Subgroups — C₁₁×#17819 #14595012

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 248 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×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1574	C₂	1	8	yes	maximal, complemented
4	C₁₁×#1568	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#432	—	2	2	no	—
7	C₁₁×#432	C₂²	1	4	yes	—
8	C₁₁×#431	—	2	2	no	—
9	C₁₁×#431	C₄	1	4	yes	—
10	C₁₁×#431	C₂²	1	4	yes	—
11	C₁₁×#431	C₂²	1	4	yes	—
12	C₁₁×#423	C₂²	1	4	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
14	C₁₁×#407	—	2	2	no	—
15	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
16	C₄×C₁₁×M₁₆	—	2	2	no	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#335	C₂²	1	8	yes	complemented
19	C₁₁×#334	C₂²	1	8	yes	complemented
20	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	—	2	4	no	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
33	C₁₁×C₄⋊C₈	—	2	4	no	—
34	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
35	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
36	C₁₁×C₂²⋊C₈	—	2	4	no	—
37	C₁₁×C₂²⋊C₈	—	2	4	no	—
38	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
39	C₁₁×#97	—	2	4	no	—
40	C₄×C₈×C₁₁	—	2	4	no	—
41	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
42	C₄×C₈×C₁₁	C₂³	1	4	yes	—
43	#17819	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	—	2	4	no	—
46	C₂²×C₄×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
60	C₁₁×M₁₆	—	4	8	no	—
61	C₂×C₈×C₁₁	—	2	8	no	—
62	C₂×C₈×C₁₁	—	4	4	no	—
63	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
64	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
65	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
69	C₄²×C₁₁	C₂×D₄	1	2	yes	—
70	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
73	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
74	#2920	C₂×C₁₁	1	2	yes	—
75	C₂×#431	C₂×C₁₁	1	1	yes	characteristic
76	#1574	C₂×C₁₁	1	8	yes	complemented
77	#1568	C₂×C₁₁	1	4	yes	complemented
78	C₂³×C₁₁	—	2	2	no	—
79	C₂³×C₁₁	—	4	1	no	—
80	C₂³×C₁₁	—	4	1	no	—
81	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
82	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	4	no	—
90	C₂×C₄×C₁₁	—	4	1	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	—	4	1	no	—
93	C₂×C₄×C₁₁	—	4	2	no	—
94	C₂×C₄×C₁₁	#108	1	4	yes	—
95	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
101	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
104	C₈×C₁₁	—	2	8	no	—
105	C₈×C₁₁	—	4	8	no	—
106	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
107	#432	—	2	2	no	—
108	#432	C₂²×C₁₁	1	4	yes	—
109	#431	—	2	2	no	—
110	#431	C₄×C₁₁	1	4	yes	—
111	#431	C₂²×C₁₁	1	4	yes	—
112	#431	C₂²×C₁₁	1	4	yes	—
113	#423	C₂²×C₁₁	1	4	yes	—
114	C₂×C₄⋊C₈	C₄×C₁₁	1	2	yes	—
115	#407	—	2	2	no	—
116	C₂×C₂²⋊C₈	C₄×C₁₁	1	2	yes	—
117	C₄×M₁₆	—	2	2	no	—
118	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
119	#335	C₂²×C₁₁	1	8	yes	complemented
120	#334	C₂²×C₁₁	1	8	yes	complemented
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	1	no	—
123	C₂²×C₁₁	—	2	2	no	—
124	C₂²×C₁₁	—	2	2	no	—
125	C₂²×C₁₁	—	2	2	no	—
126	C₂²×C₁₁	—	4	4	no	—
127	C₂²×C₁₁	C₂×#108	1	2	yes	—
128	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
129	C₄×C₁₁	—	2	1	no	—
130	C₄×C₁₁	—	2	2	no	—
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	—	2	1	no	—
134	C₄×C₁₁	—	2	1	no	—
135	C₄×C₁₁	C₂×#108	1	4	yes	—
136	C₄×C₁₁	#568	1	2	yes	—
137	C₄×C₁₁	#575	1	2	yes	—
138	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
139	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
140	C₂³×C₄	Q₈×C₁₁	1	1	yes	characteristic
141	C₂×M₁₆	—	2	4	no	—
142	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
143	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
144	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
145	C₂×C₄²	D₄×C₁₁	1	2	yes	—
146	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
147	C₂×C₄²	Q₈×C₁₁	1	1	yes	characteristic
148	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
149	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
150	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
151	C₄⋊C₈	—	2	4	no	—
152	C₄⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
153	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
154	C₂²⋊C₈	—	2	4	no	—
155	C₂²⋊C₈	—	2	4	no	—
156	C₂²⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
157	#97	—	2	4	no	—
158	C₄×C₈	—	2	4	no	—
159	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
160	C₄×C₈	C₂³×C₁₁	1	4	yes	—
161	C₂×C₁₁	—	2	2	no	—
162	C₂×C₁₁	—	4	2	no	—
163	C₂×C₁₁	#2905	1	1	yes	characteristic
164	C₂×C₁₁	#2911	1	1	yes	characteristic
165	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
166	C₂⁴	C₁₁×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	4	2	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	C₁₁×C₄⋊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	2	yes	—
174	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
177	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
180	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
181	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
182	M₁₆	—	4	8	no	—
183	C₂×C₈	—	2	8	no	—
184	C₂×C₈	—	4	4	no	—
185	C₂×C₈	C₂²×C₄×C₁₁	1	8	yes	—
186	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
187	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
188	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
189	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
190	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
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	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
195	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
196	C₁₁	#17819	1	1	yes	characteristic, direct product factor, Sylow
197	C₂³	—	2	2	no	—
198	C₂³	—	4	1	no	—
199	C₂³	—	4	1	no	—
200	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
201	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	C₁₁×#108	1	4	yes	—
214	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
215	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
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×C₄⋊C₄	1	2	yes	—
220	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
221	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
222	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
223	C₈	—	2	8	no	—
224	C₈	—	4	8	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	2	2	no	—
229	C₂²	—	2	2	no	—
230	C₂²	—	4	4	no	—
231	C₂²	C₂×C₁₁×#108	1	2	yes	—
232	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	C₂×C₁₁×#108	1	4	yes	—
240	C₄	C₁₁×#568	1	2	yes	—
241	C₄	C₁₁×#575	1	2	yes	—
242	C₂	—	2	2	no	—
243	C₂	—	4	2	no	—
244	C₂	C₁₁×#2905	1	1	yes	characteristic
245	C₂	C₁₁×#2911	1	1	yes	characteristic
246	C₂	C₂²×C₁₁×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ 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×#1574	C₂	semidirect
4. C₁₁×#1568	C₂	semidirect
18. C₁₁×#335	C₂²	semidirect
19. C₁₁×#334	C₂²	semidirect
43. #17819	C₁₁	direct (N × H)
76. #1574	C₂×C₁₁	semidirect
77. #1568	C₂×C₁₁	semidirect
119. #335	C₂²×C₁₁	semidirect
120. #334	C₂²×C₁₁	semidirect
196. C₁₁	#17819	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×C₁₁×#431	2
C₁₁×#1574	2
C₁₁×#1568	2
#17819	11

Subgroups — C11×#17819 #14595012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17819 #14595012