Subgroups — C₁₁×#21923 #14599116

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2298	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1923	C₂	1	4	yes	maximal
3	C₁₁×#1916	C₂	1	4	yes	maximal, complemented
4	C₁₁×#1843	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1798	C₂	1	2	yes	maximal
7	C₄×C₁₁×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
12	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
14	C₁₁×#388	C₄	1	4	yes	—
15	C₁₁×#387	C₄	1	4	yes	—
16	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
17	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₁₁×#376	C₂²	1	1	yes	characteristic
19	C₄³×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#336	C₂²	1	4	yes	—
21	C₁₁×#336	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
26	C₁₁×#117	—	2	2	no	—
27	C₁₁×#117	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
30	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
35	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₁₁×C₄⋊C₈	—	2	4	no	—
38	C₁₁×C₄⋊C₈	—	2	4	no	—
39	C₁₁×C₄⋊C₈	—	4	4	no	—
40	C₁₁×C₂²⋊C₈	—	4	4	no	—
41	C₄×C₈×C₁₁	—	4	4	no	—
42	C₁₁×#95	C₂×C₄	1	4	yes	—
43	C₁₁×#95	C₂×C₄	1	4	yes	—
44	C₁₁×#95	C₂×C₄	1	4	yes	—
45	#21923	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	—	2	1	no	—
48	C₂²×C₄×C₁₁	—	2	1	no	—
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	—	2	2	no	—
51	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
56	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
57	C₂×C₈×C₁₁	—	2	4	no	—
58	C₂×C₈×C₁₁	—	2	4	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	—	2	4	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	2	4	no	—
64	C₁₁×C₄⋊C₄	—	2	8	no	—
65	C₁₁×C₂²⋊C₄	—	2	4	no	—
66	C₁₁×C₂²⋊C₄	—	2	8	no	—
67	C₄²×C₁₁	—	2	8	no	—
68	C₄²×C₁₁	—	2	1	no	—
69	C₄²×C₁₁	—	2	1	no	—
70	C₄²×C₁₁	—	2	2	no	—
71	C₄²×C₁₁	—	2	2	no	—
72	C₄²×C₁₁	—	2	2	no	—
73	C₄²×C₁₁	—	2	2	no	—
74	C₄²×C₁₁	#41	1	2	yes	—
75	C₄²×C₁₁	#41	1	2	yes	—
76	#2298	C₂×C₁₁	1	1	yes	characteristic
77	#1923	C₂×C₁₁	1	4	yes	—
78	#1916	C₂×C₁₁	1	4	yes	complemented
79	#1843	C₂×C₁₁	1	1	yes	characteristic, complemented
80	#1832	C₂×C₁₁	1	1	yes	characteristic, complemented
81	#1798	C₂×C₁₁	1	2	yes	—
82	C₄×C₄⋊C₈	C₂×C₁₁	1	2	yes	complemented
83	C₂³×C₁₁	—	2	1	no	—
84	C₂³×C₁₁	—	2	2	no	—
85	C₂³×C₁₁	—	2	4	no	—
86	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
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	2	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	4	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	4	no	—
95	C₂×C₄×C₁₁	—	2	4	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	4	1	no	—
98	C₂×C₄×C₁₁	—	4	1	no	—
99	C₂×C₄×C₁₁	—	4	2	no	—
100	C₂×C₄×C₁₁	#117	1	4	yes	—
101	C₂×C₄×C₁₁	#131	1	8	yes	—
102	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
104	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
105	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
106	C₈×C₁₁	—	4	4	no	—
107	C₈×C₁₁	—	4	4	no	—
108	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
109	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
110	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
111	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
112	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
113	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
114	#388	C₄×C₁₁	1	4	yes	—
115	#387	C₄×C₁₁	1	4	yes	—
116	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
117	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
118	#376	C₂²×C₁₁	1	1	yes	characteristic
119	C₄³	C₂²×C₁₁	1	1	yes	characteristic
120	#336	C₂²×C₁₁	1	4	yes	—
121	#336	C₂²×C₁₁	1	4	yes	—
122	#336	C₂²×C₁₁	1	4	yes	—
