Subgroups — C₁₁×#3299 #13066137

Order 1408.

388 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	C₁₁×#554	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#484	C₂	1	2	yes	maximal, complemented
5	C₁₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#467	C₂	1	2	yes	maximal, complemented
7	C₁₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#451	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₁×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
16	C₁₁×C₄⋊Q₈	—	2	1	no	—
17	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₁×#125	—	2	1	no	—
20	C₁₁×C₂²⋊Q₈	—	2	2	no	—
21	C₁₁×C₂²⋊Q₈	—	2	2	no	—
22	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₁	—	2	1	no	—
27	C₄×D₄×C₁₁	—	2	1	no	—
28	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
30	C₁₁×#107	C₂²	1	1	yes	characteristic
31	C₁₁×#107	C₂²	1	2	yes	—
32	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₁×#103	C₂²	1	1	yes	characteristic
34	C₁₁×#103	C₂²	1	2	yes	—
35	C₁₁×#103	C₂²	1	2	yes	—
36	C₁₁×#103	C₂²	1	2	yes	—
37	C₁₁×#103	C₂²	1	1	yes	characteristic
38	C₁₁×#103	C₂²	1	2	yes	—
39	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₁₁	—	2	2	no	—
42	C₂×Q₈×C₁₁	—	2	1	no	—
43	C₂×Q₈×C₁₁	—	2	4	no	—
44	C₂×Q₈×C₁₁	—	4	2	no	—
45	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
46	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×D₄×C₁₁	D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	—	2	2	no	—
51	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
52	C₁₁×Q₁₆	—	2	2	no	—
53	C₁₁×Q₁₆	—	4	2	no	—
54	C₂×C₈×C₁₁	—	4	2	no	—
55	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂³	1	2	yes	—
58	C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₁₁×C₄⋊C₄	—	2	1	no	—
60	C₁₁×C₄⋊C₄	—	2	1	no	—
61	C₁₁×C₄⋊C₄	—	2	1	no	—
62	C₁₁×C₄⋊C₄	—	2	1	no	—
63	C₁₁×C₄⋊C₄	—	2	1	no	—
64	C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₁₁×C₄⋊C₄	—	2	2	no	—
66	C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
69	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₁₁×C₂²⋊C₄	—	2	2	no	—
72	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
73	C₄²×C₁₁	—	2	1	no	—
74	C₄²×C₁₁	—	2	1	no	—
75	C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	#3299	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₁	C₂×D₄	1	2	yes	—
78	Q₈×C₁₁	—	2	1	no	—
79	Q₈×C₁₁	—	2	1	no	—
80	Q₈×C₁₁	—	2	2	no	—
81	Q₈×C₁₁	—	2	1	no	—
82	Q₈×C₁₁	—	2	2	no	—
83	Q₈×C₁₁	—	4	4	no	—
84	Q₈×C₁₁	—	8	1	no	—
85	Q₈×C₁₁	#41	1	2	yes	—
86	D₄×C₁₁	Q₁₆	1	4	yes	complemented
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	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	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	4	4	no	—
96	C₂×C₄×C₁₁	—	8	2	no	—
97	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
99	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	—	2	1	no	—
103	C₈×C₁₁	—	2	2	no	—
104	#554	C₂×C₁₁	1	1	yes	characteristic
105	D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic
106	#487	C₂×C₁₁	1	1	yes	characteristic, complemented
107	#484	C₂×C₁₁	1	2	yes	complemented
108	#477	C₂×C₁₁	1	1	yes	characteristic, complemented
109	#467	C₂×C₁₁	1	2	yes	complemented
110	#462	C₂×C₁₁	1	1	yes	characteristic, complemented
111	#451	C₂×C₁₁	1	2	yes	complemented
112	C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
113	C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
114	C₂×#103	C₂×C₁₁	1	2	yes	complemented
115	C₂²×C₁₁	—	2	2	no	—
116	C₂²×C₁₁	—	2	2	no	—
117	C₂²×C₁₁	C₂×Q₁₆	1	4	yes	—
118	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
119	C₄×C₁₁	—	2	2	no	—
120	C₄×C₁₁	—	2	2	no	—
121	C₄×C₁₁	—	2	1	no	—
122	C₄×C₁₁	—	4	2	no	—
123	C₄×C₁₁	—	4	1	no	—
124	C₄×C₁₁	—	4	1	no	—
125	C₄×C₁₁	—	4	1	no	—
126	C₄×C₁₁	—	4	2	no	—
127	C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
128	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
129	C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
130	C₂²×Q₈	C₂²×C₁₁	1	2	yes	—
131	C₂×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
132	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
133	C₂²×C₈	C₂²×C₁₁	1	2	yes	—
