Subgroups — #15689525

Order 3008.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094016	C₂	1	2	yes	maximal
2	#13093958	C₂	1	2	yes	maximal
3	#13093956	C₂	1	2	yes	maximal
4	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₇	C₂²	1	4	yes	—
9	Dic₄₇⋊C₄	—	2	4	no	—
10	C₂×C₄×C₄₇	D₄	1	2	yes	—
11	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₂×Dic₄₇	—	2	4	no	—
13	C₈×C₄₇	Q₈	1	2	yes	—
14	C₈×C₄₇	Q₈	1	2	yes	—
15	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
16	C₄×C₄₇	—	2	2	no	—
17	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
19	Dic₄₇	—	4	4	no	—
20	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₄₇	#135	1	2	yes	—
22	#499	—	47	1	no	maximal, Sylow
23	C₄₇	#499	1	1	yes	characteristic, complemented, Sylow
24	#125	—	47	2	no	—
25	#107	—	47	2	no	—
26	#106	—	47	2	no	—
27	C₄×C₈	D₄₇	1	1	yes	characteristic
28	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
29	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
30	C₄⋊C₄	—	47	4	no	—
31	C₄⋊C₄	—	94	4	no	—
32	C₄²	C₂×D₄₇	1	1	yes	characteristic
33	C₂×C₄	—	94	4	no	—
34	C₂×C₄	D₁₈₈	1	2	yes	—
35	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
36	C₈	Dic₉₄	1	2	yes	—
37	C₈	Dic₉₄	1	2	yes	—
38	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	188	4	no	—
41	C₄	C₂×Dic₉₄	1	1	yes	characteristic
42	C₄	C₂×Dic₉₄	1	1	yes	characteristic
43	C₂	#13094024	1	1	yes	characteristic
44	C₂	#13094046	1	2	yes	—

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

N	H ≅ G/N	type
23. C₄₇	#499	semidirect

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