Subgroups — C₂×D₄×C₁₁×M₁₆ #14637331

Order 2816.

3218 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	C₂³×C₁₁×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₁×M₁₆	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₈×D₄×C₁₁	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#407	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₁	C₄	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
12	C₂²×C₁₁×M₁₆	—	2	16	no	—
13	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×M₁₆	C₂²	1	4	yes	complemented
17	C₂²×C₁₁×M₁₆	C₂²	1	16	yes	complemented
18	C₂³×C₈×C₁₁	C₂²	1	4	yes	complemented
19	C₂×C₄×D₄×C₁₁	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁	C₄	1	8	yes	—
22	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	—
27	C₂²×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₂²×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
29	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#436	C₂²	1	16	yes	complemented
31	C₁₁×#435	C₂²	1	32	yes	complemented
32	C₈×D₄×C₁₁	C₂²	1	16	yes	complemented
33	C₁₁×#423	C₂²	1	8	yes	complemented
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	complemented
35	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	complemented
36	C₁₁×#407	C₂²	1	16	yes	complemented
37	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
38	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
39	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
40	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₁	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₁	—	2	8	no	—
44	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	—
46	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	—	2	8	no	—
49	C₂³×C₄×C₁₁	—	2	8	no	—
50	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₁	C₂×C₄	1	8	yes	—
54	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
57	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	—	2	8	no	—
61	C₂×C₁₁×M₁₆	—	2	4	no	—
62	C₂×C₁₁×M₁₆	—	2	64	no	—
63	C₂×C₁₁×M₁₆	—	2	16	no	—
64	C₂×C₁₁×M₁₆	D₄	1	8	yes	direct product factor
65	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	16	yes	complemented
69	C₂²×C₈×C₁₁	—	2	16	no	—
70	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₁	C₂³	1	16	yes	complemented
74	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
75	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
76	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
77	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
78	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
79	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
80	C₄×D₄×C₁₁	C₂³	1	4	yes	—
81	C₄×D₄×C₁₁	C₂³	1	8	yes	—
82	C₄×D₄×C₁₁	C₂³	1	4	yes	—
83	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
85	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	16	yes	—
92	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
95	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
98	C₁₁×C₄⋊C₈	C₂³	1	8	yes	complemented
99	C₁₁×C₄⋊C₈	C₂³	1	8	yes	complemented
100	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
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×D₄×M₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₁	—	2	8	no	—
106	C₂⁴×C₁₁	—	2	8	no	—
107	C₂⁴×C₁₁	—	4	4	no	—
108	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
109	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
110	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₁	—	2	8	no	—
113	C₂×D₄×C₁₁	—	2	32	no	—
114	C₂×D₄×C₁₁	—	2	4	no	—
115	C₂×D₄×C₁₁	M₁₆	1	8	yes	direct product factor
116	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
118	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₁	—	2	8	no	—
120	C₂²×C₄×C₁₁	—	2	8	no	—
121	C₂²×C₄×C₁₁	—	2	32	no	—
122	C₂²×C₄×C₁₁	—	2	8	no	—
123	C₂²×C₄×C₁₁	—	2	4	no	—
124	C₂²×C₄×C₁₁	—	2	4	no	—
125	C₂²×C₄×C₁₁	—	2	16	no	—
126	C₂²×C₄×C₁₁	—	2	4	no	—
127	C₂²×C₄×C₁₁	—	2	4	no	—
128	C₂²×C₄×C₁₁	—	2	4	no	—
129	C₂²×C₄×C₁₁	—	2	16	no	—
130	C₂²×C₄×C₁₁	—	4	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	1	yes	characteristic
