Subgroups — C₂×C₁₁×#2957 #14637374

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#568	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2957	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#444	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#443	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#421	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×#41	C₂²	1	2	yes	—
10	C₂×C₁₁×#135	C₄	1	2	yes	complemented
11	C₂×C₁₁×#135	C₄	1	2	yes	complemented
12	C₂×C₁₁×#135	C₄	1	8	yes	complemented
13	C₂×C₁₁×#135	C₂²	1	2	yes	—
14	C₂×C₁₁×#135	C₂²	1	2	yes	—
15	C₂×C₁₁×#135	C₂²	1	8	yes	—
16	C₂²×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₁₁×SD₁₆	C₄	1	2	yes	complemented
18	C₂²×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#568	—	2	8	no	—
20	C₁₁×#568	C₂²	1	16	yes	complemented
21	C₂×C₁₁×#131	—	2	4	no	—
22	C₂×C₁₁×#131	C₂²	1	8	yes	complemented
23	C₂²×C₁₁×M₁₆	—	2	4	no	—
24	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
25	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
28	C₁₁×#444	C₂²	1	32	yes	complemented
29	C₁₁×#443	C₂²	1	32	yes	complemented
30	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
31	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
32	C₂×C₁₁×#108	C₂²	1	8	yes	complemented
33	C₁₁×#421	C₂²	1	16	yes	complemented
34	C₂×C₁₁×#104	C₂²	1	8	yes	complemented
35	C₁₁×#405	C₂²	1	8	yes	complemented
36	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
37	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
38	C₂×C₁₁×#41	—	2	2	no	—
39	C₂×C₁₁×#41	—	2	4	no	—
40	C₂×C₁₁×#41	—	2	2	no	—
41	C₂×C₁₁×#41	—	2	4	no	—
42	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
43	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
44	C₂×C₁₁×#41	C₂³	1	4	yes	—
45	C₂×C₁₁×#41	C₂³	1	8	yes	—
46	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₁	—	2	2	no	—
48	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₁	—	2	2	no	—
50	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×#135	C₂×C₄	1	8	yes	—
52	C₁₁×#135	C₂×C₄	1	8	yes	—
53	C₁₁×#135	C₂×C₄	1	16	yes	complemented
54	C₁₁×#135	C₂×C₄	1	16	yes	complemented
55	C₁₁×#135	C₂³	1	8	yes	—
56	C₁₁×#135	C₂³	1	8	yes	—
57	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	complemented
60	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
62	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
63	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
64	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
65	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
66	C₁₁×#131	—	2	32	no	—
67	C₁₁×#131	—	2	16	no	—
68	C₁₁×#131	C₂³	1	32	yes	complemented
69	C₂×C₁₁×M₁₆	—	2	2	no	—
70	C₂×C₁₁×M₁₆	—	2	4	no	—
71	C₂×C₁₁×M₁₆	—	2	32	no	—
72	C₂×C₁₁×M₁₆	—	2	8	no	—
73	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
74	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
75	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
76	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
77	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
78	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₁	—	2	2	no	—
80	C₂²×C₈×C₁₁	—	2	8	no	—
81	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
86	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
89	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
90	C₁₁×#117	—	2	2	no	—
91	C₁₁×#117	C₂³	1	4	yes	—
92	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
95	C₁₁×#108	C₂³	1	8	yes	complemented
96	C₁₁×#108	C₂³	1	8	yes	complemented
97	C₁₁×#104	C₂³	1	32	yes	complemented
98	C₁₁×#97	C₂³	1	8	yes	complemented
99	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
