Subgroups — C₁₁×#60649 #14637842

Order 2816.

3178 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#577	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₁×#576	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3500	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3156	C₂	1	3	yes	maximal, complemented
6	C₁₁×#3155	C₂	1	3	yes	maximal, complemented
7	C₁₁×#3154	C₂	1	6	yes	maximal, complemented
8	C₁₁×#3153	C₂	1	6	yes	maximal, complemented
9	C₁₁×#3147	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₁×#495	C₂	1	3	yes	maximal, complemented
11	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	—
14	C₁₁×#578	—	2	8	no	—
15	C₁₁×#577	—	2	16	no	—
16	C₁₁×#576	—	2	8	no	—
17	C₂×C₁₁×#137	C₂²	1	6	yes	complemented
18	C₂×C₁₁×#137	C₂²	1	6	yes	complemented
19	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	6	yes	—
20	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
21	C₂×C₁₁×#135	C₂²	1	3	yes	—
22	C₂×C₁₁×#135	C₂²	1	6	yes	complemented
23	C₂×C₁₁×#135	C₂²	1	3	yes	complemented
24	C₂²×C₁₁×Q₁₆	C₂²	1	3	yes	complemented
25	C₂²×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
26	C₂²×C₁₁×D₈	C₂²	1	3	yes	—
27	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
29	C₁₁×#548	—	2	4	no	—
30	C₁₁×#546	—	2	12	no	—
31	C₁₁×#536	C₂²	1	6	yes	complemented
32	C₁₁×#535	C₂²	1	6	yes	complemented
33	C₁₁×#532	C₂²	1	6	yes	complemented
34	C₂×C₁₁×#124	C₂²	1	6	yes	complemented
35	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
36	C₁₁×#497	C₂²	1	12	yes	complemented
37	C₁₁×#496	C₂²	1	12	yes	complemented
38	C₁₁×#495	C₂²	1	3	yes	complemented
39	C₁₁×#495	C₂²	1	6	yes	complemented
40	C₁₁×#495	C₂²	1	6	yes	complemented
41	C₁₁×#495	C₂²	1	6	yes	complemented
42	C₁₁×#495	C₂²	1	1	yes	characteristic, complemented
43	C₁₁×#495	C₂²	1	6	yes	complemented
44	C₁₁×#494	C₂²	1	3	yes	complemented
45	C₁₁×#493	C₂²	1	3	yes	complemented
46	C₁₁×#492	C₂²	1	6	yes	complemented
47	C₁₁×#405	C₂²	1	3	yes	complemented
48	C₁₁×#405	C₂²	1	3	yes	complemented
49	C₄×C₁₁×M₁₆	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	complemented
51	C₁₁×2₋¹⁺⁴	—	2	8	no	—
52	C₁₁×2₋¹⁺⁴	—	2	8	no	—
53	C₁₁×H(5,𝔽₂)	—	2	8	no	—
54	C₁₁×H(5,𝔽₂)	—	2	8	no	—
55	C₂×C₁₁×#41	—	2	2	no	—
56	C₂×C₁₁×#41	—	2	6	no	—
57	C₂×C₁₁×#41	C₂³	1	6	yes	—
58	C₂×C₁₁×#41	C₂³	1	6	yes	—
59	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₁	—	2	2	no	—
61	C₂²×Q₈×C₁₁	C₂³	1	6	yes	—
62	C₂²×D₄×C₁₁	—	2	6	no	—
63	C₂²×D₄×C₁₁	C₂³	1	6	yes	—
64	C₁₁×#137	—	2	24	no	—
65	C₁₁×#137	—	2	24	no	—
66	C₁₁×AGL(1,ℤ/8)	—	2	24	no	—
67	C₁₁×AGL(1,ℤ/8)	—	2	24	no	—
68	C₁₁×#135	—	2	12	no	—
69	C₁₁×#135	—	2	24	no	—
