Subgroups — C₂×C₁₁×#1665 #14596291

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1665	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×SD₁₆	—	2	1	no	—
10	C₂²×C₁₁×SD₁₆	—	2	1	no	—
11	C₂²×C₁₁×D₈	—	2	1	no	—
12	C₂³×C₈×C₁₁	—	2	1	no	—
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#492	—	2	2	no	—
17	C₁₁×#492	C₂²	1	4	yes	complemented
18	C₁₁×#474	—	2	2	no	—
19	C₁₁×#474	C₂²	1	4	yes	complemented
20	C₁₁×#459	—	2	2	no	—
21	C₁₁×#459	C₂²	1	4	yes	—
22	C₈×D₄×C₁₁	—	2	2	no	—
23	C₈×D₄×C₁₁	C₂²	1	4	yes	complemented
24	C₂×C₁₁×#107	—	2	1	no	—
25	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#102	—	2	1	no	—
29	C₂×C₁₁×#102	—	2	1	no	—
30	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#334	C₂²	1	4	yes	complemented
33	C₁₁×#332	C₂²	1	4	yes	complemented
34	C₁₁×#331	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₁	—	2	1	no	—
36	C₂²×D₄×C₁₁	—	2	1	no	—
37	C₂²×D₄×C₁₁	—	2	1	no	—
38	C₂²×D₄×C₁₁	—	2	1	no	—
39	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁	—	2	1	no	—
41	C₂×C₁₁×SD₁₆	—	2	4	no	—
42	C₂×C₁₁×SD₁₆	—	2	4	no	—
43	C₂×C₁₁×SD₁₆	—	4	4	no	—
44	C₂×C₁₁×SD₁₆	—	4	4	no	—
45	C₂×C₁₁×D₈	—	2	4	no	—
46	C₂×C₁₁×D₈	—	4	4	no	—
47	C₂²×C₈×C₁₁	—	2	1	no	—
48	C₂²×C₈×C₁₁	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	—	2	4	no	—
51	C₂²×C₈×C₁₁	—	4	4	no	—
52	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
54	C₁₁×C₄⋊Q₈	—	2	1	no	—
55	C₁₁×C₄⋊Q₈	—	2	1	no	—
56	C₁₁×C₄⋊Q₈	—	2	1	no	—
57	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₁×#127	—	2	1	no	—
59	C₁₁×#127	—	2	1	no	—
60	C₁₁×#127	—	2	1	no	—
61	C₁₁×#127	C₂³	1	2	yes	—
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	D₄	1	2	yes	—
65	C₄×D₄×C₁₁	C₂³	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#107	—	2	4	no	—
72	C₁₁×C₄⋊C₈	—	2	1	no	—
73	C₁₁×C₄⋊C₈	—	2	1	no	—
74	C₁₁×C₄⋊C₈	—	2	1	no	—
75	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₁₁×#102	—	2	4	no	—
79	C₁₁×#102	—	2	4	no	—
80	C₁₁×C₂²⋊C₈	—	2	4	no	—
81	C₄×C₈×C₁₁	D₄	1	2	yes	—
82	C₄×C₈×C₁₁	C₂³	1	2	yes	—
83	C₂×#1665	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	—	2	1	no	—
85	C₂⁴×C₁₁	—	4	1	no	—
86	C₂×Q₈×C₁₁	—	2	2	no	—
87	C₂×Q₈×C₁₁	—	4	1	no	—
88	C₂×Q₈×C₁₁	—	4	2	no	—
89	C₂×Q₈×C₁₁	—	4	2	no	—
90	C₂×D₄×C₁₁	—	2	1	no	—
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	—	4	1	no	—
96	C₂×D₄×C₁₁	—	4	1	no	—
97	C₂×D₄×C₁₁	—	4	1	no	—
98	C₂×D₄×C₁₁	—	4	2	no	—
99	C₂×D₄×C₁₁	—	4	2	no	—
100	C₂×D₄×C₁₁	—	4	2	no	—
101	C₂×D₄×C₁₁	—	4	2	no	—
102	C₂×D₄×C₁₁	—	8	2	no	—
103	C₂×D₄×C₁₁	SD₁₆	1	4	yes	complemented
104	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	4	2	no	—
109	C₂²×C₄×C₁₁	—	4	2	no	—
110	C₂²×C₄×C₁₁	—	4	1	no	—
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
114	C₁₁×SD₁₆	—	4	8	no	—
115	C₁₁×SD₁₆	—	4	8	no	—
116	C₁₁×D₈	—	4	8	no	—
117	C₂×C₈×C₁₁	—	2	2	no	—
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	4	8	no	—
122	C₂×C₈×C₁₁	—	4	2	no	—
123	C₂×C₈×C₁₁	—	4	2	no	—
124	C₂×C₈×C₁₁	—	4	2	no	—
125	C₂×C₈×C₁₁	D₈	1	4	yes	complemented
126	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
128	C₁₁×C₄⋊C₄	—	2	1	no	—
129	C₁₁×C₄⋊C₄	—	2	2	no	—
130	C₁₁×C₄⋊C₄	—	2	2	no	—
131	C₁₁×C₄⋊C₄	—	4	1	no	—
132	C₁₁×C₄⋊C₄	—	4	1	no	—
133	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₁₁×C₂²⋊C₄	—	2	2	no	—
135	C₁₁×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₁	#41	1	1	yes	characteristic
139	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
140	C₂×#492	C₂×C₁₁	1	1	yes	characteristic, complemented
141	C₂×#474	C₂×C₁₁	1	1	yes	characteristic, complemented
142	C₂×#459	C₂×C₁₁	1	1	yes	characteristic
