Subgroups — #13129772

Order 1664.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#6092	C₂	1	2	yes	maximal
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	C₂×#6092	—	2	2	no	—
7	C₄⋊#1055	—	2	2	no	—
8	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
9	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₁₃	—	2	1	no	—
12	C₄²×C₁₃	—	2	1	no	—
13	C₂×#1055	—	2	1	no	—
14	C₂×#1055	—	4	1	no	—
15	C₂×#1055	—	4	1	no	—
16	C₂×#1055	D₄	1	2	yes	—
17	#6092	—	4	2	no	—
18	#1322	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₂×C₈	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	—	2	1	no	—
25	C₂×C₄×C₁₃	—	4	1	no	—
26	C₂×C₄×C₁₃	C₁₆	1	2	yes	complemented
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
29	#1055	—	2	2	no	—
30	#1055	—	4	1	no	—
31	C₂×C₄⋊C₈	—	13	1	no	—
32	C₂²⋊C₁₆	—	13	2	no	—
33	C₂²×C₁₃	—	2	1	no	—
34	C₂²×C₁₃	—	2	1	no	—
35	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₂²×C₁₃	C₂×C₁₆	1	1	yes	characteristic
37	C₂²×C₁₃	M₃₂	1	1	yes	characteristic
38	C₄×C₁₃	—	2	1	no	—
39	C₄×C₁₃	—	2	2	no	—
40	C₄×C₁₃	—	4	1	no	—
41	C₄×C₁₃	#99	1	1	yes	characteristic
42	C₄×C₁₃	#101	1	1	yes	characteristic
43	C₂²×C₈	—	13	1	no	—
44	C₂²×C₈	—	13	1	no	—
45	C₂×C₄²	#261	1	1	yes	characteristic
46	C₂×C₁₆	—	26	2	no	—
47	C₄⋊C₈	—	26	2	no	—
48	C₂×C₁₃	—	2	1	no	—
49	C₂×C₁₃	—	2	1	no	—
50	C₂×C₁₃	#324	1	1	yes	characteristic
51	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
52	C₂×C₁₃	#349	1	1	yes	characteristic
53	C₂²×C₄	#1057	1	1	yes	characteristic
54	C₂²×C₄	#1057	1	1	yes	characteristic
55	C₂²×C₄	C₂×#261	1	1	yes	characteristic
56	C₂×C₈	—	13	2	no	—
57	C₂×C₈	—	26	1	no	—
58	C₂×C₈	—	52	1	no	—
59	C₂×C₈	—	52	1	no	—
60	C₄²	—	2	1	no	—
61	C₄²	—	2	1	no	—
62	C₁₆	—	52	2	no	—
63	C₁₃	#1322	1	1	yes	characteristic, complemented, Sylow
64	C₂³	C₂×#1057	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	#6092	1	2	yes	complemented
72	C₂×C₄	#6122	1	1	yes	characteristic
73	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
74	C₈	—	26	2	no	—
75	C₈	—	52	1	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	C₂×#6092	1	1	yes	characteristic
79	C₂²	#88106	1	1	yes	characteristic
80	C₂²	C₂²⋊#1057	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	#88107	1	1	yes	characteristic
85	C₄	#88113	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	C₂²⋊#6092	1	1	yes	characteristic
89	C₂	#11718284	1	1	yes	characteristic
90	C₂	#11718285	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂²×C₁₃	C₂×C₁₆
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	#1322
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
26. C₂×C₄×C₁₃	C₁₆	semidirect
63. C₁₃	#1322	semidirect
71. C₂×C₄	#6092	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#1055	2
C₂²⋊#6092	2
#1322	13