Subgroups — C₁₁×#61054 #14638247

Order 2816.

2710 conjugacy classes of subgroups.

The subgroup lattice has 682 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	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3487	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3287	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3271	C₂	1	8	yes	maximal, complemented
7	C₁₁×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3043	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3010	C₂	1	2	yes	maximal, complemented
12	C₁₁×#3005	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₁×2₋¹⁺⁴	C₂²	1	2	yes	—
16	C₂²×C₁₁×#41	C₂²	1	2	yes	—
17	C₁₁×#578	—	2	8	no	—
18	C₂×C₁₁×#137	C₂²	1	2	yes	—
19	C₂×C₁₁×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₁×#135	—	2	8	no	—
22	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#135	C₂²	1	4	yes	—
24	C₂×C₁₁×#135	C₂²	1	4	yes	—
25	C₂×C₁₁×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
29	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#550	—	2	4	no	—
33	C₁₁×#550	C₂²	1	8	yes	complemented
34	C₁₁×#548	—	2	4	no	—
35	C₁₁×#548	C₂²	1	8	yes	complemented
36	C₁₁×#535	—	2	4	no	—
37	C₁₁×#535	C₂²	1	2	yes	—
38	C₁₁×#535	C₂²	1	2	yes	—
39	C₁₁×#525	—	2	4	no	—
40	C₁₁×#525	C₂²	1	2	yes	—
41	C₁₁×#525	C₂²	1	1	yes	characteristic
42	C₁₁×#519	C₂²	1	2	yes	—
43	C₁₁×#496	C₂²	1	4	yes	complemented
44	C₁₁×#495	C₂²	1	2	yes	complemented
45	C₁₁×#493	C₂²	1	2	yes	complemented
46	C₁₁×#469	C₂²	1	4	yes	complemented
47	C₁₁×#467	C₂²	1	2	yes	complemented
48	C₁₁×#466	C₂²	1	4	yes	complemented
49	C₁₁×#466	C₂²	1	2	yes	complemented
50	C₁₁×#465	C₂²	1	4	yes	complemented
51	C₁₁×#464	C₂²	1	8	yes	complemented
52	C₁₁×#460	C₂²	1	8	yes	complemented
53	C₁₁×#452	C₂²	1	8	yes	complemented
54	C₁₁×#449	C₂²	1	8	yes	complemented
55	C₁₁×#449	C₂²	1	8	yes	complemented
56	C₁₁×#448	C₂²	1	8	yes	complemented
57	C₁₁×#441	C₂²	1	4	yes	complemented
58	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
59	C₁₁×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₁₁	C₂²	1	4	yes	complemented
61	C₁₁×#427	C₂²	1	1	yes	characteristic
62	C₁₁×#424	C₂²	1	1	yes	characteristic
63	C₁₁×#419	C₂²	1	2	yes	—
64	C₁₁×#418	C₂²	1	2	yes	—
65	C₁₁×#416	C₂²	1	2	yes	—
66	C₁₁×#408	C₂²	1	1	yes	characteristic
67	C₁₁×#407	C₂²	1	1	yes	characteristic
68	C₁₁×#405	C₂²	1	1	yes	characteristic
69	C₁₁×2₋¹⁺⁴	—	2	8	no	—
70	C₁₁×2₋¹⁺⁴	—	4	4	no	—
71	C₂×C₁₁×#41	—	2	4	no	—
72	C₂×C₁₁×#41	—	2	2	no	—
73	C₂×C₁₁×#41	—	2	4	no	—
74	C₂×C₁₁×#41	—	2	8	no	—
75	C₂×C₁₁×#41	—	4	4	no	—
76	C₂×C₁₁×#41	C₂³	1	2	yes	—
77	C₂×C₁₁×#41	C₂³	1	8	yes	—
78	C₂×C₁₁×#41	C₂³	1	4	yes	—
79	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₁	—	2	2	no	—
81	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₁	—	2	2	no	—
