Subgroups — C₂×C₁₁×#3298 #14638309

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#547	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3298	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#483	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#448	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#103	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₁×#41	—	2	1	no	—
14	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
15	C₂²×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
17	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
18	D₄×Q₈×C₁₁	—	2	4	no	—
19	D₄×Q₈×C₁₁	C₂²	1	8	yes	complemented
20	C₁₁×#547	—	2	4	no	—
21	C₁₁×#547	C₂²	1	8	yes	—
22	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#123	—	2	2	no	—
26	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
28	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₁×#121	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₁	—	2	1	no	—
32	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
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×#483	C₂²	1	16	yes	complemented
37	C₁₁×#475	C₂²	1	8	yes	complemented
38	C₁₁×#465	C₂²	1	16	yes	complemented
39	C₁₁×#461	C₂²	1	8	yes	complemented
40	C₁₁×#448	C₂²	1	16	yes	complemented
41	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₁	C₂²	1	8	yes	complemented
43	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
44	C₂×C₁₁×#106	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	2	yes	—
51	C₂×C₁₁×#103	C₂²	1	16	yes	complemented
52	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
55	C₂×C₁₁×#41	—	2	8	no	—
56	C₂×C₁₁×#41	—	4	8	no	—
57	C₂²×Q₈×C₁₁	—	2	2	no	—
58	C₂²×Q₈×C₁₁	—	2	1	no	—
59	C₂²×Q₈×C₁₁	—	2	4	no	—
60	C₂²×Q₈×C₁₁	—	2	8	no	—
61	C₂²×Q₈×C₁₁	—	4	4	no	—
62	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
63	C₂²×Q₈×C₁₁	C₂³	1	8	yes	—
64	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₁	—	2	2	no	—
66	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₁	—	2	2	no	—
69	C₂³×C₄×C₁₁	—	2	2	no	—
70	C₂³×C₄×C₁₁	—	2	1	no	—
71	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
72	C₂×C₁₁×SD₁₆	—	2	4	no	—
73	C₂×C₁₁×SD₁₆	—	4	4	no	—
74	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
76	C₂²×C₈×C₁₁	—	4	4	no	—
77	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
81	C₁₁×C₄⋊Q₈	—	2	8	no	—
82	C₁₁×C₄⋊Q₈	—	2	2	no	—
83	C₁₁×C₄⋊Q₈	—	2	2	no	—
84	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₁×#123	—	2	16	no	—
87	C₁₁×C₂²⋊Q₈	—	2	4	no	—
88	C₁₁×C₂²⋊Q₈	—	2	8	no	—
89	C₁₁×C₂²⋊Q₈	—	2	16	no	—
90	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
91	C₁₁×#121	—	2	4	no	—
92	C₁₁×#121	C₂³	1	8	yes	—
93	C₄×Q₈×C₁₁	—	2	2	no	—
94	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
95	C₄×D₄×C₁₁	—	2	8	no	—
96	C₄×D₄×C₁₁	—	2	2	no	—
97	C₄×D₄×C₁₁	D₄	1	4	yes	—
98	C₄×D₄×C₁₁	C₂³	1	4	yes	—
99	C₄×D₄×C₁₁	C₂³	1	4	yes	—
100	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
102	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
116	C₂×C₄²×C₁₁	—	2	1	no	—
117	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
118	C₁₁×#106	C₂³	1	4	yes	—
119	C₁₁×#106	C₂³	1	8	yes	—
120	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₁×#103	C₂³	1	4	yes	—
122	C₁₁×#103	C₂³	1	8	yes	—
123	C₁₁×#103	C₂³	1	8	yes	—
124	C₁₁×#103	C₂³	1	8	yes	—
125	C₁₁×#103	C₂³	1	8	yes	—
