Subgroups — #13131179

Order 1664.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88106	C₂	1	2	yes	maximal
2	#11718658	C₂	1	1	yes	maximal, characteristic
3	#11718233	C₂	1	4	yes	maximal, complemented
4	C₁₃×#117	C₄	1	1	yes	characteristic
5	C₂×#6099	C₄	1	1	yes	characteristic
6	C₂²×#1055	C₂²	1	1	yes	characteristic
7	#88106	—	2	2	no	—
8	#88106	C₂²	1	4	yes	—
9	C₂×#6092	—	2	2	no	—
10	#88043	C₄	1	2	yes	—
11	C₄×#1055	C₂²	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₁₃×C₂²⋊C₄	—	2	1	no	—
15	C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	#6099	C₈	1	4	yes	—
17	C₂×#1055	C₂×C₄	1	1	yes	characteristic
18	C₂×#1055	C₂×C₄	1	2	yes	—
19	C₂×#1055	D₄	1	2	yes	—
20	C₂×#1055	Q₈	1	2	yes	—
21	C₂×#1055	C₂³	1	1	yes	characteristic
22	#6092	—	2	4	no	—
23	#2153	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	2	no	—
26	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	#1055	C₄⋊C₄	1	2	yes	—
31	#1055	C₂×C₈	1	4	yes	—
32	#1055	C₂×D₄	1	1	yes	characteristic
33	#1055	C₂×Q₈	1	1	yes	characteristic
34	C₂×M₃₂	—	13	2	no	—
35	#405	—	13	1	no	—
36	#364	—	13	4	no	—
37	C₂²×C₁₃	—	4	1	no	—
38	C₂²×C₁₃	C₄⋊C₈	1	2	yes	—
39	C₂²×C₁₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₁₃	—	4	2	no	—
41	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
42	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₂×M₁₆	—	13	1	no	—
45	C₂²×C₈	—	13	1	no	—
46	#117	#261	1	1	yes	characteristic
47	M₃₂	—	13	4	no	—
48	M₃₂	—	26	2	no	—
49	C₂×C₁₆	—	26	2	no	—
50	#97	—	13	2	no	—
51	C₄×C₈	—	13	2	no	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	—	2	2	no	—
54	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
55	C₂²×C₄	C₂×#261	1	1	yes	characteristic
56	M₁₆	—	13	4	no	—
57	C₂×C₈	—	13	2	no	—
58	C₂×C₈	—	13	2	no	—
59	C₂×C₈	—	13	1	no	—
60	C₂×C₈	—	13	2	no	—
61	C₂×C₈	—	13	1	no	—
62	C₄⋊C₄	—	2	1	no	—
63	C₂²⋊C₄	—	2	1	no	—
64	C₄²	C₂×#261	1	2	yes	—
65	C₁₆	—	26	4	no	—
66	C₁₃	#2153	1	1	yes	characteristic, complemented, Sylow
67	C₂³	#6122	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
70	C₂×C₄	C₄⋊#261	1	2	yes	—
71	C₂×C₄	#6122	1	1	yes	characteristic
72	C₂×C₄	C₂²×#261	1	1	yes	characteristic
73	C₈	—	13	4	no	—
74	C₈	—	13	1	no	—
75	C₈	—	13	2	no	—
76	C₈	—	13	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#88112	1	2	yes	—
79	C₂²	C₂×#6122	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#88112	1	2	yes	—
82	C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
83	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#88112	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#117	C₄
socle	C₂×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	M₁₆
cosocle	C₂×#1055	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#2153
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #11718233	C₂	semidirect
66. C₁₃	#2153	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88106	2
#11718658	2
#11718233	2
#2153	13