84	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₁	—	2	2	no	—
86	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
87	C₁₁×#137	—	2	8	no	—
88	C₁₁×#137	—	2	16	no	—
89	C₁₁×AGL(1,ℤ/8)	—	4	4	no	—
90	C₁₁×#135	—	2	16	no	—
91	C₁₁×#135	—	2	16	no	—
92	C₁₁×#135	—	2	8	no	—
93	C₁₁×#135	—	2	4	no	—
94	C₂×C₁₁×Q₁₆	—	2	8	no	—
95	C₂×C₁₁×Q₁₆	D₄	1	8	yes	complemented
96	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₁×SD₁₆	—	2	8	no	—
101	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
103	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₁×D₈	—	2	4	no	—
106	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
107	C₂×C₁₁×D₈	C₂³	1	2	yes	—
108	C₂×C₁₁×D₈	C₂³	1	2	yes	—
109	C₂×C₁₁×D₈	C₂³	1	4	yes	—
110	C₁₁×#131	—	2	4	no	—
111	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
114	C₂²×C₈×C₁₁	—	2	4	no	—
115	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
117	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
118	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
120	C₁₁×#127	—	2	8	no	—
121	C₁₁×#127	—	2	2	no	—
122	C₁₁×#127	C₂³	1	4	yes	—
123	C₁₁×#124	—	2	2	no	—
124	C₁₁×#124	—	2	8	no	—
125	C₁₁×#124	C₂³	1	4	yes	—
126	C₁₁×#123	—	2	2	no	—
127	C₁₁×#123	D₄	1	2	yes	—
128	C₁₁×C₂²⋊Q₈	—	2	8	no	—
129	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₁×#121	—	2	8	no	—
132	C₁₁×#121	—	2	4	no	—
133	C₁₁×#121	—	2	8	no	—
134	C₁₁×#121	—	2	8	no	—
135	C₁₁×#121	D₄	1	2	yes	—
136	C₁₁×#121	C₂³	1	4	yes	—
137	C₁₁×#121	C₂³	1	8	yes	—
138	C₁₁×#120	—	2	2	no	—
139	C₁₁×#120	—	2	4	no	—
140	C₁₁×#120	—	2	4	no	—
141	C₁₁×#120	D₄	1	2	yes	—
142	C₄×Q₈×C₁₁	—	2	4	no	—
143	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
144	C₄×D₄×C₁₁	—	2	4	no	—
145	C₄×D₄×C₁₁	—	2	8	no	—
146	C₄×D₄×C₁₁	—	2	8	no	—
147	C₄×D₄×C₁₁	C₂³	1	4	yes	—
148	C₁₁×#117	—	2	4	no	—
149	C₁₁×#117	C₂³	1	2	yes	—
150	C₁₁×#117	C₂³	1	1	yes	characteristic
151	C₁₁×#107	C₂³	1	2	yes	—
152	C₁₁×#106	C₂³	1	2	yes	—
153	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
154	C₁₁×#103	C₂³	1	4	yes	—
155	C₁₁×#103	C₂³	1	8	yes	—
156	C₁₁×#102	C₂³	1	4	yes	—
157	C₁₁×#102	C₂³	1	8	yes	—
158	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₁₁×#97	C₂³	1	2	yes	—
161	C₄×C₈×C₁₁	C₂³	1	2	yes	—
162	#61054	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₁	—	2	2	no	—
164	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₁₁×#41	—	2	2	no	—
166	C₁₁×#41	—	2	2	no	—
167	C₁₁×#41	—	2	16	no	—
168	C₁₁×#41	—	2	8	no	—
169	C₁₁×#41	—	2	4	no	—
170	C₁₁×#41	—	2	4	no	—
171	C₁₁×#41	—	4	8	no	—
172	C₁₁×#41	—	4	4	no	—
173	C₁₁×#41	—	4	16	no	—
174	C₁₁×#41	—	4	16	no	—
175	C₁₁×#41	—	4	8	no	—
176	C₂×Q₈×C₁₁	—	2	2	no	—
177	C₂×Q₈×C₁₁	—	2	4	no	—
178	C₂×Q₈×C₁₁	—	2	4	no	—
179	C₂×Q₈×C₁₁	—	2	8	no	—
180	C₂×Q₈×C₁₁	—	4	4	no	—
