Subgroups — C₂×C₁₁×#2901 #14637285

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2901	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#421	C₂	1	6	yes	maximal, complemented
6	C₂²×C₁₁×#104	C₂	1	6	yes	maximal, complemented
7	C₁₁×#585	—	2	4	no	—
8	C₁₁×#585	—	2	4	no	—
9	C₁₁×#585	C₄	1	8	yes	complemented
10	C₁₁×#585	C₂²	1	8	yes	—
11	C₂×C₁₁×2₋¹⁺⁴	—	2	1	no	—
12	C₂×C₁₁×2₋¹⁺⁴	C₄	1	4	yes	complemented
13	C₂×C₁₁×H(5,𝔽₂)	—	2	3	no	—
14	C₂×C₁₁×H(5,𝔽₂)	C₄	1	4	yes	complemented
15	C₂²×C₁₁×#41	—	2	4	no	—
16	C₂²×C₁₁×#41	C₂²	1	6	yes	—
17	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
18	C₁₁×#568	—	2	4	no	—
19	C₁₁×#568	C₂²	1	8	yes	complemented
20	C₂×C₁₁×#131	—	2	4	no	—
21	C₂²×C₁₁×M₁₆	C₂²	1	6	yes	complemented
22	C₄×C₁₁×#41	—	2	4	no	—
23	C₄×C₁₁×#41	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
25	C₂×C₄×D₄×C₁₁	—	2	3	no	—
26	C₂×C₁₁×#117	C₂²	1	3	yes	complemented
27	C₂²×C₄²×C₁₁	C₂²	1	3	yes	complemented
28	C₁₁×#421	C₂²	1	48	yes	complemented
29	C₂×C₁₁×#104	C₂²	1	4	yes	complemented
30	C₂×C₁₁×#104	C₂²	1	12	yes	complemented
31	C₂×C₁₁×#104	C₂²	1	48	yes	complemented
32	C₁₁×2₋¹⁺⁴	—	2	16	no	—
33	C₁₁×2₋¹⁺⁴	—	2	8	no	—
34	C₁₁×2₋¹⁺⁴	—	2	8	no	—
35	C₁₁×2₋¹⁺⁴	C₂×C₄	1	32	yes	complemented
36	C₁₁×H(5,𝔽₂)	—	2	16	no	—
37	C₁₁×H(5,𝔽₂)	—	2	24	no	—
38	C₁₁×H(5,𝔽₂)	—	2	24	no	—
39	C₁₁×H(5,𝔽₂)	C₂×C₄	1	32	yes	complemented
40	C₂×C₁₁×#41	—	2	32	no	—
41	C₂×C₁₁×#41	—	2	32	no	—
42	C₂×C₁₁×#41	—	2	4	no	—
43	C₂×C₁₁×#41	—	2	12	no	—
44	C₂×C₁₁×#41	—	2	6	no	—
45	C₂×C₁₁×#41	—	2	6	no	—
46	C₂×C₁₁×#41	—	2	12	no	—
47	C₂×C₁₁×#41	—	2	12	no	—
48	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
49	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
50	C₂×C₁₁×#41	C₂×C₄	1	12	yes	complemented
51	C₂×C₁₁×#41	C₂×C₄	1	24	yes	complemented
52	C₂×C₁₁×#41	D₄	1	4	yes	—
53	C₂×C₁₁×#41	D₄	1	4	yes	—
54	C₂×C₁₁×#41	D₄	1	4	yes	—
55	C₂×C₁₁×#41	C₂³	1	4	yes	—
56	C₂×C₁₁×#41	C₂³	1	24	yes	—
57	C₂×C₁₁×#41	C₂³	1	4	yes	—
58	C₂²×Q₈×C₁₁	—	2	4	no	—
59	C₂²×Q₈×C₁₁	C₂×C₄	1	6	yes	complemented
60	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₁	—	2	6	no	—
62	C₂²×D₄×C₁₁	—	2	12	no	—
63	C₂²×D₄×C₁₁	C₂×C₄	1	6	yes	complemented
64	C₂²×D₄×C₁₁	D₄	1	3	yes	—
65	C₂³×C₄×C₁₁	—	2	6	no	—
66	C₂³×C₄×C₁₁	—	2	3	no	—
67	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
68	C₁₁×#131	—	2	32	no	—
69	C₂×C₁₁×M₁₆	—	2	6	no	—
70	C₂×C₁₁×M₁₆	—	2	12	no	—
71	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
72	C₂×C₁₁×M₁₆	C₂³	1	24	yes	complemented
73	C₂²×C₈×C₁₁	—	2	6	no	—
74	C₄×Q₈×C₁₁	—	2	8	no	—
75	C₄×D₄×C₁₁	—	2	24	no	—
76	C₁₁×#117	—	2	6	no	—
77	C₁₁×#117	C₂³	1	12	yes	complemented
78	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	3	no	—
80	C₂×C₄²×C₁₁	—	2	3	no	—
81	C₂×C₄²×C₁₁	—	2	6	no	—
82	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
84	C₂×C₄²×C₁₁	C₂³	1	12	yes	complemented
85	C₁₁×#104	C₂³	1	16	yes	complemented
86	C₁₁×#104	C₂³	1	48	yes	complemented
