Finite Group Databasebeta

← #7574960

Subgroups — #7574960

Order 512.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C211yesmaximal, characteristic, complemented
2#36526C211yesmaximal, characteristic, complemented
3#32659C211yesmaximal, characteristic, complemented
4#32550C211yesmaximal, characteristic, complemented
5#32002C211yesmaximal, characteristic, complemented
6#30416C211yesmaximal, characteristic
7#29582C211yesmaximal, characteristic, complemented
8#29576C211yesmaximal, characteristic, complemented
9#28869C211yesmaximal, characteristic, complemented
10#28841C211yesmaximal, characteristic, complemented
11#27846C211yesmaximal, characteristic, complemented
12#27534C211yesmaximal, characteristic, complemented
13#27458C211yesmaximal, characteristic, complemented
14#27167C211yesmaximal, characteristic, complemented
15#27111C211yesmaximal, characteristic, complemented
16#27047C211yesmaximal, characteristic, complemented
17#26657C211yesmaximal, characteristic, complemented
18#26564C211yesmaximal, characteristic, complemented
19#25072C211yesmaximal, characteristic, complemented
20#25038C211yesmaximal, characteristic, complemented
21#24991C211yesmaximal, characteristic, complemented
22#24950C211yesmaximal, characteristic, complemented
23#24893C211yesmaximal, characteristic, complemented
24#24869C211yesmaximal, characteristic, complemented
25#23270C211yesmaximal, characteristic, complemented
26#23140C211yesmaximal, characteristic, complemented
27#22944C211yesmaximal, characteristic, complemented
28#22858C211yesmaximal, characteristic, complemented
29#22574C211yesmaximal, characteristic, complemented
30#21122C211yesmaximal, characteristic, complemented
31#21118C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#482C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#447C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C22×#102C2211yescharacteristic
39#2864C2211yescharacteristic, complemented
40#2852—21no—
41#2728—21no—
42#2697—21no—
43#2609—21no—
44#2597—21no—
45#2580C2211yescharacteristic, complemented
46#2578—21no—
47#2575—21no—
48#2557—21no—
49#2538C2211yescharacteristic
50#2538C2211yescharacteristic
51#2535C2211yescharacteristic
52#2523—21no—
53#2496C2211yescharacteristic
54#2496C2211yescharacteristic
55#2496C2211yescharacteristic, complemented
56#2495C2211yescharacteristic
57#2486C2211yescharacteristic
58#2480—21no—
59#2480—21no—
60#2467—21no—
61#2457—21no—
62#2457—21no—
63#2422C2211yescharacteristic
64#2422C2211yescharacteristic
65#2422C2211yescharacteristic
66#2420C2211yescharacteristic, complemented
67#2408C2211yescharacteristic
68#2363C2211yescharacteristic, complemented
69#2361C2211yescharacteristic
70#2361C2211yescharacteristic
71#2361C2211yescharacteristic
72#2355C2211yescharacteristic, complemented
73#2352C2211yescharacteristic
74#2347C2211yescharacteristic, complemented
75#2345C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77D4×C22⋊C4C2211yescharacteristic
78C4×#124C2211yescharacteristic
79C4×#123—21no—
80#2293C2211yescharacteristic
81#2293C2211yescharacteristic
82C42×D4C2211yescharacteristic, complemented
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2076C2211yescharacteristic, complemented
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic, complemented
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#1999C2211yescharacteristic
115#1985C2211yescharacteristic, complemented
116#1984C2211yescharacteristic, complemented
117#1972C2211yescharacteristic
118#1948C2211yescharacteristic, complemented
119#1947C2211yescharacteristic, complemented
120#1944C2211yescharacteristic, complemented
121#1943C2211yescharacteristic, complemented
122#1943C2211yescharacteristic, complemented
123#1942C2211yescharacteristic, complemented
124#1941C2211yescharacteristic, complemented
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1934C2211yescharacteristic
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic, complemented
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1926C2211yescharacteristic
136#1925C2211yescharacteristic
137#1924C2211yescharacteristic
138#1924C2211yescharacteristic, complemented
139#1923C2211yescharacteristic
140#1923C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1895C2211yescharacteristic
152#1893C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1875C2211yescharacteristic
160#1874C2211yescharacteristic, complemented
