Finite Group Databasebeta

← #6877496

Subgroups — #6877496

Order 512.

1524 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39191C211yesmaximal, characteristic, complemented
2#38202C211yesmaximal, characteristic, complemented
3#33132C211yesmaximal, characteristic, complemented
4#32211C211yesmaximal, characteristic, complemented
5#32021C211yesmaximal, characteristic, complemented
6#32005C211yesmaximal, characteristic, complemented
7#31606C211yesmaximal, characteristic, complemented
8#30919C211yesmaximal, characteristic, complemented
9#30609C211yesmaximal, characteristic, complemented
10#30412C211yesmaximal, characteristic, complemented
11#30396C211yesmaximal, characteristic, complemented
12#30379C211yesmaximal, characteristic, complemented
13#30373C211yesmaximal, characteristic, complemented
14#29578C211yesmaximal, characteristic, complemented
15#29499C211yesmaximal, characteristic, complemented
16#29484C211yesmaximal, characteristic, complemented
17#29469C211yesmaximal, characteristic, complemented
18#27550C211yesmaximal, characteristic, complemented
19#27520C211yesmaximal, characteristic, complemented
20#27507C211yesmaximal, characteristic, complemented
21#27484C211yesmaximal, characteristic, complemented
22#27427C211yesmaximal, characteristic, complemented
23#27399C211yesmaximal, characteristic, complemented
24#26390C211yesmaximal, characteristic, complemented
25#25168C211yesmaximal, characteristic, complemented
26#24717C211yesmaximal, characteristic, complemented
27#24512C211yesmaximal, characteristic, complemented
28#22145C211yesmaximal, characteristic, complemented
29#22056C211yesmaximal, characteristic, complemented
30#21541C211yesmaximal, characteristic, complemented
31#21111C211yesmaximal, characteristic, complemented
32C2×#478C2211yescharacteristic, complemented
33C2×#469C2211yescharacteristic
34C2×#466C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#433C2211yescharacteristic
40C2×#405C2211yescharacteristic, complemented
41#2860C2211yescharacteristic
42#2859C2211yescharacteristic, complemented
43#2757—21no—
44#2756—21no—
45#2753—21no—
46#2753—21no—
47#2735—21no—
48#2711—21no—
49#2711—21no—
50#2685—21no—
51#2629C2211yescharacteristic
52#2624C2211yescharacteristic
53#2624C2211yescharacteristic
54#2624C2211yescharacteristic, complemented
55#2554—21no—
56#2537C2211yescharacteristic
57#2537C2211yescharacteristic
58#2512C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic, complemented
61#2490C2211yescharacteristic
62#2487—21no—
63#2485—21no—
64#2485C2211yescharacteristic
65#2480—21no—
66#2479—21no—
67#2454C2211yescharacteristic
68#2428C2211yescharacteristic
69#2428C2211yescharacteristic, complemented
70#2422C2211yescharacteristic
71#2416—21no—
72#2414—21no—
73#2411—21no—
74#2408C2211yescharacteristic
75#2354C2211yescharacteristic, complemented
76D4×C4⋊C4C2211yescharacteristic, complemented
77#2347C2211yescharacteristic
78D4×C22⋊C4C2211yescharacteristic
79#2324C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic, complemented
82#2309C2211yescharacteristic
83C4×#127C2211yescharacteristic, complemented
84#2293C2211yescharacteristic
85#2293C2211yescharacteristic
86#2100C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2041C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2025C2211yescharacteristic, complemented
123#2011C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1989C2211yescharacteristic, complemented
127#1982C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1948C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic, complemented
148#1934C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1870C2211yescharacteristic
177#1869C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1851C2211yescharacteristic, complemented
189#1850C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1807C2211yescharacteristic, complemented
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×C4⋊C8C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C22⋊C4—21no—
243#478—42no—
244#469—24no—
245#466—42no—
246#459—24no—
247#447—24no—
248#447—42no—
249#442—42no—
250#433—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297#405—42no—
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#399—21no—
307#399—21no—
308#399—21no—
309#399—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#394—21no—
326#394—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#394—21no—
340#394—21no—
341#392—21no—
342#392—21no—
343#392—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390D411yescharacteristic
353#390D411yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389D411yescharacteristic
369#389D411yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
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#388—21no—
398#388—21no—
399#388D411yescharacteristic
400#388D411yescharacteristic
401#388D411yescharacteristic
402#388D411yescharacteristic
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#382—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8#4114yes—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—41no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542#127—22no—
543#127—41no—
544#126—82no—
545#126—82no—
546#125—41no—
547#125—41no—
548#125—82no—
549#123—82no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—82no—
563#121—82no—
564#121—82no—
565#121—82no—
566#120—82no—
567C4×D4—22no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—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—41no—
580C4×D4—41no—
581C4×D4—82no—
582C4×D4—82no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—41no—
589#117—82no—
590#117—82no—
