Subgroups — C₂×C₁₁×#1366 #14589148

Order 2816.

294 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1366	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₁₁×#125	C₄	1	2	yes	—
6	C₂×C₁₁×M₃₂	—	2	1	no	—
7	C₂×C₁₁×M₃₂	—	2	1	no	—
8	C₁₁×#499	—	2	1	no	—
9	C₁₁×#499	—	2	1	no	—
10	C₁₁×#499	C₄	1	2	yes	—
11	C₁₁×#499	C₂²	1	2	yes	—
12	C₂×C₁₁×#107	—	2	1	no	—
13	C₂×C₁₁×#106	—	2	1	no	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#364	—	2	1	no	—
16	C₁₁×#364	—	2	1	no	—
17	C₁₁×#364	C₂²	1	2	yes	—
18	C₁₁×#364	C₂²	1	2	yes	—
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₁₁×#125	—	2	2	no	—
22	C₁₁×#125	—	4	2	no	—
23	C₁₁×#125	C₂×C₄	1	4	yes	—
24	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₁₁×M₃₂	—	2	2	no	—
28	C₁₁×M₃₂	—	2	2	no	—
29	C₁₁×M₃₂	—	4	1	no	—
30	C₁₁×M₃₂	—	4	1	no	—
31	C₂×C₁₁×C₁₆	—	4	1	no	—
32	C₂×C₁₁×C₁₆	—	4	1	no	—
33	C₁₁×#107	—	2	2	no	—
34	C₁₁×#107	—	2	2	no	—
35	C₁₁×#106	—	2	2	no	—
36	C₁₁×#106	—	2	2	no	—
37	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₂×#1366	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₁	—	2	1	no	—
43	C₂²×C₄×C₁₁	—	4	2	no	—
44	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
50	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
52	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
53	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
54	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₁₁×C₄⋊C₄	—	2	4	no	—
58	C₁₁×C₄⋊C₄	—	4	4	no	—
59	C₁₁×C₄⋊C₄	—	4	4	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₄²×C₁₁	—	2	1	no	—
62	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₁₁×C₁₆	—	4	2	no	—
65	C₁₁×C₁₆	—	4	2	no	—
66	C₂×#499	C₂×C₁₁	1	1	yes	characteristic
67	C₂×#364	C₂×C₁₁	1	1	yes	characteristic
68	C₂×#364	C₂×C₁₁	1	1	yes	characteristic
69	#1366	C₂×C₁₁	1	4	yes	direct product factor
70	C₂³×C₁₁	#100	1	1	yes	characteristic
71	C₂×C₄×C₁₁	—	2	1	no	—
72	C₂×C₄×C₁₁	—	2	1	no	—
73	C₂×C₄×C₁₁	—	4	2	no	—
74	C₂×C₄×C₁₁	—	4	4	no	—
75	C₂×C₄×C₁₁	—	8	4	no	—
76	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₈×C₁₁	#103	1	1	yes	characteristic
83	C₈×C₁₁	#103	1	1	yes	characteristic
84	C₈×C₁₁	#103	1	1	yes	characteristic
85	C₈×C₁₁	#103	1	1	yes	characteristic
86	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
87	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
88	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
89	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×#125	C₄×C₁₁	1	2	yes	—
91	C₂×M₃₂	—	2	1	no	—
92	C₂×M₃₂	—	2	1	no	—
93	#499	—	2	1	no	—
94	#499	—	2	1	no	—
95	#499	C₄×C₁₁	1	2	yes	—
96	#499	C₂²×C₁₁	1	2	yes	—
97	C₂×#107	—	2	1	no	—
98	C₂×#106	—	2	1	no	—
99	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
100	#364	—	2	1	no	—
101	#364	—	2	1	no	—
102	#364	C₂²×C₁₁	1	2	yes	—
103	#364	C₂²×C₁₁	1	2	yes	—
104	C₂²×C₁₁	—	2	2	no	—
105	C₂²×C₁₁	#333	1	1	yes	characteristic
106	C₂²×C₁₁	#333	1	1	yes	characteristic
107	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
108	C₄×C₁₁	—	4	1	no	—
109	C₄×C₁₁	—	4	1	no	—
110	C₄×C₁₁	—	8	4	no	—
111	C₄×C₁₁	#333	1	1	yes	characteristic
112	C₄×C₁₁	#333	1	1	yes	characteristic
113	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
114	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
115	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