70	C₁₁×#135	—	2	12	no	—
71	C₂×C₁₁×Q₁₆	—	2	12	no	—
72	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×Q₁₆	C₂³	1	3	yes	—
74	C₂×C₁₁×Q₁₆	C₂³	1	6	yes	—
75	C₂×C₁₁×Q₁₆	C₂³	1	6	yes	—
76	C₂×C₁₁×SD₁₆	—	2	24	no	—
77	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
78	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
79	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
80	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
81	C₂×C₁₁×SD₁₆	C₂³	1	12	yes	—
82	C₂×C₁₁×D₈	—	2	12	no	—
83	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
84	C₂×C₁₁×D₈	C₂³	1	3	yes	—
85	C₂×C₁₁×D₈	C₂³	1	6	yes	—
86	C₂×C₁₁×D₈	C₂³	1	6	yes	—
87	C₁₁×#131	D₄	1	8	yes	complemented
88	C₁₁×#131	D₄	1	8	yes	complemented
89	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
90	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
91	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
92	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
93	C₁₁×C₄⋊Q₈	C₂³	1	6	yes	—
94	C₁₁×#127	C₂³	1	6	yes	—
95	C₁₁×#124	—	2	12	no	—
96	C₁₁×#124	C₂³	1	6	yes	—
97	C₁₁×#124	C₂³	1	2	yes	—
98	C₁₁×#124	C₂³	1	12	yes	—
99	C₁₁×#123	—	2	12	no	—
100	C₁₁×C₂²⋊Q₈	—	2	12	no	—
101	C₁₁×#121	—	2	12	no	—
102	C₁₁×#121	—	2	12	no	—
103	C₁₁×#120	—	2	12	no	—
104	C₄×Q₈×C₁₁	D₄	1	2	yes	—
105	C₄×D₄×C₁₁	—	2	12	no	—
106	C₄×D₄×C₁₁	D₄	1	6	yes	—
107	C₁₁×#117	C₂³	1	3	yes	—
108	C₂×C₁₁×C₂²⋊C₄	—	2	12	no	—
109	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
110	C₁₁×#97	C₂³	1	6	yes	—
111	C₄×C₈×C₁₁	C₂³	1	3	yes	—
112	C₄×C₈×C₁₁	C₂³	1	3	yes	—
113	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
114	C₄×C₈×C₁₁	C₂³	1	3	yes	—
115	#60649	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₁	—	2	6	no	—
117	C₁₁×#41	—	2	12	no	—
118	C₁₁×#41	—	2	12	no	—
119	C₁₁×#41	—	2	12	no	—
120	C₁₁×#41	—	2	12	no	—
121	C₁₁×#41	—	4	8	no	—
122	C₁₁×#41	—	4	24	no	—
123	C₁₁×#41	C₂×D₄	1	4	yes	—
124	C₁₁×#41	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₁	—	2	6	no	—
126	C₂×Q₈×C₁₁	—	2	12	no	—
127	C₂×Q₈×C₁₁	—	2	12	no	—
128	C₂×Q₈×C₁₁	—	4	8	no	—
129	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₁	C₂⁴	1	6	yes	—
131	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
132	C₂×D₄×C₁₁	—	2	6	no	—
133	C₂×D₄×C₁₁	—	2	6	no	—
134	C₂×D₄×C₁₁	—	2	12	no	—
135	C₂×D₄×C₁₁	—	2	12	no	—
136	C₂×D₄×C₁₁	—	2	6	no	—
137	C₂×D₄×C₁₁	—	2	12	no	—
138	C₂×D₄×C₁₁	—	4	24	no	—
139	C₂×D₄×C₁₁	C₂×D₄	1	3	yes	—
140	C₂×D₄×C₁₁	C₂⁴	1	6	yes	—
141	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₁	—	2	6	no	—
143	C₂²×C₄×C₁₁	—	2	6	no	—
144	C₂²×C₄×C₁₁	—	2	6	no	—
145	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
