Finite Group Databasebeta

← #6916443

Subgroups — #6916443

Order 512.

1567 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36171C211yesmaximal, characteristic, complemented
2#35007C211yesmaximal, characteristic
3#32823C211yesmaximal, characteristic, complemented
4#32747C211yesmaximal, characteristic, complemented
5#32486C211yesmaximal, characteristic, complemented
6#32484C211yesmaximal, characteristic, complemented
7#32208C211yesmaximal, characteristic, complemented
8#32206C211yesmaximal, characteristic, complemented
9#31977C211yesmaximal, characteristic, complemented
10#31973C211yesmaximal, characteristic, complemented
11#31499C211yesmaximal, characteristic, complemented
12#31495C211yesmaximal, characteristic, complemented
13#30381C211yesmaximal, characteristic, complemented
14#30189C211yesmaximal, characteristic, complemented
15#30153C211yesmaximal, characteristic, complemented
16#29956C211yesmaximal, characteristic, complemented
17#29925C211yesmaximal, characteristic, complemented
18#29348C211yesmaximal, characteristic, complemented
19#29161C211yesmaximal, characteristic, complemented
20#28097C211yesmaximal, characteristic, complemented
21#28094C211yesmaximal, characteristic, complemented
22#27859C211yesmaximal, characteristic, complemented
23#27651C211yesmaximal, characteristic, complemented
24#25994C211yesmaximal, characteristic, complemented
25#25990C211yesmaximal, characteristic, complemented
26#25238C211yesmaximal, characteristic, complemented
27#25232C211yesmaximal, characteristic, complemented
28#24478C211yesmaximal, characteristic, complemented
29#24476C211yesmaximal, characteristic, complemented
30C2×#2073C211yesmaximal, characteristic, complemented
31#22696C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#481C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×C8×D4C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39#2864C2211yescharacteristic, complemented
40#2860C2211yescharacteristic
41#2858C2211yescharacteristic
42#2856C2211yescharacteristic
43#2854C2211yescharacteristic
44#2851C2211yescharacteristic
45#2851C2211yescharacteristic, complemented
46#2662—21no—
47#2661—21no—
48#2575—21no—
49#2555—21no—
50#2554—21no—
51#2528—21no—
52#2524—21no—
53#2517—21no—
54#2512C2211yescharacteristic
55#2509C2211yescharacteristic, complemented
56#2508C2211yescharacteristic, complemented
57#2495C2211yescharacteristic, complemented
58#2494C2211yescharacteristic, complemented
59#2493—21no—
60#2491C2211yescharacteristic
61#2487C2211yescharacteristic
62#2486C2211yescharacteristic
63#2472—21no—
64#2445C2211yescharacteristic
65#2440C2211yescharacteristic
66#2433C2211yescharacteristic
67#2428C2211yescharacteristic
68#2424—21no—
69#2419—21no—
70#2416C2211yescharacteristic
71#2408C2211yescharacteristic
72#2359—21no—
73#2345C2211yescharacteristic
74#2344C2211yescharacteristic
75#2343—21no—
76#2321—21no—
77C4×#125C2211yescharacteristic, complemented
78C4×#121C2211yescharacteristic
79C2×#390C2211yescharacteristic
80#2283C2211yescharacteristic, complemented
81C2×#382C2211yescharacteristic
82C42×D4C2211yescharacteristic
83#2101C2211yescharacteristic, complemented
84#2100C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic, complemented
108#2073C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic, complemented
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic, complemented
123#2059C2211yescharacteristic, complemented
124#2058C2211yescharacteristic, complemented
125#2057C2211yescharacteristic, complemented
126#2041C2211yescharacteristic
127#2041C2211yescharacteristic
128#2041C2211yescharacteristic
129#2041C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic, complemented
133#2033C2211yescharacteristic
134#2033C2211yescharacteristic
135#2033C2211yescharacteristic, complemented
136#2025C2211yescharacteristic
137#2025C2211yescharacteristic
138#2025C2211yescharacteristic, complemented
139#1987C2211yescharacteristic, complemented
140#1987C2211yescharacteristic, complemented
141#1982C2211yescharacteristic
142#1982C2211yescharacteristic
143#1982C2211yescharacteristic
144#1982C2211yescharacteristic
145#1949C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1947C2211yescharacteristic, complemented
149#1942C2211yescharacteristic, complemented
150#1941C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1939C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic, complemented
158#1934C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1921C2211yescharacteristic, complemented
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1893C2211yescharacteristic
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1893C2211yescharacteristic
