Subgroups — C₂×C₁₁×#3375 #14638504

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3375	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#489	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#460	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₁₁×#559	—	2	4	no	—
16	C₁₁×#559	C₂²	1	8	yes	—
17	Q₈²×C₁₁	—	2	4	no	—
18	Q₈²×C₁₁	C₂²	1	8	yes	complemented
19	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₁×C₄⋊Q₈	—	2	2	no	—
21	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#124	—	2	1	no	—
25	C₂×C₁₁×#124	C₂²	1	2	yes	—
26	C₂×C₁₁×#123	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₁	—	2	1	no	—
33	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
34	C₁₁×#489	C₂²	1	16	yes	complemented
35	C₁₁×#486	C₂²	1	8	yes	—
36	C₁₁×#477	C₂²	1	8	yes	complemented
37	C₁₁×#474	C₂²	1	16	yes	complemented
38	C₁₁×#464	C₂²	1	16	yes	complemented
39	C₁₁×#460	C₂²	1	8	yes	—
40	C₁₁×#446	C₂²	1	8	yes	complemented
41	C₁₁×#440	C₂²	1	16	yes	complemented
42	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
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×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₁×#103	C₂²	1	2	yes	—
50	C₂×C₁₁×#102	C₂²	1	2	yes	—
51	C₂×C₁₁×#102	C₂²	1	2	yes	—
52	C₂×C₁₁×#102	C₂²	1	2	yes	—
53	C₂×C₁₁×#97	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	1	no	—
57	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₁	—	2	1	no	—
61	C₂²×D₄×C₁₁	—	2	1	no	—
62	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₁	—	2	2	no	—
64	C₂×C₁₁×Q₁₆	—	2	4	no	—
65	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
66	C₂×C₁₁×SD₁₆	—	2	8	no	—
67	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
71	C₁₁×C₄⋊Q₈	—	2	8	no	—
72	C₁₁×C₄⋊Q₈	—	2	16	no	—
73	C₁₁×C₄⋊Q₈	—	2	4	no	—
74	C₁₁×C₄⋊Q₈	—	2	2	no	—
75	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
76	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₁×#127	—	2	2	no	—
78	C₁₁×#127	C₂³	1	4	yes	—
79	C₁₁×#124	—	2	8	no	—
80	C₁₁×#124	—	2	4	no	—
81	C₁₁×#124	C₂³	1	8	yes	—
82	C₁₁×#123	—	2	16	no	—
83	C₄×Q₈×C₁₁	—	2	8	no	—
84	C₄×Q₈×C₁₁	—	2	4	no	—
85	C₄×Q₈×C₁₁	—	2	2	no	—
86	C₄×Q₈×C₁₁	—	2	2	no	—
87	C₄×Q₈×C₁₁	D₄	1	4	yes	—
88	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
89	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
90	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
91	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
92	C₄×D₄×C₁₁	—	2	8	no	—
93	C₄×D₄×C₁₁	—	2	4	no	—
94	C₄×D₄×C₁₁	C₂³	1	8	yes	—
95	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₁	—	2	1	no	—
109	C₂×C₄²×C₁₁	—	2	2	no	—
110	C₂×C₄²×C₁₁	—	2	1	no	—
111	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
113	C₁₁×#107	C₂³	1	4	yes	—
114	C₁₁×#107	C₂³	1	8	yes	—
115	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
116	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₁×#103	C₂³	1	4	yes	—
118	C₁₁×#103	C₂³	1	8	yes	—
119	C₁₁×#103	C₂³	1	4	yes	—
120	C₁₁×#102	C₂³	1	8	yes	—
121	C₁₁×#102	C₂³	1	8	yes	—
122	C₁₁×#102	C₂³	1	8	yes	—
123	C₁₁×#97	C₂³	1	8	yes	—
124	C₄×C₈×C₁₁	C₂³	1	4	yes	—
125	C₂×#3375	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₁	—	2	2	no	—
127	C₂×Q₈×C₁₁	—	2	4	no	—
128	C₂×Q₈×C₁₁	—	2	1	no	—
129	C₂×Q₈×C₁₁	—	2	1	no	—
130	C₂×Q₈×C₁₁	—	2	8	no	—
131	C₂×Q₈×C₁₁	—	2	4	no	—
132	C₂×Q₈×C₁₁	—	2	2	no	—
133	C₂×Q₈×C₁₁	—	2	2	no	—
134	C₂×Q₈×C₁₁	—	2	2	no	—
135	C₂×Q₈×C₁₁	—	8	4	no	—
136	C₂×Q₈×C₁₁	—	8	2	no	—
137	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₁₁	#41	1	4	yes	—
139	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
140	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₁	—	2	2	no	—
