Subgroups — C₂×C₁₁×#2640 #14611808

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2640	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#397	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#393	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#390	C₂	1	2	yes	maximal
8	C₂×C₁₁×#376	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₁₁×#124	—	2	8	no	—
15	C₂×C₁₁×#124	C₂²	1	8	yes	—
16	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#397	C₂²	1	32	yes	complemented
24	C₁₁×#393	C₂²	1	32	yes	complemented
25	C₁₁×#391	C₂²	1	16	yes	complemented
26	C₁₁×#390	C₂²	1	16	yes	—
27	C₁₁×#376	C₂²	1	8	yes	complemented
28	C₂×C₁₁×#95	C₂²	1	2	yes	—
29	C₂×C₁₁×#95	C₂²	1	8	yes	—
30	C₂×C₁₁×#95	C₂²	1	2	yes	—
31	C₂⁵×C₁₁	C₂³	1	2	yes	—
32	C₂²×Q₈×C₁₁	—	2	4	no	—
33	C₂²×Q₈×C₁₁	—	2	8	no	—
34	C₂²×Q₈×C₁₁	—	2	8	no	—
35	C₂²×Q₈×C₁₁	—	4	8	no	—
36	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₁₁	C₂³	1	8	yes	—
38	C₂²×D₄×C₁₁	—	2	4	no	—
39	C₂²×D₄×C₁₁	—	2	8	no	—
40	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×C₄⋊Q₈	—	2	32	no	—
48	C₁₁×#124	—	2	32	no	—
49	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
50	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
51	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
52	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
53	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
54	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
55	C₂×C₁₁×C₂²⋊C₄	—	4	16	no	—
56	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
57	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
58	C₂×C₁₁×C₂²⋊C₄	C₂³	1	32	yes	—
59	C₂×C₄²×C₁₁	—	2	8	no	—
60	C₂×C₄²×C₁₁	D₄	1	8	yes	—
61	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
62	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
63	C₁₁×#95	C₂³	1	8	yes	—
64	C₁₁×#95	C₂³	1	8	yes	—
65	C₁₁×#95	C₂³	1	32	yes	—
66	C₂×#2640	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₁	—	2	4	no	—
68	C₂⁴×C₁₁	—	2	8	no	—
69	C₂⁴×C₁₁	—	2	8	no	—
70	C₂⁴×C₁₁	—	2	8	no	—
71	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
72	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₁₁	—	2	8	no	—
74	C₂×Q₈×C₁₁	—	2	16	no	—
75	C₂×Q₈×C₁₁	—	2	16	no	—
76	C₂×Q₈×C₁₁	—	4	16	no	—
77	C₂×Q₈×C₁₁	—	4	32	no	—
78	C₂×Q₈×C₁₁	—	4	16	no	—
79	C₂×D₄×C₁₁	—	2	8	no	—
80	C₂×D₄×C₁₁	—	2	16	no	—
81	C₂×D₄×C₁₁	—	4	16	no	—
82	C₂²×C₄×C₁₁	—	2	4	no	—
83	C₂²×C₄×C₁₁	—	2	4	no	—
84	C₂²×C₄×C₁₁	—	2	4	no	—
85	C₂²×C₄×C₁₁	—	2	8	no	—
86	C₂²×C₄×C₁₁	—	2	8	no	—
87	C₂²×C₄×C₁₁	—	2	8	no	—
88	C₂²×C₄×C₁₁	—	2	8	no	—
89	C₂²×C₄×C₁₁	—	2	16	no	—
90	C₂²×C₄×C₁₁	—	2	8	no	—
91	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₁	#41	1	8	yes	—
95	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
96	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
101	C₁₁×C₄⋊C₄	—	2	16	no	—
102	C₁₁×C₄⋊C₄	—	2	16	no	—
103	C₁₁×C₂²⋊C₄	—	2	16	no	—
104	C₁₁×C₂²⋊C₄	—	2	16	no	—
105	C₁₁×C₂²⋊C₄	—	4	32	no	—
106	C₄²×C₁₁	—	2	16	no	—
107	C₄²×C₁₁	C₂×D₄	1	16	yes	—
108	C₂²×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
109	C₂²×#124	C₂×C₁₁	1	1	yes	characteristic
110	#2640	C₂×C₁₁	1	16	yes	direct product factor
111	C₂×#397	C₂×C₁₁	1	4	yes	complemented
112	C₂×#393	C₂×C₁₁	1	4	yes	complemented
113	C₂×#391	C₂×C₁₁	1	2	yes	complemented
114	C₂×#390	C₂×C₁₁	1	2	yes	—
115	C₂×#376	C₂×C₁₁	1	1	yes	characteristic, complemented
116	C₂³×C₁₁	—	2	4	no	—
117	C₂³×C₁₁	—	2	8	no	—
118	C₂³×C₁₁	—	2	8	no	—
119	C₂³×C₁₁	—	2	8	no	—
120	C₂³×C₁₁	—	4	8	no	—
121	C₂³×C₁₁	—	4	8	no	—
122	C₂³×C₁₁	—	4	8	no	—
123	C₂³×C₁₁	—	4	32	no	—
124	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
