Subgroups — C₁₁×#3219 #13066057

Order 1408.

396 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#464	C₂	1	2	yes	maximal, complemented
8	C₁₁×#463	C₂	1	2	yes	maximal, complemented
9	C₁₁×#452	C₂	1	2	yes	maximal, complemented
10	C₁₁×#449	C₂	1	2	yes	maximal, complemented
11	C₁₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#41	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₁₁×D₈	C₂²	1	2	yes	—
17	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₁×#127	C₂²	1	1	yes	characteristic
19	C₁₁×#126	—	2	1	no	—
20	C₁₁×#125	C₂²	1	1	yes	characteristic
21	C₁₁×#124	C₂²	1	1	yes	characteristic
22	C₁₁×#124	C₂²	1	2	yes	—
23	C₁₁×#123	—	2	1	no	—
24	C₁₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₁×#121	—	2	1	no	—
26	C₁₁×#121	—	2	1	no	—
27	C₁₁×#121	C₂²	1	1	yes	characteristic
28	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₁₁	—	2	1	no	—
30	C₄×D₄×C₁₁	—	2	1	no	—
31	C₄×D₄×C₁₁	—	2	1	no	—
32	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
33	C₁₁×#117	—	2	1	no	—
34	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
36	C₁₁×#103	C₂²	1	2	yes	—
37	C₁₁×#103	C₂²	1	2	yes	—
38	C₁₁×#102	C₂²	1	2	yes	—
39	C₁₁×#102	C₂²	1	2	yes	—
40	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₁₁×#97	C₂²	1	1	yes	characteristic
42	C₁₁×#97	C₂²	1	1	yes	characteristic
43	C₁₁×#41	—	4	2	no	—
44	C₁₁×#41	—	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	1	no	—
48	C₂×D₄×C₁₁	—	2	2	no	—
49	C₂×D₄×C₁₁	—	2	1	no	—
50	C₂×D₄×C₁₁	—	2	1	no	—
51	C₂×D₄×C₁₁	C₂³	1	2	yes	—
52	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	—	2	1	no	—
54	C₂²×C₄×C₁₁	—	2	2	no	—
55	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×Q₁₆	—	4	2	no	—
59	C₁₁×SD₁₆	—	4	2	no	—
60	C₁₁×SD₁₆	—	4	2	no	—
61	C₁₁×D₈	—	4	2	no	—
62	C₂×C₈×C₁₁	C₂³	1	2	yes	—
63	C₂×C₈×C₁₁	C₂³	1	2	yes	—
64	C₁₁×C₄⋊C₄	—	2	1	no	—
65	C₁₁×C₄⋊C₄	—	2	1	no	—
66	C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₁₁×C₄⋊C₄	—	2	1	no	—
69	C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₁₁×C₂²⋊C₄	—	2	1	no	—
73	C₁₁×C₂²⋊C₄	—	2	1	no	—
74	C₁₁×C₂²⋊C₄	—	2	1	no	—
75	C₁₁×C₂²⋊C₄	—	2	2	no	—
76	C₁₁×C₂²⋊C₄	—	2	2	no	—
77	C₁₁×C₂²⋊C₄	—	2	1	no	—
78	C₁₁×C₂²⋊C₄	—	2	1	no	—
79	C₄²×C₁₁	—	2	1	no	—
80	C₄²×C₁₁	D₄	1	1	yes	characteristic
81	C₄²×C₁₁	D₄	1	1	yes	characteristic
82	C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₄²×C₁₁	C₂³	1	1	yes	characteristic
84	#3219	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂³×C₁₁	—	2	1	no	—
86	C₂³×C₁₁	—	2	2	no	—
87	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
88	Q₈×C₁₁	—	2	2	no	—
89	Q₈×C₁₁	—	2	2	no	—
90	Q₈×C₁₁	—	2	2	no	—
91	D₄×C₁₁	—	2	2	no	—
92	D₄×C₁₁	—	2	2	no	—
93	D₄×C₁₁	—	2	2	no	—
94	D₄×C₁₁	—	4	2	no	—
95	D₄×C₁₁	—	4	2	no	—
96	D₄×C₁₁	—	4	2	no	—
97	D₄×C₁₁	—	4	4	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	2	1	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	4	1	no	—
104	C₂×C₄×C₁₁	—	4	1	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	4	no	—
107	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
