Subgroups — #13116592

Order 1664.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	2	yes	maximal
3	C₄⋊#6090	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₄×C₈×C₁₃	C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	#88052	—	2	4	no	—
10	C₂×#6090	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₃	C₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₃	—	2	2	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	D₄	1	2	yes	—
17	C₂×C₈×C₁₃	Q₈	1	2	yes	—
18	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₄²×C₁₃	C₈	1	1	yes	characteristic
20	C₄²×C₁₃	C₈	1	1	yes	characteristic
21	C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	#6090	—	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	C₈×C₁₃	—	2	2	no	—
33	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×M₃₂	—	13	2	no	—
37	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
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	Dic₁₃	1	1	yes	characteristic
48	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
49	C₂×C₄²	Dic₁₃	1	1	yes	characteristic
50	M₃₂	—	26	4	no	—
51	C₂×C₁₆	—	13	4	no	—
52	C₄×C₈	Dic₁₃	1	2	yes	—
53	C₄×C₈	C₂×D₁₃	1	2	yes	—
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	#1055	1	2	yes	—
58	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	Dic₂₆	1	2	yes	—
61	C₂×C₈	D₅₂	1	2	yes	—
62	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
63	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
65	C₄²	#1055	1	1	yes	characteristic
66	C₄²	#1055	1	1	yes	characteristic
67	C₄²	C₂×Dic₁₃	1	2	yes	—
68	C₁₆	—	26	4	no	—
69	C₁₃	#2150	1	1	yes	characteristic, complemented, Sylow
70	C₂³	C₂×#1055	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	C₂×#1055	1	2	yes	—
73	C₂×C₄	C₂×#1055	1	1	yes	characteristic
74	C₂×C₄	C₂×#1055	1	2	yes	—
75	C₂×C₄	#6099	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
77	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₈	C₄⋊Dic₁₃	1	2	yes	—
80	C₈	C₂×Dic₂₆	1	1	yes	characteristic
81	C₈	C₂×D₅₂	1	1	yes	characteristic
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊#1055	1	2	yes	—
84	C₂²	C₂²×#1055	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	C₄⋊#1055	1	2	yes	—
87	C₄	#88052	1	4	yes	complemented
88	C₄	C₂×#6099	1	1	yes	characteristic
89	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#1055	1	1	yes	characteristic
92	C₂	C₂×#88052	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₂×C₄×C₈×C₁₃	C₂
prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	#2150
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄⋊#6090	C₂	semidirect
44. C₄×C₁₃	M₃₂	semidirect
69. C₁₃	#2150	semidirect
87. C₄	#88052	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₁₃	2
C₂×#88052	2
C₄⋊#6090	2
#2150	13