134	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
140	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₁	#41	1	4	yes	—
148	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
152	C₁₁×M₁₆	—	2	32	no	—
153	C₁₁×M₁₆	—	2	16	no	—
154	C₁₁×M₁₆	—	2	8	no	—
155	C₁₁×M₁₆	C₂×D₄	1	16	yes	direct product factor
156	C₂×C₈×C₁₁	—	2	32	no	—
157	C₂×C₈×C₁₁	—	2	8	no	—
158	C₂×C₈×C₁₁	—	2	4	no	—
159	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	complemented
160	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
161	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
162	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
163	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
164	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
165	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
166	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
167	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
168	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
169	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
170	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
171	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
172	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
173	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
174	C₄²×C₁₁	C₂⁴	1	2	yes	—
175	C₄²×C₁₁	C₂⁴	1	2	yes	—
176	C₂³×M₁₆	C₂×C₁₁	1	2	yes	complemented
177	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
178	D₄×M₁₆	C₂×C₁₁	1	16	yes	direct product factor
179	C₂×#436	C₂×C₁₁	1	2	yes	complemented
180	C₂×#435	C₂×C₁₁	1	4	yes	complemented
181	C₂×C₈×D₄	C₂×C₁₁	1	2	yes	complemented
182	C₂×#423	C₂×C₁₁	1	1	yes	characteristic, complemented
183	C₂×#407	C₂×C₁₁	1	2	yes	complemented
184	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂³×C₁₁	—	2	4	no	—
186	C₂³×C₁₁	—	2	2	no	—
187	C₂³×C₁₁	—	2	2	no	—
188	C₂³×C₁₁	—	2	4	no	—
189	C₂³×C₁₁	—	2	16	no	—
190	C₂³×C₁₁	—	2	4	no	—
191	C₂³×C₁₁	—	2	4	no	—
192	C₂³×C₁₁	—	2	16	no	—
193	C₂³×C₁₁	—	2	4	no	—
194	C₂³×C₁₁	—	4	8	no	—
195	C₂³×C₁₁	—	4	32	no	—
196	C₂³×C₁₁	C₄×D₄	1	4	yes	—
197	C₂³×C₁₁	C₂×M₁₆	1	8	yes	complemented
198	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
199	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
200	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
201	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
202	D₄×C₁₁	—	2	16	no	—
203	D₄×C₁₁	—	2	8	no	—
204	D₄×C₁₁	C₂×M₁₆	1	16	yes	direct product factor
205	C₂×C₄×C₁₁	—	2	16	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	2	no	—
211	C₂×C₄×C₁₁	—	2	8	no	—
212	C₂×C₄×C₁₁	—	2	16	no	—
213	C₂×C₄×C₁₁	—	2	16	no	—
214	C₂×C₄×C₁₁	—	2	8	no	—
215	C₂×C₄×C₁₁	—	2	8	no	—
216	C₂×C₄×C₁₁	—	2	4	no	—
217	C₂×C₄×C₁₁	—	2	4	no	—
218	C₂×C₄×C₁₁	—	2	4	no	—
219	C₂×C₄×C₁₁	—	2	4	no	—
220	C₂×C₄×C₁₁	—	4	4	no	—
221	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
222	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
223	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	complemented
224	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
228	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
229	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
230	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
236	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
237	C₈×C₁₁	—	2	8	no	—
238	C₈×C₁₁	—	2	4	no	—
239	C₈×C₁₁	C₂²×D₄	1	8	yes	complemented
240	C₂³×D₄	C₄×C₁₁	1	1	yes	characteristic
241	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
242	C₂²×M₁₆	—	2	16	no	—
243	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
245	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₁₁	1	4	yes	complemented
247	C₂²×M₁₆	C₂²×C₁₁	1	16	yes	complemented
248	C₂³×C₈	C₂²×C₁₁	1	4	yes	complemented
249	C₂×C₄×D₄	C₄×C₁₁	1	2	yes	—
250	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
251	C₂×C₄×D₄	C₄×C₁₁	1	8	yes	—
252	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	—
257	C₂²×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
259	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
