Subgroups — C₁₁×#61951 #14639144

Order 2816.

2168 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3498	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3392	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3295	C₂	1	6	yes	maximal, complemented
6	D₄×C₁₁×SD₁₆	C₂	1	6	yes	maximal, complemented
7	C₁₁×#3246	C₂	1	3	yes	maximal, complemented
8	C₁₁×#3208	C₂	1	3	yes	maximal, complemented
9	C₁₁×#3103	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₁×#460	C₂	1	3	yes	maximal, complemented
11	C₁₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×H(5,𝔽₂)	—	2	1	no	—
13	C₂²×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
14	Q₈²×C₁₁	C₂²	1	1	yes	characteristic, complemented
15	C₁₁×#557	—	2	1	no	—
16	C₁₁×#557	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#554	—	2	3	no	—
18	C₁₁×#554	C₂²	1	3	yes	complemented
19	C₁₁×#550	—	2	1	no	—
20	C₁₁×#550	C₂²	1	2	yes	—
21	D₄×Q₈×C₁₁	C₂²	1	3	yes	complemented
22	D₄²×C₁₁	—	2	3	no	—
23	D₄²×C₁₁	C₂²	1	6	yes	—
24	C₁₁×#535	—	2	3	no	—
25	C₁₁×#533	—	2	3	no	—
26	C₁₁×#533	C₂²	1	3	yes	complemented
27	C₁₁×#532	C₂²	1	3	yes	—
28	C₂×C₁₁×#127	C₂²	1	3	yes	—
29	C₄×C₁₁×#41	—	2	1	no	—
30	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₁	C₂²	1	3	yes	complemented
32	C₁₁×#492	C₂²	1	6	yes	complemented
33	C₁₁×#486	C₂²	1	6	yes	complemented
34	C₁₁×#481	C₂²	1	6	yes	complemented
35	C₁₁×#476	C₂²	1	6	yes	complemented
36	C₁₁×#475	C₂²	1	3	yes	complemented
37	C₁₁×#475	C₂²	1	1	yes	characteristic, complemented
38	C₁₁×#465	C₂²	1	12	yes	complemented
39	C₁₁×#461	C₂²	1	6	yes	complemented
40	C₁₁×#460	C₂²	1	3	yes	complemented
41	C₁₁×#460	C₂²	1	6	yes	complemented
42	C₁₁×#460	C₂²	1	6	yes	complemented
43	C₁₁×#460	C₂²	1	3	yes	complemented
44	C₁₁×#460	C₂²	1	6	yes	complemented
45	C₁₁×#450	C₂²	1	12	yes	complemented
46	C₁₁×#448	C₂²	1	6	yes	complemented
47	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
48	C₄×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
49	C₄×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
50	C₈×D₄×C₁₁	C₂²	1	6	yes	complemented
51	C₁₁×#431	C₂²	1	3	yes	complemented
52	C₂×C₁₁×C₄⋊C₈	C₂²	1	3	yes	complemented
53	C₂×C₁₁×#102	C₂²	1	6	yes	complemented
54	C₁₁×H(5,𝔽₂)	—	4	8	no	—
55	C₂×C₁₁×#41	—	2	2	no	—
56	C₂×C₁₁×#41	—	2	3	no	—
57	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₁	C₂³	1	3	yes	—
59	C₂²×D₄×C₁₁	—	2	6	no	—
60	C₂²×D₄×C₁₁	—	2	3	no	—
61	C₂²×D₄×C₁₁	—	2	3	no	—
62	C₂²×D₄×C₁₁	C₂³	1	6	yes	—
63	C₂×C₁₁×SD₁₆	—	4	12	no	—
64	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
65	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
66	C₂×C₁₁×SD₁₆	C₂³	1	12	yes	—
67	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
68	C₁₁×C₄⋊Q₈	—	2	3	no	—
