Subgroups — C₁₁×#34247 #14611440

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#126	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2373	C₂	1	4	yes	maximal, complemented
3	C₁₁×#2373	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2345	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2344	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2342	C₂	1	2	yes	maximal
7	C₁₁×#2342	C₂	1	2	yes	maximal
8	C₁₁×#2334	C₂	1	4	yes	maximal, complemented
9	C₁₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#2312	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×#126	C₂	1	4	yes	maximal, complemented
12	C₁₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#2273	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×#126	C₄	1	16	yes	complemented
17	C₂×C₁₁×#126	C₂²	1	2	yes	—
18	C₂×C₁₁×#126	C₂²	1	2	yes	—
19	C₂×C₁₁×#126	C₂²	1	2	yes	—
20	C₂×C₁₁×#126	C₂²	1	2	yes	—
21	C₂×C₁₁×#117	C₂²	1	2	yes	—
22	C₂×C₁₁×#117	C₂²	1	2	yes	—
23	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#389	C₂²	1	4	yes	complemented
32	C₁₁×#389	C₂²	1	4	yes	complemented
33	C₁₁×#388	C₂²	1	4	yes	—
34	C₁₁×#388	C₂²	1	4	yes	—
35	C₁₁×#388	C₂²	1	4	yes	—
36	C₁₁×#388	C₂²	1	4	yes	—
37	C₁₁×#388	C₂²	1	4	yes	—
38	C₁₁×#388	C₂²	1	4	yes	—
39	C₁₁×#387	C₂²	1	4	yes	complemented
40	C₁₁×#387	C₂²	1	4	yes	complemented
41	C₁₁×#387	C₂²	1	4	yes	complemented
42	C₁₁×#387	C₂²	1	4	yes	complemented
43	C₁₁×#387	C₂²	1	4	yes	complemented
44	C₁₁×#387	C₂²	1	4	yes	complemented
45	C₁₁×#385	C₂²	1	4	yes	—
46	C₁₁×#385	C₂²	1	4	yes	—
47	C₁₁×#383	C₂²	1	2	yes	complemented
48	C₁₁×#382	C₂²	1	2	yes	complemented
49	C₁₁×#381	C₂²	1	2	yes	—
50	C₁₁×#381	C₂²	1	2	yes	—
51	C₁₁×#380	C₂²	1	2	yes	—
52	C₁₁×#380	C₂²	1	2	yes	—
53	C₁₁×#380	C₂²	1	2	yes	—
54	C₁₁×#379	C₂²	1	2	yes	—
55	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
56	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
57	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
58	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
59	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
61	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
63	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
69	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₁₁×#376	C₂²	1	2	yes	complemented
74	C₁₁×#376	C₂²	1	2	yes	complemented
75	C₄³×C₁₁	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×#126	C₂×C₄	1	16	yes	complemented
85	C₁₁×#126	C₂×C₄	1	16	yes	complemented
86	C₁₁×#126	C₂×C₄	1	16	yes	complemented
87	C₁₁×#126	C₂×C₄	1	16	yes	complemented
88	C₁₁×#117	—	2	8	no	—
89	C₁₁×#117	—	2	8	no	—
90	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
91	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
92	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
105	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
106	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₁	C₂×C₄	1	8	yes	complemented
122	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
135	C₁₁×#95	C₂³	1	2	yes	—
136	C₁₁×#95	C₂³	1	4	yes	—
137	C₁₁×#95	C₂³	1	4	yes	—
138	C₁₁×#95	C₂³	1	2	yes	—
139	C₁₁×#95	C₂³	1	4	yes	—
140	C₁₁×#95	C₂³	1	2	yes	—
141	C₁₁×#95	C₂³	1	4	yes	—
142	C₁₁×#95	C₂³	1	4	yes	—
143	C₁₁×#95	C₂³	1	2	yes	—
144	C₁₁×#95	C₂³	1	4	yes	—
145	C₁₁×#95	C₂³	1	4	yes	—
146	C₁₁×#95	C₂³	1	4	yes	—
147	C₁₁×#95	C₂³	1	4	yes	—
148	C₁₁×#95	C₂³	1	4	yes	—
149	#34247	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₁	—	2	4	no	—
151	C₂⁴×C₁₁	—	4	2	no	—
152	C₂⁴×C₁₁	—	4	2	no	—
153	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
154	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
