Subgroups — C₂×#13113053 #15783968

Order 3328.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀₈	C₂	1	1	yes	maximal, characteristic
2	#13113053	C₂	1	4	yes	maximal, direct product factor
3	C₂×#11718035	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₃₂	—	2	1	no	—
6	C₂×Dic₁₀₄	—	2	1	no	—
7	C₁₃×Q₆₄	—	2	1	no	—
8	C₁₃×Q₆₄	C₂²	1	2	yes	—
9	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
10	Dic₂₀₈	—	2	1	no	—
11	Dic₂₀₈	C₂²	1	2	yes	—
12	#11718035	C₂²	1	2	yes	—
13	C₂×C₁₃×Q₁₆	—	4	1	no	—
14	C₂×Dic₅₂	—	4	1	no	—
15	C₁₃×Q₃₂	—	2	2	no	—
16	C₁₃×Q₃₂	—	4	1	no	—
17	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	Dic₁₀₄	—	2	2	no	—
19	Dic₁₀₄	—	4	1	no	—
20	C₁₃×C₃₂	D₄	1	1	yes	characteristic
21	C₁₃×C₃₂	C₂³	1	1	yes	characteristic
22	C₂×Q₁₂₈	—	13	1	no	maximal, Sylow
23	C₂×Q₈×C₁₃	—	8	1	no	—
24	C₂×Dic₂₆	—	8	1	no	—
25	C₁₃×Q₁₆	—	4	2	no	—
26	C₁₃×Q₁₆	—	8	1	no	—
27	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
28	Dic₅₂	—	4	2	no	—
29	Dic₅₂	—	8	1	no	—
30	C₁₃×C₁₆	D₈	1	1	yes	characteristic
31	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₆₄	—	13	1	no	—
33	C₂×Q₆₄	D₁₃	1	1	yes	characteristic
34	Q₁₂₈	—	13	4	no	—
35	C₂×C₆₄	—	13	1	no	—
36	Q₈×C₁₃	—	8	2	no	—
37	Q₈×C₁₃	—	16	1	no	—
38	C₂×C₄×C₁₃	—	16	1	no	—
39	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
40	C₂×Dic₁₃	—	16	1	no	—
41	Dic₂₆	—	8	2	no	—
42	Dic₂₆	—	16	1	no	—
43	C₈×C₁₃	D₁₆	1	1	yes	characteristic
44	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
45	C₂×Q₃₂	—	2	1	no	—
46	C₂×Q₃₂	—	26	1	no	—
47	Q₆₄	—	2	1	no	—
48	Q₆₄	—	13	2	no	—
49	Q₆₄	—	26	1	no	—
50	Q₆₄	C₂×D₁₃	1	2	yes	—
51	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
52	C₆₄	—	13	2	no	—
53	C₂²×C₁₃	D₃₂	1	1	yes	characteristic
54	C₄×C₁₃	—	16	2	no	—
55	C₄×C₁₃	D₃₂	1	1	yes	characteristic
56	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
57	Dic₁₃	—	16	2	no	—
58	C₂×Q₁₆	—	4	1	no	—
59	C₂×Q₁₆	—	52	1	no	—
60	Q₃₂	—	2	2	no	—
61	Q₃₂	—	4	1	no	—
62	Q₃₂	—	26	2	no	—
63	Q₃₂	—	52	1	no	—
64	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₃₂	C₂²⋊D₁₃	1	1	yes	characteristic
66	C₃₂	C₂²×D₁₃	1	1	yes	characteristic
67	C₂×C₁₃	Q₁₂₈	1	2	yes	complemented
68	C₂×C₁₃	C₂×D₃₂	1	1	yes	characteristic
69	C₂×Q₈	—	8	1	no	—
70	C₂×Q₈	—	104	1	no	—
71	Q₁₆	—	4	2	no	—
72	Q₁₆	—	8	1	no	—
73	Q₁₆	—	52	2	no	—
74	Q₁₆	—	104	1	no	—
75	C₂×C₈	#6104	1	1	yes	characteristic
76	C₁₆	#6104	1	1	yes	characteristic
77	C₁₆	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
78	C₁₃	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
79	Q₈	—	8	2	no	—
80	Q₈	—	16	1	no	—
81	Q₈	—	104	2	no	—
82	Q₈	—	208	1	no	—
83	C₂×C₄	—	16	1	no	—
84	C₂×C₄	—	208	1	no	—
85	C₂×C₄	#88066	1	1	yes	characteristic
86	C₈	#88066	1	1	yes	characteristic
87	C₈	C₂×#6104	1	1	yes	characteristic
88	C₂²	#11718111	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	208	2	no	—
91	C₄	#11718111	1	1	yes	characteristic
92	C₄	C₂×#88066	1	1	yes	characteristic
93	C₂	#13113053	1	2	yes	direct product factor
94	C₂	C₂×#11718111	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718111
commutator, cosocle	C₁₃×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₃
Fitting	C₂×C₁₃×Q₆₄	C₂
socle, prime radical	C₂²×C₁₃	D₃₂
hypercenter	C₂×Q₆₄	D₁₃
hypocenter	C₁₃	C₂×Q₁₂₈
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
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. #13113053	C₂	direct (N × H)
67. C₂×C₁₃	Q₁₂₈	semidirect
78. C₁₃	C₂×Q₁₂₈	semidirect
93. C₂	#13113053	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×Dic₂₀₈	2
#13113053	2
C₂×#11718035	2
C₂×C₁₃×Q₆₄	2
C₂×Q₁₂₈	13

Subgroups — C2×#13113053 #15783968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113053 #15783968