Subgroups — C₂²×#88052 #13127932

Order 1664.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#88052	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#6090	C₂	1	2	yes	maximal, complemented
4	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₃	C₄	1	6	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	6	yes	—
8	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	#88052	C₂²	1	16	yes	direct product factor
10	C₂×#6090	C₂²	1	12	yes	complemented
11	C₂⁴×C₁₃	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₁₃	C₈	1	6	yes	—
13	C₂²×C₄×C₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₁₃	C₂×C₄	1	6	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂×C₄	1	12	yes	—
17	C₂×C₈×C₁₃	C₂×C₄	1	6	yes	—
18	C₂×C₈×C₁₃	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₁₃	C₂³	1	3	yes	—
20	C₂×C₈×C₁₃	C₂³	1	4	yes	—
21	#6090	C₂³	1	8	yes	complemented
22	C₂²×M₃₂	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	—	2	4	no	—
24	C₂³×C₁₃	C₂×C₈	1	6	yes	—
25	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	12	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₁₃	C₂×C₈	1	3	yes	—
29	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
31	C₈×C₁₃	C₂²×C₄	1	3	yes	—
32	C₈×C₁₃	C₂²×C₄	1	4	yes	—
33	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
34	C₂³×C₈	D₁₃	1	1	yes	characteristic
35	C₂×M₃₂	—	13	12	no	—
36	C₂²×C₁₆	—	13	2	no	—
37	C₂²×C₁₃	—	2	12	no	—
38	C₂²×C₁₃	M₃₂	1	4	yes	complemented
39	C₂²×C₁₃	C₂²×C₈	1	4	yes	—
40	C₂²×C₁₃	C₂²×C₈	1	3	yes	—
41	C₄×C₁₃	C₂²×C₈	1	3	yes	—
42	C₄×C₁₃	C₂²×C₈	1	4	yes	—
43	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
44	C₂³×C₄	Dic₁₃	1	1	yes	characteristic
45	C₂²×C₈	Dic₁₃	1	1	yes	characteristic
46	C₂²×C₈	Dic₁₃	1	6	yes	—
47	C₂²×C₈	C₂×D₁₃	1	6	yes	—
48	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
49	M₃₂	—	13	16	no	—
50	C₂×C₁₆	—	13	12	no	—
51	C₂×C₁₃	—	2	4	no	—
52	C₂×C₁₃	C₂×M₃₂	1	6	yes	complemented
53	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
54	C₂⁴	#1055	1	1	yes	characteristic
55	C₂²×C₄	#1055	1	6	yes	—
56	C₂²×C₄	#1055	1	1	yes	characteristic
57	C₂²×C₄	C₂×Dic₁₃	1	6	yes	—
58	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
59	C₂×C₈	C₂×Dic₁₃	1	6	yes	—
60	C₂×C₈	C₂×Dic₁₃	1	12	yes	—
61	C₂×C₈	C₂×Dic₁₃	1	3	yes	—
62	C₂×C₈	C₂²×D₁₃	1	3	yes	—
63	C₂×C₈	C₂²×D₁₃	1	4	yes	—
64	C₁₆	—	13	8	no	—
65	C₁₃	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	2	4	no	—
67	C₂³	C₂×#1055	1	6	yes	—
68	C₂³	C₂×#1055	1	1	yes	characteristic
69	C₂×C₄	C₂×#1055	1	12	yes	—
70	C₂×C₄	C₂×#1055	1	6	yes	—
71	C₂×C₄	C₂×#1055	1	3	yes	—
72	C₂×C₄	C₂²×Dic₁₃	1	4	yes	—
73	C₂×C₄	C₂²×Dic₁₃	1	3	yes	—
74	C₈	C₂²×Dic₁₃	1	4	yes	—
75	C₈	C₂²×Dic₁₃	1	3	yes	—
76	C₈	C₂³×D₁₃	1	1	yes	characteristic
77	C₂²	—	2	12	no	—
78	C₂²	#88052	1	4	yes	direct product factor
79	C₂²	C₂²×#1055	1	4	yes	—
80	C₂²	C₂²×#1055	1	3	yes	—
81	C₄	C₂²×#1055	1	3	yes	—
82	C₄	C₂²×#1055	1	4	yes	—
83	C₄	C₂³×Dic₁₃	1	1	yes	characteristic
84	C₂	—	2	4	no	—
85	C₂	C₂×#88052	1	6	yes	direct product factor
86	C₂	C₂³×#1055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₈	C₂³×D₁₃
Fitting	C₂³×C₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂×C₈
prime radical	C₂⁴×C₁₃	C₈
cosocle	C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₈	D₁₃
hypocenter	C₁₃	C₂²×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#88052	C₂	direct (N × H)
3. C₂²×#6090	C₂	semidirect
9. #88052	C₂²	direct (N × H)
10. C₂×#6090	C₂²	semidirect
21. #6090	C₂³	semidirect
38. C₂²×C₁₃	M₃₂	semidirect
52. C₂×C₁₃	C₂×M₃₂	semidirect
65. C₁₃	C₂²×M₃₂	semidirect
78. C₂²	#88052	direct (N × H)
85. C₂	C₂×#88052	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈×C₁₃	2
C₂×#88052	2
C₂²×#6090	2
C₂²×M₃₂	13

Subgroups — C22×#88052 #13127932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88052 #13127932