Subgroups — #15688891

Order 3008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₄₇	C₄	1	2	yes	—
6	M₁₆×C₄₇	—	2	1	no	—
7	M₁₆×C₄₇	C₄	1	2	yes	complemented
8	C₂×C₈×C₄₇	—	2	1	no	—
9	C₄⋊Dic₄₇	—	2	1	no	—
10	C₄⋊Dic₄₇	—	2	1	no	—
11	#10625329	—	2	1	no	—
12	#10625329	C₄	1	2	yes	complemented
13	C₂×C₄₇⋊C₈	—	2	1	no	—
14	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	Q₈	1	1	yes	characteristic
21	C₂×Dic₄₇	—	2	2	no	—
22	C₂×Dic₄₇	—	4	2	no	—
23	C₈×C₄₇	—	2	2	no	—
24	C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇	—	2	1	no	—
26	C₂²×C₄₇	—	2	1	no	—
27	C₂²×C₄₇	C₄²	1	1	yes	characteristic
28	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₄₇	—	4	2	no	—
35	C₂×C₄₇	—	2	1	no	—
36	C₂×C₄₇	—	2	1	no	—
37	C₂×C₄₇	#95	1	1	yes	characteristic
38	C₂×C₄₇	#100	1	1	yes	characteristic
39	C₂×C₄₇	#101	1	1	yes	characteristic
40	#343	—	47	1	no	maximal, Sylow
41	C₄₇	#343	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	47	1	no	—
43	C₂×M₁₆	D₄₇	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	47	1	no	—
45	C₂²×C₄	—	47	2	no	—
46	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
47	M₁₆	—	2	1	no	—
48	M₁₆	—	47	2	no	—
49	M₁₆	—	94	1	no	—
50	M₁₆	Dic₄₇	1	2	yes	complemented
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	—	94	1	no	—
53	C₄⋊C₄	—	94	1	no	—
54	C₄⋊C₄	—	94	1	no	—
55	C₂³	C₄×D₄₇	1	1	yes	characteristic
56	C₂×C₄	—	94	2	no	—
57	C₂×C₄	—	188	2	no	—
58	C₂×C₄	Dic₉₄	1	1	yes	characteristic
59	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
60	C₂×C₄	D₁₈₈	1	1	yes	characteristic
61	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	94	2	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	C₄×Dic₄₇	1	1	yes	characteristic
69	C₂²	Dic₄₇⋊C₄	1	1	yes	characteristic
70	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
71	C₄	—	188	2	no	—
72	C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
73	C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
74	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
75	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	C₄₇⋊#95	1	1	yes	characteristic
79	C₂	#13093940	1	1	yes	characteristic
80	C₂	#13093942	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄₇	C₄²
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	C₂×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²⋊C₄
prime radical	C₂³×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	C₂×M₁₆	D₄₇
hypocenter	C₄₇	#343
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
7. M₁₆×C₄₇	C₄	semidirect
12. #10625329	C₄	semidirect
41. C₄₇	#343	semidirect
50. M₁₆	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625329	2
C₂×C₄⋊Dic₄₇	2
C₂×M₁₆×C₄₇	2
#343	47