Subgroups — C₁₁×#61110 #14638303

Order 2816.

2684 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3585	C₂	1	4	yes	maximal, complemented
2	C₁₁×#3292	C₂	1	4	yes	maximal, complemented
3	C₁₁×#3291	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3288	C₂	1	8	yes	maximal, complemented
5	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#3068	C₂	1	4	yes	maximal, complemented
7	C₁₁×#3018	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#453	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2956	C₂	1	2	yes	maximal, complemented
10	C₁₁×#585	C₂²	1	2	yes	complemented
11	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	complemented
12	C₁₁×#577	—	2	8	no	—
13	C₁₁×#577	C₂²	1	16	yes	complemented
14	C₁₁×#576	—	2	8	no	—
15	C₁₁×#576	C₂²	1	16	yes	complemented
16	C₁₁×#575	—	2	8	no	—
17	C₁₁×#575	C₂²	1	2	yes	—
18	C₁₁×#575	C₂²	1	4	yes	complemented
19	C₂×C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
20	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₁₁×#568	C₂²	1	4	yes	complemented
23	C₁₁×#532	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₁×#496	C₂²	1	4	yes	complemented
26	C₁₁×#493	C₂²	1	2	yes	complemented
27	C₁₁×#492	C₂²	1	2	yes	complemented
28	C₁₁×#472	C₂²	1	16	yes	complemented
29	C₁₁×#471	C₂²	1	16	yes	complemented
30	C₁₁×#456	C₂²	1	4	yes	complemented
31	C₁₁×#455	C₂²	1	4	yes	complemented
32	C₁₁×#454	C₂²	1	4	yes	complemented
33	C₁₁×#453	C₂²	1	8	yes	complemented
34	C₁₁×#453	C₂²	1	8	yes	complemented
35	C₁₁×#453	C₂²	1	4	yes	complemented
36	C₁₁×#444	C₂²	1	8	yes	complemented
37	C₁₁×#443	C₂²	1	8	yes	complemented
38	C₁₁×#430	C₂²	1	2	yes	complemented
39	C₂×C₁₁×#104	C₂²	1	4	yes	complemented
40	C₁₁×#413	C₂²	1	2	yes	complemented
41	C₂×C₁₁×#100	C₂²	1	2	yes	complemented
42	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₁₁×2₋¹⁺⁴	—	2	4	no	—
44	C₁₁×2₋¹⁺⁴	C₂³	1	4	yes	—
45	C₁₁×H(5,𝔽₂)	—	2	8	no	—
46	C₁₁×H(5,𝔽₂)	—	2	4	no	—
47	C₁₁×H(5,𝔽₂)	—	4	2	no	—
48	C₁₁×H(5,𝔽₂)	—	4	2	no	—
49	C₁₁×H(5,𝔽₂)	C₂³	1	4	yes	—
50	C₁₁×H(5,𝔽₂)	C₂³	1	8	yes	complemented
51	C₂×C₁₁×#41	—	2	8	no	—
52	C₂×C₁₁×#41	—	2	4	no	—
53	C₂×C₁₁×#41	—	4	2	no	—
54	C₂×C₁₁×#41	C₂³	1	4	yes	—
55	C₂×C₁₁×#41	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₁	—	2	4	no	—
57	C₂²×D₄×C₁₁	—	4	1	no	—
58	C₂²×D₄×C₁₁	—	4	2	no	—
59	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
60	C₁₁×#137	—	2	4	no	—
61	C₁₁×#137	—	2	16	no	—
62	C₁₁×#137	D₄	1	8	yes	complemented
63	C₁₁×#137	C₂³	1	8	yes	complemented
64	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
65	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
