Subgroups — #13116713

Order 1664.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₀₄	C₂	1	2	yes	maximal, complemented
3	C₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718101	C₂	1	2	yes	maximal, complemented
5	#11718097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₀₄	C₂²	1	2	yes	—
7	C₄×D₅₂	—	2	2	no	—
8	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	#88061	—	2	2	no	—
12	#88058	C₂²	1	2	yes	—
13	D₂₀₈	C₄	1	4	yes	complemented
14	C₂×D₅₂	—	2	2	no	—
15	C₂×C₄×D₁₃	—	4	2	no	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₄²×C₁₃	D₄	1	1	yes	characteristic
19	#6103	—	4	2	no	—
20	C₄⋊Dic₁₃	—	2	2	no	—
21	D₁₀₄	—	2	2	no	—
22	D₁₀₄	C₂×C₄	1	4	yes	complemented
23	C₁₃×C₁₆	—	2	1	no	—
24	C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
25	#2177	—	13	1	no	maximal, Sylow
26	C₂²×D₁₃	—	4	2	no	—
27	C₂×C₄×C₁₃	D₈	1	2	yes	—
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	2	no	—
30	D₅₂	—	2	4	no	—
31	D₅₂	—	4	2	no	—
32	C₄×D₁₃	—	8	4	no	—
33	C₈×C₁₃	—	2	1	no	—
34	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₃	#41	1	1	yes	characteristic
36	C₂×D₁₆	—	13	1	no	—
37	C₄×D₈	—	13	2	no	—
38	#367	—	13	1	no	—
39	#357	—	13	2	no	—
40	#346	D₁₃	1	1	yes	characteristic, complemented
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₃	—	4	4	no	—
43	C₂×D₁₃	—	8	2	no	—
44	C₂×D₁₃	—	8	2	no	—
45	C₄×C₁₃	—	2	2	no	—
46	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
47	C₄×C₁₃	#135	1	1	yes	characteristic
48	Dic₁₃	—	8	2	no	—
49	C₂×D₈	—	13	2	no	—
50	C₄×D₄	—	26	2	no	—
51	D₁₆	—	13	4	no	—
52	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
53	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
54	#107	—	13	2	no	—
55	#102	—	26	2	no	—
56	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
57	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
58	C₂×C₁₃	#509	1	2	yes	—
59	D₁₃	—	8	4	no	—
60	C₂×D₄	—	26	2	no	—
61	C₂²×C₄	—	52	2	no	—
62	D₈	—	13	4	no	—
63	D₈	—	26	2	no	—
64	C₂×C₈	D₅₂	1	1	yes	characteristic
65	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
66	C₄⋊C₄	—	26	2	no	—
67	C₂²⋊C₄	—	52	2	no	—
68	C₄²	D₅₂	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	C₄×D₁₃	1	2	yes	complemented
71	C₁₃	#2177	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	52	2	no	—
73	D₄	—	26	4	no	—
74	D₄	—	52	2	no	—
75	C₂×C₄	—	52	2	no	—
76	C₂×C₄	—	104	4	no	—
77	C₂×C₄	D₁₀₄	1	2	yes	—
78	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
81	C₈	#6127	1	1	yes	characteristic
82	C₂²	—	52	4	no	—
83	C₂²	—	104	2	no	—
84	C₂²	—	104	2	no	—
85	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	104	2	no	—
88	C₄	C₄×D₅₂	1	1	yes	characteristic
89	C₄	#88158	1	1	yes	characteristic
90	C₂	—	104	4	no	—
91	C₂	C₄×D₁₀₄	1	1	yes	characteristic
92	C₂	#11718569	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#346	C₂
socle	C₂²×C₁₃	C₂×D₈
prime radical	C₂×D₂₀₈	C₂
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	#346	D₁₃
hypocenter	C₁₃	#2177
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₀₄	C₂	semidirect
3. C₁₃×#346	C₂	semidirect
4. #11718101	C₂	semidirect
5. #11718097	C₂	semidirect
13. D₂₀₈	C₄	semidirect
22. D₁₀₄	C₂×C₄	semidirect
24. C₁₃×C₁₆	C₂×C₄	semidirect
40. #346	D₁₃	semidirect
70. C₁₆	C₄×D₁₃	semidirect
71. C₁₃	#2177	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₀₈	2
C₄×D₁₀₄	2
C₁₃×#346	2
#11718101	2
#11718097	2
#2177	13