Subgroups — #13129795

Order 1664.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718533	C₂	1	1	yes	maximal, characteristic
2	#11718258	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₀₄	C₄	1	1	yes	characteristic
5	#88147	—	2	1	no	—
6	C₄⋊#1057	—	2	1	no	—
7	C₂×#6092	—	2	1	no	—
8	C₁₃×#107	C₄	1	1	yes	characteristic
9	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	#88049	—	2	1	no	—
11	C₂×D₅₂	—	2	1	no	—
12	C₂×C₄×D₁₃	—	4	1	no	—
13	C₂×#1057	—	4	1	no	—
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₁₃×C₄⋊C₄	—	2	1	no	—
16	#6103	—	4	1	no	—
17	C₄×Dic₁₃	D₄	1	1	yes	characteristic
18	C₂×#1055	D₄	1	1	yes	characteristic
19	D₁₀₄	—	2	1	no	—
20	D₁₀₄	C₈	1	2	yes	complemented
21	#6092	—	2	2	no	—
22	#1333	—	13	1	no	maximal, Sylow
23	C₂²×D₁₃	—	4	1	no	—
24	C₂×C₄×C₁₃	—	4	1	no	—
25	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₃	D₈	1	1	yes	characteristic
27	C₂×Dic₁₃	SD₁₆	1	1	yes	characteristic
28	D₅₂	—	2	2	no	—
29	D₅₂	—	4	1	no	—
30	C₄×D₁₃	—	8	2	no	—
31	#1057	—	8	1	no	—
32	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₃	M₁₆	1	1	yes	characteristic
34	#1055	—	2	1	no	—
35	C₄×D₈	—	13	1	no	—
36	#346	—	13	1	no	—
37	#334	—	13	1	no	—
38	C₂²×C₁₃	#102	1	1	yes	characteristic
39	C₂×D₁₃	—	4	2	no	—
40	C₂×D₁₃	—	8	1	no	—
41	C₂×D₁₃	—	8	1	no	—
42	C₄×C₁₃	—	8	1	no	—
43	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₁₃	#104	1	1	yes	characteristic
45	Dic₁₃	—	2	1	no	—
46	Dic₁₃	—	2	1	no	—
47	C₂×D₈	—	13	1	no	—
48	C₄×D₄	—	26	1	no	—
49	C₂×C₁₆	—	26	1	no	—
50	#107	#261	1	1	yes	characteristic
51	C₄⋊C₈	—	26	1	no	—
52	#102	—	26	1	no	—
53	C₄×C₈	—	13	1	no	—
54	C₂×C₁₃	D₄⋊C₈	1	1	yes	characteristic
55	C₂×C₁₃	#360	1	1	yes	characteristic
56	C₂×C₁₃	#361	1	1	yes	characteristic
57	D₁₃	—	8	2	no	—
58	C₂×D₄	—	26	1	no	—
59	C₂²×C₄	—	52	1	no	—
60	D₈	—	13	2	no	—
61	D₈	—	26	1	no	—
62	C₂×C₈	—	13	1	no	—
63	C₂×C₈	—	52	1	no	—
64	C₂×C₈	C₂×#261	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₂²⋊C₄	—	52	1	no	—
67	C₄²	—	13	1	no	—
68	C₁₆	—	26	2	no	—
69	C₁₃	#1333	1	1	yes	characteristic, complemented, Sylow
70	C₂³	—	52	1	no	—
71	D₄	—	26	2	no	—
72	D₄	—	52	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	—	13	1	no	—
76	C₂×C₄	—	104	2	no	—
77	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
78	C₈	—	26	1	no	—
79	C₈	—	104	1	no	—
80	C₈	D₁₃⋊C₈	1	1	yes	characteristic
81	C₈	#6118	1	1	yes	characteristic
82	C₂²	—	52	2	no	—
83	C₂²	—	104	1	no	—
84	C₂²	—	104	1	no	—
85	C₂²	#88115	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	—	26	1	no	—
88	C₄	—	26	1	no	—
89	C₄	#88111	1	1	yes	characteristic
90	C₄	#88118	1	1	yes	characteristic
91	C₂	—	104	2	no	—
92	C₂	#11718243	1	1	yes	characteristic
93	C₂	#11718278	1	1	yes	characteristic
94	C₂	#11718279	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88115
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#107	C₄
socle	C₂²×C₁₃	#102
prime radical	C₂×D₁₀₄	C₄
cosocle	C₈×Dic₁₃	C₂²
hypercenter	#107	#261
hypocenter	C₁₃	#1333
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
2. #11718258	C₂	semidirect
3. #11718253	C₂	semidirect
20. D₁₀₄	C₈	semidirect
69. C₁₃	#1333	semidirect

Maximal subgroups

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

subgroup	index
#11718533	2
#11718258	2
#11718253	2
#1333	13