260	#436	C₂²×C₁₁	1	16	yes	complemented
261	#435	C₂²×C₁₁	1	32	yes	complemented
262	C₈×D₄	C₂²×C₁₁	1	16	yes	complemented
263	#423	C₂²×C₁₁	1	8	yes	complemented
264	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	complemented
265	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	complemented
266	#407	C₂²×C₁₁	1	16	yes	complemented
267	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
268	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
269	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
270	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
271	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
272	C₂²×C₁₁	—	2	4	no	—
273	C₂²×C₁₁	—	2	8	no	—
274	C₂²×C₁₁	—	2	16	no	—
275	C₂²×C₁₁	—	2	2	no	—
276	C₂²×C₁₁	—	2	2	no	—
277	C₂²×C₁₁	—	2	4	no	—
278	C₂²×C₁₁	—	2	4	no	—
279	C₂²×C₁₁	—	2	4	no	—
280	C₂²×C₁₁	—	2	4	no	—
281	C₂²×C₁₁	—	4	32	no	—
282	C₂²×C₁₁	—	4	8	no	—
283	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
284	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
285	C₂²×C₁₁	C₂²×M₁₆	1	2	yes	—
286	C₂²×C₁₁	C₂²×M₁₆	1	8	yes	complemented
287	C₂²×C₁₁	#568	1	2	yes	—
288	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
289	C₄×C₁₁	—	2	4	no	—
290	C₄×C₁₁	—	2	4	no	—
291	C₄×C₁₁	—	2	2	no	—
292	C₄×C₁₁	—	2	2	no	—
293	C₄×C₁₁	—	2	2	no	—
294	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
295	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
296	C₄×C₁₁	C₂²×M₁₆	1	4	yes	complemented
297	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
299	C₂⁵	C₂×C₄×C₁₁	1	2	yes	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
302	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	—
303	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
305	C₂³×C₄	—	2	8	no	—
306	C₂³×C₄	—	2	8	no	—
307	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
308	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
310	C₂³×C₄	C₂×C₄×C₁₁	1	8	yes	—
311	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
312	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
316	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
317	C₂×M₁₆	—	2	8	no	—
318	C₂×M₁₆	—	2	4	no	—
319	C₂×M₁₆	—	2	64	no	—
320	C₂×M₁₆	—	2	16	no	—
321	C₂×M₁₆	D₄×C₁₁	1	8	yes	direct product factor
322	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
323	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
324	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
325	C₂×M₁₆	C₂³×C₁₁	1	16	yes	complemented
326	C₂²×C₈	—	2	16	no	—
327	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
328	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₁	1	16	yes	complemented
331	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
332	C₄×D₄	C₂×C₄×C₁₁	1	4	yes	—
333	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
334	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
335	C₄×D₄	C₂×C₄×C₁₁	1	4	yes	—
336	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
337	C₄×D₄	C₂³×C₁₁	1	4	yes	—
338	C₄×D₄	C₂³×C₁₁	1	8	yes	—
339	C₄×D₄	C₂³×C₁₁	1	4	yes	—
340	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
341	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	16	yes	—
349	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
351	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
352	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
355	C₄⋊C₈	C₂³×C₁₁	1	8	yes	complemented
356	C₄⋊C₈	C₂³×C₁₁	1	8	yes	complemented
357	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
358	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
359	#97	C₂³×C₁₁	1	8	yes	complemented
360	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
361	C₂×C₁₁	—	2	4	no	—
362	C₂×C₁₁	—	2	8	no	—
363	C₂×C₁₁	—	4	4	no	—
364	C₂×C₁₁	D₄×M₁₆	1	4	yes	direct product factor
365	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
366	C₂×C₁₁	C₂³×M₁₆	1	1	yes	characteristic
367	C₂×C₁₁	C₂×#568	1	1	yes	characteristic
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
372	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
373	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