155	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	—	2	4	no	—
157	C₂²×C₄×C₁₁	—	2	4	no	—
158	C₂²×C₄×C₁₁	—	2	8	no	—
159	C₂²×C₄×C₁₁	—	4	2	no	—
160	C₂²×C₄×C₁₁	—	4	2	no	—
161	C₂²×C₄×C₁₁	—	4	2	no	—
162	C₂²×C₄×C₁₁	—	4	2	no	—
163	C₂²×C₄×C₁₁	—	4	4	no	—
164	C₂²×C₄×C₁₁	—	4	4	no	—
165	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
184	C₁₁×C₄⋊C₄	—	2	8	no	—
185	C₁₁×C₄⋊C₄	—	2	8	no	—
186	C₁₁×C₄⋊C₄	—	4	4	no	—
187	C₁₁×C₄⋊C₄	—	4	4	no	—
188	C₁₁×C₄⋊C₄	—	4	4	no	—
189	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
190	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
191	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
192	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
193	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
194	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
195	C₁₁×C₂²⋊C₄	—	2	4	no	—
196	C₁₁×C₂²⋊C₄	—	2	4	no	—
197	C₁₁×C₂²⋊C₄	—	2	4	no	—
198	C₁₁×C₂²⋊C₄	—	2	8	no	—
199	C₁₁×C₂²⋊C₄	—	4	4	no	—
200	C₁₁×C₂²⋊C₄	—	4	4	no	—
201	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
202	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
203	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
204	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
205	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
206	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
207	C₁₁×C₂²⋊C₄	#41	1	8	yes	—
208	C₄²×C₁₁	—	2	8	no	—
209	C₄²×C₁₁	—	2	8	no	—
210	C₄²×C₁₁	—	4	2	no	—
211	C₄²×C₁₁	—	4	4	no	—
212	C₄²×C₁₁	—	4	4	no	—
213	C₄²×C₁₁	—	4	4	no	—
214	C₄²×C₁₁	—	4	2	no	—
215	C₄²×C₁₁	—	4	2	no	—
216	C₄²×C₁₁	—	4	2	no	—
217	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
218	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
219	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
220	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
221	C₂²×#126	C₂×C₁₁	1	1	yes	characteristic
222	#2373	C₂×C₁₁	1	4	yes	complemented
223	#2373	C₂×C₁₁	1	4	yes	complemented
224	#2345	C₂×C₁₁	1	2	yes	complemented
225	#2344	C₂×C₁₁	1	2	yes	complemented
226	#2342	C₂×C₁₁	1	2	yes	—
227	#2342	C₂×C₁₁	1	2	yes	—
228	#2334	C₂×C₁₁	1	4	yes	complemented
229	#2313	C₂×C₁₁	1	1	yes	characteristic, complemented
230	#2312	C₂×C₁₁	1	1	yes	characteristic
231	C₄×#126	C₂×C₁₁	1	4	yes	complemented
232	#2283	C₂×C₁₁	1	1	yes	characteristic, complemented
233	#2274	C₂×C₁₁	1	1	yes	characteristic, complemented
234	#2273	C₂×C₁₁	1	1	yes	characteristic
235	C₄×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
236	C₂³×C₁₁	—	2	2	no	—
237	C₂³×C₁₁	—	2	2	no	—
238	C₂³×C₁₁	—	2	2	no	—
239	C₂³×C₁₁	—	2	2	no	—
240	C₂³×C₁₁	—	2	4	no	—
241	C₂³×C₁₁	—	2	4	no	—
242	C₂³×C₁₁	—	2	8	no	—
243	C₂³×C₁₁	—	4	4	no	—
244	C₂³×C₁₁	—	4	4	no	—
245	C₂³×C₁₁	—	8	8	no	—
246	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
247	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
248	C₂³×C₁₁	C₂×#41	1	4	yes	—
249	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
250	C₂×C₄×C₁₁	—	2	8	no	—
251	C₂×C₄×C₁₁	—	2	8	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	2	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	2	no	—
259	C₂×C₄×C₁₁	—	2	4	no	—
260	C₂×C₄×C₁₁	—	2	4	no	—
261	C₂×C₄×C₁₁	—	2	4	no	—
262	C₂×C₄×C₁₁	—	2	4	no	—
263	C₂×C₄×C₁₁	—	2	2	no	—
264	C₂×C₄×C₁₁	—	2	4	no	—
265	C₂×C₄×C₁₁	—	2	4	no	—
266	C₂×C₄×C₁₁	—	2	4	no	—
267	C₂×C₄×C₁₁	—	2	4	no	—
268	C₂×C₄×C₁₁	—	2	4	no	—
269	C₂×C₄×C₁₁	—	2	4	no	—
270	C₂×C₄×C₁₁	—	2	4	no	—
271	C₂×C₄×C₁₁	—	2	4	no	—
272	C₂×C₄×C₁₁	—	2	4	no	—
273	C₂×C₄×C₁₁	—	4	4	no	—
274	C₂×C₄×C₁₁	—	4	4	no	—
275	C₂×C₄×C₁₁	—	4	4	no	—
276	C₂×C₄×C₁₁	—	4	4	no	—
277	C₂×C₄×C₁₁	—	8	8	no	—
278	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
