Subgroups — #15689230

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₄₇	C₂	1	2	yes	maximal
2	#13093956	C₂	1	1	yes	maximal, characteristic
3	#13093948	C₂	1	2	yes	maximal
4	#13093934	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
7	Q₁₆×C₄₇	C₄	1	4	yes	complemented
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₇	—	2	2	no	—
10	C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₄×Dic₄₇	—	2	2	no	—
12	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	Q₈×C₄₇	—	2	2	no	—
15	Q₈×C₄₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₄₇	—	2	2	no	—
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₇	—	2	2	no	—
19	C₂×Dic₄₇	D₄	1	2	yes	—
20	C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₄₇⋊C₈	—	2	1	no	—
22	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₄₇	—	2	4	no	—
24	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₇	#41	1	1	yes	characteristic
26	Dic₄₇	—	2	2	no	—
27	Dic₄₇	—	4	2	no	—
28	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
29	C₂×C₄₇	#137	1	2	yes	—
30	#441	—	47	1	no	maximal, Sylow
31	C₄₇	#441	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	D₄₇	1	1	yes	characteristic
33	C₄×Q₈	—	47	2	no	—
34	#106	—	47	1	no	—
35	#103	—	47	2	no	—
36	#97	—	47	1	no	—
37	C₂×Q₈	C₂×D₄₇	1	2	yes	—
38	Q₁₆	Dic₄₇	1	4	yes	complemented
39	C₂×C₈	—	47	1	no	—
40	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
41	C₄⋊C₄	—	47	2	no	—
42	C₄⋊C₄	—	94	2	no	—
43	C₄²	—	47	1	no	—
44	C₄²	—	94	2	no	—
45	Q₈	—	2	2	no	—
46	Q₈	C₂×Dic₄₇	1	4	yes	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	47	2	no	—
49	C₂×C₄	—	94	2	no	—
50	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
51	C₈	—	94	1	no	—
52	C₈	C₂×Dic₄₇	1	2	yes	—
53	C₂²	D₄×D₄₇	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	94	2	no	—
56	C₄	—	188	2	no	—
57	C₄	#10625352	1	1	yes	characteristic
58	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
59	C₂	D₄×Dic₄₇	1	1	yes	characteristic
60	C₂	#13094056	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	#441
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
7. Q₁₆×C₄₇	C₄	semidirect
31. C₄₇	#441	semidirect
38. Q₁₆	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₄₇	2
#13093956	2
#13093948	2
#13093934	2
C₂×Q₁₆×C₄₇	2
#441	47