Subgroups — C₂×C₁₁×#3299 #14638310

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3299	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#484	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#467	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#451	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₁×#103	C₂	1	2	yes	maximal, complemented
13	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
14	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
16	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
17	C₁₁×#554	—	2	4	no	—
18	C₁₁×#554	C₂²	1	8	yes	—
19	D₄×Q₈×C₁₁	—	2	4	no	—
20	D₄×Q₈×C₁₁	C₂²	1	8	yes	—
21	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#125	—	2	1	no	—
25	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₁	—	2	1	no	—
32	C₂×C₄×D₄×C₁₁	—	2	1	no	—
33	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
34	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₁×#487	C₂²	1	8	yes	complemented
36	C₁₁×#484	C₂²	1	16	yes	complemented
37	C₁₁×#477	C₂²	1	8	yes	complemented
38	C₁₁×#467	C₂²	1	16	yes	complemented
39	C₁₁×#462	C₂²	1	8	yes	complemented
40	C₁₁×#451	C₂²	1	16	yes	complemented
41	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₁	C₂²	1	8	yes	—
43	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₁×#107	C₂²	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₁×#103	C₂²	1	2	yes	—
48	C₂×C₁₁×#103	C₂²	1	2	yes	—
49	C₂×C₁₁×#103	C₂²	1	2	yes	—
50	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₁×#103	C₂²	1	2	yes	—
52	C₂×C₁₁×#103	C₂²	1	16	yes	complemented
53	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₁	—	2	2	no	—
56	C₂²×Q₈×C₁₁	—	2	4	no	—
57	C₂²×Q₈×C₁₁	—	2	1	no	—
58	C₂²×Q₈×C₁₁	—	2	8	no	—
59	C₂²×Q₈×C₁₁	—	4	4	no	—
60	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₁	C₂³	1	8	yes	—
63	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₁	—	2	2	no	—
66	C₂³×C₄×C₁₁	—	2	2	no	—
67	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
68	C₂×C₁₁×Q₁₆	—	2	4	no	—
69	C₂×C₁₁×Q₁₆	—	4	4	no	—
70	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
71	C₂×C₁₁×Q₁₆	C₂³	1	8	yes	—
72	C₂²×C₈×C₁₁	—	4	4	no	—
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
77	C₁₁×C₄⋊Q₈	—	2	8	no	—
78	C₁₁×C₄⋊Q₈	—	2	2	no	—
79	C₁₁×C₄⋊Q₈	—	2	2	no	—
80	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
81	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₁×#125	—	2	8	no	—
83	C₁₁×C₂²⋊Q₈	—	2	4	no	—
84	C₁₁×C₂²⋊Q₈	—	2	4	no	—
85	C₁₁×C₂²⋊Q₈	—	2	16	no	—
86	C₁₁×C₂²⋊Q₈	—	2	16	no	—
87	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₄×Q₈×C₁₁	—	2	2	no	—
90	C₄×Q₈×C₁₁	—	2	2	no	—
91	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
92	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
93	C₄×D₄×C₁₁	—	2	8	no	—
94	C₄×D₄×C₁₁	—	2	8	no	—
95	C₄×D₄×C₁₁	D₄	1	4	yes	—
96	C₄×D₄×C₁₁	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
99	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₄²×C₁₁	—	2	1	no	—
115	C₂×C₄²×C₁₁	—	2	1	no	—
116	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
117	C₁₁×#107	C₂³	1	4	yes	—
118	C₁₁×#107	C₂³	1	8	yes	—
