Subgroups — C₁₁×#3329 #13066167

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#555	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#485	C₂	1	2	yes	maximal, complemented
5	C₁₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#468	C₂	1	2	yes	maximal, complemented
7	C₁₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#448	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#419	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₁₁×M₁₆	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×#124	—	2	2	no	—
20	C₁₁×C₂²⋊Q₈	—	2	2	no	—
21	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₁₁×#121	—	2	1	no	—
23	C₁₁×#121	C₂²	1	2	yes	—
24	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₁₁	—	2	1	no	—
26	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#117	—	2	1	no	—
29	C₁₁×#117	C₂²	1	2	yes	—
30	C₁₁×#107	C₂²	1	2	yes	—
31	C₁₁×#106	C₂²	1	1	yes	characteristic
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	2	yes	—
38	C₁₁×#102	C₂²	1	1	yes	characteristic
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×D₄×C₁₁	—	2	2	no	—
48	C₂×D₄×C₁₁	D₄	1	1	yes	characteristic
49	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	—	2	2	no	—
51	C₂²×C₄×C₁₁	—	2	1	no	—
52	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
53	C₁₁×SD₁₆	—	2	2	no	—
54	C₁₁×SD₁₆	—	4	2	no	—
55	C₁₁×M₁₆	—	4	2	no	—
56	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂³	1	2	yes	—
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	2	no	—
64	C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₁₁×C₂²⋊C₄	—	2	2	no	—
69	C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₁₁×C₂²⋊C₄	—	2	1	no	—
72	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
73	C₄²×C₁₁	—	2	2	no	—
74	C₄²×C₁₁	—	2	1	no	—
75	C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	#3329	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₁	—	2	1	no	—
78	C₂³×C₁₁	C₂×D₄	1	2	yes	—
79	Q₈×C₁₁	—	2	1	no	—
80	Q₈×C₁₁	—	2	2	no	—
81	Q₈×C₁₁	—	2	2	no	—
82	Q₈×C₁₁	—	4	4	no	—
83	Q₈×C₁₁	—	8	1	no	—
84	Q₈×C₁₁	#41	1	2	yes	—
85	D₄×C₁₁	—	2	2	no	—
86	D₄×C₁₁	—	2	1	no	—
87	D₄×C₁₁	—	2	1	no	—
88	D₄×C₁₁	—	8	2	no	—
89	C₂×C₄×C₁₁	—	2	1	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	1	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	4	4	no	—
97	C₂×C₄×C₁₁	—	4	2	no	—
98	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
99	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
102	C₈×C₁₁	—	2	1	no	—
103	C₈×C₁₁	—	2	1	no	—
104	C₈×C₁₁	—	2	2	no	—
105	#555	C₂×C₁₁	1	1	yes	characteristic
106	D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
107	#487	C₂×C₁₁	1	1	yes	characteristic, complemented
108	#485	C₂×C₁₁	1	2	yes	complemented
109	#477	C₂×C₁₁	1	1	yes	characteristic, complemented
110	#468	C₂×C₁₁	1	2	yes	complemented
111	#461	C₂×C₁₁	1	1	yes	characteristic, complemented
112	#448	C₂×C₁₁	1	2	yes	complemented
113	C₄×SD₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
114	#436	C₂×C₁₁	1	1	yes	characteristic, complemented
115	#419	C₂×C₁₁	1	2	yes	complemented
116	C₂²×C₁₁	—	2	2	no	—
117	C₂²×C₁₁	—	2	2	no	—
118	C₂²×C₁₁	—	2	2	no	—
119	C₂²×C₁₁	—	4	1	no	—
120	C₂²×C₁₁	—	4	1	no	—
121	C₂²×C₁₁	—	4	1	no	—
122	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	—	2	2	no	—
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	4	2	no	—
127	C₄×C₁₁	—	4	1	no	—
128	C₄×C₁₁	—	4	1	no	—
129	C₄×C₁₁	—	4	2	no	—
130	C₄×C₁₁	#137	1	2	yes	—
131	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
132	C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
133	C₂²×Q₈	C₂²×C₁₁	1	2	yes	—
134	C₂×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
135	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
136	C₂×M₁₆	C₂²×C₁₁	1	2	yes	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
139	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
140	#124	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
143	#121	—	2	1	no	—
144	#121	C₂²×C₁₁	1	2	yes	—
