Subgroups — #15688862

Order 3008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094012	C₂	1	1	yes	maximal, characteristic
2	#13093935	C₂	1	1	yes	maximal, characteristic, complemented
3	#97×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₈	C₄	1	1	yes	characteristic
5	C₂×Dic₉₄	C₄	1	1	yes	characteristic
6	C₂×C₈×C₄₇	—	2	1	no	—
7	C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	(C₂×D₄₇)⋊C₄	—	2	1	no	—
9	(C₂×D₄₇)⋊C₄	—	2	1	no	—
10	C₂×C₄₇⋊C₈	—	2	1	no	—
11	C₂²×D₄₇	—	2	1	no	—
12	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×Dic₄₇	—	2	1	no	—
16	D₁₈₈	—	4	1	no	—
17	Dic₉₄	—	4	1	no	—
18	C₈×C₄₇	—	2	2	no	—
19	C₄₇⋊C₈	—	2	2	no	—
20	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₄₇	—	4	1	no	—
22	C₂×D₄₇	—	4	1	no	—
23	C₂×D₄₇	—	4	1	no	—
24	C₄×C₄₇	—	2	1	no	—
25	C₄×C₄₇	—	2	1	no	—
26	C₄×C₄₇	—	2	1	no	—
27	Dic₄₇	—	4	1	no	—
28	C₂×C₄₇	#100	1	1	yes	characteristic
29	C₂×C₄₇	#104	1	1	yes	characteristic
30	C₂×C₄₇	#104	1	1	yes	characteristic
31	D₄₇	—	8	1	no	—
32	#329	—	47	1	no	maximal, Sylow
33	C₄₇	#329	1	1	yes	characteristic, complemented, Sylow
34	#124	—	47	1	no	—
35	#97	—	47	1	no	—
36	#97	D₄₇	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	47	1	no	—
38	C₂×D₄	—	47	1	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	94	1	no	—
41	C₂²⋊C₄	—	94	1	no	—
42	C₂²⋊C₄	—	94	1	no	—
43	C₄²	C₂×D₄₇	1	1	yes	characteristic
44	C₂³	—	94	1	no	—
45	Q₈	—	188	1	no	—
46	D₄	—	188	1	no	—
47	C₂×C₄	—	94	1	no	—
48	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
49	C₂×C₄	D₁₈₈	1	1	yes	characteristic
50	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	94	2	no	—
53	C₂²	—	188	1	no	—
54	C₂²	—	188	1	no	—
55	C₂²	—	188	1	no	—
56	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	188	1	no	—
61	C₂	—	376	1	no	—
62	C₂	#13093940	1	1	yes	characteristic
63	C₂	#13093950	1	1	yes	characteristic
64	C₂	#13093952	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄
Frattini	C₄²	C₂×D₄₇
Fitting	#97×C₄₇	C₂
socle	C₂²×C₄₇	C₂²⋊C₄
prime radical	C₂×D₁₈₈	C₄
cosocle	C₄²×C₄₇	C₂²
hypercenter	#97	D₄₇
hypocenter	C₄₇	#329
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #13093935	C₂	semidirect
3. #97×C₄₇	C₂	semidirect
33. C₄₇	#329	semidirect
36. #97	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094012	2
#13093935	2
#97×C₄₇	2
#329	47