Subgroups — #13117092

Order 1664.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88040	C₂	1	4	yes	maximal, complemented
2	#11718360	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718356	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₅₂	—	2	1	no	—
6	C₂×Dic₅₂	C₂²	1	2	yes	—
7	C₂×D₁₀₄	—	2	1	no	—
8	C₂×D₁₀₄	C₂²	1	2	yes	—
9	#88128	—	2	1	no	—
10	#88123	—	2	1	no	—
11	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
12	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#88040	—	2	8	no	—
14	C₂×D₅₂	—	2	2	no	—
15	C₂×D₅₂	—	4	2	no	—
16	C₂×Dic₂₆	—	2	2	no	—
17	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₃	—	4	2	no	—
21	Dic₅₂	—	2	4	no	—
22	Dic₅₂	—	4	2	no	—
23	D₁₀₄	—	2	4	no	—
24	D₁₀₄	—	4	2	no	—
25	C₁₃×C₁₆	D₄	1	4	yes	complemented
26	#2248	—	13	1	no	maximal, Sylow
27	C₂²×D₁₃	—	4	2	no	—
28	C₂×C₄×C₁₃	D₈	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₃	—	4	2	no	—
31	D₅₂	—	4	2	no	—
32	D₅₂	—	4	2	no	—
33	D₅₂	—	8	4	no	—
34	Dic₂₆	—	4	2	no	—
35	Dic₂₆	—	4	2	no	—
36	C₈×C₁₃	D₈	1	2	yes	—
37	C₈×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×SD₃₂	—	13	4	no	—
39	#494	—	13	1	no	—
40	#493	—	13	1	no	—
41	C₄×C₁₆	D₁₃	1	1	yes	characteristic, complemented
42	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
43	C₂×D₁₃	—	8	2	no	—
44	C₂×D₁₃	—	8	4	no	—
45	C₄×C₁₃	SD₃₂	1	4	yes	complemented
46	C₄×C₁₃	#127	1	1	yes	characteristic
47	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
48	Dic₁₃	—	8	2	no	—
49	C₂×Q₁₆	—	13	2	no	—
50	C₂×Q₁₆	—	26	1	no	—
51	C₂×D₈	—	13	2	no	—
52	C₂×D₈	—	26	1	no	—
53	C₄⋊Q₈	—	26	1	no	—
54	#127	—	26	1	no	—
55	SD₃₂	—	26	8	no	—
56	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
57	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₁₃	#493	1	1	yes	characteristic
59	C₂×C₁₃	C₂×SD₃₂	1	2	yes	—
60	D₁₃	—	16	2	no	—
61	C₂×Q₈	—	26	2	no	—
62	C₂×D₄	—	26	2	no	—
63	C₂×D₄	—	52	2	no	—
64	Q₁₆	—	26	4	no	—
65	Q₁₆	—	52	2	no	—
66	D₈	—	26	4	no	—
67	D₈	—	52	2	no	—
68	C₂×C₈	D₅₂	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
70	C₄⋊C₄	—	52	2	no	—
71	C₄²	D₅₂	1	1	yes	characteristic
72	C₁₆	D₅₂	1	4	yes	complemented
73	C₁₃	#2248	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	52	2	no	—
75	Q₈	—	52	2	no	—
76	Q₈	—	52	2	no	—
77	D₄	—	52	2	no	—
78	D₄	—	52	2	no	—
79	D₄	—	104	4	no	—
80	C₂×C₄	—	52	2	no	—
81	C₂×C₄	D₁₀₄	1	2	yes	—
82	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
83	C₈	D₁₀₄	1	2	yes	—
84	C₈	C₂×D₅₂	1	2	yes	—
85	C₂²	—	104	4	no	—
86	C₂²	—	104	2	no	—
87	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
88	C₄	—	104	2	no	—
89	C₄	#88040	1	4	yes	complemented
90	C₄	#88128	1	1	yes	characteristic
91	C₄	C₂×D₁₀₄	1	1	yes	characteristic
92	C₂	—	208	2	no	—
93	C₂	#11718356	1	1	yes	characteristic
94	C₂	C₂×#88040	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	C₂×D₈
prime radical	#11718356	C₂
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	#2248
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#88040	C₂	semidirect
2. #11718360	C₂	semidirect
4. C₄×C₁₃×C₁₆	C₂	semidirect
25. C₁₃×C₁₆	D₄	semidirect
41. C₄×C₁₆	D₁₃	semidirect
45. C₄×C₁₃	SD₃₂	semidirect
72. C₁₆	D₅₂	semidirect
73. C₁₃	#2248	semidirect
89. C₄	#88040	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88040	2
#11718360	2
#11718356	2
C₄×C₁₃×C₁₆	2
#2248	13