145	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
146	C₄×D₄	—	2	1	no	—
147	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
148	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
149	#117	—	2	1	no	—
150	#117	C₂²×C₁₁	1	2	yes	—
151	#107	C₂²×C₁₁	1	2	yes	—
152	#106	C₂²×C₁₁	1	1	yes	characteristic
153	C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
154	#103	C₂²×C₁₁	1	1	yes	characteristic
155	#103	C₂²×C₁₁	1	2	yes	—
156	#103	C₂²×C₁₁	1	2	yes	—
157	#103	C₂²×C₁₁	1	2	yes	—
158	#103	C₂²×C₁₁	1	2	yes	—
159	#102	C₂²×C₁₁	1	1	yes	characteristic
160	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
161	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
162	C₂×C₁₁	—	4	2	no	—
163	C₂×C₁₁	—	8	1	no	—
164	C₂×C₁₁	#546	1	1	yes	characteristic
165	C₂×C₁₁	C₂×#137	1	1	yes	characteristic
166	C₂×C₁₁	#577	1	1	yes	characteristic
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	4	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
172	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	D₄×C₁₁	1	1	yes	characteristic
175	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
179	SD₁₆	—	2	2	no	—
180	SD₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
183	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
184	C₂×C₈	C₂³×C₁₁	1	2	yes	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
191	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
192	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
193	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
194	C₂²⋊C₄	—	2	2	no	—
195	C₂²⋊C₄	—	2	2	no	—
196	C₂²⋊C₄	—	2	2	no	—
197	C₂²⋊C₄	—	2	1	no	—
198	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	1	no	—
201	C₄²	C₂³×C₁₁	1	1	yes	characteristic
202	C₁₁	#3329	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³	—	2	1	no	—
204	C₂³	C₂×D₄×C₁₁	1	2	yes	—
205	Q₈	—	2	1	no	—
206	Q₈	—	2	2	no	—
207	Q₈	—	2	2	no	—
208	Q₈	—	4	4	no	—
209	Q₈	—	8	1	no	—
210	Q₈	C₁₁×#41	1	2	yes	—
211	D₄	—	2	2	no	—
212	D₄	—	2	1	no	—
213	D₄	—	2	1	no	—
214	D₄	—	8	2	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
225	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
226	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
227	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
228	C₈	—	2	1	no	—
229	C₈	—	2	1	no	—
230	C₈	—	2	2	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	2	no	—
234	C₂²	—	4	1	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	1	no	—
237	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	1	no	—
241	C₄	—	4	2	no	—
242	C₄	—	4	1	no	—
243	C₄	—	4	2	no	—
244	C₄	—	4	1	no	—
245	C₄	C₁₁×#137	1	2	yes	—
246	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
247	C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
248	C₂	—	4	2	no	—
249	C₂	—	8	1	no	—
250	C₂	C₁₁×#546	1	1	yes	characteristic
251	C₂	C₂×C₁₁×#137	1	1	yes	characteristic
252	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	C₁₁×#555	C₂
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
2. D₄×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#487	C₂	semidirect
4. C₁₁×#485	C₂	semidirect
5. C₁₁×#477	C₂	semidirect
6. C₁₁×#468	C₂	semidirect
7. C₁₁×#461	C₂	semidirect
8. C₁₁×#448	C₂	semidirect
9. C₄×C₁₁×SD₁₆	C₂	semidirect
10. C₁₁×#436	C₂	semidirect
11. C₁₁×#419	C₂	semidirect
76. #3329	C₁₁	direct (N × H)
106. D₄×Q₈	C₂×C₁₁	semidirect
107. #487	C₂×C₁₁	semidirect
108. #485	C₂×C₁₁	semidirect
109. #477	C₂×C₁₁	semidirect
110. #468	C₂×C₁₁	semidirect
111. #461	C₂×C₁₁	semidirect
112. #448	C₂×C₁₁	semidirect
113. C₄×SD₁₆	C₂×C₁₁	semidirect
114. #436	C₂×C₁₁	semidirect
115. #419	C₂×C₁₁	semidirect
202. C₁₁	#3329	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×#555	2
D₄×Q₈×C₁₁	2
C₁₁×#487	2
C₁₁×#485	2
C₁₁×#477	2
C₁₁×#468	2
C₁₁×#461	2
C₁₁×#448	2
C₄×C₁₁×SD₁₆	2
C₁₁×#436	2
C₁₁×#419	2
#3329	11

Subgroups — C11×#3329 #13066167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3329 #13066167