146	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
147	C₁₁×Q₁₆	—	2	6	no	—
148	C₁₁×Q₁₆	—	2	12	no	—
149	C₁₁×Q₁₆	—	2	2	no	—
150	C₁₁×Q₁₆	—	2	12	no	—
151	C₁₁×SD₁₆	—	2	12	no	—
152	C₁₁×SD₁₆	—	2	24	no	—
153	C₁₁×SD₁₆	—	2	4	no	—
154	C₁₁×SD₁₆	—	2	12	no	—
155	C₁₁×SD₁₆	—	2	12	no	—
156	C₁₁×D₈	—	2	6	no	—
157	C₁₁×D₈	—	2	12	no	—
158	C₁₁×D₈	—	2	2	no	—
159	C₁₁×D₈	—	2	12	no	—
160	C₁₁×M₁₆	C₂×D₄	1	12	yes	—
161	C₁₁×M₁₆	C₂×D₄	1	12	yes	—
162	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
163	C₂×C₈×C₁₁	C₂×D₄	1	12	yes	—
164	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₁₁	C₂⁴	1	3	yes	—
167	C₂×C₈×C₁₁	C₂⁴	1	3	yes	—
168	C₁₁×C₄⋊C₄	—	2	12	no	—
169	C₁₁×C₄⋊C₄	C₂×D₄	1	6	yes	—
170	C₁₁×C₂²⋊C₄	—	2	12	no	—
171	C₁₁×C₂²⋊C₄	—	2	24	no	—
172	C₁₁×C₂²⋊C₄	—	2	4	no	—
173	C₁₁×C₂²⋊C₄	C₂×D₄	1	6	yes	—
174	C₄²×C₁₁	C₂×D₄	1	6	yes	—
175	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
176	C₄²×C₁₁	C₂⁴	1	3	yes	—
177	C₂×#578	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₂×#577	C₂×C₁₁	1	2	yes	complemented
179	C₂×#576	C₂×C₁₁	1	1	yes	characteristic, complemented
180	#3500	C₂×C₁₁	1	2	yes	complemented
181	#3156	C₂×C₁₁	1	3	yes	complemented
182	#3155	C₂×C₁₁	1	3	yes	complemented
183	#3154	C₂×C₁₁	1	6	yes	complemented
184	#3153	C₂×C₁₁	1	6	yes	complemented
185	#3147	C₂×C₁₁	1	3	yes	complemented
186	C₂×#495	C₂×C₁₁	1	3	yes	complemented
187	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂³×C₁₁	—	2	6	no	—
189	C₂³×C₁₁	—	2	2	no	—
190	C₂³×C₁₁	—	4	12	no	—
191	C₂³×C₁₁	—	8	12	no	—
192	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
193	Q₈×C₁₁	—	2	6	no	—
194	Q₈×C₁₁	—	2	2	no	—
195	Q₈×C₁₁	—	2	6	no	—
196	Q₈×C₁₁	—	2	2	no	—
197	Q₈×C₁₁	—	4	12	no	—
198	Q₈×C₁₁	#127	1	4	yes	—
199	D₄×C₁₁	—	2	6	no	—
200	D₄×C₁₁	—	2	2	no	—
201	D₄×C₁₁	—	2	6	no	—
202	D₄×C₁₁	—	2	2	no	—
203	D₄×C₁₁	—	4	12	no	—
204	D₄×C₁₁	—	4	12	no	—
205	D₄×C₁₁	—	4	12	no	—
206	D₄×C₁₁	—	8	12	no	—
207	D₄×C₁₁	#127	1	12	yes	—
208	C₂×C₄×C₁₁	—	2	6	no	—
209	C₂×C₄×C₁₁	—	2	2	no	—
210	C₂×C₄×C₁₁	—	4	6	no	—
211	C₂×C₄×C₁₁	—	4	12	no	—
212	C₂×C₄×C₁₁	—	4	12	no	—
213	C₂×C₄×C₁₁	—	4	12	no	—
214	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
216	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
218	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
219	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
220	C₈×C₁₁	C₂²×D₄	1	2	yes	—
221	C₈×C₁₁	C₂²×D₄	1	2	yes	—
222	C₈×C₁₁	C₂²×D₄	1	6	yes	—
223	C₈×C₁₁	C₂²×D₄	1	6	yes	—
224	C₂×2₋¹⁺⁴	C₂²×C₁₁	1	2	yes	—
225	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	2	yes	—
226	#578	—	2	8	no	—
227	#577	—	2	16	no	—
228	#576	—	2	8	no	—
