Subgroups — #13129804

Order 1664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718685	C₂	1	1	yes	maximal, characteristic
2	#11718231	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#6092	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂×#6092	—	2	1	no	—
6	C₂×#6092	—	2	1	no	—
7	C₄⋊#1055	—	2	1	no	—
8	C₄⋊#1055	C₄	1	1	yes	characteristic
9	#88043	—	2	1	no	—
10	C₄×#1055	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	—	2	1	no	—
13	C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
14	C₄²×C₁₃	—	2	1	no	—
15	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×#1055	—	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	#1338	—	13	1	no	maximal, Sylow
22	Q₈×C₁₃	—	4	1	no	—
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	—	2	1	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
28	#1055	—	2	1	no	—
29	#1055	—	4	1	no	—
30	#1055	SD₁₆	1	1	yes	characteristic
31	#1055	Q₁₆	1	1	yes	characteristic
32	#446	—	13	1	no	—
33	C₄⋊C₁₆	—	13	1	no	—
34	#346	—	13	1	no	—
35	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₃	—	2	1	no	—
37	C₄×C₁₃	—	2	1	no	—
38	C₄×C₁₃	—	4	1	no	—
39	C₄×C₁₃	—	4	1	no	—
40	C₄×C₁₃	#103	1	1	yes	characteristic
41	C₄×C₁₃	#104	1	1	yes	characteristic
42	C₄×Q₈	#261	1	1	yes	characteristic
43	C₂×C₁₆	—	26	1	no	—
44	C₂×C₁₆	—	26	1	no	—
45	C₄⋊C₈	—	13	1	no	—
46	C₄⋊C₈	—	26	1	no	—
47	#97	—	26	1	no	—
48	C₄×C₈	—	13	1	no	—
49	C₂×C₁₃	Q₈⋊C₈	1	1	yes	characteristic
50	C₂×C₁₃	#349	1	1	yes	characteristic
51	C₂×C₁₃	#350	1	1	yes	characteristic
52	C₂×Q₈	#1057	1	1	yes	characteristic
53	C₂×C₈	—	13	1	no	—
54	C₂×C₈	—	13	1	no	—
55	C₂×C₈	—	26	1	no	—
56	C₄⋊C₄	—	2	1	no	—
57	C₄⋊C₄	#1057	1	1	yes	characteristic
58	C₄²	—	2	1	no	—
59	C₄²	C₂×#261	1	1	yes	characteristic
60	C₁₆	—	26	2	no	—
61	C₁₆	—	52	1	no	—
62	C₁₃	#1338	1	1	yes	characteristic, complemented, Sylow
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×#1057	1	1	yes	characteristic
67	C₂×C₄	#6122	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
69	C₈	—	13	1	no	—
70	C₈	—	13	1	no	—
71	C₈	—	26	1	no	—
72	C₈	—	52	1	no	—
73	C₂²	C₂²⋊#1057	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#88117	1	1	yes	characteristic
79	C₄	#88118	1	1	yes	characteristic
80	C₂	#11718284	1	1	yes	characteristic
81	C₂	Q₈⋊#1057	1	1	yes	characteristic
82	C₂	#11718304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂×C₄×C₁₃	C₂×C₈
Frattini	C₄²	C₂×#261
Fitting	C₄×Q₈×C₁₃	C₄
socle, prime radical	C₂²×C₁₃	C₂²⋊C₈
cosocle	C₄×#1055	C₂²
hypercenter	C₄×Q₈	#261
hypocenter	C₁₃	#1338
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
62. C₁₃	#1338	semidirect

Maximal subgroups

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

subgroup	index
#11718685	2
#11718231	2
C₄⋊#6092	2
#1338	13