Subgroups — C₂×C₁₁×#2103 #14600945

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#430	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2103	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₁×#344	C₂	1	2	yes	maximal
5	C₂×C₁₁×#341	C₂	1	2	yes	maximal
6	C₂×C₁₁×#338	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
12	C₁₁×#430	—	2	2	no	—
13	C₁₁×#430	C₂²	1	4	yes	—
14	C₂×C₁₁×#108	—	2	2	no	—
15	C₁₁×#424	—	2	2	no	—
16	C₁₁×#424	C₂²	1	4	yes	—
17	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
18	C₁₁×#344	C₂²	1	8	yes	—
19	C₁₁×#341	C₂²	1	8	yes	—
20	C₁₁×#338	C₂²	1	4	yes	—
21	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	—	2	2	no	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	—	2	2	no	—
32	C₂×C₁₁×M₁₆	—	2	2	no	—
33	C₂×C₁₁×M₁₆	—	2	2	no	—
34	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
35	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
36	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
37	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₁	—	2	1	no	—
39	C₂²×C₈×C₁₁	—	2	1	no	—
40	C₂²×C₈×C₁₁	—	2	2	no	—
41	C₂²×C₈×C₁₁	—	2	2	no	—
42	C₂²×C₈×C₁₁	—	2	2	no	—
43	C₂²×C₈×C₁₁	—	2	2	no	—
44	C₂²×C₈×C₁₁	D₄	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₁₁×#117	—	2	1	no	—
47	C₁₁×#117	—	2	1	no	—
48	C₁₁×#117	Q₈	1	2	yes	—
49	C₁₁×#117	C₂³	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₁×C₂²⋊C₄	Q₈	1	2	yes	—
52	C₂×C₄²×C₁₁	—	2	1	no	—
53	C₁₁×#108	—	2	8	no	—
54	C₁₁×C₄⋊C₈	—	2	8	no	—
55	C₂×#2103	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	—	2	2	no	—
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	#41	1	2	yes	—
64	C₂²×C₄×C₁₁	#41	1	2	yes	—
65	C₂²×C₄×C₁₁	#41	1	2	yes	—
66	C₂²×C₄×C₁₁	#41	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
68	C₁₁×M₁₆	—	2	4	no	—
69	C₁₁×M₁₆	—	2	4	no	—
70	C₁₁×M₁₆	—	2	4	no	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	2	4	no	—
73	C₁₁×M₁₆	—	2	4	no	—
74	C₁₁×M₁₆	—	4	2	no	—
75	C₁₁×M₁₆	—	4	2	no	—
76	C₁₁×M₁₆	—	4	2	no	—
77	C₁₁×M₁₆	—	4	2	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	—	2	4	no	—
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	—	4	1	no	—
85	C₂×C₈×C₁₁	—	4	1	no	—
86	C₂×C₈×C₁₁	—	4	2	no	—
87	C₂×C₈×C₁₁	—	4	2	no	—
88	C₂×C₈×C₁₁	—	4	2	no	—
89	C₂×C₈×C₁₁	—	4	2	no	—
90	C₂×C₈×C₁₁	—	4	2	no	—
91	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₁₁×C₂²⋊C₄	—	2	2	no	—
95	C₁₁×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
96	C₄²×C₁₁	—	2	2	no	—
97	C₄²×C₁₁	—	2	2	no	—
98	C₂×#430	C₂×C₁₁	1	1	yes	characteristic
99	C₂×#424	C₂×C₁₁	1	1	yes	characteristic
100	#2103	C₂×C₁₁	1	8	yes	direct product factor
101	C₂×#344	C₂×C₁₁	1	2	yes	—
102	C₂×#341	C₂×C₁₁	1	2	yes	—
103	C₂×#338	C₂×C₁₁	1	1	yes	characteristic
104	C₂³×C₁₁	—	4	2	no	—
105	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
106	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂³×C₁₁	#125	1	2	yes	—
108	C₂³×C₁₁	#125	1	2	yes	—
109	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
110	C₂×C₄×C₁₁	—	2	4	no	—
111	C₂×C₄×C₁₁	—	4	4	no	—
112	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
