Subgroups — #15689308

Order 3008.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094072	C₂	1	1	yes	maximal, characteristic
2	#13094057	C₂	1	2	yes	maximal, complemented
3	#13094022	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093950	C₂	1	2	yes	maximal, complemented
5	#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	#10625354	—	2	2	no	—
8	Q₈×D₄₇	—	2	2	no	—
9	#10625350	—	2	2	no	—
10	#10625350	C₂²	1	2	yes	—
11	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
12	M₁₆×C₄₇	C₂²	1	2	yes	—
13	Dic₄₇⋊C₄	—	2	2	no	—
14	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	Dic₁₈₈	—	2	2	no	—
16	#10625325	—	2	2	no	—
17	Q₈×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	D₄	1	2	yes	—
19	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²⋊D₄₇	—	2	2	no	—
21	C₂×Dic₄₇	—	2	1	no	—
22	C₂×Dic₄₇	—	2	1	no	—
23	D₁₈₈	—	2	2	no	—
24	D₁₈₈	D₄	1	2	yes	—
25	C₄×D₄₇	—	2	4	no	—
26	C₄×D₄₇	—	2	2	no	—
27	Dic₉₄	—	2	2	no	—
28	Dic₉₄	—	2	2	no	—
29	Dic₉₄	D₄	1	2	yes	—
30	C₈×C₄₇	—	2	2	no	—
31	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₄₇	—	2	2	no	—
33	C₄×C₄₇	—	2	2	no	—
34	C₄×C₄₇	C₂×D₄	1	2	yes	—
35	Dic₄₇	—	2	2	no	—
36	Dic₄₇	—	2	2	no	—
37	Dic₄₇	—	4	1	no	—
38	C₂×C₄₇	—	2	1	no	—
39	C₂×C₄₇	#120	1	1	yes	characteristic
40	D₄₇	—	4	2	no	—
41	#456	—	47	1	no	maximal, Sylow
42	C₄₇	#456	1	1	yes	characteristic, complemented, Sylow
43	2₋¹⁺⁴	—	47	1	no	—
44	#137	—	47	2	no	—
45	C₄⋊Q₈	—	47	1	no	—
46	#104	—	47	2	no	—
47	#101	D₄₇	1	1	yes	characteristic, complemented
48	#41	—	47	2	no	—
49	#41	—	94	2	no	—
50	#41	—	94	2	no	—
51	C₂×Q₈	—	47	1	no	—
52	C₂×Q₈	—	94	2	no	—
53	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
54	Q₁₆	—	94	2	no	—
55	SD₁₆	—	94	2	no	—
56	M₁₆	C₂×D₄₇	1	2	yes	—
57	C₄⋊C₄	—	94	2	no	—
58	C₄²	—	47	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	47	2	no	—
61	Q₈	—	94	2	no	—
62	Q₈	—	94	2	no	—
63	D₄	—	47	2	no	—
64	D₄	—	94	2	no	—
65	D₄	—	94	2	no	—
66	C₂×C₄	—	94	4	no	—
67	C₂×C₄	—	94	1	no	—
68	C₂×C₄	—	94	2	no	—
69	C₂×C₄	—	94	1	no	—
70	C₂×C₄	D₁₈₈	1	2	yes	—
71	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	94	2	no	—
74	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	94	2	no	—
77	C₄	—	94	2	no	—
78	C₄	—	188	1	no	—
79	C₄	D₄×D₄₇	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	188	2	no	—
82	C₂	#13093994	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093994
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#101×C₄₇	C₂
socle	C₂×C₄₇	#120
prime radical	#13094072	C₂
hypercenter	#101	D₄₇
hypocenter	C₄₇	#456
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #13094057	C₂	semidirect
3. #13094022	C₂	semidirect
4. #13093950	C₂	semidirect
5. #101×C₄₇	C₂	semidirect
42. C₄₇	#456	semidirect
47. #101	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094072	2
#13094057	2
#13094022	2
#13093950	2
#101×C₄₇	2
#456	47