Subgroups — C₂²×C₁₁×#443 #14637370

Order 2816.

2750 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#131	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₁×#443	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×#104	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×#41	C₂²	1	2	yes	—
8	C₂×C₁₁×#135	C₄	1	12	yes	complemented
9	C₂×C₁₁×#135	C₂²	1	12	yes	—
10	C₂²×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₁₁×SD₁₆	C₄	1	2	yes	complemented
12	C₂²×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₁×#131	—	2	12	no	—
14	C₂×C₁₁×#131	C₂²	1	24	yes	complemented
15	C₂²×C₁₁×M₁₆	—	2	2	no	—
16	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
17	C₂³×C₈×C₁₁	—	2	2	no	—
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#443	C₂²	1	64	yes	direct product factor
22	C₂×C₁₁×#108	C₂²	1	12	yes	complemented
23	C₂×C₁₁×#104	C₂²	1	24	yes	complemented
24	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	complemented
25	C₂×C₁₁×#41	—	2	6	no	—
26	C₂×C₁₁×#41	—	2	6	no	—
27	C₂×C₁₁×#41	C₂×C₄	1	12	yes	—
28	C₂×C₁₁×#41	C₂³	1	12	yes	—
29	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₁	—	2	2	no	—
31	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₁	—	2	1	no	—
33	C₂³×C₄×C₁₁	—	2	2	no	—
34	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
35	C₁₁×#135	C₂×C₄	1	48	yes	complemented
36	C₁₁×#135	C₂³	1	16	yes	—
37	C₂×C₁₁×Q₁₆	C₂×C₄	1	12	yes	complemented
38	C₂×C₁₁×SD₁₆	C₂×C₄	1	24	yes	complemented
39	C₂×C₁₁×D₈	C₂×C₄	1	12	yes	complemented
40	C₁₁×#131	—	2	48	no	—
41	C₁₁×#131	C₂³	1	32	yes	complemented
42	C₂×C₁₁×M₁₆	—	2	6	no	—
43	C₂×C₁₁×M₁₆	—	2	24	no	—
44	C₂×C₁₁×M₁₆	C₂³	1	12	yes	—
45	C₂²×C₈×C₁₁	—	2	2	no	—
46	C₂²×C₈×C₁₁	—	2	24	no	—
47	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	6	yes	—
50	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	D₄	1	6	yes	—
52	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
55	C₂×C₄²×C₁₁	—	2	3	no	—
56	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
57	C₁₁×#108	C₂³	1	16	yes	complemented
58	C₁₁×#104	C₂³	1	32	yes	complemented
59	C₄×C₈×C₁₁	C₂³	1	16	yes	complemented
60	C₂²×#443	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₁	—	2	2	no	—
62	C₂⁴×C₁₁	#41	1	1	yes	characteristic
63	C₁₁×#41	—	2	24	no	—
64	C₁₁×#41	—	2	12	no	—
65	C₁₁×#41	—	2	12	no	—
66	C₁₁×#41	C₂²×C₄	1	24	yes	—
67	C₁₁×#41	C₂⁴	1	8	yes	—
68	C₂×Q₈×C₁₁	—	2	6	no	—
69	C₂×Q₈×C₁₁	C₂²×C₄	1	12	yes	—
70	C₂×D₄×C₁₁	—	2	12	no	—
71	C₂×D₄×C₁₁	—	2	12	no	—
72	C₂×D₄×C₁₁	—	2	6	no	—
73	C₂×D₄×C₁₁	C₂²×C₄	1	12	yes	—
74	C₂²×C₄×C₁₁	—	2	8	no	—
75	C₂²×C₄×C₁₁	—	2	2	no	—
76	C₂²×C₄×C₁₁	—	2	6	no	—
77	C₂²×C₄×C₁₁	—	2	12	no	—
78	C₂²×C₄×C₁₁	—	2	12	no	—
79	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
81	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
83	C₂²×C₄×C₁₁	#41	1	3	yes	—
84	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
85	C₁₁×Q₁₆	C₂²×C₄	1	16	yes	complemented
86	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
87	C₁₁×D₈	C₂²×C₄	1	16	yes	complemented
88	C₁₁×M₁₆	—	2	32	no	—
89	C₁₁×M₁₆	—	2	12	no	—
90	C₁₁×M₁₆	C₂⁴	1	8	yes	—
91	C₂×C₈×C₁₁	—	2	32	no	—
92	C₂×C₈×C₁₁	—	2	12	no	—
93	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
94	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
95	C₂×C₈×C₁₁	C₂²×C₄	1	12	yes	—
96	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
