Subgroups — #13117148

Order 1664.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718113	C₂	1	2	yes	maximal, complemented
4	#11718111	C₂	1	2	yes	maximal, complemented
5	#11718091	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#135	—	2	1	no	—
7	C₂×D₁₀₄	—	2	1	no	—
8	C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
9	C₁₃×SD₃₂	—	2	1	no	—
10	C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	D₂₀₈	—	2	1	no	—
13	D₂₀₈	C₂²	1	2	yes	—
14	#88034	C₂²	1	2	yes	complemented
15	C₁₃×#41	—	4	1	no	—
16	C₂×D₅₂	—	4	1	no	—
17	C₁₃×Q₁₆	—	2	1	no	—
18	C₁₃×SD₁₆	—	4	1	no	—
19	C₁₃×D₈	—	2	1	no	—
20	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
21	D₁₀₄	—	2	2	no	—
22	D₁₀₄	—	4	1	no	—
23	C₁₃×C₁₆	D₄	1	1	yes	characteristic
24	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
25	#2263	—	13	1	no	maximal, Sylow
26	C₂²×D₁₃	—	8	1	no	—
27	Q₈×C₁₃	—	4	1	no	—
28	D₄×C₁₃	—	4	1	no	—
29	D₄×C₁₃	—	8	1	no	—
30	C₂×C₄×C₁₃	—	8	1	no	—
31	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
32	D₅₂	—	4	2	no	—
33	D₅₂	—	8	1	no	—
34	C₈×C₁₃	D₈	1	1	yes	characteristic
35	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
36	#508	D₁₃	1	1	yes	characteristic, complemented
37	C₂×D₁₆	—	13	1	no	—
38	SD₆₄	—	13	2	no	—
39	D₃₂	—	13	2	no	—
40	M₆₄	—	13	1	no	—
41	C₂²×C₁₃	—	8	1	no	—
42	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
43	C₂×D₁₃	—	8	2	no	—
44	C₂×D₁₃	—	16	2	no	—
45	C₄×C₁₃	—	8	1	no	—
46	C₄×C₁₃	D₁₆	1	1	yes	characteristic
47	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
48	#135	—	2	1	no	—
49	C₂×D₈	—	26	1	no	—
50	Q₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
51	SD₃₂	—	2	1	no	—
52	D₁₆	—	13	2	no	—
53	D₁₆	—	26	1	no	—
54	D₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
55	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
56	C₃₂	—	13	2	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	—	16	1	no	—
59	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
60	D₁₃	—	16	2	no	—
61	#41	—	4	1	no	—
62	C₂×D₄	—	52	1	no	—
63	Q₁₆	—	2	1	no	—
64	SD₁₆	—	4	1	no	—
65	D₈	—	2	1	no	—
66	D₈	—	26	2	no	—
67	D₈	—	52	1	no	—
68	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
70	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
71	C₁₃	#2263	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	104	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	8	1	no	—
76	D₄	—	52	2	no	—
77	D₄	—	104	1	no	—
78	C₂×C₄	—	8	1	no	—
79	C₂×C₄	#6104	1	1	yes	characteristic
80	C₈	#6104	1	1	yes	characteristic
81	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
82	C₂²	—	8	1	no	—
83	C₂²	—	104	2	no	—
84	C₂²	—	208	2	no	—
85	C₂²	#88066	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	#88066	1	1	yes	characteristic
88	C₄	C₂×#6104	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	16	1	no	—
91	C₂	—	208	2	no	—
92	C₂	C₂×#88066	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#88066
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₁₃×#508	C₂
socle	C₂×C₁₃	C₂×D₁₆
hypercenter	#508	D₁₃
hypocenter	C₁₃	#2263
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₁₃×#508	C₂	semidirect
2. C₂×D₂₀₈	C₂	semidirect
3. #11718113	C₂	semidirect
4. #11718111	C₂	semidirect
5. #11718091	C₂	semidirect
8. C₁₃×Q₃₂	C₂²	semidirect
10. C₁₃×D₁₆	C₂²	semidirect
14. #88034	C₂²	semidirect
36. #508	D₁₃	semidirect
50. Q₃₂	C₂×D₁₃	semidirect
54. D₁₆	C₂×D₁₃	semidirect
71. C₁₃	#2263	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#508	2
C₂×D₂₀₈	2
#11718113	2
#11718111	2
#11718091	2
#2263	13