Finite Group Databasebeta

← #7594480

Subgroups — #7594480

Order 512.

1437 conjugacy classes of subgroups.

The subgroup lattice has 1235 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45320C211yesmaximal, characteristic, complemented
2#45234C211yesmaximal, characteristic
3#31558C211yesmaximal, characteristic, complemented
4#31553C211yesmaximal, characteristic, complemented
5#31267C211yesmaximal, characteristic, complemented
6#31264C211yesmaximal, characteristic
7#29425C211yesmaximal, characteristic, complemented
8#29423C211yesmaximal, characteristic, complemented
9#28710C211yesmaximal, characteristic, complemented
10#27854C211yesmaximal, characteristic, complemented
11#27841C211yesmaximal, characteristic, complemented
12#27548C211yesmaximal, characteristic, complemented
13#27538C211yesmaximal, characteristic, complemented
14#27526C211yesmaximal, characteristic, complemented
15#27521C211yesmaximal, characteristic, complemented
16#27453C211yesmaximal, characteristic, complemented
17#27449C211yesmaximal, characteristic, complemented
18#27432C211yesmaximal, characteristic, complemented
19#27423C211yesmaximal, characteristic, complemented
20#26494C211yesmaximal, characteristic, complemented
21#26483C211yesmaximal, characteristic, complemented
22#25049C211yesmaximal, characteristic, complemented
23#25037C211yesmaximal, characteristic, complemented
24#24276C211yesmaximal, characteristic
25#22818C211yesmaximal, characteristic, complemented
26#22806C211yesmaximal, characteristic, complemented
27#22445C211yesmaximal, characteristic, complemented
28#22444C211yesmaximal, characteristic, complemented
29#21571C211yesmaximal, characteristic, complemented
30#21543C211yesmaximal, characteristic, complemented
31#21537C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#441C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×C4×Q16C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2798—21no—
43#2796—21no—
44#2758—21no—
45#2756—21no—
46#2755—21no—
47#2752—21no—
48#2741—21no—
49#2738—21no—
50#2562C2211yescharacteristic
51#2562C2211yescharacteristic
52#2532—21no—
53#2530—21no—
54#2526—21no—
55#2526—21no—
56#2522—21no—
57#2518—21no—
58#2510—21no—
59#2497C2211yescharacteristic
60#2495C2211yescharacteristic
61#2495C2211yescharacteristic
62#2494C2211yescharacteristic
63#2493—21no—
64#2454C2211yescharacteristic
65#2453C2211yescharacteristic
66#2453C2211yescharacteristic
67#2453C2211yescharacteristic
68#2423C2211yescharacteristic
69#2421C2211yescharacteristic
70#2421C2211yescharacteristic
71#2420C2211yescharacteristic
72#2409C2211yescharacteristic
73#2407C2211yescharacteristic
74#2395C2211yescharacteristic
75#2357C2211yescharacteristic
76#2356C2211yescharacteristic
77#2356C2211yescharacteristic
78#2355C2211yescharacteristic
79#2341C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81Q8×C22⋊C4C2211yescharacteristic
82#2339C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic
85#2323C2211yescharacteristic
86#2323C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2099C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2071C2211yescharacteristic
103#2066C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2065C2211yescharacteristic
107#2056C2211yescharacteristic
108#2055C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#2001C2211yescharacteristic
118#2000C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1973C2211yescharacteristic
122#1971C2211yescharacteristic
123#1969C2211yescharacteristic
124#1969C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1944C2211yescharacteristic
128#1943C2211yescharacteristic
129#1942C2211yescharacteristic
130#1942C2211yescharacteristic
131#1936C2211yescharacteristic
132#1935C2211yescharacteristic
133#1933C2211yescharacteristic
134#1933C2211yescharacteristic
135#1928C2211yescharacteristic
136#1928C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1918C2211yescharacteristic
149#1917C2211yescharacteristic
150#1916C2211yescharacteristic
151#1893C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1892C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1869C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1850C2211yescharacteristic
173#1847C2211yescharacteristic
174#1846C2211yescharacteristic
175#1818C2211yescharacteristic
176#1809C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1805C2211yescharacteristic
182#1805C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1787C2211yescharacteristic
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1771C2211yescharacteristic
195C8×C4⋊C4C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C2×#137—24no—
206C2×#137—24no—
207C2×#137—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117C2311yescharacteristic
231#499—42no—
232#470—24no—
233#468—24no—
234#441—24no—
235#440—42no—
236C4×Q16—42no—
237C4×SD16—24no—
238#436—42no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283#405—42no—
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#401—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400D411yescharacteristic
303#399—21no—
304#399—21no—
305#399D411yescharacteristic
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398D411yescharacteristic
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397D411yescharacteristic
318#397D411yescharacteristic
319#397D411yescharacteristic
320#396—21no—
321#396—21no—
322#395—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394D411yescharacteristic
328#394D411yescharacteristic