175#1893C2211yescharacteristic, complemented
176#1893C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1850C2211yescharacteristic
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic, complemented
184#1850C2211yescharacteristic, complemented
185#1831C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1823C2211yescharacteristic
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic, complemented
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic, complemented
192#1804C2211yescharacteristic, complemented
193#1804C2211yescharacteristic, complemented
194#1797C2211yescharacteristic
195#1797C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic, complemented
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#538—48no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124—21no—
217C2×#124—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×#120—21no—
233C2×C4×D4—21no—
234C2×C4×D4D411yescharacteristic
235C2×C4×D4D411yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#481—42no—
247#480—42no—
248C8×D4—42no—
249C8×D4—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#102—42no—
271C2×#102—42no—
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#401—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#393—21no—
326#392—21no—
327#392—21no—
328#392—21no—
329#392—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390—21no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
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#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
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#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#383—21no—
402#383—21no—
403#382—21no—
404#382—21no—
405#382—21no—
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#381—21no—
414#380—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#379—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4D411yescharacteristic
438C4×C22⋊C4D411yescharacteristic
439C4×C22⋊C4D411yescharacteristic
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
444C2×#95—21no—
445C2×#95—21no—
446C43C2311yescharacteristic
447#340C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C25—21no—
486C22×Q8—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538#127—41no—
539#127—41no—
540#127—41no—
541#127—41no—
542#126—44no—
543#126—44no—
544#125—41no—
545#125—41no—
546#124—44no—
547#124—44no—
548#124—82no—
549#123—44no—
550#123—44no—
551#123—44no—
552C22⋊Q8—44no—
553#121—22no—
554#121—22no—
555#121—44no—
556#121—44no—
557#121—44no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—82no—
565#120—44no—
566#120—44no—
567#120—44no—
568C4×D4—24no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—24no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—44no—
575#117—44no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
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—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
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—44no—
654C2×C22⋊C4—82no—
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—41no—
667C2×C42—41no—
668C2×C42—41no—
669C2×C42—41no—
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#107—41no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C4×C8—41no—
732C4×C8—41no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
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#95—21no—
769#95—21no—
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C24—42no—
780C24—42no—
781C24—42no—
782C24—81no—
783C24—81no—
784C24—81no—
785C24—81no—
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C2×Q8—42no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
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—44no—
812C2×D4—44no—
813C2×D4—42no—
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—82no—
825C2×D4—82no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4AGL(1,ℤ/8)14yes—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
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—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
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×C4—81no—
889C22×C4—81no—
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×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4H(5,𝔽2)12yes—
903C22×C42−1+412yes—
904C22×C4C2511yescharacteristic
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—21no—
929C2×C8—82no—
930C2×C8—82no—
931C2×C8—82no—
932C2×C8—82no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
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—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
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—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