161#1870C2211yescharacteristic
162#1869C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic, complemented
168#1864C2211yescharacteristic, complemented
169#1864C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic, complemented
173#1854C2211yescharacteristic, complemented
174#1853C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic, complemented
177#1847C2211yescharacteristic, complemented
178#1834C2211yescharacteristic, complemented
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic, complemented
181#1809C2211yescharacteristic, complemented
182#1808C2211yescharacteristic
183#1807C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189C4×#106C2211yescharacteristic, complemented
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic, complemented
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic, complemented
196#1753C2211yescharacteristic, complemented
197#1753C2211yescharacteristic, complemented
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1745C2211yescharacteristic, complemented
201#1744C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#551—48no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#126—21no—
212C2×#124D411yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
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
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C42—21no—
244#482—24no—
245#469—24no—
246#447—24no—
247#442—24no—
248C4×D8—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
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×#102—24no—
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#399—21no—
303#398—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#393—21no—
324#392—21no—
325#392—21no—
326#391—21no—
327#391D411yescharacteristic
328#390—21no—
329#390D411yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388D411yescharacteristic
363#388D411yescharacteristic
364#388D411yescharacteristic
365#388D411yescharacteristic
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#383—21no—
402#383—21no—
403#382D411yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#379—21no—
421#379—21no—
422#379—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444C43C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
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#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C25—21no—
486C22×Q8C2×D411yescharacteristic
487C22×D4—22no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8#4114yes—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#126—44no—
534#126—44no—
535#126—82no—
536#124—24no—
537#123—44no—
538#123—44no—
539#123—44no—
540#123—44no—
541C22⋊Q8—44no—
542C22⋊Q8—44no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—41no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—44no—
571C4×D4—44no—
572C4×D4—82no—
573#117—22no—
574#117—44no—
575#117—44no—
576#117—41no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊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—44no—
655C2×C22⋊C4—44no—
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—82no—
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684#107—22no—
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102#4114yes—
720C22⋊C8—22no—
721C22⋊C8—22no—
722C22⋊C8—41no—
723C22⋊C8—41no—
724C22⋊C8—41no—
725C22⋊C8—41no—
726#97—22no—
727#97—41no—
728#97—41no—
729C4×C8—22no—
730C4×C8—41no—
731C4×C8—41no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C24—21no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—81no—
780C24—81no—
781C24—81no—
782C24—81no—
783C24C22×D411yescharacteristic
784C24C22×D411yescharacteristic
785C2×Q8—22no—
786C2×Q8—41no—
787C2×Q8—41no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—41no—
805C2×D4—41no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—81no—
817C2×D4—82no—
818C2×D4—82no—
819C2×D4—82no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4C2×#4112yes—
826C2×D4C2×#4112yes—
827C2×D4C2×#4112yes—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C2511yescharacteristic
893D8—44no—
894D8—44no—
895M16—82no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
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—82no—
919C2×C8C2×#4112yes—
920C2×C8C2×#4112yes—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4C2×#4112yes—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4AGL(1,ℤ/8)14yes—
