Subgroups — C₂×C₁₁×#2930 #14637327

Order 2816.

2870 conjugacy classes of subgroups.

The subgroup lattice has 488 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	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#525	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2930	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#436	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#435	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#131	—	2	8	no	—
14	C₂×C₁₁×#131	C₂²	1	8	yes	complemented
15	C₂²×C₁₁×M₁₆	—	2	8	no	—
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁×M₁₆	C₂²	1	8	yes	complemented
21	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	complemented
22	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₁	C₂²	1	2	yes	complemented
25	C₁₁×#525	C₄	1	8	yes	—
26	C₁₁×#525	C₂²	1	8	yes	—
27	C₂×C₁₁×#123	C₄	1	2	yes	—
28	C₂×C₁₁×C₂²⋊Q₈	C₄	1	2	yes	—
29	C₂×C₁₁×#121	C₄	1	2	yes	—
30	C₂×C₁₁×#120	C₄	1	2	yes	—
31	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
32	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
33	C₁₁×#436	C₂²	1	32	yes	complemented
34	C₁₁×#435	C₂²	1	32	yes	complemented
35	C₁₁×#424	C₂²	1	8	yes	complemented
36	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	complemented
37	C₁₁×#408	C₂²	1	8	yes	complemented
38	C₁₁×#407	C₂²	1	8	yes	complemented
39	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
40	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
41	C₁₁×#405	C₂²	1	8	yes	complemented
42	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₁×#41	—	2	4	no	—
46	C₂×C₁₁×#41	—	2	4	no	—
47	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
48	C₂×C₁₁×#41	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₁₁	—	2	4	no	—
54	C₂³×C₄×C₁₁	—	2	4	no	—
55	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
56	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₁	C₂×C₄	1	4	yes	—
58	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₁₁×#131	—	2	32	no	—
63	C₂×C₁₁×M₁₆	—	2	4	no	—
64	C₂×C₁₁×M₁₆	—	2	4	no	—
65	C₂×C₁₁×M₁₆	—	2	8	no	—
66	C₂×C₁₁×M₁₆	—	2	8	no	—
67	C₂×C₁₁×M₁₆	—	2	8	no	—
68	C₂×C₁₁×M₁₆	—	2	32	no	—
69	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
70	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
71	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
72	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
73	C₂×C₁₁×M₁₆	C₂³	1	8	yes	complemented
74	C₂²×C₈×C₁₁	—	2	4	no	—
75	C₂²×C₈×C₁₁	—	2	8	no	—
76	C₂²×C₈×C₁₁	D₄	1	8	yes	complemented
77	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
78	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₁	C₂³	1	8	yes	complemented
85	C₁₁×#123	C₂×C₄	1	16	yes	—
86	C₁₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
87	C₁₁×#121	C₂×C₄	1	16	yes	—
88	C₁₁×#120	C₂×C₄	1	16	yes	—
89	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
90	C₄×D₄×C₁₁	C₂³	1	16	yes	—
91	C₁₁×#117	C₂×C₄	1	4	yes	—
92	C₁₁×#117	C₂³	1	4	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
95	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
96	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
97	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
98	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
99	C₁₁×C₄⋊C₈	C₂³	1	16	yes	complemented
100	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
101	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
102	C₁₁×#97	C₂³	1	8	yes	complemented
103	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
104	C₂×#2930	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₁	—	2	4	no	—
106	C₂⁴×C₁₁	—	4	4	no	—
107	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
109	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
111	C₁₁×#41	—	2	16	no	—
112	C₁₁×#41	—	2	8	no	—
113	C₁₁×#41	—	2	8	no	—
114	C₂×Q₈×C₁₁	—	2	4	no	—
115	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
116	C₂×D₄×C₁₁	—	2	8	no	—
117	C₂×D₄×C₁₁	—	2	4	no	—
118	C₂×D₄×C₁₁	—	4	8	no	—
119	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
120	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
121	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
122	C₂²×C₄×C₁₁	—	2	4	no	—
123	C₂²×C₄×C₁₁	—	2	8	no	—
124	C₂²×C₄×C₁₁	—	2	16	no	—
125	C₂²×C₄×C₁₁	—	2	4	no	—
126	C₂²×C₄×C₁₁	—	2	4	no	—
127	C₂²×C₄×C₁₁	—	2	8	no	—
128	C₂²×C₄×C₁₁	—	2	4	no	—
129	C₂²×C₄×C₁₁	—	2	8	no	—
130	C₂²×C₄×C₁₁	—	2	4	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
137	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₁	#41	1	4	yes	—
142	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