229	C₂×#137	C₂²×C₁₁	1	6	yes	complemented
230	C₂×#137	C₂²×C₁₁	1	6	yes	complemented
231	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	6	yes	—
232	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	6	yes	complemented
233	C₂×#135	C₂²×C₁₁	1	3	yes	—
234	C₂×#135	C₂²×C₁₁	1	6	yes	complemented
235	C₂×#135	C₂²×C₁₁	1	3	yes	complemented
236	C₂²×Q₁₆	C₂²×C₁₁	1	3	yes	complemented
237	C₂²×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
238	C₂²×D₈	C₂²×C₁₁	1	3	yes	—
239	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
241	#548	—	2	4	no	—
242	#546	—	2	12	no	—
243	#536	C₂²×C₁₁	1	6	yes	complemented
244	#535	C₂²×C₁₁	1	6	yes	complemented
245	#532	C₂²×C₁₁	1	6	yes	complemented
246	C₂×#124	C₂²×C₁₁	1	6	yes	complemented
247	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
248	#497	C₂²×C₁₁	1	12	yes	complemented
249	#496	C₂²×C₁₁	1	12	yes	complemented
250	#495	C₂²×C₁₁	1	3	yes	complemented
251	#495	C₂²×C₁₁	1	6	yes	complemented
252	#495	C₂²×C₁₁	1	6	yes	complemented
253	#495	C₂²×C₁₁	1	6	yes	complemented
254	#495	C₂²×C₁₁	1	1	yes	characteristic, complemented
255	#495	C₂²×C₁₁	1	6	yes	complemented
256	#494	C₂²×C₁₁	1	3	yes	complemented
257	#493	C₂²×C₁₁	1	3	yes	complemented
258	#492	C₂²×C₁₁	1	6	yes	complemented
259	#405	C₂²×C₁₁	1	3	yes	complemented
260	#405	C₂²×C₁₁	1	3	yes	complemented
261	C₄×M₁₆	C₂²×C₁₁	1	3	yes	complemented
262	C₂×C₄×C₈	C₂²×C₁₁	1	3	yes	complemented
263	C₂²×C₁₁	—	2	6	no	—
264	C₂²×C₁₁	—	4	4	no	—
265	C₂²×C₁₁	—	4	12	no	—
266	C₂²×C₁₁	—	4	2	no	—
267	C₂²×C₁₁	—	4	6	no	—
268	C₂²×C₁₁	—	16	12	no	—
269	C₂²×C₁₁	C₂×#127	1	6	yes	—
270	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₁₁	—	2	2	no	—
272	C₄×C₁₁	—	2	6	no	—
273	C₄×C₁₁	—	4	2	no	—
274	C₄×C₁₁	—	4	6	no	—
275	C₄×C₁₁	C₂×#127	1	6	yes	—
276	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
278	2₋¹⁺⁴	—	2	8	no	—
279	2₋¹⁺⁴	—	2	8	no	—
280	H(5,𝔽₂)	—	2	8	no	—
281	H(5,𝔽₂)	—	2	8	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	6	no	—
284	C₂×#41	C₂³×C₁₁	1	6	yes	—
285	C₂×#41	C₂³×C₁₁	1	6	yes	—
286	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	C₂³×C₁₁	1	6	yes	—
289	C₂²×D₄	—	2	6	no	—
290	C₂²×D₄	C₂³×C₁₁	1	6	yes	—
291	#137	—	2	24	no	—
292	#137	—	2	24	no	—
293	AGL(1,ℤ/8)	—	2	24	no	—
294	AGL(1,ℤ/8)	—	2	24	no	—
295	#135	—	2	12	no	—
296	#135	—	2	24	no	—
297	#135	—	2	12	no	—
298	C₂×Q₁₆	—	2	12	no	—
299	C₂×Q₁₆	C₂³×C₁₁	1	3	yes	—
300	C₂×Q₁₆	C₂³×C₁₁	1	6	yes	—
301	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
302	C₂×Q₁₆	C₂³×C₁₁	1	6	yes	—
303	C₂×SD₁₆	—	2	24	no	—
304	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
