Subgroups — C₂×C₁₁×#2946 #14637352

Order 2816.

2946 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2946	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#442	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₁×D₈	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	16	yes	complemented
16	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	8	yes	—
17	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
19	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#520	—	2	4	no	—
22	C₁₁×#520	C₂²	1	8	yes	complemented
23	C₁₁×#518	—	2	4	no	—
24	C₁₁×#518	C₂²	1	8	yes	complemented
25	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₁	—	2	1	no	—
27	C₂×C₄×D₄×C₁₁	—	2	1	no	—
28	C₂×C₄×D₄×C₁₁	—	2	2	no	—
29	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
32	C₂×C₁₁×#117	—	2	1	no	—
33	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
36	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₁×C₂²⋊C₄	—	2	2	no	—
38	C₁₁×#442	C₂²	1	16	yes	complemented
39	C₁₁×#440	C₂²	1	16	yes	complemented
40	C₄×C₁₁×SD₁₆	C₂²	1	16	yes	complemented
41	C₄×C₁₁×D₈	C₂²	1	16	yes	complemented
42	C₁₁×#428	C₂²	1	8	yes	complemented
43	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
44	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
45	C₁₁×#416	C₂²	1	8	yes	complemented
46	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₁×#102	C₂²	1	2	yes	—
49	C₂×C₁₁×#102	C₂²	1	2	yes	—
50	C₂×C₁₁×#102	C₂²	1	8	yes	complemented
51	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic, complemented
53	C₁₁×#405	C₂²	1	8	yes	complemented
54	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
56	C₂⁵×C₁₁	—	2	1	no	—
57	C₂×C₁₁×#41	—	2	2	no	—
58	C₂×C₁₁×#41	—	2	4	no	—
59	C₂×C₁₁×#41	C₂×C₄	1	8	yes	complemented
60	C₂×C₁₁×#41	C₂³	1	4	yes	—
61	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₁	—	2	1	no	—
63	C₂²×D₄×C₁₁	—	2	1	no	—
64	C₂²×D₄×C₁₁	—	2	2	no	—
65	C₂²×D₄×C₁₁	—	2	4	no	—
66	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	complemented
67	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₁	—	2	1	no	—
71	C₂³×C₄×C₁₁	—	2	1	no	—
72	C₂³×C₄×C₁₁	—	2	2	no	—
73	C₂³×C₄×C₁₁	—	2	2	no	—
74	C₂³×C₄×C₁₁	—	2	2	no	—
75	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	64	yes	complemented
77	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
78	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
79	C₂×C₁₁×D₈	C₂×C₄	1	16	yes	complemented
80	C₂×C₁₁×D₈	C₂³	1	8	yes	—
81	C₂×C₁₁×M₁₆	C₂×C₄	1	8	yes	complemented
82	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
83	C₂²×C₈×C₁₁	—	2	4	no	—
84	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
87	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
88	C₄×Q₈×C₁₁	—	2	4	no	—
89	C₄×Q₈×C₁₁	C₂³	1	8	yes	complemented
90	C₄×D₄×C₁₁	—	2	8	no	—
91	C₄×D₄×C₁₁	—	2	8	no	—
92	C₄×D₄×C₁₁	—	2	16	no	—
93	C₄×D₄×C₁₁	—	2	4	no	—
94	C₄×D₄×C₁₁	—	2	4	no	—
95	C₄×D₄×C₁₁	—	2	4	no	—
96	C₄×D₄×C₁₁	C₂³	1	8	yes	—
97	C₄×D₄×C₁₁	C₂³	1	8	yes	—
98	C₄×D₄×C₁₁	C₂³	1	8	yes	complemented
99	C₁₁×#117	—	2	2	no	—
100	C₁₁×#117	—	2	8	no	—
101	C₁₁×#117	D₄	1	4	yes	—
102	C₁₁×#117	C₂³	1	4	yes	—
103	C₁₁×#117	C₂³	1	4	yes	—
104	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
108	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₁×C₂²⋊C₄	—	2	16	no	—
119	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
120	C₂×C₄²×C₁₁	—	2	2	no	—
121	C₂×C₄²×C₁₁	—	2	1	no	—
122	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
123	C₁₁×#107	C₂³	1	8	yes	complemented
124	C₁₁×#106	C₂³	1	8	yes	complemented
125	C₁₁×#103	C₂³	1	4	yes	complemented
126	C₁₁×#103	C₂³	1	4	yes	complemented