97	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
98	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
99	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
100	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
101	C₄²×C₁₁	—	2	6	no	—
102	C₄²×C₁₁	C₂⁴	1	4	yes	—
103	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
104	C₂²×#131	C₂×C₁₁	1	2	yes	complemented
105	C₂×#443	C₂×C₁₁	1	24	yes	direct product factor
106	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
107	C₂²×#104	C₂×C₁₁	1	2	yes	complemented
108	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
109	C₂³×C₁₁	—	2	4	no	—
110	C₂³×C₁₁	—	2	12	no	—
111	C₂³×C₁₁	—	4	8	no	—
112	C₂³×C₁₁	C₄×D₄	1	3	yes	—
113	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
114	C₂³×C₁₁	C₂×#41	1	3	yes	—
115	Q₈×C₁₁	—	2	12	no	—
116	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
117	D₄×C₁₁	—	2	24	no	—
118	D₄×C₁₁	—	2	8	no	—
119	D₄×C₁₁	—	2	12	no	—
120	D₄×C₁₁	C₂³×C₄	1	8	yes	—
121	C₂×C₄×C₁₁	—	2	24	no	—
122	C₂×C₄×C₁₁	—	2	12	no	—
123	C₂×C₄×C₁₁	—	2	4	no	—
124	C₂×C₄×C₁₁	—	2	24	no	—
125	C₂×C₄×C₁₁	—	2	8	no	—
126	C₂×C₄×C₁₁	C₄×D₄	1	3	yes	—
127	C₂×C₄×C₁₁	C₄×D₄	1	3	yes	—
128	C₂×C₄×C₁₁	C₄×D₄	1	6	yes	—
129	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
130	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
131	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
132	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
133	C₂×C₄×C₁₁	C₂×#41	1	3	yes	—
134	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
135	C₈×C₁₁	—	2	8	no	—
136	C₈×C₁₁	C₂³×C₄	1	4	yes	—
137	C₈×C₁₁	C₂³×C₄	1	4	yes	—
138	C₈×C₁₁	C₂²×D₄	1	4	yes	—
139	C₈×C₁₁	C₂²×D₄	1	4	yes	—
140	C₂²×#41	C₂²×C₁₁	1	2	yes	—
141	C₂×#135	C₄×C₁₁	1	12	yes	complemented
142	C₂×#135	C₂²×C₁₁	1	12	yes	—
143	C₂²×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
144	C₂²×SD₁₆	C₄×C₁₁	1	2	yes	complemented
145	C₂²×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
146	C₂×#131	—	2	12	no	—
147	C₂×#131	C₂²×C₁₁	1	24	yes	complemented
148	C₂²×M₁₆	—	2	2	no	—
149	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
150	C₂³×C₈	—	2	2	no	—
151	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
152	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
153	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
154	#443	C₂²×C₁₁	1	64	yes	direct product factor
155	C₂×#108	C₂²×C₁₁	1	12	yes	complemented
156	C₂×#104	C₂²×C₁₁	1	24	yes	complemented
157	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	complemented
158	C₂²×C₁₁	—	2	6	no	—
159	C₂²×C₁₁	—	2	6	no	—
160	C₂²×C₁₁	—	2	8	no	—
161	C₂²×C₁₁	—	4	24	no	—
162	C₂²×C₁₁	#443	1	4	yes	direct product factor
163	C₂²×C₁₁	C₂×C₄×D₄	1	3	yes	—
164	C₂²×C₁₁	C₂×C₄×D₄	1	3	yes	—
165	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
166	C₄×C₁₁	—	2	8	no	—
167	C₄×C₁₁	—	2	8	no	—
168	C₄×C₁₁	C₂×C₄×D₄	1	3	yes	—
169	C₄×C₁₁	C₂×C₄×D₄	1	3	yes	—
170	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
171	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
172	C₂×#41	—	2	6	no	—
173	C₂×#41	—	2	6	no	—
174	C₂×#41	C₂×C₄×C₁₁	1	12	yes	—
175	C₂×#41	C₂³×C₁₁	1	12	yes	—
176	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
177	C₂²×D₄	—	2	2	no	—
178	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
179	C₂³×C₄	—	2	1	no	—
180	C₂³×C₄	—	2	2	no	—
181	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
