Subgroups — C₂×#11718114 #13117140

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₀₄	C₂	1	1	yes	maximal, characteristic
3	#11718114	C₂	1	4	yes	maximal, direct product factor
4	C₂×#88034	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₁₆	—	2	1	no	—
6	C₂×Dic₅₂	—	2	1	no	—
7	C₁₃×Q₃₂	—	2	1	no	—
8	C₁₃×Q₃₂	C₂²	1	2	yes	—
9	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	Dic₁₀₄	—	2	1	no	—
11	Dic₁₀₄	C₂²	1	2	yes	—
12	#88034	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₃	—	4	1	no	—
14	C₂×Dic₂₆	—	4	1	no	—
15	C₁₃×Q₁₆	—	2	2	no	—
16	C₁₃×Q₁₆	—	4	1	no	—
17	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
18	Dic₅₂	—	2	2	no	—
19	Dic₅₂	—	4	1	no	—
20	C₁₃×C₁₆	D₄	1	1	yes	characteristic
21	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×Q₆₄	—	13	1	no	maximal, Sylow
23	Q₈×C₁₃	—	4	2	no	—
24	Q₈×C₁₃	—	8	1	no	—
25	C₂×C₄×C₁₃	—	8	1	no	—
26	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
27	C₂×Dic₁₃	—	8	1	no	—
28	Dic₂₆	—	4	2	no	—
29	Dic₂₆	—	8	1	no	—
30	C₈×C₁₃	D₈	1	1	yes	characteristic
31	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₃₂	—	13	1	no	—
33	C₂×Q₃₂	D₁₃	1	1	yes	characteristic
34	Q₆₄	—	13	4	no	—
35	C₂×C₃₂	—	13	1	no	—
36	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
37	C₄×C₁₃	—	8	2	no	—
38	C₄×C₁₃	D₁₆	1	1	yes	characteristic
39	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
40	Dic₁₃	—	8	2	no	—
41	C₂×Q₁₆	—	2	1	no	—
42	C₂×Q₁₆	—	26	1	no	—
43	Q₃₂	—	2	1	no	—
44	Q₃₂	—	13	2	no	—
45	Q₃₂	—	26	1	no	—
46	Q₃₂	C₂×D₁₃	1	2	yes	—
47	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
48	C₃₂	—	13	2	no	—
49	C₂×C₁₃	Q₆₄	1	2	yes	complemented
50	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
51	C₂×Q₈	—	4	1	no	—
52	C₂×Q₈	—	52	1	no	—
53	Q₁₆	—	2	2	no	—
54	Q₁₆	—	4	1	no	—
55	Q₁₆	—	26	2	no	—
56	Q₁₆	—	52	1	no	—
57	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
58	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
59	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
60	C₁₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	52	2	no	—
64	Q₈	—	104	1	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	104	1	no	—
67	C₂×C₄	#6104	1	1	yes	characteristic
68	C₈	#6104	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
70	C₂²	#88066	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	104	2	no	—
73	C₄	#88066	1	1	yes	characteristic
74	C₄	C₂×#6104	1	1	yes	characteristic
75	C₂	#11718114	1	2	yes	direct product factor
76	C₂	C₂×#88066	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88066
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×Q₃₂	C₂
socle, prime radical	C₂²×C₁₃	D₁₆
hypercenter	C₂×Q₃₂	D₁₃
hypocenter	C₁₃	C₂×Q₆₄
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
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. #11718114	C₂	direct (N × H)
49. C₂×C₁₃	Q₆₄	semidirect
60. C₁₃	C₂×Q₆₄	semidirect
75. C₂	#11718114	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×C₁₃×Q₃₂	2
C₂×Dic₁₀₄	2
#11718114	2
C₂×#88034	2
C₂×Q₆₄	13

Subgroups — C2×#11718114 #13117140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718114 #13117140