Subgroups — #13129883

Order 1664.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88106	C₂	1	2	yes	maximal
2	C₂×#88043	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
4	C₂²×#1055	C₄	1	1	yes	characteristic
5	C₂²×#1055	C₂²	1	1	yes	characteristic
6	#88106	—	2	2	no	—
7	#88106	C₄	1	4	yes	complemented
8	C₂×#6092	—	2	2	no	—
9	#88043	—	2	2	no	—
10	C₂²×C₄×C₁₃	C₈	1	2	yes	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₁₃	—	2	1	no	—
13	C₄²×C₁₃	—	2	1	no	—
14	C₂×#1055	—	2	1	no	—
15	C₂×#1055	—	2	1	no	—
16	C₂×#1055	C₈	1	2	yes	—
17	C₂×#1055	C₂×C₄	1	2	yes	—
18	C₂×#1055	D₄	1	1	yes	characteristic
19	C₂×#1055	D₄	1	2	yes	—
20	C₂×#1055	Q₈	1	1	yes	characteristic
21	#6092	—	2	4	no	—
22	#1377	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₃	—	2	2	no	—
25	C₂×C₄×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	#1055	—	2	2	no	—
33	#1055	C₂²⋊C₄	1	2	yes	—
34	#1055	C₄⋊C₄	1	2	yes	—
35	C₂×M₃₂	—	13	2	no	—
36	C₂×#97	—	13	1	no	—
37	C₂²×C₁₃	—	2	2	no	—
38	C₂²×C₁₃	C₄×C₈	1	1	yes	characteristic
39	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
40	C₂²×C₁₃	C₄⋊C₈	1	1	yes	characteristic
41	C₄×C₁₃	—	4	2	no	—
42	C₄×C₁₃	#95	1	1	yes	characteristic
43	C₄×C₁₃	#97	1	1	yes	characteristic
44	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
45	C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
46	C₂²×C₈	—	13	1	no	—
47	C₂²×C₈	—	13	1	no	—
48	C₂×C₄²	#261	1	1	yes	characteristic
49	M₃₂	—	13	4	no	—
50	M₃₂	—	26	2	no	—
51	C₂×C₁₆	—	26	2	no	—
52	#97	—	26	2	no	—
53	C₂×C₁₃	—	2	1	no	—
54	C₂×C₁₃	—	2	1	no	—
55	C₂×C₁₃	#336	1	1	yes	characteristic
56	C₂×C₁₃	#349	1	2	yes	—
57	C₂²×C₄	#1057	1	2	yes	—
58	C₂²×C₄	C₂×#261	1	1	yes	characteristic
59	C₂×C₈	—	13	2	no	—
60	C₂×C₈	—	13	1	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	13	2	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	26	1	no	—
65	C₂×C₈	—	26	1	no	—
66	C₄²	—	2	1	no	—
67	C₄²	—	2	1	no	—
68	C₁₆	—	26	4	no	—
69	C₁₃	#1377	1	1	yes	characteristic, complemented, Sylow
70	C₂³	C₂×#1057	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
74	C₂×C₄	#6118	1	1	yes	characteristic
75	C₂×C₄	C₄×#261	1	1	yes	characteristic
76	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
77	C₂×C₄	#6122	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
79	C₈	—	13	2	no	—
80	C₈	—	13	2	no	—
81	C₈	—	26	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×#1057	1	1	yes	characteristic
84	C₂²	C₄⋊#1057	1	1	yes	characteristic
85	C₂²	C₂²⋊#1057	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	#88110	1	1	yes	characteristic
88	C₄	#88111	1	1	yes	characteristic
89	C₄	#88112	1	1	yes	characteristic
90	C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#11718284	1	2	yes	—
94	C₂	#11718290	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂²×C₁₃	C₄×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle	C₂²×C₁₃	C₂²⋊C₈
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂²×#1055	C₂²
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1377
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. #88106	C₄	semidirect
69. C₁₃	#1377	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88106	2
C₂×#88043	2
#1377	13