Finite Group Databasebeta

← #6593424

Subgroups — #6593424

Order 512.

1791 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39567C211yesmaximal, characteristic, complemented
2#34275C211yesmaximal, characteristic, complemented
3#33152C211yesmaximal, characteristic, complemented
4#33014C211yesmaximal, characteristic, complemented
5#32986C211yesmaximal, characteristic, complemented
6#29104C211yesmaximal, characteristic, complemented
7#28114C211yesmaximal, characteristic, complemented
8#27622C211yesmaximal, characteristic, complemented
9#27106C211yesmaximal, characteristic, complemented
10#27095C211yesmaximal, characteristic, complemented
11#27046C211yesmaximal, characteristic, complemented
12#27038C211yesmaximal, characteristic, complemented
13#26747C211yesmaximal, characteristic, complemented
14#26723C211yesmaximal, characteristic, complemented
15#26669C211yesmaximal, characteristic, complemented
16#26656C211yesmaximal, characteristic, complemented
17#26438C211yesmaximal, characteristic, complemented
18#26423C211yesmaximal, characteristic, complemented
19#25227C211yesmaximal, characteristic, complemented
20#25214C211yesmaximal, characteristic, complemented
21#24612C211yesmaximal, characteristic, complemented
22#24390C211yesmaximal, characteristic
23#24013C211yesmaximal, characteristic, complemented
24#23143C211yesmaximal, characteristic, complemented
25#23130C211yesmaximal, characteristic, complemented
26#22943C211yesmaximal, characteristic, complemented
27#22916C211yesmaximal, characteristic, complemented
28#22560C211yesmaximal, characteristic, complemented
29C4×#482C211yesmaximal, characteristic, complemented
30#20744C211yesmaximal, characteristic, complemented
31#20703C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#480C2211yescharacteristic
39C2×#469C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#433C2211yescharacteristic
43C2×#408C2211yescharacteristic
44#2851C2211yescharacteristic
45#2798—21no—
46#2797—21no—
47#2752—21no—
48#2749—21no—
49#2624C2211yescharacteristic
50#2615C2211yescharacteristic
51#2602—21no—
52#2598—21no—
53#2523—21no—
54#2504C2211yescharacteristic, complemented
55#2495C2211yescharacteristic, complemented
56#2495C2211yescharacteristic, complemented
57#2490C2211yescharacteristic, complemented
58#2471—21no—
59#2441C2211yescharacteristic, complemented
60#2422C2211yescharacteristic, complemented
61#2363C2211yescharacteristic
62#2363C2211yescharacteristic
63#2363C2211yescharacteristic
64#2363C2211yescharacteristic
65#2363C2211yescharacteristic, complemented
66#2361C2211yescharacteristic
67#2361C2211yescharacteristic
68#2361C2211yescharacteristic
69#2361C2211yescharacteristic
70#2358—21no—
71#2358—21no—
72#2358—21no—
73#2358—21no—
74#2344C2211yescharacteristic, complemented
75#2328—21no—
76#2326—21no—
77#2317C2211yescharacteristic
78#2314C2211yescharacteristic
79#2311C2211yescharacteristic
80C4×#127—21no—
81C4×#124—21no—
82C4×#121C2211yescharacteristic
83#2297C2211yescharacteristic
84C2×#390C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2100C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2087C2211yescharacteristic, complemented
89#2086C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic, complemented
97#2065C2211yescharacteristic, complemented
98#2054C2211yescharacteristic
99#2054C2211yescharacteristic
100#2034C2211yescharacteristic
101#2034C2211yescharacteristic
102#2034C2211yescharacteristic
103#2033C2211yescharacteristic
104#2033C2211yescharacteristic
105#2033C2211yescharacteristic
106#2025C2211yescharacteristic
107#2025C2211yescharacteristic
108#1999C2211yescharacteristic
109#1999C2211yescharacteristic
110#1989C2211yescharacteristic, complemented
111#1989C2211yescharacteristic, complemented
112#1949C2211yescharacteristic, complemented
113#1949C2211yescharacteristic, complemented
114#1944C2211yescharacteristic, complemented
115#1942C2211yescharacteristic, complemented
116#1936C2211yescharacteristic, complemented
117#1934C2211yescharacteristic
118#1934C2211yescharacteristic
119#1934C2211yescharacteristic
120#1934C2211yescharacteristic
121#1934C2211yescharacteristic, complemented
122#1926C2211yescharacteristic, complemented
123#1925C2211yescharacteristic
124#1925C2211yescharacteristic
125#1925C2211yescharacteristic, complemented
126#1924C2211yescharacteristic, complemented
127#1923C2211yescharacteristic, complemented
128#1923C2211yescharacteristic, complemented
129#1923C2211yescharacteristic, complemented
130#1921C2211yescharacteristic, complemented
131#1921C2211yescharacteristic, complemented
132#1921C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1919C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1918C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1895C2211yescharacteristic
