Subgroups — #15688918

Order 3008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093939	C₂	1	2	yes	maximal
2	#124×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
4	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₂²⋊C₄×C₄₇	—	2	2	no	—
6	C₄²×C₄₇	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊Dic₄₇	—	2	2	no	—
8	C₂³×C₄₇	D₄	1	2	yes	—
9	Q₈×C₄₇	—	4	1	no	—
10	D₄×C₄₇	—	4	1	no	—
11	C₂×C₄×C₄₇	—	2	1	no	—
12	C₂×C₄×C₄₇	—	2	1	no	—
13	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₄₇	—	4	2	no	—
15	C₂²×C₄₇	—	2	2	no	—
16	C₂²×C₄₇	—	4	2	no	—
17	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₄₇	—	2	1	no	—
19	C₄×C₄₇	—	4	1	no	—
20	C₄×C₄₇	—	4	1	no	—
21	Dic₄₇	—	8	2	no	—
22	C₂×C₄₇	—	2	1	no	—
23	C₂×C₄₇	—	4	2	no	—
24	C₂×C₄₇	#99	1	1	yes	characteristic
25	#354	—	47	1	no	maximal, Sylow
26	C₄₇	#354	1	1	yes	characteristic, complemented, Sylow
27	#124	D₄₇	1	1	yes	characteristic
28	#99	—	47	2	no	—
29	C₂×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
30	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
31	C₂²⋊C₄	—	2	2	no	—
32	C₂²⋊C₄	—	94	2	no	—
33	C₄²	Dic₄₇	1	1	yes	characteristic, complemented
34	C₂³	C₂²⋊D₄₇	1	2	yes	—
35	Q₈	—	4	1	no	—
36	D₄	—	4	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	—	188	2	no	—
40	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
41	C₂²	—	2	2	no	—
42	C₂²	—	4	2	no	—
43	C₂²	C₂²⋊Dic₄₇	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	4	1	no	—
47	C₄	—	376	2	no	—
48	C₂	—	2	1	no	—
49	C₂	—	4	2	no	—
50	C₂	#13093939	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093939
commutator	C₂×C₄×C₄₇	C₂×C₄
Frattini	C₂×D₄	C₂×D₄₇
Fitting	#124×C₄₇	C₂
socle	C₂×C₄₇	#99
prime radical, cosocle	C₂×D₄×C₄₇	C₂²
hypercenter	#124	D₄₇
hypocenter	C₄₇	#354
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #124

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×C₄₇	C₄	semidirect
6. C₄²×C₄₇	C₄	semidirect
26. C₄₇	#354	semidirect
29. C₂×Q₈	Dic₄₇	semidirect
33. C₄²	Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13093939	2
#124×C₄₇	2
#354	47