Finite Group Databasebeta

← #6703097

Subgroups — #6703097

Order 512.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40164C211yesmaximal, characteristic
2#36484C211yesmaximal, characteristic, complemented
3#33081C211yesmaximal, characteristic, complemented
4#32617C211yesmaximal, characteristic, complemented
5#32560C211yesmaximal, characteristic, complemented
6#32418C211yesmaximal, characteristic, complemented
7#32299C211yesmaximal, characteristic, complemented
8#31514C211yesmaximal, characteristic, complemented
9#31314C211yesmaximal, characteristic, complemented
10#30578C211yesmaximal, characteristic, complemented
11#30424C211yesmaximal, characteristic, complemented
12#30381C211yesmaximal, characteristic, complemented
13#30077C211yesmaximal, characteristic, complemented
14#27394C211yesmaximal, characteristic, complemented
15#27170C211yesmaximal, characteristic, complemented
16#27120C211yesmaximal, characteristic, complemented
17#26971C211yesmaximal, characteristic, complemented
18#26947C211yesmaximal, characteristic, complemented
19#26556C211yesmaximal, characteristic, complemented
20#26334C211yesmaximal, characteristic, complemented
21#26224C211yesmaximal, characteristic, complemented
22#25222C211yesmaximal, characteristic, complemented
23#25093C211yesmaximal, characteristic, complemented
24#25069C211yesmaximal, characteristic, complemented
25#25037C211yesmaximal, characteristic, complemented
26#24901C211yesmaximal, characteristic, complemented
27#24882C211yesmaximal, characteristic, complemented
28#22931C211yesmaximal, characteristic, complemented
29#22580C211yesmaximal, characteristic, complemented
30#22393C211yesmaximal, characteristic, complemented
31C4×#460C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic, complemented
33C2×#480C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic, complemented
40C2×#418C2211yescharacteristic
41#2865—21no—
42#2864C2211yescharacteristic, complemented
43#2860C2211yescharacteristic
44#2753—21no—
45#2714—21no—
46#2685—21no—
47#2670—21no—
48#2635—21no—
49#2596—21no—
50#2595—21no—
51#2588—21no—
52#2581C2211yescharacteristic, complemented
53#2580C2211yescharacteristic
54#2577—21no—
55#2548C2211yescharacteristic
56#2536C2211yescharacteristic
57#2524—21no—
58#2521—21no—
59#2500C2211yescharacteristic
60#2497C2211yescharacteristic
61#2496C2211yescharacteristic, complemented
62#2495C2211yescharacteristic
63#2459—21no—
64#2433C2211yescharacteristic
65#2428C2211yescharacteristic
66#2428C2211yescharacteristic
67#2424—21no—
68#2423C2211yescharacteristic
69#2421C2211yescharacteristic, complemented
70#2420C2211yescharacteristic
71#2414C2211yescharacteristic
72#2408C2211yescharacteristic
73#2363C2211yescharacteristic
74#2362C2211yescharacteristic
75#2360C2211yescharacteristic, complemented
76#2355C2211yescharacteristic, complemented
77#2352C2211yescharacteristic
78#2347C2211yescharacteristic
79#2345C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81#2321—21no—
82C4×#127C2211yescharacteristic
83C4×#126—21no—
84C4×#124C2211yescharacteristic
85C42×Q8C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2075C2211yescharacteristic
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2071C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic, complemented
122#2033C2211yescharacteristic
123#2014C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic, complemented
126#1985C2211yescharacteristic, complemented
127#1985C2211yescharacteristic, complemented
128#1982C2211yescharacteristic
129#1982C2211yescharacteristic
130#1973C2211yescharacteristic, complemented
131#1961C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1949C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic, complemented
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic, complemented
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic, complemented
183#1854C2211yescharacteristic, complemented
184#1851C2211yescharacteristic
185#1851C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1839C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1803C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196C4×C4⋊C8C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#124—21no—
214C2×#124D411yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121—21no—
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×#120—21no—
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240#485—42no—
241#480—24no—
242#468—42no—
243#468—42no—
244#460—24no—
245#450—42no—
246C4×SD16—42no—
247C4×SD16—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265#418—24no—
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#393—21no—
328#392—21no—
329#392—21no—
330#392—21no—
331#392—21no—
332#392—21no—
333#392—21no—
334#391—21no—
335#391D411yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390D411yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
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#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388D411yescharacteristic
382#388D411yescharacteristic
383#388D411yescharacteristic
384#388D411yescharacteristic
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#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#382D411yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#381—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C43—21no—
452C43C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C2×M16—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538#127—22no—