279	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
282	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
284	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
285	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
286	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
287	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
288	C₂×#126	C₄×C₁₁	1	16	yes	complemented
289	C₂×#126	C₂²×C₁₁	1	2	yes	—
290	C₂×#126	C₂²×C₁₁	1	2	yes	—
291	C₂×#126	C₂²×C₁₁	1	2	yes	—
292	C₂×#126	C₂²×C₁₁	1	2	yes	—
293	C₂×#117	C₂²×C₁₁	1	2	yes	—
294	C₂×#117	C₂²×C₁₁	1	2	yes	—
295	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
303	#389	C₂²×C₁₁	1	4	yes	complemented
304	#389	C₂²×C₁₁	1	4	yes	complemented
305	#388	C₂²×C₁₁	1	4	yes	—
306	#388	C₂²×C₁₁	1	4	yes	—
307	#388	C₂²×C₁₁	1	4	yes	—
308	#388	C₂²×C₁₁	1	4	yes	—
309	#388	C₂²×C₁₁	1	4	yes	—
310	#388	C₂²×C₁₁	1	4	yes	—
311	#387	C₂²×C₁₁	1	4	yes	complemented
312	#387	C₂²×C₁₁	1	4	yes	complemented
313	#387	C₂²×C₁₁	1	4	yes	complemented
314	#387	C₂²×C₁₁	1	4	yes	complemented
315	#387	C₂²×C₁₁	1	4	yes	complemented
316	#387	C₂²×C₁₁	1	4	yes	complemented
317	#385	C₂²×C₁₁	1	4	yes	—
318	#385	C₂²×C₁₁	1	4	yes	—
319	#383	C₂²×C₁₁	1	2	yes	complemented
320	#382	C₂²×C₁₁	1	2	yes	complemented
321	#381	C₂²×C₁₁	1	2	yes	—
322	#381	C₂²×C₁₁	1	2	yes	—
323	#380	C₂²×C₁₁	1	2	yes	—
324	#380	C₂²×C₁₁	1	2	yes	—
325	#380	C₂²×C₁₁	1	2	yes	—
326	#379	C₂²×C₁₁	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
328	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
329	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
330	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
331	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
332	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
333	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
334	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
339	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
341	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
342	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
343	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
344	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
345	#376	C₂²×C₁₁	1	2	yes	complemented
346	#376	C₂²×C₁₁	1	2	yes	complemented
347	C₄³	C₂²×C₁₁	1	2	yes	complemented
348	C₂²×C₁₁	—	2	2	no	—
349	C₂²×C₁₁	—	2	2	no	—
350	C₂²×C₁₁	—	2	8	no	—
351	C₂²×C₁₁	—	2	4	no	—
352	C₂²×C₁₁	—	2	4	no	—
353	C₂²×C₁₁	—	2	4	no	—
354	C₂²×C₁₁	—	4	4	no	—
355	C₂²×C₁₁	—	4	4	no	—
356	C₂²×C₁₁	—	8	8	no	—
357	C₂²×C₁₁	C₄×#41	1	4	yes	—
358	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
359	C₂²×C₁₁	C₂²×#41	1	2	yes	—
360	C₂²×C₁₁	#585	1	2	yes	—
361	C₂²×C₁₁	#585	1	2	yes	—
362	C₄×C₁₁	—	2	2	no	—
363	C₄×C₁₁	—	2	4	no	—
364	C₄×C₁₁	—	2	2	no	—
365	C₄×C₁₁	—	2	2	no	—
366	C₄×C₁₁	—	2	2	no	—
367	C₄×C₁₁	—	2	2	no	—
368	C₄×C₁₁	—	2	4	no	—
369	C₄×C₁₁	—	2	4	no	—
370	C₄×C₁₁	—	2	2	no	—
371	C₄×C₁₁	—	2	8	no	—
372	C₄×C₁₁	—	4	4	no	—
373	C₄×C₁₁	—	4	4	no	—
374	C₄×C₁₁	—	4	4	no	—
375	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
379	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
383	#126	C₂×C₄×C₁₁	1	16	yes	complemented
384	#126	C₂×C₄×C₁₁	1	16	yes	complemented
385	#126	C₂×C₄×C₁₁	1	16	yes	complemented
386	#126	C₂×C₄×C₁₁	1	16	yes	complemented
387	#117	—	2	8	no	—
388	#117	—	2	8	no	—
389	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	complemented
390	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	complemented
391	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	complemented
392	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
