Subgroups — C₂²×C₁₁×#444 #14637371

Order 2816.

2710 conjugacy classes of subgroups.

The subgroup lattice has 300 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×#444	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×C₁₁×#97	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×#444	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×C₁₁×#97	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	2	no	—
33	C₂³×C₄×C₁₁	—	2	1	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	6	yes	—
51	C₂²×C₈×C₁₁	D₄	1	2	yes	—
52	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
54	C₂×C₄²×C₁₁	—	2	3	no	—
55	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
56	C₁₁×#108	C₂³	1	16	yes	complemented
57	C₁₁×#104	C₂³	1	32	yes	complemented
58	C₁₁×#97	C₂³	1	16	yes	complemented
59	C₂²×#444	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂⁴×C₁₁	—	2	2	no	—
61	C₂⁴×C₁₁	#41	1	1	yes	characteristic
62	C₁₁×#41	—	2	24	no	—
63	C₁₁×#41	—	2	12	no	—
64	C₁₁×#41	—	2	12	no	—
65	C₁₁×#41	C₂²×C₄	1	24	yes	—
66	C₁₁×#41	C₂⁴	1	8	yes	—
67	C₂×Q₈×C₁₁	—	2	6	no	—
68	C₂×Q₈×C₁₁	C₂²×C₄	1	12	yes	—
69	C₂×D₄×C₁₁	—	2	12	no	—
70	C₂×D₄×C₁₁	—	2	12	no	—
71	C₂×D₄×C₁₁	—	2	6	no	—
72	C₂×D₄×C₁₁	C₂²×C₄	1	12	yes	—
73	C₂²×C₄×C₁₁	—	2	2	no	—
74	C₂²×C₄×C₁₁	—	2	12	no	—
75	C₂²×C₄×C₁₁	—	2	12	no	—
76	C₂²×C₄×C₁₁	—	2	6	no	—
77	C₂²×C₄×C₁₁	—	4	4	no	—
78	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
80	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
81	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	#41	1	3	yes	—
83	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
84	C₁₁×Q₁₆	C₂²×C₄	1	16	yes	complemented
85	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
86	C₁₁×D₈	C₂²×C₄	1	16	yes	complemented
87	C₁₁×M₁₆	—	2	32	no	—
88	C₁₁×M₁₆	—	2	12	no	—
89	C₁₁×M₁₆	C₂⁴	1	8	yes	—
90	C₂×C₈×C₁₁	—	2	32	no	—
91	C₂×C₈×C₁₁	—	2	12	no	—
92	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
93	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
94	C₂×C₈×C₁₁	C₂²×C₄	1	12	yes	—
95	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
96	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
97	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
98	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
99	C₄²×C₁₁	—	2	6	no	—
100	C₄²×C₁₁	C₂⁴	1	4	yes	—
101	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
102	C₂²×#131	C₂×C₁₁	1	2	yes	complemented
103	C₂×#444	C₂×C₁₁	1	24	yes	direct product factor
104	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
105	C₂²×#104	C₂×C₁₁	1	2	yes	complemented
106	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
107	C₂³×C₁₁	—	2	4	no	—
108	C₂³×C₁₁	—	2	12	no	—
109	C₂³×C₁₁	—	4	8	no	—
110	C₂³×C₁₁	C₄×D₄	1	3	yes	—
111	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
112	C₂³×C₁₁	C₂×#41	1	3	yes	—
113	Q₈×C₁₁	—	2	12	no	—
114	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
115	D₄×C₁₁	—	2	24	no	—
116	D₄×C₁₁	—	2	8	no	—
117	D₄×C₁₁	—	2	12	no	—
118	D₄×C₁₁	C₂³×C₄	1	8	yes	—
119	C₂×C₄×C₁₁	—	2	12	no	—
120	C₂×C₄×C₁₁	—	2	24	no	—
121	C₂×C₄×C₁₁	—	2	8	no	—
122	C₂×C₄×C₁₁	—	2	4	no	—
123	C₂×C₄×C₁₁	—	4	12	no	—
124	C₂×C₄×C₁₁	C₄×D₄	1	3	yes	—
125	C₂×C₄×C₁₁	C₄×D₄	1	3	yes	—
126	C₂×C₄×C₁₁	C₄×D₄	1	6	yes	—
127	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
128	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
129	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
130	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
131	C₂×C₄×C₁₁	C₂×#41	1	3	yes	—
132	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
133	C₈×C₁₁	—	2	8	no	—
134	C₈×C₁₁	C₂³×C₄	1	4	yes	—
135	C₈×C₁₁	C₂³×C₄	1	4	yes	—
136	C₈×C₁₁	C₂²×D₄	1	8	yes	—
137	C₂²×#41	C₂²×C₁₁	1	2	yes	—
138	C₂×#135	C₄×C₁₁	1	12	yes	complemented
139	C₂×#135	C₂²×C₁₁	1	12	yes	—
140	C₂²×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
