Subgroups — C₁₁×#60167 #14637360

Order 2816.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 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	C₁₁×#3428	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2952	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2951	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2950	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2949	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2948	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2943	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₁×#135	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2896	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	2	yes	—
14	C₂×C₁₁×#135	C₄	1	16	yes	complemented
15	C₂×C₁₁×#135	C₂²	1	2	yes	—
16	C₂×C₁₁×#135	C₂²	1	2	yes	—
17	C₂×C₁₁×#135	C₂²	1	2	yes	—
18	C₂×C₁₁×#135	C₂²	1	2	yes	—
19	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
21	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#520	—	2	4	no	—
25	C₁₁×#520	C₂²	1	8	yes	complemented
26	C₁₁×#519	C₂²	1	4	yes	—
27	C₁₁×#518	—	2	4	no	—
28	C₁₁×#518	C₂²	1	4	yes	—
29	C₄×C₁₁×#41	—	2	4	no	—
30	C₄×C₁₁×#41	C₂²	1	8	yes	complemented
31	C₂×C₁₁×#117	—	2	4	no	—
32	C₂×C₁₁×#117	C₂²	1	2	yes	—
33	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
34	C₁₁×#442	C₂²	1	8	yes	complemented
35	C₁₁×#441	C₂²	1	8	yes	complemented
36	C₁₁×#440	C₂²	1	16	yes	complemented
37	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
38	C₄×C₁₁×SD₁₆	C₂²	1	16	yes	complemented
39	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
40	C₁₁×#427	C₂²	1	2	yes	—
41	C₁₁×#427	C₂²	1	2	yes	—
42	C₁₁×#427	C₂²	1	2	yes	complemented
43	C₁₁×#427	C₂²	1	2	yes	complemented
44	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
45	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
46	C₁₁×#419	C₂²	1	4	yes	—
47	C₁₁×#418	C₂²	1	4	yes	—
48	C₁₁×#417	C₂²	1	8	yes	complemented
49	C₁₁×#416	C₂²	1	8	yes	complemented
50	C₁₁×#405	C₂²	1	2	yes	—
51	C₁₁×#405	C₂²	1	2	yes	—
52	C₁₁×#405	C₂²	1	2	yes	complemented
53	C₁₁×#405	C₂²	1	2	yes	complemented
54	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
56	C₂×C₁₁×#41	—	2	2	no	—
57	C₂×C₁₁×#41	—	2	2	no	—
58	C₂×C₁₁×#41	—	2	8	no	—
59	C₂×C₁₁×#41	C₂×C₄	1	16	yes	complemented
60	C₂×C₁₁×#41	C₂³	1	4	yes	—
61	C₂×C₁₁×#41	C₂³	1	4	yes	—
62	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₁	—	2	2	no	—
64	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₁	—	2	2	no	—
66	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#135	C₂×C₄	1	16	yes	complemented
68	C₁₁×#135	C₂×C₄	1	16	yes	complemented
69	C₁₁×#135	C₂×C₄	1	16	yes	complemented
70	C₁₁×#135	C₂×C₄	1	16	yes	complemented
71	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	complemented
72	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
75	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
78	C₂×C₁₁×D₈	C₂³	1	2	yes	—
79	C₂×C₁₁×D₈	C₂³	1	2	yes	—
80	C₂×C₁₁×M₁₆	—	2	4	no	—
81	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
82	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	complemented
84	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
85	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₁₁	—	2	8	no	—
92	C₄×Q₈×C₁₁	C₂³	1	16	yes	—
93	C₄×D₄×C₁₁	—	2	16	no	—
94	C₄×D₄×C₁₁	—	2	8	no	—
95	C₄×D₄×C₁₁	—	2	16	no	—
96	C₄×D₄×C₁₁	C₂³	1	16	yes	—
97	C₁₁×#117	—	2	2	no	—
98	C₁₁×#117	—	2	2	no	—
99	C₁₁×#117	—	2	8	no	—
100	C₁₁×#117	—	2	8	no	—
101	C₁₁×#117	—	2	8	no	—
102	C₁₁×#117	D₄	1	2	yes	—
103	C₁₁×#117	D₄	1	2	yes	—
104	C₁₁×#117	C₂³	1	4	yes	—
105	C₁₁×#117	C₂³	1	4	yes	—
106	C₁₁×#117	C₂³	1	2	yes	—
107	C₁₁×#117	C₂³	1	2	yes	—
108	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
109	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
113	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₄²×C₁₁	—	2	2	no	—
115	C₂×C₄²×C₁₁	—	2	8	no	—
116	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
117	C₁₁×#107	C₂³	1	4	yes	—
118	C₁₁×#107	C₂³	1	4	yes	—
