Subgroups — C₂×C₁₁×#2935 #14637332

Order 2816.

2850 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#131	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2935	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₈×D₄×C₁₁	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#408	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×#41	C₂²	1	2	yes	—
11	C₂×C₁₁×#131	—	2	16	no	—
12	C₂×C₁₁×#131	C₂²	1	16	yes	complemented
13	C₂²×C₁₁×M₁₆	C₂²	1	4	yes	—
14	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
17	C₂³×C₈×C₁₁	C₂²	1	4	yes	—
18	C₁₁×#532	C₄	1	8	yes	—
19	C₁₁×#532	C₂²	1	8	yes	—
20	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
21	C₂×C₁₁×#127	C₄	1	1	yes	characteristic
22	C₂×C₁₁×#124	C₄	1	2	yes	—
23	C₂×C₁₁×#121	C₄	1	2	yes	—
24	C₂×C₁₁×#121	C₄	1	2	yes	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#436	C₂²	1	16	yes	complemented
29	C₁₁×#435	C₂²	1	32	yes	complemented
30	C₈×D₄×C₁₁	C₂²	1	16	yes	complemented
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	complemented
35	C₁₁×#408	C₂²	1	16	yes	complemented
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
37	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
39	C₂×C₁₁×#97	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
41	C₂×C₁₁×#41	—	2	8	no	—
42	C₂×C₁₁×#41	—	2	8	no	—
43	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
44	C₂×C₁₁×#41	C₂³	1	8	yes	—
45	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×#131	—	2	64	no	—
55	C₂×C₁₁×M₁₆	—	2	4	no	—
56	C₂×C₁₁×M₁₆	—	2	16	no	—
57	C₂×C₁₁×M₁₆	D₄	1	8	yes	complemented
58	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
59	C₂×C₁₁×M₁₆	C₂³	1	16	yes	—
60	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₁	—	2	8	no	—
62	C₂²×C₈×C₁₁	—	2	16	no	—
63	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
64	C₂²×C₈×C₁₁	C₂³	1	16	yes	—
65	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
69	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
70	C₁₁×#127	C₂×C₄	1	8	yes	—
71	C₁₁×#124	C₂×C₄	1	16	yes	—
72	C₁₁×#121	C₂×C₄	1	16	yes	—
73	C₁₁×#121	C₂×C₄	1	16	yes	—
74	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
75	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
76	C₄×D₄×C₁₁	C₂³	1	8	yes	—
77	C₄×D₄×C₁₁	C₂³	1	8	yes	—
78	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
81	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
82	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
89	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
90	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
91	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
92	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
93	C₁₁×#97	C₂³	1	8	yes	—
94	C₄×C₈×C₁₁	C₂³	1	8	yes	—
95	C₂×#2935	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
97	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₁₁×#41	—	2	32	no	—
99	C₁₁×#41	—	2	16	no	—
100	C₁₁×#41	—	2	16	no	—
101	C₂×Q₈×C₁₁	—	2	8	no	—
102	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
103	C₂×D₄×C₁₁	—	2	16	no	—
104	C₂×D₄×C₁₁	—	2	8	no	—
105	C₂×D₄×C₁₁	—	2	8	no	—
106	C₂×D₄×C₁₁	—	4	4	no	—
107	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
108	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
109	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
110	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
111	C₂²×C₄×C₁₁	—	2	4	no	—
112	C₂²×C₄×C₁₁	—	2	8	no	—
113	C₂²×C₄×C₁₁	—	2	8	no	—
114	C₂²×C₄×C₁₁	—	4	2	no	—
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
121	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₁	#41	1	4	yes	—
127	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₁₁×M₁₆	—	2	32	no	—
131	C₁₁×M₁₆	—	2	8	no	—
132	C₁₁×M₁₆	C₂×D₄	1	16	yes	complemented
133	C₂×C₈×C₁₁	—	2	32	no	—
134	C₂×C₈×C₁₁	—	2	4	no	—
135	C₂×C₈×C₁₁	—	2	4	no	—
136	C₂×C₈×C₁₁	—	2	16	no	—
137	C₂×C₈×C₁₁	—	2	4	no	—
138	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
139	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
140	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
141	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
142	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
143	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
144	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
145	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
146	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
147	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
148	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
149	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
150	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
151	C₄²×C₁₁	C₂⁴	1	2	yes	—
152	C₄²×C₁₁	C₂⁴	1	2	yes	—
153	C₂²×#131	C₂×C₁₁	1	2	yes	complemented
154	C₂×#532	C₂×C₁₁	1	1	yes	characteristic
155	#2935	C₂×C₁₁	1	16	yes	direct product factor
156	C₂×#436	C₂×C₁₁	1	2	yes	complemented
157	C₂×#435	C₂×C₁₁	1	4	yes	complemented
158	C₂×C₈×D₄	C₂×C₁₁	1	2	yes	complemented
159	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂×#408	C₂×C₁₁	1	2	yes	complemented
161	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
162	C₂³×C₁₁	—	2	2	no	—
163	C₂³×C₁₁	—	2	2	no	—
164	C₂³×C₁₁	—	2	8	no	—
165	C₂³×C₁₁	—	2	8	no	—
166	C₂³×C₁₁	—	2	8	no	—