114	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
115	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#123	1	2	yes	—
117	C₂×C₄×C₁₁	#124	1	2	yes	—
118	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
119	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
120	C₂×C₄×C₁₁	#125	1	2	yes	—
121	C₂×C₄×C₁₁	#125	1	2	yes	—
122	C₂×C₄×C₁₁	#126	1	2	yes	—
123	C₂×C₄×C₁₁	#126	1	2	yes	—
124	C₂×C₄×C₁₁	#126	1	2	yes	—
125	C₂×C₄×C₁₁	#126	1	2	yes	—
126	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
128	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
129	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
130	C₈×C₁₁	—	2	4	no	—
131	C₈×C₁₁	—	4	2	no	—
132	C₈×C₁₁	—	4	4	no	—
133	C₈×C₁₁	—	4	4	no	—
134	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
135	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
136	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
137	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
138	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
139	#430	—	2	2	no	—
140	#430	C₂²×C₁₁	1	4	yes	—
141	C₂×#108	—	2	2	no	—
142	#424	—	2	2	no	—
143	#424	C₂²×C₁₁	1	4	yes	—
144	C₂×C₄⋊C₈	—	2	2	no	—
145	#344	C₂²×C₁₁	1	8	yes	—
146	#341	C₂²×C₁₁	1	8	yes	—
147	#338	C₂²×C₁₁	1	4	yes	—
148	C₂²×C₁₁	—	2	2	no	—
149	C₂²×C₁₁	—	2	4	no	—
150	C₂²×C₁₁	—	4	1	no	—
151	C₂²×C₁₁	—	4	2	no	—
152	C₂²×C₁₁	—	4	1	no	—
153	C₂²×C₁₁	#400	1	1	yes	characteristic
154	C₂²×C₁₁	#400	1	2	yes	—
155	C₂²×C₁₁	#400	1	1	yes	characteristic
156	C₂²×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
157	C₂²×C₁₁	C₂×#125	1	2	yes	—
158	C₄×C₁₁	—	4	4	no	—
159	C₄×C₁₁	#400	1	1	yes	characteristic
160	C₄×C₁₁	#400	1	2	yes	—
161	C₄×C₁₁	#400	1	1	yes	characteristic
162	C₄×C₁₁	C₂×#123	1	1	yes	characteristic
163	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
164	C₄×C₁₁	C₂×#126	1	2	yes	—
165	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	2	no	—
171	C₂×M₁₆	—	2	2	no	—
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂×M₁₆	—	2	2	no	—
175	C₂×M₁₆	—	2	2	no	—
176	C₂×M₁₆	—	2	2	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
179	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
180	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
181	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	—	2	1	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	—	2	2	no	—
186	C₂²×C₈	—	2	2	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	D₄×C₁₁	1	2	yes	—
189	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
190	#117	—	2	1	no	—
191	#117	—	2	1	no	—
192	#117	Q₈×C₁₁	1	2	yes	—
193	#117	C₂³×C₁₁	1	2	yes	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₂²⋊C₄	Q₈×C₁₁	1	2	yes	—
196	C₂×C₄²	—	2	1	no	—
197	#108	—	2	8	no	—
198	C₄⋊C₈	—	2	8	no	—
199	C₂×C₁₁	—	2	1	no	—
200	C₂×C₁₁	—	2	2	no	—
201	C₂×C₁₁	—	2	1	no	—
202	C₂×C₁₁	—	2	2	no	—
203	C₂×C₁₁	#2103	1	2	yes	direct product factor
204	C₂×C₁₁	C₂×#400	1	1	yes	characteristic
205	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
209	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
210	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