142	C₂×D₄×C₁₁	—	2	4	no	—
143	C₂×D₄×C₁₁	—	2	4	no	—
144	C₂×D₄×C₁₁	—	2	4	no	—
145	C₂×D₄×C₁₁	—	2	4	no	—
146	C₂×D₄×C₁₁	—	4	4	no	—
147	C₂×D₄×C₁₁	—	8	2	no	—
148	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₁	—	2	1	no	—
150	C₂²×C₄×C₁₁	—	2	1	no	—
151	C₂²×C₄×C₁₁	—	2	1	no	—
152	C₂²×C₄×C₁₁	—	2	2	no	—
153	C₂²×C₄×C₁₁	—	2	1	no	—
154	C₂²×C₄×C₁₁	—	2	8	no	—
155	C₂²×C₄×C₁₁	—	8	4	no	—
156	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
161	C₁₁×Q₁₆	—	2	8	no	—
162	C₁₁×SD₁₆	—	2	16	no	—
163	C₂×C₈×C₁₁	—	2	4	no	—
164	C₂×C₈×C₁₁	—	2	2	no	—
165	C₂×C₈×C₁₁	—	2	2	no	—
166	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
167	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
169	C₁₁×C₄⋊C₄	—	2	8	no	—
170	C₁₁×C₄⋊C₄	—	2	4	no	—
171	C₁₁×C₄⋊C₄	—	2	4	no	—
172	C₁₁×C₄⋊C₄	—	2	8	no	—
173	C₁₁×C₄⋊C₄	—	2	4	no	—
174	C₁₁×C₄⋊C₄	—	2	1	no	—
175	C₁₁×C₄⋊C₄	—	2	1	no	—
176	C₁₁×C₄⋊C₄	—	2	2	no	—
177	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
179	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
180	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
181	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₁×C₂²⋊C₄	—	2	8	no	—
183	C₁₁×C₂²⋊C₄	—	2	8	no	—
184	C₁₁×C₂²⋊C₄	—	2	8	no	—
185	C₄²×C₁₁	—	2	4	no	—
186	C₄²×C₁₁	—	2	8	no	—
187	C₄²×C₁₁	—	2	4	no	—
188	C₄²×C₁₁	C₂×D₄	1	4	yes	—
189	C₄²×C₁₁	C₂×D₄	1	2	yes	—
190	C₄²×C₁₁	C₂⁴	1	2	yes	—
191	C₄²×C₁₁	C₂⁴	1	4	yes	—
192	C₂×#559	C₂×C₁₁	1	1	yes	characteristic
193	C₂×Q₈²	C₂×C₁₁	1	1	yes	characteristic, complemented
194	#3375	C₂×C₁₁	1	16	yes	direct product factor
195	C₂×#489	C₂×C₁₁	1	2	yes	complemented
196	C₂×#486	C₂×C₁₁	1	1	yes	characteristic
197	C₂×#477	C₂×C₁₁	1	1	yes	characteristic, complemented
198	C₂×#474	C₂×C₁₁	1	2	yes	complemented
199	C₂×#464	C₂×C₁₁	1	2	yes	complemented
200	C₂×#460	C₂×C₁₁	1	1	yes	characteristic
201	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
202	C₂×#440	C₂×C₁₁	1	2	yes	complemented
203	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
204	C₂³×C₁₁	—	2	4	no	—
205	C₂³×C₁₁	—	4	4	no	—
206	C₂³×C₁₁	—	4	4	no	—
207	C₂³×C₁₁	—	4	4	no	—
208	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₁	—	2	4	no	—
210	Q₈×C₁₁	—	2	8	no	—
211	Q₈×C₁₁	—	2	2	no	—
212	Q₈×C₁₁	—	2	2	no	—
213	Q₈×C₁₁	—	2	2	no	—
214	Q₈×C₁₁	—	4	2	no	—
215	Q₈×C₁₁	—	8	8	no	—
216	Q₈×C₁₁	—	8	4	no	—
217	Q₈×C₁₁	C₂×#41	1	4	yes	—
218	D₄×C₁₁	—	2	4	no	—
219	D₄×C₁₁	—	2	4	no	—
220	D₄×C₁₁	—	4	4	no	—
221	D₄×C₁₁	—	4	8	no	—
222	D₄×C₁₁	—	8	4	no	—
223	C₂×C₄×C₁₁	—	2	4	no	—
224	C₂×C₄×C₁₁	—	2	4	no	—
225	C₂×C₄×C₁₁	—	2	4	no	—
226	C₂×C₄×C₁₁	—	2	2	no	—
227	C₂×C₄×C₁₁	—	2	2	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	2	no	—
230	C₂×C₄×C₁₁	—	2	4	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	4	2	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	4	2	no	—
235	C₂×C₄×C₁₁	—	4	4	no	—
236	C₂×C₄×C₁₁	—	8	8	no	—
237	C₂×C₄×C₁₁	#137	1	4	yes	—
238	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
245	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
246	C₈×C₁₁	—	2	4	no	—
247	C₈×C₁₁	—	2	2	no	—
248	C₈×C₁₁	—	2	2	no	—
249	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
250	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
251	#559	—	2	4	no	—
252	#559	C₂²×C₁₁	1	8	yes	—
253	Q₈²	—	2	4	no	—
254	Q₈²	C₂²×C₁₁	1	8	yes	complemented
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	—	2	2	no	—
257	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
259	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
260	C₂×#124	—	2	1	no	—
261	C₂×#124	C₂²×C₁₁	1	2	yes	—
262	C₂×#123	—	2	2	no	—
263	C₂×C₄×Q₈	—	2	1	no	—
