Subgroups — #15689104

Order 3008.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625352	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₄₇	C₂	1	2	yes	maximal, complemented
3	#13093942	C₂	1	2	yes	maximal, complemented
4	#13093941	C₂	1	1	yes	maximal, characteristic, complemented
5	#100×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₄₇	C₄	1	2	yes	—
8	C₂²×Dic₄₇	C₄	1	2	yes	—
9	#10625352	—	2	2	no	—
10	#10625352	—	2	2	no	—
11	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
13	M₁₆×C₄₇	C₂²	1	2	yes	—
14	#10625329	C₂²	1	2	yes	—
15	#10625324	—	2	2	no	—
16	C₈×D₄₇	—	2	2	no	—
17	C₂³×C₄₇	C₂×C₄	1	2	yes	—
18	C₂²×D₄₇	C₂×C₄	1	1	yes	characteristic
19	D₄×C₄₇	—	2	2	no	—
20	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²⋊D₄₇	—	2	4	no	—
22	C₂×Dic₄₇	—	2	2	no	—
23	C₂×Dic₄₇	—	2	2	no	—
24	C₂×Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₄×D₄₇	D₄	1	2	yes	—
27	C₄×D₄₇	D₄	1	2	yes	—
28	Dic₉₄	—	2	2	no	—
29	C₈×C₄₇	—	2	2	no	—
30	C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇	—	2	2	no	—
32	C₂²×C₄₇	—	4	2	no	—
33	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×D₄₇	—	4	1	no	—
35	C₂×D₄₇	C₂²⋊C₄	1	2	yes	—
36	C₄×C₄₇	C₂×D₄	1	2	yes	—
37	Dic₄₇	—	2	2	no	—
38	Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄₇	—	2	1	no	—
41	C₂×C₄₇	—	4	2	no	—
42	C₂×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	D₄₇	—	2	2	no	—
44	#413	—	47	1	no	maximal, Sylow
45	C₄₇	#413	1	1	yes	characteristic, complemented, Sylow
46	C₂×#41	—	47	1	no	—
47	C₂×M₁₆	—	47	2	no	—
48	#101	—	47	2	no	—
49	#100	—	47	1	no	—
50	#100	D₄₇	1	1	yes	characteristic, complemented
51	#41	—	94	2	no	—
52	#41	—	94	2	no	—
53	C₂×Q₈	—	47	1	no	—
54	C₂×D₄	—	47	2	no	—
55	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
56	C₂²×C₄	—	47	1	no	—
57	C₂²×C₄	—	47	2	no	—
58	M₁₆	—	47	2	no	—
59	M₁₆	—	94	2	no	—
60	M₁₆	C₂×D₄₇	1	2	yes	—
61	C₂×C₈	—	94	2	no	—
62	C₂³	—	47	1	no	—
63	C₂³	C₄×D₄₇	1	2	yes	—
64	Q₈	—	94	2	no	—
65	D₄	—	2	2	no	—
66	D₄	—	94	4	no	—
67	C₂×C₄	—	47	1	no	—
68	C₂×C₄	—	47	2	no	—
69	C₂×C₄	—	47	2	no	—
70	C₂×C₄	—	47	2	no	—
71	C₂×C₄	—	94	2	no	—
72	C₂×C₄	—	94	2	no	—
73	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	94	2	no	—
76	C₂²	—	2	2	no	—
77	C₂²	—	4	2	no	—
78	C₂²	—	47	2	no	—
79	C₂²	—	188	1	no	—
80	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
81	C₄	—	47	1	no	—
82	C₄	—	47	1	no	—
83	C₄	—	94	2	no	—
84	C₄	D₄×D₄₇	1	2	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	4	2	no	—
87	C₂	—	94	2	no	—
88	C₂	C₂²⋊C₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#100×C₄₇	C₂
socle	C₂×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#10625352	C₂
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#100	D₄₇
hypocenter	C₄₇	#413
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₄₇	C₂	semidirect
3. #13093942	C₂	semidirect
4. #13093941	C₂	semidirect
5. #100×C₄₇	C₂	semidirect
45. C₄₇	#413	semidirect
50. #100	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625352	2
M₁₆×D₄₇	2
#13093942	2
#13093941	2
#100×C₄₇	2
#413	47