Subgroups — #15688863

Order 3008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093935	C₂	1	2	yes	maximal, complemented
2	#124×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₇	C₄	1	1	yes	characteristic
4	C₂×D₄×C₄₇	C₄	1	1	yes	characteristic
5	C₂²⋊C₄×C₄₇	—	2	2	no	—
6	C₄²×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄₇⋊C₈	—	2	2	no	—
8	C₂³×C₄₇	—	2	1	no	—
9	Q₈×C₄₇	—	4	1	no	—
10	D₄×C₄₇	—	4	1	no	—
11	C₂×C₄×C₄₇	—	2	1	no	—
12	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	D₄	1	2	yes	—
14	C₄₇⋊C₈	—	2	4	no	—
15	C₂²×C₄₇	—	4	1	no	—
16	C₂²×C₄₇	—	4	2	no	—
17	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₄₇	—	2	1	no	—
19	C₄×C₄₇	—	2	2	no	—
20	C₄×C₄₇	—	4	1	no	—
21	C₂×C₄₇	—	8	1	no	—
22	C₂×C₄₇	#100	1	1	yes	characteristic
23	C₂×C₄₇	#104	1	2	yes	—
24	#329	—	47	1	no	maximal, Sylow
25	C₄₇	#329	1	1	yes	characteristic, complemented, Sylow
26	#124	D₄₇	1	1	yes	characteristic
27	#97	—	47	2	no	—
28	C₂×Q₈	Dic₄₇	1	1	yes	characteristic
29	C₂×D₄	Dic₄₇	1	1	yes	characteristic
30	C₂×C₈	—	94	2	no	—
31	C₂²⋊C₄	—	2	2	no	—
32	C₄²	C₂×D₄₇	1	1	yes	characteristic
33	C₂³	—	2	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
38	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
39	C₈	—	94	4	no	—
40	C₂²	—	4	1	no	—
41	C₂²	—	4	2	no	—
42	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	2	2	no	—
45	C₄	—	4	1	no	—
46	C₂	—	8	1	no	—
47	C₂	#13093941	1	1	yes	characteristic
48	C₂	#13093951	1	2	yes	—

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

N	H ≅ G/N	type
1. #13093935	C₂	semidirect
25. C₄₇	#329	semidirect

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