126	C₁₁×#102	C₂³	1	4	yes	—
127	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₈×C₁₁	C₂³	1	4	yes	—
129	C₂×#3298	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₁	—	2	1	no	—
131	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
132	C₁₁×#41	—	4	32	no	—
133	C₂×Q₈×C₁₁	—	2	1	no	—
134	C₂×Q₈×C₁₁	—	2	8	no	—
135	C₂×Q₈×C₁₁	—	2	2	no	—
136	C₂×Q₈×C₁₁	—	2	4	no	—
137	C₂×Q₈×C₁₁	—	2	2	no	—
138	C₂×Q₈×C₁₁	—	2	16	no	—
139	C₂×Q₈×C₁₁	—	2	4	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	—	4	4	no	—
145	C₂×Q₈×C₁₁	#41	1	4	yes	complemented
146	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
147	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₁	—	2	8	no	—
149	C₂×D₄×C₁₁	—	2	1	no	—
150	C₂×D₄×C₁₁	—	2	2	no	—
151	C₂×D₄×C₁₁	—	2	2	no	—
152	C₂×D₄×C₁₁	—	4	8	no	—
153	C₂×D₄×C₁₁	SD₁₆	1	8	yes	complemented
154	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
155	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₁	—	2	1	no	—
157	C₂²×C₄×C₁₁	—	2	4	no	—
158	C₂²×C₄×C₁₁	—	2	4	no	—
159	C₂²×C₄×C₁₁	—	2	8	no	—
160	C₂²×C₄×C₁₁	—	2	8	no	—
161	C₂²×C₄×C₁₁	—	2	1	no	—
162	C₂²×C₄×C₁₁	—	2	2	no	—
163	C₂²×C₄×C₁₁	—	2	1	no	—
164	C₂²×C₄×C₁₁	—	2	2	no	—
165	C₂²×C₄×C₁₁	—	2	4	no	—
166	C₂²×C₄×C₁₁	—	4	8	no	—
167	C₂²×C₄×C₁₁	—	4	8	no	—
168	C₂²×C₄×C₁₁	—	4	4	no	—
169	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
175	C₁₁×SD₁₆	—	2	8	no	—
176	C₁₁×SD₁₆	—	4	8	no	—
177	C₂×C₈×C₁₁	—	2	2	no	—
178	C₂×C₈×C₁₁	—	2	2	no	—
179	C₂×C₈×C₁₁	—	2	4	no	—
180	C₂×C₈×C₁₁	—	4	8	no	—
181	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
182	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
183	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
184	C₁₁×C₄⋊C₄	—	2	1	no	—
185	C₁₁×C₄⋊C₄	—	2	2	no	—
186	C₁₁×C₄⋊C₄	—	2	8	no	—
187	C₁₁×C₄⋊C₄	—	2	4	no	—
188	C₁₁×C₄⋊C₄	—	2	4	no	—
189	C₁₁×C₄⋊C₄	—	2	4	no	—
190	C₁₁×C₄⋊C₄	—	2	8	no	—
191	C₁₁×C₄⋊C₄	—	2	4	no	—
192	C₁₁×C₄⋊C₄	—	2	1	no	—
193	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₁×C₂²⋊C₄	—	2	8	no	—
198	C₁₁×C₂²⋊C₄	—	2	4	no	—
199	C₁₁×C₂²⋊C₄	—	2	8	no	—
200	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	C₂×D₄	1	2	yes	—
203	C₄²×C₁₁	C₂⁴	1	2	yes	—
204	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
205	C₂×#547	C₂×C₁₁	1	1	yes	characteristic
206	#3298	C₂×C₁₁	1	16	yes	direct product factor
207	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
208	C₂×#483	C₂×C₁₁	1	2	yes	complemented
209	C₂×#475	C₂×C₁₁	1	1	yes	characteristic, complemented
210	C₂×#465	C₂×C₁₁	1	2	yes	complemented
211	C₂×#461	C₂×C₁₁	1	1	yes	characteristic, complemented
212	C₂×#448	C₂×C₁₁	1	2	yes	complemented
213	C₂×C₄×SD₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
214	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂²×#103	C₂×C₁₁	1	2	yes	complemented
216	C₂³×C₁₁	—	2	4	no	—
217	C₂³×C₁₁	—	2	4	no	—
218	C₂³×C₁₁	—	2	2	no	—
219	C₂³×C₁₁	—	4	2	no	—
220	C₂³×C₁₁	—	4	2	no	—
221	C₂³×C₁₁	—	4	2	no	—
222	C₂³×C₁₁	C₂×SD₁₆	1	8	yes	—
223	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
224	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₁	—	2	4	no	—
226	Q₈×C₁₁	—	2	2	no	—
227	Q₈×C₁₁	—	2	4	no	—
228	Q₈×C₁₁	—	2	4	no	—
229	Q₈×C₁₁	—	4	16	no	—
230	Q₈×C₁₁	—	4	4	no	—
231	Q₈×C₁₁	—	4	8	no	—
232	Q₈×C₁₁	C₂×#41	1	4	yes	complemented
233	D₄×C₁₁	—	2	2	no	—
234	D₄×C₁₁	—	2	2	no	—
235	D₄×C₁₁	—	4	16	no	—
