Subgroups — C₂×C₁₁×#3355 #14638441

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#553	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3355	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#480	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#428	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
13	C₁₁×#553	—	2	8	no	—
14	C₁₁×#553	C₂²	1	16	yes	complemented
15	C₂×C₁₁×#126	—	2	2	no	—
16	C₂×C₁₁×#125	C₂²	1	2	yes	—
17	C₂×C₁₁×#123	—	2	2	no	—
18	C₂×C₁₁×#121	—	2	2	no	—
19	C₂×C₁₁×#121	C₂²	1	2	yes	—
20	C₂×C₁₁×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₁	—	2	2	no	—
22	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#117	C₂²	1	2	yes	—
25	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₁×#499	C₂²	1	8	yes	complemented
27	C₁₁×#482	C₂²	1	16	yes	complemented
28	C₁₁×#480	C₂²	1	16	yes	complemented
29	C₁₁×#478	C₂²	1	16	yes	complemented
30	C₁₁×#469	C₂²	1	16	yes	complemented
31	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
32	C₁₁×#436	C₂²	1	8	yes	complemented
33	C₁₁×#428	C₂²	1	16	yes	complemented
34	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×#107	C₂²	1	2	yes	—
38	C₂×C₁₁×#106	C₂²	1	2	yes	—
39	C₂×C₁₁×#106	C₂²	1	2	yes	—
40	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₁×#102	C₂²	1	2	yes	—
42	C₂×C₁₁×#102	C₂²	1	2	yes	—
43	C₂×C₁₁×#102	C₂²	1	2	yes	—
44	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
46	C₂²×D₄×C₁₁	—	2	2	no	—
47	C₂²×D₄×C₁₁	—	2	2	no	—
48	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₁	—	2	2	no	—
51	C₂³×C₄×C₁₁	—	2	2	no	—
52	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
53	C₂×C₁₁×D₈	—	2	4	no	—
54	C₂×C₁₁×D₈	C₂³	1	4	yes	—
55	C₂×C₁₁×M₁₆	—	2	8	no	—
56	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₁₁×#126	—	2	16	no	—
61	C₁₁×#125	—	2	4	no	—
62	C₁₁×#125	C₂³	1	8	yes	—
63	C₁₁×#123	—	2	16	no	—
64	C₁₁×#121	—	2	16	no	—
65	C₁₁×#121	—	2	4	no	—
66	C₁₁×#121	—	2	4	no	—
67	C₁₁×#121	C₂³	1	8	yes	—
68	C₁₁×#121	C₂³	1	8	yes	—
69	C₄×D₄×C₁₁	—	2	16	no	—
70	C₄×D₄×C₁₁	—	2	4	no	—
71	C₄×D₄×C₁₁	D₄	1	4	yes	—
72	C₄×D₄×C₁₁	C₂³	1	8	yes	—
73	C₄×D₄×C₁₁	C₂³	1	4	yes	—
74	C₁₁×#117	—	2	4	no	—
75	C₁₁×#117	C₂³	1	8	yes	—
76	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
78	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
90	C₂×C₄²×C₁₁	—	2	2	no	—
91	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
92	C₁₁×#107	C₂³	1	4	yes	—
93	C₁₁×#107	C₂³	1	4	yes	—
94	C₁₁×#107	C₂³	1	4	yes	—
95	C₁₁×#107	C₂³	1	8	yes	—
96	C₁₁×#106	C₂³	1	8	yes	—
97	C₁₁×#106	C₂³	1	8	yes	—
98	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
99	C₁₁×#102	C₂³	1	8	yes	—
100	C₁₁×#102	C₂³	1	8	yes	—
101	C₁₁×#102	C₂³	1	8	yes	—
102	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
103	C₄×C₈×C₁₁	C₂³	1	4	yes	—
104	C₂×#3355	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₁	—	2	2	no	—
106	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₁	—	2	8	no	—
108	C₂×D₄×C₁₁	—	2	8	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	4	no	—
111	C₂×D₄×C₁₁	—	2	4	no	—
112	C₂×D₄×C₁₁	—	4	2	no	—
113	C₂×D₄×C₁₁	—	4	8	no	—
114	C₂×D₄×C₁₁	—	8	4	no	—