181	C₂×Q₈×C₁₁	—	4	8	no	—
182	C₂×Q₈×C₁₁	C₂×D₄	1	8	yes	—
183	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
185	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
186	C₂×D₄×C₁₁	—	2	2	no	—
187	C₂×D₄×C₁₁	—	2	8	no	—
188	C₂×D₄×C₁₁	—	2	4	no	—
189	C₂×D₄×C₁₁	—	2	8	no	—
190	C₂×D₄×C₁₁	—	2	4	no	—
191	C₂×D₄×C₁₁	—	2	4	no	—
192	C₂×D₄×C₁₁	—	2	2	no	—
193	C₂×D₄×C₁₁	—	2	8	no	—
194	C₂×D₄×C₁₁	—	2	4	no	—
195	C₂×D₄×C₁₁	—	4	8	no	—
196	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
200	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₁	—	2	2	no	—
202	C₂²×C₄×C₁₁	—	2	2	no	—
203	C₂²×C₄×C₁₁	—	2	2	no	—
204	C₂²×C₄×C₁₁	—	2	4	no	—
205	C₂²×C₄×C₁₁	—	2	4	no	—
206	C₂²×C₄×C₁₁	—	2	2	no	—
207	C₂²×C₄×C₁₁	—	2	8	no	—
208	C₂²×C₄×C₁₁	—	4	8	no	—
209	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
214	C₁₁×Q₁₆	—	2	2	no	—
215	C₁₁×Q₁₆	—	2	8	no	—
216	C₁₁×Q₁₆	C₂×D₄	1	8	yes	—
217	C₁₁×Q₁₆	C₂×D₄	1	8	yes	—
218	C₁₁×SD₁₆	—	2	4	no	—
219	C₁₁×SD₁₆	—	2	16	no	—
220	C₁₁×SD₁₆	—	2	8	no	—
221	C₁₁×SD₁₆	—	4	4	no	—
222	C₁₁×D₈	—	2	4	no	—
223	C₁₁×D₈	—	2	4	no	—
224	C₁₁×D₈	—	2	2	no	—
225	C₁₁×D₈	—	4	4	no	—
226	C₁₁×M₁₆	—	2	4	no	—
227	C₁₁×M₁₆	—	2	2	no	—
228	C₁₁×M₁₆	—	2	2	no	—
229	C₂×C₈×C₁₁	—	2	4	no	—
230	C₂×C₈×C₁₁	—	2	4	no	—
231	C₂×C₈×C₁₁	—	2	4	no	—
232	C₂×C₈×C₁₁	—	2	2	no	—
233	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
234	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
237	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
239	C₁₁×C₄⋊C₄	—	2	8	no	—
240	C₁₁×C₄⋊C₄	—	2	4	no	—
241	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
243	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
244	C₁₁×C₂²⋊C₄	—	2	2	no	—
245	C₁₁×C₂²⋊C₄	—	2	4	no	—
246	C₁₁×C₂²⋊C₄	—	2	4	no	—
247	C₁₁×C₂²⋊C₄	—	2	8	no	—
248	C₁₁×C₂²⋊C₄	—	2	8	no	—
249	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
251	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
252	C₄²×C₁₁	—	2	8	no	—
253	C₄²×C₁₁	—	2	2	no	—
254	C₄²×C₁₁	C₂⁴	1	2	yes	—
255	C₂×#578	C₂×C₁₁	1	1	yes	characteristic, complemented
256	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic, complemented
257	#3487	C₂×C₁₁	1	2	yes	complemented
258	#3287	C₂×C₁₁	1	4	yes	complemented
259	#3285	C₂×C₁₁	1	4	yes	complemented
260	#3271	C₂×C₁₁	1	8	yes	complemented
261	#3155	C₂×C₁₁	1	1	yes	characteristic, complemented
262	#3058	C₂×C₁₁	1	1	yes	characteristic, complemented
263	#3050	C₂×C₁₁	1	1	yes	characteristic, complemented
264	#3043	C₂×C₁₁	1	2	yes	complemented
265	#3010	C₂×C₁₁	1	2	yes	complemented
266	#3005	C₂×C₁₁	1	2	yes	complemented
267	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
268	#2929	C₂×C₁₁	1	1	yes	characteristic, complemented
269	C₂³×C₁₁	—	2	2	no	—
270	C₂³×C₁₁	—	2	4	no	—
271	C₂³×C₁₁	—	2	2	no	—
272	C₂³×C₁₁	—	4	2	no	—