236	D₄×C₁₁	—	4	2	no	—
237	D₄×C₁₁	C₂×SD₁₆	1	16	yes	complemented
238	C₂×C₄×C₁₁	—	2	4	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	8	no	—
243	C₂×C₄×C₁₁	—	2	4	no	—
244	C₂×C₄×C₁₁	—	2	4	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	4	no	—
247	C₂×C₄×C₁₁	—	2	2	no	—
248	C₂×C₄×C₁₁	—	2	4	no	—
249	C₂×C₄×C₁₁	—	4	16	no	—
250	C₂×C₄×C₁₁	—	4	4	no	—
251	C₂×C₄×C₁₁	—	4	2	no	—
252	C₂×C₄×C₁₁	—	4	4	no	—
253	C₂×C₄×C₁₁	—	4	16	no	—
254	C₂×C₄×C₁₁	—	4	2	no	—
255	C₂×C₄×C₁₁	—	4	8	no	—
256	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
257	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
259	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
262	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
263	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
264	C₈×C₁₁	—	2	2	no	—
265	C₈×C₁₁	—	2	2	no	—
266	C₈×C₁₁	—	2	4	no	—
267	C₂²×#41	—	2	1	no	—
268	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
269	C₂²×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
270	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
271	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
272	D₄×Q₈	—	2	4	no	—
273	D₄×Q₈	C₂²×C₁₁	1	8	yes	complemented
274	#547	—	2	4	no	—
275	#547	C₂²×C₁₁	1	8	yes	—
276	C₂×C₄⋊Q₈	—	2	1	no	—
277	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×#123	—	2	2	no	—
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₂²⋊Q₈	—	2	2	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
283	C₂×#121	C₂²×C₁₁	1	2	yes	—
284	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
285	C₂×C₄×D₄	—	2	1	no	—
286	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
289	#487	C₂²×C₁₁	1	8	yes	complemented
290	#483	C₂²×C₁₁	1	16	yes	complemented
291	#475	C₂²×C₁₁	1	8	yes	complemented
292	#465	C₂²×C₁₁	1	16	yes	complemented
293	#461	C₂²×C₁₁	1	8	yes	complemented
294	#448	C₂²×C₁₁	1	16	yes	complemented
295	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
296	C₈×D₄	C₂²×C₁₁	1	8	yes	complemented
297	C₂×#106	C₂²×C₁₁	1	2	yes	—
298	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
300	C₂×#103	C₂²×C₁₁	1	2	yes	—
301	C₂×#103	C₂²×C₁₁	1	2	yes	—
302	C₂×#103	C₂²×C₁₁	1	2	yes	—
303	C₂×#103	C₂²×C₁₁	1	2	yes	—
304	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₁	1	16	yes	complemented
306	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
308	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
309	C₂²×C₁₁	—	2	4	no	—
310	C₂²×C₁₁	—	2	16	no	—
311	C₂²×C₁₁	—	2	4	no	—
312	C₂²×C₁₁	—	4	2	no	—
313	C₂²×C₁₁	—	4	2	no	—
314	C₂²×C₁₁	—	4	2	no	—
315	C₂²×C₁₁	—	8	4	no	—
316	C₂²×C₁₁	#546	1	2	yes	—
317	C₂²×C₁₁	C₂²×SD₁₆	1	8	yes	—
318	C₂²×C₁₁	C₂²×SD₁₆	1	2	yes	—
319	C₂²×C₁₁	#578	1	2	yes	—
320	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₁₁	—	2	4	no	—
322	C₄×C₁₁	—	2	4	no	—
323	C₄×C₁₁	—	2	2	no	—
324	C₄×C₁₁	—	4	4	no	—
325	C₄×C₁₁	—	4	2	no	—
326	C₄×C₁₁	—	4	4	no	—
327	C₄×C₁₁	—	4	2	no	—
328	C₄×C₁₁	#546	1	2	yes	—
329	C₄×C₁₁	C₂²×SD₁₆	1	4	yes	—
330	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
331	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×#41	—	2	8	no	—
333	C₂×#41	—	4	8	no	—
334	C₂²×Q₈	—	2	2	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	4	no	—
337	C₂²×Q₈	—	2	8	no	—
338	C₂²×Q₈	—	4	4	no	—
339	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
340	C₂²×Q₈	C₂³×C₁₁	1	8	yes	—