69	C₁₁×C₄⋊Q₈	—	2	3	no	—
70	C₁₁×C₄⋊Q₈	C₂³	1	3	yes	—
71	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₁×#127	—	2	3	no	—
74	C₁₁×#127	—	2	3	no	—
75	C₁₁×#127	C₂³	1	6	yes	—
76	C₁₁×#127	C₂³	1	3	yes	—
77	C₁₁×#125	—	2	3	no	—
78	C₁₁×#125	—	2	3	no	—
79	C₁₁×#125	—	2	3	no	—
80	C₁₁×#124	—	2	3	no	—
81	C₁₁×C₂²⋊Q₈	—	2	3	no	—
82	C₁₁×C₂²⋊Q₈	—	2	6	no	—
83	C₁₁×C₂²⋊Q₈	—	2	6	no	—
84	C₁₁×C₂²⋊Q₈	C₂³	1	6	yes	—
85	C₁₁×#121	—	2	3	no	—
86	C₁₁×#121	—	2	6	no	—
87	C₁₁×#121	—	2	6	no	—
88	C₁₁×#121	C₂³	1	6	yes	—
89	C₁₁×#120	—	2	12	no	—
90	C₄×Q₈×C₁₁	—	2	1	no	—
91	C₄×Q₈×C₁₁	—	2	1	no	—
92	C₄×Q₈×C₁₁	—	2	3	no	—
93	C₄×Q₈×C₁₁	—	2	3	no	—
94	C₄×Q₈×C₁₁	—	2	3	no	—
95	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
98	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
99	C₄×Q₈×C₁₁	C₂³	1	3	yes	—
100	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₁	—	2	3	no	—
102	C₄×D₄×C₁₁	—	2	3	no	—
103	C₄×D₄×C₁₁	—	2	3	no	—
104	C₄×D₄×C₁₁	D₄	1	3	yes	—
105	C₄×D₄×C₁₁	C₂³	1	6	yes	—
106	C₄×D₄×C₁₁	C₂³	1	3	yes	—
107	C₁₁×#117	—	2	3	no	—
108	C₁₁×#117	D₄	1	3	yes	—
109	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
111	C₂×C₄²×C₁₁	—	2	3	no	—
112	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
113	C₁₁×#106	C₂³	1	2	yes	—
114	C₁₁×#106	C₂³	1	6	yes	—
115	C₁₁×C₄⋊C₈	C₂³	1	3	yes	—
116	C₁₁×C₄⋊C₈	C₂³	1	6	yes	—
117	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₁×#103	C₂³	1	2	yes	—
119	C₁₁×#103	C₂³	1	6	yes	—
120	C₁₁×#102	C₂³	1	6	yes	—
121	C₁₁×#102	C₂³	1	12	yes	—
122	C₁₁×#102	C₂³	1	6	yes	—
123	C₁₁×C₂²⋊C₈	C₂³	1	6	yes	—
124	C₄×C₈×C₁₁	C₂³	1	6	yes	—
125	#61951	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₁	—	2	6	no	—
127	C₁₁×#41	—	4	8	no	—
128	C₁₁×#41	—	4	12	no	—
129	C₁₁×#41	SD₁₆	1	8	yes	complemented
130	C₂×Q₈×C₁₁	—	2	3	no	—
131	C₂×Q₈×C₁₁	—	2	1	no	—
132	C₂×Q₈×C₁₁	—	2	3	no	—
133	C₂×Q₈×C₁₁	—	2	6	no	—
134	C₂×Q₈×C₁₁	—	4	3	no	—
135	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₁	C₂⁴	1	3	yes	—
137	C₂×Q₈×C₁₁	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₁	—	2	6	no	—
139	C₂×D₄×C₁₁	—	2	3	no	—
140	C₂×D₄×C₁₁	—	2	6	no	—
141	C₂×D₄×C₁₁	—	2	3	no	—
142	C₂×D₄×C₁₁	—	2	6	no	—
143	C₂×D₄×C₁₁	—	2	6	no	—
144	C₂×D₄×C₁₁	—	4	6	no	—
145	C₂×D₄×C₁₁	—	4	6	no	—
146	C₂×D₄×C₁₁	—	4	24	no	—
147	C₂×D₄×C₁₁	—	4	12	no	—
148	C₂×D₄×C₁₁	—	8	6	no	—
149	C₂×D₄×C₁₁	C₂×D₄	1	3	yes	—
150	C₂×D₄×C₁₁	C₂⁴	1	6	yes	—
151	C₂²×C₄×C₁₁	—	2	3	no	—
152	C₂²×C₄×C₁₁	—	2	3	no	—
153	C₂²×C₄×C₁₁	—	2	6	no	—
154	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
157	C₁₁×SD₁₆	—	2	12	no	—
158	C₁₁×SD₁₆	—	4	12	no	—
159	C₁₁×SD₁₆	—	4	6	no	—
160	C₂×C₈×C₁₁	—	4	6	no	—
161	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
162	C₂×C₈×C₁₁	C₂⁴	1	6	yes	—
163	C₁₁×C₄⋊C₄	—	2	1	no	—
