Subgroups — #13116631

Order 1664.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#88059	C₂	1	2	yes	maximal
3	#11718098	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×#6099	—	2	2	no	—
6	C₁₃×M₃₂	C₄	1	4	yes	—
7	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
8	#88059	—	2	2	no	—
9	#88059	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₃	Q₈	1	2	yes	—
14	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	#6099	—	2	4	no	—
16	#6099	—	4	2	no	—
17	C₂×#1055	—	4	2	no	—
18	C₁₃×C₁₆	C₂×C₄	1	4	yes	—
19	#2161	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	Q₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₁₃	D₈	1	2	yes	—
23	C₂×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
26	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
28	#1055	—	4	4	no	—
29	C₂×M₃₂	D₁₃	1	1	yes	characteristic
30	C₂×#108	—	13	2	no	—
31	#368	—	13	4	no	—
32	C₂²×C₁₃	—	4	1	no	—
33	C₂²×C₁₃	#107	1	2	yes	—
34	C₂²×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
35	C₄×C₁₃	#107	1	2	yes	—
36	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
38	C₂×M₁₆	—	26	2	no	—
39	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
40	M₃₂	Dic₁₃	1	4	yes	—
41	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
42	#108	—	13	4	no	—
43	#108	—	26	2	no	—
44	C₂×C₁₃	—	2	2	no	—
45	C₂×C₁₃	—	2	1	no	—
46	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
47	C₂²×C₄	D₅₂	1	1	yes	characteristic
48	M₁₆	—	26	4	no	—
49	M₁₆	—	52	2	no	—
50	C₂×C₈	—	52	2	no	—
51	C₂×C₈	Dic₂₆	1	2	yes	—
52	C₂×C₈	D₅₂	1	1	yes	characteristic
53	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
54	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
55	C₁₆	C₂×Dic₁₃	1	4	yes	—
56	C₁₃	#2161	1	1	yes	characteristic, complemented, Sylow
57	C₂³	Dic₅₂	1	1	yes	characteristic
58	C₂×C₄	D₁₀₄	1	2	yes	—
59	C₂×C₄	Dic₅₂	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
61	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
62	C₈	—	52	4	no	—
63	C₈	C₄⋊Dic₁₃	1	2	yes	—
64	C₈	C₂×Dic₂₆	1	1	yes	characteristic
65	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
66	C₂²	—	4	1	no	—
67	C₂²	#88058	1	2	yes	—
68	C₂²	C₂×Dic₅₂	1	1	yes	characteristic
69	C₄	#88058	1	2	yes	—
70	C₄	C₂×D₁₀₄	1	1	yes	characteristic
71	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
72	C₂	—	2	1	no	—
73	C₂	—	2	2	no	—
74	C₂	C₂×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×M₃₂	C₂
socle	C₂×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂×M₃₂	D₁₃
hypocenter	C₁₃	#2161
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #11718098	C₂	semidirect
56. C₁₃	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×M₃₂	2
C₂×#88059	2
#11718098	2
#2161	13