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—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—82no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
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—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—22no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749#97—22no—
750#97—22no—
751#97—41no—
752C4×C8—41no—
753C4×C8—41no—
754C4×C8—41no—
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#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—42no—
790C24—42no—
791C24—81no—
792C24—81no—
793C24—81no—
794C24—81no—
795C24—81no—
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798C2×D4—22no—
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—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—82no—
838C2×D4—82no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
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—
855C2×D4C2×#4112yes—
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—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2511yescharacteristic
911D8—44no—
912D8—82no—
913D8—82no—
914D8—82no—
915M16—44no—
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×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—44no—
939C2×C8C2×#4112yes—
940C2×C8H(5,𝔽2)12yes—
941C4⋊C4—22no—
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—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
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—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C42—22no—
1050C42—22no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—41no—
1062C42—41no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—22no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—84no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23C23×D411yescharacteristic
1118D4—22no—
1119D4—22no—
1120D4—22no—
1121D4—22no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—82no—
1135D4—84no—
1136D4—84no—
1137D4—84no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
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—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
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—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—84no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4#57612yes—
1229C2×C4#57712yes—
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—22no—
1237C8—22no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C22—41no—
1245C22—41no—
1246C22—42no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—42no—
1251C22—42no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—168no—
1287C22#344911yescharacteristic
1288C22D4×#4111yescharacteristic
1289C22#349611yescharacteristic
1290C22C2×#57611yescharacteristic
1291C22C2×#57711yescharacteristic
1292C22#358511yescharacteristic
1293C22#358511yescharacteristic
1294C4—22no—
1295C4—22no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4#350511yescharacteristic
1319C4#352111yescharacteristic
1320C4#353311yescharacteristic
1321C4#356611yescharacteristic
1322C2—81no—
1323C2—81no—
1324C2—82no—
1325C2—82no—
1326C2—161no—
1327C2—161no—
1328C2#3994211yescharacteristic
1329C2#6097811yescharacteristic
1330C2#6098911yescharacteristic
1331C2#6149611yescharacteristic
1332C2#6150611yescharacteristic
1333C2#6234911yescharacteristic
1334C2#6235511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39191C2semidirect
2. #38202C2semidirect
3. #33132C2semidirect
4. #32211C2semidirect
5. #32021C2semidirect
6. #32005C2semidirect
7. #31606C2semidirect
8. #30919C2semidirect
9. #30609C2semidirect
10. #30412C2semidirect
11. #30396C2semidirect
12. #30379C2semidirect
13. #30373C2semidirect
14. #29578C2semidirect
15. #29499C2semidirect
16. #29484C2semidirect
17. #29469C2semidirect
18. #27550C2semidirect
19. #27520C2semidirect
20. #27507C2semidirect
21. #27484C2semidirect
22. #27427C2semidirect
23. #27399C2semidirect
24. #26390C2semidirect
25. #25168C2semidirect
26. #24717C2semidirect
27. #24512C2semidirect
28. #22145C2semidirect
29. #22056C2semidirect
30. #21541C2semidirect
31. #21111C2semidirect
32. C2×#478C22semidirect
40. C2×#405C22semidirect
42. #2859C22semidirect
54. #2624C22semidirect
60. #2497C22semidirect
69. #2428C22semidirect
75. #2354C22semidirect
76. D4×C4⋊C4C22semidirect
81. #2324C22semidirect
83. C4×#127C22semidirect
86. #2100C22semidirect
87. #2099C22semidirect
88. #2099C22semidirect
90. #2094C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
96. #2084C22semidirect
100. #2077C22semidirect
102. #2075C22semidirect
110. #2059C22semidirect
113. #2041C22semidirect
118. #2034C22semidirect
119. #2034C22semidirect
122. #2025C22semidirect
126. #1989C22semidirect
127. #1982C22semidirect
133. #1948C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
137. #1944C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
142. #1936C22semidirect
143. #1936C22semidirect
147. #1934C22semidirect
148. #1934C22semidirect
149. #1934C22semidirect
152. #1926C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
163. #1895C22semidirect
165. #1893C22semidirect
181. #1864C22semidirect
182. #1864C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
185. #1862C22semidirect
188. #1851C22semidirect
189. #1850C22semidirect
190. #1809C22semidirect
191. #1807C22semidirect
193. #1802C22semidirect
196. #1776C22semidirect
197. C4×C4⋊C8C22semidirect
199. C4×#102C22semidirect
201. #1750C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#391912
#382022
#331322
#322112
#320212
#320052
#316062
#309192
#306092
#304122
#303962
#303792
#303732
#295782
#294992
#294842
#294692
#275502
#275202
#275072
#274842
#274272
#273992
#263902
#251682
#247172
#245122
#221452
#220562
#215412
#211112