87	C₂×#2901	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₁	—	2	6	no	—
89	C₂⁴×C₁₁	C₂×D₄	1	3	yes	—
90	C₁₁×#41	—	2	32	no	—
91	C₁₁×#41	—	2	96	no	—
92	C₁₁×#41	—	2	24	no	—
93	C₁₁×#41	—	2	24	no	—
94	C₁₁×#41	—	2	24	no	—
95	C₁₁×#41	—	2	4	no	—
96	C₁₁×#41	—	2	24	no	—
97	C₁₁×#41	—	2	4	no	—
98	C₁₁×#41	—	2	24	no	—
99	C₁₁×#41	C₂²⋊C₄	1	16	yes	—
100	C₁₁×#41	C₂²⋊C₄	1	16	yes	—
101	C₁₁×#41	C₂²×C₄	1	8	yes	—
102	C₁₁×#41	C₂²×C₄	1	16	yes	—
103	C₁₁×#41	C₂²×C₄	1	48	yes	complemented
104	C₁₁×#41	C₂×D₄	1	16	yes	—
105	C₁₁×#41	C₂⁴	1	8	yes	—
106	C₂×Q₈×C₁₁	—	2	32	no	—
107	C₂×Q₈×C₁₁	—	2	6	no	—
108	C₂×Q₈×C₁₁	—	2	12	no	—
109	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
110	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
111	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
112	C₂×Q₈×C₁₁	C₂²×C₄	1	24	yes	complemented
113	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₁₁	—	2	12	no	—
115	C₂×D₄×C₁₁	—	2	24	no	—
116	C₂×D₄×C₁₁	—	2	4	no	—
117	C₂×D₄×C₁₁	—	2	24	no	—
118	C₂×D₄×C₁₁	—	2	96	no	—
119	C₂×D₄×C₁₁	—	2	6	no	—
120	C₂×D₄×C₁₁	—	2	12	no	—
121	C₂×D₄×C₁₁	C₂²⋊C₄	1	12	yes	—
122	C₂×D₄×C₁₁	C₂²⋊C₄	1	12	yes	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	complemented
125	C₂×D₄×C₁₁	C₂×D₄	1	12	yes	—
126	C₂²×C₄×C₁₁	—	2	6	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	12	no	—
129	C₂²×C₄×C₁₁	—	2	24	no	—
130	C₂²×C₄×C₁₁	—	2	24	no	—
131	C₂²×C₄×C₁₁	—	2	4	no	—
132	C₂²×C₄×C₁₁	—	2	3	no	—
133	C₂²×C₄×C₁₁	—	2	12	no	—
134	C₂²×C₄×C₁₁	—	4	12	no	—
135	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
137	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
138	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
139	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
140	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
141	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
142	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
143	C₁₁×M₁₆	—	2	4	no	—
144	C₁₁×M₁₆	—	2	24	no	—
145	C₁₁×M₁₆	C₂⁴	1	8	yes	—
146	C₂×C₈×C₁₁	—	2	24	no	—
147	C₂×C₈×C₁₁	—	2	4	no	—
148	C₁₁×C₄⋊C₄	—	2	12	no	—
149	C₁₁×C₂²⋊C₄	—	2	12	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	3	no	—
152	C₄²×C₁₁	—	2	12	no	—
153	C₄²×C₁₁	C₂⁴	1	2	yes	—
154	C₄²×C₁₁	C₂⁴	1	6	yes	—
155	C₂×#585	C₂×C₁₁	1	1	yes	characteristic
156	C₂×#568	C₂×C₁₁	1	1	yes	characteristic, complemented
157	C₂×C₄×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#2901	C₂×C₁₁	1	16	yes	direct product factor
159	C₂×#421	C₂×C₁₁	1	6	yes	complemented
160	C₂²×#104	C₂×C₁₁	1	6	yes	complemented
161	C₂³×C₁₁	—	2	4	no	—
162	C₂³×C₁₁	—	2	24	no	—
163	C₂³×C₁₁	—	4	6	no	—
164	C₂³×C₁₁	—	8	12	no	—
165	C₂³×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
166	C₂³×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
167	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
168	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
