Subgroups — C₂×C₁₁×#3341 #14638425

Order 2816.

1982 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#555	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3341	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#482	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#476	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#555	—	2	8	no	—
13	C₁₁×#555	C₂²	1	16	yes	complemented
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₁×#124	—	2	4	no	—
16	C₂×C₁₁×#121	—	2	2	no	—
17	C₂×C₁₁×#121	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#117	—	2	2	no	—
21	C₂×C₁₁×#117	C₂²	1	4	yes	—
22	C₁₁×#500	C₂²	1	8	yes	complemented
23	C₁₁×#482	C₂²	1	32	yes	complemented
24	C₁₁×#476	C₂²	1	16	yes	complemented
25	C₁₁×#466	C₂²	1	16	yes	complemented
26	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
27	C₈×D₄×C₁₁	C₂²	1	8	yes	complemented
28	C₁₁×#427	C₂²	1	16	yes	complemented
29	C₂×C₁₁×#107	C₂²	1	2	yes	—
30	C₂×C₁₁×#107	C₂²	1	2	yes	—
31	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#106	C₂²	1	4	yes	—
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#102	C₂²	1	2	yes	—
35	C₂×C₁₁×#102	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×D₄×C₁₁	—	2	4	no	—
40	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁	—	2	2	no	—
43	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
44	C₂×C₁₁×D₈	—	2	4	no	—
45	C₂×C₁₁×D₈	C₂³	1	4	yes	—
46	C₂²×C₈×C₁₁	—	2	8	no	—
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×C₄⋊Q₈	—	2	4	no	—
52	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
53	C₁₁×#124	—	2	32	no	—
54	C₁₁×#121	—	2	16	no	—
55	C₁₁×#121	—	2	8	no	—
56	C₁₁×#121	C₂³	1	16	yes	—
57	C₄×D₄×C₁₁	—	2	4	no	—
58	C₄×D₄×C₁₁	D₄	1	4	yes	—
59	C₄×D₄×C₁₁	C₂³	1	8	yes	—
60	C₄×D₄×C₁₁	C₂³	1	4	yes	—
61	C₁₁×#117	—	2	8	no	—
62	C₁₁×#117	—	2	16	no	—
63	C₁₁×#117	C₂³	1	16	yes	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₁	—	2	4	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×#106	C₂³	1	16	yes	—
78	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₁×#102	C₂³	1	8	yes	—
80	C₁₁×#102	C₂³	1	16	yes	—
81	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₁₁	C₂³	1	4	yes	—
83	C₂×#3341	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	—	2	2	no	—
85	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
86	C₂×Q₈×C₁₁	—	2	8	no	—
87	C₂×Q₈×C₁₁	—	8	4	no	—
88	C₂×D₄×C₁₁	—	2	16	no	—
89	C₂×D₄×C₁₁	—	2	4	no	—
90	C₂×D₄×C₁₁	—	2	2	no	—
91	C₂×D₄×C₁₁	—	2	4	no	—
92	C₂×D₄×C₁₁	—	2	4	no	—
93	C₂×D₄×C₁₁	—	8	8	no	—
94	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
95	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₁₁	—	2	4	no	—
97	C₂²×C₄×C₁₁	—	2	4	no	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	4	no	—
100	C₂²×C₄×C₁₁	—	2	8	no	—
101	C₂²×C₄×C₁₁	—	4	8	no	—
102	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
108	C₁₁×D₈	—	2	8	no	—
109	C₂×C₈×C₁₁	—	2	16	no	—
110	C₂×C₈×C₁₁	—	2	4	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	#41	1	4	yes	—
113	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
114	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
115	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
116	C₁₁×C₄⋊C₄	—	2	8	no	—
117	C₁₁×C₄⋊C₄	—	2	2	no	—
118	C₁₁×C₄⋊C₄	—	2	4	no	—
119	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
120	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
121	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
122	C₁₁×C₂²⋊C₄	—	2	16	no	—
123	C₁₁×C₂²⋊C₄	—	2	16	no	—
124	C₁₁×C₂²⋊C₄	—	2	8	no	—
125	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
126	C₄²×C₁₁	—	2	16	no	—
127	C₄²×C₁₁	C₂×D₄	1	2	yes	—
128	C₄²×C₁₁	C₂⁴	1	2	yes	—
129	C₂×#555	C₂×C₁₁	1	2	yes	complemented
130	#3341	C₂×C₁₁	1	16	yes	direct product factor
131	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
132	C₂×#482	C₂×C₁₁	1	4	yes	complemented