123	C₂²×C₁₁	—	4	1	no	—
124	C₂²×C₁₁	—	4	2	no	—
125	C₂²×C₁₁	—	4	4	no	—
126	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
127	C₂²×C₁₁	#520	1	2	yes	—
128	C₂²×C₁₁	C₂×#131	1	4	yes	—
129	C₄×C₁₁	—	2	4	no	—
130	C₄×C₁₁	—	2	8	no	—
131	C₄×C₁₁	—	4	1	no	—
132	C₄×C₁₁	—	4	2	no	—
133	C₄×C₁₁	—	4	4	no	—
134	C₄×C₁₁	#540	1	1	yes	characteristic
135	C₄×C₁₁	#541	1	1	yes	characteristic
136	C₄×C₁₁	#542	1	2	yes	—
137	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
138	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
139	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
140	#117	—	2	2	no	—
141	#117	—	2	2	no	—
142	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
143	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
144	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
145	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
146	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
147	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
148	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
149	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
150	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
151	C₄⋊C₈	—	2	4	no	—
152	C₄⋊C₈	—	2	4	no	—
153	C₄⋊C₈	—	4	4	no	—
154	C₂²⋊C₈	—	4	4	no	—
155	C₄×C₈	—	4	4	no	—
156	#95	C₂×C₄×C₁₁	1	4	yes	—
157	#95	C₂×C₄×C₁₁	1	4	yes	—
158	#95	C₂×C₄×C₁₁	1	4	yes	—
159	C₂×C₁₁	—	8	1	no	—
160	C₂×C₁₁	#2314	1	1	yes	characteristic
161	C₂×C₁₁	#2922	1	2	yes	—
162	C₂×C₁₁	#2994	1	4	yes	—
163	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
169	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
171	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
173	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄⋊C₄	—	2	8	no	—
182	C₂²⋊C₄	—	2	4	no	—
183	C₂²⋊C₄	—	2	8	no	—
184	C₄²	—	2	8	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	2	1	no	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	C₁₁×#41	1	2	yes	—
192	C₄²	C₁₁×#41	1	2	yes	—
193	C₁₁	#21923	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³	—	2	1	no	—
195	C₂³	—	2	2	no	—
196	C₂³	—	2	4	no	—
197	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	C₁₁×#117	1	4	yes	—
212	C₂×C₄	C₁₁×#131	1	8	yes	—
213	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
214	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
215	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
216	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
217	C₈	—	4	4	no	—
218	C₈	—	4	4	no	—
219	C₂²	—	4	2	no	—
220	C₂²	—	4	4	no	—
221	C₂²	—	4	1	no	—
222	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
223	C₂²	C₁₁×#520	1	2	yes	—
224	C₂²	C₂×C₁₁×#131	1	4	yes	—
225	C₄	—	2	4	no	—
226	C₄	—	2	8	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	1	no	—
230	C₄	C₁₁×#540	1	1	yes	characteristic
231	C₄	C₁₁×#541	1	1	yes	characteristic
232	C₄	C₁₁×#542	1	2	yes	—
233	C₂	—	8	1	no	—
234	C₂	C₁₁×#2314	1	1	yes	characteristic
235	C₂	C₁₁×#2922	1	2	yes	—
236	C₂	C₁₁×#2994	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂⁴×C₁₁	C₂²×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
3. C₁₁×#1916	C₂	semidirect
4. C₁₁×#1843	C₂	semidirect
5. C₁₁×#1832	C₂	semidirect
7. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
45. #21923	C₁₁	direct (N × H)
78. #1916	C₂×C₁₁	semidirect
79. #1843	C₂×C₁₁	semidirect
80. #1832	C₂×C₁₁	semidirect
82. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
193. C₁₁	#21923	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×#2298	2
C₁₁×#1923	2
C₁₁×#1916	2
C₁₁×#1843	2
C₁₁×#1832	2
C₁₁×#1798	2
C₄×C₁₁×C₄⋊C₈	2
#21923	11

Subgroups — C11×#21923 #14599116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21923 #14599116