Finite Group Databasebeta

← #7549534

Subgroups — #7549534

Order 512.

1621 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45108C211yesmaximal, characteristic
2#36006C211yesmaximal, characteristic, complemented
3#32220C211yesmaximal, characteristic, complemented
4#32187C211yesmaximal, characteristic, complemented
5#31806C211yesmaximal, characteristic, complemented
6#31306C211yesmaximal, characteristic, complemented
7#29027C211yesmaximal, characteristic, complemented
8#28925C211yesmaximal, characteristic, complemented
9#27405C211yesmaximal, characteristic, complemented
10#27274C211yesmaximal, characteristic, complemented
11#27224C211yesmaximal, characteristic, complemented
12#27210C211yesmaximal, characteristic, complemented
13#27019C211yesmaximal, characteristic, complemented
14#26780C211yesmaximal, characteristic, complemented
15#26750C211yesmaximal, characteristic, complemented
16#26338C211yesmaximal, characteristic, complemented
17#26223C211yesmaximal, characteristic, complemented
18#25514C211yesmaximal, characteristic, complemented
19#25273C211yesmaximal, characteristic, complemented
20#25105C211yesmaximal, characteristic, complemented
21#25089C211yesmaximal, characteristic, complemented
22#24783C211yesmaximal, characteristic, complemented
23#24517C211yesmaximal, characteristic, complemented
24#24452C211yesmaximal, characteristic
25#23138C211yesmaximal, characteristic, complemented
26#23107C211yesmaximal, characteristic, complemented
27#22911C211yesmaximal, characteristic, complemented
28#22584C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic
30#21397C211yesmaximal, characteristic, complemented
31#21068C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#476C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#467C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#433C2211yescharacteristic, complemented
44C22×#106C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#416C2211yescharacteristic
48#2708—21no—
49#2695—21no—
50#2687—21no—
51#2684—21no—
52#2650—21no—
53#2625C2211yescharacteristic, complemented
54#2595—21no—
55#2560—21no—
56#2547C2211yescharacteristic
57#2534—21no—
58#2530—21no—
59#2520—21no—
60#2519—21no—
61#2511C2211yescharacteristic, complemented
62#2506C2211yescharacteristic, complemented
63#2496C2211yescharacteristic
64#2492C2211yescharacteristic
65#2492C2211yescharacteristic
66#2489—21no—
67#2480—21no—
68#2452C2211yescharacteristic
69#2447C2211yescharacteristic
70#2440C2211yescharacteristic, complemented
71#2437—21no—
72#2435C2211yescharacteristic
73#2432C2211yescharacteristic
74#2429C2211yescharacteristic
75#2427—21no—
76#2417C2211yescharacteristic
77#2417C2211yescharacteristic
78#2402—21no—
79#2395C2211yescharacteristic
80#2369C2211yescharacteristic, complemented
81#2367C2211yescharacteristic
82#2362C2211yescharacteristic
83#2362C2211yescharacteristic, complemented
84#2361C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2354C2211yescharacteristic
87#2346C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2311C2211yescharacteristic
90#2274C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2094C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2072C2211yescharacteristic, complemented
96#2072C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2066C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2043C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2024C2211yescharacteristic, complemented
118#2023C2211yescharacteristic
119#2016C2211yescharacteristic, complemented
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#2001C2211yescharacteristic
123#1988C2211yescharacteristic, complemented
124#1987C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1981C2211yescharacteristic, complemented
129#1971C2211yescharacteristic, complemented
130#1971C2211yescharacteristic, complemented
131#1968C2211yescharacteristic
132#1959C2211yescharacteristic
133#1959C2211yescharacteristic
134#1948C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic, complemented
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1873C2211yescharacteristic, complemented
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1853C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1809C2211yescharacteristic
187#1802C2211yescharacteristic
188#1788C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#542—24no—
215#542—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#124—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#487—42no—
254#476—42no—
255#470—42no—
256#468—24no—
257#467—42no—
258#464—24no—
259#452—42no—
260#450—42no—
261#435—42no—
262#433—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106—42no—
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#418—24no—
278#417—42no—
279#416—24no—
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×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#393—21no—
360#393—21no—
361#393—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
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#387—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#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#382—21no—
428#382—21no—
429#381—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#126—44no—
564#126—82no—
565#125—82no—
566#124—22no—
567#124—22no—
568#124—22no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—44no—
573#123—44no—
574#123—44no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—44no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—82no—
587C22⋊Q8—82no—
588#121—22no—
589#121—44no—
590#121#4114yes—
591#120—44no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—82no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—41no—
610#117—41no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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—44no—
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×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—22no—
