Subgroups — #15688872

Order 3008.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₇	C₄	1	2	yes	—
4	C₄⋊C₄×C₄₇	—	2	2	no	—
5	C₄²×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄₇⋊C₈	—	2	2	no	—
7	Q₈×C₄₇	—	4	2	no	—
8	C₂×C₄×C₄₇	—	2	2	no	—
9	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₄₇	D₄	1	2	yes	—
11	C₄₇⋊C₈	—	4	2	no	—
12	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₄₇	—	2	1	no	—
14	C₄×C₄₇	—	4	2	no	—
15	C₄×C₄₇	SD₁₆	1	2	yes	—
16	C₄×C₄₇	Q₁₆	1	2	yes	—
17	C₂×C₄₇	#100	1	1	yes	characteristic
18	C₂×C₄₇	#103	1	2	yes	—
19	#333	—	47	1	no	maximal, Sylow
20	C₄₇	#333	1	1	yes	characteristic, complemented, Sylow
21	C₄⋊Q₈	D₄₇	1	1	yes	characteristic
22	C₄⋊C₈	—	47	2	no	—
23	C₂×Q₈	Dic₄₇	1	2	yes	—
24	C₂×C₈	—	94	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₄₇	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
31	C₈	—	188	2	no	—
32	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#10625336	1	2	yes	—
36	C₄	#10625337	1	2	yes	—
37	C₂	#13093941	1	1	yes	characteristic
38	C₂	#13093948	1	2	yes	—

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

N	H ≅ G/N	type
20. C₄₇	#333	semidirect

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