Subgroups — #13129782

Order 1664.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718585	C₂	1	1	yes	maximal, characteristic
2	#11718284	C₂	1	2	yes	maximal
3	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
4	C₂×#6099	C₄	1	1	yes	characteristic
5	C₂×#6099	C₂²	1	1	yes	characteristic
6	#88106	—	2	2	no	—
7	C₄⋊#1055	—	2	2	no	—
8	C₂²×C₄×C₁₃	—	2	1	no	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₁₃	—	2	1	no	—
11	C₄²×C₁₃	C₈	1	1	yes	characteristic
12	C₄²×C₁₃	C₈	1	1	yes	characteristic
13	#6099	—	4	1	no	—
14	#6099	—	4	1	no	—
15	C₂×#1055	—	2	1	no	—
16	C₂×#1055	D₄	1	2	yes	—
17	#6092	—	4	2	no	—
18	#1327	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	4	2	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
27	#1055	—	2	2	no	—
28	#1055	—	4	1	no	—
29	#423	—	13	1	no	—
30	#349	—	13	2	no	—
31	C₂²×C₁₃	—	2	1	no	—
32	C₂²×C₁₃	—	4	1	no	—
33	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₁₃	—	2	2	no	—
35	C₄×C₁₃	—	2	1	no	—
36	C₄×C₁₃	—	4	1	no	—
37	C₄×C₁₃	#99	1	1	yes	characteristic
38	C₄×C₁₃	#101	1	1	yes	characteristic
39	C₂×M₁₆	—	13	1	no	—
40	C₂×M₁₆	—	13	1	no	—
41	C₂×C₄²	#261	1	1	yes	characteristic
42	M₃₂	—	26	2	no	—
43	C₄⋊C₈	—	26	2	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	—	4	1	no	—
46	C₂×C₁₃	#324	1	1	yes	characteristic
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×#261	1	1	yes	characteristic
49	M₁₆	—	52	1	no	—
50	M₁₆	—	52	1	no	—
51	C₂×C₈	—	13	2	no	—
52	C₂×C₈	—	26	1	no	—
53	C₄²	—	2	1	no	—
54	C₄²	#1057	1	1	yes	characteristic
55	C₄²	#1057	1	1	yes	characteristic
56	C₁₆	—	52	2	no	—
57	C₁₃	#1327	1	1	yes	characteristic, complemented, Sylow
58	C₂³	#6122	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×#1057	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
66	C₈	—	26	2	no	—
67	C₈	—	52	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊#1057	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#88107	1	1	yes	characteristic
75	C₄	#88113	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#11718285	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88107
commutator	C₂×C₄×C₁₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle	C₂×C₁₃	#324
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×#6099	C₂²
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#1327
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
57. C₁₃	#1327	semidirect

Maximal subgroups

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

subgroup	index
#11718585	2
#11718284	2
#1327	13