Finite Group Databasebeta

← #6880071

Subgroups — #6880071

Order 512.

1340 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39297C211yesmaximal, characteristic, complemented
2#38254C211yesmaximal, characteristic, complemented
3#33275C211yesmaximal, characteristic, complemented
4#32457C211yesmaximal, characteristic, complemented
5#32231C211yesmaximal, characteristic, complemented
6#31739C211yesmaximal, characteristic, complemented
7#31705C211yesmaximal, characteristic, complemented
8#31645C211yesmaximal, characteristic, complemented
9#31298C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic, complemented
11#30535C211yesmaximal, characteristic
12#30374C211yesmaximal, characteristic, complemented
13#30340C211yesmaximal, characteristic, complemented
14#29527C211yesmaximal, characteristic, complemented
15#29510C211yesmaximal, characteristic, complemented
16#29473C211yesmaximal, characteristic, complemented
17#29444C211yesmaximal, characteristic, complemented
18#29353C211yesmaximal, characteristic, complemented
19#29116C211yesmaximal, characteristic, complemented
20#27523C211yesmaximal, characteristic, complemented
21#27434C211yesmaximal, characteristic, complemented
22#27240C211yesmaximal, characteristic
23#27217C211yesmaximal, characteristic, complemented
24#27059C211yesmaximal, characteristic, complemented
25#27014C211yesmaximal, characteristic, complemented
26#26734C211yesmaximal, characteristic, complemented
27#26691C211yesmaximal, characteristic, complemented
28#22114C211yesmaximal, characteristic, complemented
29#22056C211yesmaximal, characteristic
30#21654C211yesmaximal, characteristic, complemented
31#21436C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#447C2211yescharacteristic
35#2861C2211yescharacteristic
36#2860C2211yescharacteristic, complemented
37#2808—21no—
38#2796—21no—
39#2786—21no—
40#2759—21no—
41#2745—21no—
42#2740—21no—
43#2735—21no—
44#2735—21no—
45#2644C2211yescharacteristic
46#2644C2211yescharacteristic, complemented
47#2628C2211yescharacteristic
48#2625C2211yescharacteristic
49#2601—21no—
50#2592—21no—
51#2577—21no—
52#2563C2211yescharacteristic, complemented
53#2550C2211yescharacteristic, complemented
54#2521—21no—
55#2516—21no—
56#2512C2211yescharacteristic
57#2495C2211yescharacteristic
58#2494C2211yescharacteristic
59#2491C2211yescharacteristic
60#2490C2211yescharacteristic
61#2482—21no—
62#2480—21no—
63#2469—21no—
64#2454C2211yescharacteristic
65#2448C2211yescharacteristic
66#2447C2211yescharacteristic
67#2441C2211yescharacteristic
68#2435C2211yescharacteristic
69#2365C2211yescharacteristic, complemented
70#2362C2211yescharacteristic
71#2357C2211yescharacteristic, complemented
72D4×C22⋊C4C2211yescharacteristic
73#2331C2211yescharacteristic, complemented
74#2326C2211yescharacteristic
75#2324C2211yescharacteristic
76#2309C2211yescharacteristic
77C4×#125C2211yescharacteristic, complemented
78#2298C2211yescharacteristic
79#2293C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2097C2211yescharacteristic, complemented
83#2092C2211yescharacteristic
84#2088C2211yescharacteristic, complemented
85#2084C2211yescharacteristic, complemented
86#2077C2211yescharacteristic
87#2077C2211yescharacteristic
88#2076C2211yescharacteristic
89#2074C2211yescharacteristic, complemented
90#2073C2211yescharacteristic
91#2073C2211yescharacteristic
92#2073C2211yescharacteristic
93#2071C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2067C2211yescharacteristic, complemented
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2059C2211yescharacteristic, complemented
99#2058C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2055C2211yescharacteristic, complemented
102#2054C2211yescharacteristic
103#2054C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2033C2211yescharacteristic
110#2026C2211yescharacteristic, complemented
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic, complemented
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2000C2211yescharacteristic
120#1990C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1989C2211yescharacteristic, complemented
123#1989C2211yescharacteristic, complemented
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1970C2211yescharacteristic
130#1968C2211yescharacteristic, complemented
131#1958C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1875C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1836C2211yescharacteristic, complemented
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1804C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1767C2211yescharacteristic, complemented
194C4×C4⋊C8C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1726C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C22⋊C4—21no—
227#489—24no—
228#478—24no—
229#447—24no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#401—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#399—21no—
286#399—21no—
287#399—21no—
288#399—21no—
289#398—21no—
290#398—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#395—21no—
312#395—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391—21no—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
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#388—21no—
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#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#388D411yescharacteristic
385#388D411yescharacteristic
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#387D411yescharacteristic
398#387D411yescharacteristic
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384C2311yescharacteristic
408#383—21no—
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#379—21no—
422#379—21no—
423#379—21no—
424#379—21no—
425#379—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376C2311yescharacteristic
442C43C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×Q8C2411yescharacteristic
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C2×SD16—41no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—41no—
