Subgroups — C₂×C₁₁×#3138 #14637806

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3138	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#490	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#486	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#418	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₁	—	2	2	no	—
9	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
10	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
11	C₁₁×#533	—	2	4	no	—
12	C₁₁×#533	C₂²	1	8	yes	complemented
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₂×C₁₁×#127	—	2	2	no	—
15	C₂×C₁₁×#127	—	2	4	no	—
16	C₂×C₁₁×#127	C₂²	1	2	yes	—
17	C₂×C₁₁×#127	C₂²	1	2	yes	—
18	C₂×C₁₁×#127	C₂²	1	8	yes	—
19	C₂×C₁₁×#125	C₂²	1	2	yes	complemented
20	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₁	—	2	2	no	—
22	C₂×C₁₁×#117	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#490	C₂²	1	32	yes	complemented
25	C₁₁×#486	C₂²	1	32	yes	complemented
26	C₁₁×#418	C₂²	1	32	yes	complemented
27	C₂×C₁₁×#102	C₂²	1	16	yes	complemented
28	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
29	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
30	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
31	C₂⁵×C₁₁	—	2	2	no	—
32	C₂²×Q₈×C₁₁	—	2	2	no	—
33	C₂²×D₄×C₁₁	—	2	4	no	—
34	C₂²×D₄×C₁₁	—	2	2	no	—
35	C₂²×D₄×C₁₁	—	2	16	no	—
36	C₂²×D₄×C₁₁	—	2	4	no	—
37	C₂²×D₄×C₁₁	—	2	4	no	—
38	C₂²×D₄×C₁₁	—	2	16	no	—
39	C₂²×D₄×C₁₁	—	4	16	no	—
40	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
42	C₂³×C₄×C₁₁	D₄	1	2	yes	—
43	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₂×C₁₁×M₁₆	—	2	8	no	—
45	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
47	C₁₁×C₄⋊Q₈	—	2	4	no	—
48	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
49	C₁₁×#127	—	2	16	no	—
50	C₁₁×#127	—	2	4	no	—
51	C₁₁×#127	—	2	4	no	—
52	C₁₁×#127	C₂³	1	8	yes	—
53	C₁₁×#127	C₂³	1	8	yes	—
54	C₁₁×#125	—	2	4	no	—
55	C₁₁×#125	C₂³	1	8	yes	complemented
56	C₁₁×C₂²⋊Q₈	—	2	16	no	—
57	C₄×Q₈×C₁₁	—	2	16	no	—
58	C₁₁×#117	—	2	4	no	—
59	C₁₁×#117	C₂³	1	8	yes	—
60	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₁	—	2	2	no	—
65	C₂×C₄²×C₁₁	D₄	1	2	yes	—
66	C₂×C₄²×C₁₁	D₄	1	4	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
70	C₁₁×#102	C₂³	1	64	yes	complemented
71	C₁₁×#97	C₂³	1	8	yes	complemented
72	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
73	C₂×#3138	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₁	—	2	8	no	—
75	C₂⁴×C₁₁	—	2	4	no	—
76	C₂⁴×C₁₁	—	4	16	no	—
77	C₂⁴×C₁₁	—	4	8	no	—
78	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₁₁	—	2	8	no	—
80	C₂×Q₈×C₁₁	—	4	8	no	—
81	C₂×D₄×C₁₁	—	2	8	no	—
82	C₂×D₄×C₁₁	—	2	4	no	—
83	C₂×D₄×C₁₁	—	2	16	no	—
84	C₂×D₄×C₁₁	—	2	16	no	—
85	C₂×D₄×C₁₁	—	2	16	no	—
86	C₂×D₄×C₁₁	—	2	32	no	—
87	C₂×D₄×C₁₁	—	4	16	no	—
88	C₂×D₄×C₁₁	—	4	64	no	—
89	C₂×D₄×C₁₁	—	4	16	no	—
90	C₂×D₄×C₁₁	—	4	8	no	—
91	C₂×D₄×C₁₁	—	4	16	no	—
92	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
93	C₂²×C₄×C₁₁	—	2	8	no	—
94	C₂²×C₄×C₁₁	—	2	4	no	—
