Subgroups — C₁₁×#22025 #14599218

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2295	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1985	C₂	1	2	yes	maximal
3	C₁₁×#1940	C₂	1	2	yes	maximal
4	C₁₁×#1917	C₂	1	4	yes	maximal
5	C₁₁×#1840	C₂	1	2	yes	maximal
6	C₁₁×#1832	C₂	1	2	yes	maximal
7	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1745	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
12	C₂×C₁₁×#97	C₂²	1	2	yes	—
13	C₂×C₁₁×#97	C₂²	1	2	yes	—
14	C₁₁×#391	C₄	1	2	yes	—
15	C₁₁×#389	C₄	1	2	yes	—
16	C₁₁×#387	C₄	1	4	yes	—
17	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₁×#376	C₂²	1	2	yes	—
20	C₄³×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#336	C₂²	1	2	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₁₁×#336	C₂²	1	4	yes	—
24	C₁₁×#336	C₂²	1	4	yes	—
25	C₁₁×#336	C₂²	1	1	yes	characteristic
26	C₁₁×#336	C₂²	1	1	yes	characteristic
27	C₁₁×#336	C₂²	1	2	yes	—
28	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
31	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
32	C₄×Q₈×C₁₁	—	2	4	no	—
33	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
34	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
35	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
41	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×C₄⋊C₈	—	2	4	no	—
45	C₁₁×C₄⋊C₈	—	4	4	no	—
46	C₁₁×#97	—	2	4	no	—
47	C₁₁×#97	—	4	2	no	—
48	C₁₁×#95	C₂×C₄	1	4	yes	—
49	C₁₁×#95	C₂×C₄	1	4	yes	—
50	C₁₁×#95	C₂×C₄	1	2	yes	—
51	C₁₁×#95	C₂×C₄	1	4	yes	—
52	#22025	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×Q₈×C₁₁	—	2	2	no	—
54	C₂×Q₈×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
63	C₂×C₈×C₁₁	—	2	2	no	—
64	C₂×C₈×C₁₁	—	2	2	no	—
65	C₂×C₈×C₁₁	—	2	4	no	—
66	C₂×C₈×C₁₁	—	2	4	no	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	2	2	no	—
69	C₂×C₈×C₁₁	—	2	2	no	—
70	C₂×C₈×C₁₁	—	2	2	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₁₁×C₄⋊C₄	—	2	2	no	—
73	C₁₁×C₄⋊C₄	—	2	4	no	—
74	C₁₁×C₄⋊C₄	—	4	2	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₄²×C₁₁	—	2	4	no	—
77	C₄²×C₁₁	—	2	1	no	—
78	C₄²×C₁₁	—	2	2	no	—
79	C₄²×C₁₁	—	2	2	no	—
80	C₄²×C₁₁	—	2	1	no	—
81	C₄²×C₁₁	—	2	2	no	—
82	C₄²×C₁₁	—	4	2	no	—
83	C₄²×C₁₁	—	4	2	no	—
84	C₄²×C₁₁	#41	1	4	yes	—
85	#2295	C₂×C₁₁	1	1	yes	characteristic
86	#1985	C₂×C₁₁	1	2	yes	—
87	#1940	C₂×C₁₁	1	2	yes	—
88	#1917	C₂×C₁₁	1	4	yes	—
89	#1840	C₂×C₁₁	1	2	yes	—
90	#1832	C₂×C₁₁	1	2	yes	—
91	#1767	C₂×C₁₁	1	1	yes	characteristic
92	#1745	C₂×C₁₁	1	1	yes	characteristic
93	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
94	Q₈×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	2	no	—
100	C₂×C₄×C₁₁	—	2	2	no	—
101	C₂×C₄×C₁₁	—	2	4	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	2	no	—
104	C₂×C₄×C₁₁	—	2	2	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	—	2	4	no	—
107	C₂×C₄×C₁₁	—	2	4	no	—
108	C₂×C₄×C₁₁	—	2	4	no	—
109	C₂×C₄×C₁₁	—	2	4	no	—
110	C₂×C₄×C₁₁	#117	1	2	yes	—
111	C₂×C₄×C₁₁	#117	1	2	yes	—
112	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
113	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
114	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
115	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
116	C₈×C₁₁	—	4	2	no	—
117	C₈×C₁₁	—	4	2	no	—
118	C₈×C₁₁	—	4	4	no	—
119	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
120	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
121	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
122	C₂×#97	C₂²×C₁₁	1	2	yes	—
123	C₂×#97	C₂²×C₁₁	1	2	yes	—
124	#391	C₄×C₁₁	1	2	yes	—
125	#389	C₄×C₁₁	1	2	yes	—
126	#387	C₄×C₁₁	1	4	yes	—
127	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
128	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
129	#376	C₂²×C₁₁	1	2	yes	—
130	C₄³	C₂²×C₁₁	1	1	yes	characteristic
131	#336	C₂²×C₁₁	1	1	yes	characteristic
132	#336	C₂²×C₁₁	1	2	yes	—
133	#336	C₂²×C₁₁	1	4	yes	—
134	#336	C₂²×C₁₁	1	1	yes	characteristic
135	#336	C₂²×C₁₁	1	4	yes	—
