Subgroups — C₂×C₁₁×#1312 #14588593

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1312	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×C₁₆	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₄×C₁₁×C₁₆	C₄	1	4	yes	—
9	C₄×C₁₁×C₁₆	C₂²	1	4	yes	—
10	C₈²×C₁₁	C₄	1	2	yes	—
11	C₈²×C₁₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₁	C₈	1	2	yes	—
13	C₂²×C₈×C₁₁	C₈	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₁×C₁₆	—	2	8	no	—
17	C₂×C₁₁×C₁₆	C₂×C₄	1	8	yes	—
18	C₄×C₈×C₁₁	C₈	1	2	yes	—
19	C₄×C₈×C₁₁	C₈	1	2	yes	—
20	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
25	C₂×#1312	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈×C₁₁	—	2	4	no	—
30	C₂×C₈×C₁₁	C₁₆	1	8	yes	complemented
31	C₂×C₈×C₁₁	C₄²	1	2	yes	—
32	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₁	M₁₆	1	8	yes	—
35	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
36	C₄²×C₁₁	C₄²	1	1	yes	characteristic
37	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
38	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
39	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₁₁×C₁₆	—	2	8	no	—
41	C₂×C₄×C₁₆	C₂×C₁₁	1	2	yes	—
42	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
43	#1312	C₂×C₁₁	1	4	yes	direct product factor
44	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₁	#97	1	4	yes	—
49	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	—
50	C₂×C₄×C₁₁	M₃₂	1	4	yes	—
51	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₁₁	—	2	4	no	—
55	C₈×C₁₁	#97	1	4	yes	—
56	C₈×C₁₁	C₂×C₁₆	1	8	yes	complemented
57	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
58	C₂²×C₁₆	C₄×C₁₁	1	4	yes	—
59	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
60	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
61	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
62	C₄×C₁₆	C₄×C₁₁	1	4	yes	—
63	C₄×C₁₆	C₂²×C₁₁	1	4	yes	—
64	C₈²	C₄×C₁₁	1	2	yes	—
65	C₈²	C₂²×C₁₁	1	2	yes	—
66	C₂²×C₁₁	#322	1	2	yes	—
67	C₂²×C₁₁	C₄×C₁₆	1	2	yes	—
68	C₂²×C₁₁	#346	1	2	yes	—
69	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
70	C₄×C₁₁	#322	1	2	yes	—
71	C₄×C₁₁	C₄×C₁₆	1	2	yes	—
72	C₄×C₁₁	#346	1	2	yes	—
73	C₄×C₁₁	C₂×#97	1	2	yes	—
74	C₄×C₁₁	C₂²×C₁₆	1	2	yes	—
75	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
76	C₂²×C₈	C₈×C₁₁	1	2	yes	—
77	C₂²×C₈	C₈×C₁₁	1	2	yes	—
78	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
79	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
80	C₂×C₁₆	—	2	8	no	—
81	C₂×C₁₆	C₂×C₄×C₁₁	1	8	yes	—
82	C₄×C₈	C₈×C₁₁	1	2	yes	—
83	C₄×C₈	C₈×C₁₁	1	2	yes	—
84	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
85	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
86	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
87	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
88	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
89	C₂×C₁₁	#1312	1	4	yes	direct product factor
90	C₂×C₁₁	C₂×#322	1	1	yes	characteristic
91	C₂×C₁₁	C₂×C₄×C₁₆	1	1	yes	characteristic
92	C₂×C₁₁	C₂×#346	1	1	yes	characteristic
93	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
94	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
95	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
96	C₂×C₈	—	2	4	no	—
97	C₂×C₈	C₁₁×C₁₆	1	8	yes	complemented
98	C₂×C₈	C₄²×C₁₁	1	2	yes	—
99	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
100	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
101	C₂×C₈	C₁₁×M₁₆	1	8	yes	—
102	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
103	C₄²	C₄²×C₁₁	1	1	yes	characteristic
104	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
105	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
106	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
107	C₁₆	—	2	8	no	—
108	C₁₁	C₂×#1312	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³	C₄×C₈×C₁₁	1	1	yes	characteristic
110	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
111	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
112	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
113	C₂×C₄	C₁₁×#97	1	4	yes	—
114	C₂×C₄	C₂×C₁₁×C₁₆	1	4	yes	—
115	C₂×C₄	C₁₁×M₃₂	1	4	yes	—
116	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
117	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
118	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
119	C₈	—	2	4	no	—
120	C₈	C₁₁×#97	1	4	yes	—
121	C₈	C₂×C₁₁×C₁₆	1	8	yes	complemented
122	C₈	C₂×C₁₁×M₁₆	1	4	yes	—
123	C₂²	C₁₁×#322	1	2	yes	—
124	C₂²	C₄×C₁₁×C₁₆	1	2	yes	—
125	C₂²	C₁₁×#346	1	2	yes	—
126	C₂²	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
127	C₄	C₁₁×#322	1	2	yes	—
128	C₄	C₄×C₁₁×C₁₆	1	2	yes	—
129	C₄	C₁₁×#346	1	2	yes	—
130	C₄	C₂×C₁₁×#97	1	2	yes	—
131	C₄	C₂²×C₁₁×C₁₆	1	2	yes	—
132	C₄	C₂×C₁₁×M₃₂	1	2	yes	—
133	C₂	C₁₁×#1312	1	4	yes	direct product factor
134	C₂	C₂×C₁₁×#322	1	1	yes	characteristic
135	C₂	C₂×C₄×C₁₁×C₁₆	1	1	yes	characteristic
136	C₂	C₂×C₁₁×#346	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈×C₁₁	C₂²
commutator	C₂	C₂×C₄×C₁₁×C₁₆
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1312	C₂	direct (N × H)
25. C₂×#1312	C₁₁	direct (N × H)
30. C₂×C₈×C₁₁	C₁₆	semidirect
43. #1312	C₂×C₁₁	direct (N × H)
56. C₈×C₁₁	C₂×C₁₆	semidirect
89. C₂×C₁₁	#1312	direct (N × H)
97. C₂×C₈	C₁₁×C₁₆	semidirect
108. C₁₁	C₂×#1312	direct (N × H)
121. C₈	C₂×C₁₁×C₁₆	semidirect
133. C₂	C₁₁×#1312	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₁×C₁₆	2
C₂×C₈²×C₁₁	2
C₁₁×#1312	2
C₂×#1312	11

Subgroups — C2×C11×#1312 #14588593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1312 #14588593