Subgroups — C₁₁×#7920 #14585113

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 244 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	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1281	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#432	—	2	2	no	—
7	C₁₁×#432	C₄	1	4	yes	—
8	C₁₁×#431	—	2	2	no	—
9	C₁₁×#431	C₂²	1	4	yes	—
10	C₁₁×#423	—	2	2	no	—
11	C₁₁×#407	C₄	1	4	yes	—
12	C₄×C₁₁×M₁₆	—	2	2	no	—
13	C₄×C₁₁×M₁₆	—	2	2	no	—
14	C₄×C₁₁×M₁₆	—	2	2	no	—
15	C₂×C₁₁×#97	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
19	C₂×C₁₁×M₁₆	—	2	2	no	—
20	C₂×C₁₁×M₁₆	—	2	2	no	—
21	C₂×C₁₁×M₁₆	—	2	4	no	—
22	C₂×C₁₁×M₁₆	—	2	8	no	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₁	D₄	1	2	yes	—
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×C₄⋊C₈	—	2	4	no	—
34	C₁₁×C₄⋊C₈	—	2	4	no	—
35	C₁₁×C₂²⋊C₈	—	2	4	no	—
36	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
37	C₁₁×#97	—	2	4	no	—
38	C₁₁×#97	—	2	4	no	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	C₄×C₈×C₁₁	—	2	4	no	—
41	#7920	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	—	2	4	no	—
44	C₂²×C₄×C₁₁	—	4	4	no	—
45	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₁₁×M₁₆	—	2	8	no	—
58	C₁₁×M₁₆	—	2	8	no	—
59	C₁₁×M₁₆	—	4	8	no	—
60	C₂×C₈×C₁₁	—	2	8	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	M₁₆	1	8	yes	complemented
64	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
70	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×D₄	1	2	yes	—
73	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
74	#2920	C₂×C₁₁	1	2	yes	—
75	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic
76	#1281	C₂×C₁₁	1	4	yes	complemented
77	C₂³×C₁₁	—	2	2	no	—
78	C₂³×C₁₁	—	4	2	no	—
79	C₂³×C₁₁	#95	1	1	yes	characteristic
80	C₂³×C₁₁	#95	1	1	yes	characteristic
81	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	2	4	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	4	2	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	—	4	2	no	—
93	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
94	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
95	C₂×C₄×C₁₁	#95	1	2	yes	—
96	C₂×C₄×C₁₁	#95	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
98	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
100	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
102	C₈×C₁₁	—	2	8	no	—
103	C₈×C₁₁	—	4	8	no	—
104	C₂²×M₁₆	C₄×C₁₁	1	2	yes	—
105	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
106	#432	—	2	2	no	—
107	#432	C₄×C₁₁	1	4	yes	—
108	#431	—	2	2	no	—
109	#431	C₂²×C₁₁	1	4	yes	—
110	#423	—	2	2	no	—
111	#407	C₄×C₁₁	1	4	yes	—
112	C₄×M₁₆	—	2	2	no	—
113	C₄×M₁₆	—	2	2	no	—
114	C₄×M₁₆	—	2	2	no	—
115	C₂×#97	C₂²×C₁₁	1	2	yes	—
116	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
117	C₂²×C₁₁	—	2	2	no	—
118	C₂²×C₁₁	—	2	1	no	—
119	C₂²×C₁₁	—	2	1	no	—
120	C₂²×C₁₁	—	2	2	no	—
121	C₂²×C₁₁	—	2	2	no	—
122	C₂²×C₁₁	—	4	4	no	—
123	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
124	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	—	2	2	no	—
128	C₄×C₁₁	—	2	2	no	—
129	C₄×C₁₁	—	2	2	no	—
130	C₄×C₁₁	#344	1	4	yes	—
131	C₄×C₁₁	#407	1	2	yes	—
132	C₄×C₁₁	#423	1	2	yes	—
133	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
134	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
135	C₂×M₁₆	—	2	2	no	—
136	C₂×M₁₆	—	2	2	no	—
137	C₂×M₁₆	—	2	4	no	—
138	C₂×M₁₆	—	2	8	no	—
139	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
140	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
141	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
142	C₂×C₄²	D₄×C₁₁	1	2	yes	—
143	C₂×C₄²	D₄×C₁₁	1	2	yes	—
144	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
145	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
146	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
147	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
148	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
149	C₄⋊C₈	—	2	4	no	—
150	C₄⋊C₈	—	2	4	no	—
151	C₂²⋊C₈	—	2	4	no	—
152	C₂²⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
153	#97	—	2	4	no	—
154	#97	—	2	4	no	—
155	C₄×C₈	—	2	4	no	—
156	C₄×C₈	—	2	4	no	—
157	C₂×C₁₁	—	2	2	no	—
158	C₂×C₁₁	—	4	1	no	—
159	C₂×C₁₁	—	4	1	no	—
160	C₂×C₁₁	#1728	1	1	yes	characteristic
161	C₂×C₁₁	C₂×#344	1	2	yes	—
162	C₂⁴	C₄²×C₁₁	1	1	yes	characteristic
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	4	4	no	—
165	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
166	C₂²×C₄	C₄²×C₁₁	1	2	yes	—
167	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
172	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
176	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
177	M₁₆	—	2	8	no	—
178	M₁₆	—	2	8	no	—
179	M₁₆	—	4	8	no	—
180	C₂×C₈	—	2	4	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	2	8	no	—
183	C₂×C₈	C₁₁×M₁₆	1	8	yes	complemented
184	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
185	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
186	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
187	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
188	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
189	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
190	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
191	C₄²	C₂×D₄×C₁₁	1	2	yes	—
192	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
193	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
194	C₁₁	#7920	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	—	2	2	no	—
196	C₂³	—	4	2	no	—
197	C₂³	C₁₁×#95	1	1	yes	characteristic
198	C₂³	C₁₁×#95	1	1	yes	characteristic
199	C₂³	C₂×C₄²×C₁₁	1	1	yes	characteristic
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₁₁×#95	1	1	yes	characteristic
212	C₂×C₄	C₁₁×#95	1	1	yes	characteristic
213	C₂×C₄	C₁₁×#95	1	2	yes	—
214	C₂×C₄	C₁₁×#95	1	2	yes	—
215	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
218	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
220	C₈	—	2	8	no	—
221	C₈	—	4	8	no	—
222	C₂²	—	2	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	4	4	no	—
228	C₂²	C₂×C₁₁×#95	1	1	yes	characteristic
229	C₂²	C₄×C₁₁×M₁₆	1	2	yes	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	C₁₁×#344	1	4	yes	—
236	C₄	C₁₁×#407	1	2	yes	—
237	C₄	C₁₁×#423	1	2	yes	—
238	C₂	—	2	2	no	—
239	C₂	—	4	1	no	—
240	C₂	—	4	1	no	—
241	C₂	C₁₁×#1728	1	1	yes	characteristic
242	C₂	C₂×C₁₁×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1281	C₂	semidirect
41. #7920	C₁₁	direct (N × H)
63. C₂×C₈×C₁₁	M₁₆	semidirect
76. #1281	C₂×C₁₁	semidirect
183. C₂×C₈	C₁₁×M₁₆	semidirect
194. C₁₁	#7920	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2920	2
C₂×C₄×C₁₁×M₁₆	2
C₁₁×#1281	2
#7920	11

Subgroups — C11×#7920 #14585113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7920 #14585113