127	C₁₁×#102	C₂³	1	8	yes	—
128	C₁₁×#102	C₂³	1	8	yes	—
129	C₁₁×#102	C₂³	1	4	yes	complemented
130	C₁₁×#102	C₂³	1	4	yes	complemented
131	C₁₁×#97	C₂³	1	8	yes	complemented
132	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
133	C₂×#2946	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₁	—	2	1	no	—
135	C₂⁴×C₁₁	—	2	2	no	—
136	C₂⁴×C₁₁	—	2	8	no	—
137	C₂⁴×C₁₁	—	2	4	no	—
138	C₂⁴×C₁₁	—	8	2	no	—
139	C₂⁴×C₁₁	—	8	2	no	—
140	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
141	C₁₁×#41	—	2	16	no	—
142	C₁₁×#41	—	2	8	no	—
143	C₁₁×#41	C₂²×C₄	1	16	yes	complemented
144	C₂×Q₈×C₁₁	—	2	1	no	—
145	C₂×Q₈×C₁₁	—	2	2	no	—
146	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
147	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₁	—	2	8	no	—
149	C₂×D₄×C₁₁	—	2	4	no	—
150	C₂×D₄×C₁₁	—	2	8	no	—
151	C₂×D₄×C₁₁	—	2	16	no	—
152	C₂×D₄×C₁₁	—	2	4	no	—
153	C₂×D₄×C₁₁	—	2	2	no	—
154	C₂×D₄×C₁₁	—	2	1	no	—
155	C₂×D₄×C₁₁	—	2	4	no	—
156	C₂×D₄×C₁₁	—	2	8	no	—
157	C₂×D₄×C₁₁	—	2	2	no	—
158	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
159	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
160	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	complemented
161	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
162	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₁	—	2	1	no	—
164	C₂²×C₄×C₁₁	—	2	8	no	—
165	C₂²×C₄×C₁₁	—	2	4	no	—
166	C₂²×C₄×C₁₁	—	2	1	no	—
167	C₂²×C₄×C₁₁	—	2	1	no	—
168	C₂²×C₄×C₁₁	—	2	2	no	—
169	C₂²×C₄×C₁₁	—	2	4	no	—
170	C₂²×C₄×C₁₁	—	2	8	no	—
171	C₂²×C₄×C₁₁	—	2	8	no	—
172	C₂²×C₄×C₁₁	—	2	8	no	—
173	C₂²×C₄×C₁₁	—	8	4	no	—
174	C₂²×C₄×C₁₁	—	8	4	no	—
175	C₂²×C₄×C₁₁	—	8	4	no	—
176	C₂²×C₄×C₁₁	—	8	2	no	—
177	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₁	#41	1	4	yes	—
183	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
185	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
186	C₁₁×D₈	C₂²×C₄	1	32	yes	complemented
187	C₁₁×M₁₆	C₂²×C₄	1	16	yes	complemented
188	C₂×C₈×C₁₁	—	2	2	no	—
189	C₂×C₈×C₁₁	—	2	2	no	—
190	C₂×C₈×C₁₁	—	2	8	no	—
191	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
192	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
193	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
194	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
195	C₁₁×C₄⋊C₄	—	2	4	no	—
196	C₁₁×C₄⋊C₄	—	2	8	no	—
197	C₁₁×C₄⋊C₄	—	2	2	no	—
198	C₁₁×C₄⋊C₄	—	2	1	no	—
199	C₁₁×C₄⋊C₄	—	2	1	no	—
200	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
201	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
204	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
205	C₁₁×C₂²⋊C₄	—	2	4	no	—
206	C₁₁×C₂²⋊C₄	—	2	8	no	—
207	C₁₁×C₂²⋊C₄	—	2	8	no	—
208	C₁₁×C₂²⋊C₄	—	2	8	no	—
209	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
210	C₄²×C₁₁	—	2	8	no	—
211	C₄²×C₁₁	—	2	4	no	—
212	C₄²×C₁₁	C₂×D₄	1	4	yes	—
213	C₄²×C₁₁	C₂⁴	1	4	yes	—
214	C₂²×AGL(1,ℤ/8)	C₂×C₁₁	1	1	yes	characteristic
215	C₂×#520	C₂×C₁₁	1	1	yes	characteristic, complemented
216	C₂×#518	C₂×C₁₁	1	1	yes	characteristic, complemented
217	#2946	C₂×C₁₁	1	16	yes	direct product factor
218	C₂×#442	C₂×C₁₁	1	2	yes	complemented
219	C₂×#440	C₂×C₁₁	1	2	yes	complemented
220	C₂×C₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
221	C₂×C₄×D₈	C₂×C₁₁	1	2	yes	complemented
222	C₂×#428	C₂×C₁₁	1	1	yes	characteristic, complemented
223	C₂×#416	C₂×C₁₁	1	1	yes	characteristic, complemented
224	C₂²×#102	C₂×C₁₁	1	1	yes	characteristic, complemented
225	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
226	C₂³×C₁₁	—	2	2	no	—
227	C₂³×C₁₁	—	2	2	no	—
228	C₂³×C₁₁	—	2	4	no	—
229	C₂³×C₁₁	—	2	8	no	—
230	C₂³×C₁₁	—	2	2	no	—