136	#336	C₂²×C₁₁	1	4	yes	—
137	#336	C₂²×C₁₁	1	2	yes	—
138	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
139	C₂²×C₁₁	#519	1	1	yes	characteristic
140	C₂²×C₁₁	#520	1	1	yes	characteristic
141	C₂²×C₁₁	#568	1	2	yes	—
142	C₂²×C₁₁	#568	1	2	yes	—
143	C₄×C₁₁	—	2	2	no	—
144	C₄×C₁₁	—	2	2	no	—
145	C₄×C₁₁	—	4	2	no	—
146	C₄×C₁₁	—	4	2	no	—
147	C₄×C₁₁	—	4	2	no	—
148	C₄×C₁₁	—	4	2	no	—
149	C₄×C₁₁	—	4	4	no	—
150	C₄×C₁₁	#541	1	2	yes	—
151	C₄×C₁₁	#542	1	2	yes	—
152	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
153	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
154	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
155	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
156	C₄×Q₈	—	2	4	no	—
157	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
158	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
160	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
161	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
162	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
163	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
164	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
165	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
166	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
167	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
168	C₄⋊C₈	—	2	4	no	—
169	C₄⋊C₈	—	4	4	no	—
170	#97	—	2	4	no	—
171	#97	—	4	2	no	—
172	#95	C₂×C₄×C₁₁	1	4	yes	—
173	#95	C₂×C₄×C₁₁	1	4	yes	—
174	#95	C₂×C₄×C₁₁	1	2	yes	—
175	#95	C₂×C₄×C₁₁	1	4	yes	—
176	C₂×C₁₁	#2320	1	1	yes	characteristic
177	C₂×C₁₁	#2921	1	1	yes	characteristic
178	C₂×C₁₁	#2923	1	1	yes	characteristic
179	C₂×C₁₁	#2987	1	2	yes	—
180	C₂×C₁₁	#2995	1	2	yes	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
184	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
185	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
186	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
187	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
188	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
189	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
190	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	4	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	4	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	4	4	no	—
204	C₄²	—	2	4	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	2	1	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	4	2	no	—
211	C₄²	—	4	2	no	—
212	C₄²	C₁₁×#41	1	4	yes	—
213	C₁₁	#22025	1	1	yes	characteristic, direct product factor, Sylow
214	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
215	Q₈	—	4	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	4	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	C₁₁×#117	1	2	yes	—
232	C₂×C₄	C₁₁×#117	1	2	yes	—
233	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
234	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
237	C₈	—	4	2	no	—
238	C₈	—	4	2	no	—
239	C₈	—	4	4	no	—
240	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
241	C₂²	C₁₁×#519	1	1	yes	characteristic
242	C₂²	C₁₁×#520	1	1	yes	characteristic
243	C₂²	C₁₁×#568	1	2	yes	—
244	C₂²	C₁₁×#568	1	2	yes	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	4	2	no	—
248	C₄	—	4	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	4	2	no	—
251	C₄	—	4	4	no	—
252	C₄	C₁₁×#541	1	2	yes	—
253	C₄	C₁₁×#542	1	2	yes	—
254	C₂	C₁₁×#2320	1	1	yes	characteristic
255	C₂	C₁₁×#2921	1	1	yes	characteristic
256	C₂	C₁₁×#2923	1	1	yes	characteristic
257	C₂	C₁₁×#2987	1	2	yes	—
258	C₂	C₁₁×#2995	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
52. #22025	C₁₁	direct (N × H)
213. C₁₁	#22025	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×#2295	2
C₁₁×#1985	2
C₁₁×#1940	2
C₁₁×#1917	2
C₁₁×#1840	2
C₁₁×#1832	2
C₁₁×#1767	2
C₁₁×#1745	2
#22025	11

Subgroups — C11×#22025 #14599218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22025 #14599218