116	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
117	#125	—	2	2	no	—
118	#125	—	4	2	no	—
119	#125	C₂×C₄×C₁₁	1	4	yes	—
120	C₂×C₄⋊C₄	—	2	2	no	—
121	C₂×C₄⋊C₄	—	4	2	no	—
122	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
123	M₃₂	—	2	2	no	—
124	M₃₂	—	2	2	no	—
125	M₃₂	—	4	1	no	—
126	M₃₂	—	4	1	no	—
127	C₂×C₁₆	—	4	1	no	—
128	C₂×C₁₆	—	4	1	no	—
129	#107	—	2	2	no	—
130	#107	—	2	2	no	—
131	#106	—	2	2	no	—
132	#106	—	2	2	no	—
133	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
134	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
135	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
136	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
137	C₂×C₁₁	—	2	1	no	—
138	C₂×C₁₁	—	2	1	no	—
139	C₂×C₁₁	#1366	1	2	yes	direct product factor
140	C₂×C₁₁	C₂×#333	1	1	yes	characteristic
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	4	2	no	—
143	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₈	C₁₁×SD₁₆	1	1	yes	characteristic
147	C₂×C₈	C₁₁×SD₁₆	1	1	yes	characteristic
148	C₂×C₈	C₁₁×SD₁₆	1	1	yes	characteristic
149	C₂×C₈	C₁₁×SD₁₆	1	1	yes	characteristic
150	C₂×C₈	C₁₁×Q₁₆	1	1	yes	characteristic
151	C₂×C₈	C₁₁×Q₁₆	1	1	yes	characteristic
152	C₂×C₈	C₁₁×Q₁₆	1	1	yes	characteristic
153	C₂×C₈	C₁₁×Q₁₆	1	1	yes	characteristic
154	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
155	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
162	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
163	C₁₆	—	4	2	no	—
164	C₁₆	—	4	2	no	—
165	C₁₁	C₂×#1366	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	C₁₁×#100	1	1	yes	characteristic
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	8	4	no	—
172	C₂×C₄	C₁₁×#100	1	1	yes	characteristic
173	C₂×C₄	C₁₁×#103	1	1	yes	characteristic
174	C₂×C₄	C₁₁×#103	1	1	yes	characteristic
175	C₂×C₄	C₁₁×#103	1	1	yes	characteristic
176	C₂×C₄	C₁₁×#103	1	1	yes	characteristic
177	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
178	C₈	C₁₁×#103	1	1	yes	characteristic
179	C₈	C₁₁×#103	1	1	yes	characteristic
180	C₈	C₁₁×#103	1	1	yes	characteristic
181	C₈	C₁₁×#103	1	1	yes	characteristic
182	C₈	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
183	C₈	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
184	C₈	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
185	C₈	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
186	C₂²	—	2	2	no	—
187	C₂²	C₁₁×#333	1	1	yes	characteristic
188	C₂²	C₁₁×#333	1	1	yes	characteristic
189	C₂²	C₂×C₁₁×#100	1	1	yes	characteristic
190	C₄	—	4	1	no	—
191	C₄	—	4	1	no	—
192	C₄	—	8	4	no	—
193	C₄	C₁₁×#333	1	1	yes	characteristic
194	C₄	C₁₁×#333	1	1	yes	characteristic
195	C₄	C₂×C₁₁×#103	1	1	yes	characteristic
196	C₄	C₂×C₁₁×#103	1	1	yes	characteristic
197	C₂	—	2	1	no	—
198	C₂	—	2	1	no	—
199	C₂	C₁₁×#1366	1	2	yes	direct product factor
200	C₂	C₂×C₁₁×#333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	#333
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1366	C₂	direct (N × H)
41. C₂×#1366	C₁₁	direct (N × H)
69. #1366	C₂×C₁₁	direct (N × H)
139. C₂×C₁₁	#1366	direct (N × H)
165. C₁₁	C₂×#1366	direct (N × H)
199. C₂	C₁₁×#1366	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×#499	2
C₂×C₁₁×#364	2
C₁₁×#1366	2
C₂×#1366	11

Subgroups — C2×C11×#1366 #14589148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1366 #14589148