716#107—41no—
717#106—22no—
718#106—22no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
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#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102#4114yes—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765#97—41no—
766#97—41no—
767#97—41no—
768C4×C8—41no—
769C4×C8—41no—
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#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826#41—44no—
827#41—44no—
828#41—82no—
829#41—82no—
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—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—81no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4C2×#4112yes—
881C2×D4C2×#4112yes—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—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—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
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×C4—81no—
923C22×C4—81no—
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×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2×#4112yes—
937C22×C4H(5,𝔽2)12yes—
938C22×C4C2511yescharacteristic
939Q16—82no—
940Q16—82no—
941SD16—82no—
942SD16—82no—
943M16—82no—
944M16—82no—
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×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—44no—
969C2×C8C2×#4112yes—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
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—21no—
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—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
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⋊C4C2×#4112yes—
1022C4⋊C4C2×#4112yes—
1023C4⋊C4H(5,𝔽2)12yes—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
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—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—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—21no—
1095C23—21no—
1096C23—22no—
1097C23—21no—
1098C23—21no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23#54612yes—
1119C23C23×D411yescharacteristic
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—162no—
1133Q8—162no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—22no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—82no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
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—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—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
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—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—84no—
1231C2×C4—162no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4#54612yes—
1237C2×C4#57712yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C8—22no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22C2×#54611yescharacteristic
1282C22D4×#4111yescharacteristic
1283C22#348811yescharacteristic
1284C22C2×#57711yescharacteristic
1285C22#358511yescharacteristic
1286C22#358611yescharacteristic
1287C22#358611yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—42no—
1294C4—41no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4#347511yescharacteristic
1315C4#351411yescharacteristic
1316C4#351911yescharacteristic
1317C4#356011yescharacteristic
1318C2—42no—
1319C2—81no—
1320C2—82no—
1321C2—82no—
1322C2#5909111yescharacteristic
1323C2#6118111yescharacteristic
1324C2#6120011yescharacteristic
1325C2#6151811yescharacteristic
1326C2#6154111yescharacteristic
1327C2#6201911yescharacteristic
1328C2#6208711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36006C2semidirect
3. #32220C2semidirect
4. #32187C2semidirect
5. #31806C2semidirect
6. #31306C2semidirect
7. #29027C2semidirect
8. #28925C2semidirect
9. #27405C2semidirect
10. #27274C2semidirect
11. #27224C2semidirect
12. #27210C2semidirect
13. #27019C2semidirect
14. #26780C2semidirect
15. #26750C2semidirect
16. #26338C2semidirect
17. #26223C2semidirect
18. #25514C2semidirect
19. #25273C2semidirect
20. #25105C2semidirect
21. #25089C2semidirect
22. #24783C2semidirect
23. #24517C2semidirect
25. #23138C2semidirect
26. #23107C2semidirect
27. #22911C2semidirect
28. #22584C2semidirect
30. #21397C2semidirect
31. #21068C2semidirect
34. C2×#487C22semidirect
38. C2×#467C22semidirect
43. C2×#433C22semidirect
44. C22×#106C22semidirect
53. #2625C22semidirect
61. #2511C22semidirect
62. #2506C22semidirect
70. #2440C22semidirect
80. #2369C22semidirect
83. #2362C22semidirect
85. #2355C22semidirect
90. #2274C22semidirect
91. #2100C22semidirect
93. #2088C22semidirect
95. #2072C22semidirect
96. #2072C22semidirect
97. #2068C22semidirect
98. #2066C22semidirect
99. #2066C22semidirect
100. #2066C22semidirect
103. #2058C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
108. #2043C22semidirect
117. #2024C22semidirect
119. #2016C22semidirect
123. #1988C22semidirect
124. #1987C22semidirect
128. #1981C22semidirect
129. #1971C22semidirect
130. #1971C22semidirect
134. #1948C22semidirect
135. #1944C22semidirect
136. #1939C22semidirect
139. #1935C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1927C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
146. #1927C22semidirect
147. #1927C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1920C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1917C22semidirect
162. #1894C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
174. #1873C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
179. #1863C22semidirect
182. #1853C22semidirect
184. #1850C22semidirect
191. #1771C22semidirect
192. #1763C22semidirect
193. #1763C22semidirect
196. C4×#103C22semidirect
200. #1753C22semidirect
201. #1736C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#451082
#360062
#322202
#321872
#318062
#313062
#290272
#289252
#274052
#272742
#272242
#272102
#270192
#267802
#267502
#263382
#262232
#255142
#252732
#251052
#250892
#247832
#245172
#244522
#231382
#231072
#229112
#225842
#224242
#213972
#210682