167	C₂³×C₁₁	C₄×D₄	1	4	yes	—
168	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
169	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
170	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
171	Q₈×C₁₁	—	2	16	no	—
172	D₄×C₁₁	—	2	32	no	—
173	D₄×C₁₁	—	2	16	no	—
174	D₄×C₁₁	—	2	16	no	—
175	D₄×C₁₁	—	4	8	no	—
176	C₂×C₄×C₁₁	—	2	8	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	16	no	—
181	C₂×C₄×C₁₁	—	2	8	no	—
182	C₂×C₄×C₁₁	—	2	8	no	—
183	C₂×C₄×C₁₁	—	2	8	no	—
184	C₂×C₄×C₁₁	—	4	4	no	—
185	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
187	C₂×C₄×C₁₁	#131	1	4	yes	complemented
188	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
189	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
192	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
194	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
199	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
200	C₈×C₁₁	—	2	4	no	—
201	C₈×C₁₁	—	2	4	no	—
202	C₈×C₁₁	—	2	4	no	—
203	C₈×C₁₁	C₂²×D₄	1	8	yes	—
204	C₂²×#41	C₂²×C₁₁	1	2	yes	—
205	C₂×#131	—	2	16	no	—
206	C₂×#131	C₂²×C₁₁	1	16	yes	complemented
207	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₁	1	4	yes	—
209	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
211	C₂³×C₈	C₂²×C₁₁	1	4	yes	—
212	#532	C₄×C₁₁	1	8	yes	—
213	#532	C₂²×C₁₁	1	8	yes	—
214	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
215	C₂×#127	C₄×C₁₁	1	1	yes	characteristic
216	C₂×#124	C₄×C₁₁	1	2	yes	—
217	C₂×#121	C₄×C₁₁	1	2	yes	—
218	C₂×#121	C₄×C₁₁	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
220	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
222	#436	C₂²×C₁₁	1	16	yes	complemented
223	#435	C₂²×C₁₁	1	32	yes	complemented
224	C₈×D₄	C₂²×C₁₁	1	16	yes	complemented
225	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	complemented
229	#408	C₂²×C₁₁	1	16	yes	complemented
230	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
232	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
233	C₂×#97	C₂²×C₁₁	1	2	yes	—
234	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
235	C₂²×C₁₁	—	2	8	no	—
236	C₂²×C₁₁	—	2	2	no	—
237	C₂²×C₁₁	—	2	2	no	—
238	C₂²×C₁₁	—	2	8	no	—
239	C₂²×C₁₁	—	2	8	no	—
240	C₂²×C₁₁	—	2	8	no	—
241	C₂²×C₁₁	—	4	16	no	—
242	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
243	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
244	C₂²×C₁₁	C₂×#131	1	2	yes	—
245	C₂²×C₁₁	#568	1	2	yes	—
246	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
247	C₄×C₁₁	—	2	8	no	—
248	C₄×C₁₁	—	2	2	no	—
249	C₄×C₁₁	—	2	2	no	—
250	C₄×C₁₁	—	2	2	no	—
251	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
252	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
253	C₄×C₁₁	C₂×#131	1	4	yes	complemented
254	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
256	C₂×#41	—	2	8	no	—
257	C₂×#41	—	2	8	no	—
258	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
259	C₂×#41	C₂³×C₁₁	1	8	yes	—
260	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
261	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
262	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
263	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
264	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
265	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
268	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
269	#131	—	2	64	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	2	16	no	—
272	C₂×M₁₆	D₄×C₁₁	1	8	yes	complemented
273	C₂×M₁₆	C₂³×C₁₁	1	16	yes	—
274	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
275	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
276	C₂²×C₈	—	2	8	no	—
277	C₂²×C₈	—	2	16	no	—
278	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
281	C₂²×C₈	C₂³×C₁₁	1	16	yes	—
282	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
284	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
285	#127	C₂×C₄×C₁₁	1	8	yes	—
286	#124	C₂×C₄×C₁₁	1	16	yes	—
287	#121	C₂×C₄×C₁₁	1	16	yes	—
288	#121	C₂×C₄×C₁₁	1	16	yes	—
289	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
290	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
291	C₄×D₄	C₂³×C₁₁	1	8	yes	—
292	C₄×D₄	C₂³×C₁₁	1	8	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
297	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
298	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
299	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
300	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
303	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
304	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
305	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
306	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
307	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
308	#97	C₂³×C₁₁	1	8	yes	—
309	C₄×C₈	C₂³×C₁₁	1	8	yes	—
310	C₂×C₁₁	—	2	4	no	—
311	C₂×C₁₁	—	4	8	no	—
312	C₂×C₁₁	#2935	1	4	yes	direct product factor
313	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
314	C₂×C₁₁	C₂²×#131	1	1	yes	characteristic
315	C₂×C₁₁	C₂×#568	1	1	yes	characteristic
316	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
317	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
318	#41	—	2	32	no	—