273	C₂³×C₁₁	—	4	4	no	—
274	C₂³×C₁₁	—	8	4	no	—
275	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
276	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
277	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₁₁	—	2	8	no	—
279	Q₈×C₁₁	—	2	2	no	—
280	Q₈×C₁₁	—	2	4	no	—
281	Q₈×C₁₁	—	2	2	no	—
282	Q₈×C₁₁	—	2	2	no	—
283	Q₈×C₁₁	—	4	8	no	—
284	Q₈×C₁₁	C₂²×D₄	1	8	yes	—
285	D₄×C₁₁	—	2	4	no	—
286	D₄×C₁₁	—	2	2	no	—
287	D₄×C₁₁	—	2	4	no	—
288	D₄×C₁₁	—	2	2	no	—
289	D₄×C₁₁	—	2	2	no	—
290	D₄×C₁₁	—	2	4	no	—
291	D₄×C₁₁	—	4	4	no	—
292	D₄×C₁₁	—	4	16	no	—
293	D₄×C₁₁	—	4	8	no	—
294	D₄×C₁₁	—	4	4	no	—
295	D₄×C₁₁	—	4	4	no	—
296	D₄×C₁₁	—	8	8	no	—
297	D₄×C₁₁	—	8	8	no	—
298	D₄×C₁₁	—	8	4	no	—
299	C₂×C₄×C₁₁	—	2	2	no	—
300	C₂×C₄×C₁₁	—	2	8	no	—
301	C₂×C₄×C₁₁	—	2	4	no	—
302	C₂×C₄×C₁₁	—	2	4	no	—
303	C₂×C₄×C₁₁	—	2	2	no	—
304	C₂×C₄×C₁₁	—	2	2	no	—
305	C₂×C₄×C₁₁	—	2	2	no	—
306	C₂×C₄×C₁₁	—	2	2	no	—
307	C₂×C₄×C₁₁	—	2	4	no	—
308	C₂×C₄×C₁₁	—	2	2	no	—
309	C₂×C₄×C₁₁	—	4	16	no	—
310	C₂×C₄×C₁₁	—	4	8	no	—
311	C₂×C₄×C₁₁	—	4	8	no	—
312	C₂×C₄×C₁₁	—	4	4	no	—
313	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
319	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
320	C₈×C₁₁	—	2	2	no	—
321	C₈×C₁₁	—	2	2	no	—
322	C₈×C₁₁	—	2	2	no	—
323	C₈×C₁₁	C₂²×D₄	1	2	yes	—
324	C₈×C₁₁	C₂²×D₄	1	2	yes	—
325	C₂×2₋¹⁺⁴	C₂²×C₁₁	1	2	yes	—
326	C₂²×#41	C₂²×C₁₁	1	2	yes	—
327	#578	—	2	8	no	—
328	C₂×#137	C₂²×C₁₁	1	2	yes	—
329	C₂×#137	C₂²×C₁₁	1	4	yes	complemented
330	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
331	C₂×#135	—	2	8	no	—
332	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
333	C₂×#135	C₂²×C₁₁	1	4	yes	—
334	C₂×#135	C₂²×C₁₁	1	4	yes	—
335	C₂×#135	C₂²×C₁₁	1	2	yes	complemented
336	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
337	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	complemented
338	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
339	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
340	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
341	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
342	#550	—	2	4	no	—
343	#550	C₂²×C₁₁	1	8	yes	complemented
344	#548	—	2	4	no	—
345	#548	C₂²×C₁₁	1	8	yes	complemented
346	#535	—	2	4	no	—
347	#535	C₂²×C₁₁	1	2	yes	—
348	#535	C₂²×C₁₁	1	2	yes	—
349	#525	—	2	4	no	—
350	#525	C₂²×C₁₁	1	2	yes	—
351	#525	C₂²×C₁₁	1	1	yes	characteristic
352	#519	C₂²×C₁₁	1	2	yes	—
353	#496	C₂²×C₁₁	1	4	yes	complemented
354	#495	C₂²×C₁₁	1	2	yes	complemented
355	#493	C₂²×C₁₁	1	2	yes	complemented
356	#469	C₂²×C₁₁	1	4	yes	complemented
357	#467	C₂²×C₁₁	1	2	yes	complemented
358	#466	C₂²×C₁₁	1	4	yes	complemented
359	#466	C₂²×C₁₁	1	2	yes	complemented
360	#465	C₂²×C₁₁	1	4	yes	complemented
361	#464	C₂²×C₁₁	1	8	yes	complemented
