Subgroups — C₄₇×#1712 #20239322

Order 6016.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#493	C₂	1	6	yes	maximal, complemented
2	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×C₄₇	—	2	12	no	—
4	#127×C₄₇	C₂²	1	4	yes	—
5	C₄×C₈×C₄₇	C₂²	1	3	yes	—
6	C₂×D₄×C₄₇	—	2	12	no	—
7	D₈×C₄₇	—	4	24	no	—
8	C₂×C₈×C₄₇	D₄	1	6	yes	—
9	C₄²×C₄₇	C₂³	1	1	yes	characteristic
10	C₂³×C₄₇	—	4	4	no	—
11	D₄×C₄₇	—	4	24	no	—
12	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
13	C₈×C₄₇	D₈	1	12	yes	complemented
14	C₂²×C₄₇	—	8	12	no	—
15	C₂²×C₄₇	#127	1	1	yes	characteristic
16	C₄×C₄₇	C₂×D₈	1	6	yes	—
17	#1712	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₄₇	—	16	4	no	—
19	C₂×C₄₇	#493	1	3	yes	—
20	#493	C₂×C₄₇	1	6	yes	complemented
21	C₈²	C₂×C₄₇	1	1	yes	characteristic, complemented
22	C₄₇	#1712	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×D₈	—	2	12	no	—
24	#127	C₂²×C₄₇	1	4	yes	—
25	C₄×C₈	C₂²×C₄₇	1	3	yes	—
26	C₂×D₄	—	2	12	no	—
27	D₈	—	4	24	no	—
28	C₂×C₈	D₄×C₄₇	1	6	yes	—
29	C₄²	C₂³×C₄₇	1	1	yes	characteristic
30	C₂³	—	4	4	no	—
31	D₄	—	4	24	no	—
32	C₂×C₄	C₂×D₄×C₄₇	1	3	yes	—
33	C₈	D₈×C₄₇	1	12	yes	complemented
34	C₂²	—	8	12	no	—
35	C₂²	#127×C₄₇	1	1	yes	characteristic
36	C₄	C₂×D₈×C₄₇	1	6	yes	—
37	C₂	—	16	4	no	—
38	C₂	C₄₇×#493	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

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.