115	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
116	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₁₁	—	2	4	no	—
118	C₂²×C₄×C₁₁	—	2	4	no	—
119	C₂²×C₄×C₁₁	—	2	2	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	2	2	no	—
122	C₂²×C₄×C₁₁	—	2	8	no	—
123	C₂²×C₄×C₁₁	—	2	8	no	—
124	C₂²×C₄×C₁₁	—	8	4	no	—
125	C₂²×C₄×C₁₁	—	8	4	no	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
132	C₁₁×D₈	—	2	8	no	—
133	C₁₁×M₁₆	—	2	16	no	—
134	C₂×C₈×C₁₁	—	2	4	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	#41	1	4	yes	—
137	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
138	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
139	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
140	C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₁₁×C₄⋊C₄	—	2	2	no	—
142	C₁₁×C₄⋊C₄	—	2	8	no	—
143	C₁₁×C₄⋊C₄	—	2	8	no	—
144	C₁₁×C₄⋊C₄	—	2	8	no	—
145	C₁₁×C₄⋊C₄	—	2	2	no	—
146	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
147	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
148	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
149	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
150	C₁₁×C₂²⋊C₄	—	2	8	no	—
151	C₁₁×C₂²⋊C₄	—	2	8	no	—
152	C₁₁×C₂²⋊C₄	—	2	8	no	—
153	C₁₁×C₂²⋊C₄	—	2	8	no	—
154	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
155	C₄²×C₁₁	—	2	8	no	—
156	C₄²×C₁₁	C₂×D₄	1	2	yes	—
157	C₄²×C₁₁	C₂⁴	1	2	yes	—
158	C₂×#553	C₂×C₁₁	1	2	yes	complemented
159	#3355	C₂×C₁₁	1	16	yes	direct product factor
160	C₂×#499	C₂×C₁₁	1	1	yes	characteristic, complemented
161	C₂×#482	C₂×C₁₁	1	2	yes	complemented
162	C₂×#480	C₂×C₁₁	1	2	yes	complemented
163	C₂×#478	C₂×C₁₁	1	2	yes	complemented
164	C₂×#469	C₂×C₁₁	1	2	yes	complemented
165	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂×#428	C₂×C₁₁	1	2	yes	complemented
168	C₂³×C₁₁	—	2	4	no	—
169	C₂³×C₁₁	—	2	4	no	—
170	C₂³×C₁₁	—	2	4	no	—
171	C₂³×C₁₁	—	2	4	no	—
172	C₂³×C₁₁	—	4	4	no	—
173	C₂³×C₁₁	—	4	4	no	—
174	C₂³×C₁₁	—	4	4	no	—
175	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	D₄×C₁₁	—	2	4	no	—
178	D₄×C₁₁	—	2	4	no	—
179	D₄×C₁₁	—	4	4	no	—
180	D₄×C₁₁	—	4	16	no	—
181	D₄×C₁₁	—	4	4	no	—
182	D₄×C₁₁	—	8	8	no	—
183	C₂×C₄×C₁₁	—	2	4	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	8	no	—
187	C₂×C₄×C₁₁	—	2	4	no	—
188	C₂×C₄×C₁₁	—	2	4	no	—
189	C₂×C₄×C₁₁	—	2	4	no	—
190	C₂×C₄×C₁₁	—	2	4	no	—
191	C₂×C₄×C₁₁	—	2	4	no	—
192	C₂×C₄×C₁₁	—	4	4	no	—
193	C₂×C₄×C₁₁	—	4	4	no	—
194	C₂×C₄×C₁₁	—	4	4	no	—
195	C₂×C₄×C₁₁	—	8	8	no	—
196	C₂×C₄×C₁₁	—	8	8	no	—
197	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
203	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₁	—	2	4	no	—
205	C₈×C₁₁	—	2	2	no	—
206	C₈×C₁₁	C₂×#41	1	4	yes	—
207	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
209	#553	—	2	8	no	—
210	#553	C₂²×C₁₁	1	16	yes	complemented
211	C₂×#126	—	2	2	no	—
212	C₂×#125	C₂²×C₁₁	1	2	yes	—
213	C₂×#123	—	2	2	no	—
214	C₂×#121	—	2	2	no	—
215	C₂×#121	C₂²×C₁₁	1	2	yes	—
216	C₂×#121	C₂²×C₁₁	1	2	yes	—
217	C₂×C₄×D₄	—	2	2	no	—
218	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
220	C₂×#117	C₂²×C₁₁	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