211	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
212	C₂²×C₄	C₁₁×#41	1	2	yes	—
213	C₂²×C₄	C₁₁×#41	1	2	yes	—
214	C₂²×C₄	C₁₁×#41	1	2	yes	—
215	C₂²×C₄	C₁₁×#41	1	2	yes	—
216	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
217	M₁₆	—	2	4	no	—
218	M₁₆	—	2	4	no	—
219	M₁₆	—	2	4	no	—
220	M₁₆	—	2	4	no	—
221	M₁₆	—	2	4	no	—
222	M₁₆	—	2	4	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	4	2	no	—
225	M₁₆	—	4	2	no	—
226	M₁₆	—	4	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₂×C₈	—	2	2	no	—
230	C₂×C₈	—	2	4	no	—
231	C₂×C₈	—	2	4	no	—
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	4	1	no	—
234	C₂×C₈	—	4	1	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	—	4	2	no	—
237	C₂×C₈	—	4	2	no	—
238	C₂×C₈	—	4	2	no	—
239	C₂×C₈	—	4	2	no	—
240	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	2	2	no	—
243	C₂²⋊C₄	—	2	2	no	—
244	C₂²⋊C₄	C₂×Q₈×C₁₁	1	4	yes	—
245	C₄²	—	2	2	no	—
246	C₄²	—	2	2	no	—
247	C₁₁	C₂×#2103	1	1	yes	characteristic, direct product factor, Sylow
248	C₂³	—	4	2	no	—
249	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂³	C₁₁×#125	1	2	yes	—
252	C₂³	C₁₁×#125	1	2	yes	—
253	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
259	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
260	C₂×C₄	C₁₁×#123	1	2	yes	—
261	C₂×C₄	C₁₁×#124	1	2	yes	—
262	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
263	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
264	C₂×C₄	C₁₁×#125	1	2	yes	—
265	C₂×C₄	C₁₁×#125	1	2	yes	—
266	C₂×C₄	C₁₁×#126	1	2	yes	—
267	C₂×C₄	C₁₁×#126	1	2	yes	—
268	C₂×C₄	C₁₁×#126	1	2	yes	—
269	C₂×C₄	C₁₁×#126	1	2	yes	—
270	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
272	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
273	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
274	C₈	—	2	4	no	—
275	C₈	—	4	2	no	—
276	C₈	—	4	4	no	—
277	C₈	—	4	4	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	4	1	no	—
281	C₂²	—	4	2	no	—
282	C₂²	—	4	1	no	—
283	C₂²	C₁₁×#400	1	1	yes	characteristic
284	C₂²	C₁₁×#400	1	2	yes	—
285	C₂²	C₁₁×#400	1	1	yes	characteristic
286	C₂²	C₂×C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
287	C₂²	C₂×C₁₁×#125	1	2	yes	—
288	C₄	—	4	4	no	—
289	C₄	C₁₁×#400	1	1	yes	characteristic
290	C₄	C₁₁×#400	1	1	yes	characteristic
291	C₄	C₁₁×#400	1	2	yes	—
292	C₄	C₂×C₁₁×#123	1	1	yes	characteristic
293	C₄	C₂×C₁₁×#124	1	1	yes	characteristic
294	C₄	C₂×C₁₁×#126	1	2	yes	—
295	C₂	—	2	1	no	—
296	C₂	—	2	2	no	—
297	C₂	—	2	1	no	—
298	C₂	—	2	2	no	—
299	C₂	C₁₁×#2103	1	2	yes	direct product factor
300	C₂	C₂×C₁₁×#400	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	#400
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2103	C₂	direct (N × H)
55. C₂×#2103	C₁₁	direct (N × H)
100. #2103	C₂×C₁₁	direct (N × H)
203. C₂×C₁₁	#2103	direct (N × H)
247. C₁₁	C₂×#2103	direct (N × H)
299. C₂	C₁₁×#2103	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#430	2
C₂×C₁₁×#424	2
C₁₁×#2103	2
C₂×C₁₁×#344	2
C₂×C₁₁×#341	2
C₂×C₁₁×#338	2
C₂×#2103	11

Subgroups — C2×C11×#2103 #14600945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2103 #14600945