66	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
67	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
68	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
69	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
70	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
71	C₁₁×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
72	C₁₁×AGL(1,ℤ/8)	C₂³	1	16	yes	—
73	C₁₁×AGL(1,ℤ/8)	C₂³	1	8	yes	complemented
74	C₁₁×#135	—	2	8	no	—
75	C₁₁×#135	—	2	16	no	—
76	C₁₁×#135	—	2	16	no	—
77	C₁₁×#135	C₂³	1	8	yes	—
78	C₂×C₁₁×SD₁₆	—	2	4	no	—
79	C₂×C₁₁×SD₁₆	—	2	16	no	—
80	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	complemented
81	C₂×C₁₁×D₈	—	2	4	no	—
82	C₂×C₁₁×D₈	—	2	16	no	—
83	C₂×C₁₁×D₈	C₂³	1	8	yes	complemented
84	C₁₁×#131	—	2	8	no	—
85	C₁₁×#131	C₂³	1	16	yes	complemented
86	C₂×C₁₁×M₁₆	—	2	8	no	—
87	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
88	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
89	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
90	C₁₁×#127	—	4	1	no	—
91	C₁₁×#127	C₂³	1	2	yes	—
92	C₁₁×#127	C₂³	1	2	yes	—
93	C₁₁×#127	C₂³	1	1	yes	characteristic, complemented
94	C₁₁×#124	C₂³	1	2	yes	complemented
95	C₁₁×#121	—	4	1	no	—
96	C₄×D₄×C₁₁	—	4	1	no	—
97	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
98	C₁₁×#108	C₂³	1	8	yes	complemented
99	C₁₁×#104	C₂³	1	8	yes	complemented
100	C₁₁×#104	C₂³	1	8	yes	complemented
101	C₁₁×#101	C₂³	1	4	yes	complemented
102	C₁₁×#100	C₂³	1	8	yes	complemented
103	C₁₁×#100	C₂³	1	4	yes	complemented
104	C₁₁×#97	C₂³	1	2	yes	complemented
105	C₄×C₈×C₁₁	C₂³	1	2	yes	complemented
106	#61110	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₁	—	2	2	no	—
108	C₂⁴×C₁₁	—	4	2	no	—
109	C₁₁×#41	—	2	4	no	—
110	C₁₁×#41	—	2	4	no	—
111	C₁₁×#41	—	2	8	no	—
112	C₁₁×#41	—	2	16	no	—
113	C₁₁×#41	—	2	8	no	—
114	C₁₁×#41	—	2	4	no	—
115	C₁₁×#41	—	2	4	no	—
116	C₁₁×#41	—	4	4	no	—
117	C₁₁×#41	—	4	4	no	—
118	C₁₁×#41	—	4	8	no	—
119	C₁₁×#41	—	4	8	no	—
120	C₁₁×#41	—	4	4	no	—
121	C₁₁×#41	C₂×D₄	1	8	yes	—
122	C₁₁×#41	C₂⁴	1	8	yes	—
123	C₂×Q₈×C₁₁	—	2	8	no	—
124	C₂×Q₈×C₁₁	—	4	2	no	—
125	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
127	C₂×D₄×C₁₁	—	2	4	no	—
128	C₂×D₄×C₁₁	—	2	8	no	—
129	C₂×D₄×C₁₁	—	2	16	no	—
130	C₂×D₄×C₁₁	—	2	2	no	—
131	C₂×D₄×C₁₁	—	2	4	no	—
132	C₂×D₄×C₁₁	—	2	4	no	—
133	C₂×D₄×C₁₁	—	2	2	no	—
134	C₂×D₄×C₁₁	—	4	8	no	—
135	C₂×D₄×C₁₁	—	4	4	no	—
136	C₂×D₄×C₁₁	—	4	1	no	—
137	C₂×D₄×C₁₁	—	4	2	no	—
138	C₂×D₄×C₁₁	—	4	2	no	—
139	C₂×D₄×C₁₁	—	4	8	no	—
140	C₂×D₄×C₁₁	—	4	4	no	—
141	C₂×D₄×C₁₁	—	4	8	no	—
142	C₂×D₄×C₁₁	—	4	2	no	—
143	C₂×D₄×C₁₁	—	4	8	no	—
144	C₂×D₄×C₁₁	—	8	4	no	—
