Subgroups — #13094120

Order 1512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₇×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#92591	—	3	1	no	maximal
5	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
6	D₇×C₂₇	—	2	1	no	—
7	C₇×D₂₇	—	2	1	no	—
8	C₂×C₇×D₉	—	3	1	no	—
9	C₂×C₉×D₇	D₃	1	1	yes	characteristic
10	Dic₆₃	—	3	1	no	—
11	#6171	—	7	1	no	maximal, Hall
12	C₇×C₂₇	D₄	1	1	yes	characteristic, complemented, Hall
13	#4245	—	9	1	no	—
14	C₂×C₇×C₉	C₂×D₃	1	1	yes	characteristic
15	C₉×D₇	—	2	1	no	—
16	C₇×D₉	—	6	1	no	—
17	C₂²×C₂₇	—	7	1	no	—
18	C₂×D₂₇	D₇	1	1	yes	characteristic, complemented
19	Dic₂₇	—	7	1	no	—
20	C₂×D₃×C₇	—	9	1	no	—
21	C₂×C₃×D₇	D₉	1	1	yes	characteristic
22	Dic₂₁	—	9	1	no	—
23	#611	—	21	1	no	—
24	C₇×C₉	#67	1	1	yes	characteristic
25	C₂²⋊D₇	—	27	1	no	Hall
26	C₂×C₂₇	—	14	1	no	—
27	C₂×C₂₇	C₂×D₇	1	1	yes	characteristic
28	D₂₇	—	2	1	no	—
29	C₂×C₃×C₇	C₂×D₉	1	1	yes	characteristic
30	C₃×D₇	—	2	1	no	—
31	D₃×C₇	—	18	1	no	—
32	C₂²×C₉	—	7	1	no	—
33	C₂×D₉	—	3	1	no	—
34	Dic₉	—	21	1	no	—
35	C₂²×C₇	—	27	1	no	—
36	C₂×D₇	D₂₇	1	1	yes	characteristic, complemented
37	Dic₇	—	27	1	no	—
38	C₂₇	C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
39	#67	—	63	1	no	—
40	C₃×C₇	#611	1	1	yes	characteristic
41	C₂×C₉	—	14	1	no	—
42	C₂×C₉	D₃×D₇	1	1	yes	characteristic
43	D₉	—	6	1	no	—
44	C₂×C₇	—	54	1	no	—
45	C₂×C₇	C₂×D₂₇	1	1	yes	characteristic
46	D₇	—	2	1	no	—
47	C₂²×C₃	—	7	1	no	—
48	C₂×D₃	—	9	1	no	—
49	Dic₃	—	63	1	no	—
50	C₉	#4245	1	1	yes	characteristic
51	D₄	—	189	1	no	Sylow
52	C₇	#6171	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃	—	14	1	no	—
54	C₂×C₃	D₇×D₉	1	1	yes	characteristic
55	D₃	—	18	1	no	—
56	C₂²	—	7	1	no	—
57	C₂²	—	27	1	no	—
58	C₄	—	189	1	no	—
59	C₃	#92591	1	1	yes	characteristic
60	C₂	—	14	1	no	—
61	C₂	—	54	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×C₇×D₂₇	C₂	semidirect
2. C₂×D₇×C₂₇	C₂	semidirect
3. Dic₁₈₉	C₂	semidirect
12. C₇×C₂₇	D₄	semidirect
18. C₂×D₂₇	D₇	semidirect
36. C₂×D₇	D₂₇	semidirect
38. C₂₇	C₂²⋊D₇	semidirect
52. C₇	#6171	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×D₂₇	2
C₂×D₇×C₂₇	2
Dic₁₈₉	2
#92591	3
#6171	7