Subgroups — C₂×C₁₁×#3339 #14638423

Order 2816.

1994 conjugacy classes of subgroups.

The subgroup lattice has 524 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×#3339	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#481	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#553	—	2	8	no	—
17	C₁₁×#553	C₂²	1	16	yes	complemented
18	C₂×C₁₁×#126	—	2	2	no	—
19	C₂×C₁₁×#125	C₂²	1	2	yes	—
20	C₂×C₁₁×#123	—	2	2	no	—
21	C₂×C₁₁×#121	—	2	2	no	—
22	C₂×C₁₁×#121	C₂²	1	2	yes	—
23	C₂×C₁₁×#121	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₁	—	2	2	no	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#117	C₂²	1	2	yes	—
28	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
29	C₁₁×#499	C₂²	1	8	yes	complemented
30	C₁₁×#482	C₂²	1	16	yes	complemented
31	C₁₁×#481	C₂²	1	16	yes	complemented
32	C₁₁×#478	C₂²	1	16	yes	complemented
33	C₁₁×#466	C₂²	1	8	yes	complemented
34	C₁₁×#466	C₂²	1	8	yes	complemented
35	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
36	C₈×D₄×C₁₁	C₂²	1	8	yes	complemented
37	C₁₁×#427	C₂²	1	8	yes	complemented
38	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₁×#107	C₂²	1	2	yes	—
42	C₂×C₁₁×#107	C₂²	1	8	yes	complemented
43	C₂×C₁₁×#106	C₂²	1	2	yes	—
44	C₂×C₁₁×#106	C₂²	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₁×#102	C₂²	1	2	yes	—
47	C₂×C₁₁×#102	C₂²	1	2	yes	—
48	C₂×C₁₁×#102	C₂²	1	2	yes	—
49	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
52	C₂²×D₄×C₁₁	—	2	2	no	—
53	C₂²×D₄×C₁₁	—	2	2	no	—
54	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁	—	2	2	no	—
57	C₂³×C₄×C₁₁	—	2	2	no	—
58	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×D₈	—	2	4	no	—
61	C₂×C₁₁×D₈	C₂³	1	4	yes	—
62	C₂²×C₈×C₁₁	—	2	4	no	—
63	C₂²×C₈×C₁₁	—	2	4	no	—
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×#126	—	2	16	no	—
71	C₁₁×#125	—	2	4	no	—
72	C₁₁×#125	C₂³	1	8	yes	—
73	C₁₁×#123	—	2	16	no	—
74	C₁₁×#121	—	2	16	no	—
75	C₁₁×#121	—	2	4	no	—
76	C₁₁×#121	—	2	4	no	—
77	C₁₁×#121	C₂³	1	8	yes	—
78	C₁₁×#121	C₂³	1	8	yes	—
79	C₄×D₄×C₁₁	—	2	16	no	—
80	C₄×D₄×C₁₁	—	2	4	no	—
81	C₄×D₄×C₁₁	D₄	1	4	yes	—
82	C₄×D₄×C₁₁	C₂³	1	8	yes	—
83	C₄×D₄×C₁₁	C₂³	1	4	yes	—
84	C₁₁×#117	—	2	4	no	—
85	C₁₁×#117	C₂³	1	8	yes	—
86	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
88	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₁	—	2	2	no	—
102	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
103	C₁₁×#107	C₂³	1	4	yes	—
104	C₁₁×#107	C₂³	1	4	yes	—
105	C₁₁×#107	C₂³	1	4	yes	—
106	C₁₁×#107	C₂³	1	8	yes	—
107	C₁₁×#106	C₂³	1	8	yes	—
108	C₁₁×#106	C₂³	1	8	yes	—
109	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₁×#102	C₂³	1	8	yes	—
111	C₁₁×#102	C₂³	1	8	yes	—
112	C₁₁×#102	C₂³	1	8	yes	—
113	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
115	C₄×C₈×C₁₁	C₂³	1	4	yes	—
116	C₂×#3339	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₁	—	2	2	no	—
118	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₁₁	—	2	4	no	—
121	C₂×D₄×C₁₁	—	2	8	no	—
122	C₂×D₄×C₁₁	—	2	8	no	—
123	C₂×D₄×C₁₁	—	2	2	no	—
124	C₂×D₄×C₁₁	—	2	4	no	—
125	C₂×D₄×C₁₁	—	2	4	no	—
126	C₂×D₄×C₁₁	—	4	8	no	—
127	C₂×D₄×C₁₁	—	8	4	no	—
128	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₁	—	2	2	no	—
131	C₂²×C₄×C₁₁	—	2	2	no	—
132	C₂²×C₄×C₁₁	—	2	2	no	—
133	C₂²×C₄×C₁₁	—	2	2	no	—
134	C₂²×C₄×C₁₁	—	2	2	no	—
135	C₂²×C₄×C₁₁	—	2	2	no	—
136	C₂²×C₄×C₁₁	—	2	2	no	—
137	C₂²×C₄×C₁₁	—	2	8	no	—
138	C₂²×C₄×C₁₁	—	2	8	no	—