169	Q₈×C₁₁	—	2	4	no	—
170	Q₈×C₁₁	—	2	24	no	—
171	Q₈×C₁₁	C₂×C₂²⋊C₄	1	16	yes	—
172	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
173	D₄×C₁₁	—	2	8	no	—
174	D₄×C₁₁	—	2	48	no	—
175	D₄×C₁₁	—	2	8	no	—
176	D₄×C₁₁	—	2	4	no	—
177	D₄×C₁₁	—	2	24	no	—
178	D₄×C₁₁	C₂×C₂²⋊C₄	1	48	yes	—
179	D₄×C₁₁	C₂³×C₄	1	8	yes	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	4	no	—
182	C₂×C₄×C₁₁	—	2	24	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	8	no	—
185	C₂×C₄×C₁₁	—	2	48	no	—
186	C₂×C₄×C₁₁	—	2	8	no	—
187	C₂×C₄×C₁₁	—	2	6	no	—
188	C₂×C₄×C₁₁	—	4	24	no	—
189	C₂×C₄×C₁₁	—	4	6	no	—
190	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
191	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	12	yes	—
192	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	12	yes	—
193	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
194	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂³×C₄	1	12	yes	—
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
199	C₂×C₄×C₁₁	C₂²×D₄	1	12	yes	—
200	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
203	C₈×C₁₁	—	2	8	no	—
204	#585	—	2	4	no	—
205	#585	—	2	4	no	—
206	#585	C₄×C₁₁	1	8	yes	complemented
207	#585	C₂²×C₁₁	1	8	yes	—
208	C₂×2₋¹⁺⁴	—	2	1	no	—
209	C₂×2₋¹⁺⁴	C₄×C₁₁	1	4	yes	complemented
210	C₂×H(5,𝔽₂)	—	2	3	no	—
211	C₂×H(5,𝔽₂)	C₄×C₁₁	1	4	yes	complemented
212	C₂²×#41	—	2	4	no	—
213	C₂²×#41	C₂²×C₁₁	1	6	yes	—
214	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
215	#568	—	2	4	no	—
216	#568	C₂²×C₁₁	1	8	yes	complemented
217	C₂×#131	—	2	4	no	—
218	C₂²×M₁₆	C₂²×C₁₁	1	6	yes	complemented
219	C₄×#41	—	2	4	no	—
220	C₄×#41	C₂²×C₁₁	1	8	yes	complemented
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×D₄	—	2	3	no	—
223	C₂×#117	C₂²×C₁₁	1	3	yes	complemented
224	C₂²×C₄²	C₂²×C₁₁	1	3	yes	complemented
225	#421	C₂²×C₁₁	1	48	yes	complemented
226	C₂×#104	C₂²×C₁₁	1	4	yes	complemented
227	C₂×#104	C₂²×C₁₁	1	12	yes	complemented
228	C₂×#104	C₂²×C₁₁	1	48	yes	complemented
229	C₂²×C₁₁	—	2	2	no	—
230	C₂²×C₁₁	—	2	12	no	—
231	C₂²×C₁₁	—	2	8	no	—
232	C₂²×C₁₁	—	4	6	no	—
233	C₂²×C₁₁	—	4	6	no	—
234	C₂²×C₁₁	—	4	8	no	—
235	C₂²×C₁₁	—	8	24	no	—
236	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
237	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₁₁	—	2	4	no	—
241	C₄×C₁₁	—	2	8	no	—
242	C₄×C₁₁	—	4	6	no	—
243	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₄×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
245	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
246	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
247	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
248	2₋¹⁺⁴	—	2	16	no	—
249	2₋¹⁺⁴	—	2	8	no	—
250	2₋¹⁺⁴	—	2	8	no	—
251	2₋¹⁺⁴	C₂×C₄×C₁₁	1	32	yes	complemented
252	H(5,𝔽₂)	—	2	16	no	—
253	H(5,𝔽₂)	—	2	24	no	—
254	H(5,𝔽₂)	—	2	24	no	—
255	H(5,𝔽₂)	C₂×C₄×C₁₁	1	32	yes	complemented
256	C₂×#41	—	2	32	no	—
