Subgroups — #15689166

Order 3008.

118 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	#13093957	C₂	1	2	yes	maximal, complemented
4	#13093955	C₂	1	2	yes	maximal, complemented
5	#117×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₇	—	2	1	no	—
8	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²⋊C₄×C₄₇	—	2	1	no	—
11	C₄²×C₄₇	—	2	1	no	—
12	C₄⋊Dic₄₇	—	2	1	no	—
13	C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	#10625329	C₄	1	4	yes	complemented
15	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	—	2	1	no	—
18	C₂×C₄×C₄₇	—	2	1	no	—
19	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	Q₈	1	2	yes	—
22	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₇	—	2	2	no	—
24	C₂×Dic₄₇	—	4	2	no	—
25	C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
26	C₂²×C₄₇	—	2	1	no	—
27	C₂²×C₄₇	—	2	1	no	—
28	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₄₇	—	4	1	no	—
31	C₄×C₄₇	—	4	1	no	—
32	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
33	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
35	Dic₄₇	—	4	2	no	—
36	C₂×C₄₇	—	2	2	no	—
37	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₄₇	#137	1	1	yes	characteristic
40	#428	—	47	1	no	maximal, Sylow
41	C₄₇	#428	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	47	1	no	—
43	#117	D₄₇	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	47	1	no	—
45	#107	—	47	2	no	—
46	#106	—	47	2	no	—
47	C₂²×C₄	—	94	1	no	—
48	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
49	M₁₆	—	47	4	no	—
50	C₂×C₈	—	47	2	no	—
51	C₄⋊C₄	—	47	2	no	—
52	C₄⋊C₄	—	94	1	no	—
53	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
54	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
55	C₂²⋊C₄	—	2	1	no	—
56	C₄²	—	2	1	no	—
57	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	94	2	no	—
61	C₂×C₄	—	188	2	no	—
62	C₂×C₄	Dic₉₄	1	2	yes	—
63	C₂×C₄	C₄×D₄₇	1	2	yes	—
64	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₈	—	47	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	Dic₄₇⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	188	2	no	—
74	C₄	Dic₄₇⋊C₄	1	2	yes	—
75	C₄	C₂×Dic₉₄	1	1	yes	characteristic
76	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
79	C₂	#13094049	1	1	yes	characteristic
80	C₂	#13094054	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#117×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂³×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#117	D₄₇
hypocenter	C₄₇	#428
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #13093957	C₂	semidirect
4. #13093955	C₂	semidirect
14. #10625329	C₄	semidirect
25. C₄₇⋊C₈	C₂×C₄	semidirect
41. C₄₇	#428	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
#13093957	2
#13093955	2
#117×C₄₇	2
#428	47