139	C₂²×C₄×C₁₁	—	8	4	no	—
140	C₂²×C₄×C₁₁	—	8	4	no	—
141	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
150	C₁₁×D₈	—	2	8	no	—
151	C₂×C₈×C₁₁	—	2	8	no	—
152	C₂×C₈×C₁₁	—	2	8	no	—
153	C₂×C₈×C₁₁	—	2	2	no	—
154	C₂×C₈×C₁₁	—	2	2	no	—
155	C₂×C₈×C₁₁	—	2	2	no	—
156	C₂×C₈×C₁₁	#41	1	4	yes	—
157	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
159	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
160	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
161	C₁₁×C₄⋊C₄	—	2	2	no	—
162	C₁₁×C₄⋊C₄	—	2	2	no	—
163	C₁₁×C₄⋊C₄	—	2	8	no	—
164	C₁₁×C₄⋊C₄	—	2	8	no	—
165	C₁₁×C₄⋊C₄	—	2	8	no	—
166	C₁₁×C₄⋊C₄	—	2	2	no	—
167	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
168	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
169	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
171	C₁₁×C₂²⋊C₄	—	2	8	no	—
172	C₁₁×C₂²⋊C₄	—	2	8	no	—
173	C₁₁×C₂²⋊C₄	—	2	8	no	—
174	C₁₁×C₂²⋊C₄	—	2	8	no	—
175	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
177	C₄²×C₁₁	—	2	8	no	—
178	C₄²×C₁₁	C₂×D₄	1	2	yes	—
179	C₄²×C₁₁	C₂⁴	1	2	yes	—
180	C₂×#553	C₂×C₁₁	1	2	yes	complemented
181	#3339	C₂×C₁₁	1	16	yes	direct product factor
182	C₂×#499	C₂×C₁₁	1	1	yes	characteristic, complemented
183	C₂×#481	C₂×C₁₁	1	2	yes	complemented
184	C₂×#482	C₂×C₁₁	1	2	yes	complemented
185	C₂×#478	C₂×C₁₁	1	2	yes	complemented
186	C₂×#466	C₂×C₁₁	1	1	yes	characteristic, complemented
187	C₂×#466	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
189	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
190	C₂×#427	C₂×C₁₁	1	1	yes	characteristic, complemented
191	C₂²×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	2	2	no	—
194	C₂³×C₁₁	—	2	2	no	—
195	C₂³×C₁₁	—	2	2	no	—
196	C₂³×C₁₁	—	2	2	no	—
197	C₂³×C₁₁	—	2	4	no	—
198	C₂³×C₁₁	—	4	4	no	—
199	C₂³×C₁₁	—	4	4	no	—
200	C₂³×C₁₁	—	4	4	no	—
201	C₂³×C₁₁	#135	1	4	yes	—
202	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
204	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
205	D₄×C₁₁	—	2	8	no	—
206	D₄×C₁₁	—	2	4	no	—
207	D₄×C₁₁	—	2	4	no	—
208	D₄×C₁₁	—	4	16	no	—
209	D₄×C₁₁	—	4	4	no	—
210	D₄×C₁₁	—	8	8	no	—
211	C₂×C₄×C₁₁	—	2	2	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	2	no	—
215	C₂×C₄×C₁₁	—	2	4	no	—
216	C₂×C₄×C₁₁	—	2	4	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	2	2	no	—
220	C₂×C₄×C₁₁	—	2	2	no	—
221	C₂×C₄×C₁₁	—	2	4	no	—
222	C₂×C₄×C₁₁	—	2	4	no	—
223	C₂×C₄×C₁₁	—	2	4	no	—
224	C₂×C₄×C₁₁	—	4	4	no	—
225	C₂×C₄×C₁₁	—	4	4	no	—
226	C₂×C₄×C₁₁	—	4	4	no	—
227	C₂×C₄×C₁₁	—	8	8	no	—
228	C₂×C₄×C₁₁	—	8	8	no	—
229	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
236	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
237	C₈×C₁₁	—	2	2	no	—
238	C₈×C₁₁	—	2	2	no	—
239	C₈×C₁₁	—	2	2	no	—
240	C₈×C₁₁	C₂×#41	1	4	yes	—
241	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
244	#553	—	2	8	no	—
245	#553	C₂²×C₁₁	1	16	yes	complemented
246	C₂×#126	—	2	2	no	—
247	C₂×#125	C₂²×C₁₁	1	2	yes	—
248	C₂×#123	—	2	2	no	—
249	C₂×#121	—	2	2	no	—
250	C₂×#121	C₂²×C₁₁	1	2	yes	—
251	C₂×#121	C₂²×C₁₁	1	2	yes	—
252	C₂×C₄×D₄	—	2	2	no	—
253	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
255	C₂×#117	C₂²×C₁₁	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
257	#499	C₂²×C₁₁	1	8	yes	complemented
258	#482	C₂²×C₁₁	1	16	yes	complemented
259	#481	C₂²×C₁₁	1	16	yes	complemented
260	#478	C₂²×C₁₁	1	16	yes	complemented
261	#466	C₂²×C₁₁	1	8	yes	complemented
262	#466	C₂²×C₁₁	1	8	yes	complemented