257	C₂×#41	—	2	32	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	12	no	—
260	C₂×#41	—	2	6	no	—
261	C₂×#41	—	2	6	no	—
262	C₂×#41	—	2	12	no	—
263	C₂×#41	—	2	12	no	—
264	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
265	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
266	C₂×#41	C₂×C₄×C₁₁	1	12	yes	complemented
267	C₂×#41	C₂×C₄×C₁₁	1	24	yes	complemented
268	C₂×#41	D₄×C₁₁	1	4	yes	—
269	C₂×#41	D₄×C₁₁	1	4	yes	—
270	C₂×#41	D₄×C₁₁	1	4	yes	—
271	C₂×#41	C₂³×C₁₁	1	4	yes	—
272	C₂×#41	C₂³×C₁₁	1	24	yes	—
273	C₂×#41	C₂³×C₁₁	1	4	yes	—
274	C₂²×Q₈	—	2	4	no	—
275	C₂²×Q₈	C₂×C₄×C₁₁	1	6	yes	complemented
276	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
277	C₂²×D₄	—	2	6	no	—
278	C₂²×D₄	—	2	12	no	—
279	C₂²×D₄	C₂×C₄×C₁₁	1	6	yes	complemented
280	C₂²×D₄	D₄×C₁₁	1	3	yes	—
281	C₂³×C₄	—	2	6	no	—
282	C₂³×C₄	—	2	3	no	—
283	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
284	#131	—	2	32	no	—
285	C₂×M₁₆	—	2	6	no	—
286	C₂×M₁₆	—	2	12	no	—
287	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
288	C₂×M₁₆	C₂³×C₁₁	1	24	yes	complemented
289	C₂²×C₈	—	2	6	no	—
290	C₄×Q₈	—	2	8	no	—
291	C₄×D₄	—	2	24	no	—
292	#117	—	2	6	no	—
293	#117	C₂³×C₁₁	1	12	yes	complemented
294	C₂×C₄⋊C₄	—	2	3	no	—
295	C₂×C₂²⋊C₄	—	2	3	no	—
296	C₂×C₄²	—	2	3	no	—
297	C₂×C₄²	—	2	6	no	—
298	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
299	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₁	1	12	yes	complemented
301	#104	C₂³×C₁₁	1	16	yes	complemented
302	#104	C₂³×C₁₁	1	48	yes	complemented
303	C₂×C₁₁	—	2	1	no	—
304	C₂×C₁₁	—	2	1	no	—
305	C₂×C₁₁	—	2	12	no	—
306	C₂×C₁₁	—	4	8	no	—
307	C₂×C₁₁	#2901	1	2	yes	direct product factor
308	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
309	C₂⁴	—	2	6	no	—
310	C₂⁴	C₂×D₄×C₁₁	1	3	yes	—
311	#41	—	2	32	no	—
312	#41	—	2	96	no	—
313	#41	—	2	24	no	—
314	#41	—	2	24	no	—
315	#41	—	2	24	no	—
316	#41	—	2	4	no	—
317	#41	—	2	24	no	—
318	#41	—	2	4	no	—
319	#41	—	2	24	no	—
320	#41	C₁₁×C₂²⋊C₄	1	16	yes	—
321	#41	C₁₁×C₂²⋊C₄	1	16	yes	—
322	#41	C₂²×C₄×C₁₁	1	8	yes	—
323	#41	C₂²×C₄×C₁₁	1	16	yes	—
324	#41	C₂²×C₄×C₁₁	1	48	yes	complemented
325	#41	C₂×D₄×C₁₁	1	16	yes	—
326	#41	C₂⁴×C₁₁	1	8	yes	—
327	C₂×Q₈	—	2	32	no	—
328	C₂×Q₈	—	2	6	no	—
329	C₂×Q₈	—	2	12	no	—
330	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
331	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
332	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
333	C₂×Q₈	C₂²×C₄×C₁₁	1	24	yes	complemented
334	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
335	C₂×D₄	—	2	12	no	—
336	C₂×D₄	—	2	24	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	24	no	—
339	C₂×D₄	—	2	96	no	—
340	C₂×D₄	—	2	6	no	—
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	C₁₁×C₂²⋊C₄	1	12	yes	—
343	C₂×D₄	C₁₁×C₂²⋊C₄	1	12	yes	—
344	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
345	C₂×D₄	C₂²×C₄×C₁₁	1	24	yes	complemented