222	#499	C₂²×C₁₁	1	8	yes	complemented
223	#482	C₂²×C₁₁	1	16	yes	complemented
224	#480	C₂²×C₁₁	1	16	yes	complemented
225	#478	C₂²×C₁₁	1	16	yes	complemented
226	#469	C₂²×C₁₁	1	16	yes	complemented
227	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
228	#436	C₂²×C₁₁	1	8	yes	complemented
229	#428	C₂²×C₁₁	1	16	yes	complemented
230	C₂×#107	C₂²×C₁₁	1	2	yes	—
231	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
233	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×#106	C₂²×C₁₁	1	2	yes	—
235	C₂×#106	C₂²×C₁₁	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
237	C₂×#102	C₂²×C₁₁	1	2	yes	—
238	C₂×#102	C₂²×C₁₁	1	2	yes	—
239	C₂×#102	C₂²×C₁₁	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂²×C₁₁	—	2	4	no	—
243	C₂²×C₁₁	—	2	4	no	—
244	C₂²×C₁₁	—	2	4	no	—
245	C₂²×C₁₁	—	4	8	no	—
246	C₂²×C₁₁	—	4	4	no	—
247	C₂²×C₁₁	—	4	4	no	—
248	C₂²×C₁₁	—	4	4	no	—
249	C₂²×C₁₁	—	8	8	no	—
250	C₂²×C₁₁	#547	1	2	yes	—
251	C₂²×C₁₁	#575	1	2	yes	—
252	C₂²×C₁₁	#576	1	2	yes	—
253	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
254	C₄×C₁₁	—	2	4	no	—
255	C₄×C₁₁	—	2	2	no	—
256	C₄×C₁₁	—	2	2	no	—
257	C₄×C₁₁	—	4	4	no	—
258	C₄×C₁₁	—	4	4	no	—
259	C₄×C₁₁	—	4	4	no	—
260	C₄×C₁₁	#547	1	2	yes	—
261	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
262	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
266	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
270	C₂×D₈	—	2	4	no	—
271	C₂×D₈	C₂³×C₁₁	1	4	yes	—
272	C₂×M₁₆	—	2	8	no	—
273	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
274	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
277	#126	—	2	16	no	—
278	#125	—	2	4	no	—
279	#125	C₂³×C₁₁	1	8	yes	—
280	#123	—	2	16	no	—
281	#121	—	2	16	no	—
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	#121	C₂³×C₁₁	1	8	yes	—
285	#121	C₂³×C₁₁	1	8	yes	—
286	C₄×D₄	—	2	16	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	D₄×C₁₁	1	4	yes	—
289	C₄×D₄	C₂³×C₁₁	1	8	yes	—
290	C₄×D₄	C₂³×C₁₁	1	4	yes	—
291	#117	—	2	4	no	—
292	#117	C₂³×C₁₁	1	8	yes	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
309	#107	C₂³×C₁₁	1	4	yes	—
310	#107	C₂³×C₁₁	1	8	yes	—
311	#107	C₂³×C₁₁	1	4	yes	—
312	#107	C₂³×C₁₁	1	4	yes	—
313	#106	C₂³×C₁₁	1	8	yes	—
314	#106	C₂³×C₁₁	1	8	yes	—
315	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
316	#102	C₂³×C₁₁	1	8	yes	—
317	#102	C₂³×C₁₁	1	8	yes	—
318	#102	C₂³×C₁₁	1	8	yes	—
319	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
320	C₄×C₈	C₂³×C₁₁	1	4	yes	—
321	C₂×C₁₁	—	4	4	no	—
322	C₂×C₁₁	—	8	4	no	—
323	C₂×C₁₁	#3355	1	4	yes	direct product factor
324	C₂×C₁₁	C₂×#547	1	1	yes	characteristic
325	C₂×C₁₁	C₂×#575	1	1	yes	characteristic
326	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
327	C₂⁴	—	2	2	no	—
328	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	8	no	—
336	C₂×D₄	—	8	4	no	—
337	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
338	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	8	4	no	—
347	C₂²×C₄	—	8	4	no	—
348	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
354	D₈	—	2	8	no	—
355	M₁₆	—	2	16	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₁₁×#41	1	4	yes	—