145	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
147	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₁	—	2	4	no	—
149	C₂²×C₄×C₁₁	—	2	1	no	—
150	C₂²×C₄×C₁₁	—	2	2	no	—
151	C₂²×C₄×C₁₁	—	4	2	no	—
152	C₂²×C₄×C₁₁	—	4	4	no	—
153	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
154	C₁₁×Q₁₆	—	2	8	no	—
155	C₁₁×Q₁₆	C₂×D₄	1	8	yes	complemented
156	C₁₁×SD₁₆	—	2	16	no	—
157	C₁₁×SD₁₆	—	2	16	no	—
158	C₁₁×SD₁₆	—	2	8	no	—
159	C₁₁×SD₁₆	—	2	8	no	—
160	C₁₁×SD₁₆	C₂×D₄	1	16	yes	complemented
161	C₁₁×D₈	—	2	16	no	—
162	C₁₁×D₈	—	2	16	no	—
163	C₁₁×D₈	—	2	8	no	—
164	C₁₁×D₈	C₂×D₄	1	8	yes	complemented
165	C₁₁×M₁₆	—	2	16	no	—
166	C₁₁×M₁₆	—	2	4	no	—
167	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
168	C₁₁×M₁₆	C₂⁴	1	8	yes	—
169	C₂×C₈×C₁₁	—	2	16	no	—
170	C₂×C₈×C₁₁	—	2	4	no	—
171	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
172	C₁₁×C₄⋊C₄	—	4	1	no	—
173	C₁₁×C₂²⋊C₄	—	4	2	no	—
174	C₄²×C₁₁	—	2	1	no	—
175	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
176	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
177	#3585	C₂×C₁₁	1	4	yes	complemented
178	#3292	C₂×C₁₁	1	4	yes	complemented
179	#3291	C₂×C₁₁	1	4	yes	complemented
180	#3288	C₂×C₁₁	1	8	yes	complemented
181	#3151	C₂×C₁₁	1	1	yes	characteristic, complemented
182	#3068	C₂×C₁₁	1	4	yes	complemented
183	#3018	C₂×C₁₁	1	2	yes	complemented
184	C₂×#453	C₂×C₁₁	1	2	yes	complemented
185	#2956	C₂×C₁₁	1	2	yes	complemented
186	C₂³×C₁₁	—	2	4	no	—
187	C₂³×C₁₁	—	2	2	no	—
188	C₂³×C₁₁	—	2	4	no	—
189	C₂³×C₁₁	—	4	4	no	—
190	C₂³×C₁₁	—	4	8	no	—
191	C₂³×C₁₁	—	4	2	no	—
192	C₂³×C₁₁	—	4	2	no	—
193	C₂³×C₁₁	—	8	4	no	—
194	C₂³×C₁₁	—	16	4	no	—
195	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
196	Q₈×C₁₁	—	2	4	no	—
197	Q₈×C₁₁	—	2	4	no	—
198	Q₈×C₁₁	—	4	4	no	—
199	Q₈×C₁₁	C₂²×D₄	1	8	yes	—
200	D₄×C₁₁	—	2	8	no	—
201	D₄×C₁₁	—	2	8	no	—
202	D₄×C₁₁	—	2	4	no	—
203	D₄×C₁₁	—	2	4	no	—
204	D₄×C₁₁	—	2	8	no	—
205	D₄×C₁₁	—	4	16	no	—
206	D₄×C₁₁	—	4	8	no	—
207	D₄×C₁₁	—	4	4	no	—
208	D₄×C₁₁	—	4	4	no	—
209	D₄×C₁₁	—	4	4	no	—
210	D₄×C₁₁	—	8	2	no	—
211	D₄×C₁₁	—	8	4	no	—
212	D₄×C₁₁	—	8	4	no	—
213	D₄×C₁₁	C₂²×D₄	1	8	yes	—
214	C₂×C₄×C₁₁	—	2	4	no	—
215	C₂×C₄×C₁₁	—	2	1	no	—
216	C₂×C₄×C₁₁	—	2	8	no	—
217	C₂×C₄×C₁₁	—	2	8	no	—
218	C₂×C₄×C₁₁	—	2	1	no	—
219	C₂×C₄×C₁₁	—	2	2	no	—
220	C₂×C₄×C₁₁	—	4	8	no	—
221	C₂×C₄×C₁₁	—	4	4	no	—
222	C₂×C₄×C₁₁	—	4	8	no	—
223	C₂×C₄×C₁₁	—	4	2	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
229	C₈×C₁₁	—	2	8	no	—
230	C₈×C₁₁	C₂²×D₄	1	8	yes	—
231	#585	C₂²×C₁₁	1	2	yes	complemented
232	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	2	yes	complemented
233	#577	—	2	8	no	—
