Subgroups — #15689378

Order 3008.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625324	C₂	1	1	yes	maximal, characteristic
2	#13094000	C₂	1	2	yes	maximal
3	#13093956	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093948	C₂	1	2	yes	maximal, complemented
5	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
7	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
8	Q₁₆×C₄₇	—	2	2	no	—
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	(C₂×D₄₇)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	Dic₄₇⋊C₄	—	2	2	no	—
13	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#10625324	—	2	2	no	—
15	C₂²×D₄₇	D₄	1	1	yes	characteristic
16	Q₈×C₄₇	—	2	2	no	—
17	Q₈×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	2	2	no	—
19	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₇	—	2	2	no	—
21	C₂×Dic₄₇	D₄	1	1	yes	characteristic
22	C₄×D₄₇	—	2	1	no	—
23	C₄×D₄₇	—	2	1	no	—
24	C₈×C₄₇	D₄	1	2	yes	—
25	C₄₇⋊C₈	—	2	1	no	—
26	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄₇	—	2	1	no	—
28	C₂×D₄₇	—	2	2	no	—
29	C₄×C₄₇	—	4	2	no	—
30	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₇	#41	1	1	yes	characteristic
32	Dic₄₇	—	2	1	no	—
33	Dic₄₇	—	4	2	no	—
34	C₂×C₄₇	#121	1	1	yes	characteristic
35	C₂×C₄₇	#137	1	2	yes	—
36	D₄₇	—	4	1	no	—
37	#470	—	47	1	no	maximal, Sylow
38	C₄₇	#470	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
40	C₂×M₁₆	—	47	1	no	—
41	C₂²⋊Q₈	—	47	2	no	—
42	#106	—	47	1	no	—
43	#103	—	47	2	no	—
44	C₂×Q₈	C₂×D₄₇	1	2	yes	—
45	C₂²×C₄	—	47	1	no	—
46	Q₁₆	—	2	2	no	—
47	M₁₆	—	94	2	no	—
48	C₂×C₈	—	47	1	no	—
49	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
50	C₄⋊C₄	—	47	2	no	—
51	C₄⋊C₄	—	94	2	no	—
52	C₂²⋊C₄	—	94	2	no	—
53	C₂³	—	47	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	47	1	no	—
58	C₂×C₄	—	94	1	no	—
59	C₂×C₄	—	94	1	no	—
60	C₂×C₄	—	94	2	no	—
61	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
62	C₈	—	94	1	no	—
63	C₈	C₂²⋊D₄₇	1	2	yes	—
64	C₂²	—	94	1	no	—
65	C₂²	—	94	2	no	—
66	C₂²	D₄×D₄₇	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	94	1	no	—
69	C₄	—	188	2	no	—
70	C₄	#10625352	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
72	C₂	—	188	1	no	—
73	C₂	#13093995	1	1	yes	characteristic
74	C₂	#13094056	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂²×D₄₇	D₄
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	#470
LCS	G ▷ C₂×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
3. #13093956	C₂	semidirect
4. #13093948	C₂	semidirect
5. C₂×Q₁₆×C₄₇	C₂	semidirect
38. C₄₇	#470	semidirect
39. C₂×Q₁₆	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625324	2
#13094000	2
#13093956	2
#13093948	2
C₂×Q₁₆×C₄₇	2
#470	47