264	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
267	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
270	#489	C₂²×C₁₁	1	16	yes	complemented
271	#486	C₂²×C₁₁	1	8	yes	—
272	#477	C₂²×C₁₁	1	8	yes	complemented
273	#474	C₂²×C₁₁	1	16	yes	complemented
274	#464	C₂²×C₁₁	1	16	yes	complemented
275	#460	C₂²×C₁₁	1	8	yes	—
276	#446	C₂²×C₁₁	1	8	yes	complemented
277	#440	C₂²×C₁₁	1	16	yes	complemented
278	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
279	C₂×#107	C₂²×C₁₁	1	2	yes	—
280	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
283	C₂×#103	C₂²×C₁₁	1	2	yes	—
284	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
285	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₁	1	2	yes	—
287	C₂×#102	C₂²×C₁₁	1	2	yes	—
288	C₂×#102	C₂²×C₁₁	1	2	yes	—
289	C₂×#97	C₂²×C₁₁	1	2	yes	—
290	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
291	C₂²×C₁₁	—	4	4	no	—
292	C₂²×C₁₁	—	4	4	no	—
293	C₂²×C₁₁	—	4	4	no	—
294	C₂²×C₁₁	—	8	8	no	—
295	C₂²×C₁₁	#548	1	2	yes	—
296	C₂²×C₁₁	C₂×#137	1	2	yes	—
297	C₂²×C₁₁	#576	1	2	yes	—
298	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₁₁	—	2	4	no	—
300	C₄×C₁₁	—	2	4	no	—
301	C₄×C₁₁	—	2	4	no	—
302	C₄×C₁₁	—	2	2	no	—
303	C₄×C₁₁	—	4	2	no	—
304	C₄×C₁₁	—	4	2	no	—
305	C₄×C₁₁	—	4	2	no	—
306	C₄×C₁₁	—	4	4	no	—
307	C₄×C₁₁	#548	1	2	yes	—
308	C₄×C₁₁	C₂×#137	1	4	yes	—
309	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
310	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂²×Q₈	—	2	2	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
319	C₂³×C₄	—	2	2	no	—
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
322	C₂×SD₁₆	—	2	8	no	—
323	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
324	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
325	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	8	no	—
328	C₄⋊Q₈	—	2	16	no	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
332	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
333	#127	—	2	2	no	—
334	#127	C₂³×C₁₁	1	4	yes	—
335	#124	—	2	8	no	—
336	#124	—	2	4	no	—
337	#124	C₂³×C₁₁	1	8	yes	—
338	#123	—	2	16	no	—
339	C₄×Q₈	—	2	8	no	—
340	C₄×Q₈	—	2	4	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	D₄×C₁₁	1	4	yes	—
344	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
345	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
346	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
347	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
348	C₄×D₄	—	2	8	no	—
349	C₄×D₄	—	2	4	no	—
350	C₄×D₄	C₂³×C₁₁	1	8	yes	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
357	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
368	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
369	#107	C₂³×C₁₁	1	4	yes	—
370	#107	C₂³×C₁₁	1	8	yes	—
371	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
372	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
373	#103	C₂³×C₁₁	1	4	yes	—
374	#103	C₂³×C₁₁	1	4	yes	—
375	#103	C₂³×C₁₁	1	8	yes	—
376	#102	C₂³×C₁₁	1	8	yes	—
377	#102	C₂³×C₁₁	1	8	yes	—
378	#102	C₂³×C₁₁	1	8	yes	—
379	#97	C₂³×C₁₁	1	8	yes	—
380	C₄×C₈	C₂³×C₁₁	1	4	yes	—
381	C₂×C₁₁	—	8	4	no	—
382	C₂×C₁₁	#3375	1	4	yes	direct product factor
383	C₂×C₁₁	C₂×#548	1	1	yes	characteristic
384	C₂×C₁₁	C₂²×#137	1	1	yes	characteristic
385	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
386	C₂⁴	—	2	2	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	8	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	8	4	no	—
396	C₂×Q₈	—	8	2	no	—
397	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
398	C₂×Q₈	C₁₁×#41	1	4	yes	—
399	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
