Subgroups — C₁₁×#9905 #14587098

Order 2816.

506 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2868	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1296	C₂	1	4	yes	maximal
5	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₁×C₄⋊Q₈	C₄	1	2	yes	—
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₁×#97	—	2	1	no	—
11	C₁₁×#384	—	2	1	no	—
12	C₁₁×#384	—	2	1	no	—
13	C₁₁×#384	C₄	1	2	yes	—
14	C₁₁×#384	C₂²	1	2	yes	—
15	C₄³×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#336	—	2	1	no	—
17	C₁₁×#336	—	2	1	no	—
18	C₁₁×#336	—	2	1	no	—
19	C₂²×Q₈×C₁₁	—	2	2	no	—
20	C₂²×C₈×C₁₁	—	2	2	no	—
21	C₂²×C₈×C₁₁	—	2	2	no	—
22	C₁₁×C₄⋊Q₈	—	4	4	no	—
23	C₁₁×C₄⋊Q₈	—	4	4	no	—
24	C₁₁×C₄⋊Q₈	—	4	2	no	—
25	C₁₁×C₄⋊Q₈	—	4	2	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
39	C₁₁×C₄⋊C₈	—	2	2	no	—
40	C₁₁×C₄⋊C₈	—	2	4	no	—
41	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
42	C₁₁×#97	—	4	2	no	—
43	#9905	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₁	—	4	4	no	—
45	C₂×Q₈×C₁₁	—	4	4	no	—
46	C₂×Q₈×C₁₁	—	4	4	no	—
47	C₂²×C₄×C₁₁	—	2	4	no	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	—	2	4	no	—
56	C₂×C₈×C₁₁	—	4	2	no	—
57	C₂×C₈×C₁₁	—	4	2	no	—
58	C₂×C₈×C₁₁	—	4	2	no	—
59	C₂×C₈×C₁₁	—	4	2	no	—
60	C₂×C₈×C₁₁	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	4	no	—
62	C₁₁×C₄⋊C₄	—	4	4	no	—
63	C₁₁×C₄⋊C₄	—	4	4	no	—
64	C₁₁×C₄⋊C₄	—	4	4	no	—
65	C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₁₁×C₄⋊C₄	—	4	2	no	—
67	C₁₁×C₄⋊C₄	—	4	4	no	—
68	C₄²×C₁₁	—	2	2	no	—
69	C₄²×C₁₁	—	2	2	no	—
70	C₄²×C₁₁	—	2	2	no	—
71	C₄²×C₁₁	—	2	2	no	—
72	C₄²×C₁₁	—	2	2	no	—
73	C₄²×C₁₁	D₈	1	2	yes	—
74	C₄²×C₁₁	SD₁₆	1	2	yes	—
75	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
76	C₄²×C₁₁	#41	1	2	yes	—
77	#2868	C₂×C₁₁	1	1	yes	characteristic
78	#1831	C₂×C₁₁	1	1	yes	characteristic
79	#1767	C₂×C₁₁	1	1	yes	characteristic
80	#1296	C₂×C₁₁	1	4	yes	—
81	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₁₁	—	8	8	no	—
83	C₂×C₄×C₁₁	—	2	1	no	—
84	C₂×C₄×C₁₁	—	2	1	no	—
85	C₂×C₄×C₁₁	—	2	1	no	—
86	C₂×C₄×C₁₁	—	2	1	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	4	4	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	4	4	no	—
96	C₂×C₄×C₁₁	#100	1	2	yes	—
97	C₂×C₄×C₁₁	#101	1	2	yes	—
98	C₂×C₄×C₁₁	#102	1	2	yes	—
99	C₂×C₄×C₁₁	#102	1	2	yes	—
100	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
101	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
102	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₁	#137	1	2	yes	—
108	C₂×C₄×C₁₁	#137	1	2	yes	—
109	C₈×C₁₁	—	4	4	no	—
110	C₈×C₁₁	—	8	2	no	—
111	C₂×C₄⋊Q₈	—	2	1	no	—
112	C₂×C₄⋊Q₈	—	2	1	no	—
113	C₂×C₄⋊Q₈	C₄×C₁₁	1	2	yes	—
114	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
115	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
116	C₂×#97	—	2	1	no	—
117	#384	—	2	1	no	—
118	#384	—	2	1	no	—
119	#384	C₄×C₁₁	1	2	yes	—
120	#384	C₂²×C₁₁	1	2	yes	—
121	C₄³	C₂²×C₁₁	1	1	yes	characteristic
122	#336	—	2	1	no	—
123	#336	—	2	1	no	—
124	#336	—	2	1	no	—
125	C₂²×C₁₁	#391	1	1	yes	characteristic
126	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
127	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
128	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
129	C₂²×C₁₁	#418	1	1	yes	characteristic
130	C₂²×C₁₁	#419	1	1	yes	characteristic
131	C₂²×C₁₁	#419	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	—	2	2	no	—
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	2	2	no	—
137	C₄×C₁₁	—	8	4	no	—
138	C₄×C₁₁	#474	1	2	yes	—