263	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
264	C₈×D₄	C₂²×C₁₁	1	8	yes	complemented
265	#427	C₂²×C₁₁	1	8	yes	complemented
266	C₂×#107	C₂²×C₁₁	1	2	yes	—
267	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
269	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×#107	C₂²×C₁₁	1	8	yes	complemented
271	C₂×#106	C₂²×C₁₁	1	2	yes	—
272	C₂×#106	C₂²×C₁₁	1	2	yes	—
273	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₁	1	2	yes	—
275	C₂×#102	C₂²×C₁₁	1	2	yes	—
276	C₂×#102	C₂²×C₁₁	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
280	C₂²×C₁₁	—	2	8	no	—
281	C₂²×C₁₁	—	2	2	no	—
282	C₂²×C₁₁	—	2	2	no	—
283	C₂²×C₁₁	—	2	2	no	—
284	C₂²×C₁₁	—	2	2	no	—
285	C₂²×C₁₁	—	2	2	no	—
286	C₂²×C₁₁	—	4	4	no	—
287	C₂²×C₁₁	—	4	4	no	—
288	C₂²×C₁₁	—	4	4	no	—
289	C₂²×C₁₁	—	4	4	no	—
290	C₂²×C₁₁	—	8	8	no	—
291	C₂²×C₁₁	#547	1	2	yes	—
292	C₂²×C₁₁	C₂×#135	1	4	yes	—
293	C₂²×C₁₁	C₂×#135	1	2	yes	—
294	C₂²×C₁₁	#576	1	2	yes	—
295	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₁₁	—	2	2	no	—
297	C₄×C₁₁	—	2	2	no	—
298	C₄×C₁₁	—	2	2	no	—
299	C₄×C₁₁	—	2	2	no	—
300	C₄×C₁₁	—	4	4	no	—
301	C₄×C₁₁	—	4	4	no	—
302	C₄×C₁₁	—	4	4	no	—
303	C₄×C₁₁	#547	1	2	yes	—
304	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
305	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
314	C₂×D₈	—	2	4	no	—
315	C₂×D₈	C₂³×C₁₁	1	4	yes	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	—	2	4	no	—
318	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
321	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
322	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
324	#126	—	2	16	no	—
325	#125	—	2	4	no	—
326	#125	C₂³×C₁₁	1	8	yes	—
327	#123	—	2	16	no	—
328	#121	—	2	16	no	—
329	#121	—	2	4	no	—
330	#121	—	2	4	no	—
331	#121	C₂³×C₁₁	1	8	yes	—
332	#121	C₂³×C₁₁	1	8	yes	—
333	C₄×D₄	—	2	16	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	D₄×C₁₁	1	4	yes	—
336	C₄×D₄	C₂³×C₁₁	1	8	yes	—
337	C₄×D₄	C₂³×C₁₁	1	4	yes	—
338	#117	—	2	4	no	—
339	#117	C₂³×C₁₁	1	8	yes	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	4	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
357	#107	C₂³×C₁₁	1	4	yes	—
358	#107	C₂³×C₁₁	1	4	yes	—
359	#107	C₂³×C₁₁	1	8	yes	—
360	#107	C₂³×C₁₁	1	4	yes	—
361	#106	C₂³×C₁₁	1	8	yes	—
362	#106	C₂³×C₁₁	1	8	yes	—
363	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
364	#102	C₂³×C₁₁	1	8	yes	—
365	#102	C₂³×C₁₁	1	8	yes	—
366	#102	C₂³×C₁₁	1	8	yes	—
367	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
368	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
369	C₄×C₈	C₂³×C₁₁	1	4	yes	—
370	C₂×C₁₁	—	2	4	no	—
371	C₂×C₁₁	—	4	2	no	—
372	C₂×C₁₁	—	8	4	no	—
373	C₂×C₁₁	#3339	1	4	yes	direct product factor
374	C₂×C₁₁	C₂×#547	1	1	yes	characteristic
375	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
376	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
377	C₂⁴	—	2	2	no	—
378	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	8	4	no	—
388	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
389	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	8	4	no	—
400	C₂²×C₄	—	8	4	no	—
401	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
410	D₈	—	2	8	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	8	no	—
415	C₂×C₈	—	2	8	no	—
416	C₂×C₈	C₁₁×#41	1	4	yes	—
417	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
418	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
