Finite Group Databasebeta

← #7188666

Subgroups — #7188666

Order 512.

1488 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59155C211yesmaximal, characteristic, complemented
2#38941C211yesmaximal, characteristic, complemented
3#32237C211yesmaximal, characteristic, complemented
4#32236C211yesmaximal, characteristic, complemented
5#31768C211yesmaximal, characteristic, complemented
6#31738C211yesmaximal, characteristic, complemented
7#31527C211yesmaximal, characteristic, complemented
8#31527C211yesmaximal, characteristic, complemented
9#31374C211yesmaximal, characteristic, complemented
10#31364C211yesmaximal, characteristic, complemented
11#29096C211yesmaximal, characteristic, complemented
12#29072C211yesmaximal, characteristic, complemented
13#28650C211yesmaximal, characteristic, complemented
14#27826C211yesmaximal, characteristic, complemented
15#27825C211yesmaximal, characteristic, complemented
16#27814C211yesmaximal, characteristic, complemented
17#26737C211yesmaximal, characteristic, complemented
18#26720C211yesmaximal, characteristic, complemented
19#26672C211yesmaximal, characteristic, complemented
20#26657C211yesmaximal, characteristic, complemented
21#26456C211yesmaximal, characteristic, complemented
22#26291C211yesmaximal, characteristic, complemented
23#25946C211yesmaximal, characteristic, complemented
24#25913C211yesmaximal, characteristic, complemented
25#25330C211yesmaximal, characteristic, complemented
26#24650C211yesmaximal, characteristic
27#23764C211yesmaximal, characteristic, complemented
28#23231C211yesmaximal, characteristic, complemented
29#23052C211yesmaximal, characteristic, complemented
30#22526C211yesmaximal, characteristic, complemented
31#21836C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#459C2211yescharacteristic
37C2×#446C2211yescharacteristic
38C2×#431C2211yescharacteristic
39#2856C2211yescharacteristic
40#2737—21no—
41#2737—21no—
42#2720—21no—
43#2704—21no—
44#2686—21no—
45#2686—21no—
46#2640—21no—
47#2584C2211yescharacteristic
48#2566C2211yescharacteristic
49#2563C2211yescharacteristic
50#2563C2211yescharacteristic
51#2556—21no—
52#2552C2211yescharacteristic
53#2551C2211yescharacteristic
54#2550C2211yescharacteristic
55#2548C2211yescharacteristic
56#2513C2211yescharacteristic
57#2513C2211yescharacteristic
58#2491—21no—
59#2491C2211yescharacteristic
60#2491C2211yescharacteristic
61#2473—21no—
62#2454C2211yescharacteristic
63#2454C2211yescharacteristic
64#2449—21no—
65#2449—21no—
66#2442C2211yescharacteristic
67#2440C2211yescharacteristic
68#2427—21no—
69#2420C2211yescharacteristic
70#2420C2211yescharacteristic
71#2417—21no—
72#2370C2211yescharacteristic
73#2366C2211yescharacteristic
74#2361C2211yescharacteristic
75#2361C2211yescharacteristic
76#2355C2211yescharacteristic
77D4×C4⋊C4—21no—
78#2319—21no—
79C4×C22⋊Q8C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2283C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2100C2211yescharacteristic
87#2092C2211yescharacteristic
88#2087C2211yescharacteristic
89#2086C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2077C2211yescharacteristic
94#2075C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2071C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2057C2211yescharacteristic
103#2057C2211yescharacteristic
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2034C2211yescharacteristic
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#1999C2211yescharacteristic
121#1999C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1992C2211yescharacteristic
125#1992C2211yescharacteristic
126#1991C2211yescharacteristic
127#1991C2211yescharacteristic
128#1991C2211yescharacteristic
129#1991C2211yescharacteristic
130#1991C2211yescharacteristic
131#1990C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1989C2211yescharacteristic
136#1989C2211yescharacteristic
137#1988C2211yescharacteristic
138#1988C2211yescharacteristic
139#1987C2211yescharacteristic
140#1985C2211yescharacteristic
141#1982C2211yescharacteristic
142#1970C2211yescharacteristic
143#1970C2211yescharacteristic
144#1947C2211yescharacteristic
145#1940C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1921C2211yescharacteristic
163#1921C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1823C2211yescharacteristic
185#1823C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1776C2211yescharacteristic
192#1776C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205#554—24no—
206#554—42no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125—24no—
213C2×#125—21no—
214C2×#125—21no—
215C2×#125—42no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8D411yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C22×C4⋊C4—21no—
245C22×C4⋊C4—21no—
246C22×C4⋊C4—21no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#490—24no—
251#490—42no—
252#459—42no—
253#446—42no—
254#431—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#399—21no—
301#399—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#393—21no—
333#393—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391D411yescharacteristic
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389D411yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387D411yescharacteristic
383#387D411yescharacteristic
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385D411yescharacteristic
400#385D411yescharacteristic
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
411#381—21no—
412#381—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380D411yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376—21no—
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