329#393—21no—
330#392—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#390—21no—
345#390—21no—
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
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#388—21no—
383#388—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#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#383—21no—
415#383—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454#376—21no—
455C2×#95—21no—
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516#137—416no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—41no—
522C2×Q16#4114yes—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16#4114yes—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546#125—41no—
547#125—41no—
548#125—41no—
549#125—41no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556#121—22no—
557#121—41no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—22no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576#117—41no—
577#117—41no—
578C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—22no—
671#107—22no—
672#107—41no—
673#107—41no—
674#107—41no—
675#106—22no—
676#106—22no—
677#106—22no—
678#106—41no—
679#106—41no—
680#106—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#102—22no—
703#102—22no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712C22⋊C8—41no—
713#97—22no—
714#97—22no—
715#97—41no—
716C4×C8—22no—
717C4×C8—22no—
718C4×C8—22no—
719C4×C8—41no—
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#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#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
777#95C2×D411yescharacteristic
778C24—21no—
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781#41—44no—
782#41—82no—
783#41—82no—
784#41—82no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—44no—
803C2×Q8—81no—
804C2×Q8—82no—
805C2×Q8—82no—
806C2×Q8—82no—
807C2×Q8C2×#4112yes—
808C2×Q8C2×#4112yes—
809C2×Q8C2×#4112yes—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4C2×#4112yes—
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—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—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
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×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C2511yescharacteristic
877Q16—28no—
878Q16—44no—
879SD16—28no—
880SD16—44no—
881M16—44no—
882M16—44no—
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—44no—
905C2×C8C2×#4112yes—
906C2×C8C2×#4112yes—
907C2×C8H(5,𝔽2)12yes—
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—21no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
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—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⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
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—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—22no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23C23×D411yescharacteristic
1038Q8—22no—
1039Q8—22no—
1040Q8—22no—
1041Q8—22no—
1042Q8—22no—
1043Q8—22no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—84no—
1051D4—22no—
1052D4—22no—
1053D4—41no—
1054D4—41no—
1055D4—82no—
1056D4—84no—
1057D4—162no—
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—22no—
1083C2×C4—22no—
1084C2×C4—22no—
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—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—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—84no—
1148C2×C4—84no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4C22×#4111yescharacteristic
1152C2×C4C22×#4111yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8#55114yes—
1165C22—41no—
1166C22—42no—
1167C22—41no—
1168C22—42no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—42no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22D4×#4111yescharacteristic
1187C22D4×#4111yescharacteristic
1188C22#349611yescharacteristic
1189C22#358411yescharacteristic
1190C22#358411yescharacteristic
1191C22#358611yescharacteristic
1192C22#358611yescharacteristic
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4C2×#55111yescharacteristic
1221C4#352111yescharacteristic
1222C4#352111yescharacteristic
1223C4#354011yescharacteristic
1224C2—81no—
1225C2—81no—
1226C2—82no—
1227C2#5937511yescharacteristic
1228C2#6150011yescharacteristic
1229C2#6151411yescharacteristic
1230C2#6154911yescharacteristic
1231C2#6154911yescharacteristic
1232C2#6232211yescharacteristic
1233C2#6235211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45320C2semidirect
3. #31558C2semidirect
4. #31553C2semidirect
5. #31267C2semidirect
7. #29425C2semidirect
8. #29423C2semidirect
9. #28710C2semidirect
10. #27854C2semidirect
11. #27841C2semidirect
12. #27548C2semidirect
13. #27538C2semidirect
14. #27526C2semidirect
15. #27521C2semidirect
16. #27453C2semidirect
17. #27449C2semidirect
18. #27432C2semidirect
19. #27423C2semidirect
20. #26494C2semidirect
21. #26483C2semidirect
22. #25049C2semidirect
23. #25037C2semidirect
25. #22818C2semidirect
26. #22806C2semidirect
27. #22445C2semidirect
28. #22444C2semidirect
29. #21571C2semidirect
30. #21543C2semidirect
31. #21537C2semidirect

Maximal subgroups

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

subgroupindex
#453202
#452342
#315582
#315532
#312672
#312642
#294252
#294232
#287102
#278542
#278412
#275482
#275382
#275262
#275212
#274532
#274492
#274322
#274232
#264942
#264832
#250492
#250372
#242762
#228182
#228062
#224452
#224442
#215712
#215432
#215372