146	C₁₁×M₁₆	—	2	16	no	—
147	C₁₁×M₁₆	—	2	16	no	—
148	C₁₁×M₁₆	—	2	16	no	—
149	C₁₁×M₁₆	—	2	8	no	—
150	C₁₁×M₁₆	—	2	8	no	—
151	C₂×C₈×C₁₁	—	2	16	no	—
152	C₂×C₈×C₁₁	—	2	4	no	—
153	C₂×C₈×C₁₁	—	2	4	no	—
154	C₂×C₈×C₁₁	—	2	8	no	—
155	C₂×C₈×C₁₁	—	2	4	no	—
156	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
157	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
158	C₂×C₈×C₁₁	C₂×D₄	1	16	yes	complemented
159	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
160	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
161	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
162	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
163	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
164	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
165	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
166	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
167	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
168	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
169	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
170	C₄²×C₁₁	C₂⁴	1	4	yes	—
171	C₂²×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₂³×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
173	C₂×#525	C₂×C₁₁	1	1	yes	characteristic
174	#2930	C₂×C₁₁	1	16	yes	direct product factor
175	C₂×#436	C₂×C₁₁	1	4	yes	complemented
176	C₂×#435	C₂×C₁₁	1	4	yes	complemented
177	C₂×#424	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₂×#408	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂×#407	C₂×C₁₁	1	1	yes	characteristic, complemented
180	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₂³×C₁₁	—	2	4	no	—
182	C₂³×C₁₁	—	2	8	no	—
183	C₂³×C₁₁	—	2	4	no	—
184	C₂³×C₁₁	—	2	4	no	—
185	C₂³×C₁₁	—	2	4	no	—
186	C₂³×C₁₁	—	2	8	no	—
187	C₂³×C₁₁	—	2	4	no	—
188	C₂³×C₁₁	—	4	8	no	—
189	C₂³×C₁₁	—	4	16	no	—
190	C₂³×C₁₁	C₄×D₄	1	4	yes	—
191	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
192	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
193	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
194	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
195	Q₈×C₁₁	—	2	8	no	—
196	D₄×C₁₁	—	2	16	no	—
197	D₄×C₁₁	—	2	8	no	—
198	D₄×C₁₁	—	4	16	no	—
199	C₂×C₄×C₁₁	—	2	8	no	—
200	C₂×C₄×C₁₁	—	2	4	no	—
201	C₂×C₄×C₁₁	—	2	4	no	—
202	C₂×C₄×C₁₁	—	2	8	no	—
203	C₂×C₄×C₁₁	—	2	8	no	—
204	C₂×C₄×C₁₁	—	2	16	no	—
205	C₂×C₄×C₁₁	—	2	8	no	—
206	C₂×C₄×C₁₁	—	2	4	no	—
207	C₂×C₄×C₁₁	—	2	4	no	—
208	C₂×C₄×C₁₁	—	2	4	no	—
209	C₂×C₄×C₁₁	—	2	4	no	—
210	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
211	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
212	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
213	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
215	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
220	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
221	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
222	C₈×C₁₁	—	2	4	no	—
223	C₈×C₁₁	—	2	4	no	—
224	C₈×C₁₁	—	2	4	no	—
225	C₈×C₁₁	C₂²×D₄	1	4	yes	—
226	C₈×C₁₁	C₂²×D₄	1	4	yes	—
227	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×#131	—	2	8	no	—
230	C₂×#131	C₂²×C₁₁	1	8	yes	complemented
231	C₂²×M₁₆	—	2	8	no	—
232	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
236	C₂²×M₁₆	C₂²×C₁₁	1	8	yes	complemented
237	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	complemented
238	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₁₁	1	2	yes	complemented
241	#525	C₄×C₁₁	1	8	yes	—
242	#525	C₂²×C₁₁	1	8	yes	—
243	C₂×#123	C₄×C₁₁	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₄×C₁₁	1	2	yes	—
245	C₂×#121	C₄×C₁₁	1	2	yes	—
246	C₂×#120	C₄×C₁₁	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
248	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
249	#436	C₂²×C₁₁	1	32	yes	complemented
250	#435	C₂²×C₁₁	1	32	yes	complemented
251	#424	C₂²×C₁₁	1	8	yes	complemented
252	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
253	#408	C₂²×C₁₁	1	8	yes	complemented
254	#407	C₂²×C₁₁	1	8	yes	complemented
255	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
257	#405	C₂²×C₁₁	1	8	yes	complemented
258	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
259	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
260	C₂²×C₁₁	—	2	8	no	—
261	C₂²×C₁₁	—	2	4	no	—
262	C₂²×C₁₁	—	2	4	no	—
263	C₂²×C₁₁	—	2	4	no	—
264	C₂²×C₁₁	—	2	4	no	—
265	C₂²×C₁₁	—	2	8	no	—
266	C₂²×C₁₁	—	2	4	no	—
267	C₂²×C₁₁	—	4	16	no	—
268	C₂²×C₁₁	—	4	8	no	—
269	C₂²×C₁₁	—	4	8	no	—
270	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