119	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
120	C₁₁×#103	C₂³	1	4	yes	—
121	C₁₁×#103	C₂³	1	8	yes	—
122	C₁₁×#103	C₂³	1	8	yes	—
123	C₁₁×#103	C₂³	1	8	yes	—
124	C₁₁×#103	C₂³	1	4	yes	—
125	C₁₁×#103	C₂³	1	8	yes	—
126	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₄×C₈×C₁₁	C₂³	1	4	yes	—
128	C₂×#3299	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
130	C₂×Q₈×C₁₁	—	2	1	no	—
131	C₂×Q₈×C₁₁	—	2	1	no	—
132	C₂×Q₈×C₁₁	—	2	8	no	—
133	C₂×Q₈×C₁₁	—	2	2	no	—
134	C₂×Q₈×C₁₁	—	2	4	no	—
135	C₂×Q₈×C₁₁	—	2	2	no	—
136	C₂×Q₈×C₁₁	—	2	16	no	—
137	C₂×Q₈×C₁₁	—	2	2	no	—
138	C₂×Q₈×C₁₁	—	2	4	no	—
139	C₂×Q₈×C₁₁	—	2	2	no	—
140	C₂×Q₈×C₁₁	—	2	4	no	—
141	C₂×Q₈×C₁₁	—	4	8	no	—
142	C₂×Q₈×C₁₁	—	4	8	no	—
143	C₂×Q₈×C₁₁	—	4	16	no	—
144	C₂×Q₈×C₁₁	—	8	2	no	—
145	C₂×Q₈×C₁₁	#41	1	4	yes	—
146	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
147	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
148	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
149	C₂×D₄×C₁₁	Q₁₆	1	8	yes	complemented
150	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₁	—	2	1	no	—
152	C₂²×C₄×C₁₁	—	2	4	no	—
153	C₂²×C₄×C₁₁	—	2	4	no	—
154	C₂²×C₄×C₁₁	—	2	8	no	—
155	C₂²×C₄×C₁₁	—	2	1	no	—
156	C₂²×C₄×C₁₁	—	2	1	no	—
157	C₂²×C₄×C₁₁	—	2	1	no	—
158	C₂²×C₄×C₁₁	—	2	2	no	—
159	C₂²×C₄×C₁₁	—	2	2	no	—
160	C₂²×C₄×C₁₁	—	2	8	no	—
161	C₂²×C₄×C₁₁	—	4	8	no	—
162	C₂²×C₄×C₁₁	—	8	4	no	—
163	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
169	C₁₁×Q₁₆	—	2	8	no	—
170	C₁₁×Q₁₆	—	4	8	no	—
171	C₂×C₈×C₁₁	—	2	2	no	—
172	C₂×C₈×C₁₁	—	2	2	no	—
173	C₂×C₈×C₁₁	—	2	4	no	—
174	C₂×C₈×C₁₁	—	4	8	no	—
175	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
176	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
177	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
178	C₁₁×C₄⋊C₄	—	2	1	no	—
179	C₁₁×C₄⋊C₄	—	2	8	no	—
180	C₁₁×C₄⋊C₄	—	2	2	no	—
181	C₁₁×C₄⋊C₄	—	2	4	no	—
182	C₁₁×C₄⋊C₄	—	2	4	no	—
183	C₁₁×C₄⋊C₄	—	2	4	no	—
184	C₁₁×C₄⋊C₄	—	2	4	no	—
185	C₁₁×C₄⋊C₄	—	2	4	no	—
186	C₁₁×C₄⋊C₄	—	2	8	no	—
187	C₁₁×C₄⋊C₄	—	2	8	no	—
188	C₁₁×C₄⋊C₄	—	2	1	no	—
189	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
190	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
191	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
193	C₁₁×C₂²⋊C₄	—	2	8	no	—
194	C₁₁×C₂²⋊C₄	—	2	8	no	—
195	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
196	C₄²×C₁₁	—	2	4	no	—
197	C₄²×C₁₁	—	2	4	no	—
198	C₄²×C₁₁	C₂×D₄	1	2	yes	—
199	C₄²×C₁₁	C₂⁴	1	2	yes	—
200	C₂×#554	C₂×C₁₁	1	1	yes	characteristic
201	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic
202	#3299	C₂×C₁₁	1	16	yes	direct product factor
203	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
204	C₂×#484	C₂×C₁₁	1	2	yes	complemented
205	C₂×#477	C₂×C₁₁	1	1	yes	characteristic, complemented
206	C₂×#467	C₂×C₁₁	1	2	yes	complemented
207	C₂×#462	C₂×C₁₁	1	1	yes	characteristic, complemented
208	C₂×#451	C₂×C₁₁	1	2	yes	complemented
209	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
210	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
211	C₂²×#103	C₂×C₁₁	1	2	yes	complemented
212	C₂³×C₁₁	—	2	4	no	—
