Subgroups — #13114507

Order 1664.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718360	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718355	C₂	1	2	yes	maximal
3	#11718354	C₂	1	1	yes	maximal, characteristic
4	#11718343	C₂	1	2	yes	maximal, complemented
5	C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₅₂	—	2	2	no	—
7	C₂×#6095	—	2	2	no	—
8	#88128	C₂²	1	1	yes	characteristic
9	#88123	C₂²	1	1	yes	characteristic
10	#88123	C₂²	1	2	yes	—
11	C₄×C₈×C₁₃	C₂²	1	2	yes	—
12	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#88061	—	2	4	no	—
14	#88058	—	2	4	no	—
15	C₂×D₅₂	—	2	1	no	—
16	C₂×D₅₂	—	2	2	no	—
17	C₂×Dic₂₆	—	2	1	no	—
18	C₂×Dic₂₆	—	2	2	no	—
19	C₂×C₈×C₁₃	D₄	1	4	yes	—
20	C₂×C₈×C₁₃	D₄	1	2	yes	—
21	C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₁₃	—	2	2	no	—
23	C₄⋊Dic₁₃	—	2	2	no	—
24	C₄⋊Dic₁₃	—	2	2	no	—
25	Dic₅₂	—	4	4	no	—
26	#6095	—	4	4	no	—
27	#1722	—	13	1	no	maximal, Sylow
28	C₂²×D₁₃	—	4	1	no	—
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
31	C₂×Dic₁₃	—	4	1	no	—
32	C₂×Dic₁₃	—	4	2	no	—
33	D₅₂	—	4	2	no	—
34	D₅₂	—	4	4	no	—
35	Dic₂₆	—	4	2	no	—
36	Dic₂₆	—	4	4	no	—
37	C₈×C₁₃	—	2	4	no	—
38	C₈×C₁₃	D₈	1	4	yes	—
39	#500	—	13	2	no	—
40	#494	—	13	1	no	—
41	#492	—	13	1	no	—
42	#486	—	13	2	no	—
43	#322	D₁₃	1	1	yes	characteristic, complemented
44	C₂²×C₁₃	#127	1	1	yes	characteristic
45	C₂×D₁₃	—	8	1	no	—
46	C₂×D₁₃	—	8	2	no	—
47	C₄×C₁₃	C₂×D₈	1	2	yes	—
48	C₄×C₁₃	#137	1	4	yes	—
49	Dic₁₃	—	8	1	no	—
50	Dic₁₃	—	8	2	no	—
51	C₂×Q₁₆	—	26	2	no	—
52	C₂×SD₁₆	—	26	2	no	—
53	C₄⋊Q₈	—	13	2	no	—
54	C₄⋊Q₈	—	13	1	no	—
55	#127	—	13	1	no	—
56	#107	—	26	4	no	—
57	#102	—	26	4	no	—
58	C₄×C₈	C₂×D₁₃	1	2	yes	—
59	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
60	C₂×C₁₃	#493	1	1	yes	characteristic
61	C₂×C₁₃	#497	1	2	yes	—
62	D₁₃	—	16	1	no	—
63	C₂×Q₈	—	26	1	no	—
64	C₂×Q₈	—	26	2	no	—
65	C₂×D₄	—	26	2	no	—
66	C₂×D₄	—	26	1	no	—
67	Q₁₆	—	52	4	no	—
68	SD₁₆	—	52	4	no	—
69	C₂×C₈	D₅₂	1	4	yes	—
70	C₂×C₈	D₅₂	1	2	yes	—
71	C₄⋊C₄	—	26	2	no	—
72	C₄⋊C₄	—	26	2	no	—
73	C₄⋊C₄	—	26	2	no	—
74	C₄²	C₂²×D₁₃	1	1	yes	characteristic
75	C₁₃	#1722	1	1	yes	characteristic, complemented, Sylow
76	C₂³	—	52	1	no	—
77	Q₈	—	52	2	no	—
78	Q₈	—	52	4	no	—
79	D₄	—	52	2	no	—
80	D₄	—	52	4	no	—
81	C₂×C₄	—	52	2	no	—
82	C₂×C₄	—	52	1	no	—
83	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
84	C₂×C₄	C₂×D₅₂	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₁₀₄	1	4	yes	—
87	C₂²	—	104	1	no	—
88	C₂²	—	104	2	no	—
89	C₂²	#88128	1	1	yes	characteristic
90	C₄	—	104	1	no	—
91	C₄	—	104	2	no	—
92	C₄	C₂×D₁₀₄	1	2	yes	—
93	C₄	#88163	1	4	yes	—
94	C₂	—	208	1	no	—
95	C₂	#11718356	1	1	yes	characteristic
96	C₂	#11718376	1	2	yes	—

	subgroup	G/H
center	C₂²	#88128
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#322	C₂
socle	C₂²×C₁₃	#127
prime radical	#88128	C₂²
hypercenter	#322	D₁₃
hypocenter	C₁₃	#1722
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #11718360	C₂	semidirect
4. #11718343	C₂	semidirect
5. C₁₃×#322	C₂	semidirect
43. #322	D₁₃	semidirect
75. C₁₃	#1722	semidirect

Maximal subgroups

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

subgroup	index
#11718360	2
#11718355	2
#11718354	2
#11718343	2
C₁₃×#322	2
#1722	13