemented
5#32709C211yesmaximal, characteristic, complemented
6#32709C211yesmaximal, characteristic, complemented
7#32418C211yesmaximal, characteristic, complemented
8#32019C211yesmaximal, characteristic, complemented
9#32001C211yesmaximal, characteristic, complemented
10#31622C211yesmaximal, characteristic, complemented
11#31615C211yesmaximal, characteristic, complemented
12#30861C211yesmaximal, characteristic, complemented
13#30724C211yesmaximal, characteristic, complemented
14#30704C211yesmaximal, characteristic, complemented
15#30618C211yesmaximal, characteristic, complemented
16#30595C211yesmaximal, characteristic, complemented
17#30586C211yesmaximal, characteristic, complemented
18#30574C211yesmaximal, characteristic, complemented
19#29063C211yesmaximal, characteristic, complemented
20#29061C211yesmaximal, characteristic, complemented
21#28860C211yesmaximal, characteristic, complemented
22#28853C211yesmaximal, characteristic, complemented
23#28566C211yesmaximal, characteristic, complemented
24#28155C211yesmaximal, characteristic, complemented
25#26982C211yesmaximal, characteristic, complemented
26#26979C211yesmaximal, characteristic, complemented
27#25401C211yesmaximal, characteristic, complemented
28#25389C211yesmaximal, characteristic, complemented
29#25251C211yesmaximal, characteristic, complemented
30#25237C211yesmaximal, characteristic, complemented
31#21439C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#485C2211yescharacteristic, complemented
34C2×#482C2211yescharacteristic, complemented
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×#465C2211yescharacteristic, complemented
42C2×#464C2211yescharacteristic, complemented
43C2×#463C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic, complemented
45C2×#435C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2847C2211yescharacteristic
51#2847C2211yescharacteristic
52#2826—21no—
53#2812—21no—
54#2797—21no—
55#2797—21no—
56#2796—21no—
57#2796—21no—
58#2780—21no—
59#2778—21no—
60#2757—21no—
61#2749—21no—
62#2746—21no—
63#2691—21no—
64#2685—21no—
65#2678—21no—
66#2540C2211yescharacteristic
67#2540C2211yescharacteristic
68#2538C2211yescharacteristic
69#2537C2211yescharacteristic
70#2536C2211yescharacteristic
71#2535C2211yescharacteristic
72#2497C2211yescharacteristic
73#2496C2211yescharacteristic
74#2495C2211yescharacteristic
75#2494C2211yescharacteristic
76#2485C2211yescharacteristic
77#2485C2211yescharacteristic
78#2427C2211yescharacteristic
79#2427C2211yescharacteristic
80#2426C2211yescharacteristic
81#2426C2211yescharacteristic
82#2423C2211yescharacteristic
83#2422C2211yescharacteristic
84#2421C2211yescharacteristic
85#2420C2211yescharacteristic
86#2415C2211yescharacteristic
87#2415C2211yescharacteristic
88#2414C2211yescharacteristic
89#2414C2211yescharacteristic
90#2376—21no—
91#2375—21no—
92C4×#120C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2087C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2085C2211yescharacteristic, complemented
102#2084C2211yescharacteristic, complemented
103#2083C2211yescharacteristic, complemented
104#2077C2211yescharacteristic
105#2077C2211yescharacteristic
106#2076C2211yescharacteristic
107#2076C2211yescharacteristic
108#2076C2211yescharacteristic, complemented
109#2075C2211yescharacteristic
110#2075C2211yescharacteristic
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic, complemented
130#2015C2211yescharacteristic, complemented
131#2012C2211yescharacteristic, complemented
132#2001C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic, complemented
140#1999C2211yescharacteristic, complemented
141#1959C2211yescharacteristic, complemented
142#1958C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1948C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1926C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1879C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1875C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic
186#1850C2211yescharacteristic
187#1836C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1779C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1752C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16—42no—
209C22×M16—42no—
210C22×M16—42no—
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×#126—21no—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×#120D411yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251#485—42no—
252#482—42no—
253#470—42no—
254#470—42no—
255#469—42no—
256#469—42no—
257#467—42no—
258#466—42no—
259#465—42no—
260#464—42no—
261#463—42no—
262#440—42no—
263#435—42no—
264#435—42no—
265C8×D4—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
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
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#401—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389—21no—
380#389—21no—
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
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#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386D411yescharacteristic
423#386D411yescharacteristic
424#386D411yescharacteristic
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385D411yescharacteristic
433#385D411yescharacteristic
