Subgroups — #13094024

Order 1504.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₄	C₂	1	2	yes	maximal
2	C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₄₇	C₂	1	4	yes	maximal
4	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₄₇	C₂²	1	2	yes	—
6	C₂×Dic₄₇	C₂²	1	4	yes	—
7	Dic₉₄	—	2	4	no	—
8	C₂²×C₄₇	C₂³	1	1	yes	characteristic
9	C₄×C₄₇	D₄	1	2	yes	—
10	C₄×C₄₇	Q₈	1	4	yes	complemented
11	Dic₄₇	—	2	4	no	—
12	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
13	C₂×C₄₇	C₂×Q₈	1	2	yes	—
14	C₄₇	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	47	1	no	maximal, Sylow
16	C₂×Q₈	—	47	2	no	—
17	C₄⋊C₄	—	47	4	no	—
18	C₄²	D₄₇	1	1	yes	characteristic
19	Q₈	—	94	4	no	—
20	C₂×C₄	—	47	4	no	—
21	C₂×C₄	C₂×D₄₇	1	2	yes	—
22	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
23	C₂²	C₂²×D₄₇	1	1	yes	characteristic
24	C₄	—	94	4	no	—
25	C₄	Dic₉₄	1	4	yes	complemented
26	C₄	D₁₈₈	1	2	yes	—
27	C₂	C₂×Dic₉₄	1	2	yes	—
28	C₂	C₂×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₇
commutator, socle, prime radical, cosocle	C₂²×C₄₇	C₂³
Fitting	C₄²×C₄₇	C₂
hypercenter	C₄²	D₄₇
hypocenter	C₄₇	C₄⋊Q₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄²

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

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