Subgroups — #13131168

Order 1664.

172 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	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#6092	C₂	1	4	yes	maximal, complemented
4	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×#1055	C₄	1	1	yes	characteristic
6	C₂²×#1055	C₂²	1	1	yes	characteristic
7	#88106	—	2	4	no	—
8	C₂×#6092	C₂²	1	4	yes	—
9	C₄×#1055	C₄	1	2	yes	—
10	C₄×#1055	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₃	C₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₁₃	C₈	1	1	yes	characteristic
14	C₄²×C₁₃	C₈	1	1	yes	characteristic
15	C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×#1055	—	2	2	no	—
17	C₂×#1055	C₂×C₄	1	2	yes	—
18	C₂×#1055	C₂×C₄	1	1	yes	characteristic
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	#2150	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	4	no	—
26	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₃	M₁₆	1	2	yes	—
31	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	#1055	—	2	2	no	—
33	#1055	C₄⋊C₄	1	2	yes	—
34	#1055	C₂×D₄	1	1	yes	characteristic
35	#1055	C₂×Q₈	1	1	yes	characteristic
36	C₂×M₃₂	—	13	2	no	—
37	C₂×C₄×C₈	—	13	1	no	—
38	C₄⋊C₁₆	—	13	4	no	—
39	C₂²×C₁₃	—	2	2	no	—
40	C₂²×C₁₃	C₄⋊C₈	1	2	yes	—
41	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₁₃	—	2	2	no	—
43	C₄×C₁₃	C₄⋊C₈	1	2	yes	—
44	C₄×C₁₃	M₃₂	1	4	yes	complemented
45	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
47	C₂²×C₈	—	13	1	no	—
48	C₂²×C₈	—	13	1	no	—
49	C₂×C₄²	#261	1	1	yes	characteristic
50	M₃₂	—	26	4	no	—
51	C₂×C₁₆	—	13	4	no	—
52	C₄×C₈	—	13	2	no	—
53	C₄×C₈	—	13	2	no	—
54	C₂×C₁₃	—	2	2	no	—
55	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₁₃	C₂×M₃₂	1	2	yes	—
57	C₂²×C₄	#1057	1	2	yes	—
58	C₂²×C₄	C₂×#261	1	1	yes	characteristic
59	C₂×C₈	—	13	2	no	—
60	C₂×C₈	—	13	2	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	13	1	no	—
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	26	2	no	—
65	C₄²	#1057	1	1	yes	characteristic
66	C₄²	#1057	1	1	yes	characteristic
67	C₄²	C₂×#261	1	2	yes	—
68	C₁₆	—	26	4	no	—
69	C₁₃	#2150	1	1	yes	characteristic, complemented, Sylow
70	C₂³	C₂×#1057	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	#6118	1	2	yes	—
73	C₂×C₄	C₄⋊#261	1	2	yes	—
74	C₂×C₄	C₂×#1057	1	2	yes	—
75	C₂×C₄	C₂×#1057	1	2	yes	—
76	C₂×C₄	C₂×#1057	1	1	yes	characteristic
77	C₂×C₄	C₂²×#261	1	1	yes	characteristic
78	C₈	—	13	1	no	—
79	C₈	—	13	2	no	—
80	C₈	—	13	1	no	—
81	C₈	—	26	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊#1057	1	2	yes	—
84	C₂²	C₂²×#1057	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	#88106	1	4	yes	complemented
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×#88106	1	2	yes	—
92	C₂	C₂×C₄⋊#1057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₄²×C₁₃	C₄
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
hypercenter	C₂×C₄²	#261
hypocenter	C₁₃	#2150
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄⋊#6092	C₂	semidirect
44. C₄×C₁₃	M₃₂	semidirect
69. C₁₃	#2150	semidirect
86. C₄	#88106	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
C₂×C₄×#1055	2
C₄⋊#6092	2
#2150	13