164	C₁₁×C₄⋊C₄	—	2	3	no	—
165	C₁₁×C₄⋊C₄	—	2	3	no	—
166	C₁₁×C₄⋊C₄	—	2	3	no	—
167	C₁₁×C₄⋊C₄	—	2	3	no	—
168	C₁₁×C₄⋊C₄	—	2	3	no	—
169	C₁₁×C₄⋊C₄	—	2	3	no	—
170	C₁₁×C₄⋊C₄	—	2	1	no	—
171	C₁₁×C₄⋊C₄	—	2	3	no	—
172	C₁₁×C₄⋊C₄	—	2	6	no	—
173	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
174	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
175	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
176	C₁₁×C₄⋊C₄	C₂⁴	1	3	yes	—
177	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
178	C₁₁×C₂²⋊C₄	—	2	6	no	—
179	C₁₁×C₂²⋊C₄	—	2	6	no	—
180	C₁₁×C₂²⋊C₄	—	2	6	no	—
181	C₁₁×C₂²⋊C₄	C₂×D₄	1	6	yes	—
182	C₄²×C₁₁	—	2	1	no	—
183	C₄²×C₁₁	—	2	3	no	—
184	C₄²×C₁₁	—	2	3	no	—
185	C₄²×C₁₁	—	2	3	no	—
186	C₄²×C₁₁	C₂×D₄	1	3	yes	—
187	C₄²×C₁₁	C₂×D₄	1	3	yes	—
188	C₄²×C₁₁	C₂⁴	1	3	yes	—
189	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
190	#3498	C₂×C₁₁	1	1	yes	characteristic
191	Q₈×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#3392	C₂×C₁₁	1	2	yes	complemented
193	#3362	C₂×C₁₁	1	2	yes	complemented
194	#3295	C₂×C₁₁	1	6	yes	complemented
195	D₄×SD₁₆	C₂×C₁₁	1	6	yes	complemented
196	#3246	C₂×C₁₁	1	3	yes	complemented
197	#3208	C₂×C₁₁	1	3	yes	complemented
198	#3103	C₂×C₁₁	1	3	yes	complemented
199	C₂×#460	C₂×C₁₁	1	3	yes	complemented
200	#2988	C₂×C₁₁	1	1	yes	characteristic, complemented
201	C₂³×C₁₁	—	2	6	no	—
202	C₂³×C₁₁	—	4	12	no	—
203	C₂³×C₁₁	—	8	6	no	—
204	C₂³×C₁₁	—	8	6	no	—
205	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
206	Q₈×C₁₁	—	2	1	no	—
207	Q₈×C₁₁	—	2	3	no	—
208	Q₈×C₁₁	—	2	3	no	—
209	Q₈×C₁₁	—	4	6	no	—
210	Q₈×C₁₁	—	4	2	no	—
211	Q₈×C₁₁	—	8	3	no	—
212	Q₈×C₁₁	C₂×SD₁₆	1	4	yes	complemented
213	Q₈×C₁₁	H(5,𝔽₂)	1	2	yes	complemented
214	D₄×C₁₁	—	2	6	no	—
215	D₄×C₁₁	—	2	6	no	—
216	D₄×C₁₁	—	4	6	no	—
217	D₄×C₁₁	—	4	12	no	—
218	D₄×C₁₁	—	4	12	no	—
219	D₄×C₁₁	—	4	6	no	—
220	D₄×C₁₁	—	8	6	no	—
221	D₄×C₁₁	—	8	6	no	—
222	D₄×C₁₁	C₂×SD₁₆	1	12	yes	complemented
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	3	no	—
225	C₂×C₄×C₁₁	—	2	3	no	—
226	C₂×C₄×C₁₁	—	2	1	no	—
227	C₂×C₄×C₁₁	—	2	3	no	—
228	C₂×C₄×C₁₁	—	2	3	no	—
229	C₂×C₄×C₁₁	—	2	2	no	—
230	C₂×C₄×C₁₁	—	4	3	no	—
231	C₂×C₄×C₁₁	—	4	6	no	—
232	C₂×C₄×C₁₁	—	4	12	no	—
233	C₂×C₄×C₁₁	—	8	3	no	—
234	C₂×C₄×C₁₁	C₂×SD₁₆	1	12	yes	complemented
235	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
237	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
238	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
240	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
241	C₈×C₁₁	—	2	6	no	—
242	C₈×C₁₁	—	2	2	no	—
243	C₂×H(5,𝔽₂)	—	2	1	no	—
244	C₂²×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
245	Q₈²	C₂²×C₁₁	1	1	yes	characteristic, complemented
246	#557	—	2	1	no	—
