Finite Group Databasebeta

← #7086797

Subgroups — #7086797

Order 512.

1365 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45286C211yesmaximal, characteristic, complemented
2#42903C211yesmaximal, characteristic, complemented
3#32247C211yesmaximal, characteristic, complemented
4#32183C211yesmaximal, characteristic, complemented
5#32172C211yesmaximal, characteristic, complemented
6#32127C211yesmaximal, characteristic, complemented
7#31805C211yesmaximal, characteristic, complemented
8#31088C211yesmaximal, characteristic, complemented
9#30532C211yesmaximal, characteristic
10#30528C211yesmaximal, characteristic, complemented
11#29564C211yesmaximal, characteristic, complemented
12#29358C211yesmaximal, characteristic, complemented
13#29065C211yesmaximal, characteristic, complemented
14#28992C211yesmaximal, characteristic, complemented
15#28013C211yesmaximal, characteristic, complemented
16#27772C211yesmaximal, characteristic, complemented
17#27532C211yesmaximal, characteristic, complemented
18#27331C211yesmaximal, characteristic, complemented
19#27272C211yesmaximal, characteristic, complemented
20#27012C211yesmaximal, characteristic, complemented
21#26917C211yesmaximal, characteristic, complemented
22#26821C211yesmaximal, characteristic, complemented
23#26715C211yesmaximal, characteristic, complemented
24#26625C211yesmaximal, characteristic, complemented
25#25281C211yesmaximal, characteristic, complemented
26#24488C211yesmaximal, characteristic, complemented
27#23689C211yesmaximal, characteristic, complemented
28#23287C211yesmaximal, characteristic, complemented
29#23218C211yesmaximal, characteristic, complemented
30#22863C211yesmaximal, characteristic, complemented
31#22229C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×#417C2211yescharacteristic
41#2829—21no—
42#2803—21no—
43#2798—21no—
44#2797—21no—
45#2787—21no—
46#2781—21no—
47#2750—21no—
48#2745—21no—
49#2740—21no—
50#2649—21no—
51#2648—21no—
52#2641C2211yescharacteristic
53#2594—21no—
54#2576—21no—
55#2550C2211yescharacteristic
56#2545C2211yescharacteristic
57#2544C2211yescharacteristic
58#2513C2211yescharacteristic
59#2513C2211yescharacteristic
60#2513C2211yescharacteristic
61#2494C2211yescharacteristic
62#2491C2211yescharacteristic
63#2490C2211yescharacteristic
64#2489C2211yescharacteristic
65#2485—21no—
66#2474—21no—
67#2454C2211yescharacteristic
68#2453C2211yescharacteristic
69#2448C2211yescharacteristic
70#2447—21no—
71#2442C2211yescharacteristic
72#2432C2211yescharacteristic
73#2431C2211yescharacteristic
74#2426C2211yescharacteristic
75#2420C2211yescharacteristic
76#2401C2211yescharacteristic
77#2370C2211yescharacteristic
78#2370C2211yescharacteristic
79#2367C2211yescharacteristic
80#2361C2211yescharacteristic
81#2344C2211yescharacteristic
82#2341C2211yescharacteristic
83#2331C2211yescharacteristic
84#2327C2211yescharacteristic
85#2319C2211yescharacteristic
86#2101C2211yescharacteristic
87#2088C2211yescharacteristic
88#2085C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic
91#2073C2211yescharacteristic
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2068C2211yescharacteristic
96#2066C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2043C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2041C2211yescharacteristic
111#2036C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2013C2211yescharacteristic
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic
135#1972C2211yescharacteristic
136#1970C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1960C2211yescharacteristic
140#1958C2211yescharacteristic
141#1942C2211yescharacteristic
142#1939C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1916C2211yescharacteristic
172#1895C2211yescharacteristic
173#1895C2211yescharacteristic
174#1894C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1872C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1852C2211yescharacteristic
187#1851C2211yescharacteristic
188#1846C2211yescharacteristic
189#1805C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192C4×#107C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195#1768C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229C22×C4⋊C4C2311yescharacteristic
230#488—24no—
231#488—42no—
232#487—24no—
233#481—42no—
234#478—42no—
235#449—24no—
236#440—42no—
237C4×SD16—42no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251#417—42no—
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#401—21no—
295#401D411yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400D411yescharacteristic
300#400D411yescharacteristic
301#400D411yescharacteristic
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397D411yescharacteristic
319#397D411yescharacteristic
320#397D411yescharacteristic
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396D411yescharacteristic
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#393—21no—
340#392—21no—
341#392—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#381—21no—
429#381—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2411yescharacteristic