231	C₂³×C₁₁	—	2	4	no	—
232	C₂³×C₁₁	—	2	16	no	—
233	C₂³×C₁₁	—	4	2	no	—
234	C₂³×C₁₁	—	4	4	no	—
235	C₂³×C₁₁	—	4	4	no	—
236	C₂³×C₁₁	—	4	2	no	—
237	C₂³×C₁₁	—	8	16	no	—
238	C₂³×C₁₁	—	8	4	no	—
239	C₂³×C₁₁	—	8	4	no	—
240	C₂³×C₁₁	C₄×D₄	1	4	yes	—
241	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
242	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₁	—	2	4	no	—
244	Q₈×C₁₁	—	2	2	no	—
245	Q₈×C₁₁	C₂³×C₄	1	4	yes	—
246	D₄×C₁₁	—	2	16	no	—
247	D₄×C₁₁	—	2	8	no	—
248	D₄×C₁₁	—	2	16	no	—
249	D₄×C₁₁	—	2	4	no	—
250	D₄×C₁₁	—	2	4	no	—
251	D₄×C₁₁	—	2	2	no	—
252	D₄×C₁₁	C₂³×C₄	1	4	yes	—
253	D₄×C₁₁	C₂³×C₄	1	8	yes	—
254	C₂×C₄×C₁₁	—	2	4	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	16	no	—
259	C₂×C₄×C₁₁	—	2	2	no	—
260	C₂×C₄×C₁₁	—	2	2	no	—
261	C₂×C₄×C₁₁	—	2	4	no	—
262	C₂×C₄×C₁₁	—	4	2	no	—
263	C₂×C₄×C₁₁	—	4	4	no	—
264	C₂×C₄×C₁₁	—	4	2	no	—
265	C₂×C₄×C₁₁	—	8	8	no	—
266	C₂×C₄×C₁₁	—	8	8	no	—
267	C₂×C₄×C₁₁	—	8	8	no	—
268	C₂×C₄×C₁₁	—	8	4	no	—
269	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
270	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
271	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
278	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
279	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
280	C₈×C₁₁	—	2	2	no	—
281	C₈×C₁₁	—	2	2	no	—
282	C₈×C₁₁	C₂³×C₄	1	8	yes	—
283	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
285	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	16	yes	complemented
286	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	8	yes	—
287	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
288	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
289	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
290	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
291	#520	—	2	4	no	—
292	#520	C₂²×C₁₁	1	8	yes	complemented
293	#518	—	2	4	no	—
294	#518	C₂²×C₁₁	1	8	yes	complemented
295	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	—	2	1	no	—
298	C₂×C₄×D₄	—	2	2	no	—
299	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
300	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
301	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	complemented
302	C₂×#117	—	2	1	no	—
303	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
304	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	—	2	1	no	—
306	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	—	2	2	no	—
308	#442	C₂²×C₁₁	1	16	yes	complemented
309	#440	C₂²×C₁₁	1	16	yes	complemented
310	C₄×SD₁₆	C₂²×C₁₁	1	16	yes	complemented
311	C₄×D₈	C₂²×C₁₁	1	16	yes	complemented
312	#428	C₂²×C₁₁	1	8	yes	complemented
313	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
314	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
315	#416	C₂²×C₁₁	1	8	yes	complemented
316	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic, complemented
317	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic, complemented
318	C₂×#102	C₂²×C₁₁	1	2	yes	—
319	C₂×#102	C₂²×C₁₁	1	2	yes	—
320	C₂×#102	C₂²×C₁₁	1	8	yes	complemented
321	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic, complemented
322	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic, complemented
323	#405	C₂²×C₁₁	1	8	yes	complemented
324	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
325	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
326	C₂²×C₁₁	—	2	8	no	—
327	C₂²×C₁₁	—	2	2	no	—
328	C₂²×C₁₁	—	2	2	no	—
329	C₂²×C₁₁	—	2	4	no	—
330	C₂²×C₁₁	—	2	8	no	—
331	C₂²×C₁₁	—	4	8	no	—
332	C₂²×C₁₁	—	4	16	no	—
333	C₂²×C₁₁	—	4	2	no	—
334	C₂²×C₁₁	—	4	4	no	—
335	C₂²×C₁₁	—	4	4	no	—