506C2×D8—41no—
507C2×D8—41no—
508C2×D8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521#126—82no—
522#126—82no—
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#124—22no—
528#124—41no—
529#124—41no—
530#124—41no—
531#124—82no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534#121—22no—
535#121—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—82no—
539C4×D4—22no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545#117—41no—
546#117—41no—
547#117—41no—
548#117—41no—
549#117—82no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
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—82no—
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#106—22no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664C4⋊C8—22no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668#103—22no—
669#103—22no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102#4114yes—
694C22⋊C8—22no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698#97—22no—
699#97—41no—
700#97—41no—
701#97—41no—
702C4×C8—41no—
703C4×C8—41no—
704C4×C8—41no—
705C4×C8—41no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
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#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24—21no—
754C24—21no—
755C24—42no—
756C24—42no—
757C24—81no—
758C24—81no—
759C24—81no—
760C24—81no—
761C24—81no—
762C24C22×D411yescharacteristic
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×Q8—81no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4—82no—
798C2×D4—82no—
799C2×D4—82no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4C2×#4112yes—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C2511yescharacteristic
845SD16—82no—
846D8—82no—
847D8—82no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8C2×#4112yes—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4C2×#4112yes—
924C22⋊C4—41no—
925C22⋊C4—41no—
926C22⋊C4—41no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—41no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—22no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—84no—
1023C23—84no—
1024C23—162no—
1025C23—162no—
1026C23—162no—
1027C23—162no—
1028C23—162no—
1029C23C23×D411yescharacteristic
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—84no—
1035Q8—162no—
1036D4—22no—
1037D4—22no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—84no—
1049D4—162no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
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—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
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—84no—
1133C2×C4—162no—
1134C2×C4—162no—
1135C2×C4C22×#4111yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C2×C4#58511yescharacteristic
1140C2×C4#58511yescharacteristic
1141C8—22no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C22—41no—
1150C22—42no—
1151C22—41no—
1152C22—42no—
1153C22—42no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—168no—
1178C22#344911yescharacteristic
1179C22D4×#4111yescharacteristic
1180C22#350011yescharacteristic
1181C22#358411yescharacteristic
1182C22#358411yescharacteristic
1183C22#358511yescharacteristic
1184C22#358511yescharacteristic
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—42no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4#351011yescharacteristic
1212C4#352111yescharacteristic
1213C4#356611yescharacteristic
1214C4#356811yescharacteristic
1215C2—81no—
1216C2—82no—
1217C2—161no—
1218C2—161no—
1219C2#3994711yescharacteristic
1220C2#6099811yescharacteristic
1221C2#6099811yescharacteristic
1222C2#6150011yescharacteristic
1223C2#6150511yescharacteristic
1224C2#6260711yescharacteristic
1225C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39297C2semidirect
2. #38254C2semidirect
3. #33275C2semidirect
4. #32457C2semidirect
5. #32231C2semidirect
6. #31739C2semidirect
7. #31705C2semidirect
8. #31645C2semidirect
9. #31298C2semidirect
10. #30831C2semidirect
12. #30374C2semidirect
13. #30340C2semidirect
14. #29527C2semidirect
15. #29510C2semidirect
16. #29473C2semidirect
17. #29444C2semidirect
18. #29353C2semidirect
19. #29116C2semidirect
20. #27523C2semidirect
21. #27434C2semidirect
23. #27217C2semidirect
24. #27059C2semidirect
25. #27014C2semidirect
26. #26734C2semidirect
27. #26691C2semidirect
28. #22114C2semidirect
30. #21654C2semidirect
31. #21436C2semidirect
36. #2860C22semidirect
46. #2644C22semidirect
52. #2563C22semidirect
53. #2550C22semidirect
69. #2365C22semidirect
71. #2357C22semidirect
73. #2331C22semidirect
77. C4×#125C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2097C22semidirect
84. #2088C22semidirect
85. #2084C22semidirect
89. #2074C22semidirect
93. #2071C22semidirect
94. #2068C22semidirect
95. #2067C22semidirect
98. #2059C22semidirect
99. #2058C22semidirect
100. #2057C22semidirect
101. #2055C22semidirect
110. #2026C22semidirect
112. #2025C22semidirect
113. #2024C22semidirect
120. #1990C22semidirect
121. #1989C22semidirect
122. #1989C22semidirect
123. #1989C22semidirect
130. #1968C22semidirect
132. #1949C22semidirect
133. #1944C22semidirect
134. #1943C22semidirect
135. #1943C22semidirect
136. #1942C22semidirect
137. #1941C22semidirect
141. #1936C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
155. #1926C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1920C22semidirect
167. #1920C22semidirect
168. #1919C22semidirect
169. #1919C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
173. #1916C22semidirect
174. #1880C22semidirect
179. #1877C22semidirect
181. #1865C22semidirect
184. #1862C22semidirect
186. #1836C22semidirect
193. #1767C22semidirect
194. C4×C4⋊C8C22semidirect
195. #1763C22semidirect
197. C4×#103C22semidirect
201. #1746C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#392972
#382542
#332752
#324572
#322312
#317392
#317052
#316452
#312982
#308312
#305352
#303742
#303402
#295272
#295102
#294732
#294442
#293532
#291162
#275232
#274342
#272402
#272172
#270592
#270142
#267342
#266912
#221142
#220562
#216542
#214362