359	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
360	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
361	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
369	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
377	C₄²	—	2	8	no	—
378	C₄²	C₂×D₄×C₁₁	1	2	yes	—
379	C₄²	C₂⁴×C₁₁	1	2	yes	—
380	C₁₁	C₂×#3355	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
389	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
390	D₄	—	2	4	no	—
391	D₄	—	2	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	16	no	—
394	D₄	—	4	4	no	—
395	D₄	—	8	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	—	8	8	no	—
410	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
411	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
415	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	2	2	no	—
419	C₈	C₂×C₁₁×#41	1	4	yes	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	8	no	—
428	C₂²	C₁₁×#547	1	2	yes	—
429	C₂²	C₁₁×#575	1	2	yes	—
430	C₂²	C₁₁×#576	1	2	yes	—
431	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
432	C₄	—	2	4	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	C₁₁×#547	1	2	yes	—
439	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
440	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂	—	4	4	no	—
442	C₂	—	8	4	no	—
443	C₂	C₁₁×#3355	1	4	yes	direct product factor
444	C₂	C₂×C₁₁×#547	1	1	yes	characteristic
445	C₂	C₂×C₁₁×#575	1	1	yes	characteristic
446	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×#553	C₂	semidirect
2. C₁₁×#3355	C₂	direct (N × H)
3. C₂×C₁₁×#499	C₂	semidirect
4. C₂×C₁₁×#482	C₂	semidirect
5. C₂×C₁₁×#480	C₂	semidirect
6. C₂×C₁₁×#478	C₂	semidirect
7. C₂×C₁₁×#469	C₂	semidirect
8. C₂×C₄×C₁₁×D₈	C₂	semidirect
9. C₂×C₁₁×#436	C₂	semidirect
10. C₂×C₁₁×#428	C₂	semidirect
14. C₁₁×#553	C₂²	semidirect
26. C₁₁×#499	C₂²	semidirect
27. C₁₁×#482	C₂²	semidirect
28. C₁₁×#480	C₂²	semidirect
29. C₁₁×#478	C₂²	semidirect
30. C₁₁×#469	C₂²	semidirect
31. C₄×C₁₁×D₈	C₂²	semidirect
32. C₁₁×#436	C₂²	semidirect
33. C₁₁×#428	C₂²	semidirect
104. C₂×#3355	C₁₁	direct (N × H)
158. C₂×#553	C₂×C₁₁	semidirect
159. #3355	C₂×C₁₁	direct (N × H)
160. C₂×#499	C₂×C₁₁	semidirect
161. C₂×#482	C₂×C₁₁	semidirect
162. C₂×#480	C₂×C₁₁	semidirect
163. C₂×#478	C₂×C₁₁	semidirect
164. C₂×#469	C₂×C₁₁	semidirect
165. C₂×C₄×D₈	C₂×C₁₁	semidirect
166. C₂×#436	C₂×C₁₁	semidirect
167. C₂×#428	C₂×C₁₁	semidirect
210. #553	C₂²×C₁₁	semidirect
222. #499	C₂²×C₁₁	semidirect
223. #482	C₂²×C₁₁	semidirect
224. #480	C₂²×C₁₁	semidirect
225. #478	C₂²×C₁₁	semidirect
226. #469	C₂²×C₁₁	semidirect
227. C₄×D₈	C₂²×C₁₁	semidirect
228. #436	C₂²×C₁₁	semidirect
229. #428	C₂²×C₁₁	semidirect
323. C₂×C₁₁	#3355	direct (N × H)
380. C₁₁	C₂×#3355	direct (N × H)
443. C₂	C₁₁×#3355	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×#553	2
C₁₁×#3355	2
C₂×C₁₁×#499	2
C₂×C₁₁×#482	2
C₂×C₁₁×#480	2
C₂×C₁₁×#478	2
C₂×C₁₁×#469	2
C₂×C₄×C₁₁×D₈	2
C₂×C₁₁×#436	2
C₂×C₁₁×#428	2
C₂×#3355	11

Subgroups — C2×C11×#3355 #14638441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3355 #14638441