Subgroups — #15688845

Order 3008.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₇	C₄	1	2	yes	—
5	C₄²×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₄₇⋊C₈	C₄	1	2	yes	—
7	C₂×C₄₇⋊C₈	C₄	1	2	yes	—
8	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₄₇	—	2	2	no	—
12	C₄₇⋊C₈	—	2	2	no	—
13	C₄₇⋊C₈	C₈	1	4	yes	complemented
14	C₂²×C₄₇	C₄²	1	1	yes	characteristic
15	C₄×C₄₇	C₂×C₈	1	2	yes	—
16	C₄×C₄₇	M₁₆	1	2	yes	—
17	C₄×C₄₇	M₁₆	1	2	yes	—
18	C₂×C₄₇	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄₇	#97	1	1	yes	characteristic
20	C₂×C₄₇	#97	1	1	yes	characteristic
21	#322	—	47	1	no	maximal, Sylow
22	C₄₇	#322	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₈	—	47	1	no	—
24	C₄×C₈	—	47	1	no	—
25	C₄×C₈	D₄₇	1	1	yes	characteristic
26	C₂×C₈	—	47	2	no	—
27	C₂×C₈	—	47	2	no	—
28	C₂×C₈	Dic₄₇	1	2	yes	—
29	C₄²	C₂×D₄₇	1	1	yes	characteristic
30	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
31	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	47	4	no	—
35	C₈	—	94	2	no	—
36	C₂²	C₄×Dic₄₇	1	1	yes	characteristic
37	C₄	C₈×D₄₇	1	2	yes	—
38	C₄	#10625324	1	2	yes	—
39	C₄	#10625329	1	2	yes	—
40	C₂	C₈×Dic₄₇	1	1	yes	characteristic
41	C₂	#13093934	1	1	yes	characteristic
42	C₂	#13093935	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×D₄₇
commutator	C₂×C₄₇	C₄×C₈
Fitting	C₄×C₈×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₄²
cosocle	C₄²×C₄₇	C₂²
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	#322
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
13. C₄₇⋊C₈	C₈	semidirect
22. C₄₇	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄₇⋊C₈	2
C₄×C₈×C₄₇	2
#322	47