Finite Group Databasebeta

← #7569232

Subgroups — #7569232

Order 512.

1525 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59440C211yesmaximal, characteristic, complemented
2#36269C211yesmaximal, characteristic
3#32233C211yesmaximal, characteristic, complemented
4#32142C211yesmaximal, characteristic, complemented
5#32040C211yesmaximal, characteristic, complemented
6#30731C211yesmaximal, characteristic, complemented
7#29336C211yesmaximal, characteristic, complemented
8#29006C211yesmaximal, characteristic, complemented
9#28582C211yesmaximal, characteristic, complemented
10#28568C211yesmaximal, characteristic, complemented
11#28087C211yesmaximal, characteristic, complemented
12#27344C211yesmaximal, characteristic, complemented
13#27111C211yesmaximal, characteristic, complemented
14#27077C211yesmaximal, characteristic, complemented
15#26760C211yesmaximal, characteristic, complemented
16#26750C211yesmaximal, characteristic, complemented
17#26683C211yesmaximal, characteristic, complemented
18#26224C211yesmaximal, characteristic, complemented
19#26217C211yesmaximal, characteristic, complemented
20#26148C211yesmaximal, characteristic, complemented
21#25562C211yesmaximal, characteristic, complemented
22#25552C211yesmaximal, characteristic, complemented
23#24961C211yesmaximal, characteristic, complemented
24#24795C211yesmaximal, characteristic, complemented
25#23138C211yesmaximal, characteristic, complemented
26#23121C211yesmaximal, characteristic, complemented
27#22925C211yesmaximal, characteristic, complemented
28#22503C211yesmaximal, characteristic, complemented
29#22499C211yesmaximal, characteristic, complemented
30#21583C211yesmaximal, characteristic, complemented
31#21034C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#428C2211yescharacteristic
42#2861—21no—
43#2850C2211yescharacteristic
44#2772—21no—
45#2739—21no—
46#2611—21no—
47#2610—21no—
48#2601—21no—
49#2590—21no—
50#2569—21no—
51#2559—21no—
52#2557—21no—
53#2550C2211yescharacteristic
54#2540C2211yescharacteristic
55#2521—21no—
56#2511C2211yescharacteristic
57#2508C2211yescharacteristic
58#2496C2211yescharacteristic
59#2492C2211yescharacteristic
60#2490C2211yescharacteristic
61#2485C2211yescharacteristic
62#2481—21no—
63#2464—21no—
64#2444—21no—
65#2421C2211yescharacteristic
66#2417C2211yescharacteristic
67#2417C2211yescharacteristic
68#2417C2211yescharacteristic
69#2415C2211yescharacteristic
70#2414C2211yescharacteristic
71#2367C2211yescharacteristic
72#2362C2211yescharacteristic
73#2362C2211yescharacteristic
74#2361C2211yescharacteristic
75#2352—21no—
76#2352C2211yescharacteristic
77#2352C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79#2344C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2293—21no—
83C2×#389C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2096C2211yescharacteristic
89#2088C2211yescharacteristic
90#2085C2211yescharacteristic
91#2083C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2074C2211yescharacteristic
96#2073C2211yescharacteristic
97#2068C2211yescharacteristic
98#2065C2211yescharacteristic
99#2059C2211yescharacteristic
100#2057C2211yescharacteristic
101#2056C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2026C2211yescharacteristic
112#2024C2211yescharacteristic
113#2015C2211yescharacteristic
114#2001C2211yescharacteristic
115#2001C2211yescharacteristic
116#2000C2211yescharacteristic
117#1991C2211yescharacteristic
118#1990C2211yescharacteristic
119#1989C2211yescharacteristic
120#1987C2211yescharacteristic
121#1968C2211yescharacteristic
122#1942C2211yescharacteristic
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1935C2211yescharacteristic
126#1935C2211yescharacteristic
127#1933C2211yescharacteristic
128#1933C2211yescharacteristic
129#1928C2211yescharacteristic
130#1928C2211yescharacteristic
131#1927C2211yescharacteristic
132#1927C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1924C2211yescharacteristic
136#1924C2211yescharacteristic
137#1921C2211yescharacteristic
138#1921C2211yescharacteristic
139#1921C2211yescharacteristic
140#1920C2211yescharacteristic
141#1920C2211yescharacteristic
142#1920C2211yescharacteristic
143#1919C2211yescharacteristic
144#1919C2211yescharacteristic
145#1918C2211yescharacteristic
146#1918C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1916C2211yescharacteristic
150#1916C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic
157#1880C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1877C2211yescharacteristic
161#1875C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1872C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1824C2211yescharacteristic
185#1809C2211yescharacteristic
186#1805C2211yescharacteristic
187#1802C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#102C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1749C2211yescharacteristic
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#555—24no—
210#555—42no—
211#552—24no—
