Subgroups — C₂×#13130005 #16791497

Order 3328.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11718037	C₂	1	2	yes	maximal, complemented
3	C₂²×#88034	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×#88034	C₄	1	2	yes	—
6	C₂×#88034	C₄	1	1	yes	characteristic
7	C₂×#88034	C₂²	1	1	yes	characteristic
8	C₂×#88034	C₂²	1	2	yes	—
9	#11718037	C₂²	1	4	yes	complemented
10	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
11	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
13	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
14	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
15	#88034	C₂×C₄	1	1	yes	characteristic
16	#88034	C₂×C₄	1	2	yes	—
17	#88034	C₂³	1	1	yes	characteristic
18	C₂×M₁₂₈	—	13	1	no	maximal, Sylow
19	C₂²×C₄×C₁₃	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₁₆	1	2	yes	—
21	C₂×C₈×C₁₃	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
23	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
25	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
26	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₃₂	—	13	1	no	—
28	M₁₂₈	—	13	4	no	—
29	C₂×C₆₄	—	13	2	no	—
30	C₂³×C₁₃	C₃₂	1	1	yes	characteristic
31	C₂×C₄×C₁₃	C₃₂	1	2	yes	—
32	C₂×C₄×C₁₃	C₃₂	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
34	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
35	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
36	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
37	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
38	C₂²×C₁₆	#261	1	1	yes	characteristic
39	C₂×C₃₂	—	13	2	no	—
40	C₂×C₃₂	—	13	2	no	—
41	C₂×C₃₂	—	13	1	no	—
42	C₂×C₃₂	—	13	1	no	—
43	C₆₄	—	13	4	no	—
44	C₂²×C₁₃	—	2	2	no	—
45	C₂²×C₁₃	C₂×C₃₂	1	2	yes	—
46	C₂²×C₁₃	C₂×C₃₂	1	1	yes	characteristic
47	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
48	C₄×C₁₃	C₂×C₃₂	1	2	yes	—
49	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
50	C₂²×C₈	#1057	1	1	yes	characteristic
51	C₂×C₁₆	#1057	1	1	yes	characteristic
52	C₂×C₁₆	#1057	1	2	yes	—
53	C₂×C₁₆	C₂×#261	1	2	yes	—
54	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
55	C₃₂	—	13	1	no	—
56	C₃₂	—	13	2	no	—
57	C₃₂	—	13	1	no	—
58	C₂×C₁₃	—	2	2	no	—
59	C₂×C₁₃	M₁₂₈	1	2	yes	complemented
60	C₂×C₁₃	C₂²×C₃₂	1	1	yes	characteristic
61	C₂²×C₄	#6092	1	1	yes	characteristic
62	C₂×C₈	#6092	1	1	yes	characteristic
63	C₂×C₈	#6092	1	2	yes	—
64	C₂×C₈	C₂×#1057	1	2	yes	—
65	C₂×C₈	C₂×#1057	1	1	yes	characteristic
66	C₁₆	C₂×#1057	1	2	yes	—
67	C₁₆	C₂×#1057	1	1	yes	characteristic
68	C₁₆	C₂²×#261	1	1	yes	characteristic
69	C₁₃	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
70	C₂³	#88036	1	1	yes	characteristic
71	C₂×C₄	#88036	1	2	yes	—
72	C₂×C₄	#88036	1	1	yes	characteristic
73	C₂×C₄	C₂×#6092	1	2	yes	—
74	C₂×C₄	C₂×#6092	1	1	yes	characteristic
75	C₈	C₂×#6092	1	2	yes	—
76	C₈	C₂×#6092	1	1	yes	characteristic
77	C₈	C₂²×#1057	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#88036	1	2	yes	—
80	C₂²	C₂×#88036	1	1	yes	characteristic
81	C₄	C₂×#88036	1	2	yes	—
82	C₄	C₂×#88036	1	1	yes	characteristic
83	C₄	C₂²×#6092	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#13130005	1	2	yes	direct product factor
86	C₂	C₂²×#88036	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₂²×C₃₂
Frattini	C₁₆	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₃₂
prime radical	C₂³×C₁₃	C₃₂
cosocle	#88034	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂×M₁₂₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. #13130005	C₂	direct (N × H)
2. C₂×#11718037	C₂	semidirect
9. #11718037	C₂²	semidirect
59. C₂×C₁₃	M₁₂₈	semidirect
69. C₁₃	C₂×M₁₂₈	semidirect
85. C₂	#13130005	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13130005	2
C₂×#11718037	2
C₂²×#88034	2
C₂×M₁₂₈	13

Subgroups — C2×#13130005 #16791497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130005 #16791497