141	C₂²×SD₁₆	C₄×C₁₁	1	2	yes	complemented
142	C₂²×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
143	C₂×#131	—	2	12	no	—
144	C₂×#131	C₂²×C₁₁	1	24	yes	complemented
145	C₂²×M₁₆	—	2	2	no	—
146	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
147	C₂³×C₈	—	2	2	no	—
148	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
149	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
150	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
151	#444	C₂²×C₁₁	1	64	yes	direct product factor
152	C₂×#108	C₂²×C₁₁	1	12	yes	complemented
153	C₂×#104	C₂²×C₁₁	1	24	yes	complemented
154	C₂×#97	C₂²×C₁₁	1	12	yes	complemented
155	C₂²×C₁₁	—	2	6	no	—
156	C₂²×C₁₁	—	2	6	no	—
157	C₂²×C₁₁	—	2	8	no	—
158	C₂²×C₁₁	—	4	24	no	—
159	C₂²×C₁₁	#444	1	4	yes	direct product factor
160	C₂²×C₁₁	C₂×C₄×D₄	1	3	yes	—
161	C₂²×C₁₁	C₂×C₄×D₄	1	3	yes	—
162	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
163	C₄×C₁₁	—	2	8	no	—
164	C₄×C₁₁	—	4	4	no	—
165	C₄×C₁₁	C₂×C₄×D₄	1	3	yes	—
166	C₄×C₁₁	C₂×C₄×D₄	1	3	yes	—
167	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
168	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
169	C₂×#41	—	2	6	no	—
170	C₂×#41	—	2	6	no	—
171	C₂×#41	C₂×C₄×C₁₁	1	12	yes	—
172	C₂×#41	C₂³×C₁₁	1	12	yes	—
173	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
174	C₂²×D₄	—	2	2	no	—
175	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
176	C₂³×C₄	—	2	2	no	—
177	C₂³×C₄	—	2	1	no	—
178	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
179	#135	C₂×C₄×C₁₁	1	48	yes	complemented
180	#135	C₂³×C₁₁	1	16	yes	—
181	C₂×Q₁₆	C₂×C₄×C₁₁	1	12	yes	complemented
182	C₂×SD₁₆	C₂×C₄×C₁₁	1	24	yes	complemented
183	C₂×D₈	C₂×C₄×C₁₁	1	12	yes	complemented
184	#131	—	2	48	no	—
185	#131	C₂³×C₁₁	1	32	yes	complemented
186	C₂×M₁₆	—	2	6	no	—
187	C₂×M₁₆	—	2	24	no	—
188	C₂×M₁₆	C₂³×C₁₁	1	12	yes	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	—	2	24	no	—
191	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
193	C₂²×C₈	C₂×C₄×C₁₁	1	6	yes	—
194	C₂²×C₈	D₄×C₁₁	1	2	yes	—
195	C₂²×C₈	D₄×C₁₁	1	6	yes	—
196	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
197	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
198	C₂×C₄²	—	2	3	no	—
199	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
200	#108	C₂³×C₁₁	1	16	yes	complemented
201	#104	C₂³×C₁₁	1	32	yes	complemented
202	#97	C₂³×C₁₁	1	16	yes	complemented
203	C₂×C₁₁	—	2	1	no	—
204	C₂×C₁₁	—	2	3	no	—
205	C₂×C₁₁	—	4	8	no	—
206	C₂×C₁₁	C₂×#444	1	6	yes	direct product factor
207	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
208	C₂⁴	—	2	2	no	—
209	C₂⁴	C₁₁×#41	1	1	yes	characteristic
210	#41	—	2	24	no	—
211	#41	—	2	12	no	—
212	#41	—	2	12	no	—
213	#41	C₂²×C₄×C₁₁	1	24	yes	—
214	#41	C₂⁴×C₁₁	1	8	yes	—
215	C₂×Q₈	—	2	6	no	—
216	C₂×Q₈	C₂²×C₄×C₁₁	1	12	yes	—
217	C₂×D₄	—	2	12	no	—
218	C₂×D₄	—	2	12	no	—
219	C₂×D₄	—	2	6	no	—
220	C₂×D₄	C₂²×C₄×C₁₁	1	12	yes	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	2	12	no	—
223	C₂²×C₄	—	2	12	no	—
224	C₂²×C₄	—	2	6	no	—
225	C₂²×C₄	—	4	4	no	—
226	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
227	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
228	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
229	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
230	C₂²×C₄	C₁₁×#41	1	3	yes	—
231	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
232	Q₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
233	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
234	D₈	C₂²×C₄×C₁₁	1	16	yes	complemented
235	M₁₆	—	2	12	no	—
236	M₁₆	—	2	32	no	—
237	M₁₆	C₂⁴×C₁₁	1	8	yes	—
238	C₂×C₈	—	2	12	no	—
239	C₂×C₈	—	2	32	no	—
240	C₂×C₈	C₂²×C₄×C₁₁	1	6	yes	—
241	C₂×C₈	C₂²×C₄×C₁₁	1	6	yes	—
242	C₂×C₈	C₂²×C₄×C₁₁	1	12	yes	—
243	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
