Subgroups — C₂×#13066833 #14674822

Order 2816.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₆	C₂	1	1	yes	maximal, characteristic
2	#13066833	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×Q₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×Q₃₂	—	2	1	no	—
6	C₂×Dic₈₈	—	2	1	no	—
7	C₁₁×Q₆₄	—	2	1	no	—
8	C₁₁×Q₆₄	C₂²	1	2	yes	—
9	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
10	Dic₁₇₆	—	2	1	no	—
11	Dic₁₇₆	C₂²	1	2	yes	—
12	C₁₁⋊C₆₄	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₁₆	—	4	1	no	—
14	C₂×Dic₄₄	—	4	1	no	—
15	C₁₁×Q₃₂	—	2	2	no	—
16	C₁₁×Q₃₂	—	4	1	no	—
17	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	Dic₈₈	—	2	2	no	—
19	Dic₈₈	—	4	1	no	—
20	C₁₁×C₃₂	D₄	1	1	yes	characteristic
21	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
22	C₂×Q₁₂₈	—	11	1	no	maximal, Sylow
23	C₂×Q₈×C₁₁	—	8	1	no	—
24	C₂×Dic₂₂	—	8	1	no	—
25	C₁₁×Q₁₆	—	4	2	no	—
26	C₁₁×Q₁₆	—	8	1	no	—
27	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
28	Dic₄₄	—	4	2	no	—
29	Dic₄₄	—	8	1	no	—
30	C₁₁×C₁₆	D₈	1	1	yes	characteristic
31	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₆₄	—	11	1	no	—
33	C₂×Q₆₄	D₁₁	1	1	yes	characteristic
34	Q₁₂₈	—	11	4	no	—
35	C₂×C₆₄	—	11	1	no	—
36	Q₈×C₁₁	—	8	2	no	—
37	Q₈×C₁₁	—	16	1	no	—
38	C₂×C₄×C₁₁	—	16	1	no	—
39	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
40	C₂×Dic₁₁	—	16	1	no	—
41	Dic₂₂	—	8	2	no	—
42	Dic₂₂	—	16	1	no	—
43	C₈×C₁₁	D₁₆	1	1	yes	characteristic
44	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
45	C₂×Q₃₂	—	2	1	no	—
46	C₂×Q₃₂	—	22	1	no	—
47	Q₆₄	—	2	1	no	—
48	Q₆₄	—	11	2	no	—
49	Q₆₄	—	22	1	no	—
50	Q₆₄	C₂×D₁₁	1	2	yes	—
51	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
52	C₆₄	—	11	2	no	—
53	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
54	C₄×C₁₁	—	16	2	no	—
55	C₄×C₁₁	D₃₂	1	1	yes	characteristic
56	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
57	Dic₁₁	—	16	2	no	—
58	C₂×Q₁₆	—	4	1	no	—
59	C₂×Q₁₆	—	44	1	no	—
60	Q₃₂	—	2	2	no	—
61	Q₃₂	—	4	1	no	—
62	Q₃₂	—	22	2	no	—
63	Q₃₂	—	44	1	no	—
64	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
65	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
66	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
67	C₂×C₁₁	Q₁₂₈	1	2	yes	complemented
68	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
69	C₂×Q₈	—	8	1	no	—
70	C₂×Q₈	—	88	1	no	—
71	Q₁₆	—	4	2	no	—
72	Q₁₆	—	8	1	no	—
73	Q₁₆	—	44	2	no	—
74	Q₁₆	—	88	1	no	—
75	C₂×C₈	#4323	1	1	yes	characteristic
76	C₁₆	#4323	1	1	yes	characteristic
77	C₁₆	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
78	C₁₁	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
79	Q₈	—	8	2	no	—
80	Q₈	—	16	1	no	—
81	Q₈	—	88	2	no	—
82	Q₈	—	176	1	no	—
83	C₂×C₄	—	16	1	no	—
84	C₂×C₄	—	176	1	no	—
85	C₂×C₄	#66890	1	1	yes	characteristic
86	C₈	#66890	1	1	yes	characteristic
87	C₈	C₂×#4323	1	1	yes	characteristic
88	C₂²	#10622157	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	176	2	no	—
91	C₄	#10622157	1	1	yes	characteristic
92	C₄	C₂×#66890	1	1	yes	characteristic
93	C₂	#13066833	1	2	yes	direct product factor
94	C₂	C₂×#10622157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622157
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₂×C₁₁×Q₆₄	C₂
socle, prime radical	C₂²×C₁₁	D₃₂
hypercenter	C₂×Q₆₄	D₁₁
hypocenter	C₁₁	C₂×Q₁₂₈
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
2. #13066833	C₂	direct (N × H)
67. C₂×C₁₁	Q₁₂₈	semidirect
78. C₁₁	C₂×Q₁₂₈	semidirect
93. C₂	#13066833	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×Dic₁₇₆	2
#13066833	2
C₂×C₁₁⋊C₆₄	2
C₂×C₁₁×Q₆₄	2
C₂×Q₁₂₈	11

Subgroups — C2×#13066833 #14674822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066833 #14674822