Finite Group Databasebeta

← #7594329

Subgroups — #7594329

Order 512.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59316C211yesmaximal, characteristic, complemented
2#59304C211yesmaximal, characteristic
3#31932C211yesmaximal, characteristic, complemented
4#31932C211yesmaximal, characteristic, complemented
5#31691C211yesmaximal, characteristic, complemented
6#31686C211yesmaximal, characteristic, complemented
7#28867C211yesmaximal, characteristic, complemented
8#28847C211yesmaximal, characteristic, complemented
9#28802C211yesmaximal, characteristic, complemented
10#28154C211yesmaximal, characteristic, complemented
11#27709C211yesmaximal, characteristic, complemented
12#27695C211yesmaximal, characteristic, complemented
13#27680C211yesmaximal, characteristic, complemented
14#27650C211yesmaximal, characteristic, complemented
15#26122C211yesmaximal, characteristic, complemented
16#26032C211yesmaximal, characteristic, complemented
17#25560C211yesmaximal, characteristic, complemented
18#25556C211yesmaximal, characteristic, complemented
19#25257C211yesmaximal, characteristic, complemented
20#25245C211yesmaximal, characteristic, complemented
21#24982C211yesmaximal, characteristic, complemented
22#24979C211yesmaximal, characteristic, complemented
23#24955C211yesmaximal, characteristic, complemented
24#24949C211yesmaximal, characteristic, complemented
25#22781C211yesmaximal, characteristic, complemented
26#22711C211yesmaximal, characteristic, complemented
27#22504C211yesmaximal, characteristic, complemented
28#22491C211yesmaximal, characteristic, complemented
29#21540C211yesmaximal, characteristic, complemented
30#21490C211yesmaximal, characteristic, complemented
31#20764C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#553—21no—
34C2×#552C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#436C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×C4×M16C2211yescharacteristic
43#2722—21no—
44#2718—21no—
45#2718—21no—
46#2672—21no—
47#2553—21no—
48#2552C2211yescharacteristic
49#2550C2211yescharacteristic
50#2537C2211yescharacteristic
51#2536C2211yescharacteristic
52#2521—21no—
53#2519—21no—
54#2501C2211yescharacteristic
55#2501C2211yescharacteristic
56#2496C2211yescharacteristic
57#2496C2211yescharacteristic
58#2487—21no—
59#2485C2211yescharacteristic
60#2485C2211yescharacteristic
61#2479—21no—
62#2462—21no—
63#2443—21no—
64#2443—21no—
65#2441—21no—
66#2441C2211yescharacteristic
67#2440C2211yescharacteristic
68#2423C2211yescharacteristic
69#2423C2211yescharacteristic
70#2422—21no—
71#2416C2211yescharacteristic
72#2416C2211yescharacteristic
73#2362—21no—
74#2354C2211yescharacteristic
75#2352C2211yescharacteristic
76#2351C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C4×#121C2211yescharacteristic
83#2285C2211yescharacteristic
84C2×#384C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2096C2211yescharacteristic
90#2096C2211yescharacteristic
91#2088C2211yescharacteristic
92#2086C2211yescharacteristic
93#2084C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2057C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2025C2211yescharacteristic
114#2023C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#1992C2211yescharacteristic
118#1990C2211yescharacteristic
119#1989C2211yescharacteristic
120#1988C2211yescharacteristic
121#1968C2211yescharacteristic
122#1955C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1948C2211yescharacteristic
127#1944C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1940C2211yescharacteristic
131#1936C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic
135#1923C2211yescharacteristic
136#1923C2211yescharacteristic
137#1921C2211yescharacteristic
138#1920C2211yescharacteristic
139#1919C2211yescharacteristic
140#1918C2211yescharacteristic
141#1895C2211yescharacteristic
142#1895C2211yescharacteristic
143#1894C2211yescharacteristic
144#1894C2211yescharacteristic
145#1893C2211yescharacteristic
146#1892C2211yescharacteristic
147#1880C2211yescharacteristic
148#1880C2211yescharacteristic
149#1875C2211yescharacteristic
150#1874C2211yescharacteristic
151#1872C2211yescharacteristic
152#1872C2211yescharacteristic
153#1872C2211yescharacteristic
154#1872C2211yescharacteristic
155#1870C2211yescharacteristic
156#1870C2211yescharacteristic
157#1865C2211yescharacteristic
158#1863C2211yescharacteristic
159#1854C2211yescharacteristic
160#1853C2211yescharacteristic
161#1853C2211yescharacteristic
162#1853C2211yescharacteristic
163#1853C2211yescharacteristic
164#1852C2211yescharacteristic
165#1836C2211yescharacteristic
166#1836C2211yescharacteristic
167#1836C2211yescharacteristic
168#1836C2211yescharacteristic
169#1834C2211yescharacteristic
170#1834C2211yescharacteristic
171#1834C2211yescharacteristic
172#1834C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1824C2211yescharacteristic
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1807C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1797C2211yescharacteristic
189#1776C2211yescharacteristic
190#1771C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic
195#1753C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#556—24no—
209#556—42no—
210#553—48no—
211#552—24no—
212#552—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121D411yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4—21no—
257C22×C4⋊C4—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#482—42no—
265#482—42no—
266#468—24no—
267#440—24no—
268#436—42no—
269#435—24no—
270#435—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C4×M16—24no—
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#391—21no—
348#391C2311yescharacteristic
349#390D411yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389D411yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
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#388D411yescharacteristic
381#388D411yescharacteristic
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386D411yescharacteristic