336	C₂²×C₁₁	—	4	2	no	—
337	C₂²×C₁₁	—	8	16	no	—
338	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
339	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
340	C₂²×C₁₁	#576	1	2	yes	—
341	C₂²×C₁₁	#577	1	2	yes	—
342	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₁₁	—	2	4	no	—
344	C₄×C₁₁	—	2	4	no	—
345	C₄×C₁₁	—	2	4	no	—
346	C₄×C₁₁	—	4	2	no	—
347	C₄×C₁₁	—	4	4	no	—
348	C₄×C₁₁	—	4	2	no	—
349	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
350	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
351	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
352	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
353	C₂⁵	—	2	1	no	—
354	C₂×#41	—	2	2	no	—
355	C₂×#41	—	2	4	no	—
356	C₂×#41	C₂×C₄×C₁₁	1	8	yes	complemented
357	C₂×#41	C₂³×C₁₁	1	4	yes	—
358	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	2	no	—
362	C₂²×D₄	—	2	4	no	—
363	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	complemented
364	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	—	2	2	no	—
370	C₂³×C₄	—	2	2	no	—
371	C₂³×C₄	—	2	2	no	—
372	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
373	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	64	yes	complemented
374	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
375	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
376	C₂×D₈	C₂×C₄×C₁₁	1	16	yes	complemented
377	C₂×D₈	C₂³×C₁₁	1	8	yes	—
378	C₂×M₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
379	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
380	C₂²×C₈	—	2	4	no	—
381	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
384	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×Q₈	C₂³×C₁₁	1	8	yes	complemented
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	16	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	C₂³×C₁₁	1	8	yes	—
394	C₄×D₄	C₂³×C₁₁	1	8	yes	—
395	C₄×D₄	C₂³×C₁₁	1	8	yes	complemented
396	#117	—	2	2	no	—
397	#117	—	2	8	no	—
398	#117	D₄×C₁₁	1	4	yes	—
399	#117	C₂³×C₁₁	1	4	yes	—
400	#117	C₂³×C₁₁	1	4	yes	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	8	no	—
405	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	—	2	16	no	—
416	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
420	#107	C₂³×C₁₁	1	8	yes	complemented
421	#106	C₂³×C₁₁	1	8	yes	complemented
422	#103	C₂³×C₁₁	1	4	yes	complemented
423	#103	C₂³×C₁₁	1	4	yes	complemented
424	#102	C₂³×C₁₁	1	8	yes	—
425	#102	C₂³×C₁₁	1	8	yes	—
426	#102	C₂³×C₁₁	1	4	yes	complemented
427	#102	C₂³×C₁₁	1	4	yes	complemented
428	#97	C₂³×C₁₁	1	8	yes	complemented
429	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
430	C₂×C₁₁	—	2	4	no	—
431	C₂×C₁₁	—	4	4	no	—
432	C₂×C₁₁	—	4	8	no	—
433	C₂×C₁₁	#2946	1	4	yes	direct product factor
434	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
435	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
436	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	8	no	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	8	2	no	—
442	C₂⁴	—	8	2	no	—
443	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
444	#41	—	2	16	no	—
445	#41	—	2	8	no	—
446	#41	C₂²×C₄×C₁₁	1	16	yes	complemented
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
450	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	16	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
462	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
463	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	complemented
464	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
465	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	8	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	8	4	no	—