125	C₂³×C₁₁	C₂×#41	1	4	yes	—
126	C₂³×C₁₁	H(5,𝔽₂)	1	4	yes	—
127	C₂³×C₁₁	2₋¹⁺⁴	1	4	yes	—
128	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
129	Q₈×C₁₁	—	4	32	no	—
130	Q₈×C₁₁	—	4	16	no	—
131	D₄×C₁₁	—	4	16	no	—
132	C₂×C₄×C₁₁	—	2	8	no	—
133	C₂×C₄×C₁₁	—	2	8	no	—
134	C₂×C₄×C₁₁	—	2	4	no	—
135	C₂×C₄×C₁₁	—	2	4	no	—
136	C₂×C₄×C₁₁	—	2	4	no	—
137	C₂×C₄×C₁₁	—	2	8	no	—
138	C₂×C₄×C₁₁	—	2	8	no	—
139	C₂×C₄×C₁₁	—	2	8	no	—
140	C₂×C₄×C₁₁	—	2	8	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	—	4	16	no	—
145	C₂×C₄×C₁₁	—	4	16	no	—
146	C₂×C₄×C₁₁	#124	1	16	yes	—
147	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
149	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
151	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
152	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
153	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
154	C₂×C₄⋊Q₈	—	2	8	no	—
155	C₂×C₄⋊Q₈	C₂²×C₁₁	1	8	yes	complemented
156	C₂×#124	—	2	8	no	—
157	C₂×#124	C₂²×C₁₁	1	8	yes	—
158	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
159	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
160	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
161	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
162	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	—
163	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
164	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
165	#397	C₂²×C₁₁	1	32	yes	complemented
166	#393	C₂²×C₁₁	1	32	yes	complemented
167	#391	C₂²×C₁₁	1	16	yes	complemented
168	#390	C₂²×C₁₁	1	16	yes	—
169	#376	C₂²×C₁₁	1	8	yes	complemented
170	C₂×#95	C₂²×C₁₁	1	2	yes	—
171	C₂×#95	C₂²×C₁₁	1	8	yes	—
172	C₂×#95	C₂²×C₁₁	1	2	yes	—
173	C₂²×C₁₁	—	4	4	no	—
174	C₂²×C₁₁	—	4	4	no	—
175	C₂²×C₁₁	—	4	4	no	—
176	C₂²×C₁₁	—	4	16	no	—
177	C₂²×C₁₁	—	8	16	no	—
178	C₂²×C₁₁	C₂×#124	1	4	yes	—
179	C₂²×C₁₁	#535	1	4	yes	—
180	C₂²×C₁₁	#536	1	4	yes	—
181	C₂²×C₁₁	#542	1	16	yes	—
182	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
183	C₂²×C₁₁	C₂²×#41	1	2	yes	—
184	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
185	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	2	yes	—
186	C₄×C₁₁	—	2	4	no	—
187	C₄×C₁₁	—	2	4	no	—
188	C₄×C₁₁	—	4	4	no	—
189	C₄×C₁₁	—	4	8	no	—
190	C₄×C₁₁	—	4	8	no	—
191	C₄×C₁₁	C₂×#124	1	8	yes	—
192	C₂⁵	C₂³×C₁₁	1	2	yes	—
193	C₂²×Q₈	—	2	4	no	—
194	C₂²×Q₈	—	2	8	no	—
195	C₂²×Q₈	—	2	8	no	—
196	C₂²×Q₈	—	4	8	no	—
197	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
198	C₂²×Q₈	C₂³×C₁₁	1	8	yes	—
199	C₂²×D₄	—	2	4	no	—
200	C₂²×D₄	—	2	8	no	—
201	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
202	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
203	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
204	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
208	C₄⋊Q₈	—	2	32	no	—
209	#124	—	2	32	no	—
210	C₂×C₄⋊C₄	—	2	8	no	—
211	C₂×C₄⋊C₄	—	2	8	no	—
212	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
214	C₂×C₂²⋊C₄	—	2	8	no	—
215	C₂×C₂²⋊C₄	—	2	8	no	—
216	C₂×C₂²⋊C₄	—	4	16	no	—
217	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₁₁	1	32	yes	—
220	C₂×C₄²	—	2	8	no	—
221	C₂×C₄²	D₄×C₁₁	1	8	yes	—
222	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
223	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
224	#95	C₂³×C₁₁	1	8	yes	—
225	#95	C₂³×C₁₁	1	8	yes	—
226	#95	C₂³×C₁₁	1	32	yes	—
227	C₂×C₁₁	—	8	4	no	—
228	C₂×C₁₁	#2640	1	8	yes	direct product factor
229	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
230	C₂×C₁₁	C₂×#535	1	1	yes	characteristic
231	C₂×C₁₁	C₂×#536	1	1	yes	characteristic
232	C₂×C₁₁	C₂×#542	1	4	yes	—
233	C₂⁴	—	2	4	no	—
