Subgroups — C₁₁×#2637 #13065475

Order 1408.

450 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#126	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#398	C₂	1	2	yes	maximal, complemented
5	C₁₁×#397	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#396	C₂	1	2	yes	maximal
7	C₁₁×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#393	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#388	C₂	1	2	yes	maximal
10	C₁₁×#387	C₂	1	2	yes	maximal, complemented
11	C₁₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#126	—	2	4	no	—
14	C₄×Q₈×C₁₁	—	2	4	no	—
15	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#95	C₂²	1	2	yes	—
31	C₁₁×#95	C₂²	1	1	yes	characteristic
32	C₁₁×#95	C₂²	1	1	yes	characteristic
33	C₁₁×#95	C₂²	1	2	yes	—
34	C₁₁×#95	C₂²	1	2	yes	—
35	C₁₁×#95	C₂²	1	2	yes	—
36	C₁₁×#95	C₂²	1	2	yes	—
37	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
38	C₂×Q₈×C₁₁	—	2	2	no	—
39	C₂×Q₈×C₁₁	—	2	4	no	—
40	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
50	C₁₁×C₄⋊C₄	—	2	4	no	—
51	C₁₁×C₄⋊C₄	—	2	2	no	—
52	C₁₁×C₄⋊C₄	—	2	2	no	—
53	C₁₁×C₄⋊C₄	—	2	2	no	—
54	C₁₁×C₄⋊C₄	—	2	2	no	—
55	C₁₁×C₄⋊C₄	—	2	4	no	—
56	C₁₁×C₄⋊C₄	—	4	2	no	—
57	C₁₁×C₄⋊C₄	—	4	2	no	—
58	C₁₁×C₂²⋊C₄	—	2	2	no	—
59	C₁₁×C₂²⋊C₄	—	2	2	no	—
60	C₁₁×C₂²⋊C₄	—	2	2	no	—
61	C₁₁×C₂²⋊C₄	—	2	4	no	—
62	C₁₁×C₂²⋊C₄	—	4	2	no	—
63	C₄²×C₁₁	—	2	4	no	—
64	C₄²×C₁₁	D₄	1	4	yes	—
65	#2637	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₁₁	—	2	1	no	—
67	C₂³×C₁₁	—	2	2	no	—
68	C₂³×C₁₁	—	2	1	no	—
69	C₂³×C₁₁	—	2	2	no	—
70	C₂³×C₁₁	—	2	1	no	—
71	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
72	Q₈×C₁₁	—	2	8	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	1	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	2	1	no	—
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	—	2	1	no	—
81	C₂×C₄×C₁₁	—	2	1	no	—
82	C₂×C₄×C₁₁	—	2	1	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
96	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
98	C₂×C₄×C₁₁	#41	1	4	yes	—
99	C₂×#126	C₂×C₁₁	1	1	yes	characteristic
100	C₂×C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
101	#398	C₂×C₁₁	1	1	yes	characteristic, complemented
102	#398	C₂×C₁₁	1	2	yes	complemented
103	#397	C₂×C₁₁	1	1	yes	characteristic
104	#396	C₂×C₁₁	1	2	yes	—
105	#395	C₂×C₁₁	1	1	yes	characteristic, complemented
106	#393	C₂×C₁₁	1	1	yes	characteristic
107	#388	C₂×C₁₁	1	2	yes	—
108	#387	C₂×C₁₁	1	2	yes	complemented
109	#382	C₂×C₁₁	1	1	yes	characteristic, complemented
110	C₂²×C₁₁	—	4	1	no	—
111	C₂²×C₁₁	—	4	1	no	—
112	C₂²×C₁₁	—	4	1	no	—
113	C₂²×C₁₁	—	4	2	no	—
114	C₂²×C₁₁	—	4	2	no	—
115	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
116	C₂²×C₁₁	C₂×#41	1	2	yes	—
117	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
118	C₂²×C₁₁	2₋¹⁺⁴	1	2	yes	—
119	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
120	C₄×C₁₁	—	2	2	no	—
121	C₄×C₁₁	—	2	4	no	—
122	C₄×C₁₁	—	2	2	no	—
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	—	4	1	no	—
125	C₄×C₁₁	—	4	1	no	—
126	C₄×C₁₁	—	4	2	no	—
127	C₄×C₁₁	—	4	1	no	—
128	C₄×C₁₁	—	4	2	no	—
129	C₄×C₁₁	—	4	2	no	—
130	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
131	#126	—	2	4	no	—
132	C₄×Q₈	—	2	4	no	—
133	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
134	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
135	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
136	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
137	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
