Subgroups — C₂×#13066826 #14674809

Order 2816.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#13066826	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×D₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
8	D₁₁×C₃₂	C₄	1	2	yes	—
9	D₁₁×C₃₂	C₂²	1	2	yes	—
10	C₁₁×C₆₄	C₂²	1	2	yes	complemented
11	C₁₁⋊C₆₄	C₂²	1	2	yes	complemented
12	C₂×C₈×D₁₁	C₈	1	1	yes	characteristic
13	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
15	C₁₆×D₁₁	C₈	1	2	yes	—
16	C₁₆×D₁₁	C₂×C₄	1	2	yes	—
17	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₃₂	C₂×C₄	1	2	yes	—
20	C₂×M₁₂₈	—	11	1	no	maximal, Sylow
21	C₂×C₄×D₁₁	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
24	C₈×D₁₁	C₁₆	1	2	yes	—
25	C₈×D₁₁	C₂×C₈	1	2	yes	—
26	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
27	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
28	C₁₁⋊C₁₆	C₂×C₈	1	2	yes	—
29	C₂²×C₃₂	—	11	1	no	—
30	M₁₂₈	—	11	4	no	—
31	C₂×C₆₄	—	11	1	no	—
32	C₂×C₆₄	D₁₁	1	1	yes	characteristic, complemented
33	C₂²×D₁₁	C₃₂	1	1	yes	characteristic
34	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
35	C₂×Dic₁₁	C₃₂	1	1	yes	characteristic
36	C₄×D₁₁	C₃₂	1	2	yes	—
37	C₄×D₁₁	C₂×C₁₆	1	2	yes	—
38	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
39	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
40	C₁₁⋊C₈	C₂×C₁₆	1	2	yes	—
41	C₂²×C₁₆	—	11	1	no	—
42	C₂×C₃₂	—	11	1	no	—
43	C₂×C₃₂	—	11	2	no	—
44	C₂×C₃₂	—	11	2	no	—
45	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
46	C₆₄	—	11	2	no	—
47	C₆₄	C₂×D₁₁	1	2	yes	complemented
48	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
49	C₂×D₁₁	—	2	2	no	—
50	C₂×D₁₁	C₂×C₃₂	1	2	yes	—
51	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
52	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
53	Dic₁₁	C₂×C₃₂	1	2	yes	—
54	C₂²×C₈	—	11	1	no	—
55	C₂×C₁₆	—	11	1	no	—
56	C₂×C₁₆	—	11	2	no	—
57	C₂×C₁₆	—	11	2	no	—
58	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
59	C₃₂	—	11	2	no	—
60	C₃₂	C₄×D₁₁	1	1	yes	characteristic
61	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
62	C₂×C₁₁	M₁₂₈	1	2	yes	complemented
63	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
64	D₁₁	—	2	2	no	—
65	C₂²×C₄	—	11	1	no	—
66	C₂×C₈	—	11	1	no	—
67	C₂×C₈	—	11	2	no	—
68	C₂×C₈	—	11	2	no	—
69	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
70	C₁₆	—	11	2	no	—
71	C₁₆	C₈×D₁₁	1	1	yes	characteristic
72	C₁₆	C₂×C₄×D₁₁	1	1	yes	characteristic
73	C₁₁	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	11	1	no	—
75	C₂×C₄	—	11	1	no	—
76	C₂×C₄	—	11	2	no	—
77	C₂×C₄	—	11	2	no	—
78	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
79	C₈	—	11	2	no	—
80	C₈	C₁₆×D₁₁	1	1	yes	characteristic
81	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
82	C₂²	—	11	2	no	—
83	C₂²	—	22	2	no	—
84	C₂²	D₁₁×C₃₂	1	1	yes	characteristic
85	C₄	—	11	2	no	—
86	C₄	D₁₁×C₃₂	1	1	yes	characteristic
87	C₄	C₂×C₁₆×D₁₁	1	1	yes	characteristic
88	C₂	—	22	2	no	—
89	C₂	#13066826	1	2	yes	direct product factor
90	C₂	C₂×D₁₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃₂	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₃₂
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle	C₂²×C₁₁	C₂×C₃₂
prime radical	C₂²×D₁₁	C₃₂
cosocle	C₁₁×C₃₂	C₂³
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	C₂×M₁₂₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. #13066826	C₂	direct (N × H)
3. C₂×C₁₁⋊C₆₄	C₂	semidirect
4. C₂×C₁₁×C₆₄	C₂	semidirect
10. C₁₁×C₆₄	C₂²	semidirect
11. C₁₁⋊C₆₄	C₂²	semidirect
32. C₂×C₆₄	D₁₁	semidirect
47. C₆₄	C₂×D₁₁	semidirect
62. C₂×C₁₁	M₁₂₈	semidirect
73. C₁₁	C₂×M₁₂₈	semidirect
89. C₂	#13066826	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×D₁₁×C₃₂	2
#13066826	2
C₂×C₁₁⋊C₆₄	2
C₂×C₁₁×C₆₄	2
C₂×M₁₂₈	11

Subgroups — C2×#13066826 #14674809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066826 #14674809