100	C₂×#2957	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₁	—	2	2	no	—
102	C₂⁴×C₁₁	#41	1	1	yes	characteristic
103	C₁₁×#41	—	2	8	no	—
104	C₁₁×#41	—	2	8	no	—
105	C₁₁×#41	—	2	8	no	—
106	C₁₁×#41	—	2	8	no	—
107	C₁₁×#41	—	2	4	no	—
108	C₁₁×#41	—	2	4	no	—
109	C₁₁×#41	—	2	8	no	—
110	C₁₁×#41	C₂²×C₄	1	8	yes	—
111	C₁₁×#41	C₂²×C₄	1	16	yes	—
112	C₁₁×#41	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₁₁	—	2	2	no	—
114	C₂×Q₈×C₁₁	—	2	4	no	—
115	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
116	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₁	—	2	4	no	—
118	C₂×D₄×C₁₁	—	2	8	no	—
119	C₂×D₄×C₁₁	—	2	4	no	—
120	C₂×D₄×C₁₁	—	2	8	no	—
121	C₂×D₄×C₁₁	—	2	2	no	—
122	C₂×D₄×C₁₁	—	2	4	no	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₁₁	—	2	2	no	—
126	C₂²×C₄×C₁₁	—	2	4	no	—
127	C₂²×C₄×C₁₁	—	2	8	no	—
128	C₂²×C₄×C₁₁	—	2	8	no	—
129	C₂²×C₄×C₁₁	—	2	4	no	—
130	C₂²×C₄×C₁₁	—	2	2	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	#41	1	2	yes	—
139	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
141	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
142	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
143	C₁₁×SD₁₆	C₂²×C₄	1	16	yes	—
144	C₁₁×SD₁₆	C₂²×C₄	1	16	yes	—
145	C₁₁×D₈	C₂²×C₄	1	8	yes	—
146	C₁₁×D₈	C₂²×C₄	1	8	yes	—
147	C₁₁×M₁₆	—	2	32	no	—
148	C₁₁×M₁₆	—	2	8	no	—
149	C₁₁×M₁₆	—	2	4	no	—
150	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
151	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
152	C₁₁×M₁₆	C₂⁴	1	8	yes	—
153	C₂×C₈×C₁₁	—	2	32	no	—
154	C₂×C₈×C₁₁	—	2	8	no	—
155	C₂×C₈×C₁₁	—	2	4	no	—
156	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
159	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
162	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
165	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
166	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
167	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
168	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
170	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
171	C₁₁×C₄⋊C₄	—	2	4	no	—
172	C₁₁×C₂²⋊C₄	—	2	4	no	—
173	C₄²×C₁₁	—	2	2	no	—
174	C₄²×C₁₁	C₂⁴	1	4	yes	—
175	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
176	C₂×#568	C₂×C₁₁	1	2	yes	complemented
177	#2957	C₂×C₁₁	1	16	yes	direct product factor
178	C₂×#444	C₂×C₁₁	1	4	yes	complemented
179	C₂×#443	C₂×C₁₁	1	4	yes	complemented
180	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₂×#421	C₂×C₁₁	1	2	yes	complemented
182	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
183	C₂³×C₁₁	—	2	4	no	—
184	C₂³×C₁₁	—	2	8	no	—
185	C₂³×C₁₁	—	4	2	no	—
186	C₂³×C₁₁	—	8	4	no	—
187	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₁₁	C₄×D₄	1	2	yes	—
190	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
191	C₂³×C₁₁	C₂×#41	1	2	yes	—
192	Q₈×C₁₁	—	2	4	no	—
193	Q₈×C₁₁	—	2	8	no	—
194	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
195	D₄×C₁₁	—	2	8	no	—
196	D₄×C₁₁	—	2	16	no	—
197	D₄×C₁₁	—	2	8	no	—
198	D₄×C₁₁	—	2	4	no	—
199	D₄×C₁₁	—	2	8	no	—
200	D₄×C₁₁	C₂³×C₄	1	8	yes	—
201	C₂×C₄×C₁₁	—	2	8	no	—
202	C₂×C₄×C₁₁	—	2	4	no	—
203	C₂×C₄×C₁₁	—	2	16	no	—
204	C₂×C₄×C₁₁	—	2	8	no	—
205	C₂×C₄×C₁₁	—	2	8	no	—
206	C₂×C₄×C₁₁	—	2	4	no	—
207	C₂×C₄×C₁₁	—	4	4	no	—
208	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
218	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
226	C₈×C₁₁	—	2	8	no	—
227	C₈×C₁₁	C₂³×C₄	1	2	yes	—
228	C₈×C₁₁	C₂³×C₄	1	2	yes	—
229	C₈×C₁₁	C₂³×C₄	1	2	yes	—
230	C₈×C₁₁	C₂³×C₄	1	2	yes	—
231	C₈×C₁₁	C₂²×D₄	1	8	yes	—
232	C₂²×#41	C₂²×C₁₁	1	2	yes	—
233	C₂×#135	C₄×C₁₁	1	2	yes	complemented