539#127—41no—
540#127—41no—
541#127—41no—
542#126—44no—
543#126—82no—
544#124—42no—
545#124—82no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550#121—22no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—82no—
559#121—82no—
560#120—44no—
561#120—82no—
562#120—82no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—82no—
580C4×D4—82no—
581#117—22no—
582#117—41no—
583#117—41no—
584#117—41no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—41no—
607C2×C4⋊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×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⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—82no—
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700C4⋊C8—22no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102#4114yes—
730C22⋊C8—22no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736#97—41no—
737#97—41no—
738C4×C8—41no—
739C4×C8—41no—
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#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—42no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—41no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8H(5,𝔽2)12yes—
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—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4C2×#4112yes—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C2511yescharacteristic
905SD16—44no—
906SD16—44no—
907SD16—82no—
908M16—82no—
909M16—82no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8C2×#4112yes—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C2×#4112yes—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C42—22no—
1026C42—22no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—41no—
1038C42—41no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—84no—
1086C23—84no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23C23×D411yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—41no—
1096Q8—41no—
1097Q8—82no—
1098D4—22no—
1099D4—22no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—84no—
1111D4—82no—
1112D4—84no—
1113D4—84no—
1114D4—162no—
1115D4—162no—
1116D4—162no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4#57512yes—
1206C2×C4#57712yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—42no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—41no—
1237C22—41no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—168no—
1257C22D4×#4111yescharacteristic
1258C22#348511yescharacteristic
1259C22#348811yescharacteristic
1260C22C2×#57511yescharacteristic
1261C22C2×#57711yescharacteristic
1262C22#358511yescharacteristic
1263C22#358511yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#345511yescharacteristic
1290C4#351311yescharacteristic
1291C4#356011yescharacteristic
1292C4#356611yescharacteristic
1293C2—81no—
1294C2—81no—
1295C2—82no—
1296C2—161no—
1297C2—161no—
1298C2#3772811yescharacteristic
1299C2#6144511yescharacteristic
1300C2#6150611yescharacteristic
1301C2#6172511yescharacteristic
1302C2#6180511yescharacteristic
1303C2#6197011yescharacteristic
1304C2#6200911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#40164C2
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. #36484C2semidirect
3. #33081C2semidirect
4. #32617C2semidirect
5. #32560C2semidirect
6. #32418C2semidirect
7. #32299C2semidirect
8. #31514C2semidirect
9. #31314C2semidirect
10. #30578C2semidirect
11. #30424C2semidirect
12. #30381C2semidirect
13. #30077C2semidirect
14. #27394C2semidirect
15. #27170C2semidirect
16. #27120C2semidirect
17. #26971C2semidirect
18. #26947C2semidirect
19. #26556C2semidirect
20. #26334C2semidirect
21. #26224C2semidirect
22. #25222C2semidirect
23. #25093C2semidirect
24. #25069C2semidirect
25. #25037C2semidirect
26. #24901C2semidirect
27. #24882C2semidirect
28. #22931C2semidirect
29. #22580C2semidirect
30. #22393C2semidirect
31. C4×#460C2semidirect
32. C2×#485C22semidirect
39. C2×C4×SD16C22semidirect
42. #2864C22semidirect
52. #2581C22semidirect
61. #2496C22semidirect
69. #2421C22semidirect
75. #2360C22semidirect
76. #2355C22semidirect
79. #2345C22semidirect
85. C42×Q8C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
92. #2092C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
102. #2074C22semidirect
105. #2073C22semidirect
106. #2071C22semidirect
109. #2065C22semidirect
121. #2034C22semidirect
125. #2000C22semidirect
126. #1985C22semidirect
127. #1985C22semidirect
130. #1973C22semidirect
132. #1949C22semidirect
133. #1949C22semidirect
134. #1948C22semidirect
135. #1942C22semidirect
136. #1941C22semidirect
139. #1935C22semidirect
142. #1927C22semidirect
145. #1926C22semidirect
150. #1925C22semidirect
152. #1924C22semidirect
154. #1923C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
161. #1895C22semidirect
166. #1880C22semidirect
170. #1874C22semidirect
173. #1865C22semidirect
176. #1864C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
180. #1862C22semidirect
182. #1854C22semidirect
183. #1854C22semidirect
185. #1851C22semidirect
186. #1847C22semidirect
187. #1839C22semidirect
191. #1803C22semidirect
195. #1776C22semidirect
196. C4×C4⋊C8C22semidirect
199. C4×#102C22semidirect
201. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#401642
#364842
#330812
#326172
#325602
#324182
#322992
#315142
#313142
#305782
#304242
#303812
#300772
#273942
#271702
#271202
#269712
#269472
#265562
#263342
#262242
#252222
#250932
#250692
#250372
#249012
#248822
#229312
#225802
#223932
C4×#4602