Subgroups — #13131803

Order 1664.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88202	C₂	1	1	yes	maximal, characteristic
2	#11719162	C₂	1	8	yes	maximal, complemented
3	C₂×#88106	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
5	#88202	C₄	1	4	yes	—
6	#88202	C₂²	1	4	yes	—
7	C₂×#6099	C₄	1	3	yes	—
8	C₂²×#1055	C₂²	1	3	yes	—
9	#88106	C₂²	1	4	yes	—
10	#88106	C₂²	1	12	yes	complemented
11	C₂×#6092	C₂²	1	12	yes	complemented
12	C₁₃×#41	C₈	1	4	yes	—
13	C₁₃×#41	C₂×C₄	1	4	yes	—
14	C₂×Q₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂×D₄×C₁₃	C₈	1	3	yes	—
16	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
17	#6099	C₂×C₄	1	12	yes	—
18	C₂×#1055	C₂×C₄	1	3	yes	—
19	C₂×#1055	C₂×C₄	1	6	yes	—
20	C₂×#1055	C₂³	1	6	yes	—
21	C₂×#1055	C₂³	1	1	yes	characteristic
22	#6092	C₂³	1	8	yes	—
23	#3407	—	13	1	no	maximal, Sylow
24	C₂³×C₁₃	C₂×C₈	1	3	yes	—
25	Q₈×C₁₃	C₂×C₈	1	4	yes	—
26	D₄×C₁₃	C₂×C₈	1	12	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
28	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂²×C₄	1	6	yes	—
31	#1055	C₂²×C₄	1	1	yes	characteristic
32	#1055	C₂²×C₄	1	6	yes	—
33	#1055	C₂⁴	1	1	yes	characteristic
34	C₂×#131	—	13	1	no	—
35	#504	—	13	8	no	—
36	C₂×M₃₂	—	13	6	no	—
37	C₂²×C₁₃	—	4	3	no	—
38	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
39	C₂²×C₁₃	C₂²×C₈	1	6	yes	—
40	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×C₈	1	6	yes	—
42	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
43	C₂×#41	#261	1	1	yes	characteristic
44	#131	—	13	4	no	—
45	#131	—	13	4	no	—
46	C₂×M₁₆	—	13	3	no	—
47	C₂²×C₈	—	13	3	no	—
48	M₃₂	—	13	4	no	—
49	M₃₂	—	13	12	no	—
50	C₂×C₁₆	—	13	12	no	—
51	C₂×C₁₃	—	2	1	no	—
52	C₂×C₁₃	—	2	6	no	—
53	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
54	#41	#1057	1	4	yes	—
55	#41	C₂×#261	1	4	yes	—
56	C₂×Q₈	#1057	1	1	yes	characteristic
57	C₂×D₄	#1057	1	3	yes	—
58	C₂²×C₄	C₂×#261	1	3	yes	—
59	M₁₆	—	13	12	no	—
60	C₂×C₈	—	13	6	no	—
61	C₂×C₈	—	13	1	no	—
62	C₂×C₈	—	13	3	no	—
63	C₂×C₈	—	13	6	no	—
64	C₁₆	—	13	8	no	—
65	C₁₃	#3407	1	1	yes	characteristic, complemented, Sylow
66	C₂³	C₂×#1057	1	3	yes	—
67	Q₈	C₂×#1057	1	4	yes	—
68	D₄	C₂×#1057	1	12	yes	—
69	C₂×C₄	C₂×#1057	1	3	yes	—
70	C₂×C₄	C₂×#1057	1	6	yes	—
71	C₂×C₄	C₂²×#261	1	1	yes	characteristic
72	C₂×C₄	C₂²×#261	1	6	yes	—
73	C₈	—	13	1	no	—
74	C₈	—	13	1	no	—
75	C₈	—	13	6	no	—
76	C₂²	—	4	3	no	—
77	C₂²	C₂²×#1057	1	1	yes	characteristic
78	C₂²	C₂²×#1057	1	6	yes	—
79	C₄	C₂²×#1057	1	1	yes	characteristic
80	C₄	C₂²×#1057	1	6	yes	—
81	C₄	C₂³×#261	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	2	6	no	—
84	C₂	C₂³×#1057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×#261
commutator, socle	C₂×C₁₃	C₂³×C₈
Fitting, prime radical	C₂×C₁₃×#41	C₄
cosocle	#1055	C₂⁴
hypercenter	C₂×#41	#261
hypocenter	C₁₃	#3407
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #11719162	C₂	semidirect
3. C₂×#88106	C₂	semidirect
10. #88106	C₂²	semidirect
11. C₂×#6092	C₂²	semidirect
65. C₁₃	#3407	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88202	2
#11719162	2
C₂×#88106	2
#3407	13