213	C₂³×C₁₁	—	2	4	no	—
214	C₂³×C₁₁	C₂×Q₁₆	1	8	yes	—
215	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
216	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₁	—	2	4	no	—
218	Q₈×C₁₁	—	2	2	no	—
219	Q₈×C₁₁	—	2	2	no	—
220	Q₈×C₁₁	—	2	4	no	—
221	Q₈×C₁₁	—	2	2	no	—
222	Q₈×C₁₁	—	2	4	no	—
223	Q₈×C₁₁	—	4	16	no	—
224	Q₈×C₁₁	—	4	2	no	—
225	Q₈×C₁₁	—	4	4	no	—
226	Q₈×C₁₁	—	8	4	no	—
227	Q₈×C₁₁	C₂×#41	1	4	yes	—
228	D₄×C₁₁	C₂×Q₁₆	1	16	yes	complemented
229	C₂×C₄×C₁₁	—	2	4	no	—
230	C₂×C₄×C₁₁	—	2	4	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	8	no	—
234	C₂×C₄×C₁₁	—	2	4	no	—
235	C₂×C₄×C₁₁	—	2	4	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	4	no	—
241	C₂×C₄×C₁₁	—	4	16	no	—
242	C₂×C₄×C₁₁	—	4	4	no	—
243	C₂×C₄×C₁₁	—	4	2	no	—
244	C₂×C₄×C₁₁	—	4	2	no	—
245	C₂×C₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	—	4	4	no	—
247	C₂×C₄×C₁₁	—	8	8	no	—
248	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
249	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
255	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
256	C₈×C₁₁	—	2	2	no	—
257	C₈×C₁₁	—	2	2	no	—
258	C₈×C₁₁	—	2	4	no	—
259	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
260	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
261	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
262	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
263	#554	—	2	4	no	—
264	#554	C₂²×C₁₁	1	8	yes	—
265	D₄×Q₈	—	2	4	no	—
266	D₄×Q₈	C₂²×C₁₁	1	8	yes	—
267	C₂×C₄⋊Q₈	—	2	1	no	—
268	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×#125	—	2	1	no	—
271	C₂×C₂²⋊Q₈	—	2	2	no	—
272	C₂×C₂²⋊Q₈	—	2	2	no	—
273	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
275	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	—	2	1	no	—
279	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
281	#487	C₂²×C₁₁	1	8	yes	complemented
282	#484	C₂²×C₁₁	1	16	yes	complemented
283	#477	C₂²×C₁₁	1	8	yes	complemented
284	#467	C₂²×C₁₁	1	16	yes	complemented
285	#462	C₂²×C₁₁	1	8	yes	complemented
286	#451	C₂²×C₁₁	1	16	yes	complemented
287	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
288	C₈×D₄	C₂²×C₁₁	1	8	yes	—
289	C₂×#107	C₂²×C₁₁	1	2	yes	—
290	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
292	C₂×#103	C₂²×C₁₁	1	2	yes	—
293	C₂×#103	C₂²×C₁₁	1	2	yes	—
294	C₂×#103	C₂²×C₁₁	1	2	yes	—
295	C₂×#103	C₂²×C₁₁	1	2	yes	—
296	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
297	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
298	C₂×#103	C₂²×C₁₁	1	16	yes	complemented
299	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
301	C₂²×C₁₁	—	2	4	no	—
302	C₂²×C₁₁	—	2	16	no	—
303	C₂²×C₁₁	—	2	4	no	—
304	C₂²×C₁₁	#546	1	2	yes	—
305	C₂²×C₁₁	C₂²×Q₁₆	1	8	yes	—
306	C₂²×C₁₁	C₂²×Q₁₆	1	2	yes	—
307	C₂²×C₁₁	#577	1	2	yes	—
308	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
309	C₄×C₁₁	—	2	4	no	—
310	C₄×C₁₁	—	2	4	no	—
311	C₄×C₁₁	—	2	2	no	—
312	C₄×C₁₁	—	4	4	no	—
313	C₄×C₁₁	—	4	2	no	—
314	C₄×C₁₁	—	4	2	no	—
315	C₄×C₁₁	—	4	2	no	—
316	C₄×C₁₁	—	4	4	no	—
317	C₄×C₁₁	#546	1	2	yes	—
318	C₄×C₁₁	C₂²×Q₁₆	1	4	yes	—
319	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
