Subgroups — #13130770

Order 1664.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88112	C₂	1	3	yes	maximal
2	C₂×C₄⋊#1057	C₂	1	3	yes	maximal
3	#11718309	C₂	1	1	yes	maximal, characteristic
4	C₂²×#1057	C₂²	1	3	yes	—
5	C₂²×#1057	C₂²	1	1	yes	characteristic
6	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
7	#88112	—	2	6	no	—
8	C₄⋊#1057	—	2	6	no	—
9	C₁₃×#95	C₄	1	1	yes	characteristic
10	#88071	C₄	1	3	yes	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
12	C₂²×Dic₁₃	C₂×C₄	1	3	yes	—
13	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
14	C₂×#1057	—	2	6	no	—
15	C₂×#1057	—	2	3	no	—
16	C₂×#1057	—	2	3	no	—
17	C₄×Dic₁₃	D₄	1	6	yes	—
18	C₄×Dic₁₃	Q₈	1	6	yes	—
19	#1843	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₃	—	2	6	no	—
22	C₂×C₄×C₁₃	C₄⋊C₄	1	6	yes	—
23	C₂×Dic₁₃	—	2	3	no	—
24	C₂×Dic₁₃	—	2	3	no	—
25	C₂×Dic₁₃	C₄⋊C₄	1	6	yes	—
26	C₂×Dic₁₃	C₂×D₄	1	3	yes	—
27	C₂×Dic₁₃	C₂×Q₈	1	3	yes	—
28	#1057	—	4	3	no	—
29	#1057	—	4	1	no	—
30	C₂×C₄⋊C₈	—	13	3	no	—
31	C₂×C₄⋊C₈	—	13	3	no	—
32	#376	—	13	1	no	—
33	C₂²×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
34	C₂²×C₁₃	#131	1	3	yes	—
35	C₂²×C₁₃	#131	1	1	yes	characteristic
36	C₄×C₁₃	—	2	6	no	—
37	Dic₁₃	—	2	6	no	—
38	Dic₁₃	#127	1	1	yes	characteristic
39	Dic₁₃	C₄⋊Q₈	1	3	yes	—
40	C₂²×C₈	—	13	3	no	—
41	C₂²×C₈	—	13	1	no	—
42	C₂×C₄²	—	13	3	no	—
43	C₄⋊C₈	—	26	6	no	—
44	C₄⋊C₈	—	26	6	no	—
45	#95	—	13	3	no	—
46	#95	#261	1	1	yes	characteristic
47	C₂×C₁₃	#384	1	1	yes	characteristic
48	C₂×C₁₃	#424	1	3	yes	—
49	C₂×C₁₃	#424	1	3	yes	—
50	C₂²×C₄	—	13	1	no	—
51	C₂²×C₄	—	13	3	no	—
52	C₂²×C₄	C₂×#261	1	3	yes	—
53	C₂×C₈	—	26	6	no	—
54	C₂×C₈	—	26	3	no	—
55	C₂×C₈	—	26	3	no	—
56	C₄²	—	13	6	no	—
57	C₄²	—	13	6	no	—
58	C₁₃	#1843	1	1	yes	characteristic, complemented, Sylow
59	C₂³	C₂²×#261	1	1	yes	characteristic
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	13	3	no	—
62	C₂×C₄	—	13	3	no	—
63	C₂×C₄	—	13	6	no	—
64	C₂×C₄	—	26	3	no	—
65	C₂×C₄	—	26	3	no	—
66	C₂×C₄	C₄⋊#261	1	6	yes	—
67	C₈	—	52	3	no	—
68	C₈	—	52	1	no	—
69	C₂²	C₂×C₄⋊#261	1	3	yes	—
70	C₂²	#88238	1	3	yes	—
71	C₂²	#88240	1	1	yes	characteristic
72	C₄	—	2	6	no	—
73	C₄	—	13	1	no	—
74	C₄	—	13	3	no	—
75	C₄	—	26	6	no	—
76	C₂	#11719059	1	1	yes	characteristic
77	C₂	#11719067	1	3	yes	—
78	C₂	#11719079	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#95	C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	#95	#261
hypocenter	C₁₃	#1843
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
58. C₁₃	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88112	2
C₂×C₄⋊#1057	2
#11718309	2
#1843	13