244	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
245	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
246	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
247	C₄²	—	2	6	no	—
248	C₄²	C₂⁴×C₁₁	1	4	yes	—
249	C₁₁	C₂²×#444	1	1	yes	characteristic, direct product factor, Sylow
250	C₂³	—	2	4	no	—
251	C₂³	—	2	12	no	—
252	C₂³	—	4	8	no	—
253	C₂³	C₄×D₄×C₁₁	1	3	yes	—
254	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
255	C₂³	C₂×C₁₁×#41	1	3	yes	—
256	Q₈	—	2	12	no	—
257	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
258	D₄	—	2	24	no	—
259	D₄	—	2	8	no	—
260	D₄	—	2	12	no	—
261	D₄	C₂³×C₄×C₁₁	1	8	yes	—
262	C₂×C₄	—	2	12	no	—
263	C₂×C₄	—	2	24	no	—
264	C₂×C₄	—	2	8	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	4	12	no	—
267	C₂×C₄	C₄×D₄×C₁₁	1	3	yes	—
268	C₂×C₄	C₄×D₄×C₁₁	1	3	yes	—
269	C₂×C₄	C₄×D₄×C₁₁	1	6	yes	—
270	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
271	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
272	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
273	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
274	C₂×C₄	C₂×C₁₁×#41	1	3	yes	—
275	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
276	C₈	—	2	8	no	—
277	C₈	C₂³×C₄×C₁₁	1	4	yes	—
278	C₈	C₂³×C₄×C₁₁	1	4	yes	—
279	C₈	C₂²×D₄×C₁₁	1	8	yes	—
280	C₂²	—	2	6	no	—
281	C₂²	—	2	6	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	4	24	no	—
284	C₂²	C₁₁×#444	1	4	yes	direct product factor
285	C₂²	C₂×C₄×D₄×C₁₁	1	3	yes	—
286	C₂²	C₂×C₄×D₄×C₁₁	1	3	yes	—
287	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
288	C₄	—	2	8	no	—
289	C₄	—	4	4	no	—
290	C₄	C₂×C₄×D₄×C₁₁	1	3	yes	—
291	C₄	C₂×C₄×D₄×C₁₁	1	3	yes	—
292	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
293	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
294	C₂	—	2	1	no	—
295	C₂	—	2	3	no	—
296	C₂	—	4	8	no	—
297	C₂	C₂×C₁₁×#444	1	6	yes	direct product factor
298	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×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×C₄×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×#444	C₂	direct (N × H)
4. C₂²×C₁₁×#108	C₂	semidirect
5. C₂²×C₁₁×#104	C₂	semidirect
6. C₂²×C₁₁×#97	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×#444	C₂²	direct (N × H)
22. C₂×C₁₁×#108	C₂²	semidirect
23. C₂×C₁₁×#104	C₂²	semidirect
24. C₂×C₁₁×#97	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
56. C₁₁×#108	C₂³	semidirect
57. C₁₁×#104	C₂³	semidirect
58. C₁₁×#97	C₂³	semidirect
59. C₂²×#444	C₁₁	direct (N × H)
84. C₁₁×Q₁₆	C₂²×C₄	semidirect
85. C₁₁×SD₁₆	C₂²×C₄	semidirect
86. C₁₁×D₈	C₂²×C₄	semidirect
102. C₂²×#131	C₂×C₁₁	semidirect
103. C₂×#444	C₂×C₁₁	direct (N × H)
104. C₂²×#108	C₂×C₁₁	semidirect
105. C₂²×#104	C₂×C₁₁	semidirect
106. C₂²×#97	C₂×C₁₁	semidirect
138. C₂×#135	C₄×C₁₁	semidirect
140. C₂²×Q₁₆	C₄×C₁₁	semidirect
141. C₂²×SD₁₆	C₄×C₁₁	semidirect
142. C₂²×D₈	C₄×C₁₁	semidirect
144. C₂×#131	C₂²×C₁₁	semidirect
151. #444	C₂²×C₁₁	direct (N × H)
152. C₂×#108	C₂²×C₁₁	semidirect
153. C₂×#104	C₂²×C₁₁	semidirect
154. C₂×#97	C₂²×C₁₁	semidirect
159. C₂²×C₁₁	#444	direct (N × H)
179. #135	C₂×C₄×C₁₁	semidirect
181. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
182. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
183. C₂×D₈	C₂×C₄×C₁₁	semidirect
185. #131	C₂³×C₁₁	semidirect
200. #108	C₂³×C₁₁	semidirect
201. #104	C₂³×C₁₁	semidirect
202. #97	C₂³×C₁₁	semidirect
206. C₂×C₁₁	C₂×#444	direct (N × H)
232. Q₁₆	C₂²×C₄×C₁₁	semidirect
233. SD₁₆	C₂²×C₄×C₁₁	semidirect
234. D₈	C₂²×C₄×C₁₁	semidirect
249. C₁₁	C₂²×#444	direct (N × H)
284. C₂²	C₁₁×#444	direct (N × H)
297. C₂	C₂×C₁₁×#444	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×#444	2
C₂²×C₁₁×#108	2
C₂²×C₁₁×#104	2
C₂²×C₁₁×#97	2
C₂²×#444	11

Subgroups — C22×C11×#444 #14637371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#444 #14637371