Subgroups — #37588219

Order 24512.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₈₃⋊#95	C₂	1	6	yes	maximal
2	C₂×C₄²×C₃₈₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₃₈₃	C₂²	1	4	yes	—
4	C₂²×C₄×C₃₈₃	C₂²	1	3	yes	—
5	C₄²×C₃₈₃	C₄	1	4	yes	complemented
6	C₂×Dic₃₈₃	—	2	12	no	—
7	C₂³×C₃₈₃	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₃₈₃	—	2	6	no	—
9	C₂×C₄×C₃₈₃	C₂×C₄	1	6	yes	—
10	C₂²×C₃₈₃	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₃₈₃	#41	1	6	yes	—
12	C₄×C₃₈₃	—	2	6	no	—
13	Dic₃₈₃	—	4	4	no	—
14	C₂×C₃₈₃	#117	1	3	yes	—
15	C₂×C₃₈₃	#126	1	4	yes	—
16	C₃₈₃	#383	1	1	yes	characteristic, complemented, Sylow
17	#383	—	383	1	no	maximal, Sylow
18	C₂×C₄²	D₃₈₃	1	1	yes	characteristic
19	#95	—	383	6	no	—
20	C₂²×C₄	—	383	4	no	—
21	C₂²×C₄	C₂×D₃₈₃	1	3	yes	—
22	C₄²	Dic₃₈₃	1	4	yes	complemented
23	C₂³	C₂²×D₃₈₃	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	766	12	no	—
26	C₂×C₄	C₂×Dic₃₈₃	1	6	yes	—
27	C₂²	C₂²×Dic₃₈₃	1	1	yes	characteristic
28	C₂²	#20259457	1	6	yes	—
29	C₄	—	2	6	no	—
30	C₄	—	1532	4	no	—
31	C₂	#27133800	1	3	yes	—
32	C₂	#27133835	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.