320	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	4	no	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	—	2	8	no	—
325	C₂²×Q₈	—	4	4	no	—
326	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
328	C₂²×Q₈	C₂³×C₁₁	1	8	yes	—
329	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
334	C₂×Q₁₆	—	2	4	no	—
335	C₂×Q₁₆	—	4	4	no	—
336	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
337	C₂×Q₁₆	C₂³×C₁₁	1	8	yes	—
338	C₂²×C₈	—	4	4	no	—
339	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
341	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
343	C₄⋊Q₈	—	2	8	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	C₄⋊Q₈	—	2	2	no	—
346	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
347	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
348	#125	—	2	8	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	16	no	—
352	C₂²⋊Q₈	—	2	16	no	—
353	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
354	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
355	C₄×Q₈	—	2	2	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
358	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	D₄×C₁₁	1	4	yes	—
362	C₄×D₄	C₂³×C₁₁	1	4	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
383	#107	C₂³×C₁₁	1	4	yes	—
384	#107	C₂³×C₁₁	1	8	yes	—
385	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
386	#103	C₂³×C₁₁	1	4	yes	—
387	#103	C₂³×C₁₁	1	8	yes	—
388	#103	C₂³×C₁₁	1	8	yes	—
389	#103	C₂³×C₁₁	1	8	yes	—
390	#103	C₂³×C₁₁	1	4	yes	—
391	#103	C₂³×C₁₁	1	8	yes	—
392	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
393	C₄×C₈	C₂³×C₁₁	1	4	yes	—
394	C₂×C₁₁	—	2	8	no	—
395	C₂×C₁₁	#3299	1	4	yes	direct product factor
396	C₂×C₁₁	C₂×#546	1	1	yes	characteristic
397	C₂×C₁₁	C₂³×Q₁₆	1	1	yes	characteristic
398	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
399	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	8	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	16	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	4	8	no	—
412	C₂×Q₈	—	4	8	no	—
413	C₂×Q₈	—	4	16	no	—
414	C₂×Q₈	—	8	2	no	—
415	C₂×Q₈	C₁₁×#41	1	4	yes	—
416	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
417	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
418	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
419	C₂×D₄	C₁₁×Q₁₆	1	8	yes	complemented
420	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	8	4	no	—
433	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
436	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
439	Q₁₆	—	2	8	no	—
440	Q₁₆	—	4	8	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	4	no	—
444	C₂×C₈	—	4	8	no	—
445	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
446	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
447	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
460	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
461	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	C₂×D₄×C₁₁	1	2	yes	—
469	C₄²	C₂⁴×C₁₁	1	2	yes	—
470	C₁₁	C₂×#3299	1	1	yes	characteristic, direct product factor, Sylow