234	#577	C₂²×C₁₁	1	16	yes	complemented
235	#576	—	2	8	no	—
236	#576	C₂²×C₁₁	1	16	yes	complemented
237	#575	—	2	8	no	—
238	#575	C₂²×C₁₁	1	2	yes	—
239	#575	C₂²×C₁₁	1	4	yes	complemented
240	C₂×AGL(1,ℤ/8)	—	2	8	no	—
241	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	4	yes	complemented
242	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	4	yes	complemented
243	#568	C₂²×C₁₁	1	4	yes	complemented
244	#532	C₂²×C₁₁	1	1	yes	characteristic, complemented
245	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	#496	C₂²×C₁₁	1	4	yes	complemented
247	#493	C₂²×C₁₁	1	2	yes	complemented
248	#492	C₂²×C₁₁	1	2	yes	complemented
249	#472	C₂²×C₁₁	1	16	yes	complemented
250	#471	C₂²×C₁₁	1	16	yes	complemented
251	#456	C₂²×C₁₁	1	4	yes	complemented
252	#455	C₂²×C₁₁	1	4	yes	complemented
253	#454	C₂²×C₁₁	1	4	yes	complemented
254	#453	C₂²×C₁₁	1	8	yes	complemented
255	#453	C₂²×C₁₁	1	8	yes	complemented
256	#453	C₂²×C₁₁	1	4	yes	complemented
257	#444	C₂²×C₁₁	1	8	yes	complemented
258	#443	C₂²×C₁₁	1	8	yes	complemented
259	#430	C₂²×C₁₁	1	2	yes	complemented
260	C₂×#104	C₂²×C₁₁	1	4	yes	complemented
261	#413	C₂²×C₁₁	1	2	yes	complemented
262	C₂×#100	C₂²×C₁₁	1	2	yes	complemented
263	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
264	C₂²×C₁₁	—	2	8	no	—
265	C₂²×C₁₁	—	4	1	no	—
266	C₂²×C₁₁	—	4	2	no	—
267	C₂²×C₁₁	—	4	4	no	—
268	C₂²×C₁₁	—	8	4	no	—
269	C₂²×C₁₁	—	8	4	no	—
270	C₂²×C₁₁	—	8	2	no	—
271	C₂²×C₁₁	—	8	4	no	—
272	C₂²×C₁₁	—	16	2	no	—
273	C₂²×C₁₁	—	16	4	no	—
274	C₂²×C₁₁	—	16	8	no	—
275	C₂²×C₁₁	D₄²	1	2	yes	—
276	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
277	C₄×C₁₁	—	2	2	no	—
278	C₄×C₁₁	—	2	8	no	—
279	C₄×C₁₁	—	4	1	no	—
280	C₄×C₁₁	—	4	2	no	—
281	C₄×C₁₁	D₄²	1	2	yes	—
282	C₄×C₁₁	C₂³×D₄	1	2	yes	—
283	2₋¹⁺⁴	—	2	4	no	—
284	2₋¹⁺⁴	C₂³×C₁₁	1	4	yes	—
285	H(5,𝔽₂)	—	2	8	no	—
286	H(5,𝔽₂)	—	2	4	no	—
287	H(5,𝔽₂)	—	4	2	no	—
288	H(5,𝔽₂)	—	4	2	no	—
289	H(5,𝔽₂)	C₂³×C₁₁	1	4	yes	—
290	H(5,𝔽₂)	C₂³×C₁₁	1	8	yes	complemented
291	C₂×#41	—	2	8	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	4	2	no	—
294	C₂×#41	C₂³×C₁₁	1	4	yes	—
295	C₂×#41	C₂³×C₁₁	1	2	yes	—
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	—	4	1	no	—
298	C₂²×D₄	—	4	2	no	—
299	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
300	#137	—	2	4	no	—
301	#137	—	2	16	no	—
302	#137	D₄×C₁₁	1	8	yes	complemented
303	#137	C₂³×C₁₁	1	8	yes	complemented
304	AGL(1,ℤ/8)	—	2	8	no	—
305	AGL(1,ℤ/8)	—	2	4	no	—
306	AGL(1,ℤ/8)	—	2	16	no	—
307	AGL(1,ℤ/8)	—	2	16	no	—
308	AGL(1,ℤ/8)	—	2	16	no	—
309	AGL(1,ℤ/8)	—	2	8	no	—
310	AGL(1,ℤ/8)	—	2	8	no	—
311	AGL(1,ℤ/8)	D₄×C₁₁	1	8	yes	complemented
