Subgroups — #13116417

Order 1664.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718786	C₂	1	1	yes	maximal, characteristic
2	#11718780	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic
4	#11718151	C₂	1	2	yes	maximal
5	#11718150	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
8	#88180	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	#88059	—	2	2	no	—
12	#88054	—	2	2	no	—
13	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×M₁₆	—	2	2	no	—
15	C₁₃×M₁₆	—	2	2	no	—
16	C₁₃×M₁₆	—	2	2	no	—
17	C₂×C₈×C₁₃	—	2	2	no	—
18	C₂×C₈×C₁₃	D₄	1	2	yes	—
19	C₂²⋊Dic₁₃	Q₈	1	2	yes	—
20	C₄⋊Dic₁₃	—	2	1	no	—
21	C₄×Dic₁₃	—	2	1	no	—
22	#6099	—	2	2	no	—
23	#6099	—	2	2	no	—
24	C₂×#1055	—	2	1	no	—
25	C₂×#1055	—	2	2	no	—
26	C₂×#1055	—	2	2	no	—
27	#2103	—	13	1	no	maximal, Sylow
28	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	#41	1	2	yes	—
31	C₂×C₄×C₁₃	#41	1	2	yes	—
32	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
33	C₂×Dic₁₃	—	2	2	no	—
34	C₈×C₁₃	—	2	2	no	—
35	C₈×C₁₃	—	4	2	no	—
36	#1055	—	4	1	no	—
37	#1055	—	4	2	no	—
38	#430	—	13	1	no	—
39	#424	—	13	1	no	—
40	#344	—	13	2	no	—
41	#341	—	13	2	no	—
42	#338	D₁₃	1	1	yes	characteristic
43	C₂²×C₁₃	—	4	1	no	—
44	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂²×C₁₃	#125	1	2	yes	—
46	C₄×C₁₃	#123	1	1	yes	characteristic
47	C₄×C₁₃	#124	1	1	yes	characteristic
48	C₄×C₁₃	#126	1	2	yes	—
49	Dic₁₃	—	4	2	no	—
50	C₂×M₁₆	—	13	2	no	—
51	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
52	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic
53	C₂²×C₈	—	13	1	no	—
54	#117	—	13	1	no	—
55	#108	—	26	2	no	—
56	C₄⋊C₈	—	26	2	no	—
57	C₂×C₁₃	—	2	1	no	—
58	C₂×C₁₃	—	2	2	no	—
59	C₂×C₁₃	#400	1	1	yes	characteristic
60	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
61	M₁₆	—	2	2	no	—
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	26	2	no	—
65	M₁₆	—	26	2	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	26	1	no	—
68	C₂×C₈	—	26	2	no	—
69	C₂×C₈	—	26	2	no	—
70	C₂×C₈	D₅₂	1	2	yes	—
71	C₄⋊C₄	—	26	1	no	—
72	C₂²⋊C₄	—	13	2	no	—
73	C₄²	—	26	1	no	—
74	C₁₃	#2103	1	1	yes	characteristic, complemented, Sylow
75	C₂³	Q₈×D₁₃	1	1	yes	characteristic
76	C₂×C₄	—	26	2	no	—
77	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
78	C₂×C₄	#6127	1	2	yes	—
79	C₂×C₄	#6129	1	1	yes	characteristic
80	C₂×C₄	#6129	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₈	—	52	2	no	—
84	C₈	—	52	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#88143	1	2	yes	—
87	C₂²	#88151	1	1	yes	characteristic
88	C₄	—	52	2	no	—
89	C₄	#88129	1	1	yes	characteristic
90	C₄	#88133	1	2	yes	—
91	C₄	#88140	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#11718320	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88129
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#338	C₂
socle	C₂×C₁₃	#400
prime radical	C₂³×C₁₃	C₂×Q₈
hypercenter	#338	D₁₃
hypocenter	C₁₃	#2103
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
74. C₁₃	#2103	semidirect

Maximal subgroups

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

subgroup	index
#11718786	2
#11718780	2
C₁₃×#338	2
#11718151	2
#11718150	2
#2103	13