182	#135	C₂×C₄×C₁₁	1	48	yes	complemented
183	#135	C₂³×C₁₁	1	16	yes	—
184	C₂×Q₁₆	C₂×C₄×C₁₁	1	12	yes	complemented
185	C₂×SD₁₆	C₂×C₄×C₁₁	1	24	yes	complemented
186	C₂×D₈	C₂×C₄×C₁₁	1	12	yes	complemented
187	#131	—	2	48	no	—
188	#131	C₂³×C₁₁	1	32	yes	complemented
189	C₂×M₁₆	—	2	6	no	—
190	C₂×M₁₆	—	2	24	no	—
191	C₂×M₁₆	C₂³×C₁₁	1	12	yes	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	24	no	—
194	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
195	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
196	C₂²×C₈	C₂×C₄×C₁₁	1	6	yes	—
197	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
198	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
199	C₂²×C₈	D₄×C₁₁	1	6	yes	—
200	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
201	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
202	C₂×C₄²	—	2	3	no	—
203	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
204	#108	C₂³×C₁₁	1	16	yes	complemented
205	#104	C₂³×C₁₁	1	32	yes	complemented
206	C₄×C₈	C₂³×C₁₁	1	16	yes	complemented
207	C₂×C₁₁	—	2	1	no	—
208	C₂×C₁₁	—	2	3	no	—
209	C₂×C₁₁	—	4	8	no	—
210	C₂×C₁₁	C₂×#443	1	6	yes	direct product factor
211	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
212	C₂⁴	—	2	2	no	—
213	C₂⁴	C₁₁×#41	1	1	yes	characteristic
214	#41	—	2	24	no	—
215	#41	—	2	12	no	—
216	#41	—	2	12	no	—
217	#41	C₂²×C₄×C₁₁	1	24	yes	—
218	#41	C₂⁴×C₁₁	1	8	yes	—
219	C₂×Q₈	—	2	6	no	—
220	C₂×Q₈	C₂²×C₄×C₁₁	1	12	yes	—
221	C₂×D₄	—	2	12	no	—
222	C₂×D₄	—	2	12	no	—
223	C₂×D₄	—	2	6	no	—
224	C₂×D₄	C₂²×C₄×C₁₁	1	12	yes	—
225	C₂²×C₄	—	2	8	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	6	no	—
228	C₂²×C₄	—	2	12	no	—
229	C₂²×C₄	—	2	12	no	—
230	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
231	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
234	C₂²×C₄	C₁₁×#41	1	3	yes	—
235	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
236	Q₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
237	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
238	D₈	C₂²×C₄×C₁₁	1	16	yes	complemented
239	M₁₆	—	2	12	no	—
240	M₁₆	—	2	32	no	—
241	M₁₆	C₂⁴×C₁₁	1	8	yes	—
242	C₂×C₈	—	2	12	no	—
243	C₂×C₈	—	2	32	no	—
244	C₂×C₈	C₂²×C₄×C₁₁	1	6	yes	—
245	C₂×C₈	C₂²×C₄×C₁₁	1	6	yes	—
246	C₂×C₈	C₂²×C₄×C₁₁	1	12	yes	—
247	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
248	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
249	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
250	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
251	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
252	C₄²	—	2	6	no	—
253	C₄²	C₂⁴×C₁₁	1	4	yes	—
254	C₁₁	C₂²×#443	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³	—	2	4	no	—
256	C₂³	—	2	12	no	—
257	C₂³	—	4	8	no	—
258	C₂³	C₄×D₄×C₁₁	1	3	yes	—
259	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
260	C₂³	C₂×C₁₁×#41	1	3	yes	—
261	Q₈	—	2	12	no	—
262	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
263	D₄	—	2	24	no	—
264	D₄	—	2	8	no	—
265	D₄	—	2	12	no	—
266	D₄	C₂³×C₄×C₁₁	1	8	yes	—
267	C₂×C₄	—	2	24	no	—
268	C₂×C₄	—	2	12	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	24	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	C₄×D₄×C₁₁	1	3	yes	—
273	C₂×C₄	C₄×D₄×C₁₁	1	3	yes	—
274	C₂×C₄	C₄×D₄×C₁₁	1	6	yes	—
275	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
