Finite Group Databasebeta

← #7597663

Subgroups — #7597663

Order 512.

1499 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59657C211yesmaximal, characteristic
2#59433C211yesmaximal, characteristic, complemented
3#31706C211yesmaximal, characteristic, complemented
4#31703C211yesmaximal, characteristic, complemented
5#30648C211yesmaximal, characteristic, complemented
6#30645C211yesmaximal, characteristic, complemented
7#29279C211yesmaximal, characteristic, complemented
8#29060C211yesmaximal, characteristic, complemented
9#29060C211yesmaximal, characteristic, complemented
10#28788C211yesmaximal, characteristic, complemented
11#28781C211yesmaximal, characteristic, complemented
12#28207C211yesmaximal, characteristic, complemented
13#28092C211yesmaximal, characteristic, complemented
14#28089C211yesmaximal, characteristic, complemented
15#27357C211yesmaximal, characteristic, complemented
16#27343C211yesmaximal, characteristic, complemented
17#27122C211yesmaximal, characteristic, complemented
18#27112C211yesmaximal, characteristic, complemented
19#25843C211yesmaximal, characteristic, complemented
20#25707C211yesmaximal, characteristic, complemented
21#25473C211yesmaximal, characteristic, complemented
22#25344C211yesmaximal, characteristic, complemented
23#25064C211yesmaximal, characteristic, complemented
24#25019C211yesmaximal, characteristic, complemented
25#22931C211yesmaximal, characteristic, complemented
26#22924C211yesmaximal, characteristic, complemented
27#22519C211yesmaximal, characteristic, complemented
28#22501C211yesmaximal, characteristic, complemented
29#21728C211yesmaximal, characteristic, complemented
30C4×#490C211yesmaximal, characteristic, complemented
31#21634C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×C8×Q8C2211yescharacteristic
41C2×#436C2211yescharacteristic
42#2789—21no—
43#2786—21no—
44#2723—21no—
45#2676—21no—
46#2596—21no—
47#2594—21no—
48#2584C2211yescharacteristic
49#2580C2211yescharacteristic
50#2562C2211yescharacteristic
51#2560—21no—
52#2540—21no—
53#2535C2211yescharacteristic
54#2528—21no—
55#2521—21no—
56#2496C2211yescharacteristic
57#2494—21no—
58#2494C2211yescharacteristic
59#2494C2211yescharacteristic
60#2494C2211yescharacteristic
61#2491C2211yescharacteristic
62#2490C2211yescharacteristic
63#2463—21no—
64#2461—21no—
65#2443—21no—
66#2442C2211yescharacteristic
67#2441C2211yescharacteristic
68#2441C2211yescharacteristic
69#2440C2211yescharacteristic
70#2428C2211yescharacteristic
71#2428C2211yescharacteristic
72#2373—21no—
73#2363C2211yescharacteristic
74#2361—21no—
75#2361C2211yescharacteristic
76#2355C2211yescharacteristic
77#2352C2211yescharacteristic
78#2346C2211yescharacteristic
79#2345C2211yescharacteristic
80C4×#127C2211yescharacteristic
81C4×#125C2211yescharacteristic
82C4×#125C2211yescharacteristic
83C4×#125C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2093C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2067C2211yescharacteristic
100#2065C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2057C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#1992C2211yescharacteristic
118#1991C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1989C2211yescharacteristic
125#1987C2211yescharacteristic
126#1984C2211yescharacteristic
127#1961C2211yescharacteristic
128#1954C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1944C2211yescharacteristic
132#1944C2211yescharacteristic
133#1943C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1941C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1918C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1853C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1846C2211yescharacteristic
176#1836C2211yescharacteristic
177#1831C2211yescharacteristic
178#1825C2211yescharacteristic
179#1823C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205#554—24no—
206#554—42no—
207#553—24no—
208#553—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124D411yescharacteristic
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246#499—24no—
247#490—24no—
248#482—24no—
249#480—24no—
250#478—42no—
251#478—42no—
252C8×Q8—42no—
253#436—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#401—21no—
305#401—21no—
306#401—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#395—21no—
325#395—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#393—21no—
333#392—21no—
334#392—21no—
335#392—21no—
336#391—21no—
337#391D411yescharacteristic
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390D411yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
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#388D411yescharacteristic
376#388D411yescharacteristic
377#388D411yescharacteristic
378#388D411yescharacteristic
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#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382—21no—
411#382D411yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#376—21no—
449C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8C2×D411yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525#127—22no—
526#127—41no—
527#126—44no—
528#126—44no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—41no—
535#125—41no—
536#125#4114yes—
537#124—42no—
538#124—82no—
539#123—44no—
540C22⋊Q8—44no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543C22⋊Q8—82no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—44no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—44no—