362	#460	C₂²×C₁₁	1	8	yes	complemented
363	#452	C₂²×C₁₁	1	8	yes	complemented
364	#449	C₂²×C₁₁	1	8	yes	complemented
365	#449	C₂²×C₁₁	1	8	yes	complemented
366	#448	C₂²×C₁₁	1	8	yes	complemented
367	#441	C₂²×C₁₁	1	4	yes	complemented
368	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	complemented
369	#435	C₂²×C₁₁	1	4	yes	complemented
370	C₈×D₄	C₂²×C₁₁	1	4	yes	complemented
371	#427	C₂²×C₁₁	1	1	yes	characteristic
372	#424	C₂²×C₁₁	1	1	yes	characteristic
373	#419	C₂²×C₁₁	1	2	yes	—
374	#418	C₂²×C₁₁	1	2	yes	—
375	#416	C₂²×C₁₁	1	2	yes	—
376	#408	C₂²×C₁₁	1	1	yes	characteristic
377	#407	C₂²×C₁₁	1	1	yes	characteristic
378	#405	C₂²×C₁₁	1	1	yes	characteristic
379	C₂²×C₁₁	—	2	2	no	—
380	C₂²×C₁₁	—	2	2	no	—
381	C₂²×C₁₁	—	2	4	no	—
382	C₂²×C₁₁	—	2	2	no	—
383	C₂²×C₁₁	—	2	2	no	—
384	C₂²×C₁₁	—	2	2	no	—
385	C₂²×C₁₁	—	4	4	no	—
386	C₂²×C₁₁	—	4	4	no	—
387	C₂²×C₁₁	—	4	8	no	—
388	C₂²×C₁₁	—	4	2	no	—
389	C₂²×C₁₁	—	4	4	no	—
390	C₂²×C₁₁	—	8	8	no	—
391	C₂²×C₁₁	D₄²	1	2	yes	—
392	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₁₁	—	2	4	no	—
394	C₄×C₁₁	—	2	2	no	—
395	C₄×C₁₁	—	2	8	no	—
396	C₄×C₁₁	—	2	2	no	—
397	C₄×C₁₁	—	4	4	no	—
398	C₄×C₁₁	—	4	2	no	—
399	C₄×C₁₁	D₄²	1	2	yes	—
400	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	2₋¹⁺⁴	—	2	8	no	—
403	2₋¹⁺⁴	—	4	4	no	—
404	C₂×#41	—	2	4	no	—
405	C₂×#41	—	2	2	no	—
406	C₂×#41	—	2	4	no	—
407	C₂×#41	—	2	8	no	—
408	C₂×#41	—	4	4	no	—
409	C₂×#41	C₂³×C₁₁	1	2	yes	—
410	C₂×#41	C₂³×C₁₁	1	8	yes	—
411	C₂×#41	C₂³×C₁₁	1	4	yes	—
412	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
413	C₂²×Q₈	—	2	2	no	—
414	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
415	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
418	C₂³×C₄	—	2	2	no	—
419	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
420	#137	—	2	8	no	—
421	#137	—	2	16	no	—
422	AGL(1,ℤ/8)	—	4	4	no	—
423	#135	—	2	16	no	—
424	#135	—	2	16	no	—
425	#135	—	2	8	no	—
426	#135	—	2	4	no	—
427	C₂×Q₁₆	—	2	8	no	—
428	C₂×Q₁₆	D₄×C₁₁	1	8	yes	complemented
429	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
430	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
431	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
432	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
433	C₂×SD₁₆	—	2	8	no	—
434	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
435	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
436	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
437	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
438	C₂×D₈	—	2	4	no	—
439	C₂×D₈	C₂³×C₁₁	1	2	yes	—
440	C₂×D₈	C₂³×C₁₁	1	2	yes	—
441	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
442	C₂×D₈	C₂³×C₁₁	1	4	yes	—
443	#131	—	2	4	no	—
444	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
