Finite Group Databasebeta

← #7526355

Subgroups — #7526355

Order 512.

1657 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59290C211yesmaximal, characteristic, complemented
2#36432C211yesmaximal, characteristic
3#31970C211yesmaximal, characteristic, complemented
4#31610C211yesmaximal, characteristic, complemented
5#31586C211yesmaximal, characteristic, complemented
6#31374C211yesmaximal, characteristic, complemented
7#29027C211yesmaximal, characteristic, complemented
8#28841C211yesmaximal, characteristic, complemented
9#27864C211yesmaximal, characteristic, complemented
10#27706C211yesmaximal, characteristic, complemented
11#27669C211yesmaximal, characteristic, complemented
12#27535C211yesmaximal, characteristic, complemented
13#27522C211yesmaximal, characteristic, complemented
14#27311C211yesmaximal, characteristic, complemented
15#27303C211yesmaximal, characteristic, complemented
16#27158C211yesmaximal, characteristic, complemented
17#26689C211yesmaximal, characteristic, complemented
18#26112C211yesmaximal, characteristic, complemented
19#25975C211yesmaximal, characteristic, complemented
20#25963C211yesmaximal, characteristic, complemented
21#24951C211yesmaximal, characteristic, complemented
22#24602C211yesmaximal, characteristic, complemented
23#24588C211yesmaximal, characteristic, complemented
24#24051C211yesmaximal, characteristic
25#22977C211yesmaximal, characteristic, complemented
26#22904C211yesmaximal, characteristic, complemented
27#22583C211yesmaximal, characteristic, complemented
28#22571C211yesmaximal, characteristic, complemented
29#22421C211yesmaximal, characteristic
30#20875C211yesmaximal, characteristic, complemented
31#20737C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C2×#548C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#431C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C22×#103C2211yescharacteristic
43#2855—21no—
44#2855C2211yescharacteristic
45#2719—21no—
46#2698—21no—
47#2552C2211yescharacteristic
48#2506C2211yescharacteristic
49#2506C2211yescharacteristic
50#2499—21no—
51#2499C2211yescharacteristic
52#2496C2211yescharacteristic
53#2496C2211yescharacteristic
54#2486C2211yescharacteristic
55#2485—21no—
56#2485C2211yescharacteristic
57#2484—21no—
58#2478—21no—
59#2462—21no—
60#2447—21no—
61#2447—21no—
62#2447C2211yescharacteristic
63#2447C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2438—21no—
67#2422—21no—
68#2422C2211yescharacteristic
69#2420—21no—
70#2420C2211yescharacteristic
71#2419—21no—
72#2365C2211yescharacteristic
73#2351C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78#2341C2211yescharacteristic
79Q8×C22⋊C4C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81C4×#123—21no—
82C4×#123C2211yescharacteristic
83C2×#389C2211yescharacteristic
84#2285C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2095C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic
92#2087C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2085C2211yescharacteristic
96#2084C2211yescharacteristic
97#2083C2211yescharacteristic
98#2083C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2024C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic
118#1983C2211yescharacteristic
119#1959C2211yescharacteristic
120#1949C2211yescharacteristic
121#1947C2211yescharacteristic
122#1944C2211yescharacteristic
123#1943C2211yescharacteristic
124#1942C2211yescharacteristic
125#1942C2211yescharacteristic
126#1939C2211yescharacteristic
127#1936C2211yescharacteristic
128#1935C2211yescharacteristic
129#1934C2211yescharacteristic
130#1933C2211yescharacteristic
131#1933C2211yescharacteristic
132#1933C2211yescharacteristic
133#1928C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1926C2211yescharacteristic
138#1925C2211yescharacteristic
139#1924C2211yescharacteristic
140#1923C2211yescharacteristic
141#1921C2211yescharacteristic
142#1919C2211yescharacteristic
143#1918C2211yescharacteristic
144#1918C2211yescharacteristic
145#1917C2211yescharacteristic
146#1916C2211yescharacteristic
147#1894C2211yescharacteristic
148#1894C2211yescharacteristic
149#1893C2211yescharacteristic
150#1874C2211yescharacteristic
151#1872C2211yescharacteristic
152#1870C2211yescharacteristic
153#1865C2211yescharacteristic
154#1865C2211yescharacteristic
155#1865C2211yescharacteristic
156#1865C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1863C2211yescharacteristic
160#1863C2211yescharacteristic
161#1863C2211yescharacteristic
162#1863C2211yescharacteristic
163#1863C2211yescharacteristic
164#1863C2211yescharacteristic
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1852C2211yescharacteristic
168#1852C2211yescharacteristic
169#1851C2211yescharacteristic
170#1850C2211yescharacteristic
171#1834C2211yescharacteristic
172#1825C2211yescharacteristic
173#1825C2211yescharacteristic
174#1824C2211yescharacteristic
175#1823C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1803C2211yescharacteristic
181#1803C2211yescharacteristic
182#1803C2211yescharacteristic
183#1803C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1787C2211yescharacteristic
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1771C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#552—48no—
209#548—24no—
210#548—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123D411yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C4×#41—24no—
229C4×#41—42no—
230C2×C4×Q8—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117—21no—
245C2×#117—21no—
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C42—21no—
253C22×C42C2311yescharacteristic
254#484—42no—
255#477—24no—
256#435—42no—
257#431—42no—
258#428—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#417—24no—
277#417—24no—
278C2×#103—24no—
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×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#395—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388D411yescharacteristic
378#388D411yescharacteristic
379#387—21no—
380#387—21no—
381#387—21no—
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#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386D411yescharacteristic
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385D411yescharacteristic
