Subgroups — C₂×#6171 #88405

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#6171	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#611	—	3	1	no	maximal
6	C₂²×C₂₇	—	2	2	no	—
7	C₂²×C₂₇	C₂²	1	1	yes	characteristic
8	C₂²×C₂₇	C₂²	1	2	yes	complemented
9	C₂×D₂₇	—	2	2	no	—
10	C₂×D₂₇	C₂²	1	2	yes	complemented
11	Dic₂₇	C₂²	1	2	yes	complemented
12	C₂³×C₉	D₃	1	1	yes	characteristic
13	C₂²×D₉	—	3	1	no	—
14	#611	—	3	4	no	—
15	C₂×Dic₉	—	3	1	no	—
16	C₂×C₂₇	—	2	2	no	—
17	C₂×C₂₇	D₄	1	2	yes	complemented
18	C₂×C₂₇	C₂³	1	1	yes	characteristic
19	D₂₇	—	2	2	no	—
20	C₂×#67	—	9	1	no	—
21	C₂²×C₉	—	2	2	no	—
22	C₂²×C₉	C₂×D₃	1	2	yes	—
23	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
24	C₂×D₉	—	3	2	no	—
25	C₂×D₉	—	6	2	no	—
26	Dic₉	—	3	2	no	—
27	C₂₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
28	C₂³×C₃	D₉	1	1	yes	characteristic
29	C₂²×D₃	—	9	1	no	—
30	#67	—	9	4	no	—
31	C₂×Dic₃	—	9	1	no	—
32	C₂×C₉	—	2	2	no	—
33	C₂×C₉	#67	1	2	yes	—
34	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
35	D₉	—	6	2	no	—
36	C₂×D₄	—	27	1	no	Sylow
37	C₂²×C₃	—	2	2	no	—
38	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
39	C₂²×C₃	C₂×D₉	1	2	yes	—
40	C₂×D₃	—	9	2	no	—
41	C₂×D₃	—	18	2	no	—
42	Dic₃	—	9	2	no	—
43	C₉	C₂×#67	1	1	yes	characteristic
44	C₂³	—	27	1	no	—
45	C₂³	D₂₇	1	1	yes	characteristic, complemented
46	D₄	—	27	4	no	—
47	C₂×C₄	—	27	1	no	—
48	C₂×C₃	—	2	2	no	—
49	C₂×C₃	#611	1	2	yes	—
50	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
51	D₃	—	18	2	no	—
52	C₂²	—	2	2	no	—
53	C₂²	—	27	2	no	—
54	C₂²	—	54	2	no	—
55	C₂²	C₂×D₂₇	1	1	yes	characteristic
56	C₂²	C₂×D₂₇	1	2	yes	complemented
57	C₄	—	27	2	no	—
58	C₃	C₂×#611	1	1	yes	characteristic
59	C₂	—	2	2	no	—
60	C₂	—	54	2	no	—
61	C₂	#6171	1	2	yes	direct product factor
62	C₂	C₂²×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₂₇
commutator, cosocle	C₂×C₂₇	C₂³
Frattini	C₂×C₉	C₂²×D₃
Fitting	C₂³×C₂₇	C₂
socle	C₂²×C₃	C₂×D₉
hypercenter	C₂³	D₂₇
hypocenter	C₂₇	C₂×D₄
LCS	G ▷ C₂×C₂₇ ▷ C₂₇
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂₇	C₂	semidirect
2. C₂²×D₂₇	C₂	semidirect
3. #6171	C₂	direct (N × H)
4. C₂×Dic₂₇	C₂	semidirect
8. C₂²×C₂₇	C₂²	semidirect
10. C₂×D₂₇	C₂²	semidirect
11. Dic₂₇	C₂²	semidirect
17. C₂×C₂₇	D₄	semidirect
27. C₂₇	C₂×D₄	semidirect
45. C₂³	D₂₇	semidirect
56. C₂²	C₂×D₂₇	semidirect
61. C₂	#6171	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂₇	2
C₂²×D₂₇	2
#6171	2
C₂×Dic₂₇	2
C₂×#611	3

Subgroups — C2×#6171 #88405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6171 #88405