113	C₈×C₁₁	—	2	2	no	—
114	C₈×C₁₁	—	2	2	no	—
115	#532	C₂×C₁₁	1	1	yes	characteristic, complemented
116	#529	C₂×C₁₁	1	1	yes	characteristic, complemented
117	#497	C₂×C₁₁	1	1	yes	characteristic, complemented
118	#496	C₂×C₁₁	1	1	yes	characteristic, complemented
119	#491	C₂×C₁₁	1	1	yes	characteristic, complemented
120	#490	C₂×C₁₁	1	1	yes	characteristic, complemented
121	#464	C₂×C₁₁	1	2	yes	complemented
122	#463	C₂×C₁₁	1	2	yes	complemented
123	#452	C₂×C₁₁	1	2	yes	complemented
124	#449	C₂×C₁₁	1	2	yes	complemented
125	#432	C₂×C₁₁	1	1	yes	characteristic, complemented
126	C₂²×C₁₁	—	2	1	no	—
127	C₂²×C₁₁	—	2	1	no	—
128	C₂²×C₁₁	—	2	1	no	—
129	C₂²×C₁₁	—	4	2	no	—
130	C₂²×C₁₁	—	4	1	no	—
131	C₂²×C₁₁	—	4	1	no	—
132	C₂²×C₁₁	—	4	2	no	—
133	C₂²×C₁₁	—	4	2	no	—
134	C₂²×C₁₁	—	4	1	no	—
135	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
136	C₄×C₁₁	—	2	1	no	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	2	1	no	—
141	C₄×C₁₁	—	4	2	no	—
142	C₄×C₁₁	—	4	1	no	—
143	C₄×C₁₁	—	4	1	no	—
144	C₄×C₁₁	—	4	1	no	—
145	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
146	C₂×#41	C₂²×C₁₁	1	2	yes	—
147	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
148	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
149	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
150	C₂×D₈	C₂²×C₁₁	1	2	yes	—
151	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
152	#127	C₂²×C₁₁	1	1	yes	characteristic
153	#126	—	2	1	no	—
154	#125	C₂²×C₁₁	1	1	yes	characteristic
155	#124	C₂²×C₁₁	1	1	yes	characteristic
156	#124	C₂²×C₁₁	1	2	yes	—
157	#123	—	2	1	no	—
158	C₂²⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
159	#121	—	2	1	no	—
160	#121	—	2	1	no	—
161	#121	C₂²×C₁₁	1	1	yes	characteristic
162	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
163	C₄×D₄	—	2	1	no	—
164	C₄×D₄	—	2	1	no	—
165	C₄×D₄	—	2	1	no	—
166	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
167	#117	—	2	1	no	—
168	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
169	C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
170	#103	C₂²×C₁₁	1	2	yes	—
171	#103	C₂²×C₁₁	1	2	yes	—
172	#102	C₂²×C₁₁	1	2	yes	—
173	#102	C₂²×C₁₁	1	2	yes	—
174	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
175	#97	C₂²×C₁₁	1	1	yes	characteristic
176	#97	C₂²×C₁₁	1	1	yes	characteristic
177	C₂×C₁₁	—	4	1	no	—
178	C₂×C₁₁	—	8	2	no	—
179	C₂×C₁₁	—	8	1	no	—
180	C₂×C₁₁	#535	1	1	yes	characteristic
181	C₂×C₁₁	#575	1	1	yes	characteristic
182	C₂×C₁₁	#575	1	1	yes	characteristic
183	#41	—	4	2	no	—
184	#41	—	4	2	no	—
185	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
186	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
187	C₂×D₄	—	2	1	no	—
188	C₂×D₄	—	2	2	no	—
189	C₂×D₄	—	2	1	no	—
190	C₂×D₄	—	2	1	no	—
191	C₂×D₄	C₂³×C₁₁	1	2	yes	—
192	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
193	C₂²×C₄	—	2	1	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
196	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
198	Q₁₆	—	4	2	no	—
199	SD₁₆	—	4	2	no	—
200	SD₁₆	—	4	2	no	—