133	C₂×#476	C₂×C₁₁	1	2	yes	complemented
134	C₂×#466	C₂×C₁₁	1	2	yes	complemented
135	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
136	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
137	C₂×#427	C₂×C₁₁	1	2	yes	complemented
138	C₂³×C₁₁	—	2	4	no	—
139	C₂³×C₁₁	—	2	4	no	—
140	C₂³×C₁₁	—	2	4	no	—
141	C₂³×C₁₁	—	2	4	no	—
142	C₂³×C₁₁	—	4	4	no	—
143	C₂³×C₁₁	—	4	4	no	—
144	C₂³×C₁₁	—	4	4	no	—
145	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
146	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₁	—	8	8	no	—
148	D₄×C₁₁	—	2	8	no	—
149	D₄×C₁₁	—	2	4	no	—
150	D₄×C₁₁	—	2	4	no	—
151	D₄×C₁₁	—	4	4	no	—
152	D₄×C₁₁	—	8	16	no	—
153	C₂×C₄×C₁₁	—	2	4	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	8	no	—
156	C₂×C₄×C₁₁	—	2	4	no	—
157	C₂×C₄×C₁₁	—	2	4	no	—
158	C₂×C₄×C₁₁	—	2	4	no	—
159	C₂×C₄×C₁₁	—	2	8	no	—
160	C₂×C₄×C₁₁	—	4	4	no	—
161	C₂×C₄×C₁₁	—	4	8	no	—
162	C₂×C₄×C₁₁	—	4	16	no	—
163	C₂×C₄×C₁₁	#135	1	4	yes	—
164	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
170	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
171	C₈×C₁₁	—	2	4	no	—
172	C₈×C₁₁	—	2	2	no	—
173	C₈×C₁₁	C₂×#41	1	4	yes	—
174	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
175	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
176	#555	—	2	8	no	—
177	#555	C₂²×C₁₁	1	16	yes	complemented
178	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
179	C₂×#124	—	2	4	no	—
180	C₂×#121	—	2	2	no	—
181	C₂×#121	C₂²×C₁₁	1	4	yes	—
182	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
183	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
184	C₂×#117	—	2	2	no	—
185	C₂×#117	C₂²×C₁₁	1	4	yes	—
186	#500	C₂²×C₁₁	1	8	yes	complemented
187	#482	C₂²×C₁₁	1	32	yes	complemented
188	#476	C₂²×C₁₁	1	16	yes	complemented
189	#466	C₂²×C₁₁	1	16	yes	complemented
190	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
191	C₈×D₄	C₂²×C₁₁	1	8	yes	complemented
192	#427	C₂²×C₁₁	1	16	yes	complemented
193	C₂×#107	C₂²×C₁₁	1	2	yes	—
194	C₂×#107	C₂²×C₁₁	1	2	yes	—
195	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×#106	C₂²×C₁₁	1	4	yes	—
197	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×#102	C₂²×C₁₁	1	2	yes	—
199	C₂×#102	C₂²×C₁₁	1	4	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
202	C₂²×C₁₁	—	2	4	no	—
203	C₂²×C₁₁	—	2	4	no	—
204	C₂²×C₁₁	—	2	4	no	—
205	C₂²×C₁₁	—	4	8	no	—
206	C₂²×C₁₁	—	4	4	no	—
207	C₂²×C₁₁	—	4	4	no	—
208	C₂²×C₁₁	—	4	4	no	—
209	C₂²×C₁₁	—	8	8	no	—
210	C₂²×C₁₁	#547	1	2	yes	—
211	C₂²×C₁₁	C₂×#135	1	2	yes	—
212	C₂²×C₁₁	#576	1	2	yes	—
213	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
214	C₄×C₁₁	—	2	4	no	—
215	C₄×C₁₁	—	2	2	no	—
216	C₄×C₁₁	—	4	4	no	—
217	C₄×C₁₁	—	4	8	no	—
218	C₄×C₁₁	#547	1	2	yes	—
219	C₄×C₁₁	C₂×#135	1	4	yes	—
220	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
221	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
225	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	C₂³×C₁₁	1	4	yes	—
230	C₂²×C₈	—	2	8	no	—
231	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
233	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	4	no	—
236	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
237	#124	—	2	32	no	—
238	#121	—	2	16	no	—
239	#121	—	2	8	no	—
240	#121	C₂³×C₁₁	1	16	yes	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	D₄×C₁₁	1	4	yes	—
243	C₄×D₄	C₂³×C₁₁	1	8	yes	—
244	C₄×D₄	C₂³×C₁₁	1	4	yes	—
245	#117	—	2	8	no	—
246	#117	—	2	16	no	—
247	#117	C₂³×C₁₁	1	16	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
258	#107	C₂³×C₁₁	1	4	yes	—
259	#107	C₂³×C₁₁	1	8	yes	—
260	#107	C₂³×C₁₁	1	8	yes	—
261	#106	C₂³×C₁₁	1	16	yes	—
262	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
263	#102	C₂³×C₁₁	1	8	yes	—
264	#102	C₂³×C₁₁	1	16	yes	—
265	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
266	C₄×C₈	C₂³×C₁₁	1	4	yes	—