212#552—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C2×#117—21no—
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C42C2311yescharacteristic
254#485—24no—
255#484—24no—
256#470—42no—
257#468—24no—
258#468—42no—
259#436—42no—
260#436—42no—
261#428—24no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#392—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390D411yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388D411yescharacteristic
381#388D411yescharacteristic
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386D411yescharacteristic
404#386D411yescharacteristic
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380D411yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376—21no—
446C2×#95—21no—
447C43—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2×D411yescharacteristic
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538#126—44no—
539#126—82no—
540#125—22no—
541#125—41no—
542#125—44no—
543#124—44no—
544#124—41no—
545#124—41no—
546#124—44no—
547#123—44no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—42no—
565#121—44no—
566#121—41no—
567#121—41no—
568C4×Q8—22no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—44no—
581C4×D4—44no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—44no—
586#117—44no—
587#117—41no—
588#117—41no—
589#117—41no—
590#117—41no—
591#117—82no—
592#117#4114yes—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
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—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—82no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—21no—
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—21no—
695C2×C42—21no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—22no—
706#107—22no—
707#107—41no—
708#107#4114yes—
709#106—22no—
710#106—22no—
711#106—22no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744#97—41no—
745#97—41no—
746C4×C8—41no—
747C4×C8—41no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C2×#4112yes—
898C22×C4H(5,𝔽2)12yes—
899C22×C4C2511yescharacteristic
900Q16—82no—
901SD16—82no—
902M16—44no—
903M16—82no—
904M16—82no—
905M16—82no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8C2×#4112yes—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4C2×#4112yes—
984C4⋊C4C2×#4112yes—
985C4⋊C4C2×#4112yes—
986C4⋊C4C2×#4112yes—
987C22⋊C4—24no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C42—24no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23#54612yes—
1075C23C23×D411yescharacteristic
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—41no—
1083Q8—41no—
1084Q8—162no—
1085D4—44no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—82no—
1091D4—82no—
1092D4—84no—
1093D4—162no—
1094D4—162no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—84no—
1184C2×C4—82no—
1185C2×C4—82no—
1186C2×C4—84no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—162no—
1190C2×C4#54612yes—
1191C2×C4#57512yes—
1192C2×C4C22×#4111yescharacteristic
1193C2×C4C22×#4111yescharacteristic
1194C2×C4C2×H(5,𝔽2)11yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C8—22no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22C2×#54611yescharacteristic
1235C22D4×#4111yescharacteristic
1236C22#348511yescharacteristic
1237C22C2×#57511yescharacteristic
1238C22#358511yescharacteristic
1239C22#358611yescharacteristic
1240C22#358611yescharacteristic
1241C4—22no—
1242C4—22no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—42no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4#348011yescharacteristic
1268C4#349411yescharacteristic
1269C4#351211yescharacteristic
1270C4#356011yescharacteristic
1271C2—42no—
1272C2—81no—
1273C2—81no—
1274C2—161no—
1275C2#5914111yescharacteristic
1276C2#6116311yescharacteristic
1277C2#6122211yescharacteristic
1278C2#6146411yescharacteristic
1279C2#6151211yescharacteristic
1280C2#6172411yescharacteristic
1281C2#6177711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36269C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59440C2semidirect
3. #32233C2semidirect
4. #32142C2semidirect
5. #32040C2semidirect
6. #30731C2semidirect
7. #29336C2semidirect
8. #29006C2semidirect
9. #28582C2semidirect
10. #28568C2semidirect
11. #28087C2semidirect
12. #27344C2semidirect
13. #27111C2semidirect
14. #27077C2semidirect
15. #26760C2semidirect
16. #26750C2semidirect
17. #26683C2semidirect
18. #26224C2semidirect
19. #26217C2semidirect
20. #26148C2semidirect
21. #25562C2semidirect
22. #25552C2semidirect
23. #24961C2semidirect
24. #24795C2semidirect
25. #23138C2semidirect
26. #23121C2semidirect
27. #22925C2semidirect
28. #22503C2semidirect
29. #22499C2semidirect
30. #21583C2semidirect
31. #21034C2semidirect

Maximal subgroups

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

subgroupindex
#594402
#362692
#322332
#321422
#320402
#307312
#293362
#290062
#285822
#285682
#280872
#273442
#271112
#270772
#267602
#267502
#266832
#262242
#262172
#261482
#255622
#255522
#249612
#247952
#231382
#231212
#229252
#225032
#224992
#215832
#210342