312	AGL(1,ℤ/8)	C₂³×C₁₁	1	16	yes	—
313	AGL(1,ℤ/8)	C₂³×C₁₁	1	8	yes	complemented
314	#135	—	2	8	no	—
315	#135	—	2	16	no	—
316	#135	—	2	16	no	—
317	#135	C₂³×C₁₁	1	8	yes	—
318	C₂×SD₁₆	—	2	4	no	—
319	C₂×SD₁₆	—	2	16	no	—
320	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	complemented
321	C₂×D₈	—	2	4	no	—
322	C₂×D₈	—	2	16	no	—
323	C₂×D₈	C₂³×C₁₁	1	8	yes	complemented
324	#131	—	2	8	no	—
325	#131	C₂³×C₁₁	1	16	yes	complemented
326	C₂×M₁₆	—	2	8	no	—
327	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
328	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic, complemented
330	#127	—	4	1	no	—
331	#127	C₂³×C₁₁	1	2	yes	—
332	#127	C₂³×C₁₁	1	2	yes	—
333	#127	C₂³×C₁₁	1	1	yes	characteristic, complemented
334	#124	C₂³×C₁₁	1	2	yes	complemented
335	#121	—	4	1	no	—
336	C₄×D₄	—	4	1	no	—
337	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
338	#108	C₂³×C₁₁	1	8	yes	complemented
339	#104	C₂³×C₁₁	1	8	yes	complemented
340	#104	C₂³×C₁₁	1	8	yes	complemented
341	#101	C₂³×C₁₁	1	4	yes	complemented
342	#100	C₂³×C₁₁	1	8	yes	complemented
343	#100	C₂³×C₁₁	1	4	yes	complemented
344	#97	C₂³×C₁₁	1	2	yes	complemented
345	C₄×C₈	C₂³×C₁₁	1	2	yes	complemented
346	C₂×C₁₁	—	2	1	no	—
347	C₂×C₁₁	—	2	2	no	—
348	C₂×C₁₁	—	4	8	no	—
349	C₂×C₁₁	—	8	4	no	—
350	C₂×C₁₁	—	8	2	no	—
351	C₂×C₁₁	C₂×D₄²	1	1	yes	characteristic
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	4	2	no	—
354	#41	—	2	4	no	—
355	#41	—	2	4	no	—
356	#41	—	2	8	no	—
357	#41	—	2	16	no	—
358	#41	—	2	8	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	4	4	no	—
362	#41	—	4	4	no	—
363	#41	—	4	8	no	—
364	#41	—	4	8	no	—
365	#41	—	4	4	no	—
366	#41	C₂×D₄×C₁₁	1	8	yes	—
367	#41	C₂⁴×C₁₁	1	8	yes	—
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
371	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	4	8	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	8	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	8	4	no	—
390	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
391	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
392	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
399	Q₁₆	—	2	8	no	—
400	Q₁₆	C₂×D₄×C₁₁	1	8	yes	complemented
401	SD₁₆	—	2	16	no	—
402	SD₁₆	—	2	8	no	—
403	SD₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	SD₁₆	C₂×D₄×C₁₁	1	16	yes	complemented
406	D₈	—	2	16	no	—
407	D₈	—	2	8	no	—
408	D₈	—	2	16	no	—
409	D₈	C₂×D₄×C₁₁	1	8	yes	complemented
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	16	no	—
412	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
413	M₁₆	C₂⁴×C₁₁	1	8	yes	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	16	no	—