141#1893C2211yescharacteristic
142#1879C2211yescharacteristic
143#1879C2211yescharacteristic
144#1879C2211yescharacteristic
145#1879C2211yescharacteristic
146#1879C2211yescharacteristic
147#1879C2211yescharacteristic
148#1875C2211yescharacteristic
149#1875C2211yescharacteristic
150#1875C2211yescharacteristic
151#1875C2211yescharacteristic, complemented
152#1875C2211yescharacteristic, complemented
153#1874C2211yescharacteristic, complemented
154#1874C2211yescharacteristic, complemented
155#1864C2211yescharacteristic
156#1864C2211yescharacteristic
157#1862C2211yescharacteristic
158#1862C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic, complemented
163#1854C2211yescharacteristic, complemented
164#1852C2211yescharacteristic, complemented
165#1852C2211yescharacteristic, complemented
166#1851C2211yescharacteristic, complemented
167#1850C2211yescharacteristic, complemented
168#1825C2211yescharacteristic
169#1825C2211yescharacteristic
170#1825C2211yescharacteristic
171#1825C2211yescharacteristic, complemented
172#1825C2211yescharacteristic, complemented
173#1824C2211yescharacteristic
174#1824C2211yescharacteristic
175#1824C2211yescharacteristic, complemented
176#1823C2211yescharacteristic
177#1823C2211yescharacteristic, complemented
178#1818C2211yescharacteristic
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1797C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1780C2211yescharacteristic
188C4×#107C2211yescharacteristic, complemented
189C4×#106C2211yescharacteristic, complemented
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196#1753C2211yescharacteristic, complemented
197C8×C22⋊C4C2211yescharacteristic, complemented
198C4×C22⋊C8C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#535—24no—
210#535—24no—
211C2×#127—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#123—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224#520—24no—
225#520—42no—
226#518—24no—
227#518—42no—
228C2×C4×Q8—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C42C2311yescharacteristic
260#482—24no—
261#481—24no—
262#480—24no—
263#480—42no—
264#469—24no—
265#466—24no—
266#447—42no—
267#433—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302#408—42no—
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#399—21no—
320#399—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#392—21no—
335#392—21no—
336#392—21no—
337#391—21no—
338#391D411yescharacteristic
339#391D411yescharacteristic
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390D411yescharacteristic
350#390D411yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386D411yescharacteristic
405#386D411yescharacteristic
406#386D411yescharacteristic
407#386D411yescharacteristic
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#383—21no—
420#383—21no—
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
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
451#376—21no—
452C43—21no—
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
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2×D411yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×M16—22no—
542C2×M16—41no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#127—28no—
556#125—41no—
557#125—41no—
558#124—28no—
559#123—82no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—41no—
571#121—41no—
572#121#4114yes—
573#121#4114yes—
574#120—28no—
575#120—28no—
576C4×Q8—44no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—44no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—82no—
593C4×D4—82no—
594C4×D4—82no—
595C4×D4—82no—
596C4×D4—82no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—41no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—82no—
609#117#4114yes—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
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—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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—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—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—22no—
723#107—22no—
724#107—22no—
725#107—22no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—22no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766#97—41no—
767C4×C8—41no—
768C4×C8—41no—
769C4×C8—41no—
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#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—24no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818#41—44no—
819#41—44no—
820#41—44no—
821#41—44no—
822C2×Q8—22no—
823C2×Q8—22no—
824C2×Q8—41no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4C2×#4112yes—