374	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	32	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	C₁₁×M₁₆	1	8	yes	direct product factor
379	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
380	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
381	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	32	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	16	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	16	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
398	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
399	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
400	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
401	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
402	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
403	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
404	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
405	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
406	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
407	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
410	C₂²×C₄	C₁₁×#41	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
415	M₁₆	—	2	16	no	—
416	M₁₆	—	2	8	no	—
417	M₁₆	—	2	32	no	—
418	M₁₆	C₂×D₄×C₁₁	1	16	yes	direct product factor
419	C₂×C₈	—	2	8	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	32	no	—
422	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	complemented
423	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
424	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
425	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
426	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
427	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
428	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
429	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
430	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
431	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
432	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
433	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
434	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
435	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
436	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
437	C₄²	C₂⁴×C₁₁	1	2	yes	—
438	C₄²	C₂⁴×C₁₁	1	2	yes	—
439	C₁₁	C₂×D₄×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	16	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	8	no	—
450	C₂³	—	4	32	no	—
451	C₂³	C₄×D₄×C₁₁	1	4	yes	—
452	C₂³	C₂×C₁₁×M₁₆	1	8	yes	complemented
453	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
454	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
455	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
456	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
457	D₄	—	2	16	no	—
458	D₄	—	2	8	no	—
459	D₄	C₂×C₁₁×M₁₆	1	16	yes	direct product factor
460	C₂×C₄	—	2	16	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
477	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
478	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	complemented
479	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
480	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
481	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
482	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
483	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
484	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
489	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
490	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
491	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
492	C₈	—	2	8	no	—
493	C₈	—	2	4	no	—
494	C₈	C₂²×D₄×C₁₁	1	8	yes	complemented
495	C₂²	—	2	4	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	16	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	32	no	—
505	C₂²	—	4	8	no	—
506	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
507	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
508	C₂²	C₂²×C₁₁×M₁₆	1	2	yes	—
