Subgroups — #13112876

Order 1664.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718354	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6095	—	2	1	no	—
5	C₂×#6095	—	2	1	no	—
6	#88128	C₄	1	1	yes	characteristic
7	#88123	C₄	1	1	yes	characteristic
8	C₁₃×M₃₂	—	2	1	no	—
9	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88052	—	2	1	no	—
11	C₂×D₅₂	—	2	1	no	—
12	C₂×D₅₂	—	4	1	no	—
13	C₂×Dic₂₆	—	2	1	no	—
14	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄⋊Dic₁₃	—	4	1	no	—
18	#6095	—	4	1	no	—
19	#6095	—	4	1	no	—
20	#6095	—	4	1	no	—
21	#6095	—	4	1	no	—
22	C₁₃×C₁₆	—	4	1	no	—
23	#6090	—	4	1	no	—
24	#1359	—	13	1	no	maximal, Sylow
25	C₂²×D₁₃	—	4	1	no	—
26	C₂×C₄×C₁₃	—	2	1	no	—
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₃	—	4	1	no	—
29	D₅₂	—	4	1	no	—
30	D₅₂	—	4	1	no	—
31	D₅₂	—	8	2	no	—
32	Dic₂₆	—	4	1	no	—
33	Dic₂₆	—	4	1	no	—
34	C₈×C₁₃	D₈	1	1	yes	characteristic
35	C₈×C₁₃	D₈	1	1	yes	characteristic
36	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
37	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
38	#492	—	13	1	no	—
39	#364	—	13	1	no	—
40	#364	D₁₃	1	1	yes	characteristic, complemented
41	C₂²×C₁₃	#100	1	1	yes	characteristic
42	C₂×D₁₃	—	8	2	no	—
43	C₂×D₁₃	—	8	1	no	—
44	C₄×C₁₃	—	2	2	no	—
45	C₄×C₁₃	#102	1	1	yes	characteristic
46	C₄×C₁₃	#102	1	1	yes	characteristic
47	Dic₁₃	—	8	1	no	—
48	C₂×SD₁₆	—	26	1	no	—
49	C₂×SD₁₆	—	26	1	no	—
50	C₄⋊Q₈	—	13	1	no	—
51	#127	—	13	1	no	—
52	M₃₂	—	2	1	no	—
53	M₃₂	—	26	1	no	—
54	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
55	C₂×C₁₃	—	2	1	no	—
56	C₂×C₁₃	#331	1	1	yes	characteristic
57	D₁₃	—	16	1	no	—
58	C₂×Q₈	—	26	1	no	—
59	C₂×D₄	—	26	1	no	—
60	C₂×D₄	—	52	1	no	—
61	SD₁₆	—	52	1	no	—
62	SD₁₆	—	52	1	no	—
63	SD₁₆	—	52	1	no	—
64	SD₁₆	—	52	1	no	—
65	C₂×C₈	D₅₂	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
67	C₄⋊C₄	—	52	1	no	—
68	C₄²	C₄×D₁₃	1	1	yes	characteristic
69	C₁₆	—	4	1	no	—
70	C₁₆	—	52	1	no	—
71	C₁₃	#1359	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	52	1	no	—
73	Q₈	—	52	1	no	—
74	Q₈	—	52	1	no	—
75	D₄	—	52	1	no	—
76	D₄	—	52	1	no	—
77	D₄	—	104	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	52	1	no	—
80	C₂×C₄	#6103	1	1	yes	characteristic
81	C₈	#6095	1	1	yes	characteristic
82	C₈	D₁₀₄	1	1	yes	characteristic
83	C₈	#6104	1	1	yes	characteristic
84	C₈	#6106	1	1	yes	characteristic
85	C₂²	—	104	2	no	—
86	C₂²	—	104	1	no	—
87	C₂²	#88063	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	104	1	no	—
90	C₄	#88049	1	1	yes	characteristic
91	C₄	#88061	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	208	1	no	—
94	C₂	#11718077	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718077
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₁₃×#364	C₂
socle	C₂×C₁₃	#331
prime radical	#88128	C₄
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	#364	D₁₃
hypocenter	C₁₃	#1359
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₁₃×#364	C₂	semidirect
3. #11718055	C₂	semidirect
40. #364	D₁₃	semidirect
71. C₁₃	#1359	semidirect

Maximal subgroups

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

subgroup	index
#11718354	2
C₁₃×#364	2
#11718055	2
#1359	13