95	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₁	#41	1	8	yes	—
101	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₁₁×M₁₆	—	2	16	no	—
104	C₂×C₈×C₁₁	—	2	8	no	—
105	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
106	C₁₁×C₄⋊C₄	—	2	16	no	—
107	C₁₁×C₄⋊C₄	—	2	8	no	—
108	C₁₁×C₄⋊C₄	—	2	4	no	—
109	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
110	C₁₁×C₂²⋊C₄	—	2	8	no	—
111	C₄²×C₁₁	—	2	8	no	—
112	C₄²×C₁₁	C₂×D₄	1	8	yes	—
113	C₄²×C₁₁	C₂×D₄	1	2	yes	—
114	C₄²×C₁₁	C₂×D₄	1	2	yes	—
115	C₄²×C₁₁	C₂⁴	1	2	yes	—
116	C₄²×C₁₁	C₂⁴	1	2	yes	—
117	C₂×#533	C₂×C₁₁	1	1	yes	characteristic, complemented
118	C₂²×#127	C₂×C₁₁	1	1	yes	characteristic
119	#3138	C₂×C₁₁	1	16	yes	direct product factor
120	C₂×#490	C₂×C₁₁	1	4	yes	complemented
121	C₂×#486	C₂×C₁₁	1	4	yes	complemented
122	C₂×#418	C₂×C₁₁	1	4	yes	complemented
123	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	2	4	no	—
125	C₂³×C₁₁	—	2	8	no	—
126	C₂³×C₁₁	—	4	32	no	—
127	C₂³×C₁₁	—	4	16	no	—
128	C₂³×C₁₁	—	4	8	no	—
129	C₂³×C₁₁	—	4	16	no	—
130	C₂³×C₁₁	—	8	32	no	—
131	C₂³×C₁₁	#124	1	4	yes	—
132	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
133	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₁	—	4	16	no	—
135	D₄×C₁₁	—	2	16	no	—
136	D₄×C₁₁	—	4	32	no	—
137	D₄×C₁₁	—	4	16	no	—
138	D₄×C₁₁	—	4	8	no	—
139	D₄×C₁₁	—	4	32	no	—
140	C₂×C₄×C₁₁	—	2	4	no	—
141	C₂×C₄×C₁₁	—	2	16	no	—
142	C₂×C₄×C₁₁	—	2	8	no	—
143	C₂×C₄×C₁₁	—	4	8	no	—
144	C₂×C₄×C₁₁	#124	1	8	yes	—
145	C₂×C₄×C₁₁	#124	1	4	yes	—
146	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	8	yes	—
147	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
152	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
153	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
154	C₈×C₁₁	—	2	8	no	—
155	C₂³×D₄	—	2	2	no	—
156	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
157	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
158	#533	—	2	4	no	—
159	#533	C₂²×C₁₁	1	8	yes	complemented
160	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
161	C₂×#127	—	2	2	no	—
162	C₂×#127	—	2	4	no	—
163	C₂×#127	C₂²×C₁₁	1	2	yes	—
164	C₂×#127	C₂²×C₁₁	1	2	yes	—
165	C₂×#127	C₂²×C₁₁	1	8	yes	—
166	C₂×#125	C₂²×C₁₁	1	2	yes	complemented
167	C₂×C₂²⋊Q₈	—	2	2	no	—
168	C₂×C₄×Q₈	—	2	2	no	—
169	C₂×#117	C₂²×C₁₁	1	2	yes	—
170	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
171	#490	C₂²×C₁₁	1	32	yes	complemented
172	#486	C₂²×C₁₁	1	32	yes	complemented
173	#418	C₂²×C₁₁	1	32	yes	complemented
174	C₂×#102	C₂²×C₁₁	1	16	yes	complemented
175	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
176	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
177	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
178	C₂²×C₁₁	—	2	8	no	—
179	C₂²×C₁₁	—	2	4	no	—
180	C₂²×C₁₁	—	4	8	no	—
181	C₂²×C₁₁	—	4	16	no	—
182	C₂²×C₁₁	—	8	32	no	—
183	C₂²×C₁₁	—	8	16	no	—
184	C₂²×C₁₁	C₂×#124	1	4	yes	—
185	C₂²×C₁₁	C₂×#124	1	2	yes	—
186	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
187	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