477	C₂²×C₄	—	8	4	no	—
478	C₂²×C₄	—	8	4	no	—
479	C₂²×C₄	—	8	2	no	—
480	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
481	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
482	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
483	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
485	C₂²×C₄	C₁₁×#41	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
488	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
489	D₈	C₂²×C₄×C₁₁	1	32	yes	complemented
490	M₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	8	no	—
494	C₂×C₈	C₂²×C₄×C₁₁	1	8	yes	—
495	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
496	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
497	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
504	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
507	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
513	C₄²	—	2	8	no	—
514	C₄²	—	2	4	no	—
515	C₄²	C₂×D₄×C₁₁	1	4	yes	—
516	C₄²	C₂⁴×C₁₁	1	4	yes	—
517	C₁₁	C₂×#2946	1	1	yes	characteristic, direct product factor, Sylow
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	16	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	8	16	no	—
530	C₂³	—	8	4	no	—
531	C₂³	—	8	4	no	—
532	C₂³	C₄×D₄×C₁₁	1	4	yes	—
533	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
534	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
535	Q₈	—	2	4	no	—
536	Q₈	—	2	2	no	—
537	Q₈	C₂³×C₄×C₁₁	1	4	yes	—
538	D₄	—	2	16	no	—
539	D₄	—	2	8	no	—
540	D₄	—	2	16	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	2	no	—
544	D₄	C₂³×C₄×C₁₁	1	4	yes	—
545	D₄	C₂³×C₄×C₁₁	1	8	yes	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	16	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	8	no	—
558	C₂×C₄	—	8	8	no	—
559	C₂×C₄	—	8	8	no	—
560	C₂×C₄	—	8	4	no	—
561	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
562	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
563	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
564	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
565	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
566	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
570	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
571	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	2	2	no	—
574	C₈	C₂³×C₄×C₁₁	1	8	yes	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	8	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	16	no	—
587	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
588	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
589	C₂²	C₁₁×#576	1	2	yes	—
590	C₂²	C₁₁×#577	1	2	yes	—
591	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	2	no	—
598	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
599	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
600	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
601	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
602	C₂	—	2	4	no	—
603	C₂	—	4	8	no	—
604	C₂	—	4	4	no	—
605	C₂	C₁₁×#2946	1	4	yes	direct product factor
606	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
607	C₂	C₂×C₁₁×#576	1	1	yes	characteristic
608	C₂	C₂×C₁₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×AGL(1,ℤ/8)	C₂
LCS	G ▷ 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
2. C₂×C₁₁×#520	C₂	semidirect
3. C₂×C₁₁×#518	C₂	semidirect
4. C₁₁×#2946	C₂	direct (N × H)
5. C₂×C₁₁×#442	C₂	semidirect
6. C₂×C₁₁×#440	C₂	semidirect
7. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
8. C₂×C₄×C₁₁×D₈	C₂	semidirect
9. C₂×C₁₁×#428	C₂	semidirect
10. C₂×C₁₁×#416	C₂	semidirect
11. C₂²×C₁₁×#102	C₂	semidirect
