Subgroups — #13129758

Order 1664.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718895	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#6092	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
4	C₂×#6099	C₄	1	1	yes	characteristic
5	C₂²×#1055	C₂²	1	1	yes	characteristic
6	C₂×#6092	—	2	2	no	—
7	C₂²⋊#1055	—	2	2	no	—
8	C₁₃×#41	—	4	1	no	—
9	C₁₃×#41	—	4	1	no	—
10	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
11	C₂×D₄×C₁₃	—	2	1	no	—
12	C₂×D₄×C₁₃	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₁₃	—	2	1	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	#6099	—	4	1	no	—
16	C₂×#1055	—	2	1	no	—
17	C₂×#1055	—	4	1	no	—
18	C₂×#1055	D₄	1	2	yes	—
19	#6092	—	4	2	no	—
20	#1315	—	13	1	no	maximal, Sylow
21	C₂³×C₁₃	—	2	1	no	—
22	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
23	Q₈×C₁₃	—	4	1	no	—
24	D₄×C₁₃	—	4	1	no	—
25	D₄×C₁₃	—	4	2	no	—
26	C₂×C₄×C₁₃	—	2	1	no	—
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	—	4	1	no	—
30	C₂×C₄×C₁₃	—	4	1	no	—
31	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
33	#1055	—	2	2	no	—
34	#1055	—	4	1	no	—
35	#408	—	13	1	no	—
36	C₂²⋊C₁₆	—	13	2	no	—
37	C₂²×C₁₃	—	2	1	no	—
38	C₂²×C₁₃	—	2	2	no	—
39	C₂²×C₁₃	—	4	1	no	—
40	C₂²×C₁₃	—	4	2	no	—
41	C₂²×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	4	1	no	—
44	C₄×C₁₃	#99	1	1	yes	characteristic
45	C₄×C₁₃	#100	1	1	yes	characteristic
46	C₂×#41	#261	1	1	yes	characteristic
47	C₂×M₁₆	—	13	1	no	—
48	C₂²×C₈	—	13	1	no	—
49	C₂×C₁₆	—	26	2	no	—
50	C₂²⋊C₈	—	26	2	no	—
51	C₂×C₁₃	—	4	1	no	—
52	C₂×C₁₃	—	8	1	no	—
53	C₂×C₁₃	#323	1	1	yes	characteristic
54	C₂×C₁₃	#350	1	2	yes	—
55	#41	—	4	1	no	—
56	#41	—	4	1	no	—
57	C₂×Q₈	#1057	1	1	yes	characteristic
58	C₂×D₄	—	2	1	no	—
59	C₂×D₄	#1057	1	1	yes	characteristic
60	C₂²×C₄	—	2	1	no	—
61	C₂²×C₄	C₂×#261	1	1	yes	characteristic
62	M₁₆	—	52	1	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	26	1	no	—
65	C₂×C₈	—	52	1	no	—
66	C₁₆	—	52	2	no	—
67	C₁₃	#1315	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	2	1	no	—
69	C₂³	#6122	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	D₄	—	4	1	no	—
72	D₄	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₂×#1057	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
80	C₈	—	26	2	no	—
81	C₈	—	52	1	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	1	no	—
84	C₂²	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂²⋊#1057	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	#88119	1	1	yes	characteristic
90	C₄	#88121	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	8	1	no	—
93	C₂	#11718304	1	2	yes	—
94	C₂	#11718305	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂×C₄×C₁₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#261
Fitting, prime radical	C₂×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂²⋊C₈
cosocle	C₂²×#1055	C₂²
hypercenter	C₂×#41	#261
hypocenter	C₁₃	#1315
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. C₂²⋊#6092	C₂	semidirect
67. C₁₃	#1315	semidirect

Maximal subgroups

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

subgroup	index
#11718895	2
C₂²⋊#6092	2
#1315	13