Subgroups — C₂×C₁₁×#3338 #14638422

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#554	C₂	1	2	yes	maximal
2	C₁₁×#3338	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#484	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#477	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₁×#107	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#554	—	2	8	no	—
13	C₁₁×#554	C₂²	1	16	yes	—
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₁×#125	—	2	2	no	—
16	C₂×C₁₁×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₁	—	2	2	no	—
20	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₂²×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
22	C₁₁×#500	C₂²	1	8	yes	complemented
23	C₁₁×#484	C₂²	1	32	yes	complemented
24	C₁₁×#477	C₂²	1	16	yes	complemented
25	C₁₁×#467	C₂²	1	16	yes	complemented
26	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
27	C₈×D₄×C₁₁	C₂²	1	8	yes	—
28	C₂×C₁₁×#107	C₂²	1	2	yes	—
29	C₂×C₁₁×#107	C₂²	1	2	yes	—
30	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#107	C₂²	1	4	yes	—
32	C₂×C₁₁×#107	C₂²	1	16	yes	complemented
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#103	C₂²	1	2	yes	—
35	C₂×C₁₁×#103	C₂²	1	4	yes	—
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₁₁	—	2	2	no	—
39	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁	—	2	4	no	—
42	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂×C₁₁×Q₁₆	—	2	4	no	—
44	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₁	—	2	8	no	—
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	—	2	4	no	—
51	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
52	C₁₁×#125	—	2	16	no	—
53	C₁₁×C₂²⋊Q₈	—	2	8	no	—
54	C₁₁×C₂²⋊Q₈	—	2	32	no	—
55	C₁₁×C₂²⋊Q₈	C₂³	1	16	yes	—
56	C₄×Q₈×C₁₁	—	2	4	no	—
57	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
58	C₄×D₄×C₁₁	—	2	16	no	—
59	C₄×D₄×C₁₁	D₄	1	4	yes	—
60	C₄×D₄×C₁₁	C₂³	1	4	yes	—
61	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
62	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
66	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₁₁×C₄⋊C₄	C₂³	1	16	yes	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₁	—	2	2	no	—
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#107	C₂³	1	8	yes	—
75	C₁₁×#107	C₂³	1	8	yes	—
76	C₁₁×#107	C₂³	1	4	yes	—
77	C₁₁×#107	C₂³	1	16	yes	—
78	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₁×#103	C₂³	1	8	yes	—
80	C₁₁×#103	C₂³	1	16	yes	—
81	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₁₁	C₂³	1	4	yes	—
83	C₂×#3338	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
85	C₂×Q₈×C₁₁	—	2	2	no	—
86	C₂×Q₈×C₁₁	—	2	8	no	—
87	C₂×Q₈×C₁₁	—	2	4	no	—
88	C₂×Q₈×C₁₁	—	2	4	no	—
89	C₂×Q₈×C₁₁	—	8	4	no	—
90	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
91	C₂×D₄×C₁₁	Q₁₆	1	8	yes	complemented
92	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₁	—	2	4	no	—
94	C₂²×C₄×C₁₁	—	2	4	no	—
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	—	2	4	no	—
98	C₂²×C₄×C₁₁	—	2	16	no	—
99	C₂²×C₄×C₁₁	—	8	8	no	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
106	C₁₁×Q₁₆	—	2	8	no	—
107	C₂×C₈×C₁₁	—	2	16	no	—
108	C₂×C₈×C₁₁	—	2	4	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	#41	1	4	yes	—
111	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
112	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
113	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
114	C₁₁×C₄⋊C₄	—	2	2	no	—
115	C₁₁×C₄⋊C₄	—	2	16	no	—
116	C₁₁×C₄⋊C₄	—	2	4	no	—
117	C₁₁×C₄⋊C₄	—	2	8	no	—
118	C₁₁×C₄⋊C₄	—	2	8	no	—
119	C₁₁×C₄⋊C₄	—	2	16	no	—
120	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
121	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
122	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
123	C₁₁×C₂²⋊C₄	—	2	16	no	—
124	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
125	C₄²×C₁₁	—	2	8	no	—
126	C₄²×C₁₁	C₂×D₄	1	2	yes	—
127	C₄²×C₁₁	C₂⁴	1	2	yes	—
128	C₂×#554	C₂×C₁₁	1	2	yes	—
129	#3338	C₂×C₁₁	1	16	yes	direct product factor