403	C₂×C₂²⋊C₄	—	2	8	no	—
404	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
420	C₂×C₄²	C₂×C₄×C₁₁	1	8	yes	complemented
421	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
423	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
426	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
430	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
434	#95	C₂³×C₁₁	1	2	yes	—
435	#95	C₂³×C₁₁	1	4	yes	—
436	#95	C₂³×C₁₁	1	4	yes	—
437	#95	C₂³×C₁₁	1	2	yes	—
438	#95	C₂³×C₁₁	1	4	yes	—
439	#95	C₂³×C₁₁	1	2	yes	—
440	#95	C₂³×C₁₁	1	4	yes	—
441	#95	C₂³×C₁₁	1	4	yes	—
442	#95	C₂³×C₁₁	1	2	yes	—
443	#95	C₂³×C₁₁	1	4	yes	—
444	#95	C₂³×C₁₁	1	4	yes	—
445	#95	C₂³×C₁₁	1	4	yes	—
446	#95	C₂³×C₁₁	1	4	yes	—
447	#95	C₂³×C₁₁	1	4	yes	—
448	C₂×C₁₁	—	2	4	no	—
449	C₂×C₁₁	—	4	4	no	—
450	C₂×C₁₁	C₂×C₄×#41	1	1	yes	characteristic
451	C₂×C₁₁	#3428	1	1	yes	characteristic
452	C₂×C₁₁	#3428	1	1	yes	characteristic
453	C₂×C₁₁	#3521	1	4	yes	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	4	2	no	—
456	C₂⁴	—	4	2	no	—
457	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
458	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
459	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
470	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
471	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
472	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	4	4	no	—
491	C₄⋊C₄	—	4	4	no	—
492	C₄⋊C₄	—	4	4	no	—
493	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
494	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
495	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
496	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
497	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
498	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	4	4	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
506	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
507	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
508	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
509	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
510	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
511	C₂²⋊C₄	C₁₁×#41	1	8	yes	—
512	C₄²	—	2	8	no	—
513	C₄²	—	2	8	no	—
514	C₄²	—	4	2	no	—
515	C₄²	—	4	4	no	—
516	C₄²	—	4	4	no	—
517	C₄²	—	4	4	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
522	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
523	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
524	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
525	C₁₁	#34247	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	8	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	8	8	no	—
536	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
537	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
538	C₂³	C₂×C₁₁×#41	1	4	yes	—
539	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	8	8	no	—
568	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
569	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
570	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
572	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
573	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
574	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
575	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
576	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
577	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	8	no	—
587	C₂²	C₄×C₁₁×#41	1	4	yes	—
588	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
589	C₂²	C₂²×C₁₁×#41	1	2	yes	—
590	C₂²	C₁₁×#585	1	2	yes	—
591	C₂²	C₁₁×#585	1	2	yes	—
