Subgroups — #383×C₅₆₃ #49113003

Order 36032.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅₆₃	C₂	1	1	yes	maximal, characteristic
2	#95×C₅₆₃	C₂	1	6	yes	maximal
3	C₂²×C₄×C₅₆₃	C₂²	1	4	yes	—
4	C₂²×C₄×C₅₆₃	C₂²	1	3	yes	—
5	C₄²×C₅₆₃	C₄	1	4	yes	complemented
6	C₂³×C₅₆₃	C₂³	1	1	yes	characteristic
7	C₂×C₄×C₅₆₃	—	2	6	no	—
8	C₂×C₄×C₅₆₃	—	2	12	no	—
9	C₂×C₄×C₅₆₃	C₂×C₄	1	6	yes	—
10	C₂²×C₅₆₃	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₅₆₃	#41	1	6	yes	—
12	C₄×C₅₆₃	—	2	6	no	—
13	C₄×C₅₆₃	—	4	4	no	—
14	C₂×C₅₆₃	#117	1	3	yes	—
15	C₂×C₅₆₃	#126	1	4	yes	—
16	C₅₆₃	#383	1	1	yes	characteristic, direct product factor, Sylow
17	#383	C₅₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₄²	C₂×C₅₆₃	1	1	yes	characteristic
19	#95	C₂×C₅₆₃	1	6	yes	—
20	C₂²×C₄	C₂²×C₅₆₃	1	4	yes	—
21	C₂²×C₄	C₂²×C₅₆₃	1	3	yes	—
22	C₄²	C₄×C₅₆₃	1	4	yes	complemented
23	C₂³	C₂³×C₅₆₃	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	2	12	no	—
26	C₂×C₄	C₂×C₄×C₅₆₃	1	6	yes	—
27	C₂²	C₂²×C₄×C₅₆₃	1	1	yes	characteristic
28	C₂²	#41×C₅₆₃	1	6	yes	—
29	C₄	—	2	6	no	—
30	C₄	—	4	4	no	—
31	C₂	#117×C₅₆₃	1	3	yes	—
32	C₂	#126×C₅₆₃	1	4	yes	—

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

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