Subgroups — #13094053

Order 1504.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625352	C₂	1	1	yes	maximal, characteristic
3	SD₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625337	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625335	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#10625324	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²⋊D₄₇	—	2	1	no	—
11	C₂×Dic₄₇	—	2	1	no	—
12	C₄×D₄₇	—	2	1	no	—
13	C₄×D₄₇	C₂²	1	1	yes	characteristic
14	Dic₉₄	—	2	1	no	—
15	Dic₉₄	C₂²	1	1	yes	characteristic
16	Dic₉₄	C₂²	1	1	yes	characteristic
17	C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₄₇	—	2	1	no	—
20	C₂×D₄₇	D₄	1	1	yes	characteristic
21	C₄×C₄₇	—	2	1	no	—
22	C₄×C₄₇	C₂³	1	1	yes	characteristic
23	Dic₄₇	—	2	1	no	—
24	Dic₄₇	—	2	1	no	—
25	Dic₄₇	D₄	1	1	yes	characteristic
26	C₂×C₄₇	—	4	1	no	—
27	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
28	D₄₇	—	2	1	no	—
29	C₄₇	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	47	1	no	maximal, Sylow
31	#41	—	47	1	no	—
32	C₂×Q₈	—	47	1	no	—
33	Q₁₆	—	47	1	no	—
34	Q₁₆	—	47	1	no	—
35	SD₁₆	—	47	1	no	—
36	SD₁₆	D₄₇	1	1	yes	characteristic, complemented
37	M₁₆	—	47	1	no	—
38	Q₈	—	47	1	no	—
39	Q₈	—	47	1	no	—
40	Q₈	—	94	1	no	—
41	Q₈	C₂×D₄₇	1	1	yes	characteristic
42	D₄	—	94	1	no	—
43	D₄	C₂×D₄₇	1	1	yes	characteristic
44	C₂×C₄	—	47	1	no	—
45	C₂×C₄	—	94	1	no	—
46	C₂×C₄	—	94	1	no	—
47	C₈	—	47	1	no	—
48	C₈	C₂×D₄₇	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	47	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	47	1	no	—
53	C₄	—	94	1	no	—
54	C₄	—	94	1	no	—
55	C₄	C₂²×D₄₇	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	94	1	no	—
58	C₂	D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₇
commutator, cosocle	C₄×C₄₇	C₂³
Frattini	C₄	C₂²×D₄₇
Fitting	SD₁₆×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₄
prime radical	#10625352	C₂
hypercenter	SD₁₆	D₄₇
hypocenter	C₄₇	#137
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₄₇	C₂	semidirect
3. SD₁₆×C₄₇	C₂	semidirect
4. #10625337	C₂	semidirect
5. #10625335	C₂	semidirect
6. Dic₁₈₈	C₂	semidirect
7. #10625324	C₂	semidirect
29. C₄₇	#137	semidirect
36. SD₁₆	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₄₇	2
#10625352	2
SD₁₆×C₄₇	2
#10625337	2
#10625335	2
Dic₁₈₈	2
#10625324	2
#137	47