Subgroups — C₂×C₁₁×#3173 #14637870

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#542	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3173	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#469	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#542	—	2	8	no	—
19	C₁₁×#542	C₂²	1	16	yes	complemented
20	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₁×#126	—	2	2	no	—
22	C₂×C₁₁×#124	—	2	2	no	—
23	C₂×C₁₁×#124	C₂²	1	2	yes	—
24	C₂×C₁₁×#123	—	2	2	no	—
25	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₁×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
30	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
31	C₁₁×#498	C₂²	1	8	yes	complemented
32	C₁₁×#495	C₂²	1	8	yes	complemented
33	C₁₁×#489	C₂²	1	16	yes	complemented
34	C₁₁×#470	C₂²	1	8	yes	complemented
35	C₁₁×#469	C₂²	1	8	yes	—
36	C₁₁×#465	C₂²	1	16	yes	complemented
37	C₁₁×#442	C₂²	1	8	yes	complemented
38	C₁₁×#441	C₂²	1	8	yes	complemented
39	C₄×C₁₁×SD₁₆	C₂²	1	16	yes	complemented
40	C₂×C₁₁×#106	C₂²	1	2	yes	—
41	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
42	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
43	C₂×C₁₁×#103	C₂²	1	2	yes	—
44	C₂×C₁₁×#103	C₂²	1	2	yes	—
45	C₂×C₁₁×#102	C₂²	1	2	yes	—
46	C₂×C₁₁×#102	C₂²	1	2	yes	—
47	C₁₁×#405	C₂²	1	8	yes	complemented
48	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
49	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₁	—	2	2	no	—
53	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₁	—	2	2	no	—
55	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁	—	2	2	no	—
57	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×Q₁₆	—	2	4	no	—
59	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
60	C₂×C₁₁×SD₁₆	—	2	8	no	—
61	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₁₁×D₈	—	2	4	no	—
63	C₂×C₁₁×D₈	C₂³	1	4	yes	—
64	C₂×C₁₁×M₁₆	—	2	4	no	—
65	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
66	C₂²×C₈×C₁₁	—	2	4	no	—
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊Q₈	—	2	4	no	—
73	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
74	C₁₁×#126	—	2	16	no	—
75	C₁₁×#124	—	2	16	no	—
76	C₁₁×#124	—	2	4	no	—
77	C₁₁×#124	C₂³	1	8	yes	—
78	C₁₁×#123	—	2	16	no	—
79	C₁₁×C₂²⋊Q₈	—	2	4	no	—
80	C₁₁×C₂²⋊Q₈	—	2	16	no	—
81	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₁₁×#121	—	2	4	no	—
83	C₁₁×#121	C₂³	1	8	yes	—
84	C₄×Q₈×C₁₁	—	2	4	no	—
85	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
86	C₄×D₄×C₁₁	—	2	4	no	—
87	C₄×D₄×C₁₁	C₂³	1	8	yes	—
88	C₁₁×#117	D₄	1	4	yes	—
89	C₁₁×#117	C₂³	1	4	yes	—
90	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
102	C₂×C₄²×C₁₁	—	2	2	no	—
103	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
105	C₁₁×#106	C₂³	1	8	yes	—
106	C₁₁×#106	C₂³	1	4	yes	—
107	C₁₁×#106	C₂³	1	4	yes	—
108	C₁₁×#103	C₂³	1	8	yes	—
109	C₁₁×#103	C₂³	1	8	yes	—
110	C₁₁×#102	C₂³	1	8	yes	—
111	C₁₁×#102	C₂³	1	8	yes	—
112	C₁₁×#97	C₂³	1	4	yes	—
113	C₁₁×#97	C₂³	1	4	yes	—
114	C₄×C₈×C₁₁	C₂³	1	4	yes	—
115	C₄×C₈×C₁₁	C₂³	1	4	yes	—
116	C₂×#3173	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₁	—	2	2	no	—
118	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₁	—	2	2	no	—
120	C₂×Q₈×C₁₁	—	2	8	no	—
121	C₂×Q₈×C₁₁	—	2	4	no	—
122	C₂×Q₈×C₁₁	—	2	4	no	—
123	C₂×Q₈×C₁₁	—	8	4	no	—
124	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