188	C₄×C₁₁	—	2	4	no	—
189	C₄×C₁₁	—	4	8	no	—
190	C₄×C₁₁	C₂×#124	1	4	yes	—
191	C₄×C₁₁	C₂×#124	1	2	yes	—
192	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	8	yes	—
193	C₄×C₁₁	C₂²×#41	1	2	yes	—
194	C₂⁵	—	2	2	no	—
195	C₂²×Q₈	—	2	2	no	—
196	C₂²×D₄	—	2	2	no	—
197	C₂²×D₄	—	2	4	no	—
198	C₂²×D₄	—	2	4	no	—
199	C₂²×D₄	—	2	16	no	—
200	C₂²×D₄	—	2	4	no	—
201	C₂²×D₄	—	2	16	no	—
202	C₂²×D₄	—	4	16	no	—
203	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
204	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
205	C₂³×C₄	D₄×C₁₁	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
207	C₂×M₁₆	—	2	8	no	—
208	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
209	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
210	C₄⋊Q₈	—	2	4	no	—
211	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	complemented
212	#127	—	2	16	no	—
213	#127	—	2	4	no	—
214	#127	—	2	4	no	—
215	#127	C₂³×C₁₁	1	8	yes	—
216	#127	C₂³×C₁₁	1	8	yes	—
217	#125	—	2	4	no	—
218	#125	C₂³×C₁₁	1	8	yes	complemented
219	C₂²⋊Q₈	—	2	16	no	—
220	C₄×Q₈	—	2	16	no	—
221	#117	—	2	4	no	—
222	#117	C₂³×C₁₁	1	8	yes	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	D₄×C₁₁	1	2	yes	—
229	C₂×C₄²	D₄×C₁₁	1	4	yes	—
230	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
233	#102	C₂³×C₁₁	1	64	yes	complemented
234	#97	C₂³×C₁₁	1	8	yes	complemented
235	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
236	C₂×C₁₁	—	2	4	no	—
237	C₂×C₁₁	—	8	8	no	—
238	C₂×C₁₁	#3138	1	4	yes	direct product factor
239	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
240	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	2	yes	—
241	C₂⁴	—	2	8	no	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	—	4	16	no	—
244	C₂⁴	—	4	8	no	—
245	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	4	8	no	—
248	C₂×D₄	—	2	8	no	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	16	no	—
253	C₂×D₄	—	2	32	no	—
254	C₂×D₄	—	4	16	no	—
255	C₂×D₄	—	4	64	no	—
256	C₂×D₄	—	4	16	no	—
257	C₂×D₄	—	4	8	no	—
258	C₂×D₄	—	4	16	no	—
259	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
264	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
267	C₂²×C₄	C₁₁×#41	1	8	yes	—
268	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
270	M₁₆	—	2	16	no	—
271	C₂×C₈	—	2	8	no	—
272	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
273	C₄⋊C₄	—	2	16	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
277	C₂²⋊C₄	—	2	8	no	—
278	C₄²	—	2	8	no	—
279	C₄²	C₂×D₄×C₁₁	1	8	yes	—
280	C₄²	C₂×D₄×C₁₁	1	2	yes	—
281	C₄²	C₂×D₄×C₁₁	1	2	yes	—
282	C₄²	C₂⁴×C₁₁	1	2	yes	—
283	C₄²	C₂⁴×C₁₁	1	2	yes	—
284	C₁₁	C₂×#3138	1	1	yes	characteristic, direct product factor, Sylow
285	C₂³	—	2	4	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	4	32	no	—
288	C₂³	—	4	16	no	—
289	C₂³	—	4	8	no	—
290	C₂³	—	4	16	no	—
291	C₂³	—	8	32	no	—
292	C₂³	C₁₁×#124	1	4	yes	—
293	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
294	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