130	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
131	C₂×#484	C₂×C₁₁	1	4	yes	complemented
132	C₂×#477	C₂×C₁₁	1	2	yes	complemented
133	C₂×#467	C₂×C₁₁	1	2	yes	complemented
134	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
135	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
136	C₂²×#107	C₂×C₁₁	1	2	yes	complemented
137	C₂³×C₁₁	—	2	4	no	—
138	C₂³×C₁₁	—	2	4	no	—
139	C₂³×C₁₁	C₂×Q₁₆	1	8	yes	—
140	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
141	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₁	—	2	4	no	—
143	Q₈×C₁₁	—	2	4	no	—
144	Q₈×C₁₁	—	4	4	no	—
145	Q₈×C₁₁	—	8	8	no	—
146	D₄×C₁₁	C₂×Q₁₆	1	16	yes	complemented
147	C₂×C₄×C₁₁	—	2	4	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	8	no	—
150	C₂×C₄×C₁₁	—	2	4	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	—	2	4	no	—
153	C₂×C₄×C₁₁	—	2	4	no	—
154	C₂×C₄×C₁₁	—	2	8	no	—
155	C₂×C₄×C₁₁	—	4	4	no	—
156	C₂×C₄×C₁₁	—	4	4	no	—
157	C₂×C₄×C₁₁	—	4	8	no	—
158	C₂×C₄×C₁₁	—	8	16	no	—
159	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
160	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
166	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
167	C₈×C₁₁	—	2	4	no	—
168	C₈×C₁₁	—	2	2	no	—
169	C₈×C₁₁	C₂×#41	1	4	yes	—
170	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
172	#554	—	2	8	no	—
173	#554	C₂²×C₁₁	1	16	yes	—
174	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
175	C₂×#125	—	2	2	no	—
176	C₂×C₂²⋊Q₈	—	2	4	no	—
177	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
178	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
179	C₂×C₄×D₄	—	2	2	no	—
180	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
182	#500	C₂²×C₁₁	1	8	yes	complemented
183	#484	C₂²×C₁₁	1	32	yes	complemented
184	#477	C₂²×C₁₁	1	16	yes	complemented
185	#467	C₂²×C₁₁	1	16	yes	complemented
186	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
187	C₈×D₄	C₂²×C₁₁	1	8	yes	—
188	C₂×#107	C₂²×C₁₁	1	4	yes	—
189	C₂×#107	C₂²×C₁₁	1	2	yes	—
190	C₂×#107	C₂²×C₁₁	1	2	yes	—
191	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×#107	C₂²×C₁₁	1	16	yes	complemented
193	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
194	C₂×#103	C₂²×C₁₁	1	4	yes	—
195	C₂×#103	C₂²×C₁₁	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂²×C₁₁	—	2	16	no	—
199	C₂²×C₁₁	—	2	4	no	—
200	C₂²×C₁₁	—	2	4	no	—
201	C₂²×C₁₁	#547	1	2	yes	—
202	C₂²×C₁₁	C₂²×Q₁₆	1	8	yes	—
203	C₂²×C₁₁	C₂²×Q₁₆	1	2	yes	—
204	C₂²×C₁₁	#576	1	2	yes	—
205	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₁₁	—	2	4	no	—
207	C₄×C₁₁	—	2	2	no	—
208	C₄×C₁₁	—	4	4	no	—
209	C₄×C₁₁	—	4	4	no	—
210	C₄×C₁₁	—	4	8	no	—
211	C₄×C₁₁	#547	1	2	yes	—
212	C₄×C₁₁	C₂²×Q₁₆	1	4	yes	—
213	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
214	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
217	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
218	C₂³×C₄	—	2	4	no	—
219	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
220	C₂×Q₁₆	—	2	4	no	—
221	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
222	C₂²×C₈	—	2	8	no	—
223	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
225	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
229	#125	—	2	16	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₂²⋊Q₈	—	2	32	no	—
232	C₂²⋊Q₈	C₂³×C₁₁	1	16	yes	—
233	C₄×Q₈	—	2	4	no	—
234	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
235	C₄×D₄	—	2	16	no	—
236	C₄×D₄	D₄×C₁₁	1	4	yes	—
237	C₄×D₄	C₂³×C₁₁	1	4	yes	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	8	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₁	1	16	yes	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
251	#107	C₂³×C₁₁	1	4	yes	—
252	#107	C₂³×C₁₁	1	8	yes	—
253	#107	C₂³×C₁₁	1	16	yes	—
254	#107	C₂³×C₁₁	1	8	yes	—
255	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
256	#103	C₂³×C₁₁	1	8	yes	—
257	#103	C₂³×C₁₁	1	16	yes	—
258	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
259	C₄×C₈	C₂³×C₁₁	1	4	yes	—
260	C₂×C₁₁	—	2	8	no	—