305	C₂×SD₁₆	C₂³×C₁₁	1	12	yes	—
306	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
307	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
308	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
309	C₂×D₈	—	2	12	no	—
310	C₂×D₈	C₂³×C₁₁	1	3	yes	—
311	C₂×D₈	C₂³×C₁₁	1	6	yes	—
312	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
313	C₂×D₈	C₂³×C₁₁	1	6	yes	—
314	#131	D₄×C₁₁	1	8	yes	complemented
315	#131	D₄×C₁₁	1	8	yes	complemented
316	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
317	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
318	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
319	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
320	C₄⋊Q₈	C₂³×C₁₁	1	6	yes	—
321	#127	C₂³×C₁₁	1	6	yes	—
322	#124	—	2	12	no	—
323	#124	C₂³×C₁₁	1	6	yes	—
324	#124	C₂³×C₁₁	1	12	yes	—
325	#124	C₂³×C₁₁	1	2	yes	—
326	#123	—	2	12	no	—
327	C₂²⋊Q₈	—	2	12	no	—
328	#121	—	2	12	no	—
329	#121	—	2	12	no	—
330	#120	—	2	12	no	—
331	C₄×Q₈	D₄×C₁₁	1	2	yes	—
332	C₄×D₄	—	2	12	no	—
333	C₄×D₄	D₄×C₁₁	1	6	yes	—
334	#117	C₂³×C₁₁	1	3	yes	—
335	C₂×C₂²⋊C₄	—	2	12	no	—
336	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
337	#97	C₂³×C₁₁	1	6	yes	—
338	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
339	C₄×C₈	C₂³×C₁₁	1	3	yes	—
340	C₄×C₈	C₂³×C₁₁	1	3	yes	—
341	C₄×C₈	C₂³×C₁₁	1	3	yes	—
342	C₂×C₁₁	—	2	6	no	—
343	C₂×C₁₁	—	8	2	no	—
344	C₂×C₁₁	—	8	6	no	—
345	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
346	C₂×C₁₁	#3584	1	2	yes	—
347	C₂⁴	—	2	6	no	—
348	#41	—	2	12	no	—
349	#41	—	2	12	no	—
350	#41	—	2	12	no	—
351	#41	—	2	12	no	—
352	#41	—	4	8	no	—
353	#41	—	4	24	no	—
354	#41	C₂×D₄×C₁₁	1	4	yes	—
355	#41	C₂×D₄×C₁₁	1	4	yes	—
356	C₂×Q₈	—	2	6	no	—
357	C₂×Q₈	—	2	12	no	—
358	C₂×Q₈	—	2	12	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
361	C₂×Q₈	C₂⁴×C₁₁	1	6	yes	—
362	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
363	C₂×D₄	—	2	6	no	—
364	C₂×D₄	—	2	6	no	—
365	C₂×D₄	—	2	12	no	—
366	C₂×D₄	—	2	12	no	—
367	C₂×D₄	—	2	6	no	—
368	C₂×D₄	—	2	12	no	—
369	C₂×D₄	—	4	24	no	—
370	C₂×D₄	C₂×D₄×C₁₁	1	3	yes	—
371	C₂×D₄	C₂⁴×C₁₁	1	6	yes	—
372	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
373	C₂²×C₄	—	2	6	no	—
374	C₂²×C₄	—	2	6	no	—
375	C₂²×C₄	—	2	6	no	—
376	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
377	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
378	Q₁₆	—	2	6	no	—
379	Q₁₆	—	2	12	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	2	12	no	—
382	SD₁₆	—	2	12	no	—
383	SD₁₆	—	2	24	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	12	no	—
386	SD₁₆	—	2	12	no	—
387	D₈	—	2	6	no	—
