Finite Group Databasebeta

← #6872973

Subgroups — #6872973

Order 512.

1607 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#36386C211yesmaximal, characteristic
2#34941C211yesmaximal, characteristic, complemented
3#33029C211yesmaximal, characteristic, complemented
4#32296C211yesmaximal, characteristic, complemented
5#32283C211yesmaximal, characteristic, complemented
6#31951C211yesmaximal, characteristic, complemented
7#31931C211yesmaximal, characteristic, complemented
8#31302C211yesmaximal, characteristic, complemented
9#31291C211yesmaximal, characteristic, complemented
10#31012C211yesmaximal, characteristic, complemented
11#30991C211yesmaximal, characteristic, complemented
12#30110C211yesmaximal, characteristic, complemented
13#30109C211yesmaximal, characteristic, complemented
14#28658C211yesmaximal, characteristic, complemented
15#28543C211yesmaximal, characteristic, complemented
16#28432C211yesmaximal, characteristic, complemented
17#28203C211yesmaximal, characteristic, complemented
18#27894C211yesmaximal, characteristic, complemented
19#27892C211yesmaximal, characteristic, complemented
20#27765C211yesmaximal, characteristic, complemented
21#27739C211yesmaximal, characteristic, complemented
22#27587C211yesmaximal, characteristic, complemented
23#27585C211yesmaximal, characteristic, complemented
24#25897C211yesmaximal, characteristic
25#25715C211yesmaximal, characteristic, complemented
26#24259C211yesmaximal, characteristic
27#24139C211yesmaximal, characteristic, complemented
28#22837C211yesmaximal, characteristic, complemented
29#22048C211yesmaximal, characteristic, complemented
30#22043C211yesmaximal, characteristic, complemented
31#21508C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#475C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic
45#2861C2211yescharacteristic
46#2857C2211yescharacteristic
47#2850C2211yescharacteristic
48#2574—21no—
49#2574—21no—
50#2567C2211yescharacteristic, complemented
51#2566C2211yescharacteristic
52#2563C2211yescharacteristic
53#2559—21no—
54#2559—21no—
55#2558—21no—
56#2558—21no—
57#2552C2211yescharacteristic, complemented
58#2545C2211yescharacteristic
59#2538C2211yescharacteristic
60#2534—21no—
61#2534—21no—
62#2508—21no—
63#2503C2211yescharacteristic
64#2500C2211yescharacteristic
65#2497C2211yescharacteristic
66#2497C2211yescharacteristic, complemented
67#2454—21no—
68#2435C2211yescharacteristic
69#2432C2211yescharacteristic
70#2423C2211yescharacteristic
71#2423C2211yescharacteristic, complemented
72#2396—21no—
73#2396—21no—
74#2342—21no—
75#2342—21no—
76C4×C4⋊Q8C2211yescharacteristic, complemented
77C4×#125—21no—
78C4×#124C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic, complemented
81#2297C2211yescharacteristic
82#2293—21no—
83C2×#390C2211yescharacteristic
84#2285C2211yescharacteristic
85#2285C2211yescharacteristic, complemented
86C42×Q8C2211yescharacteristic, complemented
87C42×D4C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2093C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2016C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1973C2211yescharacteristic
133#1971C2211yescharacteristic, complemented
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1959C2211yescharacteristic
137#1959C2211yescharacteristic
138#1959C2211yescharacteristic
139#1956C2211yescharacteristic, complemented
140#1956C2211yescharacteristic, complemented
141#1955C2211yescharacteristic
142#1955C2211yescharacteristic
143#1949C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic
174#1854C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1847C2211yescharacteristic, complemented
181#1845C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1834C2211yescharacteristic, complemented
184#1831C2211yescharacteristic, complemented
185#1817C2211yescharacteristic
186#1817C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1767C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#552—42no—
210#552—42no—
211#546—42no—
212#546—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4D411yescharacteristic
238C2×C4×D4D411yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#501—42no—
252#489—42no—
253#479—42no—
254#475—42no—
255#474—42no—
256#464—24no—
257#464—42no—
258#452—24no—
259#450—24no—
260#441—42no—
261#440—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×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#382—21no—
419#382—21no—
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4D411yescharacteristic
446C4×C4⋊C4D411yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4D411yescharacteristic
460C4×C22⋊C4D411yescharacteristic
461C4×C22⋊C4D411yescharacteristic
462C4×C22⋊C4D411yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C43—21no—
466C43C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16#4114yes—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549#126—44no—
550#125—22no—
551#125—22no—
552#125—44no—
553#125—44no—
554#124—22no—
555#124—22no—
556#124—22no—
557#124—41no—
558#124—41no—
559#124—41no—
560#123—44no—
561#123—44no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—44no—
573#121—41no—
574#121—41no—
575#120—44no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×Q8—82no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—42no—
591#117—44no—
592#117—41no—
593#117—41no—
594#117—82no—
595#117—82no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
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—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—41no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#107—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—22no—
