Subgroups — C₁₁×#23201 #14600394

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	4	yes	maximal, complemented
3	C₁₁×#1978	C₂	1	4	yes	maximal, complemented
4	C₁₁×#1887	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1772	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₁×D₈	C₂²	1	4	yes	—
7	C₂×C₁₁×#127	C₂²	1	2	yes	—
8	C₁₁×#518	C₂²	1	4	yes	—
9	C₁₁×#493	C₄	1	8	yes	complemented
10	C₁₁×#442	—	2	8	no	—
11	C₄×C₁₁×D₈	—	2	8	no	—
12	C₂×C₁₁×#108	C₂²	1	2	yes	—
13	C₁₁×#427	C₂²	1	2	yes	—
14	C₁₁×#418	C₂²	1	8	yes	—
15	C₂×C₁₁×#100	C₂²	1	4	yes	—
16	C₁₁×#405	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#339	C₂²	1	4	yes	—
19	C₂²×D₄×C₁₁	—	4	2	no	—
20	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
21	C₂×C₁₁×D₈	—	2	4	no	—
22	C₂×C₁₁×D₈	—	2	4	no	—
23	C₂×C₁₁×D₈	—	2	8	no	—
24	C₂×C₁₁×D₈	C₂×C₄	1	16	yes	complemented
25	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₁₁×#127	—	4	2	no	—
28	C₁₁×#127	C₂×C₄	1	8	yes	complemented
29	C₄×D₄×C₁₁	—	2	16	no	—
30	C₁₁×#117	C₂³	1	4	yes	—
31	C₂×C₁₁×C₂²⋊C₄	—	4	4	no	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×#108	—	2	4	no	—
34	C₁₁×#107	D₄	1	4	yes	complemented
35	C₁₁×#106	D₄	1	4	yes	complemented
36	C₁₁×#102	—	2	16	no	—
37	C₁₁×#100	—	4	4	no	—
38	C₁₁×#97	—	2	4	no	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
41	#23201	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₁	—	2	4	no	—
43	C₂×D₄×C₁₁	—	2	8	no	—
44	C₂×D₄×C₁₁	—	2	8	no	—
45	C₂×D₄×C₁₁	—	2	4	no	—
46	C₂×D₄×C₁₁	—	4	8	no	—
47	C₂×D₄×C₁₁	—	8	8	no	—
48	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
49	C₂²×C₄×C₁₁	—	2	1	no	—
50	C₂²×C₄×C₁₁	—	4	8	no	—
51	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
52	C₁₁×D₈	—	2	16	no	—
53	C₁₁×D₈	—	2	16	no	—
54	C₁₁×M₁₆	—	2	4	no	—
55	C₁₁×M₁₆	—	2	4	no	—
56	C₂×C₈×C₁₁	—	2	4	no	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
58	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₁	#41	1	4	yes	—
61	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
62	C₁₁×C₂²⋊C₄	—	2	4	no	—
63	C₁₁×C₂²⋊C₄	—	4	8	no	—
64	C₄²×C₁₁	—	2	4	no	—
65	C₄²×C₁₁	—	2	1	no	—
66	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
68	#2948	C₂×C₁₁	1	4	yes	complemented
69	#1978	C₂×C₁₁	1	4	yes	complemented
70	#1887	C₂×C₁₁	1	4	yes	complemented
71	#1772	C₂×C₁₁	1	2	yes	complemented
72	C₂³×C₁₁	—	2	8	no	—
73	C₂³×C₁₁	—	4	4	no	—
74	C₂³×C₁₁	—	4	4	no	—
75	C₂³×C₁₁	—	8	8	no	—
76	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
77	D₄×C₁₁	—	2	16	no	—
78	D₄×C₁₁	—	4	8	no	—
79	D₄×C₁₁	—	8	16	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	8	no	—
83	C₂×C₄×C₁₁	—	16	8	no	—
84	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
86	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
87	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
88	C₈×C₁₁	—	4	4	no	—
89	C₈×C₁₁	C₄×D₄	1	4	yes	—
90	C₈×C₁₁	C₄×D₄	1	4	yes	—
91	C₂²×D₈	C₂²×C₁₁	1	4	yes	—
92	C₂×#127	C₂²×C₁₁	1	2	yes	—
93	#518	C₂²×C₁₁	1	4	yes	—
94	#493	C₄×C₁₁	1	8	yes	complemented
95	#442	—	2	8	no	—
96	C₄×D₈	—	2	8	no	—
97	C₂×#108	C₂²×C₁₁	1	2	yes	—
98	#427	C₂²×C₁₁	1	2	yes	—
99	#418	C₂²×C₁₁	1	8	yes	—
100	C₂×#100	C₂²×C₁₁	1	4	yes	—
101	#405	C₂²×C₁₁	1	4	yes	—
102	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
103	#339	C₂²×C₁₁	1	4	yes	—
104	C₂²×C₁₁	—	2	2	no	—
105	C₂²×C₁₁	—	4	8	no	—
106	C₂²×C₁₁	—	8	8	no	—
107	C₂²×C₁₁	—	8	8	no	—
108	C₂²×C₁₁	—	16	4	no	—
109	C₂²×C₁₁	#518	1	1	yes	characteristic
110	C₂²×C₁₁	D₄²	1	1	yes	characteristic
111	C₂²×C₁₁	#559	1	1	yes	characteristic
112	C₄×C₁₁	—	2	4	no	—
113	C₄×C₁₁	—	4	8	no	—
114	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
115	C₄×C₁₁	#550	1	2	yes	—
116	C₂²×D₄	—	4	2	no	—