445	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
446	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
447	C₂²×C₈	—	2	4	no	—
448	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
450	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
451	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
452	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
453	#127	—	2	8	no	—
454	#127	—	2	2	no	—
455	#127	C₂³×C₁₁	1	4	yes	—
456	#124	—	2	2	no	—
457	#124	—	2	8	no	—
458	#124	C₂³×C₁₁	1	4	yes	—
459	#123	—	2	2	no	—
460	#123	D₄×C₁₁	1	2	yes	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
463	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
464	#121	—	2	8	no	—
465	#121	—	2	4	no	—
466	#121	—	2	8	no	—
467	#121	—	2	8	no	—
468	#121	D₄×C₁₁	1	2	yes	—
469	#121	C₂³×C₁₁	1	4	yes	—
470	#121	C₂³×C₁₁	1	8	yes	—
471	#120	—	2	2	no	—
472	#120	—	2	4	no	—
473	#120	—	2	4	no	—
474	#120	D₄×C₁₁	1	2	yes	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	C₂³×C₁₁	1	4	yes	—
481	#117	—	2	4	no	—
482	#117	C₂³×C₁₁	1	2	yes	—
483	#117	C₂³×C₁₁	1	1	yes	characteristic
484	#107	C₂³×C₁₁	1	2	yes	—
485	#106	C₂³×C₁₁	1	2	yes	—
486	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
487	#103	C₂³×C₁₁	1	4	yes	—
488	#103	C₂³×C₁₁	1	8	yes	—
489	#102	C₂³×C₁₁	1	4	yes	—
490	#102	C₂³×C₁₁	1	8	yes	—
491	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
492	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
493	#97	C₂³×C₁₁	1	2	yes	—
494	C₄×C₈	C₂³×C₁₁	1	2	yes	—
495	C₂×C₁₁	—	2	2	no	—
496	C₂×C₁₁	—	4	2	no	—
497	C₂×C₁₁	—	4	2	no	—
498	C₂×C₁₁	—	8	2	no	—
499	C₂×C₁₁	—	8	4	no	—
500	C₂×C₁₁	C₂×D₄²	1	1	yes	characteristic
501	C₂×C₁₁	#3584	1	2	yes	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
504	#41	—	2	2	no	—
505	#41	—	2	2	no	—
506	#41	—	2	16	no	—
507	#41	—	2	8	no	—
508	#41	—	2	4	no	—
509	#41	—	2	4	no	—
510	#41	—	4	8	no	—
511	#41	—	4	4	no	—
512	#41	—	4	16	no	—
513	#41	—	4	16	no	—
514	#41	—	4	8	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	4	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂×Q₈	—	4	8	no	—
521	C₂×Q₈	C₂×D₄×C₁₁	1	8	yes	—
522	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
523	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
524	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	4	8	no	—
535	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
537	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
538	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
539	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	4	8	no	—
548	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
553	Q₁₆	—	2	8	no	—
554	Q₁₆	—	2	2	no	—
555	Q₁₆	C₂×D₄×C₁₁	1	8	yes	—
556	Q₁₆	C₂×D₄×C₁₁	1	8	yes	—
557	SD₁₆	—	2	16	no	—