271	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
272	C₂²×C₁₁	#568	1	4	yes	—
273	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
274	C₄×C₁₁	—	2	4	no	—
275	C₄×C₁₁	—	2	4	no	—
276	C₄×C₁₁	—	2	8	no	—
277	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
278	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
279	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
281	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
285	C₂×#41	C₂³×C₁₁	1	4	yes	—
286	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
287	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
288	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
289	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	—	2	4	no	—
292	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
293	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
294	C₂³×C₄	C₂×C₄×C₁₁	1	4	yes	—
295	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
298	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
299	#131	—	2	32	no	—
300	C₂×M₁₆	—	2	4	no	—
301	C₂×M₁₆	—	2	4	no	—
302	C₂×M₁₆	—	2	8	no	—
303	C₂×M₁₆	—	2	8	no	—
304	C₂×M₁₆	—	2	8	no	—
305	C₂×M₁₆	—	2	32	no	—
306	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
307	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
308	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
309	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
310	C₂×M₁₆	C₂³×C₁₁	1	8	yes	complemented
311	C₂²×C₈	—	2	4	no	—
312	C₂²×C₈	—	2	8	no	—
313	C₂²×C₈	D₄×C₁₁	1	8	yes	complemented
314	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
315	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
316	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
317	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
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	8	yes	complemented
322	#123	C₂×C₄×C₁₁	1	16	yes	—
323	C₂²⋊Q₈	C₂×C₄×C₁₁	1	16	yes	—
324	#121	C₂×C₄×C₁₁	1	16	yes	—
325	#120	C₂×C₄×C₁₁	1	16	yes	—
326	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
327	C₄×D₄	C₂³×C₁₁	1	16	yes	—
328	#117	C₂×C₄×C₁₁	1	4	yes	—
329	#117	C₂³×C₁₁	1	4	yes	—
330	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
335	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
336	C₄⋊C₈	C₂³×C₁₁	1	16	yes	complemented
337	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
338	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
339	#97	C₂³×C₁₁	1	8	yes	complemented
340	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
341	C₂×C₁₁	—	2	4	no	—
342	C₂×C₁₁	—	4	4	no	—
343	C₂×C₁₁	—	4	4	no	—
344	C₂×C₁₁	#2930	1	4	yes	direct product factor
345	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
346	C₂×C₁₁	C₂×#568	1	2	yes	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	4	4	no	—
349	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
350	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
351	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
352	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
353	#41	—	2	16	no	—
354	#41	—	2	8	no	—
355	#41	—	2	8	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
362	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
363	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	16	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
374	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
375	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
383	C₂²×C₄	C₁₁×#41	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
388	M₁₆	—	2	8	no	—
389	M₁₆	—	2	8	no	—
390	M₁₆	—	2	16	no	—
391	M₁₆	—	2	16	no	—
392	M₁₆	—	2	16	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	2	8	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	16	no	—
398	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
399	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
400	C₂×C₈	C₂×D₄×C₁₁	1	16	yes	complemented
401	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
402	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
403	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
404	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
405	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
407	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
408	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
409	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
410	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
411	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
412	C₄²	C₂⁴×C₁₁	1	4	yes	—
413	C₁₁	C₂×#2930	1	1	yes	characteristic, direct product factor, Sylow