388	D₈	—	2	12	no	—
389	D₈	—	2	2	no	—
390	D₈	—	2	12	no	—
391	M₁₆	C₂×D₄×C₁₁	1	12	yes	—
392	M₁₆	C₂×D₄×C₁₁	1	12	yes	—
393	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
394	C₂×C₈	C₂×D₄×C₁₁	1	12	yes	—
395	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
396	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
397	C₂×C₈	C₂⁴×C₁₁	1	3	yes	—
398	C₂×C₈	C₂⁴×C₁₁	1	3	yes	—
399	C₄⋊C₄	—	2	12	no	—
400	C₄⋊C₄	C₂×D₄×C₁₁	1	6	yes	—
401	C₂²⋊C₄	—	2	12	no	—
402	C₂²⋊C₄	—	2	24	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	C₂×D₄×C₁₁	1	6	yes	—
405	C₄²	C₂×D₄×C₁₁	1	6	yes	—
406	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
407	C₄²	C₂⁴×C₁₁	1	3	yes	—
408	C₁₁	#60649	1	1	yes	characteristic, direct product factor, Sylow
409	C₂³	—	2	6	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	12	no	—
412	C₂³	—	8	12	no	—
413	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
414	Q₈	—	2	6	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	6	no	—
417	Q₈	—	2	2	no	—
418	Q₈	—	4	12	no	—
419	Q₈	C₁₁×#127	1	4	yes	—
420	D₄	—	2	6	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	6	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	12	no	—
425	D₄	—	4	12	no	—
426	D₄	—	4	12	no	—
427	D₄	—	8	12	no	—
428	D₄	C₁₁×#127	1	12	yes	—
429	C₂×C₄	—	2	6	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	6	no	—
432	C₂×C₄	—	4	12	no	—
433	C₂×C₄	—	4	12	no	—
434	C₂×C₄	—	4	12	no	—
435	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
437	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
438	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
439	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
440	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
441	C₈	C₂²×D₄×C₁₁	1	2	yes	—
442	C₈	C₂²×D₄×C₁₁	1	2	yes	—
443	C₈	C₂²×D₄×C₁₁	1	6	yes	—
444	C₈	C₂²×D₄×C₁₁	1	6	yes	—
445	C₂²	—	2	6	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	6	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	12	no	—
450	C₂²	—	16	12	no	—
451	C₂²	C₂×C₁₁×#127	1	6	yes	—
452	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	6	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	6	no	—
457	C₄	C₂×C₁₁×#127	1	6	yes	—
458	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
459	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
460	C₂	—	2	6	no	—
461	C₂	—	8	6	no	—
462	C₂	—	8	2	no	—
463	C₂	C₂²×C₁₁×#127	1	1	yes	characteristic
464	C₂	C₁₁×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#578	C₂	semidirect
2. C₂×C₁₁×#577	C₂	semidirect
3. C₂×C₁₁×#576	C₂	semidirect
4. C₁₁×#3500	C₂	semidirect
5. C₁₁×#3156	C₂	semidirect
6. C₁₁×#3155	C₂	semidirect