558	SD₁₆	—	2	8	no	—
559	SD₁₆	—	2	4	no	—
560	SD₁₆	—	4	4	no	—
561	D₈	—	2	4	no	—
562	D₈	—	2	4	no	—
563	D₈	—	2	2	no	—
564	D₈	—	4	4	no	—
565	M₁₆	—	2	2	no	—
566	M₁₆	—	2	2	no	—
567	M₁₆	—	2	4	no	—
568	C₂×C₈	—	2	2	no	—
569	C₂×C₈	—	2	4	no	—
570	C₂×C₈	—	2	4	no	—
571	C₂×C₈	—	2	4	no	—
572	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
573	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
574	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
575	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
576	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
577	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
581	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
582	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
589	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
590	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
591	C₄²	—	2	8	no	—
592	C₄²	—	2	2	no	—
593	C₄²	C₂⁴×C₁₁	1	2	yes	—
594	C₁₁	#61054	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³	—	2	2	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	8	4	no	—
601	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
602	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
603	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
604	Q₈	—	2	8	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	2	4	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	4	8	no	—
610	Q₈	C₂²×D₄×C₁₁	1	8	yes	—
611	D₄	—	2	4	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	4	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	16	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	4	no	—
622	D₄	—	8	8	no	—
623	D₄	—	8	8	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	4	16	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	8	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
640	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
641	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
643	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
644	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
645	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	—	2	2	no	—
649	C₈	C₂²×D₄×C₁₁	1	2	yes	—
650	C₈	C₂²×D₄×C₁₁	1	2	yes	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	8	no	—
662	C₂²	—	8	8	no	—
663	C₂²	D₄²×C₁₁	1	2	yes	—
664	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
665	C₄	—	2	2	no	—
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	4	no	—
671	C₄	D₄²×C₁₁	1	2	yes	—
672	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
673	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂	—	2	2	no	—
675	C₂	—	4	2	no	—
676	C₂	—	4	2	no	—
677	C₂	—	8	4	no	—
678	C₂	—	8	2	no	—
679	C₂	C₂×D₄²×C₁₁	1	1	yes	characteristic
