Subgroups — C₂×#13077011 #14959867

Order 2816.

8094 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66927	C₂	1	14	yes	maximal, complemented
2	#13077011	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄₄	C₂²	1	28	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	7	yes	—
6	C₂×#66927	—	2	112	no	—
7	C₂×#66927	C₂²	1	112	yes	complemented
8	C₄³×C₁₁	C₂²	1	8	yes	complemented
9	C₂⁴×D₁₁	C₂³	1	8	yes	—
10	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
11	C₂²×D₄₄	—	2	336	no	—
12	C₂²×D₄₄	C₂³	1	112	yes	—
13	C₂×C₄²×C₁₁	D₄	1	56	yes	complemented
14	C₂×C₄²×C₁₁	C₂³	1	28	yes	—
15	#66927	—	2	448	no	—
16	C₂×#2867	—	11	1	no	maximal, Sylow
17	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
18	C₂³×D₁₁	—	2	112	no	—
19	C₂³×D₁₁	C₂⁴	1	16	yes	—
20	C₂²×C₄×C₁₁	C₂×D₄	1	84	yes	—
21	C₂²×C₄×C₁₁	C₂⁴	1	14	yes	—
22	C₂×D₄₄	—	2	672	no	—
23	C₂×D₄₄	—	4	448	no	—
24	C₄²×C₁₁	C₂×D₄	1	112	yes	complemented
25	C₂²×#127	—	11	14	no	—
26	#2867	—	11	16	no	—
27	C₂×C₄³	D₁₁	1	1	yes	characteristic, complemented
28	C₂³×C₁₁	C₂²×D₄	1	14	yes	—
29	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
30	C₂²×D₁₁	—	2	112	no	—
31	C₂²×D₁₁	—	4	224	no	—
32	C₂×C₄×C₁₁	#127	1	112	yes	complemented
33	C₂×C₄×C₁₁	C₂²×D₄	1	84	yes	—
34	D₄₄	—	4	448	no	—
35	C₂³×D₄	—	11	28	no	—
36	C₂×#127	—	11	112	no	—
37	C₂×#127	—	22	112	no	—
38	C₂²×C₄²	C₂×D₁₁	1	7	yes	—
39	C₄³	C₂×D₁₁	1	8	yes	complemented
40	C₂²×C₁₁	C₂×#127	1	28	yes	—
41	C₂²×C₁₁	C₂³×D₄	1	7	yes	—
42	C₂×D₁₁	—	4	112	no	—
43	C₂×D₁₁	—	8	64	no	—
44	C₄×C₁₁	C₂×#127	1	56	yes	complemented
45	C₂⁵	—	11	8	no	—
46	C₂²×D₄	—	11	112	no	—
47	C₂²×D₄	—	22	336	no	—
48	C₂³×C₄	C₂²×D₁₁	1	7	yes	—
49	#127	—	22	448	no	—
50	C₂×C₄²	D₄₄	1	56	yes	complemented
51	C₂×C₄²	C₂²×D₁₁	1	28	yes	—
52	C₂×C₁₁	#2867	1	8	yes	complemented
53	C₂×C₁₁	C₂²×#127	1	7	yes	—
54	D₁₁	—	8	16	no	—
55	C₂⁴	—	11	16	no	—
56	C₂⁴	—	22	112	no	—
57	C₂⁴	C₂³×D₁₁	1	1	yes	characteristic
58	C₂×D₄	—	22	672	no	—
59	C₂×D₄	—	44	448	no	—
60	C₂²×C₄	C₂×D₄₄	1	84	yes	—
61	C₂²×C₄	C₂³×D₁₁	1	14	yes	—
62	C₄²	C₂×D₄₄	1	112	yes	complemented
63	C₁₁	C₂×#2867	1	1	yes	characteristic, complemented, Sylow
64	C₂³	—	22	112	no	—
65	C₂³	—	44	224	no	—
66	C₂³	C₂²×D₄₄	1	14	yes	—
67	C₂³	C₂⁴×D₁₁	1	1	yes	characteristic
68	D₄	—	44	448	no	—
69	C₂×C₄	#66927	1	112	yes	complemented
70	C₂×C₄	C₂²×D₄₄	1	84	yes	—
71	C₂²	—	44	112	no	—
72	C₂²	—	88	64	no	—
73	C₂²	C₂×#66927	1	28	yes	—
74	C₂²	C₂³×D₄₄	1	7	yes	—
75	C₄	C₂×#66927	1	56	yes	complemented
76	C₂	—	88	16	no	—
77	C₂	#13077011	1	8	yes	direct product factor
78	C₂	C₂²×#66927	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₁
commutator, cosocle	C₂³×C₁₁	C₂⁵
Frattini	C₂³	C₂⁴×D₁₁
Fitting	C₂×C₄³×C₁₁	C₂
socle	C₂⁴×C₁₁	C₂⁴
hypercenter	C₂×C₄³	D₁₁
hypocenter	C₁₁	C₂×#2867
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
1. C₂²×#66927	C₂	semidirect
2. #13077011	C₂	direct (N × H)
3. C₂×C₄³×C₁₁	C₂	semidirect
7. C₂×#66927	C₂²	semidirect
8. C₄³×C₁₁	C₂²	semidirect
13. C₂×C₄²×C₁₁	D₄	semidirect
24. C₄²×C₁₁	C₂×D₄	semidirect
27. C₂×C₄³	D₁₁	semidirect
32. C₂×C₄×C₁₁	#127	semidirect
39. C₄³	C₂×D₁₁	semidirect
44. C₄×C₁₁	C₂×#127	semidirect
50. C₂×C₄²	D₄₄	semidirect
52. C₂×C₁₁	#2867	semidirect
62. C₄²	C₂×D₄₄	semidirect
63. C₁₁	C₂×#2867	semidirect
69. C₂×C₄	#66927	semidirect
75. C₄	C₂×#66927	semidirect
77. C₂	#13077011	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66927	2
#13077011	2
C₂×C₄³×C₁₁	2
C₂×#2867	11

Subgroups — C2×#13077011 #14959867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13077011 #14959867