139	C₄×C₁₁	#475	1	2	yes	—
140	C₄×C₁₁	#489	1	2	yes	—
141	C₄×C₁₁	#501	1	2	yes	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₄⋊Q₈	—	4	4	no	—
146	C₄⋊Q₈	—	4	4	no	—
147	C₄⋊Q₈	—	4	2	no	—
148	C₄⋊Q₈	—	4	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
155	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
156	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
157	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
158	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
159	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
160	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
161	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	4	no	—
164	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
165	#97	—	4	2	no	—
166	C₂×C₁₁	#1545	1	1	yes	characteristic
167	C₂×C₁₁	#1546	1	1	yes	characteristic
168	C₂×C₁₁	#1556	1	1	yes	characteristic
169	C₂×C₁₁	#1558	1	1	yes	characteristic
170	C₂×C₁₁	#1988	1	1	yes	characteristic
171	C₂×C₁₁	#1993	1	1	yes	characteristic
172	C₂×C₁₁	#1997	1	1	yes	characteristic
173	C₂×Q₈	—	4	4	no	—
174	C₂×Q₈	—	4	4	no	—
175	C₂×Q₈	—	4	4	no	—
176	C₂²×C₄	—	2	4	no	—
177	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₄⋊C₄	—	4	4	no	—
191	C₄⋊C₄	—	4	4	no	—
192	C₄⋊C₄	—	4	4	no	—
193	C₄⋊C₄	—	4	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	4	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	C₁₁×D₈	1	2	yes	—
203	C₄²	C₁₁×SD₁₆	1	2	yes	—
204	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
205	C₄²	C₁₁×#41	1	2	yes	—
206	C₁₁	#9905	1	1	yes	characteristic, direct product factor, Sylow
207	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
208	Q₈	—	8	8	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	C₁₁×#100	1	2	yes	—
223	C₂×C₄	C₁₁×#101	1	2	yes	—
224	C₂×C₄	C₁₁×#102	1	2	yes	—
225	C₂×C₄	C₁₁×#102	1	2	yes	—
226	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
227	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
228	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
229	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
230	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
231	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
232	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄	C₁₁×#137	1	2	yes	—
234	C₂×C₄	C₁₁×#137	1	2	yes	—
235	C₈	—	4	4	no	—
236	C₈	—	8	2	no	—
237	C₂²	C₁₁×#391	1	1	yes	characteristic
238	C₂²	C₂×C₁₁×#100	1	1	yes	characteristic
239	C₂²	C₂×C₁₁×#101	1	1	yes	characteristic
240	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
241	C₂²	C₁₁×#418	1	1	yes	characteristic
242	C₂²	C₁₁×#419	1	1	yes	characteristic
243	C₂²	C₁₁×#419	1	1	yes	characteristic
244	C₄	—	2	2	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	8	4	no	—
250	C₄	C₁₁×#474	1	2	yes	—
251	C₄	C₁₁×#475	1	2	yes	—
252	C₄	C₁₁×#489	1	2	yes	—
253	C₄	C₁₁×#501	1	2	yes	—
254	C₂	C₁₁×#1545	1	1	yes	characteristic
255	C₂	C₁₁×#1546	1	1	yes	characteristic
256	C₂	C₁₁×#1556	1	1	yes	characteristic
257	C₂	C₁₁×#1558	1	1	yes	characteristic
258	C₂	C₁₁×#1988	1	1	yes	characteristic
259	C₂	C₁₁×#1993	1	1	yes	characteristic
260	C₂	C₁₁×#1997	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
41. C₁₁×C₄⋊C₈	Q₈	semidirect
43. #9905	C₁₁	direct (N × H)
164. C₄⋊C₈	Q₈×C₁₁	semidirect
206. C₁₁	#9905	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×#2868	2
C₁₁×#1831	2
C₁₁×#1767	2
C₁₁×#1296	2
#9905	11

Subgroups — C11×#9905 #14587098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#9905 #14587098