Subgroups — C₁₁×#20826 #14598019

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2920	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1848	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1837	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1810	C₂	1	4	yes	maximal
6	C₄×C₁₁×#108	C₂	1	4	yes	maximal, complemented
7	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#432	—	2	4	no	—
10	C₁₁×#431	—	2	4	no	—
11	C₂×C₁₁×#108	C₂²	1	8	yes	—
12	C₁₁×#423	C₂²	1	4	yes	—
13	C₁₁×#407	C₂²	1	4	yes	—
14	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
16	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#341	C₂²	1	8	yes	—
21	C₂³×C₄×C₁₁	Q₈	1	2	yes	—
22	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
24	C₂²×C₈×C₁₁	—	2	8	no	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	D₄	1	2	yes	—
31	C₂×C₄²×C₁₁	D₄	1	2	yes	—
32	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
35	C₁₁×#108	—	2	16	no	—
36	C₁₁×C₄⋊C₈	—	2	8	no	—
37	C₁₁×C₂²⋊C₈	—	2	8	no	—
38	C₁₁×#97	—	2	4	no	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	8	yes	—
43	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
45	#20826	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	—	2	8	no	—
48	C₂²×C₄×C₁₁	—	2	4	no	—
49	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
57	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
59	C₁₁×M₁₆	—	2	16	no	—
60	C₂×C₈×C₁₁	—	2	16	no	—
61	C₂×C₈×C₁₁	—	2	8	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₁₁	#41	1	8	yes	—
66	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
69	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
70	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
72	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	2	yes	—
75	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
76	#2920	C₂×C₁₁	1	2	yes	—
77	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
78	#1848	C₂×C₁₁	1	2	yes	complemented
79	#1837	C₂×C₁₁	1	2	yes	complemented
80	#1810	C₂×C₁₁	1	4	yes	—
81	C₄×#108	C₂×C₁₁	1	4	yes	complemented
82	C₂³×C₁₁	—	2	2	no	—
83	C₂³×C₁₁	—	2	4	no	—
84	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
85	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	4	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	4	no	—
90	C₂×C₄×C₁₁	—	2	4	no	—
91	C₂×C₄×C₁₁	—	2	4	no	—
92	C₂×C₄×C₁₁	—	2	4	no	—
93	C₂×C₄×C₁₁	—	2	4	no	—
94	C₂×C₄×C₁₁	#108	1	8	yes	complemented
95	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
96	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
98	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
99	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
100	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
103	C₈×C₁₁	—	2	4	no	—
104	C₈×C₁₁	—	4	8	no	—
105	C₈×C₁₁	#117	1	8	yes	—
106	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
107	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
108	#432	—	2	4	no	—
109	#431	—	2	4	no	—
110	C₂×#108	C₂²×C₁₁	1	8	yes	—
111	#423	C₂²×C₁₁	1	4	yes	—
112	#407	C₂²×C₁₁	1	4	yes	—
113	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
114	C₂×C₄×C₈	C₄×C₁₁	1	4	yes	—
115	C₂×C₄×C₈	C₄×C₁₁	1	4	yes	—
116	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
117	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
119	#341	C₂²×C₁₁	1	8	yes	—
120	C₂²×C₁₁	—	2	8	no	—
121	C₂²×C₁₁	—	2	2	no	—
122	C₂²×C₁₁	—	2	2	no	—
123	C₂²×C₁₁	—	2	2	no	—
124	C₂²×C₁₁	C₂×#108	1	4	yes	—
125	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
126	C₂²×C₁₁	#533	1	2	yes	—
127	C₄×C₁₁	—	2	2	no	—
128	C₄×C₁₁	—	2	2	no	—
129	C₄×C₁₁	—	2	2	no	—
130	C₄×C₁₁	C₂×#108	1	4	yes	—
131	C₄×C₁₁	C₂×#108	1	4	yes	—
132	C₄×C₁₁	C₂×#117	1	2	yes	—
133	C₄×C₁₁	#532	1	2	yes	—
134	C₂³×C₄	Q₈×C₁₁	1	2	yes	—
135	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
136	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
137	C₂²×C₈	—	2	8	no	—
138	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	—
139	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
140	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
141	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
142	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
143	C₂×C₄²	D₄×C₁₁	1	2	yes	—
144	C₂×C₄²	D₄×C₁₁	1	2	yes	—
145	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
146	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
147	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
148	#108	—	2	16	no	—
149	C₄⋊C₈	—	2	8	no	—
150	C₂²⋊C₈	—	2	8	no	—
151	#97	—	2	4	no	—
152	C₄×C₈	—	2	4	no	—
153	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
154	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
155	C₄×C₈	C₂×C₄×C₁₁	1	8	yes	—
156	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
157	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
158	C₂×C₁₁	—	2	2	no	—
159	C₂×C₁₁	—	2	4	no	—
160	C₂×C₁₁	#2285	1	1	yes	characteristic
161	C₂×C₁₁	C₂²×#108	1	2	yes	—
162	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
163	C₂²×C₄	—	2	8	no	—
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
166	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
167	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
168	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
169	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
170	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
171	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
172	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
173	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
174	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
175	M₁₆	—	2	16	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	2	16	no	—
178	C₂×C₈	—	2	8	no	—
179	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
180	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
181	C₂×C₈	C₁₁×#41	1	8	yes	—
182	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
183	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
184	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
185	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
186	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
187	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
188	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
189	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
191	C₄²	C₂×D₄×C₁₁	1	2	yes	—
192	C₁₁	#20826	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	—	2	2	no	—
194	C₂³	—	2	4	no	—
195	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
196	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	C₁₁×#108	1	8	yes	complemented
206	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
207	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
208	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
209	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
210	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
211	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
212	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
213	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
214	C₈	—	2	4	no	—
215	C₈	—	4	8	no	—
216	C₈	C₁₁×#117	1	8	yes	—
217	C₂²	—	2	8	no	—
218	C₂²	—	2	2	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	2	2	no	—
221	C₂²	C₂×C₁₁×#108	1	4	yes	—
222	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
223	C₂²	C₁₁×#533	1	2	yes	—
224	C₄	—	2	2	no	—
225	C₄	—	2	2	no	—
226	C₄	—	2	2	no	—
227	C₄	C₂×C₁₁×#108	1	4	yes	—
228	C₄	C₂×C₁₁×#108	1	4	yes	—
229	C₄	C₂×C₁₁×#117	1	2	yes	—
230	C₄	C₁₁×#532	1	2	yes	—
231	C₂	—	2	2	no	—
232	C₂	—	2	4	no	—
233	C₂	C₁₁×#2285	1	1	yes	characteristic
234	C₂	C₂²×C₁₁×#108	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1848	C₂	semidirect
4. C₁₁×#1837	C₂	semidirect
6. C₄×C₁₁×#108	C₂	semidirect
45. #20826	C₁₁	direct (N × H)
78. #1848	C₂×C₁₁	semidirect
79. #1837	C₂×C₁₁	semidirect
81. C₄×#108	C₂×C₁₁	semidirect
94. C₂×C₄×C₁₁	#108	semidirect
192. C₁₁	#20826	direct (N × H)
205. C₂×C₄	C₁₁×#108	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2920	2
C₂²×C₄×C₈×C₁₁	2
C₁₁×#1848	2
C₁₁×#1837	2
C₁₁×#1810	2
C₄×C₁₁×#108	2
#20826	11

Subgroups — C11×#20826 #14598019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#20826 #14598019