7. C₁₁×#3154	C₂	semidirect
8. C₁₁×#3153	C₂	semidirect
9. C₁₁×#3147	C₂	semidirect
10. C₂×C₁₁×#495	C₂	semidirect
11. C₄×C₁₁×#131	C₂	semidirect
17. C₂×C₁₁×#137	C₂²	semidirect
18. C₂×C₁₁×#137	C₂²	semidirect
20. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₁×#135	C₂²	semidirect
23. C₂×C₁₁×#135	C₂²	semidirect
24. C₂²×C₁₁×Q₁₆	C₂²	semidirect
25. C₂²×C₁₁×SD₁₆	C₂²	semidirect
31. C₁₁×#536	C₂²	semidirect
32. C₁₁×#535	C₂²	semidirect
33. C₁₁×#532	C₂²	semidirect
34. C₂×C₁₁×#124	C₂²	semidirect
36. C₁₁×#497	C₂²	semidirect
37. C₁₁×#496	C₂²	semidirect
38. C₁₁×#495	C₂²	semidirect
39. C₁₁×#495	C₂²	semidirect
40. C₁₁×#495	C₂²	semidirect
41. C₁₁×#495	C₂²	semidirect
42. C₁₁×#495	C₂²	semidirect
43. C₁₁×#495	C₂²	semidirect
44. C₁₁×#494	C₂²	semidirect
45. C₁₁×#493	C₂²	semidirect
46. C₁₁×#492	C₂²	semidirect
47. C₁₁×#405	C₂²	semidirect
48. C₁₁×#405	C₂²	semidirect
49. C₄×C₁₁×M₁₆	C₂²	semidirect
50. C₂×C₄×C₈×C₁₁	C₂²	semidirect
87. C₁₁×#131	D₄	semidirect
88. C₁₁×#131	D₄	semidirect
115. #60649	C₁₁	direct (N × H)
177. C₂×#578	C₂×C₁₁	semidirect
178. C₂×#577	C₂×C₁₁	semidirect
179. C₂×#576	C₂×C₁₁	semidirect
180. #3500	C₂×C₁₁	semidirect
181. #3156	C₂×C₁₁	semidirect
182. #3155	C₂×C₁₁	semidirect
183. #3154	C₂×C₁₁	semidirect
184. #3153	C₂×C₁₁	semidirect
185. #3147	C₂×C₁₁	semidirect
186. C₂×#495	C₂×C₁₁	semidirect
187. C₄×#131	C₂×C₁₁	semidirect
229. C₂×#137	C₂²×C₁₁	semidirect
230. C₂×#137	C₂²×C₁₁	semidirect
232. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
234. C₂×#135	C₂²×C₁₁	semidirect
235. C₂×#135	C₂²×C₁₁	semidirect
236. C₂²×Q₁₆	C₂²×C₁₁	semidirect
237. C₂²×SD₁₆	C₂²×C₁₁	semidirect
243. #536	C₂²×C₁₁	semidirect
244. #535	C₂²×C₁₁	semidirect
245. #532	C₂²×C₁₁	semidirect
246. C₂×#124	C₂²×C₁₁	semidirect
248. #497	C₂²×C₁₁	semidirect
249. #496	C₂²×C₁₁	semidirect
250. #495	C₂²×C₁₁	semidirect
251. #495	C₂²×C₁₁	semidirect
252. #495	C₂²×C₁₁	semidirect
253. #495	C₂²×C₁₁	semidirect
254. #495	C₂²×C₁₁	semidirect
255. #495	C₂²×C₁₁	semidirect
256. #494	C₂²×C₁₁	semidirect
257. #493	C₂²×C₁₁	semidirect
258. #492	C₂²×C₁₁	semidirect
259. #405	C₂²×C₁₁	semidirect
260. #405	C₂²×C₁₁	semidirect
261. C₄×M₁₆	C₂²×C₁₁	semidirect
262. C₂×C₄×C₈	C₂²×C₁₁	semidirect
314. #131	D₄×C₁₁	semidirect
315. #131	D₄×C₁₁	semidirect
408. C₁₁	#60649	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×#578	2
C₂×C₁₁×#577	2
C₂×C₁₁×#576	2
C₁₁×#3500	2
C₁₁×#3156	2
C₁₁×#3155	2
C₁₁×#3154	2
C₁₁×#3153	2
C₁₁×#3147	2
C₂×C₁₁×#495	2
C₄×C₁₁×#131	2
#60649	11

Subgroups — C11×#60649 #14637842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60649 #14637842