554#121—82no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—44no—
568C4×D4—82no—
569C4×D4—82no—
570C4×D4—82no—
571#117—22no—
572#117—22no—
573#117—41no—
574#117—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—21no—
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—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
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—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—22no—
683#107—22no—
684#107—22no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—41no—
692#106—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696C4⋊C8—22no—
697C4⋊C8—22no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102#4114yes—
716C22⋊C8—22no—
717C22⋊C8—22no—
718C22⋊C8—22no—
719C22⋊C8—22no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722#97—22no—
723#97—22no—
724#97—22no—
725#97—41no—
726C4×C8—22no—
727C4×C8—22no—
728C4×C8—41no—
729C4×C8—41no—
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#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#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C24—21no—
776C24C22×D411yescharacteristic
777C24C22×D411yescharacteristic
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—41no—
781C2×Q8—42no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
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—41no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4C2×#4112yes—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
874M16—82no—
875M16—82no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
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×C8C2×#4112yes—
898C2×C82−1+412yes—
899C2×C82−1+412yes—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
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—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4C2×#4112yes—
957C4⋊C4C2×#4112yes—
958C4⋊C4C2×#4112yes—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
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—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
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—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42C2×#4112yes—
1018C42H(5,𝔽2)12yes—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—22no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
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—
1047C23C23×D411yescharacteristic
1048Q8—44no—
1049Q8—162no—
1050D4—22no—
1051D4—22no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—82no—
1059D4—84no—
1060D4—84no—
1061D4—84no—
1062D4—84no—
1063D4—162no—
1064D4—162no—
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—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
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—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—84no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4#54612yes—
1155C2×C4#54612yes—
1156C2×C4#57512yes—
1157C2×C4C22×#4111yescharacteristic
1158C2×C4C22×#4111yescharacteristic
1159C2×C4C2×H(5,𝔽2)11yescharacteristic
1160C2×C4C2×2−1+411yescharacteristic
1161C2×C4C2×2−1+411yescharacteristic
1162C2×C4#58511yescharacteristic
1163C8—22no—
1164C8—22no—
1165C8—22no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C22—41no—
1172C22—41no—
1173C22—42no—
1174C22—41no—
1175C22—42no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—42no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22C2×#54611yescharacteristic
1200C22D4×#4111yescharacteristic
1201C22#349911yescharacteristic
1202C22C2×#57511yescharacteristic
1203C22#358411yescharacteristic
1204C22#358511yescharacteristic
1205C22#358511yescharacteristic
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—42no—
1219C4—41no—
1220C4—42no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4#348211yescharacteristic
1233C4#351111yescharacteristic
1234C4#351611yescharacteristic
1235C4#356111yescharacteristic
1236C2—81no—
1237C2—81no—
1238C2—82no—
1239C2—161no—
1240C2#5941511yescharacteristic
1241C2#6114111yescharacteristic
1242C2#6122311yescharacteristic
1243C2#6146811yescharacteristic
1244C2#6153611yescharacteristic
1245C2#6251211yescharacteristic
1246C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59657C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59433C2semidirect
3. #31706C2semidirect
4. #31703C2semidirect
5. #30648C2semidirect
6. #30645C2semidirect
7. #29279C2semidirect
8. #29060C2semidirect
9. #29060C2semidirect
10. #28788C2semidirect
11. #28781C2semidirect
12. #28207C2semidirect
13. #28092C2semidirect
14. #28089C2semidirect
15. #27357C2semidirect
16. #27343C2semidirect
17. #27122C2semidirect
18. #27112C2semidirect
19. #25843C2semidirect
20. #25707C2semidirect
21. #25473C2semidirect
22. #25344C2semidirect
23. #25064C2semidirect
24. #25019C2semidirect
25. #22931C2semidirect
26. #22924C2semidirect
27. #22519C2semidirect
28. #22501C2semidirect
29. #21728C2semidirect
30. C4×#490C2semidirect
31. #21634C2semidirect

Maximal subgroups

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

subgroupindex
#596572
#594332
#317062
#317032
#306482
#306452
#292792
#290602
#287882
#287812
#282072
#280922
#280892
#273572
#273432
#271222
#271122
#258432
#257072
#254732
#253442
#250642
#250192
#229312
#229242
#225192
#225012
#217282
C4×#4902
#216342