Subgroups — C₁₁×#13213 #14590406

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#361	C₂	1	4	yes	maximal, complemented
3	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×D₈	—	2	1	no	—
6	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
7	C₂×C₁₁×#127	—	2	1	no	—
8	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
9	C₁₁×#493	—	2	1	no	—
10	C₁₁×#493	—	2	1	no	—
11	C₁₁×#493	C₄	1	2	yes	—
12	C₁₁×#493	C₄	1	2	yes	—
13	C₂×C₁₁×#108	—	2	1	no	—
14	C₂×C₁₁×#108	C₂²	1	2	yes	—
15	C₁₁×#423	—	2	1	no	—
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#361	—	2	8	no	—
18	C₁₁×#346	—	2	1	no	—
19	C₄×C₁₁×C₁₆	—	2	1	no	—
20	C₂²×D₄×C₁₁	—	2	2	no	—
21	C₂²×D₄×C₁₁	—	4	2	no	—
22	C₂×C₁₁×D₈	—	2	2	no	—
23	C₂×C₁₁×D₈	—	2	2	no	—
24	C₂×C₁₁×D₈	—	2	4	no	—
25	C₂×C₁₁×D₈	—	2	2	no	—
26	C₂×C₁₁×D₈	—	2	4	no	—
27	C₂×C₁₁×D₈	—	4	2	no	—
28	C₂×C₁₁×D₈	—	4	2	no	—
29	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×#127	—	2	2	no	—
34	C₁₁×#127	—	2	2	no	—
35	C₁₁×#127	—	4	2	no	—
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₁₁×M₃₂	—	2	2	no	—
38	C₁₁×M₃₂	D₄	1	4	yes	complemented
39	C₂×C₁₁×C₁₆	—	2	2	no	—
40	C₁₁×#108	—	2	4	no	—
41	C₁₁×#108	—	4	2	no	—
42	C₁₁×C₄⋊C₈	—	4	2	no	—
43	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	#13213	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₁	—	4	2	no	—
49	C₂×D₄×C₁₁	—	2	4	no	—
50	C₂×D₄×C₁₁	—	4	4	no	—
51	C₂×D₄×C₁₁	—	4	4	no	—
52	C₂×D₄×C₁₁	—	4	2	no	—
53	C₂×D₄×C₁₁	—	4	2	no	—
54	C₂×D₄×C₁₁	—	4	2	no	—
55	C₂×D₄×C₁₁	—	4	2	no	—
56	C₂×D₄×C₁₁	—	4	2	no	—
57	C₂×D₄×C₁₁	—	8	8	no	—
58	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
59	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₁₁×D₈	—	2	8	no	—
61	C₁₁×D₈	—	4	4	no	—
62	C₁₁×D₈	—	4	4	no	—
63	C₁₁×D₈	—	4	4	no	—
64	C₁₁×M₁₆	—	4	2	no	—
65	C₁₁×M₁₆	—	4	2	no	—
66	C₂×C₈×C₁₁	—	4	2	no	—
67	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	D₈	1	2	yes	—
70	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
71	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₁	#41	1	2	yes	—
75	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₄²×C₁₁	D₈	1	2	yes	—
78	C₁₁×C₁₆	—	2	4	no	—
79	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
80	C₂×#361	C₂×C₁₁	1	4	yes	complemented
81	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
82	#1848	C₂×C₁₁	1	1	yes	characteristic, complemented
83	C₂³×C₁₁	—	4	4	no	—
84	C₂³×C₁₁	—	8	8	no	—
85	C₂³×C₁₁	—	8	2	no	—
86	C₂³×C₁₁	—	8	2	no	—
87	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
88	D₄×C₁₁	—	4	4	no	—
89	D₄×C₁₁	—	4	4	no	—
90	D₄×C₁₁	—	8	8	no	—
91	D₄×C₁₁	—	8	8	no	—
92	D₄×C₁₁	—	8	2	no	—
93	D₄×C₁₁	—	8	2	no	—
94	C₂×C₄×C₁₁	—	2	4	no	—
95	C₂×C₄×C₁₁	#102	1	2	yes	—
96	C₂×C₄×C₁₁	#102	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
103	C₈×C₁₁	—	8	2	no	—
104	C₈×C₁₁	#102	1	2	yes	—
105	C₈×C₁₁	#102	1	2	yes	—
106	C₈×C₁₁	C₄×D₄	1	2	yes	—
107	C₈×C₁₁	#121	1	2	yes	—
108	C₂²×D₈	—	2	1	no	—
109	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
110	C₂×#127	—	2	1	no	—
111	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
112	#493	—	2	1	no	—
113	#493	—	2	1	no	—
114	#493	C₄×C₁₁	1	2	yes	—
115	#493	C₄×C₁₁	1	2	yes	—
116	C₂×#108	—	2	1	no	—
117	C₂×#108	C₂²×C₁₁	1	2	yes	—
118	#423	—	2	1	no	—
119	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
120	#361	—	2	8	no	—
121	#346	—	2	1	no	—
122	C₄×C₁₆	—	2	1	no	—
123	C₂²×C₁₁	—	2	2	no	—
124	C₂²×C₁₁	—	8	8	no	—
125	C₂²×C₁₁	—	8	4	no	—
126	C₂²×C₁₁	—	16	4	no	—
127	C₂²×C₁₁	—	16	4	no	—
128	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
129	C₂²×C₁₁	#486	1	1	yes	characteristic
130	C₂²×C₁₁	#492	1	1	yes	characteristic
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	#361	1	4	yes	complemented
133	C₄×C₁₁	#390	1	1	yes	characteristic
134	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
135	C₄×C₁₁	#486	1	1	yes	characteristic
136	C₄×C₁₁	#493	1	1	yes	characteristic
137	C₂²×D₄	—	2	2	no	—