119	C₁₁×#106	C₂³	1	4	yes	—
120	C₁₁×#106	C₂³	1	4	yes	—
121	C₁₁×#103	C₂³	1	16	yes	—
122	C₁₁×#102	C₂³	1	16	yes	—
123	C₁₁×#97	C₂³	1	4	yes	—
124	C₁₁×#97	C₂³	1	4	yes	—
125	C₄×C₈×C₁₁	C₂³	1	4	yes	—
126	C₄×C₈×C₁₁	C₂³	1	4	yes	—
127	#60167	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₁	—	2	2	no	—
129	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₁₁×#41	—	2	16	no	—
131	C₁₁×#41	—	2	16	no	—
132	C₁₁×#41	—	2	8	no	—
133	C₁₁×#41	—	2	8	no	—
134	C₁₁×#41	C₂²×C₄	1	16	yes	—
135	C₁₁×#41	C₂²×C₄	1	16	yes	—
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	—	2	4	no	—
138	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
139	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₁	—	2	16	no	—
141	C₂×D₄×C₁₁	—	2	4	no	—
142	C₂×D₄×C₁₁	—	2	4	no	—
143	C₂×D₄×C₁₁	—	2	2	no	—
144	C₂×D₄×C₁₁	—	2	4	no	—
145	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
146	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₁	—	2	2	no	—
148	C₂²×C₄×C₁₁	—	2	16	no	—
149	C₂²×C₄×C₁₁	—	2	4	no	—
150	C₂²×C₄×C₁₁	—	2	4	no	—
151	C₂²×C₄×C₁₁	—	2	4	no	—
152	C₂²×C₄×C₁₁	—	2	16	no	—
153	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	#41	1	4	yes	—
159	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
162	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
163	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
164	C₁₁×SD₁₆	C₂²×C₄	1	16	yes	—
165	C₁₁×SD₁₆	C₂²×C₄	1	16	yes	—
166	C₁₁×D₈	C₂²×C₄	1	8	yes	—
167	C₁₁×D₈	C₂²×C₄	1	8	yes	—
168	C₁₁×M₁₆	—	2	4	no	—
169	C₁₁×M₁₆	—	2	4	no	—
170	C₂×C₈×C₁₁	—	2	4	no	—
171	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
172	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
173	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
174	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
175	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
176	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
177	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
178	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
180	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
182	C₁₁×C₄⋊C₄	—	2	4	no	—
183	C₁₁×C₄⋊C₄	—	2	16	no	—
184	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
186	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
187	C₁₁×C₂²⋊C₄	—	2	4	no	—
188	C₁₁×C₂²⋊C₄	—	2	4	no	—
189	C₁₁×C₂²⋊C₄	—	2	16	no	—
190	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
191	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
192	C₄²×C₁₁	—	2	16	no	—
193	C₄²×C₁₁	—	2	4	no	—
194	C₄²×C₁₁	—	2	4	no	—
195	C₄²×C₁₁	C₂×D₄	1	4	yes	—
196	C₄²×C₁₁	C₂⁴	1	4	yes	—
197	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
198	#3428	C₂×C₁₁	1	2	yes	complemented
199	#2952	C₂×C₁₁	1	4	yes	complemented
200	#2951	C₂×C₁₁	1	4	yes	complemented
201	#2950	C₂×C₁₁	1	2	yes	complemented
202	#2949	C₂×C₁₁	1	4	yes	complemented
203	#2948	C₂×C₁₁	1	2	yes	complemented
204	#2943	C₂×C₁₁	1	4	yes	complemented
205	C₄×#135	C₂×C₁₁	1	4	yes	complemented
206	C₂×#427	C₂×C₁₁	1	1	yes	characteristic, complemented
207	#2896	C₂×C₁₁	1	2	yes	complemented
208	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
209	C₂³×C₁₁	—	2	4	no	—
210	C₂³×C₁₁	—	2	8	no	—
211	C₂³×C₁₁	—	4	2	no	—
212	C₂³×C₁₁	—	8	4	no	—
213	C₂³×C₁₁	C₄×D₄	1	4	yes	—
214	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₁	—	2	8	no	—
218	Q₈×C₁₁	—	2	4	no	—
219	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
220	D₄×C₁₁	—	2	16	no	—
221	D₄×C₁₁	—	2	16	no	—
222	D₄×C₁₁	—	2	8	no	—
223	D₄×C₁₁	—	2	4	no	—
224	D₄×C₁₁	C₂³×C₄	1	8	yes	—
225	C₂×C₄×C₁₁	—	2	8	no	—
226	C₂×C₄×C₁₁	—	2	4	no	—
227	C₂×C₄×C₁₁	—	2	16	no	—
228	C₂×C₄×C₁₁	—	2	16	no	—
229	C₂×C₄×C₁₁	—	2	8	no	—
230	C₂×C₄×C₁₁	—	4	4	no	—
231	C₂×C₄×C₁₁	—	8	16	no	—
232	C₂×C₄×C₁₁	—	8	4	no	—
233	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
234	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
235	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
236	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
