Subgroups — #13129803

Order 1664.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718491	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6092	C₂	1	1	yes	maximal, characteristic
3	C₄×#6092	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₂₆	C₄	1	1	yes	characteristic
5	C₂×#6092	—	2	1	no	—
6	C₂×#6092	—	2	1	no	—
7	C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
8	#88054	—	2	1	no	—
9	C₈×Dic₁₃	—	2	1	no	—
10	C₄×#1055	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₆	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₃	—	2	1	no	—
13	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
15	#6101	—	2	1	no	—
16	C₄×Dic₁₃	—	2	1	no	—
17	C₂×#1055	D₄	1	1	yes	characteristic
18	C₂×#1055	D₄	1	1	yes	characteristic
19	#6092	—	2	2	no	—
20	#6092	—	4	1	no	—
21	Q₈⋊C₁₆	—	13	1	no	maximal, Sylow
22	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
25	C₂×Dic₁₃	—	2	1	no	—
26	C₂×Dic₁₃	—	2	1	no	—
27	Dic₂₆	—	2	1	no	—
28	Dic₂₆	C₁₆	1	2	yes	complemented
29	C₈×C₁₃	—	4	1	no	—
30	#1055	—	2	1	no	—
31	#1055	SD₁₆	1	1	yes	characteristic
32	#1055	Q₁₆	1	1	yes	characteristic
33	C₈×Q₈	—	13	1	no	—
34	C₄⋊C₁₆	—	13	1	no	—
35	C₄×C₁₆	—	13	1	no	—
36	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₃	—	2	1	no	—
38	C₄×C₁₃	#103	1	1	yes	characteristic
39	C₄×C₁₃	#104	1	1	yes	characteristic
40	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
41	C₄×C₁₃	M₃₂	1	1	yes	characteristic
42	Dic₁₃	—	2	2	no	—
43	Dic₁₃	—	4	1	no	—
44	C₄×Q₈	—	13	1	no	—
45	C₂×C₁₆	—	26	1	no	—
46	C₂×C₁₆	—	26	1	no	—
47	C₄⋊C₈	—	26	1	no	—
48	C₄⋊C₈	#261	1	1	yes	characteristic
49	C₄×C₈	—	13	1	no	—
50	C₄×C₈	—	26	1	no	—
51	C₂×C₁₃	Q₈⋊C₈	1	1	yes	characteristic
52	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
53	C₂×C₁₃	#350	1	1	yes	characteristic
54	C₂×Q₈	—	13	1	no	—
55	C₂×C₈	—	2	1	no	—
56	C₂×C₈	—	13	1	no	—
57	C₂×C₈	—	13	1	no	—
58	C₄⋊C₄	—	13	1	no	—
59	C₄⋊C₄	—	26	1	no	—
60	C₄²	—	26	1	no	—
61	C₄²	C₂×#261	1	1	yes	characteristic
62	C₁₆	—	26	2	no	—
63	C₁₆	—	52	1	no	—
64	C₁₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
65	Q₈	—	13	2	no	—
66	Q₈	—	26	1	no	—
67	C₂×C₄	—	26	1	no	—
68	C₂×C₄	—	26	1	no	—
69	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
70	C₂×C₄	#6118	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
72	C₈	—	4	1	no	—
73	C₈	—	13	1	no	—
74	C₈	—	13	1	no	—
75	C₈	—	26	1	no	—
76	C₂²	#88111	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	26	2	no	—
79	C₄	—	52	1	no	—
80	C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
81	C₄	#88098	1	1	yes	characteristic
82	C₄	#88116	1	1	yes	characteristic
83	C₄	#88117	1	1	yes	characteristic
84	C₂	#11718244	1	1	yes	characteristic
85	C₂	#11718259	1	1	yes	characteristic
86	C₂	#11718270	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₁₆
Frattini	C₄²	C₂×#261
Fitting	C₁₃×C₄⋊C₈	C₄
socle, prime radical	C₂²×C₁₃	C₂²⋊C₈
cosocle	C₄×#1055	C₂²
hypercenter	C₄⋊C₈	#261
hypocenter	C₁₃	Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
28. Dic₂₆	C₁₆	semidirect
64. C₁₃	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
#11718491	2
C₄⋊#6092	2
C₄×#6092	2
Q₈⋊C₁₆	13