396#386D411yescharacteristic
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384—21no—
406#384—21no—
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380D411yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
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×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2×D411yescharacteristic
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—22no—
535C4⋊Q8—41no—
536#126—44no—
537#126—44no—
538#126—44no—
539#126—44no—
540#126—44no—
541#125—22no—
542#125—41no—
543#125—44no—
544#125—44no—
545#124—44no—
546#123—44no—
547#123—44no—
548#123—44no—
549#123—82no—
550#123—82no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—41no—
555C22⋊Q8—41no—
556C22⋊Q8—44no—
557C22⋊Q8#4114yes—
558#121—24no—
559#121—22no—
560#121—22no—
561#121—44no—
562#121—44no—
563#121—44no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—44no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—44no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—44no—
593#117—41no—
594#117—44no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—22no—
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—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—44no—
644C2×C4⋊C4—82no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
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—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—22no—
701C2×C42—22no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—41no—
721#107—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#103—22no—
734#103—22no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—22no—
756#97—41no—
757#97#4114yes—
758C4×C8—22no—
759C4×C8—22no—
760C4×C8—41no—
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#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C24—21no—
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—81no—
807C2×Q8C2×#4112yes—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
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—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
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—41no—
868C22×C4—41no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2×#4112yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4C2511yescharacteristic
901SD16—44no—
902M16—44no—
903M16—44no—
904M16—82no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
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—82no—
928C2×C8C2×#4112yes—
929C2×C8C2×#4112yes—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
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—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—41no—
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—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4C2×#4112yes—
1001C22⋊C4—24no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
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⋊C4AGL(1,ℤ/8)14yes—
1037C42—22no—
1038C42—22no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42C2×#4112yes—
1056C422−1+412yes—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23#54612yes—
1084C23C2×AGL(1,ℤ/8)12yes—
1085C23C23×D411yescharacteristic
1086Q8—22no—
1087Q8—22no—
1088Q8—41no—
1089Q8—41no—
1090Q8—84no—
1091D4—44no—
1092D4—44no—
1093D4—44no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—84no—
1099D4—162no—
1100D4—162no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—22no—
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—44no—
1135C2×C4—44no—
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—41no—
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—84no—
1188C2×C4—84no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4—162no—
1192C2×C4—162no—
1193C2×C4#54612yes—
1194C2×C4#54712yes—
1195C2×C4#54712yes—
1196C2×C4C2×AGL(1,ℤ/8)12yes—
1197C2×C4C2×AGL(1,ℤ/8)12yes—
1198C2×C4#57712yes—
1199C2×C4C22×#4111yescharacteristic
1200C2×C4C22×#4111yescharacteristic
1201C2×C4C2×H(5,𝔽2)11yescharacteristic
1202C2×C4C2×2−1+411yescharacteristic
1203C2×C4#58511yescharacteristic
1204C2×C4#58511yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22C2×#54611yescharacteristic
1242C22C2×#54711yescharacteristic
1243C22#350011yescharacteristic
1244C22C22×AGL(1,ℤ/8)11yescharacteristic
1245C22C2×#57711yescharacteristic
1246C22#358611yescharacteristic
1247C22#358611yescharacteristic
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—42no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4#347511yescharacteristic
1275C4#349411yescharacteristic
1276C4#351511yescharacteristic
1277C4#355911yescharacteristic
1278C2—42no—
1279C2—42no—
1280C2—81no—
1281C2—161no—
1282C2#5931811yescharacteristic
1283C2#6116111yescharacteristic
1284C2#6120211yescharacteristic
1285C2#6125211yescharacteristic
1286C2#6127111yescharacteristic
1287C2#6253911yescharacteristic
1288C2#6256511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59304C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59316C2semidirect
3. #31932C2semidirect
4. #31932C2semidirect
5. #31691C2semidirect
6. #31686C2semidirect
7. #28867C2semidirect
8. #28847C2semidirect
9. #28802C2semidirect
10. #28154C2semidirect
11. #27709C2semidirect
12. #27695C2semidirect
13. #27680C2semidirect
14. #27650C2semidirect
15. #26122C2semidirect
16. #26032C2semidirect
17. #25560C2semidirect
18. #25556C2semidirect
19. #25257C2semidirect
20. #25245C2semidirect
21. #24982C2semidirect
22. #24979C2semidirect
23. #24955C2semidirect
24. #24949C2semidirect
25. #22781C2semidirect
26. #22711C2semidirect
27. #22504C2semidirect
28. #22491C2semidirect
29. #21540C2semidirect
30. #21490C2semidirect
31. #20764C2semidirect

Maximal subgroups

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

subgroupindex
#593162
#593042
#319322
#316912
#316862
#288672
#288472
#288022
#281542
#277092
#276952
#276802
#276502
#261222
#260322
#255602
#255562
#252572
#252452
#249822
#249792
#249552
#249492
#227812
#227112
#225042
#224912
#215402
#214902
#207642