247	#557	C₂²×C₁₁	1	1	yes	characteristic, complemented
248	#554	—	2	3	no	—
249	#554	C₂²×C₁₁	1	3	yes	complemented
250	#550	—	2	1	no	—
251	#550	C₂²×C₁₁	1	2	yes	—
252	D₄×Q₈	C₂²×C₁₁	1	3	yes	complemented
253	D₄²	—	2	3	no	—
254	D₄²	C₂²×C₁₁	1	6	yes	—
255	#535	—	2	3	no	—
256	#533	—	2	3	no	—
257	#533	C₂²×C₁₁	1	3	yes	complemented
258	#532	C₂²×C₁₁	1	3	yes	—
259	C₂×#127	C₂²×C₁₁	1	3	yes	—
260	C₄×#41	—	2	1	no	—
261	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₁₁	1	3	yes	complemented
263	#492	C₂²×C₁₁	1	6	yes	complemented
264	#486	C₂²×C₁₁	1	6	yes	complemented
265	#481	C₂²×C₁₁	1	6	yes	complemented
266	#476	C₂²×C₁₁	1	6	yes	complemented
267	#475	C₂²×C₁₁	1	1	yes	characteristic, complemented
268	#475	C₂²×C₁₁	1	3	yes	complemented
269	#465	C₂²×C₁₁	1	12	yes	complemented
270	#461	C₂²×C₁₁	1	6	yes	complemented
271	#460	C₂²×C₁₁	1	3	yes	complemented
272	#460	C₂²×C₁₁	1	3	yes	complemented
273	#460	C₂²×C₁₁	1	6	yes	complemented
274	#460	C₂²×C₁₁	1	6	yes	complemented
275	#460	C₂²×C₁₁	1	6	yes	complemented
276	#450	C₂²×C₁₁	1	12	yes	complemented
277	#448	C₂²×C₁₁	1	6	yes	complemented
278	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
279	C₄×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
280	C₄×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
281	C₈×D₄	C₂²×C₁₁	1	6	yes	complemented
282	#431	C₂²×C₁₁	1	3	yes	complemented
283	C₂×C₄⋊C₈	C₂²×C₁₁	1	3	yes	complemented
284	C₂×#102	C₂²×C₁₁	1	6	yes	complemented
285	C₂²×C₁₁	—	2	3	no	—
286	C₂²×C₁₁	—	2	3	no	—
287	C₂²×C₁₁	—	4	6	no	—
288	C₂²×C₁₁	—	4	6	no	—
289	C₂²×C₁₁	—	4	6	no	—
290	C₂²×C₁₁	—	16	12	no	—
291	C₂²×C₁₁	C₂²×SD₁₆	1	6	yes	—
292	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
293	C₄×C₁₁	—	2	1	no	—
294	C₄×C₁₁	—	2	3	no	—
295	C₄×C₁₁	—	2	3	no	—
296	C₄×C₁₁	—	2	2	no	—
297	C₄×C₁₁	—	4	1	no	—
298	C₄×C₁₁	—	4	3	no	—
299	C₄×C₁₁	—	4	3	no	—
300	C₄×C₁₁	—	4	2	no	—
301	C₄×C₁₁	C₂²×SD₁₆	1	6	yes	—
302	C₄×C₁₁	C₂²×SD₁₆	1	2	yes	—
303	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₄×C₁₁	#585	1	1	yes	characteristic
305	H(5,𝔽₂)	—	4	8	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	3	no	—
308	C₂×#41	D₄×C₁₁	1	1	yes	characteristic
309	C₂²×Q₈	C₂³×C₁₁	1	3	yes	—
310	C₂²×D₄	—	2	6	no	—
311	C₂²×D₄	—	2	3	no	—
312	C₂²×D₄	—	2	3	no	—
313	C₂²×D₄	C₂³×C₁₁	1	6	yes	—
314	C₂×SD₁₆	—	4	12	no	—
315	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
316	C₂×SD₁₆	C₂³×C₁₁	1	12	yes	—
317	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
318	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
319	C₄⋊Q₈	—	2	3	no	—
320	C₄⋊Q₈	—	2	3	no	—
321	C₄⋊Q₈	C₂³×C₁₁	1	3	yes	—
322	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₁₁	1	3	yes	—
324	#127	—	2	3	no	—
325	#127	—	2	3	no	—