1017C42—22no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C42—81no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—22no—
1049C23—21no—
1050C23—22no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—84no—
1074C23—84no—
1075C23—84no—
1076C23—162no—
1077C23—162no—
1078C23—162no—
1079C23—162no—
1080C23C2×AGL(1,ℤ/8)12yes—
1081C23C23×D411yescharacteristic
1082Q8—82no—
1083D4—22no—
1084D4—22no—
1085D4—22no—
1086D4—22no—
1087D4—22no—
1088D4—22no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—82no—
1096D4—84no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
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—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
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—84no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4C2×AGL(1,ℤ/8)12yes—
1192C2×C4C2×AGL(1,ℤ/8)12yes—
1193C2×C4C22×#4111yescharacteristic
1194C2×C4C22×#4111yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—22no—
1200C8—22no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—42no—
1216C22—41no—
1217C22—41no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—41no—
1222C22—41no—
1223C22—42no—
1224C22—42no—
1225C22—41no—
1226C22—42no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—168no—
1243C22D4×#4111yescharacteristic
1244C22D4×#4111yescharacteristic
1245C22#348511yescharacteristic
1246C22C22×AGL(1,ℤ/8)11yescharacteristic
1247C22#358411yescharacteristic
1248C22#358411yescharacteristic
1249C22#358511yescharacteristic
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4#347511yescharacteristic
1276C4#349111yescharacteristic
1277C4#352111yescharacteristic
1278C4#356611yescharacteristic
1279C2—42no—
1280C2—81no—
1281C2—82no—
1282C2—82no—
1283C2—82no—
1284C2#5915811yescharacteristic
1285C2#6143911yescharacteristic
1286C2#6145111yescharacteristic
1287C2#6150111yescharacteristic
1288C2#6153611yescharacteristic
1289C2#6173311yescharacteristic
1290C2#6180411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59843C2semidirect
2. #36526C2semidirect
3. #32659C2semidirect
4. #32550C2semidirect
5. #32002C2semidirect
7. #29582C2semidirect
8. #29576C2semidirect
9. #28869C2semidirect
10. #28841C2semidirect
11. #27846C2semidirect
12. #27534C2semidirect
13. #27458C2semidirect
14. #27167C2semidirect
15. #27111C2semidirect
16. #27047C2semidirect
17. #26657C2semidirect
18. #26564C2semidirect
19. #25072C2semidirect
20. #25038C2semidirect
21. #24991C2semidirect
22. #24950C2semidirect
23. #24893C2semidirect
24. #24869C2semidirect
25. #23270C2semidirect
26. #23140C2semidirect
27. #22944C2semidirect
28. #22858C2semidirect
29. #22574C2semidirect
30. #21122C2semidirect
31. #21118C2semidirect
39. #2864C22semidirect
45. #2580C22semidirect
55. #2496C22semidirect
66. #2420C22semidirect
68. #2363C22semidirect
72. #2355C22semidirect
74. #2347C22semidirect
82. C42×D4C22semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2101C22semidirect
86. #2100C22semidirect
88. #2093C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2084C22semidirect
95. #2083C22semidirect
98. #2076C22semidirect
104. #2071C22semidirect
106. #2065C22semidirect
109. #2034C22semidirect
115. #1985C22semidirect
116. #1984C22semidirect
118. #1948C22semidirect
119. #1947C22semidirect
120. #1944C22semidirect
121. #1943C22semidirect
122. #1943C22semidirect
123. #1942C22semidirect
124. #1941C22semidirect
130. #1934C22semidirect
138. #1924C22semidirect
140. #1923C22semidirect
141. #1921C22semidirect
142. #1921C22semidirect
143. #1921C22semidirect
144. #1920C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1919C22semidirect
149. #1919C22semidirect
150. #1918C22semidirect
160. #1874C22semidirect
167. #1864C22semidirect
168. #1864C22semidirect
169. #1864C22semidirect
172. #1862C22semidirect
173. #1854C22semidirect
176. #1853C22semidirect
177. #1847C22semidirect
178. #1834C22semidirect
180. #1824C22semidirect
181. #1809C22semidirect
188. #1776C22semidirect
189. C4×#106C22semidirect
192. #1762C22semidirect
195. C4×#102C22semidirect
196. #1753C22semidirect
197. #1753C22semidirect
200. #1745C22semidirect
201. #1744C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#598432
#365262
#326592
#325502
#320022
#304162
#295822
#295762
#288692
#288412
#278462
#275342
#274582
#271672
#271112
#270472
#266572
#265642
#250722
#250382
#249912
#249502
#248932
#248692
#232702
#231402
#229442
#228582
#225742
#211222
#211182