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#127—41no—
537#127—41no—
538#125—22no—
539#125—22no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—41no—
544#124—22no—
545#124—41no—
546#124—41no—
547#124—41no—
548#124—41no—
549#124—41no—
550#124—82no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553#121—22no—
554#121—41no—
555#121—41no—
556#121—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×D4—22no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—82no—
568#117—82no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
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—41no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—41no—
671#107—41no—
672#107—41no—
673#106—22no—
674#106—41no—
675#106—41no—
676#106—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103#4114yes—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714C22⋊C8—22no—
715C22⋊C8—41no—
716C22⋊C8—41no—
717#97—41no—
718#97—41no—
719C4×C8—22no—
720C4×C8—22no—
721C4×C8—41no—
722C4×C8—41no—
723C4×C8—41no—
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#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
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
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×D411yescharacteristic
777#41—44no—
778#41—82no—
779#41—82no—
780#41—82no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8C2×#4112yes—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
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—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
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×C4C22×D411yescharacteristic
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
874SD16—44no—
875SD16—44no—
876D8—82no—
877D8—82no—
878M16—82no—
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×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8C2×#4112yes—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
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—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4C2×#4112yes—
953C4⋊C4H(5,𝔽2)12yes—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
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—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
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—
1046C23C23×D411yescharacteristic
1047Q8—22no—
1048Q8—22no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—41no—
1053Q8—41no—
1054Q8—41no—
1055Q8—162no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—84no—
1069D4—84no—
1070D4—162no—
1071D4—162no—
1072D4—162no—
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—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—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
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—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—162no—
1158C2×C4—162no—
1159C2×C4C22×#4111yescharacteristic
1160C2×C4C2×H(5,𝔽2)11yescharacteristic
1161C2×C4#58511yescharacteristic
1162C2×C4#58511yescharacteristic
1163C2×C4#58511yescharacteristic
1164C2×C4#58511yescharacteristic
1165C8—22no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22D4×#4111yescharacteristic
1202C22#348811yescharacteristic
1203C22#350011yescharacteristic
1204C22#358411yescharacteristic
1205C22#358411yescharacteristic
1206C22#358411yescharacteristic
1207C22#358511yescharacteristic
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—42no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—42no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—42no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4#350611yescharacteristic
1235C4#352111yescharacteristic
1236C4#354011yescharacteristic
1237C4#356811yescharacteristic
1238C2—81no—
1239C2—161no—
1240C2—161no—
1241C2—161no—
1242C2#4418211yescharacteristic
1243C2#6148811yescharacteristic
1244C2#6153511yescharacteristic
1245C2#6202711yescharacteristic
1246C2#6206211yescharacteristic
1247C2#6255511yescharacteristic
1248C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45286C2semidirect
2. #42903C2semidirect
3. #32247C2semidirect
4. #32183C2semidirect
5. #32172C2semidirect
6. #32127C2semidirect
7. #31805C2semidirect
8. #31088C2semidirect
10. #30528C2semidirect
11. #29564C2semidirect
12. #29358C2semidirect
13. #29065C2semidirect
14. #28992C2semidirect
15. #28013C2semidirect
16. #27772C2semidirect
17. #27532C2semidirect
18. #27331C2semidirect
19. #27272C2semidirect
20. #27012C2semidirect
21. #26917C2semidirect
22. #26821C2semidirect
23. #26715C2semidirect
24. #26625C2semidirect
25. #25281C2semidirect
26. #24488C2semidirect
27. #23689C2semidirect
28. #23287C2semidirect
29. #23218C2semidirect
30. #22863C2semidirect
31. #22229C2semidirect

Maximal subgroups

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

subgroupindex
#452862
#429032
#322472
#321832
#321722
#321272
#318052
#310882
#305322
#305282
#295642
#293582
#290652
#289922
#280132
#277722
#275322
#273312
#272722
#270122
#269172
#268212
#267152
#266252
#252812
#244882
#236892
#232872
#232182
#228632
#222292