125	C₂×D₄×C₁₁	—	2	8	no	—
126	C₂×D₄×C₁₁	—	2	2	no	—
127	C₂×D₄×C₁₁	—	2	4	no	—
128	C₂×D₄×C₁₁	—	2	4	no	—
129	C₂×D₄×C₁₁	—	8	4	no	—
130	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₁	—	2	2	no	—
132	C₂²×C₄×C₁₁	—	2	2	no	—
133	C₂²×C₄×C₁₁	—	2	2	no	—
134	C₂²×C₄×C₁₁	—	2	2	no	—
135	C₂²×C₄×C₁₁	—	2	2	no	—
136	C₂²×C₄×C₁₁	—	2	8	no	—
137	C₂²×C₄×C₁₁	—	8	4	no	—
138	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
144	C₁₁×Q₁₆	—	2	8	no	—
145	C₁₁×SD₁₆	—	2	16	no	—
146	C₁₁×D₈	—	2	8	no	—
147	C₁₁×M₁₆	—	2	8	no	—
148	C₂×C₈×C₁₁	—	2	8	no	—
149	C₂×C₈×C₁₁	—	2	2	no	—
150	C₂×C₈×C₁₁	—	2	2	no	—
151	C₂×C₈×C₁₁	#41	1	4	yes	—
152	C₂×C₈×C₁₁	#41	1	4	yes	—
153	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
154	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
155	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
156	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
157	C₁₁×C₄⋊C₄	—	2	8	no	—
158	C₁₁×C₄⋊C₄	—	2	8	no	—
159	C₁₁×C₄⋊C₄	—	2	8	no	—
160	C₁₁×C₄⋊C₄	—	2	2	no	—
161	C₁₁×C₄⋊C₄	—	2	2	no	—
162	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
163	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
164	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
165	C₁₁×C₂²⋊C₄	—	2	8	no	—
166	C₁₁×C₂²⋊C₄	—	2	8	no	—
167	C₁₁×C₂²⋊C₄	—	2	8	no	—
168	C₁₁×C₂²⋊C₄	—	2	8	no	—
169	C₁₁×C₂²⋊C₄	—	2	8	no	—
170	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
171	C₄²×C₁₁	—	2	8	no	—
172	C₄²×C₁₁	C₂×D₄	1	2	yes	—
173	C₄²×C₁₁	C₂×D₄	1	2	yes	—
174	C₄²×C₁₁	C₂⁴	1	2	yes	—
175	C₄²×C₁₁	C₂⁴	1	2	yes	—
176	C₂×#542	C₂×C₁₁	1	2	yes	complemented
177	#3173	C₂×C₁₁	1	16	yes	direct product factor
178	C₂×#498	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂×#495	C₂×C₁₁	1	1	yes	characteristic, complemented
180	C₂×#489	C₂×C₁₁	1	2	yes	complemented
181	C₂×#470	C₂×C₁₁	1	1	yes	characteristic, complemented
182	C₂×#469	C₂×C₁₁	1	1	yes	characteristic
183	C₂×#465	C₂×C₁₁	1	2	yes	complemented
184	C₂×#442	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂×#441	C₂×C₁₁	1	1	yes	characteristic, complemented
186	C₂×C₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
187	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂³×C₁₁	—	2	2	no	—
189	C₂³×C₁₁	—	2	4	no	—
190	C₂³×C₁₁	—	2	4	no	—
191	C₂³×C₁₁	—	4	4	no	—
192	C₂³×C₁₁	—	4	4	no	—
193	C₂³×C₁₁	—	4	4	no	—
194	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
195	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₁	—	2	4	no	—
197	Q₈×C₁₁	—	2	4	no	—
198	Q₈×C₁₁	—	4	4	no	—
199	Q₈×C₁₁	—	8	8	no	—
200	D₄×C₁₁	—	2	4	no	—
201	D₄×C₁₁	—	2	4	no	—
202	D₄×C₁₁	—	4	4	no	—
203	D₄×C₁₁	—	8	8	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	4	no	—
206	C₂×C₄×C₁₁	—	2	4	no	—
207	C₂×C₄×C₁₁	—	2	4	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	2	4	no	—
211	C₂×C₄×C₁₁	—	2	4	no	—
212	C₂×C₄×C₁₁	—	2	4	no	—
213	C₂×C₄×C₁₁	—	4	4	no	—
214	C₂×C₄×C₁₁	—	4	4	no	—
215	C₂×C₄×C₁₁	—	4	4	no	—
216	C₂×C₄×C₁₁	—	8	8	no	—
217	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₁	—	2	2	no	—
225	C₈×C₁₁	—	2	2	no	—
226	C₈×C₁₁	C₂×#41	1	4	yes	—
227	C₈×C₁₁	C₂×#41	1	4	yes	—
228	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
229	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
230	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
233	#542	—	2	8	no	—
234	#542	C₂²×C₁₁	1	16	yes	complemented
