Subgroups — C₂³×#6106 #13129554

Order 1664.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₅₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6106	C₂	1	28	yes	maximal, direct product factor
4	C₂³×#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₁₃	—	2	1	no	—
6	C₂²×Q₈×C₁₃	—	2	7	no	—
7	C₂²×Q₈×C₁₃	C₂²	1	14	yes	complemented
8	C₂³×C₄×C₁₃	—	2	1	no	—
9	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×D₅₂	—	2	7	no	—
11	C₂²×D₅₂	C₂²	1	14	yes	—
12	C₂×#6106	C₂²	1	112	yes	direct product factor
13	C₂²×#1055	C₂²	1	14	yes	complemented
14	C₂⁴×C₁₃	D₄	1	1	yes	characteristic
15	C₂³×D₁₃	—	2	14	no	—
16	C₂³×D₁₃	—	4	8	no	—
17	C₂×Q₈×C₁₃	—	2	42	no	—
18	C₂×Q₈×C₁₃	C₂³	1	28	yes	complemented
19	C₂²×C₄×C₁₃	—	2	14	no	—
20	C₂²×C₄×C₁₃	D₄	1	7	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
22	C₂×D₅₂	—	2	42	no	—
23	C₂×D₅₂	C₂³	1	28	yes	—
24	#6106	C₂³	1	64	yes	direct product factor
25	C₂×#1055	C₂³	1	28	yes	complemented
26	C₂³×SD₁₆	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	SD₁₆	1	8	yes	complemented
28	C₂³×C₁₃	C₂×D₄	1	7	yes	—
29	C₂²×D₁₃	—	2	28	no	—
30	C₂²×D₁₃	—	4	56	no	—
31	Q₈×C₁₃	—	2	28	no	—
32	Q₈×C₁₃	C₂⁴	1	8	yes	complemented
33	C₂×C₄×C₁₃	—	2	28	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	21	yes	—
35	C₂×C₄×C₁₃	C₂⁴	1	7	yes	—
36	D₅₂	—	2	28	no	—
37	D₅₂	C₂⁴	1	8	yes	—
38	#1055	C₂⁴	1	8	yes	complemented
39	C₂³×Q₈	D₁₃	1	1	yes	characteristic, complemented
40	C₂³×D₄	—	13	1	no	—
41	C₂²×SD₁₆	—	13	28	no	—
42	C₂³×C₈	—	13	1	no	—
43	C₂²×C₁₃	C₂×SD₁₆	1	28	yes	complemented
44	C₂²×C₁₃	C₂²×D₄	1	7	yes	—
45	C₂×D₁₃	—	2	8	no	—
46	C₂×D₁₃	—	4	56	no	—
47	C₄×C₁₃	—	2	8	no	—
48	C₄×C₁₃	C₂²×D₄	1	7	yes	—
49	C₄×C₁₃	C₂⁵	1	1	yes	characteristic
50	C₂⁵	—	26	1	no	—
51	C₂²×Q₈	—	2	7	no	—
52	C₂²×Q₈	C₂×D₁₃	1	14	yes	complemented
53	C₂²×D₄	—	13	14	no	—
54	C₂²×D₄	—	26	7	no	—
55	C₂³×C₄	—	2	1	no	—
56	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
57	C₂×SD₁₆	—	13	112	no	—
58	C₂²×C₈	—	13	14	no	—
59	C₂×C₁₃	C₂²×SD₁₆	1	14	yes	complemented
60	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
61	D₁₃	—	4	8	no	—
62	C₂⁴	—	26	14	no	—
63	C₂⁴	—	52	8	no	—
64	C₂⁴	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₂×Q₈	—	2	42	no	—
66	C₂×Q₈	C₂²×D₁₃	1	28	yes	complemented
67	C₂×D₄	—	13	28	no	—
68	C₂×D₄	—	26	42	no	—
69	C₂²×C₄	—	2	14	no	—
70	C₂²×C₄	C₂²⋊D₁₃	1	7	yes	—
71	C₂²×C₄	C₂²×D₁₃	1	7	yes	—
72	SD₁₆	—	13	64	no	—
73	C₂×C₈	—	13	28	no	—
74	C₁₃	C₂³×SD₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₂³	—	26	28	no	—
76	C₂³	—	52	56	no	—
77	C₂³	#6106	1	8	yes	direct product factor
78	C₂³	C₂×C₂²⋊D₁₃	1	7	yes	—
79	Q₈	—	2	28	no	—
80	Q₈	C₂³×D₁₃	1	8	yes	complemented
81	D₄	—	13	8	no	—
82	D₄	—	26	28	no	—
83	C₂×C₄	—	2	28	no	—
84	C₂×C₄	C₂×C₂²⋊D₁₃	1	21	yes	—
85	C₂×C₄	C₂³×D₁₃	1	7	yes	—
86	C₈	—	13	8	no	—
87	C₂²	—	26	8	no	—
88	C₂²	—	52	56	no	—
89	C₂²	C₂×#6106	1	28	yes	direct product factor
90	C₂²	C₂²×C₂²⋊D₁₃	1	7	yes	—
91	C₄	—	2	8	no	—
92	C₄	C₂²×C₂²⋊D₁₃	1	7	yes	—
93	C₄	C₂⁴×D₁₃	1	1	yes	characteristic
94	C₂	—	52	8	no	—
95	C₂	C₂²×#6106	1	14	yes	direct product factor
96	C₂	C₂³×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁵
Frattini	C₄	C₂⁴×D₁₃
Fitting	C₂³×Q₈×C₁₃	C₂
socle	C₂⁴×C₁₃	D₄
prime radical	C₂³×D₅₂	C₂
hypercenter	C₂³×Q₈	D₁₃
hypocenter	C₁₃	C₂³×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×C₁₃	C₂	semidirect
3. C₂²×#6106	C₂	direct (N × H)
4. C₂³×#1055	C₂	semidirect
7. C₂²×Q₈×C₁₃	C₂²	semidirect
12. C₂×#6106	C₂²	direct (N × H)
13. C₂²×#1055	C₂²	semidirect
18. C₂×Q₈×C₁₃	C₂³	semidirect
24. #6106	C₂³	direct (N × H)
25. C₂×#1055	C₂³	semidirect
27. C₂³×C₁₃	SD₁₆	semidirect
32. Q₈×C₁₃	C₂⁴	semidirect
38. #1055	C₂⁴	semidirect
39. C₂³×Q₈	D₁₃	semidirect
43. C₂²×C₁₃	C₂×SD₁₆	semidirect
52. C₂²×Q₈	C₂×D₁₃	semidirect
59. C₂×C₁₃	C₂²×SD₁₆	semidirect
66. C₂×Q₈	C₂²×D₁₃	semidirect
74. C₁₃	C₂³×SD₁₆	semidirect
77. C₂³	#6106	direct (N × H)
80. Q₈	C₂³×D₁₃	semidirect
89. C₂²	C₂×#6106	direct (N × H)
95. C₂	C₂²×#6106	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×Q₈×C₁₃	2
C₂³×D₅₂	2
C₂²×#6106	2
C₂³×#1055	2
C₂³×SD₁₆	13

Subgroups — C23×#6106 #13129554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6106 #13129554