Subgroups — #15689182

Order 3008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093981	C₂	1	1	yes	maximal, characteristic
2	Dic₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	(C₂×D₄₇)⋊C₈	C₂	1	2	yes	maximal
4	#13093935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₄₇	C₂²	1	2	yes	—
8	C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
10	Dic₄₇⋊C₄	C₄	1	2	yes	—
11	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂²×D₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
18	C₄×D₄₇	—	2	2	no	—
19	C₈×C₄₇	—	2	2	no	—
20	C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
22	C₂×D₄₇	—	2	1	no	—
23	C₂×D₄₇	—	2	2	no	—
24	C₄×C₄₇	—	2	2	no	—
25	C₄×C₄₇	#41	1	2	yes	—
26	Dic₄₇	—	2	1	no	—
27	Dic₄₇	—	2	2	no	—
28	C₂×C₄₇	#117	1	1	yes	characteristic
29	C₂×C₄₇	#131	1	2	yes	—
30	D₄₇	—	4	1	no	—
31	#433	—	47	1	no	maximal, Sylow
32	C₄₇	#433	1	1	yes	characteristic, complemented, Sylow
33	#117	—	47	1	no	—
34	C₄⋊C₈	—	47	2	no	—
35	C₂²⋊C₈	—	47	2	no	—
36	#97	—	47	1	no	—
37	C₄×C₈	D₄₇	1	1	yes	characteristic, complemented
38	C₂²×C₄	—	47	1	no	—
39	C₂×C₈	—	47	2	no	—
40	C₂×C₈	C₂×D₄₇	1	2	yes	—
41	C₄⋊C₄	—	47	2	no	—
42	C₂²⋊C₄	—	47	2	no	—
43	C₄²	—	47	1	no	—
44	C₄²	C₂×D₄₇	1	1	yes	characteristic
45	C₂³	—	47	1	no	—
46	C₂×C₄	—	47	2	no	—
47	C₂×C₄	—	47	1	no	—
48	C₂×C₄	—	94	2	no	—
49	C₂×C₄	C₄×D₄₇	1	2	yes	—
50	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	94	2	no	—
53	C₂²	—	94	1	no	—
54	C₂²	—	94	2	no	—
55	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	94	1	no	—
58	C₄	—	94	2	no	—
59	C₄	#10625350	1	2	yes	—
60	C₂	—	188	1	no	—
61	C₂	#13093981	1	1	yes	characteristic
62	C₂	#13094030	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₄
Fitting	C₄×C₈×C₄₇	C₂
prime radical	C₂²×D₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	#433
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. Dic₄₇⋊C₈	C₂	semidirect
4. #13093935	C₂	semidirect
5. C₄×C₈×C₄₇	C₂	semidirect
32. C₄₇	#433	semidirect
37. C₄×C₈	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093981	2
Dic₄₇⋊C₈	2
(C₂×D₄₇)⋊C₈	2
#13093935	2
C₄×C₈×C₄₇	2
#433	47