12. C₂×C₁₁×#405	C₂	semidirect
15. C₂×C₁₁×AGL(1,ℤ/8)	C₄	semidirect
22. C₁₁×#520	C₂²	semidirect
24. C₁₁×#518	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
31. C₂×C₄×D₄×C₁₁	C₂²	semidirect
38. C₁₁×#442	C₂²	semidirect
39. C₁₁×#440	C₂²	semidirect
40. C₄×C₁₁×SD₁₆	C₂²	semidirect
41. C₄×C₁₁×D₈	C₂²	semidirect
42. C₁₁×#428	C₂²	semidirect
43. C₂×C₁₁×#107	C₂²	semidirect
44. C₂×C₁₁×#106	C₂²	semidirect
45. C₁₁×#416	C₂²	semidirect
46. C₂×C₁₁×#103	C₂²	semidirect
47. C₂×C₁₁×#103	C₂²	semidirect
50. C₂×C₁₁×#102	C₂²	semidirect
51. C₂×C₁₁×#102	C₂²	semidirect
52. C₂×C₁₁×#102	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
66. C₂²×D₄×C₁₁	C₂×C₄	semidirect
76. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
77. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
79. C₂×C₁₁×D₈	C₂×C₄	semidirect
81. C₂×C₁₁×M₁₆	C₂×C₄	semidirect
89. C₄×Q₈×C₁₁	C₂³	semidirect
98. C₄×D₄×C₁₁	C₂³	semidirect
123. C₁₁×#107	C₂³	semidirect
124. C₁₁×#106	C₂³	semidirect
125. C₁₁×#103	C₂³	semidirect
126. C₁₁×#103	C₂³	semidirect
129. C₁₁×#102	C₂³	semidirect
130. C₁₁×#102	C₂³	semidirect
131. C₁₁×#97	C₂³	semidirect
132. C₄×C₈×C₁₁	C₂³	semidirect
133. C₂×#2946	C₁₁	direct (N × H)
143. C₁₁×#41	C₂²×C₄	semidirect
160. C₂×D₄×C₁₁	C₂²×C₄	semidirect
185. C₁₁×SD₁₆	C₂²×C₄	semidirect
186. C₁₁×D₈	C₂²×C₄	semidirect
187. C₁₁×M₁₆	C₂²×C₄	semidirect
215. C₂×#520	C₂×C₁₁	semidirect
216. C₂×#518	C₂×C₁₁	semidirect
217. #2946	C₂×C₁₁	direct (N × H)
218. C₂×#442	C₂×C₁₁	semidirect
219. C₂×#440	C₂×C₁₁	semidirect
220. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
221. C₂×C₄×D₈	C₂×C₁₁	semidirect
222. C₂×#428	C₂×C₁₁	semidirect
223. C₂×#416	C₂×C₁₁	semidirect
224. C₂²×#102	C₂×C₁₁	semidirect
225. C₂×#405	C₂×C₁₁	semidirect
285. C₂×AGL(1,ℤ/8)	C₄×C₁₁	semidirect
292. #520	C₂²×C₁₁	semidirect
294. #518	C₂²×C₁₁	semidirect
295. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
301. C₂×C₄×D₄	C₂²×C₁₁	semidirect
308. #442	C₂²×C₁₁	semidirect
309. #440	C₂²×C₁₁	semidirect
310. C₄×SD₁₆	C₂²×C₁₁	semidirect
311. C₄×D₈	C₂²×C₁₁	semidirect
312. #428	C₂²×C₁₁	semidirect
313. C₂×#107	C₂²×C₁₁	semidirect
314. C₂×#106	C₂²×C₁₁	semidirect
315. #416	C₂²×C₁₁	semidirect
316. C₂×#103	C₂²×C₁₁	semidirect
317. C₂×#103	C₂²×C₁₁	semidirect
320. C₂×#102	C₂²×C₁₁	semidirect
321. C₂×#102	C₂²×C₁₁	semidirect
322. C₂×#102	C₂²×C₁₁	semidirect
323. #405	C₂²×C₁₁	semidirect
324. C₂×#97	C₂²×C₁₁	semidirect
325. C₂×C₄×C₈	C₂²×C₁₁	semidirect
356. C₂×#41	C₂×C₄×C₁₁	semidirect
363. C₂²×D₄	C₂×C₄×C₁₁	semidirect
373. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
374. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
376. C₂×D₈	C₂×C₄×C₁₁	semidirect
378. C₂×M₁₆	C₂×C₄×C₁₁	semidirect
386. C₄×Q₈	C₂³×C₁₁	semidirect
395. C₄×D₄	C₂³×C₁₁	semidirect
420. #107	C₂³×C₁₁	semidirect
421. #106	C₂³×C₁₁	semidirect
422. #103	C₂³×C₁₁	semidirect
423. #103	C₂³×C₁₁	semidirect
426. #102	C₂³×C₁₁	semidirect
427. #102	C₂³×C₁₁	semidirect
428. #97	C₂³×C₁₁	semidirect
429. C₄×C₈	C₂³×C₁₁	semidirect
433. C₂×C₁₁	#2946	direct (N × H)
446. #41	C₂²×C₄×C₁₁	semidirect
463. C₂×D₄	C₂²×C₄×C₁₁	semidirect
488. SD₁₆	C₂²×C₄×C₁₁	semidirect
489. D₈	C₂²×C₄×C₁₁	semidirect
490. M₁₆	C₂²×C₄×C₁₁	semidirect
517. C₁₁	C₂×#2946	direct (N × H)
605. C₂	C₁₁×#2946	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×AGL(1,ℤ/8)	2
C₂×C₁₁×#520	2
C₂×C₁₁×#518	2
C₁₁×#2946	2
C₂×C₁₁×#442	2
C₂×C₁₁×#440	2
C₂×C₄×C₁₁×SD₁₆	2
C₂×C₄×C₁₁×D₈	2
C₂×C₁₁×#428	2
C₂×C₁₁×#416	2
C₂²×C₁₁×#102	2
C₂×C₁₁×#405	2
C₂×#2946	11

Subgroups — C2×C11×#2946 #14637352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2946 #14637352