Finite Group Databasebeta

← #6792133

Subgroups — #6792133

Order 512.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37756C211yesmaximal, characteristic, complemented
2#35552C211yesmaximal, characteristic, complemented
3#33038C211yesmaximal, characteristic, complemented
4#31535C211yesmaximal, characteristic, complemented
5#31523C211yesmaximal, characteristic, complemented
6#31479C211yesmaximal, characteristic, complemented
7#31467C211yesmaximal, characteristic, complemented
8#31391C211yesmaximal, characteristic, complemented
9#31382C211yesmaximal, characteristic, complemented
10#31328C211yesmaximal, characteristic, complemented
11#31325C211yesmaximal, characteristic, complemented
12#29940C211yesmaximal, characteristic, complemented
13#29933C211yesmaximal, characteristic, complemented
14#29360C211yesmaximal, characteristic, complemented
15#29282C211yesmaximal, characteristic, complemented
16#28984C211yesmaximal, characteristic, complemented
17#28976C211yesmaximal, characteristic, complemented
18#28082C211yesmaximal, characteristic, complemented
19#28065C211yesmaximal, characteristic, complemented
20#27112C211yesmaximal, characteristic, complemented
21#27108C211yesmaximal, characteristic, complemented
22#26685C211yesmaximal, characteristic, complemented
23#26657C211yesmaximal, characteristic, complemented
24#24839C211yesmaximal, characteristic, complemented
25#24662C211yesmaximal, characteristic, complemented
26#24308C211yesmaximal, characteristic, complemented
27#24150C211yesmaximal, characteristic, complemented
28#22754C211yesmaximal, characteristic, complemented
29#21888C211yesmaximal, characteristic, complemented
30#21843C211yesmaximal, characteristic, complemented
31#21624C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#459C2211yescharacteristic
37C2×#433C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39#2851C2211yescharacteristic
40#2731—21no—
41#2730—21no—
42#2711—21no—
43#2676—21no—
44#2641C2211yescharacteristic
45#2619C2211yescharacteristic
46#2576—21no—
47#2571C2211yescharacteristic
48#2566C2211yescharacteristic
49#2562C2211yescharacteristic
50#2559—21no—
51#2537C2211yescharacteristic
52#2530—21no—
53#2526—21no—
54#2518—21no—
55#2496C2211yescharacteristic
56#2494C2211yescharacteristic
57#2493—21no—
58#2491C2211yescharacteristic
59#2490C2211yescharacteristic
60#2466—21no—
61#2463—21no—
62#2460—21no—
63#2454C2211yescharacteristic
64#2452C2211yescharacteristic
65#2444—21no—
66#2432—21no—
67#2420C2211yescharacteristic
68#2420C2211yescharacteristic
69#2416C2211yescharacteristic
70#2414C2211yescharacteristic
71#2407—21no—
72#2363C2211yescharacteristic
73#2361C2211yescharacteristic
74#2331C2211yescharacteristic
75#2330C2211yescharacteristic
76#2324C2211yescharacteristic
77#2314C2211yescharacteristic
78C4×#121C2211yescharacteristic
79#2290C2211yescharacteristic
80#2283C2211yescharacteristic
81#2275C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2094C2211yescharacteristic
87#2093C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2075C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2067C2211yescharacteristic
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2057C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2023C2211yescharacteristic
118#1999C2211yescharacteristic
119#1999C2211yescharacteristic
120#1999C2211yescharacteristic
121#1999C2211yescharacteristic
122#1993C2211yescharacteristic
123#1992C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1988C2211yescharacteristic
130#1987C2211yescharacteristic
131#1987C2211yescharacteristic
132#1982C2211yescharacteristic
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic
135#1972C2211yescharacteristic
136#1970C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1869C2211yescharacteristic
175#1869C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1854C2211yescharacteristic
181#1852C2211yescharacteristic
182#1832C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic
186#1823C2211yescharacteristic
187#1808C2211yescharacteristic
188#1807C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1798C2211yescharacteristic
195#1797C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1768C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41—21no—
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#544—24no—
209#544—42no—
210#532—24no—
211#532—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#478—42no—
249#474—24no—
250#459—42no—
251#433—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8—42no—
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#401—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#399—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#393—21no—
331#393—21no—
332#392—21no—
333#392—21no—
334#392—21no—
335#391—21no—
336#391—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#389—21no—
350#389—21no—
351#389—21no—
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#388—21no—
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#388—21no—
372#388D411yescharacteristic
373#388D411yescharacteristic
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#387D411yescharacteristic
385#387D411yescharacteristic
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386D411yescharacteristic
394#386D411yescharacteristic
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385D411yescharacteristic
404#385D411yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#383—21no—
408#382—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#381—21no—
414#381—21no—
415#381—21no—
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