235	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
236	C₂×#126	—	2	2	no	—
237	C₂×#124	—	2	2	no	—
238	C₂×#124	C₂²×C₁₁	1	2	yes	—
239	C₂×#123	—	2	2	no	—
240	C₂×C₂²⋊Q₈	—	2	2	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
242	C₂×#121	C₂²×C₁₁	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
245	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
246	#498	C₂²×C₁₁	1	8	yes	complemented
247	#495	C₂²×C₁₁	1	8	yes	complemented
248	#489	C₂²×C₁₁	1	16	yes	complemented
249	#470	C₂²×C₁₁	1	8	yes	complemented
250	#469	C₂²×C₁₁	1	8	yes	—
251	#465	C₂²×C₁₁	1	16	yes	complemented
252	#442	C₂²×C₁₁	1	8	yes	complemented
253	#441	C₂²×C₁₁	1	8	yes	complemented
254	C₄×SD₁₆	C₂²×C₁₁	1	16	yes	complemented
255	C₂×#106	C₂²×C₁₁	1	2	yes	—
256	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
257	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
258	C₂×#103	C₂²×C₁₁	1	2	yes	—
259	C₂×#103	C₂²×C₁₁	1	2	yes	—
260	C₂×#102	C₂²×C₁₁	1	2	yes	—
261	C₂×#102	C₂²×C₁₁	1	2	yes	—
262	#405	C₂²×C₁₁	1	8	yes	complemented
263	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
267	C₂²×C₁₁	—	2	2	no	—
268	C₂²×C₁₁	—	2	4	no	—
269	C₂²×C₁₁	—	4	4	no	—
270	C₂²×C₁₁	—	4	4	no	—
271	C₂²×C₁₁	—	4	4	no	—
272	C₂²×C₁₁	—	4	4	no	—
273	C₂²×C₁₁	—	8	8	no	—
274	C₂²×C₁₁	#532	1	2	yes	—
275	C₂²×C₁₁	#577	1	4	yes	—
276	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₁	—	2	2	no	—
278	C₄×C₁₁	—	2	4	no	—
279	C₄×C₁₁	—	2	4	no	—
280	C₄×C₁₁	—	4	4	no	—
281	C₄×C₁₁	—	4	4	no	—
282	C₄×C₁₁	—	4	4	no	—
283	C₄×C₁₁	#532	1	2	yes	—
284	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
285	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
290	C₂³×C₄	—	2	2	no	—
291	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
296	C₂×D₈	—	2	4	no	—
297	C₂×D₈	C₂³×C₁₁	1	4	yes	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
300	C₂²×C₈	—	2	4	no	—
301	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
303	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
308	#126	—	2	16	no	—
309	#124	—	2	16	no	—
310	#124	—	2	4	no	—
311	#124	C₂³×C₁₁	1	8	yes	—
312	#123	—	2	16	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	16	no	—
315	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
316	#121	—	2	4	no	—
317	#121	C₂³×C₁₁	1	8	yes	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	C₂³×C₁₁	1	8	yes	—
322	#117	D₄×C₁₁	1	4	yes	—
323	#117	C₂³×C₁₁	1	4	yes	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
339	#106	C₂³×C₁₁	1	8	yes	—
340	#106	C₂³×C₁₁	1	4	yes	—
341	#106	C₂³×C₁₁	1	4	yes	—
342	#103	C₂³×C₁₁	1	8	yes	—
343	#103	C₂³×C₁₁	1	8	yes	—
344	#102	C₂³×C₁₁	1	8	yes	—
345	#102	C₂³×C₁₁	1	8	yes	—
346	#97	C₂³×C₁₁	1	4	yes	—
347	#97	C₂³×C₁₁	1	4	yes	—
348	C₄×C₈	C₂³×C₁₁	1	4	yes	—
349	C₄×C₈	C₂³×C₁₁	1	4	yes	—
350	C₂×C₁₁	—	4	2	no	—
351	C₂×C₁₁	—	8	4	no	—
352	C₂×C₁₁	#3173	1	4	yes	direct product factor
353	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
354	C₂×C₁₁	C₂×#577	1	2	yes	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	8	4	no	—
362	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	8	4	no	—
368	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	8	4	no	—
376	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
382	Q₁₆	—	2	8	no	—
383	SD₁₆	—	2	16	no	—
384	D₈	—	2	8	no	—
385	M₁₆	—	2	8	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	8	no	—