326	#127	C₂³×C₁₁	1	3	yes	—
327	#127	C₂³×C₁₁	1	6	yes	—
328	#125	—	2	3	no	—
329	#125	—	2	3	no	—
330	#125	—	2	3	no	—
331	#124	—	2	3	no	—
332	C₂²⋊Q₈	—	2	3	no	—
333	C₂²⋊Q₈	—	2	6	no	—
334	C₂²⋊Q₈	—	2	6	no	—
335	C₂²⋊Q₈	C₂³×C₁₁	1	6	yes	—
336	#121	—	2	3	no	—
337	#121	—	2	6	no	—
338	#121	—	2	6	no	—
339	#121	C₂³×C₁₁	1	6	yes	—
340	#120	—	2	12	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	3	no	—
344	C₄×Q₈	—	2	3	no	—
345	C₄×Q₈	—	2	3	no	—
346	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
347	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
348	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
349	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
350	C₄×Q₈	C₂³×C₁₁	1	3	yes	—
351	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	2	3	no	—
355	C₄×D₄	D₄×C₁₁	1	3	yes	—
356	C₄×D₄	C₂³×C₁₁	1	6	yes	—
357	C₄×D₄	C₂³×C₁₁	1	3	yes	—
358	#117	—	2	3	no	—
359	#117	D₄×C₁₁	1	3	yes	—
360	C₂×C₄⋊C₄	—	2	3	no	—
361	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
362	C₂×C₄²	—	2	3	no	—
363	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
364	#106	C₂³×C₁₁	1	2	yes	—
365	#106	C₂³×C₁₁	1	6	yes	—
366	C₄⋊C₈	C₂³×C₁₁	1	3	yes	—
367	C₄⋊C₈	C₂³×C₁₁	1	6	yes	—
368	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
369	#103	C₂³×C₁₁	1	2	yes	—
370	#103	C₂³×C₁₁	1	6	yes	—
371	#102	C₂³×C₁₁	1	6	yes	—
372	#102	C₂³×C₁₁	1	12	yes	—
373	#102	C₂³×C₁₁	1	6	yes	—
374	C₂²⋊C₈	C₂³×C₁₁	1	6	yes	—
375	C₄×C₈	C₂³×C₁₁	1	6	yes	—
376	C₂×C₁₁	—	2	6	no	—
377	C₂×C₁₁	—	8	6	no	—
378	C₂×C₁₁	#3488	1	1	yes	characteristic
379	C₂×C₁₁	C₂³×SD₁₆	1	1	yes	characteristic
380	C₂×C₁₁	#3585	1	1	yes	characteristic
381	C₂⁴	—	2	6	no	—
382	#41	—	4	8	no	—
383	#41	—	4	12	no	—
384	#41	C₁₁×SD₁₆	1	8	yes	complemented
385	C₂×Q₈	—	2	3	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	3	no	—
388	C₂×Q₈	—	2	6	no	—
389	C₂×Q₈	—	4	3	no	—
390	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₂×Q₈	C₂⁴×C₁₁	1	3	yes	—
392	C₂×Q₈	C₂⁴×C₁₁	1	1	yes	characteristic
393	C₂×D₄	—	2	6	no	—
394	C₂×D₄	—	2	3	no	—
395	C₂×D₄	—	2	6	no	—
396	C₂×D₄	—	2	3	no	—
397	C₂×D₄	—	2	6	no	—
398	C₂×D₄	—	2	6	no	—
399	C₂×D₄	—	4	6	no	—
400	C₂×D₄	—	4	6	no	—
401	C₂×D₄	—	4	24	no	—
402	C₂×D₄	—	4	12	no	—
403	C₂×D₄	—	8	6	no	—
404	C₂×D₄	C₂×D₄×C₁₁	1	3	yes	—
405	C₂×D₄	C₂⁴×C₁₁	1	6	yes	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	2	6	no	—
409	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
410	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
411	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
412	SD₁₆	—	2	12	no	—
413	SD₁₆	—	4	12	no	—
414	SD₁₆	—	4	6	no	—
415	C₂×C₈	—	4	6	no	—
416	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