444C2×#95—21no—
445#340C2311yescharacteristic
446#340C2311yescharacteristic
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#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C2×#41—44no—
488C2×#41—82no—
489C2×#41—82no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8—41no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—22no—
535C4⋊Q8—22no—
536C4⋊Q8—41no—
537C4⋊Q8—44no—
538C4⋊Q8#4114yes—
539#127—22no—
540#127—22no—
541#126—82no—
542#125—22no—
543#125—22no—
544#125—22no—
545#125—41no—
546#125—41no—
547#125—41no—
548#125—44no—
549#124—44no—
550#124—82no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—82no—
554#121—22no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—44no—
567#121—82no—
568#121—82no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—44no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—82no—
583C4×D4—82no—
584#117—22no—
585#117—22no—
586#117—22no—
587#117—41no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
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×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—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×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706#102—22no—
707#102—22no—
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—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732#97—41no—
733#97—41no—
734C4×C8—41no—
735C4×C8—41no—
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#95C2×D411yescharacteristic
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
777C24—21no—
778C24—21no—
779C24—21no—
780C24C22×D411yescharacteristic
781C24C22×D411yescharacteristic
782#41—816no—
783C2×Q8—24no—
784C2×Q8—42no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
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—41no—
808C2×D4—41no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D42−1+412yes—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
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—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
896D8—82no—
897D8—82no—
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×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—82no—
923C2×C8—82no—
924C4⋊C4—24no—
925C4⋊C4—22no—
926C4⋊C4—22no—
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—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—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4C2×#4112yes—
975C4⋊C4C2×#4112yes—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
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—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—
1010C22⋊C4—81no—
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—
1020C42—22no—
1021C42—22no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—42no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42C2×#4112yes—
1039C42H(5,𝔽2)12yes—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—41no—
1055C23—41no—
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#57612yes—
1075C23C23×D411yescharacteristic
1076Q8—84no—
1077Q8—162no—
1078D4—22no—
1079D4—22no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—84no—
1091D4—84no—
1092D4—82no—
1093D4—84no—
1094D4—84no—
1095D4—84no—
1096D4—84no—
1097D4—162no—
1098D4—162no—
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—22no—
1126C2×C4—22no—
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—44no—
1136C2×C4—44no—
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—84no—
1183C2×C4—84no—
1184C2×C4—162no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4#54612yes—
1189C2×C4#54612yes—
1190C2×C4C22×#4111yescharacteristic
1191C2×C4C2×H(5,𝔽2)11yescharacteristic
1192C2×C4C2×2−1+411yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—41no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22#344911yescharacteristic
1240C22C2×#54611yescharacteristic
1241C22#348911yescharacteristic
1242C22C2×#57611yescharacteristic
1243C22#358411yescharacteristic
1244C22#358411yescharacteristic
1245C22#358511yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—42no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4#351611yescharacteristic
1272C4#352411yescharacteristic
1273C4#356111yescharacteristic
1274C4#356211yescharacteristic
1275C2—42no—
1276C2—81no—
1277C2—82no—
1278C2—161no—
1279C2—161no—
1280C2#3890311yescharacteristic
1281C2#6099711yescharacteristic
1282C2#6100011yescharacteristic
1283C2#6117011yescharacteristic
1284C2#6118311yescharacteristic
1285C2#6217111yescharacteristic
1286C2#6221111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37756C2semidirect
2. #35552C2semidirect
3. #33038C2semidirect
4. #31535C2semidirect
5. #31523C2semidirect
6. #31479C2semidirect
7. #31467C2semidirect
8. #31391C2semidirect
9. #31382C2semidirect
10. #31328C2semidirect
11. #31325C2semidirect
12. #29940C2semidirect
13. #29933C2semidirect
14. #29360C2semidirect
15. #29282C2semidirect
16. #28984C2semidirect
17. #28976C2semidirect
18. #28082C2semidirect
19. #28065C2semidirect
20. #27112C2semidirect
21. #27108C2semidirect
22. #26685C2semidirect
23. #26657C2semidirect
24. #24839C2semidirect
25. #24662C2semidirect
26. #24308C2semidirect
27. #24150C2semidirect
28. #22754C2semidirect
29. #21888C2semidirect
30. #21843C2semidirect
31. #21624C2semidirect

Maximal subgroups

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

subgroupindex
#377562
#355522
#330382
#315352
#315232
#314792
#314672
#313912
#313822
#313282
#313252
#299402
#299332
#293602
#292822
#289842
#289762
#280822
#280652
#271122
#271082
#266852
#266572
#248392
#246622
#243082
#241502
#227542
#218882
#218432
#216242