389	C₂×C₈	C₁₁×#41	1	4	yes	—
390	C₂×C₈	C₁₁×#41	1	4	yes	—
391	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
392	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
393	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
394	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
401	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
402	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
409	C₄²	—	2	8	no	—
410	C₄²	C₂×D₄×C₁₁	1	2	yes	—
411	C₄²	C₂×D₄×C₁₁	1	2	yes	—
412	C₄²	C₂⁴×C₁₁	1	2	yes	—
413	C₄²	C₂⁴×C₁₁	1	2	yes	—
414	C₁₁	C₂×#3173	1	1	yes	characteristic, direct product factor, Sylow
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
422	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	4	no	—
426	Q₈	—	8	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
446	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
449	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
450	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	C₂×C₁₁×#41	1	4	yes	—
454	C₈	C₂×C₁₁×#41	1	4	yes	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₁₁×#532	1	2	yes	—
463	C₂²	C₁₁×#577	1	4	yes	—
464	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₁₁×#532	1	2	yes	—
472	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
473	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
474	C₂	—	4	2	no	—
475	C₂	—	8	4	no	—
476	C₂	C₁₁×#3173	1	4	yes	direct product factor
477	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
478	C₂	C₂×C₁₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#542	C₂	semidirect
2. C₁₁×#3173	C₂	direct (N × H)
3. C₂×C₁₁×#498	C₂	semidirect
4. C₂×C₁₁×#495	C₂	semidirect
5. C₂×C₁₁×#489	C₂	semidirect
6. C₂×C₁₁×#470	C₂	semidirect
8. C₂×C₁₁×#465	C₂	semidirect
9. C₂×C₁₁×#442	C₂	semidirect
10. C₂×C₁₁×#441	C₂	semidirect
11. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
12. C₂×C₁₁×#405	C₂	semidirect
19. C₁₁×#542	C₂²	semidirect
31. C₁₁×#498	C₂²	semidirect
32. C₁₁×#495	C₂²	semidirect
33. C₁₁×#489	C₂²	semidirect
34. C₁₁×#470	C₂²	semidirect
36. C₁₁×#465	C₂²	semidirect
37. C₁₁×#442	C₂²	semidirect
38. C₁₁×#441	C₂²	semidirect
39. C₄×C₁₁×SD₁₆	C₂²	semidirect
47. C₁₁×#405	C₂²	semidirect
116. C₂×#3173	C₁₁	direct (N × H)
176. C₂×#542	C₂×C₁₁	semidirect
177. #3173	C₂×C₁₁	direct (N × H)
178. C₂×#498	C₂×C₁₁	semidirect
179. C₂×#495	C₂×C₁₁	semidirect
180. C₂×#489	C₂×C₁₁	semidirect
181. C₂×#470	C₂×C₁₁	semidirect
183. C₂×#465	C₂×C₁₁	semidirect
184. C₂×#442	C₂×C₁₁	semidirect
185. C₂×#441	C₂×C₁₁	semidirect
186. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
187. C₂×#405	C₂×C₁₁	semidirect
234. #542	C₂²×C₁₁	semidirect
246. #498	C₂²×C₁₁	semidirect
247. #495	C₂²×C₁₁	semidirect
248. #489	C₂²×C₁₁	semidirect
249. #470	C₂²×C₁₁	semidirect
251. #465	C₂²×C₁₁	semidirect
252. #442	C₂²×C₁₁	semidirect
253. #441	C₂²×C₁₁	semidirect
254. C₄×SD₁₆	C₂²×C₁₁	semidirect
262. #405	C₂²×C₁₁	semidirect
352. C₂×C₁₁	#3173	direct (N × H)
414. C₁₁	C₂×#3173	direct (N × H)
476. C₂	C₁₁×#3173	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×#542	2
C₁₁×#3173	2
C₂×C₁₁×#498	2
C₂×C₁₁×#495	2
C₂×C₁₁×#489	2
C₂×C₁₁×#470	2
C₂×C₁₁×#469	2
C₂×C₁₁×#465	2
C₂×C₁₁×#442	2
C₂×C₁₁×#441	2
C₂×C₄×C₁₁×SD₁₆	2
C₂×C₁₁×#405	2
C₂×#3173	11

Subgroups — C2×C11×#3173 #14637870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3173 #14637870