Subgroups — #15688888

Order 3008.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625329	C₂	1	2	yes	maximal
2	C₂²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
4	C₂×C₈×C₄₇	—	2	2	no	—
5	C₂×C₈×C₄₇	C₄	1	2	yes	—
6	#10625329	—	2	2	no	—
7	#10625329	C₄	1	4	yes	—
8	C₂×C₄₇⋊C₈	—	2	2	no	—
9	C₂³×C₄₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	D₄	1	2	yes	—
14	C₈×C₄₇	—	2	2	no	—
15	C₄₇⋊C₈	—	2	4	no	—
16	C₂²×C₄₇	—	2	2	no	—
17	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
18	C₂²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₄₇	C₄²	1	1	yes	characteristic
20	C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
21	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄₇	—	2	2	no	—
23	C₂×C₄₇	#95	1	1	yes	characteristic
24	C₂×C₄₇	#108	1	2	yes	—
25	#341	—	47	1	no	maximal, Sylow
26	C₄₇	#341	1	1	yes	characteristic, complemented, Sylow
27	C₂×M₁₆	—	47	2	no	—
28	C₂²×C₈	D₄₇	1	1	yes	characteristic
29	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
30	M₁₆	—	47	4	no	—
31	M₁₆	—	94	2	no	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	94	2	no	—
34	C₂×C₈	Dic₄₇	1	2	yes	—
35	C₂³	Dic₉₄	1	1	yes	characteristic
36	C₂×C₄	C₄×D₄₇	1	2	yes	—
37	C₂×C₄	D₁₈₈	1	1	yes	characteristic
38	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
39	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
40	C₈	—	2	2	no	—
41	C₈	—	94	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	Dic₄₇⋊C₄	1	2	yes	—
44	C₂²	C₄⋊Dic₄₇	1	1	yes	characteristic
45	C₄	C₄×Dic₄₇	1	1	yes	characteristic
46	C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
47	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
48	C₂	—	2	2	no	—
49	C₂	C₄₇⋊#95	1	1	yes	characteristic
50	C₂	#13093960	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₈₈
commutator	C₄×C₄₇	C₄²
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	C₂²×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₄⋊C₄
prime radical	C₂³×C₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	C₂²×C₈	D₄₇
hypocenter	C₄₇	#341
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
26. C₄₇	#341	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
C₂²×C₈×C₄₇	2
#341	47