Finite Group Databasebeta

← #6701035

Subgroups — #6701035

Order 512.

1519 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#39404C211yesmaximal, characteristic, complemented
2#36585C211yesmaximal, characteristic, complemented
3#33067C211yesmaximal, characteristic, complemented
4#32541C211yesmaximal, characteristic, complemented
5#32446C211yesmaximal, characteristic, complemented
6#32394C211yesmaximal, characteristic, complemented
7#32304C211yesmaximal, characteristic, complemented
8#31929C211yesmaximal, characteristic, complemented
9#31621C211yesmaximal, characteristic, complemented
10#31503C211yesmaximal, characteristic, complemented
11#31448C211yesmaximal, characteristic, complemented
12#30376C211yesmaximal, characteristic, complemented
13#30125C211yesmaximal, characteristic, complemented
14#29087C211yesmaximal, characteristic, complemented
15#28857C211yesmaximal, characteristic, complemented
16#27578C211yesmaximal, characteristic, complemented
17#27557C211yesmaximal, characteristic, complemented
18#27033C211yesmaximal, characteristic, complemented
19#26377C211yesmaximal, characteristic, complemented
20#26175C211yesmaximal, characteristic, complemented
21#26122C211yesmaximal, characteristic, complemented
22#25975C211yesmaximal, characteristic, complemented
23#25179C211yesmaximal, characteristic
24#24916C211yesmaximal, characteristic, complemented
25#24896C211yesmaximal, characteristic, complemented
26#24827C211yesmaximal, characteristic, complemented
27#24542C211yesmaximal, characteristic, complemented
28#22883C211yesmaximal, characteristic, complemented
29#22677C211yesmaximal, characteristic, complemented
30#22353C211yesmaximal, characteristic, complemented
31C4×#460C211yesmaximal, characteristic, complemented
32C2×#539—21no—
33C2×#477C2211yescharacteristic
34C2×#460C2211yescharacteristic
35C2×#449C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#417C2211yescharacteristic
42#2860—21no—
43#2860C2211yescharacteristic
44#2859C2211yescharacteristic
45#2723—21no—
46#2706—21no—
47#2694—21no—
48#2681—21no—
49#2633—21no—
50#2552C2211yescharacteristic
51#2542C2211yescharacteristic
52#2513—21no—
53#2513—21no—
54#2513—21no—
55#2513C2211yescharacteristic
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2512C2211yescharacteristic
59#2501C2211yescharacteristic
60#2494—21no—
61#2494—21no—
62#2494—21no—
63#2494C2211yescharacteristic
64#2494C2211yescharacteristic
65#2494C2211yescharacteristic
66#2455—21no—
67#2452C2211yescharacteristic
68#2449—21no—
69#2445C2211yescharacteristic
70#2440C2211yescharacteristic
71#2428C2211yescharacteristic
72#2422C2211yescharacteristic
73#2422C2211yescharacteristic
74#2361C2211yescharacteristic
75#2351C2211yescharacteristic
76#2351C2211yescharacteristic
77#2351C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79#2341C2211yescharacteristic
80#2341C2211yescharacteristic
81#2341C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#126—21no—
84C4×#126C2211yescharacteristic
85C42×Q8C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic
96#2086C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2065C2211yescharacteristic
114#2058C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2041C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2023C2211yescharacteristic
125#2011C2211yescharacteristic
126#1993C2211yescharacteristic
127#1982C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1942C2211yescharacteristic
137#1940C2211yescharacteristic
138#1940C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1921C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1917C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic
184#1847C2211yescharacteristic
185#1836C2211yescharacteristic
186#1831C2211yescharacteristic
187#1824C2211yescharacteristic
188#1809C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1788C2211yescharacteristic
197#1771C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#539—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#126D411yescharacteristic
215C2×#125—21no—
216C2×#125—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4C2311yescharacteristic
244#477—42no—
245#460—24no—
246#449—24no—
247#449—42no—
248#440—24no—
249#440—42no—
250C4×SD16—42no—
251C4×SD16—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#417—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#401—21no—
305#401—21no—
306#401—21no—
307#399—21no—
308#399—21no—
309#399—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#393—21no—
335#392—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
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#388D411yescharacteristic
392#388D411yescharacteristic
393#388D411yescharacteristic
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383D411yescharacteristic
416#382—21no—
417#382—21no—