143	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#1665	C₂×C₁₁	1	8	yes	direct product factor
145	C₂×#334	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂×#332	C₂×C₁₁	1	1	yes	characteristic, complemented
147	C₂×#331	C₂×C₁₁	1	1	yes	characteristic, complemented
148	C₂³×C₁₁	—	2	2	no	—
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	2	no	—
152	C₂³×C₁₁	—	4	2	no	—
153	C₂³×C₁₁	—	8	2	no	—
154	C₂³×C₁₁	—	8	2	no	—
155	C₂³×C₁₁	—	8	2	no	—
156	C₂³×C₁₁	#121	1	1	yes	characteristic
157	Q₈×C₁₁	—	4	2	no	—
158	Q₈×C₁₁	—	4	2	no	—
159	Q₈×C₁₁	—	8	2	no	—
160	D₄×C₁₁	—	2	2	no	—
161	D₄×C₁₁	—	2	4	no	—
162	D₄×C₁₁	—	4	2	no	—
163	D₄×C₁₁	—	4	2	no	—
164	D₄×C₁₁	—	4	2	no	—
165	D₄×C₁₁	—	4	2	no	—
166	D₄×C₁₁	—	8	2	no	—
167	D₄×C₁₁	—	8	2	no	—
168	D₄×C₁₁	—	8	2	no	—
169	D₄×C₁₁	—	8	2	no	—
170	D₄×C₁₁	C₂×SD₁₆	1	4	yes	complemented
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	4	2	no	—
174	C₂×C₄×C₁₁	—	4	2	no	—
175	C₂×C₄×C₁₁	—	4	2	no	—
176	C₂×C₄×C₁₁	—	4	4	no	—
177	C₂×C₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	—	8	2	no	—
179	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₁₁	#135	1	2	yes	—
185	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₁	—	2	2	no	—
190	C₈×C₁₁	—	4	2	no	—
191	C₈×C₁₁	—	4	2	no	—
192	C₈×C₁₁	—	4	2	no	—
193	C₈×C₁₁	C₂×D₈	1	4	yes	complemented
194	C₂²×SD₁₆	—	2	1	no	—
195	C₂²×SD₁₆	—	2	1	no	—
196	C₂²×D₈	—	2	1	no	—
197	C₂³×C₈	—	2	1	no	—
198	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
201	#492	—	2	2	no	—
202	#492	C₂²×C₁₁	1	4	yes	complemented
203	#474	—	2	2	no	—
204	#474	C₂²×C₁₁	1	4	yes	complemented
205	#459	—	2	2	no	—
206	#459	C₂²×C₁₁	1	4	yes	—
207	C₈×D₄	—	2	2	no	—
208	C₈×D₄	C₂²×C₁₁	1	4	yes	complemented
209	C₂×#107	—	2	1	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
213	C₂×#102	—	2	1	no	—
214	C₂×#102	—	2	1	no	—
215	C₂×C₂²⋊C₈	—	2	1	no	—
216	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
217	#334	C₂²×C₁₁	1	4	yes	complemented
218	#332	C₂²×C₁₁	1	4	yes	complemented
219	#331	C₂²×C₁₁	1	4	yes	complemented
220	C₂²×C₁₁	—	2	4	no	—
221	C₂²×C₁₁	—	4	8	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	—	4	2	no	—
224	C₂²×C₁₁	—	8	2	no	—
225	C₂²×C₁₁	—	8	2	no	—
226	C₂²×C₁₁	—	8	2	no	—
227	C₂²×C₁₁	—	16	4	no	—
228	C₂²×C₁₁	#459	1	2	yes	—
229	C₂²×C₁₁	#465	1	2	yes	—
230	C₂²×C₁₁	#471	1	2	yes	—
231	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
232	C₄×C₁₁	—	2	1	no	—
233	C₄×C₁₁	—	2	1	no	—
234	C₄×C₁₁	—	4	2	no	—
235	C₄×C₁₁	—	8	2	no	—
236	C₄×C₁₁	#459	1	2	yes	—
237	C₄×C₁₁	#465	1	2	yes	—
238	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
239	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
240	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
241	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂×SD₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	4	4	no	—
251	C₂×SD₁₆	—	4	4	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	4	4	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	4	no	—
258	C₂²×C₈	—	4	4	no	—
259	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
260	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	C₂³×C₁₁	1	2	yes	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	D₄×C₁₁	1	2	yes	—
272	C₄×D₄	C₂³×C₁₁	1	2	yes	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
278	#107	—	2	4	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
283	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
284	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
285	#102	—	2	4	no	—
286	#102	—	2	4	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₄×C₈	D₄×C₁₁	1	2	yes	—
289	C₄×C₈	C₂³×C₁₁	1	2	yes	—
290	C₂×C₁₁	—	4	4	no	—