237	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
240	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
246	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
247	C₈×C₁₁	—	2	4	no	—
248	C₈×C₁₁	C₂³×C₄	1	2	yes	—
249	C₈×C₁₁	C₂³×C₄	1	2	yes	—
250	C₈×C₁₁	C₂³×C₄	1	2	yes	—
251	C₈×C₁₁	C₂³×C₄	1	2	yes	—
252	C₂²×#41	C₂²×C₁₁	1	2	yes	—
253	C₂×#135	C₄×C₁₁	1	16	yes	complemented
254	C₂×#135	C₂²×C₁₁	1	2	yes	—
255	C₂×#135	C₂²×C₁₁	1	2	yes	—
256	C₂×#135	C₂²×C₁₁	1	2	yes	—
257	C₂×#135	C₂²×C₁₁	1	2	yes	—
258	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
259	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
260	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
263	#520	—	2	4	no	—
264	#520	C₂²×C₁₁	1	8	yes	complemented
265	#519	C₂²×C₁₁	1	4	yes	—
266	#518	—	2	4	no	—
267	#518	C₂²×C₁₁	1	4	yes	—
268	C₄×#41	—	2	4	no	—
269	C₄×#41	C₂²×C₁₁	1	8	yes	complemented
270	C₂×#117	—	2	4	no	—
271	C₂×#117	C₂²×C₁₁	1	2	yes	—
272	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
273	#442	C₂²×C₁₁	1	8	yes	complemented
274	#441	C₂²×C₁₁	1	8	yes	complemented
275	#440	C₂²×C₁₁	1	16	yes	complemented
276	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
277	C₄×SD₁₆	C₂²×C₁₁	1	16	yes	complemented
278	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
279	#427	C₂²×C₁₁	1	2	yes	—
280	#427	C₂²×C₁₁	1	2	yes	—
281	#427	C₂²×C₁₁	1	2	yes	complemented
282	#427	C₂²×C₁₁	1	2	yes	complemented
283	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
284	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
285	#419	C₂²×C₁₁	1	4	yes	—
286	#418	C₂²×C₁₁	1	4	yes	—
287	#417	C₂²×C₁₁	1	8	yes	complemented
288	#416	C₂²×C₁₁	1	8	yes	complemented
289	#405	C₂²×C₁₁	1	2	yes	—
290	#405	C₂²×C₁₁	1	2	yes	—
291	#405	C₂²×C₁₁	1	2	yes	complemented
292	#405	C₂²×C₁₁	1	2	yes	complemented
293	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
294	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
295	C₂²×C₁₁	—	2	2	no	—
296	C₂²×C₁₁	—	2	2	no	—
297	C₂²×C₁₁	—	2	2	no	—
298	C₂²×C₁₁	—	2	8	no	—
299	C₂²×C₁₁	—	4	4	no	—
300	C₂²×C₁₁	—	4	8	no	—
301	C₂²×C₁₁	—	8	8	no	—
302	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
303	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
304	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
305	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₁₁	—	2	8	no	—
307	C₄×C₁₁	—	2	8	no	—
308	C₄×C₁₁	—	4	8	no	—
309	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
310	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
311	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
312	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
313	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	8	no	—
317	C₂×#41	C₂×C₄×C₁₁	1	16	yes	complemented
318	C₂×#41	C₂³×C₁₁	1	4	yes	—
319	C₂×#41	C₂³×C₁₁	1	4	yes	—
320	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
325	#135	C₂×C₄×C₁₁	1	16	yes	complemented
326	#135	C₂×C₄×C₁₁	1	16	yes	complemented
327	#135	C₂×C₄×C₁₁	1	16	yes	complemented
328	#135	C₂×C₄×C₁₁	1	16	yes	complemented
329	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
330	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
331	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
332	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
333	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
334	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
335	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
336	C₂×D₈	C₂³×C₁₁	1	2	yes	—
337	C₂×D₈	C₂³×C₁₁	1	2	yes	—
338	C₂×M₁₆	—	2	4	no	—
339	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
340	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
341	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	complemented
342	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
343	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
349	C₄×Q₈	—	2	8	no	—
350	C₄×Q₈	C₂³×C₁₁	1	16	yes	—
351	C₄×D₄	—	2	16	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	C₂³×C₁₁	1	16	yes	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	#117	—	2	8	no	—