201	D₈	—	4	2	no	—
202	C₂×C₈	C₂³×C₁₁	1	2	yes	—
203	C₂×C₈	C₂³×C₁₁	1	2	yes	—
204	C₄⋊C₄	—	2	1	no	—
205	C₄⋊C₄	—	2	1	no	—
206	C₄⋊C₄	—	2	1	no	—
207	C₄⋊C₄	—	2	1	no	—
208	C₄⋊C₄	—	2	1	no	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
211	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
212	C₂²⋊C₄	—	2	1	no	—
213	C₂²⋊C₄	—	2	1	no	—
214	C₂²⋊C₄	—	2	1	no	—
215	C₂²⋊C₄	—	2	2	no	—
216	C₂²⋊C₄	—	2	2	no	—
217	C₂²⋊C₄	—	2	1	no	—
218	C₂²⋊C₄	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	D₄×C₁₁	1	1	yes	characteristic
221	C₄²	D₄×C₁₁	1	1	yes	characteristic
222	C₄²	C₂³×C₁₁	1	1	yes	characteristic
223	C₄²	C₂³×C₁₁	1	1	yes	characteristic
224	C₁₁	#3219	1	1	yes	characteristic, direct product factor, Sylow
225	C₂³	—	2	1	no	—
226	C₂³	—	2	2	no	—
227	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
228	Q₈	—	2	2	no	—
229	Q₈	—	2	2	no	—
230	Q₈	—	2	2	no	—
231	D₄	—	2	2	no	—
232	D₄	—	2	2	no	—
233	D₄	—	2	2	no	—
234	D₄	—	4	2	no	—
235	D₄	—	4	2	no	—
236	D₄	—	4	2	no	—
237	D₄	—	4	4	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	4	no	—
247	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
248	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
249	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
250	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
251	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
252	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
253	C₈	—	2	2	no	—
254	C₈	—	2	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	2	1	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	4	1	no	—
260	C₂²	—	4	1	no	—
261	C₂²	—	4	2	no	—
262	C₂²	—	4	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	1	no	—
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	—	4	2	no	—
271	C₄	—	4	1	no	—
272	C₄	—	4	1	no	—
273	C₄	—	4	1	no	—
274	C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
275	C₂	—	4	1	no	—
276	C₂	—	8	2	no	—
277	C₂	—	8	1	no	—
278	C₂	C₁₁×#535	1	1	yes	characteristic
279	C₂	C₁₁×#575	1	1	yes	characteristic
280	C₂	C₁₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#532	C₂	semidirect
2. C₁₁×#529	C₂	semidirect
3. C₁₁×#497	C₂	semidirect
4. C₁₁×#496	C₂	semidirect
5. C₁₁×#491	C₂	semidirect
6. C₁₁×#490	C₂	semidirect
7. C₁₁×#464	C₂	semidirect
8. C₁₁×#463	C₂	semidirect
9. C₁₁×#452	C₂	semidirect
10. C₁₁×#449	C₂	semidirect
11. C₁₁×#432	C₂	semidirect
84. #3219	C₁₁	direct (N × H)
115. #532	C₂×C₁₁	semidirect
116. #529	C₂×C₁₁	semidirect
117. #497	C₂×C₁₁	semidirect
118. #496	C₂×C₁₁	semidirect
119. #491	C₂×C₁₁	semidirect
120. #490	C₂×C₁₁	semidirect
121. #464	C₂×C₁₁	semidirect
122. #463	C₂×C₁₁	semidirect
123. #452	C₂×C₁₁	semidirect
124. #449	C₂×C₁₁	semidirect
125. #432	C₂×C₁₁	semidirect
224. C₁₁	#3219	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×#532	2
C₁₁×#529	2
C₁₁×#497	2
C₁₁×#496	2
C₁₁×#491	2
C₁₁×#490	2
C₁₁×#464	2
C₁₁×#463	2
C₁₁×#452	2
C₁₁×#449	2
C₁₁×#432	2
#3219	11

Subgroups — C11×#3219 #13066057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3219 #13066057