234	C₂×#135	C₄×C₁₁	1	2	yes	complemented
235	C₂×#135	C₄×C₁₁	1	8	yes	complemented
236	C₂×#135	C₂²×C₁₁	1	2	yes	—
237	C₂×#135	C₂²×C₁₁	1	2	yes	—
238	C₂×#135	C₂²×C₁₁	1	8	yes	—
239	C₂²×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
240	C₂²×SD₁₆	C₄×C₁₁	1	2	yes	complemented
241	C₂²×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
242	#568	—	2	8	no	—
243	#568	C₂²×C₁₁	1	16	yes	complemented
244	C₂×#131	—	2	4	no	—
245	C₂×#131	C₂²×C₁₁	1	8	yes	complemented
246	C₂²×M₁₆	—	2	4	no	—
247	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
248	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
251	#444	C₂²×C₁₁	1	32	yes	complemented
252	#443	C₂²×C₁₁	1	32	yes	complemented
253	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
254	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
255	C₂×#108	C₂²×C₁₁	1	8	yes	complemented
256	#421	C₂²×C₁₁	1	16	yes	complemented
257	C₂×#104	C₂²×C₁₁	1	8	yes	complemented
258	#405	C₂²×C₁₁	1	8	yes	complemented
259	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
260	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
261	C₂²×C₁₁	—	2	2	no	—
262	C₂²×C₁₁	—	2	2	no	—
263	C₂²×C₁₁	—	2	2	no	—
264	C₂²×C₁₁	—	2	8	no	—
265	C₂²×C₁₁	—	4	2	no	—
266	C₂²×C₁₁	—	4	2	no	—
267	C₂²×C₁₁	—	4	8	no	—
268	C₂²×C₁₁	—	8	8	no	—
269	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
270	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
271	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
274	C₄×C₁₁	—	2	8	no	—
275	C₄×C₁₁	—	4	4	no	—
276	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
277	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
279	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
281	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
287	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
288	C₂×#41	C₂³×C₁₁	1	4	yes	—
289	C₂×#41	C₂³×C₁₁	1	8	yes	—
290	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
295	#135	C₂×C₄×C₁₁	1	8	yes	—
296	#135	C₂×C₄×C₁₁	1	8	yes	—
297	#135	C₂×C₄×C₁₁	1	16	yes	complemented
298	#135	C₂×C₄×C₁₁	1	16	yes	complemented
299	#135	C₂³×C₁₁	1	8	yes	—
300	#135	C₂³×C₁₁	1	8	yes	—
301	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
302	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
303	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
304	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
305	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
306	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
307	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
308	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
309	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
310	#131	—	2	32	no	—
311	#131	—	2	16	no	—
312	#131	C₂³×C₁₁	1	32	yes	complemented
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	2	32	no	—
316	C₂×M₁₆	—	2	8	no	—
317	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
318	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
319	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
320	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
321	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
322	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	8	no	—
325	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
328	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
330	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
333	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
334	#117	—	2	2	no	—
335	#117	C₂³×C₁₁	1	4	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
339	#108	C₂³×C₁₁	1	8	yes	complemented
340	#108	C₂³×C₁₁	1	8	yes	complemented