276	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
277	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
278	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
279	C₂×C₄	C₂×C₁₁×#41	1	3	yes	—
280	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
281	C₈	—	2	8	no	—
282	C₈	C₂³×C₄×C₁₁	1	4	yes	—
283	C₈	C₂³×C₄×C₁₁	1	4	yes	—
284	C₈	C₂²×D₄×C₁₁	1	4	yes	—
285	C₈	C₂²×D₄×C₁₁	1	4	yes	—
286	C₂²	—	2	6	no	—
287	C₂²	—	2	6	no	—
288	C₂²	—	2	8	no	—
289	C₂²	—	4	24	no	—
290	C₂²	C₁₁×#443	1	4	yes	direct product factor
291	C₂²	C₂×C₄×D₄×C₁₁	1	3	yes	—
292	C₂²	C₂×C₄×D₄×C₁₁	1	3	yes	—
293	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
294	C₄	—	2	8	no	—
295	C₄	—	2	8	no	—
296	C₄	C₂×C₄×D₄×C₁₁	1	3	yes	—
297	C₄	C₂×C₄×D₄×C₁₁	1	3	yes	—
298	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
299	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
300	C₂	—	2	1	no	—
301	C₂	—	2	3	no	—
302	C₂	—	4	8	no	—
303	C₂	C₂×C₁₁×#443	1	6	yes	direct product factor
304	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₁	D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₄×D₄
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×#131	C₂	semidirect
3. C₂×C₁₁×#443	C₂	direct (N × H)
4. C₂²×C₁₁×#108	C₂	semidirect
5. C₂²×C₁₁×#104	C₂	semidirect
6. C₂²×C₄×C₈×C₁₁	C₂	semidirect
8. C₂×C₁₁×#135	C₄	semidirect
10. C₂²×C₁₁×Q₁₆	C₄	semidirect
11. C₂²×C₁₁×SD₁₆	C₄	semidirect
12. C₂²×C₁₁×D₈	C₄	semidirect
14. C₂×C₁₁×#131	C₂²	semidirect
21. C₁₁×#443	C₂²	direct (N × H)
22. C₂×C₁₁×#108	C₂²	semidirect
23. C₂×C₁₁×#104	C₂²	semidirect
24. C₂×C₄×C₈×C₁₁	C₂²	semidirect
35. C₁₁×#135	C₂×C₄	semidirect
37. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
38. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
39. C₂×C₁₁×D₈	C₂×C₄	semidirect
41. C₁₁×#131	C₂³	semidirect
57. C₁₁×#108	C₂³	semidirect
58. C₁₁×#104	C₂³	semidirect
59. C₄×C₈×C₁₁	C₂³	semidirect
60. C₂²×#443	C₁₁	direct (N × H)
85. C₁₁×Q₁₆	C₂²×C₄	semidirect
86. C₁₁×SD₁₆	C₂²×C₄	semidirect
87. C₁₁×D₈	C₂²×C₄	semidirect
104. C₂²×#131	C₂×C₁₁	semidirect
105. C₂×#443	C₂×C₁₁	direct (N × H)
106. C₂²×#108	C₂×C₁₁	semidirect
107. C₂²×#104	C₂×C₁₁	semidirect
108. C₂²×C₄×C₈	C₂×C₁₁	semidirect
141. C₂×#135	C₄×C₁₁	semidirect
143. C₂²×Q₁₆	C₄×C₁₁	semidirect
144. C₂²×SD₁₆	C₄×C₁₁	semidirect
145. C₂²×D₈	C₄×C₁₁	semidirect
147. C₂×#131	C₂²×C₁₁	semidirect
154. #443	C₂²×C₁₁	direct (N × H)
155. C₂×#108	C₂²×C₁₁	semidirect
156. C₂×#104	C₂²×C₁₁	semidirect
157. C₂×C₄×C₈	C₂²×C₁₁	semidirect
162. C₂²×C₁₁	#443	direct (N × H)
182. #135	C₂×C₄×C₁₁	semidirect
184. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
185. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
186. C₂×D₈	C₂×C₄×C₁₁	semidirect
188. #131	C₂³×C₁₁	semidirect
204. #108	C₂³×C₁₁	semidirect
205. #104	C₂³×C₁₁	semidirect
206. C₄×C₈	C₂³×C₁₁	semidirect
210. C₂×C₁₁	C₂×#443	direct (N × H)
236. Q₁₆	C₂²×C₄×C₁₁	semidirect
237. SD₁₆	C₂²×C₄×C₁₁	semidirect
238. D₈	C₂²×C₄×C₁₁	semidirect
254. C₁₁	C₂²×#443	direct (N × H)
290. C₂²	C₁₁×#443	direct (N × H)
303. C₂	C₂×C₁₁×#443	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#135	2
C₂²×C₁₁×#131	2
C₂×C₁₁×#443	2
C₂²×C₁₁×#108	2
C₂²×C₁₁×#104	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#443	11

Subgroups — C22×C11×#443 #14637370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#443 #14637370