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C43—21no—
451C43C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2411yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16#4114yes—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#127—22no—
537#127—41no—
538#126—24no—
539#126—44no—
540#126—44no—
541#125—44no—
542#125—44no—
543#123—44no—
544#123—44no—
545#123—44no—
546#123—44no—
547#123—82no—
548C22⋊Q8—44no—
549C22⋊Q8—44no—
550C22⋊Q8—44no—
551C22⋊Q8—82no—
552#121—22no—
553#121—44no—
554#121—41no—
555#121—41no—
556#121—41no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—82no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
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—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734C22⋊C8—22no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737#97—22no—
738#97—41no—
739#97—41no—
740C4×C8—41no—
741C4×C8—41no—
742#95—21no—
743#95—21no—
744#95—21no—
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#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C24—21no—
783C24C22×D411yescharacteristic
784#41—44no—
785#41—82no—
786#41—82no—
787#41—82no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—42no—
792C2×Q8—81no—
793C2×Q8—81no—
794C2×Q8C2×#4112yes—
795C2×Q8H(5,𝔽2)12yes—
796C2×Q82−1+412yes—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4C2×#4112yes—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
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—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C2511yescharacteristic
881SD16—28no—
882SD16—44no—
883D8—82no—
884D8—82no—
885M16—82no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8C2×#4112yes—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—42no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—42no—
1031C42—42no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42AGL(1,ℤ/8)14yes—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—22no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23C23×D411yescharacteristic
1065Q8—22no—
1066Q8—22no—
1067Q8—22no—
1068Q8—162no—
1069Q8#53914yescomplemented
1070D4—22no—
1071D4—22no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—84no—
1083D4—84no—
1084D4—84no—
1085D4—84no—
1086D4—162no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
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—21no—
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—21no—
1125C2×C4—21no—
1126C2×C4—41no—
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—84no—
1167C2×C4—84no—
1168C2×C4—162no—
1169C2×C4—162no—
1170C2×C4—162no—
1171C2×C4—162no—
1172C2×C4C2×AGL(1,ℤ/8)12yes—
1173C2×C4C2×AGL(1,ℤ/8)12yes—
1174C2×C4C2×AGL(1,ℤ/8)12yes—
1175C2×C4C22×#4111yescharacteristic
1176C2×C4C2×H(5,𝔽2)11yescharacteristic
1177C2×C4C2×2−1+411yescharacteristic
1178C2×C4#58511yescharacteristic
1179C2×C4#58511yescharacteristic
1180C2×C4#58511yescharacteristic
1181C8—22no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C22—41no—
1190C22—42no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—42no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—41no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22D4×#4111yescharacteristic
1218C22#348811yescharacteristic
1219C22#348911yescharacteristic
1220C22C22×AGL(1,ℤ/8)11yescharacteristic
1221C22#358411yescharacteristic
1222C22#358511yescharacteristic
1223C22#358611yescharacteristic
1224C4—22no—
1225C4—24no—
1226C4—22no—
1227C4—22no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4C2×#53911yescharacteristic
1251C4#352111yescharacteristic
1252C4#356011yescharacteristic
1253C4#356411yescharacteristic
1254C2—81no—
1255C2—82no—
1256C2—161no—
1257C2—161no—
1258C2#3772411yescharacteristic
1259C2#6143911yescharacteristic
1260C2#6150811yescharacteristic
1261C2#6196311yescharacteristic
1262C2#6202511yescharacteristic
1263C2#6211111yescharacteristic
1264C2#6219711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25179C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39404C2semidirect
2. #36585C2semidirect
3. #33067C2semidirect
4. #32541C2semidirect
5. #32446C2semidirect
6. #32394C2semidirect
7. #32304C2semidirect
8. #31929C2semidirect
9. #31621C2semidirect
10. #31503C2semidirect
11. #31448C2semidirect
12. #30376C2semidirect
13. #30125C2semidirect
14. #29087C2semidirect
15. #28857C2semidirect
16. #27578C2semidirect
17. #27557C2semidirect
18. #27033C2semidirect
19. #26377C2semidirect
20. #26175C2semidirect
21. #26122C2semidirect
22. #25975C2semidirect
24. #24916C2semidirect
25. #24896C2semidirect
26. #24827C2semidirect
27. #24542C2semidirect
28. #22883C2semidirect
29. #22677C2semidirect
30. #22353C2semidirect
31. C4×#460C2semidirect
1069. Q8#539semidirect

Maximal subgroups

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

subgroupindex
#394042
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C4×#4602