291	C₂×C₁₁	—	16	2	no	—
292	C₂×C₁₁	#1665	1	4	yes	direct product factor
293	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
294	C₂×C₁₁	C₂×#465	1	1	yes	characteristic
295	C₂×C₁₁	C₂×#471	1	1	yes	characteristic
296	C₂⁴	—	2	1	no	—
297	C₂⁴	—	4	1	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂×D₄	C₁₁×SD₁₆	1	4	yes	complemented
316	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
325	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
326	SD₁₆	—	4	8	no	—
327	SD₁₆	—	4	8	no	—
328	D₈	—	4	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	8	no	—
337	C₂×C₈	C₁₁×D₈	1	4	yes	complemented
338	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
350	C₄²	C₁₁×#41	1	1	yes	characteristic
351	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
352	C₁₁	C₂×#1665	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₁₁×#121	1	1	yes	characteristic
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	C₂×C₁₁×SD₁₆	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
385	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
386	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
388	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
389	C₂×C₄	C₁₁×#135	1	2	yes	—
390	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
393	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	C₂×C₁₁×D₈	1	4	yes	complemented
399	C₂²	—	2	4	no	—
400	C₂²	—	4	8	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	16	4	no	—
407	C₂²	C₁₁×#459	1	2	yes	—
408	C₂²	C₁₁×#465	1	2	yes	—
409	C₂²	C₁₁×#471	1	2	yes	—
410	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₁₁×#459	1	2	yes	—
416	C₄	C₁₁×#465	1	2	yes	—
417	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
418	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
419	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
420	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂	—	4	4	no	—
422	C₂	—	16	2	no	—
423	C₂	C₁₁×#1665	1	4	yes	direct product factor
424	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
425	C₂	C₂×C₁₁×#465	1	1	yes	characteristic
426	C₂	C₂×C₁₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#492	C₂	semidirect
2. C₂×C₁₁×#474	C₂	semidirect
4. C₂×C₈×D₄×C₁₁	C₂	semidirect
5. C₁₁×#1665	C₂	direct (N × H)
6. C₂×C₁₁×#334	C₂	semidirect
7. C₂×C₁₁×#332	C₂	semidirect
8. C₂×C₁₁×#331	C₂	semidirect
17. C₁₁×#492	C₂²	semidirect
19. C₁₁×#474	C₂²	semidirect
23. C₈×D₄×C₁₁	C₂²	semidirect
32. C₁₁×#334	C₂²	semidirect
33. C₁₁×#332	C₂²	semidirect
34. C₁₁×#331	C₂²	semidirect
83. C₂×#1665	C₁₁	direct (N × H)
103. C₂×D₄×C₁₁	SD₁₆	semidirect
125. C₂×C₈×C₁₁	D₈	semidirect
140. C₂×#492	C₂×C₁₁	semidirect
141. C₂×#474	C₂×C₁₁	semidirect
143. C₂×C₈×D₄	C₂×C₁₁	semidirect
144. #1665	C₂×C₁₁	direct (N × H)
145. C₂×#334	C₂×C₁₁	semidirect
146. C₂×#332	C₂×C₁₁	semidirect
147. C₂×#331	C₂×C₁₁	semidirect
170. D₄×C₁₁	C₂×SD₁₆	semidirect
193. C₈×C₁₁	C₂×D₈	semidirect
202. #492	C₂²×C₁₁	semidirect
204. #474	C₂²×C₁₁	semidirect
208. C₈×D₄	C₂²×C₁₁	semidirect
217. #334	C₂²×C₁₁	semidirect
218. #332	C₂²×C₁₁	semidirect
219. #331	C₂²×C₁₁	semidirect
292. C₂×C₁₁	#1665	direct (N × H)
315. C₂×D₄	C₁₁×SD₁₆	semidirect
337. C₂×C₈	C₁₁×D₈	semidirect
352. C₁₁	C₂×#1665	direct (N × H)
375. D₄	C₂×C₁₁×SD₁₆	semidirect
398. C₈	C₂×C₁₁×D₈	semidirect
423. C₂	C₁₁×#1665	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×#492	2
C₂×C₁₁×#474	2
C₂×C₁₁×#459	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#1665	2
C₂×C₁₁×#334	2
C₂×C₁₁×#332	2
C₂×C₁₁×#331	2
C₂×#1665	11

Subgroups — C2×C11×#1665 #14596291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1665 #14596291