Subgroups — #13094022

Order 1504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉₄	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₄	C₂	1	4	yes	maximal
4	C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₄₇	—	2	2	no	—
6	C₂×C₄×C₄₇	C₂²	1	2	yes	—
7	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₄₇	C₂²	1	2	yes	—
9	C₂×Dic₄₇	C₂²	1	2	yes	—
10	Dic₉₄	—	2	2	no	—
11	C₂²×C₄₇	C₂³	1	1	yes	characteristic
12	C₄×C₄₇	—	2	2	no	—
13	C₄×C₄₇	D₄	1	2	yes	—
14	Dic₄₇	—	2	2	no	—
15	Dic₄₇	Q₈	1	4	yes	complemented
16	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
17	C₂×C₄₇	C₂×Q₈	1	2	yes	—
18	C₄₇	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₄⋊Q₈	—	47	1	no	maximal, Sylow
20	C₂×Q₈	—	47	1	no	—
21	C₂×Q₈	D₄₇	1	1	yes	characteristic
22	C₄⋊C₄	—	47	4	no	—
23	C₄²	—	47	1	no	—
24	Q₈	—	2	2	no	—
25	Q₈	—	94	2	no	—
26	C₂×C₄	—	47	2	no	—
27	C₂×C₄	—	47	2	no	—
28	C₂×C₄	C₂×D₄₇	1	2	yes	—
29	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
30	C₂²	C₂²×D₄₇	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	—	47	4	no	—
33	C₄	—	94	2	no	—
34	C₄	C₂²⋊D₄₇	1	2	yes	—
35	C₂	Q₈×D₄₇	1	2	yes	—
36	C₂	C₂×C₂²⋊D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₇
commutator, socle, prime radical, cosocle	C₂²×C₄₇	C₂³
Fitting	C₂×Q₈×C₄₇	C₂
hypercenter	C₂×Q₈	D₄₇
hypocenter	C₄₇	C₄⋊Q₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

N	H ≅ G/N	type
15. Dic₄₇	Q₈	semidirect
18. C₄₇	C₄⋊Q₈	semidirect

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