Subgroups — #15688871

Order 3008.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094024	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₄	C₄	1	2	yes	—
5	C₂×C₈×C₄₇	—	2	1	no	—
6	C₄²×C₄₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₄₇	—	2	1	no	—
8	C₄⋊Dic₄₇	—	2	1	no	—
9	C₂×C₄₇⋊C₈	—	2	1	no	—
10	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×Dic₄₇	—	2	2	no	—
14	Dic₉₄	—	4	2	no	—
15	C₈×C₄₇	—	4	1	no	—
16	C₄₇⋊C₈	—	4	1	no	—
17	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₄₇	—	2	1	no	—
19	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₄₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₇	Q₁₆	1	1	yes	characteristic
22	C₄×C₄₇	Q₁₆	1	1	yes	characteristic
23	Dic₄₇	—	4	2	no	—
24	C₂×C₄₇	#100	1	1	yes	characteristic
25	C₂×C₄₇	#103	1	1	yes	characteristic
26	C₂×C₄₇	#103	1	1	yes	characteristic
27	#333	—	47	1	no	maximal, Sylow
28	C₄₇	#333	1	1	yes	characteristic, complemented, Sylow
29	C₄⋊Q₈	—	47	1	no	—
30	C₄⋊C₈	—	47	1	no	—
31	C₄⋊C₈	D₄₇	1	1	yes	characteristic
32	C₂×Q₈	—	47	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	94	1	no	—
35	C₄⋊C₄	—	94	1	no	—
36	C₄⋊C₄	—	94	1	no	—
37	C₄²	C₂×D₄₇	1	1	yes	characteristic
38	Q₈	—	188	2	no	—
39	C₂×C₄	—	94	2	no	—
40	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
41	C₂×C₄	D₁₈₈	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	188	1	no	—
45	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	188	2	no	—
48	C₄	#10625325	1	1	yes	characteristic
49	C₄	Dic₁₈₈	1	1	yes	characteristic
50	C₄	#10625335	1	1	yes	characteristic
51	C₄	#10625337	1	1	yes	characteristic
52	C₂	#13093940	1	1	yes	characteristic
53	C₂	#13093947	1	1	yes	characteristic
54	C₂	#13093949	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄
Frattini	C₄²	C₂×D₄₇
Fitting	C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂²
hypercenter	C₄⋊C₈	D₄₇
hypocenter	C₄₇	#333
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
28. C₄₇	#333	semidirect

Maximal subgroups

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

subgroup	index
#13094024	2
C₄⋊(C₄₇⋊C₈)	2
C₄⋊C₈×C₄₇	2
#333	47