Subgroups — #13131171

Order 1664.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88106	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6092	C₂	1	1	yes	maximal, characteristic
3	#11718658	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#6092	C₂	1	4	yes	maximal, complemented
5	C₁₃×#117	C₄	1	1	yes	characteristic
6	C₂×#6099	C₄	1	1	yes	characteristic
7	C₂²×#1055	C₂²	1	1	yes	characteristic
8	#88106	—	2	2	no	—
9	C₂×#6092	—	2	2	no	—
10	C₂×#6092	C₂²	1	2	yes	—
11	C₂×#6092	C₂²	1	2	yes	—
12	#88043	C₄	1	2	yes	—
13	C₄×#1055	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₁₃×C₄⋊C₄	C₈	1	2	yes	—
16	C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
17	C₄²×C₁₃	C₂×C₄	1	2	yes	—
18	#6099	—	2	2	no	—
19	C₂×#1055	C₂×C₄	1	2	yes	—
20	C₂×#1055	C₂×C₄	1	1	yes	characteristic
21	C₂×#1055	D₄	1	2	yes	—
22	C₂×#1055	Q₈	1	2	yes	—
23	C₂×#1055	C₂³	1	1	yes	characteristic
24	#6092	—	2	2	no	—
25	#6092	—	2	2	no	—
26	#2151	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
32	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	#1055	—	2	2	no	—
34	#1055	C₄⋊C₄	1	2	yes	—
35	#1055	C₂×D₄	1	1	yes	characteristic
36	#1055	C₂×Q₈	1	1	yes	characteristic
37	C₂×M₃₂	—	13	1	no	—
38	C₂²×C₁₆	—	13	1	no	—
39	#405	—	13	1	no	—
40	C₄⋊C₁₆	—	13	4	no	—
41	C₂²×C₁₃	—	2	2	no	—
42	C₂²×C₁₃	C₄⋊C₈	1	2	yes	—
43	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₁₃	—	2	4	no	—
45	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
46	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂×M₁₆	—	13	1	no	—
49	C₂²×C₈	—	13	1	no	—
50	#117	#261	1	1	yes	characteristic
51	M₃₂	—	26	2	no	—
52	C₂×C₁₆	—	13	2	no	—
53	C₂×C₁₆	—	13	2	no	—
54	C₂×C₁₆	—	26	2	no	—
55	#97	—	13	2	no	—
56	C₄×C₈	—	13	2	no	—
57	C₂×C₁₃	—	2	2	no	—
58	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂×C₁₃	#504	1	2	yes	—
60	C₂²×C₄	C₂×#261	1	1	yes	characteristic
61	M₁₆	—	26	2	no	—
62	C₂×C₈	—	13	2	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	13	1	no	—
65	C₂×C₈	—	13	1	no	—
66	C₂×C₈	—	13	2	no	—
67	C₄⋊C₄	#1057	1	2	yes	—
68	C₂²⋊C₄	#1057	1	2	yes	—
69	C₄²	C₂×#261	1	2	yes	—
70	C₁₆	—	26	2	no	—
71	C₁₆	—	26	2	no	—
72	C₁₃	#2151	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂×#1057	1	1	yes	characteristic
74	C₂×C₄	#6118	1	2	yes	—
75	C₂×C₄	C₄⋊#261	1	2	yes	—
76	C₂×C₄	C₂×#1057	1	4	yes	—
77	C₂×C₄	C₂×#1057	1	1	yes	characteristic
78	C₂×C₄	C₂²×#261	1	1	yes	characteristic
79	C₈	—	13	1	no	—
80	C₈	—	13	2	no	—
81	C₈	—	13	1	no	—
82	C₈	—	26	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#1057	1	2	yes	—
85	C₂²	C₂²×#1057	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#1057	1	2	yes	—
88	C₄	C₂×#6118	1	1	yes	characteristic
89	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#1057	1	1	yes	characteristic
92	C₂	#11719162	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×#117	C₄
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#2151
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. C₄⋊#6092	C₂	semidirect
72. C₁₃	#2151	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
C₂²×#6092	2
#11718658	2
C₄⋊#6092	2
#2151	13