416	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
417	C₄⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
421	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
422	C₁₁	#61110	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	16	4	no	—
432	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	4	no	—
436	Q₈	C₂²×D₄×C₁₁	1	8	yes	—
437	D₄	—	2	8	no	—
438	D₄	—	2	8	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	8	no	—
442	D₄	—	4	16	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	8	2	no	—
448	D₄	—	8	4	no	—
449	D₄	—	8	4	no	—
450	D₄	C₂²×D₄×C₁₁	1	8	yes	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
464	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
466	C₈	—	2	8	no	—
467	C₈	C₂²×D₄×C₁₁	1	8	yes	—
468	C₂²	—	2	8	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	16	2	no	—
477	C₂²	—	16	8	no	—
478	C₂²	—	16	4	no	—
479	C₂²	D₄²×C₁₁	1	2	yes	—
480	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	2	8	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	D₄²×C₁₁	1	2	yes	—
486	C₄	C₂³×D₄×C₁₁	1	2	yes	—
487	C₂	—	2	1	no	—
488	C₂	—	2	2	no	—
489	C₂	—	4	8	no	—
490	C₂	—	8	4	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂×D₄²×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3585	C₂	semidirect
2. C₁₁×#3292	C₂	semidirect
3. C₁₁×#3291	C₂	semidirect
4. C₁₁×#3288	C₂	semidirect
5. C₁₁×#3151	C₂	semidirect
6. C₁₁×#3068	C₂	semidirect
7. C₁₁×#3018	C₂	semidirect
8. C₂×C₁₁×#453	C₂	semidirect
9. C₁₁×#2956	C₂	semidirect
10. C₁₁×#585	C₂²	semidirect
11. C₂×C₁₁×H(5,𝔽₂)	C₂²	semidirect
13. C₁₁×#577	C₂²	semidirect
15. C₁₁×#576	C₂²	semidirect
18. C₁₁×#575	C₂²	semidirect
20. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₁₁×#568	C₂²	semidirect
23. C₁₁×#532	C₂²	semidirect
24. C₂×C₁₁×#127	C₂²	semidirect
25. C₁₁×#496	C₂²	semidirect
26. C₁₁×#493	C₂²	semidirect
27. C₁₁×#492	C₂²	semidirect
28. C₁₁×#472	C₂²	semidirect
29. C₁₁×#471	C₂²	semidirect
30. C₁₁×#456	C₂²	semidirect
31. C₁₁×#455	C₂²	semidirect
32. C₁₁×#454	C₂²	semidirect
33. C₁₁×#453	C₂²	semidirect
34. C₁₁×#453	C₂²	semidirect
35. C₁₁×#453	C₂²	semidirect
36. C₁₁×#444	C₂²	semidirect
37. C₁₁×#443	C₂²	semidirect
38. C₁₁×#430	C₂²	semidirect
39. C₂×C₁₁×#104	C₂²	semidirect
40. C₁₁×#413	C₂²	semidirect
41. C₂×C₁₁×#100	C₂²	semidirect
42. C₄×C₁₁×M₁₆	C₂²	semidirect
50. C₁₁×H(5,𝔽₂)	C₂³	semidirect
62. C₁₁×#137	D₄	semidirect
63. C₁₁×#137	C₂³	semidirect
71. C₁₁×AGL(1,ℤ/8)	D₄	semidirect
73. C₁₁×AGL(1,ℤ/8)	C₂³	semidirect
80. C₂×C₁₁×SD₁₆	C₂³	semidirect
83. C₂×C₁₁×D₈	C₂³	semidirect
85. C₁₁×#131	C₂³	semidirect
