Subgroups — C₂×C₈×D₂₇ #11720149

Order 864.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₂₇	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₈×D₉	—	3	1	no	maximal
6	C₂²×D₂₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₂₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₇	C₄	1	1	yes	characteristic
9	C₄×D₂₇	C₄	1	2	yes	—
10	C₄×D₂₇	C₂²	1	2	yes	—
11	C₈×C₂₇	C₂²	1	2	yes	complemented
12	C₂₇⋊C₈	C₂²	1	2	yes	complemented
13	C₂×C₄×D₉	—	3	1	no	—
14	C₂×C₈×C₉	D₃	1	1	yes	characteristic
15	C₂×C₉⋊C₈	—	3	1	no	—
16	C₈×D₉	—	3	4	no	—
17	C₂²×C₂₇	C₂×C₄	1	1	yes	characteristic
18	C₂×D₂₇	C₈	1	4	yes	direct product factor
19	C₂×D₂₇	C₂×C₄	1	2	yes	—
20	C₄×C₂₇	C₂×C₄	1	1	yes	characteristic
21	C₄×C₂₇	C₂³	1	1	yes	characteristic
22	Dic₂₇	C₂×C₄	1	2	yes	—
23	C₂×D₃×C₈	—	9	1	no	—
24	C₂²×D₉	—	3	1	no	—
25	C₂×C₄×C₉	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₉	—	3	1	no	—
27	C₄×D₉	—	3	2	no	—
28	C₄×D₉	—	3	2	no	—
29	C₈×C₉	C₂×D₃	1	2	yes	—
30	C₉⋊C₈	—	3	2	no	—
31	C₂×C₂₇	C₂×C₈	1	2	yes	complemented
32	C₂×C₂₇	C₂²×C₄	1	1	yes	characteristic
33	D₂₇	C₂×C₈	1	4	yes	direct product factor
34	C₂×C₄×D₃	—	9	1	no	—
35	C₂×C₃×C₈	D₉	1	1	yes	characteristic
36	C₂×C₃⋊C₈	—	9	1	no	—
37	D₃×C₈	—	9	4	no	—
38	C₂²×C₉	C₄×D₃	1	1	yes	characteristic
39	C₂×D₉	—	3	4	no	—
40	C₂×D₉	—	3	2	no	—
41	C₄×C₉	C₄×D₃	1	1	yes	characteristic
42	C₄×C₉	C₂²×D₃	1	1	yes	characteristic
43	Dic₉	—	3	2	no	—
44	C₂²×C₈	—	27	1	no	Sylow
45	C₂₇	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
46	C₂²×D₃	—	9	1	no	—
47	C₂×C₃×C₄	C₂×D₉	1	1	yes	characteristic
48	C₂×Dic₃	—	9	1	no	—
49	C₄×D₃	—	9	2	no	—
50	C₄×D₃	—	9	2	no	—
51	C₃×C₈	C₂×D₉	1	2	yes	—
52	C₃⋊C₈	—	9	2	no	—
53	C₂×C₉	D₃×C₈	1	2	yes	—
54	C₂×C₉	C₂×C₄×D₃	1	1	yes	characteristic
55	D₉	—	3	4	no	—
56	C₂²×C₄	—	27	1	no	—
57	C₂×C₈	—	27	1	no	—
58	C₂×C₈	—	27	4	no	—
59	C₂×C₈	D₂₇	1	1	yes	characteristic, direct product factor
60	C₂²×C₃	C₄×D₉	1	1	yes	characteristic
61	C₂×D₃	—	9	4	no	—
62	C₂×D₃	—	9	2	no	—
63	C₃×C₄	C₄×D₉	1	1	yes	characteristic
64	C₃×C₄	C₂²×D₉	1	1	yes	characteristic
65	Dic₃	—	9	2	no	—
66	C₉	C₂×D₃×C₈	1	1	yes	characteristic
67	C₂³	—	27	1	no	—
68	C₂×C₄	—	27	1	no	—
69	C₂×C₄	—	27	2	no	—
70	C₂×C₄	—	27	2	no	—
71	C₂×C₄	C₂×D₂₇	1	1	yes	characteristic
72	C₈	—	27	2	no	—
73	C₈	C₂×D₂₇	1	2	yes	direct product factor
74	C₂×C₃	C₈×D₉	1	2	yes	—
75	C₂×C₃	C₂×C₄×D₉	1	1	yes	characteristic
76	D₃	—	9	4	no	—
77	C₂²	—	27	4	no	—
78	C₂²	—	27	2	no	—
79	C₂²	C₄×D₂₇	1	1	yes	characteristic
80	C₄	—	27	2	no	—
81	C₄	C₄×D₂₇	1	1	yes	characteristic
82	C₄	C₂²×D₂₇	1	1	yes	characteristic
83	C₃	C₂×C₈×D₉	1	1	yes	characteristic
84	C₂	—	27	4	no	—
85	C₂	C₈×D₂₇	1	2	yes	direct product factor
86	C₂	C₂×C₄×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₂₇
commutator, hypocenter	C₂₇	C₂²×C₈
Frattini	C₄×C₉	C₂²×D₃
Fitting	C₂×C₈×C₂₇	C₂
socle	C₂²×C₃	C₄×D₉
prime radical	C₂²×D₂₇	C₄
cosocle	C₄×C₂₇	C₂³
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₂₇	C₂	semidirect
3. C₂×C₂₇⋊C₈	C₂	semidirect
4. C₈×D₂₇	C₂	direct (N × H)
11. C₈×C₂₇	C₂²	semidirect
12. C₂₇⋊C₈	C₂²	semidirect
18. C₂×D₂₇	C₈	direct (N × H)
31. C₂×C₂₇	C₂×C₈	semidirect
33. D₂₇	C₂×C₈	direct (N × H)
45. C₂₇	C₂²×C₈	semidirect
59. C₂×C₈	D₂₇	direct (N × H)
73. C₈	C₂×D₂₇	direct (N × H)
85. C₂	C₈×D₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₂₇	2
C₂×C₈×C₂₇	2
C₂×C₂₇⋊C₈	2
C₈×D₂₇	2
C₂×C₈×D₉	3

Subgroups — C2×C8×D27 #11720149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₂₇ #11720149