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—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
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#13514yes—
1023C42—22no—
1024C42—22no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42—41no—
1040C42—41no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—84no—
1078C23—84no—
1079C23—84no—
1080C23—162no—
1081C23—162no—
1082C23—162no—
1083C23—162no—
1084C23#53712yes—
1085C23C2×#13512yes—
1086C23C2×AGL(1,ℤ/8)12yes—
1087C23C2×AGL(1,ℤ/8)12yes—
1088C23C23×D411yescharacteristic
1089Q8—162no—
1090D4—28no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—84no—
1104D4—84no—
1105D4—162no—
1106D4—162no—
1107D4—162no—
1108D4—162no—
1109D4—162no—
1110D4—162no—
1111D4—162no—
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—22no—
1121C2×C4—22no—
1122C2×C4—22no—
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—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
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—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—82no—
1192C2×C4—82no—
1193C2×C4—82no—
1194C2×C4—82no—
1195C2×C4—84no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4—162no—
1199C2×C4#53712yes—
1200C2×C4C2×#13512yes—
1201C2×C4C2×#13512yes—
1202C2×C4C2×AGL(1,ℤ/8)12yes—
1203C2×C4C2×H(5,𝔽2)11yescharacteristic
1204C2×C4C2×2−1+411yescharacteristic
1205C2×C4#58511yescharacteristic
1206C2×C4#58511yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—168no—
1252C22#324714yes—
1253C22C2×#53711yescharacteristic
1254C22#348511yescharacteristic
1255C22#350011yescharacteristic
1256C22C22×#13511yescharacteristic
1257C22C22×AGL(1,ℤ/8)11yescharacteristic
1258C22#358411yescharacteristic
1259C22#358511yescharacteristic
1260C4—22no—
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4#353311yescharacteristic
1286C4#353311yescharacteristic
1287C4#356411yescharacteristic
1288C4#356411yescharacteristic
1289C2—24no—
1290C2—42no—
1291C2—161no—
1292C2—161no—
1293C2—161no—
1294C2#4136911yescharacteristic
1295C2C2×#324711yescharacteristic
1296C2#6092611yescharacteristic
1297C2#6170211yescharacteristic
1298C2#6173311yescharacteristic
1299C2#6253311yescharacteristic
1300C2#6257611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35007C2
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
1. #36171C2semidirect
3. #32823C2semidirect
4. #32747C2semidirect
5. #32486C2semidirect
6. #32484C2semidirect
7. #32208C2semidirect
8. #32206C2semidirect
9. #31977C2semidirect
10. #31973C2semidirect
11. #31499C2semidirect
12. #31495C2semidirect
13. #30381C2semidirect
14. #30189C2semidirect
15. #30153C2semidirect
16. #29956C2semidirect
17. #29925C2semidirect
18. #29348C2semidirect
19. #29161C2semidirect
20. #28097C2semidirect
21. #28094C2semidirect
22. #27859C2semidirect
23. #27651C2semidirect
24. #25994C2semidirect
25. #25990C2semidirect
26. #25238C2semidirect
27. #25232C2semidirect
28. #24478C2semidirect
29. #24476C2semidirect
30. C2×#2073C2semidirect
31. #22696C2semidirect
39. #2864C22semidirect
45. #2851C22semidirect
55. #2509C22semidirect
56. #2508C22semidirect
57. #2495C22semidirect
58. #2494C22semidirect
77. C4×#125C22semidirect
80. #2283C22semidirect
83. #2101C22semidirect
84. #2100C22semidirect
85. #2100C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2077C22semidirect
98. #2075C22semidirect
107. #2073C22semidirect
108. #2073C22semidirect
115. #2067C22semidirect
122. #2065C22semidirect
123. #2059C22semidirect
124. #2058C22semidirect
125. #2057C22semidirect
132. #2034C22semidirect
135. #2033C22semidirect
138. #2025C22semidirect
139. #1987C22semidirect
140. #1987C22semidirect
145. #1949C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1947C22semidirect
149. #1942C22semidirect
150. #1941C22semidirect
151. #1939C22semidirect
152. #1939C22semidirect
157. #1934C22semidirect
158. #1934C22semidirect
163. #1921C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1920C22semidirect
167. #1920C22semidirect
168. #1919C22semidirect
175. #1893C22semidirect
176. #1893C22semidirect
177. #1864C22semidirect
178. #1862C22semidirect
183. #1850C22semidirect
184. #1850C22semidirect
185. #1831C22semidirect
189. #1808C22semidirect
191. #1807C22semidirect
192. #1804C22semidirect
193. #1804C22semidirect
195. #1797C22semidirect
198. C4×C4⋊C8C22semidirect
202. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#361712
#350072
#328232
#327472
#324862
#324842
#322082
#322062
#319772
#319732
#314992
#314952
#303812
#301892
#301532
#299562
#299252
#293482
#291612
#280972
#280942
#278592
#276512
#259942
#259902
#252382
#252322
#244782
#244762
C2×#20732
#226962