346	C₂×D₄	C₂×D₄×C₁₁	1	12	yes	—
347	C₂²×C₄	—	2	6	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	12	no	—
350	C₂²×C₄	—	2	24	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	24	no	—
353	C₂²×C₄	—	2	3	no	—
354	C₂²×C₄	—	2	12	no	—
355	C₂²×C₄	—	4	12	no	—
356	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
358	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
359	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
360	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
361	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
362	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	24	no	—
366	M₁₆	C₂⁴×C₁₁	1	8	yes	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	24	no	—
369	C₄⋊C₄	—	2	12	no	—
370	C₂²⋊C₄	—	2	12	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	3	no	—
373	C₄²	—	2	12	no	—
374	C₄²	C₂⁴×C₁₁	1	2	yes	—
375	C₄²	C₂⁴×C₁₁	1	6	yes	—
376	C₁₁	C₂×#2901	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	4	no	—
378	C₂³	—	2	24	no	—
379	C₂³	—	4	6	no	—
380	C₂³	—	8	12	no	—
381	C₂³	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
382	C₂³	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
383	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
384	C₂³	C₂²×D₄×C₁₁	1	6	yes	—
385	Q₈	—	2	4	no	—
386	Q₈	—	2	24	no	—
387	Q₈	C₂×C₁₁×C₂²⋊C₄	1	16	yes	—
388	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
389	D₄	—	2	8	no	—
390	D₄	—	2	48	no	—
391	D₄	—	2	8	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	24	no	—
394	D₄	C₂×C₁₁×C₂²⋊C₄	1	48	yes	—
395	D₄	C₂³×C₄×C₁₁	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	24	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	48	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	6	no	—
404	C₂×C₄	—	4	24	no	—
405	C₂×C₄	—	4	6	no	—
406	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
407	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	12	yes	—
408	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	12	yes	—
409	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
410	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
411	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₄×C₁₁	1	12	yes	—
413	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
415	C₂×C₄	C₂²×D₄×C₁₁	1	12	yes	—
416	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
418	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
419	C₈	—	2	8	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	12	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	4	6	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	8	24	no	—
427	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
428	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
429	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
430	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	6	no	—
434	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