509	C₂²	C₂²×C₁₁×M₁₆	1	8	yes	complemented
510	C₂²	C₁₁×#568	1	2	yes	—
511	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
512	C₄	—	2	4	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
518	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
519	C₄	C₂²×C₁₁×M₁₆	1	4	yes	complemented
520	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
521	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
522	C₂	—	2	4	no	—
523	C₂	—	2	8	no	—
524	C₂	—	4	4	no	—
525	C₂	D₄×C₁₁×M₁₆	1	4	yes	direct product factor
526	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
527	C₂	C₂³×C₁₁×M₁₆	1	1	yes	characteristic
528	C₂	C₂×C₁₁×#568	1	1	yes	characteristic

	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	C₂³×D₄×C₁₁	C₄
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. C₂³×C₁₁×M₁₆	C₂	semidirect
3. D₄×C₁₁×M₁₆	C₂	direct (N × H)
4. C₂×C₁₁×#436	C₂	semidirect
5. C₂×C₁₁×#435	C₂	semidirect
6. C₂×C₈×D₄×C₁₁	C₂	semidirect
7. C₂×C₁₁×#423	C₂	semidirect
8. C₂×C₁₁×#407	C₂	semidirect
9. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
16. C₂²×C₁₁×M₁₆	C₂²	semidirect
17. C₂²×C₁₁×M₁₆	C₂²	semidirect
18. C₂³×C₈×C₁₁	C₂²	semidirect
30. C₁₁×#436	C₂²	semidirect
31. C₁₁×#435	C₂²	semidirect
32. C₈×D₄×C₁₁	C₂²	semidirect
33. C₁₁×#423	C₂²	semidirect
34. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
36. C₁₁×#407	C₂²	semidirect
37. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
38. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
39. C₄×C₁₁×M₁₆	C₂²	semidirect
40. C₂×C₁₁×#97	C₂²	semidirect
41. C₂×C₄×C₈×C₁₁	C₂²	semidirect
64. C₂×C₁₁×M₁₆	D₄	direct (N × H)
68. C₂×C₁₁×M₁₆	C₂³	semidirect
73. C₂²×C₈×C₁₁	C₂³	semidirect
98. C₁₁×C₄⋊C₈	C₂³	semidirect
99. C₁₁×C₄⋊C₈	C₂³	semidirect
100. C₁₁×C₂²⋊C₈	C₂³	semidirect
101. C₁₁×C₂²⋊C₈	C₂³	semidirect
102. C₁₁×#97	C₂³	semidirect
103. C₄×C₈×C₁₁	C₂³	semidirect
104. C₂×D₄×M₁₆	C₁₁	direct (N × H)
115. C₂×D₄×C₁₁	M₁₆	direct (N × H)
155. C₁₁×M₁₆	C₂×D₄	direct (N × H)
159. C₂×C₈×C₁₁	C₂×D₄	semidirect
176. C₂³×M₁₆	C₂×C₁₁	semidirect
178. D₄×M₁₆	C₂×C₁₁	direct (N × H)
179. C₂×#436	C₂×C₁₁	semidirect
180. C₂×#435	C₂×C₁₁	semidirect
181. C₂×C₈×D₄	C₂×C₁₁	semidirect
182. C₂×#423	C₂×C₁₁	semidirect
183. C₂×#407	C₂×C₁₁	semidirect
184. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
197. C₂³×C₁₁	C₂×M₁₆	semidirect
204. D₄×C₁₁	C₂×M₁₆	direct (N × H)
223. C₂×C₄×C₁₁	C₂×M₁₆	semidirect
239. C₈×C₁₁	C₂²×D₄	semidirect
246. C₂²×M₁₆	C₂²×C₁₁	semidirect
247. C₂²×M₁₆	C₂²×C₁₁	semidirect
248. C₂³×C₈	C₂²×C₁₁	semidirect
260. #436	C₂²×C₁₁	semidirect
261. #435	C₂²×C₁₁	semidirect
262. C₈×D₄	C₂²×C₁₁	semidirect
263. #423	C₂²×C₁₁	semidirect
264. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
265. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
266. #407	C₂²×C₁₁	semidirect
267. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
268. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
269. C₄×M₁₆	C₂²×C₁₁	semidirect
270. C₂×#97	C₂²×C₁₁	semidirect
271. C₂×C₄×C₈	C₂²×C₁₁	semidirect
286. C₂²×C₁₁	C₂²×M₁₆	semidirect
296. C₄×C₁₁	C₂²×M₁₆	semidirect
321. C₂×M₁₆	D₄×C₁₁	direct (N × H)
325. C₂×M₁₆	C₂³×C₁₁	semidirect
330. C₂²×C₈	C₂³×C₁₁	semidirect
355. C₄⋊C₈	C₂³×C₁₁	semidirect
356. C₄⋊C₈	C₂³×C₁₁	semidirect
357. C₂²⋊C₈	C₂³×C₁₁	semidirect
358. C₂²⋊C₈	C₂³×C₁₁	semidirect
359. #97	C₂³×C₁₁	semidirect
360. C₄×C₈	C₂³×C₁₁	semidirect
364. C₂×C₁₁	D₄×M₁₆	direct (N × H)
378. C₂×D₄	C₁₁×M₁₆	direct (N × H)
418. M₁₆	C₂×D₄×C₁₁	direct (N × H)
422. C₂×C₈	C₂×D₄×C₁₁	semidirect
439. C₁₁	C₂×D₄×M₁₆	direct (N × H)
452. C₂³	C₂×C₁₁×M₁₆	semidirect
459. D₄	C₂×C₁₁×M₁₆	direct (N × H)
478. C₂×C₄	C₂×C₁₁×M₁₆	semidirect
494. C₈	C₂²×D₄×C₁₁	semidirect
509. C₂²	C₂²×C₁₁×M₁₆	semidirect
519. C₄	C₂²×C₁₁×M₁₆	semidirect
525. C₂	D₄×C₁₁×M₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×M₁₆	2
C₂²×C₄×D₄×C₁₁	2
D₄×C₁₁×M₁₆	2
C₂×C₁₁×#436	2
C₂×C₁₁×#435	2
C₂×C₈×D₄×C₁₁	2
C₂×C₁₁×#423	2
C₂×C₁₁×#407	2
C₂×C₄×C₁₁×M₁₆	2
C₂×D₄×M₁₆	11

Subgroups — C2×D4×C11×M16 #14637331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₁₁×M₁₆ #14637331