358	#117	—	2	8	no	—
359	#117	—	2	8	no	—
360	#117	D₄×C₁₁	1	2	yes	—
361	#117	D₄×C₁₁	1	2	yes	—
362	#117	C₂³×C₁₁	1	4	yes	—
363	#117	C₂³×C₁₁	1	4	yes	—
364	#117	C₂³×C₁₁	1	2	yes	—
365	#117	C₂³×C₁₁	1	2	yes	—
366	C₂×C₄⋊C₄	—	2	8	no	—
367	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	8	no	—
371	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
372	C₂×C₄²	—	2	2	no	—
373	C₂×C₄²	—	2	8	no	—
374	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
375	#107	C₂³×C₁₁	1	4	yes	—
376	#107	C₂³×C₁₁	1	4	yes	—
377	#106	C₂³×C₁₁	1	4	yes	—
378	#106	C₂³×C₁₁	1	4	yes	—
379	#103	C₂³×C₁₁	1	16	yes	—
380	#102	C₂³×C₁₁	1	16	yes	—
381	#97	C₂³×C₁₁	1	4	yes	—
382	#97	C₂³×C₁₁	1	4	yes	—
383	C₄×C₈	C₂³×C₁₁	1	4	yes	—
384	C₄×C₈	C₂³×C₁₁	1	4	yes	—
385	C₂×C₁₁	—	2	2	no	—
386	C₂×C₁₁	—	2	2	no	—
387	C₂×C₁₁	—	2	2	no	—
388	C₂×C₁₁	—	4	8	no	—
389	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
390	C₂×C₁₁	#3584	1	2	yes	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
393	#41	—	2	16	no	—
394	#41	—	2	16	no	—
395	#41	—	2	8	no	—
396	#41	—	2	8	no	—
397	#41	C₂²×C₄×C₁₁	1	16	yes	—
398	#41	C₂²×C₄×C₁₁	1	16	yes	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
402	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
403	C₂×D₄	—	2	16	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
409	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	16	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	16	no	—
416	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
417	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
418	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
421	C₂²×C₄	C₁₁×#41	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
425	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
426	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
427	SD₁₆	C₂²×C₄×C₁₁	1	16	yes	—
428	SD₁₆	C₂²×C₄×C₁₁	1	16	yes	—
429	D₈	C₂²×C₄×C₁₁	1	8	yes	—
430	D₈	C₂²×C₄×C₁₁	1	8	yes	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	4	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
435	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
436	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
437	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
438	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
439	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
440	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
441	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
442	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
443	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
444	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	16	no	—
447	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
448	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
449	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	16	no	—
453	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
454	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	16	no	—
457	C₄²	—	2	4	no	—
458	C₄²	C₂×D₄×C₁₁	1	4	yes	—
459	C₄²	C₂⁴×C₁₁	1	4	yes	—
460	C₁₁	#60167	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	4	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	8	4	no	—
465	C₂³	C₄×D₄×C₁₁	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
467	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
468	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	4	no	—
471	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
472	D₄	—	2	16	no	—
473	D₄	—	2	16	no	—
474	D₄	—	2	8	no	—
475	D₄	—	2	4	no	—
476	D₄	C₂³×C₄×C₁₁	1	8	yes	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	16	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	8	16	no	—
484	C₂×C₄	—	8	4	no	—
485	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
486	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
487	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
488	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