435	C₄	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
436	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
437	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
438	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	2	12	no	—
442	C₂	—	4	8	no	—
443	C₂	C₁₁×#2901	1	2	yes	direct product factor
444	C₂	C₂³×C₁₁×C₂²⋊C₄	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	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₁×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#568	C₂	semidirect
3. C₂×C₄×C₁₁×#41	C₂	semidirect
4. C₁₁×#2901	C₂	direct (N × H)
5. C₂×C₁₁×#421	C₂	semidirect
6. C₂²×C₁₁×#104	C₂	semidirect
9. C₁₁×#585	C₄	semidirect
12. C₂×C₁₁×2₋¹⁺⁴	C₄	semidirect
14. C₂×C₁₁×H(5,𝔽₂)	C₄	semidirect
19. C₁₁×#568	C₂²	semidirect
21. C₂²×C₁₁×M₁₆	C₂²	semidirect
23. C₄×C₁₁×#41	C₂²	semidirect
26. C₂×C₁₁×#117	C₂²	semidirect
27. C₂²×C₄²×C₁₁	C₂²	semidirect
28. C₁₁×#421	C₂²	semidirect
29. C₂×C₁₁×#104	C₂²	semidirect
30. C₂×C₁₁×#104	C₂²	semidirect
31. C₂×C₁₁×#104	C₂²	semidirect
35. C₁₁×2₋¹⁺⁴	C₂×C₄	semidirect
39. C₁₁×H(5,𝔽₂)	C₂×C₄	semidirect
50. C₂×C₁₁×#41	C₂×C₄	semidirect
51. C₂×C₁₁×#41	C₂×C₄	semidirect
59. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
63. C₂²×D₄×C₁₁	C₂×C₄	semidirect
72. C₂×C₁₁×M₁₆	C₂³	semidirect
77. C₁₁×#117	C₂³	semidirect
84. C₂×C₄²×C₁₁	C₂³	semidirect
85. C₁₁×#104	C₂³	semidirect
86. C₁₁×#104	C₂³	semidirect
87. C₂×#2901	C₁₁	direct (N × H)
103. C₁₁×#41	C₂²×C₄	semidirect
112. C₂×Q₈×C₁₁	C₂²×C₄	semidirect
124. C₂×D₄×C₁₁	C₂²×C₄	semidirect
156. C₂×#568	C₂×C₁₁	semidirect
157. C₂×C₄×#41	C₂×C₁₁	semidirect
158. #2901	C₂×C₁₁	direct (N × H)
159. C₂×#421	C₂×C₁₁	semidirect
160. C₂²×#104	C₂×C₁₁	semidirect
206. #585	C₄×C₁₁	semidirect
209. C₂×2₋¹⁺⁴	C₄×C₁₁	semidirect
211. C₂×H(5,𝔽₂)	C₄×C₁₁	semidirect
216. #568	C₂²×C₁₁	semidirect
218. C₂²×M₁₆	C₂²×C₁₁	semidirect
220. C₄×#41	C₂²×C₁₁	semidirect
223. C₂×#117	C₂²×C₁₁	semidirect
224. C₂²×C₄²	C₂²×C₁₁	semidirect
225. #421	C₂²×C₁₁	semidirect
226. C₂×#104	C₂²×C₁₁	semidirect
227. C₂×#104	C₂²×C₁₁	semidirect
228. C₂×#104	C₂²×C₁₁	semidirect
251. 2₋¹⁺⁴	C₂×C₄×C₁₁	semidirect
255. H(5,𝔽₂)	C₂×C₄×C₁₁	semidirect
266. C₂×#41	C₂×C₄×C₁₁	semidirect
267. C₂×#41	C₂×C₄×C₁₁	semidirect
275. C₂²×Q₈	C₂×C₄×C₁₁	semidirect
279. C₂²×D₄	C₂×C₄×C₁₁	semidirect
288. C₂×M₁₆	C₂³×C₁₁	semidirect
293. #117	C₂³×C₁₁	semidirect
300. C₂×C₄²	C₂³×C₁₁	semidirect
301. #104	C₂³×C₁₁	semidirect
302. #104	C₂³×C₁₁	semidirect
307. C₂×C₁₁	#2901	direct (N × H)
324. #41	C₂²×C₄×C₁₁	semidirect
333. C₂×Q₈	C₂²×C₄×C₁₁	semidirect
345. C₂×D₄	C₂²×C₄×C₁₁	semidirect
376. C₁₁	C₂×#2901	direct (N × H)
443. C₂	C₁₁×#2901	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×#585	2
C₂×C₁₁×#568	2
C₂×C₄×C₁₁×#41	2
C₁₁×#2901	2
C₂×C₁₁×#421	2
C₂²×C₁₁×#104	2
C₂×#2901	11

Subgroups — C2×C11×#2901 #14637285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2901 #14637285