Subgroups — C₂×C₁₁×#1313 #14588596

Order 2816.

302 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×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1313	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
6	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#346	C₄	1	2	yes	—
10	C₁₁×#346	C₄	1	2	yes	—
11	C₁₁×#346	C₂²	1	2	yes	—
12	C₁₁×#346	C₂²	1	2	yes	—
13	C₁₁×#322	C₄	1	2	yes	—
14	C₁₁×#322	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₁	—	2	2	no	—
16	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₁×C₁₆	—	2	4	no	—
20	C₂×C₁₁×C₁₆	C₈	1	8	yes	complemented
21	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
22	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
23	C₄×C₈×C₁₁	—	2	2	no	—
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₂×#1313	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
32	C₂×C₈×C₁₁	—	2	4	no	—
33	C₂×C₈×C₁₁	—	4	4	no	—
34	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
37	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
38	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₁	C₄²	1	1	yes	characteristic
41	C₄²×C₁₁	M₁₆	1	2	yes	—
42	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₁₁×C₁₆	—	2	4	no	—
44	C₁₁×C₁₆	C₂×C₈	1	8	yes	complemented
45	C₂×#346	C₂×C₁₁	1	1	yes	characteristic
46	C₂×#346	C₂×C₁₁	1	1	yes	characteristic
47	C₂×#322	C₂×C₁₁	1	1	yes	characteristic
48	#1313	C₂×C₁₁	1	4	yes	direct product factor
49	C₂³×C₁₁	#97	1	1	yes	characteristic
50	C₂×C₄×C₁₁	—	2	4	no	—
51	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
52	C₂×C₄×C₁₁	#97	1	2	yes	—
53	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
54	C₂×C₄×C₁₁	#97	1	2	yes	—
55	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
57	C₈×C₁₁	—	4	4	no	—
58	C₈×C₁₁	C₄×C₈	1	2	yes	—
59	C₈×C₁₁	#97	1	2	yes	—
60	C₈×C₁₁	C₂²×C₈	1	2	yes	—
61	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
62	C₂²×C₁₆	C₄×C₁₁	1	2	yes	—
63	C₂²×C₁₆	C₄×C₁₁	1	2	yes	—
64	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
65	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
66	#346	C₄×C₁₁	1	2	yes	—
67	#346	C₄×C₁₁	1	2	yes	—
68	#346	C₂²×C₁₁	1	2	yes	—
69	#346	C₂²×C₁₁	1	2	yes	—
70	#322	C₄×C₁₁	1	2	yes	—
71	#322	C₂²×C₁₁	1	2	yes	—
72	C₂²×C₁₁	#322	1	2	yes	—
73	C₂²×C₁₁	#347	1	4	yes	—
74	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
75	C₄×C₁₁	—	2	2	no	—
76	C₄×C₁₁	—	2	2	no	—
77	C₄×C₁₁	#322	1	2	yes	—
78	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
79	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
80	C₂²×C₈	—	2	2	no	—
81	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
82	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
83	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
84	C₂×C₁₆	—	2	4	no	—
85	C₂×C₁₆	C₈×C₁₁	1	8	yes	complemented
86	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
87	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
88	C₄×C₈	—	2	2	no	—
89	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
90	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
91	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
92	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
93	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
94	C₂×C₁₁	#1313	1	4	yes	direct product factor
95	C₂×C₁₁	C₂×#322	1	1	yes	characteristic
96	C₂×C₁₁	C₂×#347	1	2	yes	—
97	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
98	C₂²×C₄	C₁₁×M₁₆	1	2	yes	—
99	C₂×C₈	—	2	4	no	—
100	C₂×C₈	—	4	4	no	—
101	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
102	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
103	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
104	C₂×C₈	C₁₁×M₁₆	1	4	yes	—
105	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
106	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
107	C₄²	C₄²×C₁₁	1	1	yes	characteristic
108	C₄²	C₁₁×M₁₆	1	2	yes	—
109	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
110	C₁₆	—	2	4	no	—
111	C₁₆	C₂×C₈×C₁₁	1	8	yes	complemented
112	C₁₁	C₂×#1313	1	1	yes	characteristic, direct product factor, Sylow
113	C₂³	C₁₁×#97	1	1	yes	characteristic
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	C₄×C₈×C₁₁	1	2	yes	—
116	C₂×C₄	C₁₁×#97	1	2	yes	—
117	C₂×C₄	C₁₁×#97	1	2	yes	—
118	C₂×C₄	C₁₁×#97	1	1	yes	characteristic
119	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
120	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
121	C₈	—	4	4	no	—
122	C₈	C₄×C₈×C₁₁	1	2	yes	—
123	C₈	C₁₁×#97	1	2	yes	—
124	C₈	C₂²×C₈×C₁₁	1	2	yes	—
125	C₈	C₂×C₁₁×M₁₆	1	2	yes	—
126	C₂²	C₁₁×#322	1	2	yes	—
127	C₂²	C₁₁×#347	1	4	yes	—
128	C₂²	C₂×C₁₁×#97	1	1	yes	characteristic
129	C₄	—	2	2	no	—
130	C₄	—	2	2	no	—
131	C₄	C₁₁×#322	1	2	yes	—
132	C₄	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
133	C₄	C₂×C₁₁×#97	1	1	yes	characteristic
134	C₂	C₁₁×#1313	1	4	yes	direct product factor
135	C₂	C₂×C₁₁×#322	1	1	yes	characteristic
136	C₂	C₂×C₁₁×#347	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	#97
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1313	C₂	direct (N × H)
20. C₂×C₁₁×C₁₆	C₈	semidirect
29. C₂×#1313	C₁₁	direct (N × H)
44. C₁₁×C₁₆	C₂×C₈	semidirect
48. #1313	C₂×C₁₁	direct (N × H)
85. C₂×C₁₆	C₈×C₁₁	semidirect
94. C₂×C₁₁	#1313	direct (N × H)
111. C₁₆	C₂×C₈×C₁₁	semidirect
112. C₁₁	C₂×#1313	direct (N × H)
134. C₂	C₁₁×#1313	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×C₁₁×#346	2
C₂×C₁₁×#322	2
C₁₁×#1313	2
C₂×#1313	11

Subgroups — C2×C11×#1313 #14588596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1313 #14588596