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#382—21no—
414#382—21no—
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#381D411yescharacteristic
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C2×#95—21no—
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#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41#4114yes—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—22no—
540C4⋊Q8—41no—
541#126—44no—
542#126—44no—
543#125—44no—
544#125—44no—
545#125—44no—
546#124—22no—
547#124—41no—
548#124—44no—
549#123—24no—
550#123—44no—
551#123—44no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557#121—22no—
558#121—41no—
559#121—44no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—44no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—44no—
580C4×D4—44no—
581#117—22no—
582#117—22no—
583#117—44no—
584#117—44no—
585#117—44no—
586#117—44no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
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—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—44no—
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⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—44no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694#107—22no—
695#107—22no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103#4114yes—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740#97—41no—
741#97—41no—
742C4×C8—41no—
743C4×C8—41no—
744C4×C8—41no—
745#95—21no—
746#95—21no—
747#95—21no—
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#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792C24—21no—
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795#41—28no—
796#41—44no—
797#41—44no—
798#41—44no—
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—21no—
808C2×Q8—42no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—44no—
814C2×Q8—81no—
815C2×Q8—82no—
816C2×Q8—82no—
817C2×Q8—82no—
818C2×Q8C2×#4112yes—
819C2×Q8C2×#4112yes—
820C2×Q82−1+412yes—
821C2×D4—22no—
822C2×D4—24no—
823C2×D4—22no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—41no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—81no—
835C2×D4C2×#4112yes—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—24no—
845C22×C4—22no—
846C22×C4—22no—
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—21no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
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—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
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×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C2×#4112yes—
901C22×C4H(5,𝔽2)12yes—
902C22×C4C2511yescharacteristic
903M16—44no—
904M16—82no—
905C2×C8—21no—
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—82no—
929C2×C8C2×#4112yes—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
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—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—41no—
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—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4C2×#4112yes—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
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—42no—
1015C22⋊C4—42no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4AGL(1,ℤ/8)14yes—
1022C42—22no—
1023C42—22no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23#54612yes—
1065C23C2×AGL(1,ℤ/8)12yes—
1066C23C23×D411yescharacteristic
1067Q8—22no—
1068Q8—22no—
1069Q8—22no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—84no—
1075Q8—84no—
1076Q8#55214yescomplemented
1077D4—22no—
1078D4—22no—
1079D4—48no—
1080D4—44no—
1081D4—41no—
1082D4—41no—
1083D4—84no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
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—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—48no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
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—84no—
1173C2×C4—84no—
1174C2×C4—84no—
1175C2×C4—84no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4#54612yes—
1179C2×C4C2×AGL(1,ℤ/8)12yes—
1180C2×C4C2×AGL(1,ℤ/8)12yes—
1181C2×C4#57812yes—
1182C2×C4C22×#4111yescharacteristic
1183C2×C4C22×#4111yescharacteristic
1184C2×C4C2×H(5,𝔽2)11yescharacteristic
1185C2×C4C2×2−1+411yescharacteristic
1186C2×C4#58511yescharacteristic
1187C2×C4#58511yescharacteristic
1188C8—22no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22C2×#54611yescharacteristic
1218C22D4×#4111yescharacteristic
1219C22#348911yescharacteristic
1220C22C22×AGL(1,ℤ/8)11yescharacteristic
1221C22C2×#57811yescharacteristic
1222C22#358411yescharacteristic
1223C22#358611yescharacteristic
1224C4—22no—
1225C4—24no—
1226C4—22no—
1227C4—22no—
1228C4—22no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—42no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4C2×#55211yescharacteristic
1252C4#349111yescharacteristic
1253C4#351311yescharacteristic
1254C4#353511yescharacteristic
1255C2—42no—
1256C2—42no—
1257C2—82no—
1258C2#5901211yescharacteristic
1259C2#6116111yescharacteristic
1260C2#6117311yescharacteristic
1261C2#6143911yescharacteristic
1262C2#6154411yescharacteristic
1263C2#6213211yescharacteristic
1264C2#6219811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59290C2semidirect
3. #31970C2semidirect
4. #31610C2semidirect
5. #31586C2semidirect
6. #31374C2semidirect
7. #29027C2semidirect
8. #28841C2semidirect
9. #27864C2semidirect
10. #27706C2semidirect
11. #27669C2semidirect
12. #27535C2semidirect
13. #27522C2semidirect
14. #27311C2semidirect
15. #27303C2semidirect
16. #27158C2semidirect
17. #26689C2semidirect
18. #26112C2semidirect
19. #25975C2semidirect
20. #25963C2semidirect
21. #24951C2semidirect
22. #24602C2semidirect
23. #24588C2semidirect
25. #22977C2semidirect
26. #22904C2semidirect
27. #22583C2semidirect
28. #22571C2semidirect
30. #20875C2semidirect
31. #20737C2semidirect
1076. Q8#552semidirect

Maximal subgroups

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

subgroupindex
#592902
#364322
#319702
#316102
#315862
#313742
#290272
#288412
#278642
#277062
#276692
#275352
#275222
#273112
#273032
#271582
#266892
#261122
#259752
#259632
#249512
#246022
#245882
#240512
#229772
#229042
#225832
#225712
#224212
#208752
#207372