341	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	4	4	no	—
351	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
352	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
353	C₂²×C₈	—	4	4	no	—
354	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
356	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
358	C₄⋊Q₈	—	2	8	no	—
359	C₄⋊Q₈	—	2	2	no	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
362	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
363	#123	—	2	16	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	—	2	8	no	—
366	C₂²⋊Q₈	—	2	16	no	—
367	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
368	#121	—	2	4	no	—
369	#121	C₂³×C₁₁	1	8	yes	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
372	C₄×D₄	—	2	8	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	D₄×C₁₁	1	4	yes	—
375	C₄×D₄	C₂³×C₁₁	1	4	yes	—
376	C₄×D₄	C₂³×C₁₁	1	4	yes	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
395	#106	C₂³×C₁₁	1	4	yes	—
396	#106	C₂³×C₁₁	1	8	yes	—
397	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
398	#103	C₂³×C₁₁	1	4	yes	—
399	#103	C₂³×C₁₁	1	8	yes	—
400	#103	C₂³×C₁₁	1	8	yes	—
401	#103	C₂³×C₁₁	1	8	yes	—
402	#103	C₂³×C₁₁	1	8	yes	—
403	#102	C₂³×C₁₁	1	4	yes	—
404	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
405	C₄×C₈	C₂³×C₁₁	1	4	yes	—
406	C₂×C₁₁	—	2	8	no	—
407	C₂×C₁₁	—	8	2	no	—
408	C₂×C₁₁	#3298	1	4	yes	direct product factor
409	C₂×C₁₁	C₂×#546	1	1	yes	characteristic
410	C₂×C₁₁	C₂³×SD₁₆	1	1	yes	characteristic
411	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
412	C₂⁴	—	2	1	no	—
413	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
414	#41	—	4	32	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	8	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	16	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	4	8	no	—
424	C₂×Q₈	—	4	8	no	—
425	C₂×Q₈	—	4	16	no	—
426	C₂×Q₈	—	4	4	no	—
427	C₂×Q₈	C₁₁×#41	1	4	yes	complemented
428	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
429	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	C₁₁×SD₁₆	1	8	yes	complemented
436	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
437	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	4	8	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
457	SD₁₆	—	2	8	no	—
458	SD₁₆	—	4	8	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	4	8	no	—
463	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
464	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
465	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
477	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
478	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
483	C₄²	—	2	4	no	—
484	C₄²	C₂×D₄×C₁₁	1	2	yes	—
485	C₄²	C₂⁴×C₁₁	1	2	yes	—
486	C₁₁	C₂×#3298	1	1	yes	characteristic, direct product factor, Sylow
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	C₂×C₁₁×SD₁₆	1	8	yes	—
494	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
495	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
496	Q₈	—	2	4	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	2	4	no	—
500	Q₈	—	4	16	no	—
501	Q₈	—	4	4	no	—
502	Q₈	—	4	8	no	—
503	Q₈	C₂×C₁₁×#41	1	4	yes	complemented
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	4	16	no	—
507	D₄	—	4	2	no	—
508	D₄	C₂×C₁₁×SD₁₆	1	16	yes	complemented
