Subgroups — #15689159

Order 3008.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#13093983	C₂	1	1	yes	maximal, characteristic
3	#13093957	C₂	1	2	yes	maximal, complemented
4	#13093955	C₂	1	2	yes	maximal, complemented
5	#117×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
8	C₂²⋊C₄×C₄₇	—	2	1	no	—
9	C₄²×C₄₇	—	2	1	no	—
10	C₂²⋊Dic₄₇	—	2	1	no	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₄×Dic₄₇	—	2	1	no	—
13	C₂×C₄₇⋊C₈	C₄	1	4	yes	complemented
14	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	Q₈	1	2	yes	—
21	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₇	—	2	2	no	—
23	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
24	C₄₇⋊C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₄₇	—	2	2	no	—
26	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
27	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₇	—	4	2	no	—
29	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
32	Dic₄₇	—	4	2	no	—
33	C₂×C₄₇	—	2	2	no	—
34	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄₇	#135	1	2	yes	—
36	#427	—	47	1	no	maximal, Sylow
37	C₄₇	#427	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₈	—	47	1	no	—
39	#117	—	47	1	no	—
40	#117	D₄₇	1	1	yes	characteristic
41	#107	—	47	2	no	—
42	#106	—	47	2	no	—
43	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
44	C₂×C₈	—	47	4	no	—
45	C₂×C₈	—	47	1	no	—
46	C₂×C₈	—	47	1	no	—
47	C₄⋊C₄	—	47	2	no	—
48	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	—	94	1	no	—
51	C₄²	—	2	1	no	—
52	C₄²	—	94	1	no	—
53	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	94	2	no	—
56	C₂×C₄	Dic₉₄	1	2	yes	—
57	C₂×C₄	C₄×D₄₇	1	2	yes	—
58	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
60	C₈	—	47	2	no	—
61	C₈	—	47	2	no	—
62	C₂²	—	2	2	no	—
63	C₂²	Dic₄₇⋊C₄	1	2	yes	—
64	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
65	C₄	—	4	2	no	—
66	C₄	—	188	2	no	—
67	C₄	Dic₄₇⋊C₄	1	2	yes	—
68	C₄	C₂×Dic₉₄	1	1	yes	characteristic
69	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
72	C₂	#13094044	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#117×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂³×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#117	D₄₇
hypocenter	C₄₇	#427
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #13093957	C₂	semidirect
4. #13093955	C₂	semidirect
13. C₂×C₄₇⋊C₈	C₄	semidirect
37. C₄₇	#427	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄₇⋊C₈	2
#13093983	2
#13093957	2
#13093955	2
#117×C₄₇	2
#427	47