434#385D411yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#383—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379D411yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—416no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569#126—82no—
570#124—41no—
571#124—41no—
572#124—41no—
573#124—41no—
574#123—44no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
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#121—41no—
607#121—82no—
608#120—42no—
609#120—44no—
610#120—82no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×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—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739#106—41no—
740#106—41no—
741C4⋊C8—22no—
742C4⋊C8—22no—
743C4⋊C8—41no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—22no—
778#97—41no—
779C4×C8—41no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—22no—
819C24—21no—
820C24—21no—
821C24—41no—
822C24—41no—
823C24—41no—
824C24—41no—
825C24—41no—
826C24—41no—
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
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×D4—22no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2511yescharacteristic
956Q16—82no—
957SD16—44no—
958SD16—82no—
959D8—82no—
960M16—44no—
961M16—44no—
962M16—44no—
963M16—44no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—44no—
986C2×C8—44no—
987C2×C8—82no—
988C2×C8H(5,𝔽2)12yes—
989C2×C8H(5,𝔽2)12yes—
990C2×C8H(5,𝔽2)12yes—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
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—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—44no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—82no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23—82no—
1153C23—82no—
1154C23#57512yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164D4—44no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—82no—
1174D4—82no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C8—22no—
1283C8—22no—
1284C8—22no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—88no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22#349611yescharacteristic
1334C22#349611yescharacteristic
1335C22#349611yescharacteristic
1336C22C2×#57511yescharacteristic
1337C22#358411yescharacteristic
1338C22#358511yescharacteristic
1339C22#358611yescharacteristic
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#352911yescharacteristic
1365C4#353211yescharacteristic
1366C4#353911yescharacteristic
1367C4#353911yescharacteristic
1368C2—42no—
1369C2—81no—
1370C2—81no—
1371C2—81no—
1372C2—161no—
1373C2—161no—
1374C2#4547611yescharacteristic
1375C2#6225511yescharacteristic
1376C2#6229411yescharacteristic
1377C2#6230111yescharacteristic
1378C2#6230211yescharacteristic
1379C2#6231011yescharacteristic
1380C2#6232211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45646C2semidirect
2. #45508C2semidirect
3. #32937C2semidirect
4. #32936C2semidirect
5. #32709C2semidirect
6. #32709C2semidirect
7. #32418C2semidirect
8. #32019C2semidirect
9. #32001C2semidirect
10. #31622C2semidirect
11. #31615C2semidirect
12. #30861C2semidirect
13. #30724C2semidirect
14. #30704C2semidirect
15. #30618C2semidirect
16. #30595C2semidirect
17. #30586C2semidirect
18. #30574C2semidirect
19. #29063C2semidirect
20. #29061C2semidirect
21. #28860C2semidirect
22. #28853C2semidirect
23. #28566C2semidirect
24. #28155C2semidirect
25. #26982C2semidirect
26. #26979C2semidirect
27. #25401C2semidirect
28. #25389C2semidirect
29. #25251C2semidirect
30. #25237C2semidirect
31. #21439C2semidirect
33. C2×#485C22semidirect
34. C2×#482C22semidirect
41. C2×#465C22semidirect
42. C2×#464C22semidirect
43. C2×#463C22semidirect
44. C2×#440C22semidirect
93. #2101C22semidirect
94. #2099C22semidirect
95. #2095C22semidirect
96. #2092C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2087C22semidirect
100. #2085C22semidirect
101. #2085C22semidirect
102. #2084C22semidirect
103. #2083C22semidirect
108. #2076C22semidirect
111. #2066C22semidirect
112. #2065C22semidirect
113. #2055C22semidirect
114. #2042C22semidirect
115. #2042C22semidirect
122. #2035C22semidirect
129. #2033C22semidirect
130. #2015C22semidirect
131. #2012C22semidirect
132. #2001C22semidirect
139. #2000C22semidirect
140. #1999C22semidirect
141. #1959C22semidirect
142. #1958C22semidirect
143. #1949C22semidirect
144. #1948C22semidirect
145. #1943C22semidirect
146. #1942C22semidirect
147. #1936C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
150. #1934C22semidirect
151. #1928C22semidirect
152. #1926C22semidirect
153. #1920C22semidirect
154. #1918C22semidirect
165. #1893C22semidirect
168. #1892C22semidirect
169. #1879C22semidirect
170. #1878C22semidirect
171. #1875C22semidirect
172. #1873C22semidirect
176. #1865C22semidirect
177. #1865C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
187. #1836C22semidirect
194. #1805C22semidirect
195. #1802C22semidirect
197. #1762C22semidirect
198. C4×#103C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#456462
#455082
#329372
#329362
#327092
#324182
#320192
#320012
#316222
#316152
#308612
#307242
#307042
#306182
#305952
#305862
#305742
#290632
#290612
#288602
#288532
#285662
#281552
#269822
#269792
#254012
#253892
#252512
#252372
#214392