341	#104	C₂³×C₁₁	1	32	yes	complemented
342	#97	C₂³×C₁₁	1	8	yes	complemented
343	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
344	C₂×C₁₁	—	2	1	no	—
345	C₂×C₁₁	—	2	2	no	—
346	C₂×C₁₁	—	2	1	no	—
347	C₂×C₁₁	—	2	2	no	—
348	C₂×C₁₁	—	4	8	no	—
349	C₂×C₁₁	#2957	1	2	yes	direct product factor
350	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
351	C₂⁴	—	2	2	no	—
352	C₂⁴	C₁₁×#41	1	1	yes	characteristic
353	#41	—	2	8	no	—
354	#41	—	2	8	no	—
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	2	8	no	—
360	#41	C₂²×C₄×C₁₁	1	8	yes	—
361	#41	C₂²×C₄×C₁₁	1	16	yes	—
362	#41	C₂⁴×C₁₁	1	8	yes	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
366	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
374	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
387	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
388	C₂²×C₄	C₁₁×#41	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
391	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
392	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
393	SD₁₆	C₂²×C₄×C₁₁	1	16	yes	—
394	SD₁₆	C₂²×C₄×C₁₁	1	16	yes	—
395	D₈	C₂²×C₄×C₁₁	1	8	yes	—
396	D₈	C₂²×C₄×C₁₁	1	8	yes	—
397	M₁₆	—	2	8	no	—
398	M₁₆	—	2	4	no	—
399	M₁₆	—	2	32	no	—
400	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
401	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
402	M₁₆	C₂⁴×C₁₁	1	8	yes	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	2	8	no	—
405	C₂×C₈	—	2	32	no	—
406	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
408	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
409	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
410	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
411	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
412	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
413	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
414	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
415	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
416	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
417	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
418	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
419	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
421	C₄⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂⁴×C₁₁	1	4	yes	—
425	C₁₁	C₂×#2957	1	1	yes	characteristic, direct product factor, Sylow
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
431	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
432	C₂³	C₄×D₄×C₁₁	1	2	yes	—
433	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
434	C₂³	C₂×C₁₁×#41	1	2	yes	—
435	Q₈	—	2	4	no	—
436	Q₈	—	2	8	no	—
437	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
438	D₄	—	2	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	C₂³×C₄×C₁₁	1	8	yes	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	16	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
452	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
453	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
454	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
455	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
456	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
457	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
458	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
459	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
467	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
469	C₈	—	2	8	no	—
470	C₈	C₂³×C₄×C₁₁	1	2	yes	—
471	C₈	C₂³×C₄×C₁₁	1	2	yes	—
472	C₈	C₂³×C₄×C₁₁	1	2	yes	—
473	C₈	C₂³×C₄×C₁₁	1	2	yes	—
