Subgroups — #13094030

Order 1504.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625350	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625329	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625324	C₂	1	2	yes	maximal, complemented
5	C₈×D₄₇	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²⋊D₄₇	C₄	1	2	yes	—
8	D₁₈₈	C₄	1	1	yes	characteristic
9	C₄×D₄₇	C₂²	1	2	yes	—
10	Dic₉₄	C₄	1	1	yes	characteristic
11	C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂²×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₄₇	C₂×C₄	1	2	yes	—
16	C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₄₇	C₂³	1	1	yes	characteristic
18	Dic₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₄₇	—	2	1	no	—
20	C₂×C₄₇	C₂²×C₄	1	1	yes	characteristic
21	D₄₇	—	2	2	no	—
22	C₄₇	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	47	1	no	maximal, Sylow
24	#41	—	47	1	no	—
25	M₁₆	—	47	1	no	—
26	M₁₆	—	47	2	no	—
27	C₂×C₈	—	47	2	no	—
28	C₂×C₈	D₄₇	1	1	yes	characteristic, complemented
29	Q₈	—	47	1	no	—
30	D₄	—	47	2	no	—
31	D₄	—	47	1	no	—
32	C₂×C₄	—	47	2	no	—
33	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
34	C₈	—	47	2	no	—
35	C₈	C₂×D₄₇	1	1	yes	characteristic
36	C₈	C₂×D₄₇	1	1	yes	characteristic
37	C₂²	—	47	2	no	—
38	C₂²	C₄×D₄₇	1	1	yes	characteristic
39	C₄	—	47	2	no	—
40	C₄	C₄×D₄₇	1	1	yes	characteristic
41	C₄	C₂²×D₄₇	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	94	2	no	—
44	C₂	C₂×C₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄₇
commutator, socle	C₂×C₄₇	C₂²×C₄
Frattini	C₄	C₂²×D₄₇
Fitting	C₂×C₈×C₄₇	C₂
prime radical	#10625350	C₂
cosocle	C₄×C₄₇	C₂³
hypercenter	C₂×C₈	D₄₇
hypocenter	C₄₇	#131
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₄₇	C₂	semidirect
3. #10625329	C₂	semidirect
4. #10625324	C₂	semidirect
5. C₈×D₄₇	C₂	semidirect
22. C₄₇	#131	semidirect
28. C₂×C₈	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#10625350	2
C₂×C₈×C₄₇	2
#10625329	2
#10625324	2
C₈×D₄₇	2
#131	47