261	C₂×C₁₁	#3338	1	4	yes	direct product factor
262	C₂×C₁₁	C₂×#547	1	1	yes	characteristic
263	C₂×C₁₁	C₂³×Q₁₆	1	1	yes	characteristic
264	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
265	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	8	4	no	—
271	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
272	C₂×D₄	C₁₁×Q₁₆	1	8	yes	complemented
273	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	16	no	—
280	C₂²×C₄	—	8	8	no	—
281	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
284	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
287	Q₁₆	—	2	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	16	no	—
291	C₂×C₈	C₁₁×#41	1	4	yes	—
292	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
293	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
294	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	16	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	16	no	—
301	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
302	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
303	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
304	C₂²⋊C₄	—	2	16	no	—
305	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
306	C₄²	—	2	8	no	—
307	C₄²	C₂×D₄×C₁₁	1	2	yes	—
308	C₄²	C₂⁴×C₁₁	1	2	yes	—
309	C₁₁	C₂×#3338	1	1	yes	characteristic, direct product factor, Sylow
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	C₂×C₁₁×Q₁₆	1	8	yes	—
313	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
314	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	4	4	no	—
318	Q₈	—	8	8	no	—
319	D₄	C₂×C₁₁×Q₁₆	1	16	yes	complemented
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	8	16	no	—
332	C₂×C₄	C₂×C₁₁×Q₁₆	1	4	yes	—
333	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
337	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
338	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	2	no	—
342	C₈	C₂×C₁₁×#41	1	4	yes	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	16	no	—
346	C₂²	C₁₁×#547	1	2	yes	—
347	C₂²	C₂²×C₁₁×Q₁₆	1	8	yes	—
348	C₂²	C₂²×C₁₁×Q₁₆	1	2	yes	—
349	C₂²	C₁₁×#576	1	2	yes	—
350	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	8	no	—
356	C₄	C₁₁×#547	1	2	yes	—
357	C₄	C₂²×C₁₁×Q₁₆	1	4	yes	—
358	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
359	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂	—	2	8	no	—
361	C₂	C₁₁×#3338	1	4	yes	direct product factor
362	C₂	C₂×C₁₁×#547	1	1	yes	characteristic
363	C₂	C₂³×C₁₁×Q₁₆	1	1	yes	characteristic
364	C₂	C₂×C₁₁×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3338	C₂	direct (N × H)
3. C₂×C₁₁×#500	C₂	semidirect
4. C₂×C₁₁×#484	C₂	semidirect
5. C₂×C₁₁×#477	C₂	semidirect
6. C₂×C₁₁×#467	C₂	semidirect
7. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
9. C₂²×C₁₁×#107	C₂	semidirect
22. C₁₁×#500	C₂²	semidirect
23. C₁₁×#484	C₂²	semidirect
24. C₁₁×#477	C₂²	semidirect
25. C₁₁×#467	C₂²	semidirect
26. C₄×C₁₁×Q₁₆	C₂²	semidirect
32. C₂×C₁₁×#107	C₂²	semidirect
83. C₂×#3338	C₁₁	direct (N × H)
91. C₂×D₄×C₁₁	Q₁₆	semidirect
129. #3338	C₂×C₁₁	direct (N × H)
130. C₂×#500	C₂×C₁₁	semidirect
131. C₂×#484	C₂×C₁₁	semidirect
132. C₂×#477	C₂×C₁₁	semidirect
133. C₂×#467	C₂×C₁₁	semidirect
134. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
136. C₂²×#107	C₂×C₁₁	semidirect
146. D₄×C₁₁	C₂×Q₁₆	semidirect
182. #500	C₂²×C₁₁	semidirect
183. #484	C₂²×C₁₁	semidirect
184. #477	C₂²×C₁₁	semidirect
185. #467	C₂²×C₁₁	semidirect
186. C₄×Q₁₆	C₂²×C₁₁	semidirect
192. C₂×#107	C₂²×C₁₁	semidirect
261. C₂×C₁₁	#3338	direct (N × H)
272. C₂×D₄	C₁₁×Q₁₆	semidirect
309. C₁₁	C₂×#3338	direct (N × H)
319. D₄	C₂×C₁₁×Q₁₆	semidirect
361. C₂	C₁₁×#3338	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×#554	2
C₁₁×#3338	2
C₂×C₁₁×#500	2
C₂×C₁₁×#484	2
C₂×C₁₁×#477	2
C₂×C₁₁×#467	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₈×D₄×C₁₁	2
C₂²×C₁₁×#107	2
C₂×#3338	11

Subgroups — C2×C11×#3338 #14638422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3338 #14638422