138	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
139	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
140	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
141	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
142	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
143	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
145	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
146	C₂×C₄²	C₂²×C₁₁	1	2	yes	—
147	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
148	#95	C₂²×C₁₁	1	2	yes	—
149	#95	C₂²×C₁₁	1	1	yes	characteristic
150	#95	C₂²×C₁₁	1	1	yes	characteristic
151	#95	C₂²×C₁₁	1	2	yes	—
152	#95	C₂²×C₁₁	1	2	yes	—
153	#95	C₂²×C₁₁	1	2	yes	—
154	#95	C₂²×C₁₁	1	2	yes	—
155	C₂×C₁₁	—	8	1	no	—
156	C₂×C₁₁	#525	1	1	yes	characteristic
157	C₂×C₁₁	#536	1	1	yes	characteristic
158	C₂×C₁₁	#537	1	1	yes	characteristic
159	C₂×C₁₁	#541	1	2	yes	—
160	C₂×C₁₁	#542	1	2	yes	—
161	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	4	no	—
164	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
165	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
166	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
167	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
168	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
169	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
171	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
172	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
173	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₂²⋊C₄	—	2	2	no	—
185	C₂²⋊C₄	—	2	4	no	—
186	C₂²⋊C₄	—	4	2	no	—
187	C₄²	—	2	4	no	—
188	C₄²	D₄×C₁₁	1	4	yes	—
189	C₁₁	#2637	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³	—	2	1	no	—
191	C₂³	—	2	2	no	—
192	C₂³	—	2	1	no	—
193	C₂³	—	2	2	no	—
194	C₂³	—	2	1	no	—
195	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
196	Q₈	—	2	8	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
220	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
221	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
222	C₂×C₄	C₁₁×#41	1	4	yes	—
223	C₂²	—	4	1	no	—
224	C₂²	—	4	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	2	no	—
227	C₂²	—	4	2	no	—
228	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
229	C₂²	C₂×C₁₁×#41	1	2	yes	—
230	C₂²	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²	C₁₁×2₋¹⁺⁴	1	2	yes	—
232	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
233	C₄	—	2	2	no	—
234	C₄	—	2	4	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	2	no	—
237	C₄	—	4	1	no	—
238	C₄	—	4	1	no	—
239	C₄	—	4	2	no	—
240	C₄	—	4	1	no	—
241	C₄	—	4	2	no	—
242	C₄	—	4	2	no	—
243	C₂	—	8	1	no	—
244	C₂	C₁₁×#525	1	1	yes	characteristic
245	C₂	C₁₁×#536	1	1	yes	characteristic
246	C₂	C₁₁×#537	1	1	yes	characteristic
247	C₂	C₁₁×#541	1	2	yes	—
248	C₂	C₁₁×#542	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#398	C₂	semidirect
4. C₁₁×#398	C₂	semidirect
7. C₁₁×#395	C₂	semidirect
10. C₁₁×#387	C₂	semidirect
11. C₁₁×#382	C₂	semidirect
65. #2637	C₁₁	direct (N × H)
100. C₂×C₄×Q₈	C₂×C₁₁	semidirect
101. #398	C₂×C₁₁	semidirect
102. #398	C₂×C₁₁	semidirect
105. #395	C₂×C₁₁	semidirect
108. #387	C₂×C₁₁	semidirect
109. #382	C₂×C₁₁	semidirect
189. C₁₁	#2637	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×#126	2
C₂×C₄×Q₈×C₁₁	2
C₁₁×#398	2
C₁₁×#397	2
C₁₁×#396	2
C₁₁×#395	2
C₁₁×#393	2
C₁₁×#388	2
C₁₁×#387	2
C₁₁×#382	2
#2637	11

Subgroups — C11×#2637 #13065475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2637 #13065475