319	#41	—	2	16	no	—
320	#41	—	2	16	no	—
321	C₂×Q₈	—	2	8	no	—
322	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
328	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
329	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
330	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
346	C₂²×C₄	C₁₁×#41	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
348	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
350	M₁₆	—	2	8	no	—
351	M₁₆	—	2	32	no	—
352	M₁₆	C₂×D₄×C₁₁	1	16	yes	complemented
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	16	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	32	no	—
358	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
359	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
360	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
361	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
362	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
363	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
364	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
365	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
366	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
367	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
368	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
369	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
370	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
371	C₄²	C₂⁴×C₁₁	1	2	yes	—
372	C₄²	C₂⁴×C₁₁	1	2	yes	—
373	C₁₁	C₂×#2935	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	8	no	—
379	C₂³	C₄×D₄×C₁₁	1	4	yes	—
380	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
381	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
382	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
383	Q₈	—	2	16	no	—
384	D₄	—	2	32	no	—
385	D₄	—	2	16	no	—
386	D₄	—	2	16	no	—
387	D₄	—	4	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
398	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
399	C₂×C₄	C₁₁×#131	1	4	yes	complemented
400	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
401	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
402	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
404	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
405	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
409	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
410	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
411	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	2	4	no	—
414	C₈	—	2	4	no	—
415	C₈	C₂²×D₄×C₁₁	1	8	yes	—
416	C₂²	—	2	8	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	4	16	no	—
423	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
424	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
425	C₂²	C₂×C₁₁×#131	1	2	yes	—
426	C₂²	C₁₁×#568	1	2	yes	—
427	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
428	C₄	—	2	8	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
433	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
434	C₄	C₂×C₁₁×#131	1	4	yes	complemented
435	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
436	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
437	C₂	—	2	4	no	—
438	C₂	—	4	8	no	—
439	C₂	C₁₁×#2935	1	4	yes	direct product factor
440	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
441	C₂	C₂²×C₁₁×#131	1	1	yes	characteristic
442	C₂	C₂×C₁₁×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂×C₁₁×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×#131	C₂	semidirect
3. C₁₁×#2935	C₂	direct (N × H)
4. C₂×C₁₁×#436	C₂	semidirect
5. C₂×C₁₁×#435	C₂	semidirect
6. C₂×C₈×D₄×C₁₁	C₂	semidirect
7. C₂²×C₁₁×C₄⋊C₈	C₂	semidirect
8. C₂×C₁₁×#408	C₂	semidirect
9. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
12. C₂×C₁₁×#131	C₂²	semidirect
28. C₁₁×#436	C₂²	semidirect
29. C₁₁×#435	C₂²	semidirect
30. C₈×D₄×C₁₁	C₂²	semidirect
34. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
35. C₁₁×#408	C₂²	semidirect
38. C₄×C₁₁×M₁₆	C₂²	semidirect
57. C₂×C₁₁×M₁₆	D₄	semidirect
95. C₂×#2935	C₁₁	direct (N × H)
132. C₁₁×M₁₆	C₂×D₄	semidirect
153. C₂²×#131	C₂×C₁₁	semidirect
155. #2935	C₂×C₁₁	direct (N × H)
156. C₂×#436	C₂×C₁₁	semidirect
157. C₂×#435	C₂×C₁₁	semidirect
158. C₂×C₈×D₄	C₂×C₁₁	semidirect
159. C₂²×C₄⋊C₈	C₂×C₁₁	semidirect
160. C₂×#408	C₂×C₁₁	semidirect
161. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
187. C₂×C₄×C₁₁	#131	semidirect
206. C₂×#131	C₂²×C₁₁	semidirect
222. #436	C₂²×C₁₁	semidirect
223. #435	C₂²×C₁₁	semidirect
224. C₈×D₄	C₂²×C₁₁	semidirect
228. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
229. #408	C₂²×C₁₁	semidirect
232. C₄×M₁₆	C₂²×C₁₁	semidirect
253. C₄×C₁₁	C₂×#131	semidirect
272. C₂×M₁₆	D₄×C₁₁	semidirect
312. C₂×C₁₁	#2935	direct (N × H)
352. M₁₆	C₂×D₄×C₁₁	semidirect
373. C₁₁	C₂×#2935	direct (N × H)
399. C₂×C₄	C₁₁×#131	semidirect
434. C₄	C₂×C₁₁×#131	semidirect
439. C₂	C₁₁×#2935	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×#131	2
C₂×C₁₁×#532	2
C₁₁×#2935	2
C₂×C₁₁×#436	2
C₂×C₁₁×#435	2
C₂×C₈×D₄×C₁₁	2
C₂²×C₁₁×C₄⋊C₈	2
C₂×C₁₁×#408	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#2935	11

Subgroups — C2×C11×#2935 #14637332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2935 #14637332