680	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 ◁ C₁₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#578	C₂	semidirect
2. C₂²×C₁₁×#135	C₂	semidirect
3. C₁₁×#3487	C₂	semidirect
4. C₁₁×#3287	C₂	semidirect
5. C₁₁×#3285	C₂	semidirect
6. C₁₁×#3271	C₂	semidirect
7. C₁₁×#3155	C₂	semidirect
8. C₁₁×#3058	C₂	semidirect
9. C₁₁×#3050	C₂	semidirect
10. C₁₁×#3043	C₂	semidirect
11. C₁₁×#3010	C₂	semidirect
12. C₁₁×#3005	C₂	semidirect
13. C₁₁×#2950	C₂	semidirect
14. C₁₁×#2929	C₂	semidirect
19. C₂×C₁₁×#137	C₂²	semidirect
25. C₂×C₁₁×#135	C₂²	semidirect
27. C₂²×C₁₁×Q₁₆	C₂²	semidirect
33. C₁₁×#550	C₂²	semidirect
35. C₁₁×#548	C₂²	semidirect
43. C₁₁×#496	C₂²	semidirect
44. C₁₁×#495	C₂²	semidirect
45. C₁₁×#493	C₂²	semidirect
46. C₁₁×#469	C₂²	semidirect
47. C₁₁×#467	C₂²	semidirect
48. C₁₁×#466	C₂²	semidirect
49. C₁₁×#466	C₂²	semidirect
50. C₁₁×#465	C₂²	semidirect
51. C₁₁×#464	C₂²	semidirect
52. C₁₁×#460	C₂²	semidirect
53. C₁₁×#452	C₂²	semidirect
54. C₁₁×#449	C₂²	semidirect
55. C₁₁×#449	C₂²	semidirect
56. C₁₁×#448	C₂²	semidirect
57. C₁₁×#441	C₂²	semidirect
58. C₄×C₁₁×Q₁₆	C₂²	semidirect
59. C₁₁×#435	C₂²	semidirect
60. C₈×D₄×C₁₁	C₂²	semidirect
95. C₂×C₁₁×Q₁₆	D₄	semidirect
162. #61054	C₁₁	direct (N × H)
255. C₂×#578	C₂×C₁₁	semidirect
256. C₂²×#135	C₂×C₁₁	semidirect
257. #3487	C₂×C₁₁	semidirect
258. #3287	C₂×C₁₁	semidirect
259. #3285	C₂×C₁₁	semidirect
260. #3271	C₂×C₁₁	semidirect
261. #3155	C₂×C₁₁	semidirect
262. #3058	C₂×C₁₁	semidirect
263. #3050	C₂×C₁₁	semidirect
264. #3043	C₂×C₁₁	semidirect
265. #3010	C₂×C₁₁	semidirect
266. #3005	C₂×C₁₁	semidirect
267. #2950	C₂×C₁₁	semidirect
268. #2929	C₂×C₁₁	semidirect
329. C₂×#137	C₂²×C₁₁	semidirect
335. C₂×#135	C₂²×C₁₁	semidirect
337. C₂²×Q₁₆	C₂²×C₁₁	semidirect
343. #550	C₂²×C₁₁	semidirect
345. #548	C₂²×C₁₁	semidirect
353. #496	C₂²×C₁₁	semidirect
354. #495	C₂²×C₁₁	semidirect
355. #493	C₂²×C₁₁	semidirect
356. #469	C₂²×C₁₁	semidirect
357. #467	C₂²×C₁₁	semidirect
358. #466	C₂²×C₁₁	semidirect
359. #466	C₂²×C₁₁	semidirect
360. #465	C₂²×C₁₁	semidirect
361. #464	C₂²×C₁₁	semidirect
362. #460	C₂²×C₁₁	semidirect
363. #452	C₂²×C₁₁	semidirect
364. #449	C₂²×C₁₁	semidirect
365. #449	C₂²×C₁₁	semidirect
366. #448	C₂²×C₁₁	semidirect
367. #441	C₂²×C₁₁	semidirect
368. C₄×Q₁₆	C₂²×C₁₁	semidirect
369. #435	C₂²×C₁₁	semidirect
370. C₈×D₄	C₂²×C₁₁	semidirect
428. C₂×Q₁₆	D₄×C₁₁	semidirect
594. C₁₁	#61054	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
C₂²×C₁₁×#135	2
C₁₁×#3487	2
C₁₁×#3287	2
C₁₁×#3285	2
C₁₁×#3271	2
C₁₁×#3155	2
C₁₁×#3058	2
C₁₁×#3050	2
C₁₁×#3043	2
C₁₁×#3010	2
C₁₁×#3005	2
C₁₁×#2950	2
C₁₁×#2929	2
#61054	11

Subgroups — C11×#61054 #14638247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61054 #14638247