879C2×D4C2×#4112yes—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4C2×#4112yes—
953C22×C4C2×#4112yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956D8—82no—
957D8—82no—
958M16—82no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—82no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4C2×#4112yes—
1026C4⋊C4C2×#4112yes—
1027C4⋊C4C2×#4112yes—
1028C4⋊C4C2×#4112yes—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C42—24no—
1078C42—24no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—41no—
1088C42—41no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—48no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—84no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23#52512yes—
1147C23#54612yes—
1148C23C23×D411yescharacteristic
1149Q8—44no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—22no—
1154D4—44no—
1155D4—44no—
1156D4—48no—
1157D4—44no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—84no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4—162no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4#52512yes—
1266C2×C4#54612yes—
1267C2×C4#57612yes—
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—42no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—42no—
1306C22—41no—
1307C22—42no—
1308C22—42no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—168no—
1325C22C2×#52511yescharacteristic
1326C22C2×#54611yescharacteristic
1327C22#348511yescharacteristic
1328C22C2×#57611yescharacteristic
1329C22#358411yescharacteristic
1330C22#358411yescharacteristic
1331C22#358511yescharacteristic
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—42no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4#347511yescharacteristic
1357C4#347511yescharacteristic
1358C4#351311yescharacteristic
1359C4#351311yescharacteristic
1360C2—42no—
1361C2—42no—
1362C2—81no—
1363C2—82no—
1364C2—82no—
1365C2—161no—
1366C2#3615911yescharacteristic
1367C2#6057011yescharacteristic
1368C2#6059211yescharacteristic
1369C2#6120511yescharacteristic
1370C2#6121611yescharacteristic
1371C2#6176111yescharacteristic
1372C2#6177211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24390C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39567C2semidirect
2. #34275C2semidirect
3. #33152C2semidirect
4. #33014C2semidirect
5. #32986C2semidirect
6. #29104C2semidirect
7. #28114C2semidirect
8. #27622C2semidirect
9. #27106C2semidirect
10. #27095C2semidirect
11. #27046C2semidirect
12. #27038C2semidirect
13. #26747C2semidirect
14. #26723C2semidirect
15. #26669C2semidirect
16. #26656C2semidirect
17. #26438C2semidirect
18. #26423C2semidirect
19. #25227C2semidirect
20. #25214C2semidirect
21. #24612C2semidirect
23. #24013C2semidirect
24. #23143C2semidirect
25. #23130C2semidirect
26. #22943C2semidirect
27. #22916C2semidirect
28. #22560C2semidirect
29. C4×#482C2semidirect
30. #20744C2semidirect
31. #20703C2semidirect
54. #2504C22semidirect
55. #2495C22semidirect
56. #2495C22semidirect
57. #2490C22semidirect
59. #2441C22semidirect
60. #2422C22semidirect
65. #2363C22semidirect
74. #2344C22semidirect
86. #2100C22semidirect
87. #2099C22semidirect
88. #2087C22semidirect
89. #2086C22semidirect
90. #2085C22semidirect
91. #2085C22semidirect
96. #2067C22semidirect
97. #2065C22semidirect
110. #1989C22semidirect
111. #1989C22semidirect
112. #1949C22semidirect
113. #1949C22semidirect
114. #1944C22semidirect
115. #1942C22semidirect
116. #1936C22semidirect
121. #1934C22semidirect
122. #1926C22semidirect
125. #1925C22semidirect
126. #1924C22semidirect
127. #1923C22semidirect
128. #1923C22semidirect
129. #1923C22semidirect
130. #1921C22semidirect
131. #1921C22semidirect
132. #1921C22semidirect
133. #1920C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1919C22semidirect
137. #1919C22semidirect
138. #1918C22semidirect
139. #1918C22semidirect
151. #1875C22semidirect
152. #1875C22semidirect
153. #1874C22semidirect
154. #1874C22semidirect
162. #1854C22semidirect
163. #1854C22semidirect
164. #1852C22semidirect
165. #1852C22semidirect
166. #1851C22semidirect
167. #1850C22semidirect
171. #1825C22semidirect
172. #1825C22semidirect
175. #1824C22semidirect
177. #1823C22semidirect
188. C4×#107C22semidirect
189. C4×#106C22semidirect
194. C4×#102C22semidirect
195. C4×#102C22semidirect
196. #1753C22semidirect
197. C8×C22⋊C4C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1735C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#395672
#342752
#331522
#330142
#329862
#291042
#281142
#276222
#271062
#270952
#270462
#270382
#267472
#267232
#266692
#266562
#264382
#264232
#252272
#252142
#246122
#243902
#240132
#231432
#231302
#229432
#229162
#225602
C4×#4822
#207442
#207032