Subgroups — #15688865

Order 3008.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093935	C₂	1	2	yes	maximal
2	#125×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₄₇	—	2	2	no	—
4	C₄⋊C₄×C₄₇	C₄	1	2	yes	—
5	C₄²×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄₇⋊C₈	—	2	2	no	—
7	C₂×C₄×C₄₇	—	2	2	no	—
8	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₄₇	D₄	1	2	yes	—
10	C₄₇⋊C₈	—	2	4	no	—
11	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
12	C₄×C₄₇	—	2	1	no	—
13	C₄×C₄₇	—	2	2	no	—
14	C₄×C₄₇	—	4	2	no	—
15	C₂×C₄₇	#101	1	1	yes	characteristic
16	C₂×C₄₇	#104	1	2	yes	—
17	#330	—	47	1	no	maximal, Sylow
18	C₄₇	#330	1	1	yes	characteristic, complemented, Sylow
19	#125	D₄₇	1	1	yes	characteristic
20	#97	—	47	2	no	—
21	C₂×C₈	—	94	2	no	—
22	C₄⋊C₄	—	2	2	no	—
23	C₄⋊C₄	Dic₄₇	1	2	yes	—
24	C₄²	C₂×D₄₇	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
27	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
28	C₈	—	94	4	no	—
29	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	4	2	no	—
33	C₂	#13093943	1	1	yes	characteristic
34	C₂	#13093951	1	2	yes	—

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

N	H ≅ G/N	type
18. C₄₇	#330	semidirect

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