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	4	16	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	16	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
528	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
530	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
532	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
533	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
534	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	16	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	4	no	—
545	C₂²	C₁₁×#546	1	2	yes	—
546	C₂²	C₂²×C₁₁×SD₁₆	1	8	yes	—
547	C₂²	C₂²×C₁₁×SD₁₆	1	2	yes	—
548	C₂²	C₁₁×#578	1	2	yes	—
549	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	2	no	—
557	C₄	C₁₁×#546	1	2	yes	—
558	C₄	C₂²×C₁₁×SD₁₆	1	4	yes	—
559	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
560	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂	—	2	8	no	—
562	C₂	—	8	2	no	—
563	C₂	C₁₁×#3298	1	4	yes	direct product factor
564	C₂	C₂×C₁₁×#546	1	1	yes	characteristic
565	C₂	C₂³×C₁₁×SD₁₆	1	1	yes	characteristic
566	C₂	C₂×C₁₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#547	C₂
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
1. C₂×D₄×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#3298	C₂	direct (N × H)
4. C₂×C₁₁×#487	C₂	semidirect
5. C₂×C₁₁×#483	C₂	semidirect
6. C₂×C₁₁×#475	C₂	semidirect
7. C₂×C₁₁×#465	C₂	semidirect
8. C₂×C₁₁×#461	C₂	semidirect
9. C₂×C₁₁×#448	C₂	semidirect
10. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
11. C₂×C₈×D₄×C₁₁	C₂	semidirect
12. C₂²×C₁₁×#103	C₂	semidirect
19. D₄×Q₈×C₁₁	C₂²	semidirect
35. C₁₁×#487	C₂²	semidirect
36. C₁₁×#483	C₂²	semidirect
37. C₁₁×#475	C₂²	semidirect
38. C₁₁×#465	C₂²	semidirect
39. C₁₁×#461	C₂²	semidirect
40. C₁₁×#448	C₂²	semidirect
41. C₄×C₁₁×SD₁₆	C₂²	semidirect
42. C₈×D₄×C₁₁	C₂²	semidirect
51. C₂×C₁₁×#103	C₂²	semidirect
129. C₂×#3298	C₁₁	direct (N × H)
145. C₂×Q₈×C₁₁	#41	semidirect
153. C₂×D₄×C₁₁	SD₁₆	semidirect
204. C₂×D₄×Q₈	C₂×C₁₁	semidirect
206. #3298	C₂×C₁₁	direct (N × H)
207. C₂×#487	C₂×C₁₁	semidirect
208. C₂×#483	C₂×C₁₁	semidirect
209. C₂×#475	C₂×C₁₁	semidirect
210. C₂×#465	C₂×C₁₁	semidirect
211. C₂×#461	C₂×C₁₁	semidirect
212. C₂×#448	C₂×C₁₁	semidirect
213. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
214. C₂×C₈×D₄	C₂×C₁₁	semidirect
215. C₂²×#103	C₂×C₁₁	semidirect
232. Q₈×C₁₁	C₂×#41	semidirect
237. D₄×C₁₁	C₂×SD₁₆	semidirect
273. D₄×Q₈	C₂²×C₁₁	semidirect
289. #487	C₂²×C₁₁	semidirect
290. #483	C₂²×C₁₁	semidirect
291. #475	C₂²×C₁₁	semidirect
292. #465	C₂²×C₁₁	semidirect
293. #461	C₂²×C₁₁	semidirect
294. #448	C₂²×C₁₁	semidirect
295. C₄×SD₁₆	C₂²×C₁₁	semidirect
296. C₈×D₄	C₂²×C₁₁	semidirect
305. C₂×#103	C₂²×C₁₁	semidirect
408. C₂×C₁₁	#3298	direct (N × H)
427. C₂×Q₈	C₁₁×#41	semidirect
435. C₂×D₄	C₁₁×SD₁₆	semidirect
486. C₁₁	C₂×#3298	direct (N × H)
503. Q₈	C₂×C₁₁×#41	semidirect
508. D₄	C₂×C₁₁×SD₁₆	semidirect
563. C₂	C₁₁×#3298	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×D₄×Q₈×C₁₁	2
C₂×C₁₁×#547	2
C₁₁×#3298	2
C₂×C₁₁×#487	2
C₂×C₁₁×#483	2
C₂×C₁₁×#475	2
C₂×C₁₁×#465	2
C₂×C₁₁×#461	2
C₂×C₁₁×#448	2
C₂×C₄×C₁₁×SD₁₆	2
C₂×C₈×D₄×C₁₁	2
C₂²×C₁₁×#103	2
C₂×#3298	11

Subgroups — C2×C11×#3298 #14638309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3298 #14638309