234	C₂⁴	—	2	8	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
238	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
239	C₂×Q₈	—	2	8	no	—
240	C₂×Q₈	—	2	16	no	—
241	C₂×Q₈	—	2	16	no	—
242	C₂×Q₈	—	4	16	no	—
243	C₂×Q₈	—	4	32	no	—
244	C₂×Q₈	—	4	16	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	16	no	—
247	C₂×D₄	—	4	16	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
258	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
260	C₂²×C₄	C₁₁×#41	1	8	yes	—
261	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
262	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
264	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
266	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
267	C₄⋊C₄	—	2	16	no	—
268	C₄⋊C₄	—	2	16	no	—
269	C₂²⋊C₄	—	2	16	no	—
270	C₂²⋊C₄	—	2	16	no	—
271	C₂²⋊C₄	—	4	32	no	—
272	C₄²	—	2	16	no	—
273	C₄²	C₂×D₄×C₁₁	1	16	yes	—
274	C₁₁	C₂×#2640	1	1	yes	characteristic, direct product factor, Sylow
275	C₂³	—	2	4	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	8	no	—
279	C₂³	—	4	8	no	—
280	C₂³	—	4	8	no	—
281	C₂³	—	4	8	no	—
282	C₂³	—	4	32	no	—
283	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
284	C₂³	C₂×C₁₁×#41	1	4	yes	—
285	C₂³	C₁₁×H(5,𝔽₂)	1	4	yes	—
286	C₂³	C₁₁×2₋¹⁺⁴	1	4	yes	—
287	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
288	Q₈	—	4	32	no	—
289	Q₈	—	4	16	no	—
290	D₄	—	4	16	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	16	no	—
305	C₂×C₄	C₁₁×#124	1	16	yes	—
306	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
308	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
309	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	4	no	—
312	C₂²	—	4	4	no	—
313	C₂²	—	4	16	no	—
314	C₂²	—	8	16	no	—
315	C₂²	C₂×C₁₁×#124	1	4	yes	—
316	C₂²	C₁₁×#535	1	4	yes	—
317	C₂²	C₁₁×#536	1	4	yes	—
318	C₂²	C₁₁×#542	1	16	yes	—
319	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
320	C₂²	C₂²×C₁₁×#41	1	2	yes	—
321	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
322	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	2	yes	—
323	C₄	—	2	4	no	—
324	C₄	—	2	4	no	—
325	C₄	—	4	4	no	—
326	C₄	—	4	8	no	—
327	C₄	—	4	8	no	—
328	C₄	C₂×C₁₁×#124	1	8	yes	—
329	C₂	—	8	4	no	—
330	C₂	C₁₁×#2640	1	8	yes	direct product factor
331	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
332	C₂	C₂×C₁₁×#535	1	1	yes	characteristic
333	C₂	C₂×C₁₁×#536	1	1	yes	characteristic
334	C₂	C₂×C₁₁×#542	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×C₄⋊Q₈	C₂	semidirect
3. C₁₁×#2640	C₂	direct (N × H)
4. C₂×C₁₁×#397	C₂	semidirect
5. C₂×C₁₁×#393	C₂	semidirect
6. C₂×C₁₁×#391	C₂	semidirect
8. C₂×C₁₁×#376	C₂	semidirect
13. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
23. C₁₁×#397	C₂²	semidirect
24. C₁₁×#393	C₂²	semidirect
25. C₁₁×#391	C₂²	semidirect
27. C₁₁×#376	C₂²	semidirect
66. C₂×#2640	C₁₁	direct (N × H)
108. C₂²×C₄⋊Q₈	C₂×C₁₁	semidirect
110. #2640	C₂×C₁₁	direct (N × H)
111. C₂×#397	C₂×C₁₁	semidirect
112. C₂×#393	C₂×C₁₁	semidirect
113. C₂×#391	C₂×C₁₁	semidirect
115. C₂×#376	C₂×C₁₁	semidirect
155. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
165. #397	C₂²×C₁₁	semidirect
166. #393	C₂²×C₁₁	semidirect
167. #391	C₂²×C₁₁	semidirect
169. #376	C₂²×C₁₁	semidirect
228. C₂×C₁₁	#2640	direct (N × H)
274. C₁₁	C₂×#2640	direct (N × H)
330. C₂	C₁₁×#2640	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×C₄⋊Q₈	2
C₂²×C₁₁×#124	2
C₁₁×#2640	2
C₂×C₁₁×#397	2
C₂×C₁₁×#393	2
C₂×C₁₁×#391	2
C₂×C₁₁×#390	2
C₂×C₁₁×#376	2
C₂×#2640	11

Subgroups — C2×C11×#2640 #14611808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2640 #14611808