471	C₂³	—	2	4	no	—
472	C₂³	—	2	4	no	—
473	C₂³	C₂×C₁₁×Q₁₆	1	8	yes	—
474	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	4	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	4	16	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	4	no	—
485	Q₈	—	8	4	no	—
486	Q₈	C₂×C₁₁×#41	1	4	yes	—
487	D₄	C₂×C₁₁×Q₁₆	1	16	yes	complemented
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	16	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	8	8	no	—
507	C₂×C₄	C₂×C₁₁×Q₁₆	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
510	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
512	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
513	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
514	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	16	no	—
520	C₂²	—	2	4	no	—
521	C₂²	C₁₁×#546	1	2	yes	—
522	C₂²	C₂²×C₁₁×Q₁₆	1	8	yes	—
523	C₂²	C₂²×C₁₁×Q₁₆	1	2	yes	—
524	C₂²	C₁₁×#577	1	2	yes	—
525	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	2	no	—
534	C₄	C₁₁×#546	1	2	yes	—
535	C₄	C₂²×C₁₁×Q₁₆	1	4	yes	—
536	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
537	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂	—	2	8	no	—
539	C₂	C₁₁×#3299	1	4	yes	direct product factor
540	C₂	C₂×C₁₁×#546	1	1	yes	characteristic
541	C₂	C₂³×C₁₁×Q₁₆	1	1	yes	characteristic
542	C₂	C₂×C₁₁×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#3299	C₂	direct (N × H)
4. C₂×C₁₁×#487	C₂	semidirect
5. C₂×C₁₁×#484	C₂	semidirect
6. C₂×C₁₁×#477	C₂	semidirect
7. C₂×C₁₁×#467	C₂	semidirect
8. C₂×C₁₁×#462	C₂	semidirect
9. C₂×C₁₁×#451	C₂	semidirect
10. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
12. C₂²×C₁₁×#103	C₂	semidirect
35. C₁₁×#487	C₂²	semidirect
36. C₁₁×#484	C₂²	semidirect
37. C₁₁×#477	C₂²	semidirect
38. C₁₁×#467	C₂²	semidirect
39. C₁₁×#462	C₂²	semidirect
40. C₁₁×#451	C₂²	semidirect
41. C₄×C₁₁×Q₁₆	C₂²	semidirect
52. C₂×C₁₁×#103	C₂²	semidirect
128. C₂×#3299	C₁₁	direct (N × H)
149. C₂×D₄×C₁₁	Q₁₆	semidirect
202. #3299	C₂×C₁₁	direct (N × H)
203. C₂×#487	C₂×C₁₁	semidirect
204. C₂×#484	C₂×C₁₁	semidirect
205. C₂×#477	C₂×C₁₁	semidirect
206. C₂×#467	C₂×C₁₁	semidirect
207. C₂×#462	C₂×C₁₁	semidirect
208. C₂×#451	C₂×C₁₁	semidirect
209. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
211. C₂²×#103	C₂×C₁₁	semidirect
228. D₄×C₁₁	C₂×Q₁₆	semidirect
281. #487	C₂²×C₁₁	semidirect
282. #484	C₂²×C₁₁	semidirect
283. #477	C₂²×C₁₁	semidirect
284. #467	C₂²×C₁₁	semidirect
285. #462	C₂²×C₁₁	semidirect
286. #451	C₂²×C₁₁	semidirect
287. C₄×Q₁₆	C₂²×C₁₁	semidirect
298. C₂×#103	C₂²×C₁₁	semidirect
395. C₂×C₁₁	#3299	direct (N × H)
419. C₂×D₄	C₁₁×Q₁₆	semidirect
470. C₁₁	C₂×#3299	direct (N × H)
487. D₄	C₂×C₁₁×Q₁₆	semidirect
539. C₂	C₁₁×#3299	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×#554	2
C₂×D₄×Q₈×C₁₁	2
C₁₁×#3299	2
C₂×C₁₁×#487	2
C₂×C₁₁×#484	2
C₂×C₁₁×#477	2
C₂×C₁₁×#467	2
C₂×C₁₁×#462	2
C₂×C₁₁×#451	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₈×D₄×C₁₁	2
C₂²×C₁₁×#103	2
C₂×#3299	11

Subgroups — C2×C11×#3299 #14638310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3299 #14638310