Subgroups — C₂×#10622160 #13070920

Order 1408.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₈	C₂	1	1	yes	maximal, characteristic
3	#10622160	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×Q₁₆	—	2	1	no	—
6	C₂×Dic₄₄	—	2	1	no	—
7	C₁₁×Q₃₂	—	2	1	no	—
8	C₁₁×Q₃₂	C₂²	1	2	yes	—
9	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	Dic₈₈	—	2	1	no	—
11	Dic₈₈	C₂²	1	2	yes	—
12	C₁₁⋊C₃₂	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₁	—	4	1	no	—
14	C₂×Dic₂₂	—	4	1	no	—
15	C₁₁×Q₁₆	—	2	2	no	—
16	C₁₁×Q₁₆	—	4	1	no	—
17	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
18	Dic₄₄	—	2	2	no	—
19	Dic₄₄	—	4	1	no	—
20	C₁₁×C₁₆	D₄	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×Q₆₄	—	11	1	no	maximal, Sylow
23	Q₈×C₁₁	—	4	2	no	—
24	Q₈×C₁₁	—	8	1	no	—
25	C₂×C₄×C₁₁	—	8	1	no	—
26	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
27	C₂×Dic₁₁	—	8	1	no	—
28	Dic₂₂	—	4	2	no	—
29	Dic₂₂	—	8	1	no	—
30	C₈×C₁₁	D₈	1	1	yes	characteristic
31	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₃₂	—	11	1	no	—
33	C₂×Q₃₂	D₁₁	1	1	yes	characteristic
34	Q₆₄	—	11	4	no	—
35	C₂×C₃₂	—	11	1	no	—
36	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
37	C₄×C₁₁	—	8	2	no	—
38	C₄×C₁₁	D₁₆	1	1	yes	characteristic
39	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
40	Dic₁₁	—	8	2	no	—
41	C₂×Q₁₆	—	2	1	no	—
42	C₂×Q₁₆	—	22	1	no	—
43	Q₃₂	—	2	1	no	—
44	Q₃₂	—	11	2	no	—
45	Q₃₂	—	22	1	no	—
46	Q₃₂	C₂×D₁₁	1	2	yes	—
47	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
48	C₃₂	—	11	2	no	—
49	C₂×C₁₁	Q₆₄	1	2	yes	complemented
50	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
51	C₂×Q₈	—	4	1	no	—
52	C₂×Q₈	—	44	1	no	—
53	Q₁₆	—	2	2	no	—
54	Q₁₆	—	4	1	no	—
55	Q₁₆	—	22	2	no	—
56	Q₁₆	—	44	1	no	—
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
59	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
60	C₁₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	44	2	no	—
64	Q₈	—	88	1	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	88	1	no	—
67	C₂×C₄	#4323	1	1	yes	characteristic
68	C₈	#4323	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
70	C₂²	#66890	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	88	2	no	—
73	C₄	#66890	1	1	yes	characteristic
74	C₄	C₂×#4323	1	1	yes	characteristic
75	C₂	#10622160	1	2	yes	direct product factor
76	C₂	C₂×#66890	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66890
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×Q₃₂	C₂
socle, prime radical	C₂²×C₁₁	D₁₆
hypercenter	C₂×Q₃₂	D₁₁
hypocenter	C₁₁	C₂×Q₆₄
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
3. #10622160	C₂	direct (N × H)
49. C₂×C₁₁	Q₆₄	semidirect
60. C₁₁	C₂×Q₆₄	semidirect
75. C₂	#10622160	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×C₁₁×Q₃₂	2
C₂×Dic₈₈	2
#10622160	2
C₂×C₁₁⋊C₃₂	2
C₂×Q₆₄	11

Subgroups — C2×#10622160 #13070920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10622160 #13070920