134	C₄⋊Q₈	—	2	1	no	—
135	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
136	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
137	#125	—	2	1	no	—
138	C₂²⋊Q₈	—	2	2	no	—
139	C₂²⋊Q₈	—	2	2	no	—
140	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
141	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
142	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
143	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
144	C₄×D₄	—	2	1	no	—
145	C₄×D₄	—	2	1	no	—
146	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
148	#107	C₂²×C₁₁	1	1	yes	characteristic
149	#107	C₂²×C₁₁	1	2	yes	—
150	C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
151	#103	C₂²×C₁₁	1	1	yes	characteristic
152	#103	C₂²×C₁₁	1	2	yes	—
153	#103	C₂²×C₁₁	1	2	yes	—
154	#103	C₂²×C₁₁	1	2	yes	—
155	#103	C₂²×C₁₁	1	1	yes	characteristic
156	#103	C₂²×C₁₁	1	2	yes	—
157	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
158	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
159	C₂×C₁₁	—	2	4	no	—
160	C₂×C₁₁	#546	1	1	yes	characteristic
161	C₂×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
162	C₂×C₁₁	#577	1	1	yes	characteristic
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	1	no	—
165	C₂×Q₈	—	2	4	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
168	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
169	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
170	C₂×D₄	D₄×C₁₁	1	1	yes	characteristic
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
174	Q₁₆	—	2	2	no	—
175	Q₁₆	—	4	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
178	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
179	C₂×C₈	C₂³×C₁₁	1	2	yes	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
189	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
190	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
191	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	2	2	no	—
194	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
195	C₄²	—	2	1	no	—
196	C₄²	—	2	1	no	—
197	C₄²	C₂³×C₁₁	1	1	yes	characteristic
198	C₁₁	#3299	1	1	yes	characteristic, direct product factor, Sylow
199	C₂³	C₂×D₄×C₁₁	1	2	yes	—
200	Q₈	—	2	1	no	—
201	Q₈	—	2	1	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	2	1	no	—
204	Q₈	—	2	2	no	—
205	Q₈	—	4	4	no	—
206	Q₈	—	8	1	no	—
207	Q₈	C₁₁×#41	1	2	yes	—
208	D₄	C₁₁×Q₁₆	1	4	yes	complemented
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
220	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
221	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
222	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	2	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	2	2	no	—
228	C₂²	C₂×C₁₁×Q₁₆	1	4	yes	—
229	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	2	2	no	—
232	C₄	—	2	1	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	2	no	—
237	C₄	—	4	1	no	—
238	C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
239	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
240	C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂	—	2	4	no	—
242	C₂	C₁₁×#546	1	1	yes	characteristic
243	C₂	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
244	C₂	C₁₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#487	C₂	semidirect
4. C₁₁×#484	C₂	semidirect
5. C₁₁×#477	C₂	semidirect
6. C₁₁×#467	C₂	semidirect
7. C₁₁×#462	C₂	semidirect
8. C₁₁×#451	C₂	semidirect
9. C₄×C₁₁×Q₁₆	C₂	semidirect
11. C₂×C₁₁×#103	C₂	semidirect
76. #3299	C₁₁	direct (N × H)
86. D₄×C₁₁	Q₁₆	semidirect
106. #487	C₂×C₁₁	semidirect
107. #484	C₂×C₁₁	semidirect
108. #477	C₂×C₁₁	semidirect
109. #467	C₂×C₁₁	semidirect
110. #462	C₂×C₁₁	semidirect
111. #451	C₂×C₁₁	semidirect
112. C₄×Q₁₆	C₂×C₁₁	semidirect
114. C₂×#103	C₂×C₁₁	semidirect
198. C₁₁	#3299	direct (N × H)
208. D₄	C₁₁×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#554	2
D₄×Q₈×C₁₁	2
C₁₁×#487	2
C₁₁×#484	2
C₁₁×#477	2
C₁₁×#467	2
C₁₁×#462	2
C₁₁×#451	2
C₄×C₁₁×Q₁₆	2
C₈×D₄×C₁₁	2
C₂×C₁₁×#103	2
#3299	11

Subgroups — C11×#3299 #13066137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3299 #13066137