400	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	8	4	no	—
416	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
421	Q₁₆	—	2	8	no	—
422	SD₁₆	—	2	16	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
427	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
428	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
439	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
440	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
441	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	8	no	—
447	C₄²	—	2	4	no	—
448	C₄²	C₂×D₄×C₁₁	1	4	yes	—
449	C₄²	C₂×D₄×C₁₁	1	2	yes	—
450	C₄²	C₂⁴×C₁₁	1	2	yes	—
451	C₄²	C₂⁴×C₁₁	1	4	yes	—
452	C₁₁	C₂×#3375	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
458	Q₈	—	2	4	no	—
459	Q₈	—	2	8	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	8	8	no	—
465	Q₈	—	8	4	no	—
466	Q₈	C₂×C₁₁×#41	1	4	yes	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	8	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	8	no	—
486	C₂×C₄	C₁₁×#137	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
488	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
489	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
492	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
493	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
495	C₈	—	2	4	no	—
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	8	8	no	—
502	C₂²	C₁₁×#548	1	2	yes	—
503	C₂²	C₂×C₁₁×#137	1	2	yes	—
504	C₂²	C₁₁×#576	1	2	yes	—
505	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	4	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	4	no	—
514	C₄	C₁₁×#548	1	2	yes	—
515	C₄	C₂×C₁₁×#137	1	4	yes	—
516	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
517	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂	—	8	4	no	—
519	C₂	C₁₁×#3375	1	4	yes	direct product factor
520	C₂	C₂×C₁₁×#548	1	1	yes	characteristic
521	C₂	C₂²×C₁₁×#137	1	1	yes	characteristic
522	C₂	C₂×C₁₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈²×C₁₁	C₂	semidirect
3. C₁₁×#3375	C₂	direct (N × H)
4. C₂×C₁₁×#489	C₂	semidirect
6. C₂×C₁₁×#477	C₂	semidirect
7. C₂×C₁₁×#474	C₂	semidirect
8. C₂×C₁₁×#464	C₂	semidirect
10. C₂×C₁₁×#446	C₂	semidirect
11. C₂×C₁₁×#440	C₂	semidirect
12. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
18. Q₈²×C₁₁	C₂²	semidirect
34. C₁₁×#489	C₂²	semidirect
36. C₁₁×#477	C₂²	semidirect
37. C₁₁×#474	C₂²	semidirect
38. C₁₁×#464	C₂²	semidirect
40. C₁₁×#446	C₂²	semidirect
41. C₁₁×#440	C₂²	semidirect
42. C₄×C₁₁×Q₁₆	C₂²	semidirect
125. C₂×#3375	C₁₁	direct (N × H)
193. C₂×Q₈²	C₂×C₁₁	semidirect
194. #3375	C₂×C₁₁	direct (N × H)
195. C₂×#489	C₂×C₁₁	semidirect
197. C₂×#477	C₂×C₁₁	semidirect
198. C₂×#474	C₂×C₁₁	semidirect
199. C₂×#464	C₂×C₁₁	semidirect
201. C₂×#446	C₂×C₁₁	semidirect
202. C₂×#440	C₂×C₁₁	semidirect
203. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
254. Q₈²	C₂²×C₁₁	semidirect
270. #489	C₂²×C₁₁	semidirect
272. #477	C₂²×C₁₁	semidirect
273. #474	C₂²×C₁₁	semidirect
274. #464	C₂²×C₁₁	semidirect
276. #446	C₂²×C₁₁	semidirect
277. #440	C₂²×C₁₁	semidirect
278. C₄×Q₁₆	C₂²×C₁₁	semidirect
382. C₂×C₁₁	#3375	direct (N × H)
452. C₁₁	C₂×#3375	direct (N × H)
519. C₂	C₁₁×#3375	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×#559	2
C₂×Q₈²×C₁₁	2
C₁₁×#3375	2
C₂×C₁₁×#489	2
C₂×C₁₁×#486	2
C₂×C₁₁×#477	2
C₂×C₁₁×#474	2
C₂×C₁₁×#464	2
C₂×C₁₁×#460	2
C₂×C₁₁×#446	2
C₂×C₁₁×#440	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×#3375	11

Subgroups — C2×C11×#3375 #14638504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3375 #14638504