492	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
496	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
497	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
498	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
499	C₈	—	2	4	no	—
500	C₈	C₂³×C₄×C₁₁	1	2	yes	—
501	C₈	C₂³×C₄×C₁₁	1	2	yes	—
502	C₈	C₂³×C₄×C₁₁	1	2	yes	—
503	C₈	C₂³×C₄×C₁₁	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
512	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
513	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
514	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	2	8	no	—
517	C₄	—	4	8	no	—
518	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
519	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
520	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
521	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
522	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	8	no	—
527	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
528	C₂	C₁₁×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂³×D₄
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3428	C₂	semidirect
3. C₁₁×#2952	C₂	semidirect
4. C₁₁×#2951	C₂	semidirect
5. C₁₁×#2950	C₂	semidirect
6. C₁₁×#2949	C₂	semidirect
7. C₁₁×#2948	C₂	semidirect
8. C₁₁×#2943	C₂	semidirect
9. C₄×C₁₁×#135	C₂	semidirect
10. C₂×C₁₁×#427	C₂	semidirect
11. C₁₁×#2896	C₂	semidirect
12. C₂×C₁₁×#405	C₂	semidirect
14. C₂×C₁₁×#135	C₄	semidirect
25. C₁₁×#520	C₂²	semidirect
30. C₄×C₁₁×#41	C₂²	semidirect
34. C₁₁×#442	C₂²	semidirect
35. C₁₁×#441	C₂²	semidirect
36. C₁₁×#440	C₂²	semidirect
37. C₄×C₁₁×Q₁₆	C₂²	semidirect
38. C₄×C₁₁×SD₁₆	C₂²	semidirect
39. C₄×C₁₁×D₈	C₂²	semidirect
42. C₁₁×#427	C₂²	semidirect
43. C₁₁×#427	C₂²	semidirect
44. C₂×C₁₁×#107	C₂²	semidirect
45. C₂×C₁₁×#106	C₂²	semidirect
48. C₁₁×#417	C₂²	semidirect
49. C₁₁×#416	C₂²	semidirect
52. C₁₁×#405	C₂²	semidirect
53. C₁₁×#405	C₂²	semidirect
54. C₂×C₁₁×#97	C₂²	semidirect
55. C₂×C₄×C₈×C₁₁	C₂²	semidirect
59. C₂×C₁₁×#41	C₂×C₄	semidirect
67. C₁₁×#135	C₂×C₄	semidirect
68. C₁₁×#135	C₂×C₄	semidirect
69. C₁₁×#135	C₂×C₄	semidirect
70. C₁₁×#135	C₂×C₄	semidirect
71. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
74. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
77. C₂×C₁₁×D₈	C₂×C₄	semidirect
83. C₂²×C₈×C₁₁	C₂×C₄	semidirect
127. #60167	C₁₁	direct (N × H)
198. #3428	C₂×C₁₁	semidirect
199. #2952	C₂×C₁₁	semidirect
200. #2951	C₂×C₁₁	semidirect
201. #2950	C₂×C₁₁	semidirect
202. #2949	C₂×C₁₁	semidirect
203. #2948	C₂×C₁₁	semidirect
204. #2943	C₂×C₁₁	semidirect
205. C₄×#135	C₂×C₁₁	semidirect
206. C₂×#427	C₂×C₁₁	semidirect
207. #2896	C₂×C₁₁	semidirect
208. C₂×#405	C₂×C₁₁	semidirect
253. C₂×#135	C₄×C₁₁	semidirect
264. #520	C₂²×C₁₁	semidirect
269. C₄×#41	C₂²×C₁₁	semidirect
273. #442	C₂²×C₁₁	semidirect
274. #441	C₂²×C₁₁	semidirect
275. #440	C₂²×C₁₁	semidirect
276. C₄×Q₁₆	C₂²×C₁₁	semidirect
277. C₄×SD₁₆	C₂²×C₁₁	semidirect
278. C₄×D₈	C₂²×C₁₁	semidirect
281. #427	C₂²×C₁₁	semidirect
282. #427	C₂²×C₁₁	semidirect
283. C₂×#107	C₂²×C₁₁	semidirect
284. C₂×#106	C₂²×C₁₁	semidirect
287. #417	C₂²×C₁₁	semidirect
288. #416	C₂²×C₁₁	semidirect
291. #405	C₂²×C₁₁	semidirect
292. #405	C₂²×C₁₁	semidirect
293. C₂×#97	C₂²×C₁₁	semidirect
294. C₂×C₄×C₈	C₂²×C₁₁	semidirect
317. C₂×#41	C₂×C₄×C₁₁	semidirect
325. #135	C₂×C₄×C₁₁	semidirect
326. #135	C₂×C₄×C₁₁	semidirect
327. #135	C₂×C₄×C₁₁	semidirect
328. #135	C₂×C₄×C₁₁	semidirect
329. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
332. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
335. C₂×D₈	C₂×C₄×C₁₁	semidirect
341. C₂²×C₈	C₂×C₄×C₁₁	semidirect
460. C₁₁	#60167	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
C₁₁×#3428	2
C₁₁×#2952	2
C₁₁×#2951	2
C₁₁×#2950	2
C₁₁×#2949	2
C₁₁×#2948	2
C₁₁×#2943	2
C₄×C₁₁×#135	2
C₂×C₁₁×#427	2
C₁₁×#2896	2
C₂×C₁₁×#405	2
#60167	11

Subgroups — C11×#60167 #14637360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60167 #14637360