138	C₂²×D₄	—	4	2	no	—
139	C₂×D₈	—	2	2	no	—
140	C₂×D₈	—	2	2	no	—
141	C₂×D₈	—	2	4	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	4	no	—
144	C₂×D₈	—	4	2	no	—
145	C₂×D₈	—	4	2	no	—
146	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
149	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
150	#127	—	2	2	no	—
151	#127	—	2	2	no	—
152	#127	—	4	2	no	—
153	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
154	M₃₂	—	2	2	no	—
155	M₃₂	D₄×C₁₁	1	4	yes	complemented
156	C₂×C₁₆	—	2	2	no	—
157	#108	—	2	4	no	—
158	#108	—	4	2	no	—
159	C₄⋊C₈	—	4	2	no	—
160	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
161	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
162	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
163	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₁₁	—	2	1	no	—
165	C₂×C₁₁	—	2	1	no	—
166	C₂×C₁₁	—	16	4	no	—
167	C₂×C₁₁	#1957	1	1	yes	characteristic
168	C₂×C₁₁	C₂×#361	1	2	yes	—
169	C₂⁴	—	4	2	no	—
170	C₂×D₄	—	2	4	no	—
171	C₂×D₄	—	4	4	no	—
172	C₂×D₄	—	4	4	no	—
173	C₂×D₄	—	4	2	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂×D₄	—	4	2	no	—
176	C₂×D₄	—	4	2	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	8	8	no	—
179	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
180	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
181	D₈	—	2	8	no	—
182	D₈	—	4	4	no	—
183	D₈	—	4	4	no	—
184	D₈	—	4	4	no	—
185	M₁₆	—	4	2	no	—
186	M₁₆	—	4	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₈	C₁₁×D₈	1	2	yes	—
191	C₂×C₈	C₁₁×SD₁₆	1	2	yes	—
192	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
193	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
194	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
195	C₂×C₈	C₁₁×#41	1	2	yes	—
196	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
198	C₄²	C₁₁×D₈	1	2	yes	—
199	C₁₆	—	2	4	no	—
200	C₁₁	#13213	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³	—	4	4	no	—
202	C₂³	—	8	8	no	—
203	C₂³	—	8	2	no	—
204	C₂³	—	8	2	no	—
205	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
206	D₄	—	4	4	no	—
207	D₄	—	4	4	no	—
208	D₄	—	8	8	no	—
209	D₄	—	8	2	no	—
210	D₄	—	8	8	no	—
211	D₄	—	8	2	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	C₁₁×#102	1	2	yes	—
214	C₂×C₄	C₁₁×#102	1	2	yes	—
215	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
217	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
218	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
219	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
220	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
221	C₈	—	8	2	no	—
222	C₈	C₁₁×#102	1	2	yes	—
223	C₈	C₁₁×#102	1	2	yes	—
224	C₈	C₄×D₄×C₁₁	1	2	yes	—
225	C₈	C₁₁×#121	1	2	yes	—
226	C₂²	—	2	2	no	—
227	C₂²	—	8	8	no	—
228	C₂²	—	8	4	no	—
229	C₂²	—	16	4	no	—
230	C₂²	—	16	4	no	—
231	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
232	C₂²	C₁₁×#486	1	1	yes	characteristic
233	C₂²	C₁₁×#492	1	1	yes	characteristic
234	C₄	—	2	2	no	—
235	C₄	C₁₁×#361	1	4	yes	complemented
236	C₄	C₁₁×#390	1	1	yes	characteristic
237	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
238	C₄	C₁₁×#486	1	1	yes	characteristic
239	C₄	C₁₁×#493	1	1	yes	characteristic
240	C₂	—	2	1	no	—
241	C₂	—	2	1	no	—
242	C₂	—	16	4	no	—
243	C₂	C₁₁×#1957	1	1	yes	characteristic
244	C₂	C₂×C₁₁×#361	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#361	C₂	semidirect
3. C₄×C₁₁×M₃₂	C₂	semidirect
4. C₁₁×#1848	C₂	semidirect
38. C₁₁×M₃₂	D₄	semidirect
47. #13213	C₁₁	direct (N × H)
80. C₂×#361	C₂×C₁₁	semidirect
81. C₄×M₃₂	C₂×C₁₁	semidirect
82. #1848	C₂×C₁₁	semidirect
132. C₄×C₁₁	#361	semidirect
155. M₃₂	D₄×C₁₁	semidirect
200. C₁₁	#13213	direct (N × H)
235. C₄	C₁₁×#361	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#493	2
C₂×C₁₁×#361	2
C₄×C₁₁×M₃₂	2
C₁₁×#1848	2
#13213	11

Subgroups — C11×#13213 #14590406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13213 #14590406