592	C₄	—	2	2	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	4	no	—
599	C₄	—	2	4	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	8	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	4	no	—
604	C₄	—	4	4	no	—
605	C₂	—	2	4	no	—
606	C₂	—	4	4	no	—
607	C₂	C₂×C₄×C₁₁×#41	1	1	yes	characteristic
608	C₂	C₁₁×#3428	1	1	yes	characteristic
609	C₂	C₁₁×#3428	1	1	yes	characteristic
610	C₂	C₁₁×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2373	C₂	semidirect
3. C₁₁×#2373	C₂	semidirect
4. C₁₁×#2345	C₂	semidirect
5. C₁₁×#2344	C₂	semidirect
8. C₁₁×#2334	C₂	semidirect
9. C₁₁×#2313	C₂	semidirect
11. C₄×C₁₁×#126	C₂	semidirect
12. C₁₁×#2283	C₂	semidirect
13. C₁₁×#2274	C₂	semidirect
15. C₄×C₁₁×#117	C₂	semidirect
16. C₂×C₁₁×#126	C₄	semidirect
31. C₁₁×#389	C₂²	semidirect
32. C₁₁×#389	C₂²	semidirect
39. C₁₁×#387	C₂²	semidirect
40. C₁₁×#387	C₂²	semidirect
41. C₁₁×#387	C₂²	semidirect
42. C₁₁×#387	C₂²	semidirect
43. C₁₁×#387	C₂²	semidirect
44. C₁₁×#387	C₂²	semidirect
47. C₁₁×#383	C₂²	semidirect
48. C₁₁×#382	C₂²	semidirect
55. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
56. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
57. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
58. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
59. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
60. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
61. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
73. C₁₁×#376	C₂²	semidirect
74. C₁₁×#376	C₂²	semidirect
75. C₄³×C₁₁	C₂²	semidirect
84. C₁₁×#126	C₂×C₄	semidirect
85. C₁₁×#126	C₂×C₄	semidirect
86. C₁₁×#126	C₂×C₄	semidirect
87. C₁₁×#126	C₂×C₄	semidirect
90. C₂×C₁₁×C₄⋊C₄	C₂×C₄	semidirect
91. C₂×C₁₁×C₄⋊C₄	C₂×C₄	semidirect
92. C₂×C₁₁×C₄⋊C₄	C₂×C₄	semidirect
121. C₂×C₄²×C₁₁	C₂×C₄	semidirect
149. #34247	C₁₁	direct (N × H)
222. #2373	C₂×C₁₁	semidirect
223. #2373	C₂×C₁₁	semidirect
224. #2345	C₂×C₁₁	semidirect
225. #2344	C₂×C₁₁	semidirect
228. #2334	C₂×C₁₁	semidirect
229. #2313	C₂×C₁₁	semidirect
231. C₄×#126	C₂×C₁₁	semidirect
232. #2283	C₂×C₁₁	semidirect
233. #2274	C₂×C₁₁	semidirect
235. C₄×#117	C₂×C₁₁	semidirect
288. C₂×#126	C₄×C₁₁	semidirect
303. #389	C₂²×C₁₁	semidirect
304. #389	C₂²×C₁₁	semidirect
311. #387	C₂²×C₁₁	semidirect
312. #387	C₂²×C₁₁	semidirect
313. #387	C₂²×C₁₁	semidirect
314. #387	C₂²×C₁₁	semidirect
315. #387	C₂²×C₁₁	semidirect
316. #387	C₂²×C₁₁	semidirect
319. #383	C₂²×C₁₁	semidirect
320. #382	C₂²×C₁₁	semidirect
327. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
328. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
329. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
330. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
331. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
332. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
333. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
345. #376	C₂²×C₁₁	semidirect
346. #376	C₂²×C₁₁	semidirect
347. C₄³	C₂²×C₁₁	semidirect
383. #126	C₂×C₄×C₁₁	semidirect
384. #126	C₂×C₄×C₁₁	semidirect
385. #126	C₂×C₄×C₁₁	semidirect
386. #126	C₂×C₄×C₁₁	semidirect
389. C₂×C₄⋊C₄	C₂×C₄×C₁₁	semidirect
390. C₂×C₄⋊C₄	C₂×C₄×C₁₁	semidirect
391. C₂×C₄⋊C₄	C₂×C₄×C₁₁	semidirect
420. C₂×C₄²	C₂×C₄×C₁₁	semidirect
525. C₁₁	#34247	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×#126	2
C₁₁×#2373	2
C₁₁×#2345	2
C₁₁×#2344	2
C₁₁×#2342	2
C₁₁×#2334	2
C₁₁×#2313	2
C₁₁×#2312	2
C₄×C₁₁×#126	2
C₁₁×#2283	2
C₁₁×#2274	2
C₁₁×#2273	2
C₄×C₁₁×#117	2
#34247	11

Subgroups — C11×#34247 #14611440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34247 #14611440