267	C₂×C₁₁	—	4	4	no	—
268	C₂×C₁₁	—	8	4	no	—
269	C₂×C₁₁	#3341	1	4	yes	direct product factor
270	C₂×C₁₁	C₂×#547	1	1	yes	characteristic
271	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
272	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
273	C₂⁴	—	2	2	no	—
274	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	8	4	no	—
277	C₂×D₄	—	2	16	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	8	8	no	—
283	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
284	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	4	8	no	—
291	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
297	D₈	—	2	8	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	16	no	—
301	C₂×C₈	C₁₁×#41	1	4	yes	—
302	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
303	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
304	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
309	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
310	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
315	C₄²	—	2	16	no	—
316	C₄²	C₂×D₄×C₁₁	1	2	yes	—
317	C₄²	C₂⁴×C₁₁	1	2	yes	—
318	C₁₁	C₂×#3341	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
327	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
328	Q₈	—	8	8	no	—
329	D₄	—	2	8	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	8	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	C₁₁×#135	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
349	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
350	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
351	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
352	C₈	—	2	4	no	—
353	C₈	—	2	2	no	—
354	C₈	C₂×C₁₁×#41	1	4	yes	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	C₁₁×#547	1	2	yes	—
364	C₂²	C₂×C₁₁×#135	1	2	yes	—
365	C₂²	C₁₁×#576	1	2	yes	—
366	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	8	no	—
371	C₄	C₁₁×#547	1	2	yes	—
372	C₄	C₂×C₁₁×#135	1	4	yes	—
373	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
374	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂	—	4	4	no	—
376	C₂	—	8	4	no	—
377	C₂	C₁₁×#3341	1	4	yes	direct product factor
378	C₂	C₂×C₁₁×#547	1	1	yes	characteristic
379	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
380	C₂	C₂×C₁₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
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
1. C₂×C₁₁×#555	C₂	semidirect
2. C₁₁×#3341	C₂	direct (N × H)
3. C₂×C₁₁×#500	C₂	semidirect
4. C₂×C₁₁×#482	C₂	semidirect
5. C₂×C₁₁×#476	C₂	semidirect
6. C₂×C₁₁×#466	C₂	semidirect
7. C₂×C₄×C₁₁×D₈	C₂	semidirect
8. C₂×C₈×D₄×C₁₁	C₂	semidirect
9. C₂×C₁₁×#427	C₂	semidirect
13. C₁₁×#555	C₂²	semidirect
22. C₁₁×#500	C₂²	semidirect
23. C₁₁×#482	C₂²	semidirect
24. C₁₁×#476	C₂²	semidirect
25. C₁₁×#466	C₂²	semidirect
26. C₄×C₁₁×D₈	C₂²	semidirect
27. C₈×D₄×C₁₁	C₂²	semidirect
28. C₁₁×#427	C₂²	semidirect
83. C₂×#3341	C₁₁	direct (N × H)
129. C₂×#555	C₂×C₁₁	semidirect
130. #3341	C₂×C₁₁	direct (N × H)
131. C₂×#500	C₂×C₁₁	semidirect
132. C₂×#482	C₂×C₁₁	semidirect
133. C₂×#476	C₂×C₁₁	semidirect
134. C₂×#466	C₂×C₁₁	semidirect
135. C₂×C₄×D₈	C₂×C₁₁	semidirect
136. C₂×C₈×D₄	C₂×C₁₁	semidirect
137. C₂×#427	C₂×C₁₁	semidirect
177. #555	C₂²×C₁₁	semidirect
186. #500	C₂²×C₁₁	semidirect
187. #482	C₂²×C₁₁	semidirect
188. #476	C₂²×C₁₁	semidirect
189. #466	C₂²×C₁₁	semidirect
190. C₄×D₈	C₂²×C₁₁	semidirect
191. C₈×D₄	C₂²×C₁₁	semidirect
192. #427	C₂²×C₁₁	semidirect
269. C₂×C₁₁	#3341	direct (N × H)
318. C₁₁	C₂×#3341	direct (N × H)
377. C₂	C₁₁×#3341	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×#555	2
C₁₁×#3341	2
C₂×C₁₁×#500	2
C₂×C₁₁×#482	2
C₂×C₁₁×#476	2
C₂×C₁₁×#466	2
C₂×C₄×C₁₁×D₈	2
C₂×C₈×D₄×C₁₁	2
C₂×C₁₁×#427	2
C₂×#3341	11

Subgroups — C2×C11×#3341 #14638425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3341 #14638425