474	C₈	C₂²×D₄×C₁₁	1	8	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	8	8	no	—
483	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
484	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
485	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
486	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
487	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
488	C₄	—	2	8	no	—
489	C₄	—	4	4	no	—
490	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
491	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
492	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
493	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
494	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
495	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	8	no	—
501	C₂	C₁₁×#2957	1	2	yes	direct product factor
502	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#568	C₂	semidirect
3. C₁₁×#2957	C₂	direct (N × H)
4. C₂×C₁₁×#444	C₂	semidirect
5. C₂×C₁₁×#443	C₂	semidirect
6. C₂²×C₁₁×#108	C₂	semidirect
7. C₂×C₁₁×#421	C₂	semidirect
8. C₂×C₁₁×#405	C₂	semidirect
10. C₂×C₁₁×#135	C₄	semidirect
11. C₂×C₁₁×#135	C₄	semidirect
12. C₂×C₁₁×#135	C₄	semidirect
16. C₂²×C₁₁×Q₁₆	C₄	semidirect
17. C₂²×C₁₁×SD₁₆	C₄	semidirect
18. C₂²×C₁₁×D₈	C₄	semidirect
20. C₁₁×#568	C₂²	semidirect
22. C₂×C₁₁×#131	C₂²	semidirect
28. C₁₁×#444	C₂²	semidirect
29. C₁₁×#443	C₂²	semidirect
30. C₂×C₁₁×#108	C₂²	semidirect
31. C₂×C₁₁×#108	C₂²	semidirect
32. C₂×C₁₁×#108	C₂²	semidirect
33. C₁₁×#421	C₂²	semidirect
34. C₂×C₁₁×#104	C₂²	semidirect
35. C₁₁×#405	C₂²	semidirect
36. C₂×C₁₁×#97	C₂²	semidirect
37. C₂×C₄×C₈×C₁₁	C₂²	semidirect
53. C₁₁×#135	C₂×C₄	semidirect
54. C₁₁×#135	C₂×C₄	semidirect
59. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
62. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
65. C₂×C₁₁×D₈	C₂×C₄	semidirect
68. C₁₁×#131	C₂³	semidirect
95. C₁₁×#108	C₂³	semidirect
96. C₁₁×#108	C₂³	semidirect
97. C₁₁×#104	C₂³	semidirect
98. C₁₁×#97	C₂³	semidirect
99. C₄×C₈×C₁₁	C₂³	semidirect
100. C₂×#2957	C₁₁	direct (N × H)
176. C₂×#568	C₂×C₁₁	semidirect
177. #2957	C₂×C₁₁	direct (N × H)
178. C₂×#444	C₂×C₁₁	semidirect
179. C₂×#443	C₂×C₁₁	semidirect
180. C₂²×#108	C₂×C₁₁	semidirect
181. C₂×#421	C₂×C₁₁	semidirect
182. C₂×#405	C₂×C₁₁	semidirect
233. C₂×#135	C₄×C₁₁	semidirect
234. C₂×#135	C₄×C₁₁	semidirect
235. C₂×#135	C₄×C₁₁	semidirect
239. C₂²×Q₁₆	C₄×C₁₁	semidirect
240. C₂²×SD₁₆	C₄×C₁₁	semidirect
241. C₂²×D₈	C₄×C₁₁	semidirect
243. #568	C₂²×C₁₁	semidirect
245. C₂×#131	C₂²×C₁₁	semidirect
251. #444	C₂²×C₁₁	semidirect
252. #443	C₂²×C₁₁	semidirect
253. C₂×#108	C₂²×C₁₁	semidirect
254. C₂×#108	C₂²×C₁₁	semidirect
255. C₂×#108	C₂²×C₁₁	semidirect
256. #421	C₂²×C₁₁	semidirect
257. C₂×#104	C₂²×C₁₁	semidirect
258. #405	C₂²×C₁₁	semidirect
259. C₂×#97	C₂²×C₁₁	semidirect
260. C₂×C₄×C₈	C₂²×C₁₁	semidirect
297. #135	C₂×C₄×C₁₁	semidirect
298. #135	C₂×C₄×C₁₁	semidirect
303. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
306. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
309. C₂×D₈	C₂×C₄×C₁₁	semidirect
312. #131	C₂³×C₁₁	semidirect
339. #108	C₂³×C₁₁	semidirect
340. #108	C₂³×C₁₁	semidirect
341. #104	C₂³×C₁₁	semidirect
342. #97	C₂³×C₁₁	semidirect
343. C₄×C₈	C₂³×C₁₁	semidirect
349. C₂×C₁₁	#2957	direct (N × H)
425. C₁₁	C₂×#2957	direct (N × H)
501. C₂	C₁₁×#2957	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×#135	2
C₂×C₁₁×#568	2
C₁₁×#2957	2
C₂×C₁₁×#444	2
C₂×C₁₁×#443	2
C₂²×C₁₁×#108	2
C₂×C₁₁×#421	2
C₂×C₁₁×#405	2
C₂×#2957	11

Subgroups — C2×C11×#2957 #14637374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2957 #14637374