417	C₂×C₈	C₂⁴×C₁₁	1	6	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	3	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	—	2	3	no	—
423	C₄⋊C₄	—	2	3	no	—
424	C₄⋊C₄	—	2	3	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	3	no	—
427	C₄⋊C₄	—	2	6	no	—
428	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
429	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
430	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
431	C₄⋊C₄	C₂⁴×C₁₁	1	3	yes	—
432	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
433	C₂²⋊C₄	—	2	6	no	—
434	C₂²⋊C₄	—	2	6	no	—
435	C₂²⋊C₄	—	2	6	no	—
436	C₂²⋊C₄	C₂×D₄×C₁₁	1	6	yes	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	3	no	—
439	C₄²	—	2	3	no	—
440	C₄²	—	2	3	no	—
441	C₄²	C₂×D₄×C₁₁	1	3	yes	—
442	C₄²	C₂×D₄×C₁₁	1	3	yes	—
443	C₄²	C₂⁴×C₁₁	1	3	yes	—
444	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
445	C₁₁	#61951	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	6	no	—
447	C₂³	—	4	12	no	—
448	C₂³	—	8	6	no	—
449	C₂³	—	8	6	no	—
450	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
451	Q₈	—	2	1	no	—
452	Q₈	—	2	3	no	—
453	Q₈	—	2	3	no	—
454	Q₈	—	4	6	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	8	3	no	—
457	Q₈	C₂×C₁₁×SD₁₆	1	4	yes	complemented
458	Q₈	C₁₁×H(5,𝔽₂)	1	2	yes	complemented
459	D₄	—	2	6	no	—
460	D₄	—	2	6	no	—
461	D₄	—	4	6	no	—
462	D₄	—	4	12	no	—
463	D₄	—	4	12	no	—
464	D₄	—	4	6	no	—
465	D₄	—	8	6	no	—
466	D₄	—	8	6	no	—
467	D₄	C₂×C₁₁×SD₁₆	1	12	yes	complemented
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	3	no	—
470	C₂×C₄	—	2	3	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	3	no	—
476	C₂×C₄	—	4	6	no	—
477	C₂×C₄	—	4	12	no	—
478	C₂×C₄	—	8	3	no	—
479	C₂×C₄	C₂×C₁₁×SD₁₆	1	12	yes	complemented
480	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
482	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
483	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
485	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
486	C₈	—	2	6	no	—
487	C₈	—	2	2	no	—
488	C₂²	—	2	3	no	—
489	C₂²	—	2	3	no	—
490	C₂²	—	4	6	no	—
491	C₂²	—	4	6	no	—
492	C₂²	—	4	6	no	—
493	C₂²	—	16	12	no	—
494	C₂²	C₂²×C₁₁×SD₁₆	1	6	yes	—
495	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
496	C₄	—	2	3	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	3	no	—
500	C₄	—	4	3	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	3	no	—
504	C₄	C₂²×C₁₁×SD₁₆	1	6	yes	—
505	C₄	C₂²×C₁₁×SD₁₆	1	2	yes	—
506	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄	C₁₁×#585	1	1	yes	characteristic
508	C₂	—	2	6	no	—
509	C₂	—	8	6	no	—
510	C₂	C₁₁×#3488	1	1	yes	characteristic
511	C₂	C₂³×C₁₁×SD₁₆	1	1	yes	characteristic
512	C₂	C₁₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₁₁×#3498	C₂