419	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
428	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
429	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
430	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
436	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
437	C₄²	—	2	8	no	—
438	C₄²	C₂×D₄×C₁₁	1	2	yes	—
439	C₄²	C₂⁴×C₁₁	1	2	yes	—
440	C₁₁	C₂×#3339	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	C₁₁×#135	1	4	yes	—
451	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
452	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
453	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	4	no	—
457	D₄	—	4	16	no	—
458	D₄	—	4	4	no	—
459	D₄	—	8	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	8	8	no	—
477	C₂×C₄	—	8	8	no	—
478	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
484	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	—	2	2	no	—
489	C₈	C₂×C₁₁×#41	1	4	yes	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	8	8	no	—
501	C₂²	C₁₁×#547	1	2	yes	—
502	C₂²	C₂×C₁₁×#135	1	4	yes	—
503	C₂²	C₂×C₁₁×#135	1	2	yes	—
504	C₂²	C₁₁×#576	1	2	yes	—
505	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	C₁₁×#547	1	2	yes	—
514	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
515	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂	—	2	4	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	4	no	—
519	C₂	C₁₁×#3339	1	4	yes	direct product factor
520	C₂	C₂×C₁₁×#547	1	1	yes	characteristic
521	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
522	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×#3339	C₂	direct (N × H)
3. C₂×C₁₁×#499	C₂	semidirect
4. C₂×C₁₁×#481	C₂	semidirect
5. C₂×C₁₁×#482	C₂	semidirect
6. C₂×C₁₁×#478	C₂	semidirect
7. C₂×C₁₁×#466	C₂	semidirect
8. C₂×C₁₁×#466	C₂	semidirect
9. C₂×C₄×C₁₁×D₈	C₂	semidirect
10. C₂×C₈×D₄×C₁₁	C₂	semidirect
11. C₂×C₁₁×#427	C₂	semidirect
12. C₂²×C₁₁×#107	C₂	semidirect
17. C₁₁×#553	C₂²	semidirect
29. C₁₁×#499	C₂²	semidirect
30. C₁₁×#482	C₂²	semidirect
31. C₁₁×#481	C₂²	semidirect
32. C₁₁×#478	C₂²	semidirect
33. C₁₁×#466	C₂²	semidirect
34. C₁₁×#466	C₂²	semidirect
35. C₄×C₁₁×D₈	C₂²	semidirect
36. C₈×D₄×C₁₁	C₂²	semidirect
37. C₁₁×#427	C₂²	semidirect
42. C₂×C₁₁×#107	C₂²	semidirect
116. C₂×#3339	C₁₁	direct (N × H)
180. C₂×#553	C₂×C₁₁	semidirect
181. #3339	C₂×C₁₁	direct (N × H)
182. C₂×#499	C₂×C₁₁	semidirect
183. C₂×#481	C₂×C₁₁	semidirect
184. C₂×#482	C₂×C₁₁	semidirect
185. C₂×#478	C₂×C₁₁	semidirect
186. C₂×#466	C₂×C₁₁	semidirect
187. C₂×#466	C₂×C₁₁	semidirect
188. C₂×C₄×D₈	C₂×C₁₁	semidirect
189. C₂×C₈×D₄	C₂×C₁₁	semidirect
190. C₂×#427	C₂×C₁₁	semidirect
191. C₂²×#107	C₂×C₁₁	semidirect
245. #553	C₂²×C₁₁	semidirect
257. #499	C₂²×C₁₁	semidirect
258. #482	C₂²×C₁₁	semidirect
259. #481	C₂²×C₁₁	semidirect
260. #478	C₂²×C₁₁	semidirect
261. #466	C₂²×C₁₁	semidirect
262. #466	C₂²×C₁₁	semidirect
263. C₄×D₈	C₂²×C₁₁	semidirect
264. C₈×D₄	C₂²×C₁₁	semidirect
265. #427	C₂²×C₁₁	semidirect
270. C₂×#107	C₂²×C₁₁	semidirect
373. C₂×C₁₁	#3339	direct (N × H)
440. C₁₁	C₂×#3339	direct (N × H)
519. C₂	C₁₁×#3339	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×#3339	2
C₂×C₁₁×#499	2
C₂×C₁₁×#481	2
C₂×C₁₁×#482	2
C₂×C₁₁×#478	2
C₂×C₁₁×#466	2
C₂×C₄×C₁₁×D₈	2
C₂×C₈×D₄×C₁₁	2
C₂×C₁₁×#427	2
C₂²×C₁₁×#107	2
C₂×#3339	11

Subgroups — C2×C11×#3339 #14638423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3339 #14638423