Subgroups — #15688950

Order 3008.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#13093958	C₂	1	1	yes	maximal, characteristic
3	#107×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₄₇	—	2	1	no	—
6	C₄⋊Dic₄₇	—	2	1	no	—
7	C₄₇⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₄₇	—	4	1	no	—
9	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
10	C₂×Dic₄₇	—	4	1	no	—
11	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₇	Q₈	1	1	yes	characteristic
13	C₂²×C₄₇	D₈	1	1	yes	characteristic
14	C₄×C₄₇	—	8	1	no	—
15	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₄₇	Q₁₆	1	1	yes	characteristic
17	Dic₄₇	—	8	1	no	—
18	C₂×C₄₇	#107	1	1	yes	characteristic
19	C₂×C₄₇	SD₃₂	1	1	yes	characteristic
20	C₂×C₄₇	SD₃₂	1	1	yes	characteristic
21	#367	—	47	1	no	maximal, Sylow
22	C₄₇	#367	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	47	1	no	—
24	#107	—	47	1	no	—
25	#107	D₄₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	94	1	no	—
29	C₁₆	—	47	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	188	1	no	—
32	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
33	C₈	Dic₉₄	1	1	yes	characteristic
34	C₈	C₄×D₄₇	1	1	yes	characteristic
35	C₂²	#10625334	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	376	1	no	—
38	C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
39	C₄	#10625337	1	1	yes	characteristic
40	C₂	#13093957	1	1	yes	characteristic
41	C₂	#13093967	1	1	yes	characteristic
42	C₂	#13093968	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₄₇⋊C₁₆	C₄	semidirect
22. C₄₇	#367	semidirect

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