89. C₁₁×C₄⋊Q₈	C₂³	semidirect
93. C₁₁×#127	C₂³	semidirect
94. C₁₁×#124	C₂³	semidirect
98. C₁₁×#108	C₂³	semidirect
99. C₁₁×#104	C₂³	semidirect
100. C₁₁×#104	C₂³	semidirect
101. C₁₁×#101	C₂³	semidirect
102. C₁₁×#100	C₂³	semidirect
103. C₁₁×#100	C₂³	semidirect
104. C₁₁×#97	C₂³	semidirect
105. C₄×C₈×C₁₁	C₂³	semidirect
106. #61110	C₁₁	direct (N × H)
155. C₁₁×Q₁₆	C₂×D₄	semidirect
160. C₁₁×SD₁₆	C₂×D₄	semidirect
164. C₁₁×D₈	C₂×D₄	semidirect
177. #3585	C₂×C₁₁	semidirect
178. #3292	C₂×C₁₁	semidirect
179. #3291	C₂×C₁₁	semidirect
180. #3288	C₂×C₁₁	semidirect
181. #3151	C₂×C₁₁	semidirect
182. #3068	C₂×C₁₁	semidirect
183. #3018	C₂×C₁₁	semidirect
184. C₂×#453	C₂×C₁₁	semidirect
185. #2956	C₂×C₁₁	semidirect
231. #585	C₂²×C₁₁	semidirect
232. C₂×H(5,𝔽₂)	C₂²×C₁₁	semidirect
234. #577	C₂²×C₁₁	semidirect
236. #576	C₂²×C₁₁	semidirect
239. #575	C₂²×C₁₁	semidirect
241. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
242. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
243. #568	C₂²×C₁₁	semidirect
244. #532	C₂²×C₁₁	semidirect
245. C₂×#127	C₂²×C₁₁	semidirect
246. #496	C₂²×C₁₁	semidirect
247. #493	C₂²×C₁₁	semidirect
248. #492	C₂²×C₁₁	semidirect
249. #472	C₂²×C₁₁	semidirect
250. #471	C₂²×C₁₁	semidirect
251. #456	C₂²×C₁₁	semidirect
252. #455	C₂²×C₁₁	semidirect
253. #454	C₂²×C₁₁	semidirect
254. #453	C₂²×C₁₁	semidirect
255. #453	C₂²×C₁₁	semidirect
256. #453	C₂²×C₁₁	semidirect
257. #444	C₂²×C₁₁	semidirect
258. #443	C₂²×C₁₁	semidirect
259. #430	C₂²×C₁₁	semidirect
260. C₂×#104	C₂²×C₁₁	semidirect
261. #413	C₂²×C₁₁	semidirect
262. C₂×#100	C₂²×C₁₁	semidirect
263. C₄×M₁₆	C₂²×C₁₁	semidirect
290. H(5,𝔽₂)	C₂³×C₁₁	semidirect
302. #137	D₄×C₁₁	semidirect
303. #137	C₂³×C₁₁	semidirect
311. AGL(1,ℤ/8)	D₄×C₁₁	semidirect
313. AGL(1,ℤ/8)	C₂³×C₁₁	semidirect
320. C₂×SD₁₆	C₂³×C₁₁	semidirect
323. C₂×D₈	C₂³×C₁₁	semidirect
325. #131	C₂³×C₁₁	semidirect
329. C₄⋊Q₈	C₂³×C₁₁	semidirect
333. #127	C₂³×C₁₁	semidirect
334. #124	C₂³×C₁₁	semidirect
338. #108	C₂³×C₁₁	semidirect
339. #104	C₂³×C₁₁	semidirect
340. #104	C₂³×C₁₁	semidirect
341. #101	C₂³×C₁₁	semidirect
342. #100	C₂³×C₁₁	semidirect
343. #100	C₂³×C₁₁	semidirect
344. #97	C₂³×C₁₁	semidirect
345. C₄×C₈	C₂³×C₁₁	semidirect
400. Q₁₆	C₂×D₄×C₁₁	semidirect
405. SD₁₆	C₂×D₄×C₁₁	semidirect
409. D₈	C₂×D₄×C₁₁	semidirect
422. C₁₁	#61110	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3585	2
C₁₁×#3292	2
C₁₁×#3291	2
C₁₁×#3288	2
C₁₁×#3151	2
C₁₁×#3068	2
C₁₁×#3018	2
C₂×C₁₁×#453	2
C₁₁×#2956	2
#61110	11

Subgroups — C11×#61110 #14638303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61110 #14638303