Subgroups — #13094044

Order 1504.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625337	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625336	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625335	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	D₄×C₄₇	—	2	1	no	—
10	D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₇	—	2	1	no	—
12	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²⋊D₄₇	—	2	1	no	—
14	D₁₈₈	C₂²	1	1	yes	characteristic
15	C₄×D₄₇	—	2	1	no	—
16	Dic₉₄	C₂²	1	1	yes	characteristic
17	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₄₇	—	2	1	no	—
20	C₂²×C₄₇	D₄	1	1	yes	characteristic
21	C₂×D₄₇	—	2	1	no	—
22	C₄×C₄₇	—	2	1	no	—
23	C₄×C₄₇	D₄	1	1	yes	characteristic
24	C₄×C₄₇	C₂³	1	1	yes	characteristic
25	Dic₄₇	—	2	1	no	—
26	C₂×C₄₇	—	2	1	no	—
27	C₂×C₄₇	—	4	1	no	—
28	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
29	D₄₇	—	4	1	no	—
30	C₄₇	#135	1	1	yes	characteristic, complemented, Sylow
31	#135	—	47	1	no	maximal, Sylow
32	#41	—	47	1	no	—
33	#41	D₄₇	1	1	yes	characteristic, complemented
34	Q₁₆	—	47	1	no	—
35	SD₁₆	—	47	1	no	—
36	SD₁₆	—	47	1	no	—
37	D₈	—	47	1	no	—
38	C₂×C₈	—	47	1	no	—
39	Q₈	—	47	1	no	—
40	Q₈	C₂×D₄₇	1	1	yes	characteristic
41	D₄	—	2	1	no	—
42	D₄	—	47	1	no	—
43	D₄	—	94	1	no	—
44	D₄	C₂×D₄₇	1	1	yes	characteristic
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	94	1	no	—
47	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
48	C₈	—	47	1	no	—
49	C₈	—	47	1	no	—
50	C₂²	—	2	1	no	—
51	C₂²	—	94	1	no	—
52	C₂²	C₂²⋊D₄₇	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	94	1	no	—
55	C₄	C₂²⋊D₄₇	1	1	yes	characteristic
56	C₄	C₂²×D₄₇	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	—	4	1	no	—
59	C₂	—	188	1	no	—
60	C₂	C₂×C₂²⋊D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊D₄₇
commutator, cosocle	C₄×C₄₇	C₂³
Frattini	C₄	C₂²×D₄₇
Fitting	#41×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₄
hypercenter	#41	D₄₇
hypocenter	C₄₇	#135
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #41×C₄₇	C₂	semidirect
2. #10625350	C₂	semidirect
3. #10625337	C₂	semidirect
4. #10625336	C₂	semidirect
5. #10625335	C₂	semidirect
6. #10625334	C₂	semidirect
7. C₂×C₄₇⋊C₈	C₂	semidirect
30. C₄₇	#135	semidirect
33. #41	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#41×C₄₇	2
#10625350	2
#10625337	2
#10625336	2
#10625335	2
#10625334	2
C₂×C₄₇⋊C₈	2
#135	47