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	16	no	—
423	C₂³	C₄×D₄×C₁₁	1	4	yes	—
424	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
425	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
426	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
427	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
428	Q₈	—	2	8	no	—
429	D₄	—	2	16	no	—
430	D₄	—	2	8	no	—
431	D₄	—	4	16	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	16	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
444	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
445	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
446	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
447	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
448	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
449	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
452	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
453	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
454	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	2	4	no	—
457	C₈	—	2	4	no	—
458	C₈	C₂²×D₄×C₁₁	1	4	yes	—
459	C₈	C₂²×D₄×C₁₁	1	4	yes	—
460	C₂²	—	2	8	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	16	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	8	no	—
470	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
471	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
472	C₂²	C₁₁×#568	1	4	yes	—
473	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
474	C₄	—	2	4	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	8	no	—
477	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
478	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
479	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
480	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
481	C₂	—	2	4	no	—
482	C₂	—	4	4	no	—
483	C₂	—	4	4	no	—
484	C₂	C₁₁×#2930	1	4	yes	direct product factor
485	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
486	C₂	C₂×C₁₁×#568	1	2	yes	—

	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×#525	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
2. C₂³×C₁₁×M₁₆	C₂	semidirect
4. C₁₁×#2930	C₂	direct (N × H)
5. C₂×C₁₁×#436	C₂	semidirect
6. C₂×C₁₁×#435	C₂	semidirect
7. C₂×C₁₁×#424	C₂	semidirect
8. C₂×C₁₁×#408	C₂	semidirect
9. C₂×C₁₁×#407	C₂	semidirect
10. C₂×C₁₁×#405	C₂	semidirect
14. C₂×C₁₁×#131	C₂²	semidirect
20. C₂²×C₁₁×M₁₆	C₂²	semidirect
21. C₂²×C₁₁×M₁₆	C₂²	semidirect
24. C₂³×C₈×C₁₁	C₂²	semidirect
33. C₁₁×#436	C₂²	semidirect
34. C₁₁×#435	C₂²	semidirect
35. C₁₁×#424	C₂²	semidirect
36. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
37. C₁₁×#408	C₂²	semidirect
38. C₁₁×#407	C₂²	semidirect
40. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
41. C₁₁×#405	C₂²	semidirect
42. C₂×C₁₁×#97	C₂²	semidirect
43. C₂×C₄×C₈×C₁₁	C₂²	semidirect
73. C₂×C₁₁×M₁₆	C₂³	semidirect
76. C₂²×C₈×C₁₁	D₄	semidirect
84. C₂²×C₈×C₁₁	C₂³	semidirect
99. C₁₁×C₄⋊C₈	C₂³	semidirect
101. C₁₁×C₂²⋊C₈	C₂³	semidirect
102. C₁₁×#97	C₂³	semidirect
103. C₄×C₈×C₁₁	C₂³	semidirect
104. C₂×#2930	C₁₁	direct (N × H)
158. C₂×C₈×C₁₁	C₂×D₄	semidirect
171. C₂²×#131	C₂×C₁₁	semidirect
172. C₂³×M₁₆	C₂×C₁₁	semidirect
174. #2930	C₂×C₁₁	direct (N × H)
175. C₂×#436	C₂×C₁₁	semidirect
176. C₂×#435	C₂×C₁₁	semidirect
177. C₂×#424	C₂×C₁₁	semidirect
178. C₂×#408	C₂×C₁₁	semidirect
179. C₂×#407	C₂×C₁₁	semidirect
180. C₂×#405	C₂×C₁₁	semidirect
230. C₂×#131	C₂²×C₁₁	semidirect
236. C₂²×M₁₆	C₂²×C₁₁	semidirect
237. C₂²×M₁₆	C₂²×C₁₁	semidirect
240. C₂³×C₈	C₂²×C₁₁	semidirect
249. #436	C₂²×C₁₁	semidirect
250. #435	C₂²×C₁₁	semidirect
251. #424	C₂²×C₁₁	semidirect
252. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
253. #408	C₂²×C₁₁	semidirect
254. #407	C₂²×C₁₁	semidirect
256. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
257. #405	C₂²×C₁₁	semidirect
258. C₂×#97	C₂²×C₁₁	semidirect
259. C₂×C₄×C₈	C₂²×C₁₁	semidirect
310. C₂×M₁₆	C₂³×C₁₁	semidirect
313. C₂²×C₈	D₄×C₁₁	semidirect
321. C₂²×C₈	C₂³×C₁₁	semidirect
336. C₄⋊C₈	C₂³×C₁₁	semidirect
338. C₂²⋊C₈	C₂³×C₁₁	semidirect
339. #97	C₂³×C₁₁	semidirect
340. C₄×C₈	C₂³×C₁₁	semidirect
344. C₂×C₁₁	#2930	direct (N × H)
400. C₂×C₈	C₂×D₄×C₁₁	semidirect
413. C₁₁	C₂×#2930	direct (N × H)
484. C₂	C₁₁×#2930	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
C₂³×C₁₁×M₁₆	2
C₂×C₁₁×#525	2
C₁₁×#2930	2
C₂×C₁₁×#436	2
C₂×C₁₁×#435	2
C₂×C₁₁×#424	2
C₂×C₁₁×#408	2
C₂×C₁₁×#407	2
C₂×C₁₁×#405	2
C₂×#2930	11

Subgroups — C2×C11×#2930 #14637327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2930 #14637327