295	Q₈	—	4	16	no	—
296	D₄	—	2	16	no	—
297	D₄	—	4	32	no	—
298	D₄	—	4	16	no	—
299	D₄	—	4	8	no	—
300	D₄	—	4	32	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₁₁×#124	1	8	yes	—
306	C₂×C₄	C₁₁×#124	1	4	yes	—
307	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	8	yes	—
308	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
312	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
313	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
314	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
315	C₈	—	2	8	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	4	8	no	—
319	C₂²	—	4	16	no	—
320	C₂²	—	8	32	no	—
321	C₂²	—	8	16	no	—
322	C₂²	C₂×C₁₁×#124	1	4	yes	—
323	C₂²	C₂×C₁₁×#124	1	2	yes	—
324	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	4	yes	—
325	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×C₁₁×#124	1	4	yes	—
329	C₄	C₂×C₁₁×#124	1	2	yes	—
330	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	8	yes	—
331	C₄	C₂²×C₁₁×#41	1	2	yes	—
332	C₂	—	2	4	no	—
333	C₂	—	8	8	no	—
334	C₂	C₁₁×#3138	1	4	yes	direct product factor
335	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
336	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#533	C₂	semidirect
3. C₁₁×#3138	C₂	direct (N × H)
4. C₂×C₁₁×#490	C₂	semidirect
5. C₂×C₁₁×#486	C₂	semidirect
6. C₂×C₁₁×#418	C₂	semidirect
7. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
12. C₁₁×#533	C₂²	semidirect
13. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₁×#125	C₂²	semidirect
24. C₁₁×#490	C₂²	semidirect
25. C₁₁×#486	C₂²	semidirect
26. C₁₁×#418	C₂²	semidirect
27. C₂×C₁₁×#102	C₂²	semidirect
28. C₄×C₁₁×M₁₆	C₂²	semidirect
29. C₂×C₁₁×#97	C₂²	semidirect
30. C₂×C₄×C₈×C₁₁	C₂²	semidirect
48. C₁₁×C₄⋊Q₈	C₂³	semidirect
55. C₁₁×#125	C₂³	semidirect
70. C₁₁×#102	C₂³	semidirect
71. C₁₁×#97	C₂³	semidirect
72. C₄×C₈×C₁₁	C₂³	semidirect
73. C₂×#3138	C₁₁	direct (N × H)
117. C₂×#533	C₂×C₁₁	semidirect
119. #3138	C₂×C₁₁	direct (N × H)
120. C₂×#490	C₂×C₁₁	semidirect
121. C₂×#486	C₂×C₁₁	semidirect
122. C₂×#418	C₂×C₁₁	semidirect
123. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
159. #533	C₂²×C₁₁	semidirect
160. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
166. C₂×#125	C₂²×C₁₁	semidirect
171. #490	C₂²×C₁₁	semidirect
172. #486	C₂²×C₁₁	semidirect
173. #418	C₂²×C₁₁	semidirect
174. C₂×#102	C₂²×C₁₁	semidirect
175. C₄×M₁₆	C₂²×C₁₁	semidirect
176. C₂×#97	C₂²×C₁₁	semidirect
177. C₂×C₄×C₈	C₂²×C₁₁	semidirect
211. C₄⋊Q₈	C₂³×C₁₁	semidirect
218. #125	C₂³×C₁₁	semidirect
233. #102	C₂³×C₁₁	semidirect
234. #97	C₂³×C₁₁	semidirect
235. C₄×C₈	C₂³×C₁₁	semidirect
238. C₂×C₁₁	#3138	direct (N × H)
284. C₁₁	C₂×#3138	direct (N × H)
334. C₂	C₁₁×#3138	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×#533	2
C₂²×C₁₁×#127	2
C₁₁×#3138	2
C₂×C₁₁×#490	2
C₂×C₁₁×#486	2
C₂×C₁₁×#418	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#3138	11

Subgroups — C2×C11×#3138 #14637806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3138 #14637806