117	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
118	C₂×D₈	—	2	4	no	—
119	C₂×D₈	—	2	4	no	—
120	C₂×D₈	—	2	8	no	—
121	C₂×D₈	C₂×C₄×C₁₁	1	16	yes	complemented
122	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
123	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
124	#127	—	4	2	no	—
125	#127	C₂×C₄×C₁₁	1	8	yes	complemented
126	C₄×D₄	—	2	16	no	—
127	#117	C₂³×C₁₁	1	4	yes	—
128	C₂×C₂²⋊C₄	—	4	4	no	—
129	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
130	#108	—	2	4	no	—
131	#107	D₄×C₁₁	1	4	yes	complemented
132	#106	D₄×C₁₁	1	4	yes	complemented
133	#102	—	2	16	no	—
134	#100	—	4	4	no	—
135	#97	—	2	4	no	—
136	C₄×C₈	—	2	4	no	—
137	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
138	C₂×C₁₁	—	2	1	no	—
139	C₂×C₁₁	—	2	1	no	—
140	C₂×C₁₁	—	8	8	no	—
141	C₂×C₁₁	#2366	1	1	yes	characteristic
142	C₂×C₁₁	#3292	1	2	yes	—
143	C₂⁴	—	2	4	no	—
144	C₂×D₄	—	2	8	no	—
145	C₂×D₄	—	2	8	no	—
146	C₂×D₄	—	2	4	no	—
147	C₂×D₄	—	4	8	no	—
148	C₂×D₄	—	8	8	no	—
149	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
150	C₂²×C₄	—	2	1	no	—
151	C₂²×C₄	—	4	8	no	—
152	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
153	D₈	—	2	16	no	—
154	D₈	—	2	16	no	—
155	M₁₆	—	2	4	no	—
156	M₁₆	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
159	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
160	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
161	C₂×C₈	C₁₁×#41	1	4	yes	—
162	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
163	C₂²⋊C₄	—	2	4	no	—
164	C₂²⋊C₄	—	4	8	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	1	no	—
167	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
168	C₁₁	#23201	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³	—	2	8	no	—
170	C₂³	—	4	4	no	—
171	C₂³	—	4	4	no	—
172	C₂³	—	8	8	no	—
173	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
174	D₄	—	2	16	no	—
175	D₄	—	4	8	no	—
176	D₄	—	8	16	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	8	no	—
180	C₂×C₄	—	16	8	no	—
181	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
182	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
183	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
184	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
185	C₈	—	4	4	no	—
186	C₈	C₄×D₄×C₁₁	1	4	yes	—
187	C₈	C₄×D₄×C₁₁	1	4	yes	—
188	C₂²	—	2	2	no	—
189	C₂²	—	4	8	no	—
190	C₂²	—	8	8	no	—
191	C₂²	—	8	8	no	—
192	C₂²	—	16	4	no	—
193	C₂²	C₁₁×#518	1	1	yes	characteristic
194	C₂²	D₄²×C₁₁	1	1	yes	characteristic
195	C₂²	C₁₁×#559	1	1	yes	characteristic
196	C₄	—	2	4	no	—
197	C₄	—	4	8	no	—
198	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
199	C₄	C₁₁×#550	1	2	yes	—
200	C₂	—	2	1	no	—
201	C₂	—	2	1	no	—
202	C₂	—	8	8	no	—
203	C₂	C₁₁×#2366	1	1	yes	characteristic
204	C₂	C₁₁×#3292	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2948	C₂	semidirect
3. C₁₁×#1978	C₂	semidirect
4. C₁₁×#1887	C₂	semidirect
5. C₁₁×#1772	C₂	semidirect
9. C₁₁×#493	C₄	semidirect
24. C₂×C₁₁×D₈	C₂×C₄	semidirect
28. C₁₁×#127	C₂×C₄	semidirect
34. C₁₁×#107	D₄	semidirect
35. C₁₁×#106	D₄	semidirect
40. C₄×C₈×C₁₁	C₂×C₄	semidirect
41. #23201	C₁₁	direct (N × H)
68. #2948	C₂×C₁₁	semidirect
69. #1978	C₂×C₁₁	semidirect
70. #1887	C₂×C₁₁	semidirect
71. #1772	C₂×C₁₁	semidirect
94. #493	C₄×C₁₁	semidirect
121. C₂×D₈	C₂×C₄×C₁₁	semidirect
125. #127	C₂×C₄×C₁₁	semidirect
131. #107	D₄×C₁₁	semidirect
132. #106	D₄×C₁₁	semidirect
137. C₄×C₈	C₂×C₄×C₁₁	semidirect
168. C₁₁	#23201	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×#493	2
C₁₁×#2948	2
C₁₁×#1978	2
C₁₁×#1887	2
C₁₁×#1772	2
#23201	11

Subgroups — C11×#23201 #14600394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23201 #14600394