726C4⋊C8—41no—
727#103—22no—
728#103—22no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—22no—
768#97—22no—
769#97—41no—
770#97—41no—
771C4×C8—41no—
772C4×C8—41no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810C24—21no—
811C24—21no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821#41—82no—
822#41—82no—
823#41—82no—
824#41—82no—
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—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—42no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8C2×#4112yes—
846C2×D4—22no—
847C2×D4—22no—
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—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—41no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—81no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4C2×#4112yes—
874C22×C4—21no—
875C22×C4—22no—
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—21no—
888C22×C4—22no—
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—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4#13714yes—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2511yescharacteristic
934Q16—44no—
935Q16—82no—
936SD16—44no—
937SD16—82no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8C2×#4112yes—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—41no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
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—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C42—22no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—41no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42H(5,𝔽2)12yes—
1083C42H(5,𝔽2)12yes—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—41no—
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—84no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23C2×#13712yes—
1119C23C23×D411yescharacteristic
1120Q8—22no—
1121Q8—22no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—84no—
1133D4—22no—
1134D4—22no—
1135D4—44no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—84no—
1144D4—162no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
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—44no—
1178C2×C4—44no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—82no—
1229C2×C4—82no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—162no—
1233C2×C4#53512yes—
1234C2×C4#53512yes—
1235C2×C4C2×#13712yes—
1236C2×C4C2×#13712yes—
1237C2×C4#57512yes—
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4#58511yescharacteristic
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—41no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22C2×#53511yescharacteristic
1282C22D4×#4111yescharacteristic
1283C22#348511yescharacteristic
1284C22C22×#13711yescharacteristic
1285C22C2×#57511yescharacteristic
1286C22#358411yescharacteristic
1287C22#358511yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—42no—
1300C4—41no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4#350511yescharacteristic
1315C4#351411yescharacteristic
1316C4#355111yescharacteristic
1317C4#356211yescharacteristic
1318C2—42no—
1319C2—81no—
1320C2—82no—
1321C2—161no—
1322C2#3988111yescharacteristic
1323C2#6080411yescharacteristic
1324C2#6083411yescharacteristic
1325C2#6143811yescharacteristic
1326C2#6145911yescharacteristic
1327C2#6170911yescharacteristic
1328C2#6174111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34941C2semidirect
3. #33029C2semidirect
4. #32296C2semidirect
5. #32283C2semidirect
6. #31951C2semidirect
7. #31931C2semidirect
8. #31302C2semidirect
9. #31291C2semidirect
10. #31012C2semidirect
11. #30991C2semidirect
12. #30110C2semidirect
13. #30109C2semidirect
14. #28658C2semidirect
15. #28543C2semidirect
16. #28432C2semidirect
17. #28203C2semidirect
18. #27894C2semidirect
19. #27892C2semidirect
20. #27765C2semidirect
21. #27739C2semidirect
22. #27587C2semidirect
23. #27585C2semidirect
25. #25715C2semidirect
27. #24139C2semidirect
28. #22837C2semidirect
29. #22048C2semidirect
30. #22043C2semidirect
31. #21508C2semidirect
34. C2×#501C22semidirect
36. C2×#479C22semidirect
37. C2×#475C22semidirect
43. C2×#441C22semidirect
50. #2567C22semidirect
57. #2552C22semidirect
66. #2497C22semidirect
71. #2423C22semidirect
76. C4×C4⋊Q8C22semidirect
80. C4×C22⋊Q8C22semidirect
85. #2285C22semidirect
86. C42×Q8C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2097C22semidirect
91. #2096C22semidirect
92. #2095C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2072C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
106. #2043C22semidirect
116. #2035C22semidirect
117. #2035C22semidirect
118. #2035C22semidirect
122. #2016C22semidirect
126. #2001C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
133. #1971C22semidirect
139. #1956C22semidirect
140. #1956C22semidirect
143. #1949C22semidirect
145. #1935C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1873C22semidirect
174. #1854C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
180. #1847C22semidirect
181. #1845C22semidirect
182. #1836C22semidirect
183. #1834C22semidirect
184. #1831C22semidirect
186. #1817C22semidirect
187. #1805C22semidirect
188. #1803C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1767C22semidirect
199. #1763C22semidirect
201. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#363862
#349412
#330292
#322962
#322832
#319512
#319312
#313022
#312912
#310122
#309912
#301102
#301092
#286582
#285432
#284322
#282032
#278942
#278922
#277652
#277392
#275872
#275852
#258972
#257152
#242592
#241392
#228372
#220482
#220432
#215082