Subgroups — #13094118

Order 1512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#92589	—	3	1	no	maximal
5	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
6	D₁₈₉	—	2	1	no	—
7	C₇×D₂₇	—	2	1	no	—
8	C₂×D₆₃	—	3	1	no	—
9	C₂×C₇×D₉	—	3	1	no	—
10	C₉×Dic₇	D₃	1	1	yes	characteristic
11	D₁₀₈	—	7	1	no	maximal, Hall
12	C₇×C₂₇	D₄	1	1	yes	characteristic, complemented, Hall
13	#4247	—	9	1	no	—
14	C₂×C₇×C₉	C₂×D₃	1	1	yes	characteristic
15	D₆₃	—	6	1	no	—
16	C₇×D₉	—	6	1	no	—
17	C₂×D₂₇	—	7	1	no	—
18	C₂×D₂₇	D₇	1	1	yes	characteristic, complemented
19	C₄×C₂₇	—	7	1	no	—
20	C₂×D₂₁	—	9	1	no	—
21	C₂×D₃×C₇	—	9	1	no	—
22	C₃×Dic₇	D₉	1	1	yes	characteristic
23	D₃₆	—	21	1	no	—
24	C₇×C₉	D₁₂	1	1	yes	characteristic
25	C₂²⋊D₇	—	27	1	no	Hall
26	C₂×C₂₇	C₂×D₇	1	1	yes	characteristic
27	D₂₇	—	2	1	no	—
28	D₂₇	—	14	1	no	—
29	C₂×C₃×C₇	C₂×D₉	1	1	yes	characteristic
30	D₂₁	—	18	1	no	—
31	D₃×C₇	—	18	1	no	—
32	C₂×D₉	—	3	1	no	—
33	C₂×D₉	—	21	1	no	—
34	C₄×C₉	—	7	1	no	—
35	C₂²×C₇	—	27	1	no	—
36	C₂×D₇	—	27	1	no	—
37	Dic₇	D₂₇	1	1	yes	characteristic, complemented
38	C₂₇	C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
39	D₁₂	—	63	1	no	—
40	C₃×C₇	D₃₆	1	1	yes	characteristic
41	C₂×C₉	D₃×D₇	1	1	yes	characteristic
42	D₉	—	6	1	no	—
43	D₉	—	42	1	no	—
44	C₂×C₇	—	54	1	no	—
45	C₂×C₇	C₂×D₂₇	1	1	yes	characteristic
46	D₇	—	54	1	no	—
47	C₂×D₃	—	9	1	no	—
48	C₂×D₃	—	63	1	no	—
49	C₃×C₄	—	7	1	no	—
50	C₉	#4247	1	1	yes	characteristic
51	D₄	—	189	1	no	Sylow
52	C₇	D₁₀₈	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	D₇×D₉	1	1	yes	characteristic
54	D₃	—	18	1	no	—
55	D₃	—	126	1	no	—
56	C₂²	—	27	1	no	—
57	C₂²	—	189	1	no	—
58	C₄	—	7	1	no	—
59	C₃	#92589	1	1	yes	characteristic
60	C₂	—	54	1	no	—
61	C₂	—	378	1	no	—
62	C₂	D₇×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₇×D₂₇
commutator, Fitting, cosocle	C₂×C₇×C₂₇	C₂²
Frattini	C₂×C₉	D₃×D₇
socle	C₂×C₃×C₇	C₂×D₉
hypocenter	C₇×C₂₇	D₄
LCS	G ▷ C₂×C₇×C₂₇ ▷ C₇×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₈₉	C₂	semidirect
2. C₂×C₇×D₂₇	C₂	semidirect
3. C₂₇×Dic₇	C₂	semidirect
12. C₇×C₂₇	D₄	semidirect
18. C₂×D₂₇	D₇	semidirect
37. Dic₇	D₂₇	semidirect
38. C₂₇	C₂²⋊D₇	semidirect
52. C₇	D₁₀₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₈₉	2
C₂×C₇×D₂₇	2
C₂₇×Dic₇	2
#92589	3
D₁₀₈	7