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
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2×D411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—41no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—82no—
530#127—22no—
531#127—22no—
532#125—22no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—41no—
539#125—41no—
540#125—41no—
541#125—44no—
542#125—44no—
543#125#4114yes—
544#124—82no—
545#124—82no—
546#124—82no—
547C22⋊Q8—42no—
548C22⋊Q8—44no—
549C22⋊Q8—44no—
550C22⋊Q8—44no—
551C22⋊Q8—82no—
552#121—22no—
553#121—22no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—82no—
559#121—82no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—44no—
573C4×D4—44no—
574C4×D4—82no—
575C4×D4—82no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
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—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—41no—
689#107—41no—
690#107—41no—
691#106—22no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
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—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723#97—22no—
724#97—22no—
725#97—41no—
726#97—41no—
727C4×C8—41no—
728C4×C8—41no—
729C4×C8—41no—
730C4×C8—41no—
731#95—21no—
732#95—21no—
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#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×D411yescharacteristic
774C2×Q8—22no—
775C2×Q8—41no—
776C2×Q8—41no—
777C2×Q8—42no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8—81no—
786C2×D4—24no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
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—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D42−1+412yes—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
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—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
879D8—82no—
880D8—82no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
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—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—21no—
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—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—42no—
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—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4C2×#4112yes—
966C4⋊C4C2×#4112yes—
967C4⋊C42−1+412yes—
968C22⋊C4—24no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—41no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
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—
1005C42—22no—
1006C42—22no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—42no—
1018C42—42no—
1019C42—42no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42C2×#4112yes—
1025C42H(5,𝔽2)12yes—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23#57612yes—
1054C23C23×D411yescharacteristic
1055Q8—82no—
1056Q8—162no—
1057Q8—162no—
1058Q8—162no—
1059D4—22no—
1060D4—22no—
1061D4—48no—
1062D4—41no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—84no—
1073D4—162no—
1074D4—162no—
1075D4—162no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
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—44no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
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—82no—
1157C2×C4—84no—
1158C2×C4—84no—
1159C2×C4—84no—
1160C2×C4—162no—
1161C2×C4—162no—
1162C2×C4—162no—
1163C2×C4—162no—
1164C2×C4#54612yes—
1165C2×C4#54612yes—
1166C2×C4#57512yes—
1167C2×C4C22×#4111yescharacteristic
1168C2×C4C2×H(5,𝔽2)11yescharacteristic
1169C2×C4C2×2−1+411yescharacteristic
1170C2×C4C2×2−1+411yescharacteristic
1171C2×C4#58511yescharacteristic
1172C2×C4#58511yescharacteristic
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22C2×#54611yescharacteristic
1210C22#348611yescharacteristic
1211C22#350011yescharacteristic
1212C22C2×#57511yescharacteristic
1213C22C2×#57611yescharacteristic
1214C22#358411yescharacteristic
1215C22#358511yescharacteristic
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—42no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—42no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4#351611yescharacteristic
1243C4#351811yescharacteristic
1244C4#355411yescharacteristic
1245C4#356111yescharacteristic
1246C2—42no—
1247C2—82no—
1248C2—161no—
1249C2—161no—
1250C2#4528911yescharacteristic
1251C2#6116611yescharacteristic
1252C2#6117111yescharacteristic
1253C2#6183511yescharacteristic
1254C2#6186111yescharacteristic
1255C2#6254711yescharacteristic
1256C2#6259811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24650C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59155C2semidirect
2. #38941C2semidirect
3. #32237C2semidirect
4. #32236C2semidirect
5. #31768C2semidirect
6. #31738C2semidirect
7. #31527C2semidirect
8. #31527C2semidirect
9. #31374C2semidirect
10. #31364C2semidirect
11. #29096C2semidirect
12. #29072C2semidirect
13. #28650C2semidirect
14. #27826C2semidirect
15. #27825C2semidirect
16. #27814C2semidirect
17. #26737C2semidirect
18. #26720C2semidirect
19. #26672C2semidirect
20. #26657C2semidirect
21. #26456C2semidirect
22. #26291C2semidirect
23. #25946C2semidirect
24. #25913C2semidirect
25. #25330C2semidirect
27. #23764C2semidirect
28. #23231C2semidirect
29. #23052C2semidirect
30. #22526C2semidirect
31. #21836C2semidirect

Maximal subgroups

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

subgroupindex
#591552
#389412
#322372
#322362
#317682
#317382
#315272
#313742
#313642
#290962
#290722
#286502
#278262
#278252
#278142
#267372
#267202
#266722
#266572
#264562
#262912
#259462
#259132
#253302
#246502
#237642
#232312
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