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
2. Q₈×C₁₁×#41	C₂	semidirect
3. C₁₁×#3392	C₂	semidirect
4. C₁₁×#3362	C₂	semidirect
5. C₁₁×#3295	C₂	semidirect
6. D₄×C₁₁×SD₁₆	C₂	semidirect
7. C₁₁×#3246	C₂	semidirect
8. C₁₁×#3208	C₂	semidirect
9. C₁₁×#3103	C₂	semidirect
10. C₂×C₁₁×#460	C₂	semidirect
11. C₁₁×#2988	C₂	semidirect
13. C₂²×C₁₁×SD₁₆	C₂²	semidirect
14. Q₈²×C₁₁	C₂²	semidirect
16. C₁₁×#557	C₂²	semidirect
18. C₁₁×#554	C₂²	semidirect
21. D₄×Q₈×C₁₁	C₂²	semidirect
26. C₁₁×#533	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
32. C₁₁×#492	C₂²	semidirect
33. C₁₁×#486	C₂²	semidirect
34. C₁₁×#481	C₂²	semidirect
35. C₁₁×#476	C₂²	semidirect
36. C₁₁×#475	C₂²	semidirect
37. C₁₁×#475	C₂²	semidirect
38. C₁₁×#465	C₂²	semidirect
39. C₁₁×#461	C₂²	semidirect
40. C₁₁×#460	C₂²	semidirect
41. C₁₁×#460	C₂²	semidirect
42. C₁₁×#460	C₂²	semidirect
43. C₁₁×#460	C₂²	semidirect
44. C₁₁×#460	C₂²	semidirect
45. C₁₁×#450	C₂²	semidirect
46. C₁₁×#448	C₂²	semidirect
47. C₈×Q₈×C₁₁	C₂²	semidirect
48. C₄×C₁₁×SD₁₆	C₂²	semidirect
49. C₄×C₁₁×SD₁₆	C₂²	semidirect
50. C₈×D₄×C₁₁	C₂²	semidirect
51. C₁₁×#431	C₂²	semidirect
52. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
53. C₂×C₁₁×#102	C₂²	semidirect
125. #61951	C₁₁	direct (N × H)
129. C₁₁×#41	SD₁₆	semidirect
191. Q₈×#41	C₂×C₁₁	semidirect
192. #3392	C₂×C₁₁	semidirect
193. #3362	C₂×C₁₁	semidirect
194. #3295	C₂×C₁₁	semidirect
195. D₄×SD₁₆	C₂×C₁₁	semidirect
196. #3246	C₂×C₁₁	semidirect
197. #3208	C₂×C₁₁	semidirect
198. #3103	C₂×C₁₁	semidirect
199. C₂×#460	C₂×C₁₁	semidirect
200. #2988	C₂×C₁₁	semidirect
212. Q₈×C₁₁	C₂×SD₁₆	semidirect
213. Q₈×C₁₁	H(5,𝔽₂)	semidirect
222. D₄×C₁₁	C₂×SD₁₆	semidirect
234. C₂×C₄×C₁₁	C₂×SD₁₆	semidirect
244. C₂²×SD₁₆	C₂²×C₁₁	semidirect
245. Q₈²	C₂²×C₁₁	semidirect
247. #557	C₂²×C₁₁	semidirect
249. #554	C₂²×C₁₁	semidirect
252. D₄×Q₈	C₂²×C₁₁	semidirect
257. #533	C₂²×C₁₁	semidirect
262. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
263. #492	C₂²×C₁₁	semidirect
264. #486	C₂²×C₁₁	semidirect
265. #481	C₂²×C₁₁	semidirect
266. #476	C₂²×C₁₁	semidirect
267. #475	C₂²×C₁₁	semidirect
268. #475	C₂²×C₁₁	semidirect
269. #465	C₂²×C₁₁	semidirect
270. #461	C₂²×C₁₁	semidirect
271. #460	C₂²×C₁₁	semidirect
272. #460	C₂²×C₁₁	semidirect
273. #460	C₂²×C₁₁	semidirect
274. #460	C₂²×C₁₁	semidirect
275. #460	C₂²×C₁₁	semidirect
276. #450	C₂²×C₁₁	semidirect
277. #448	C₂²×C₁₁	semidirect
278. C₈×Q₈	C₂²×C₁₁	semidirect
279. C₄×SD₁₆	C₂²×C₁₁	semidirect
280. C₄×SD₁₆	C₂²×C₁₁	semidirect
281. C₈×D₄	C₂²×C₁₁	semidirect
282. #431	C₂²×C₁₁	semidirect
283. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
284. C₂×#102	C₂²×C₁₁	semidirect
384. #41	C₁₁×SD₁₆	semidirect
445. C₁₁	#61951	direct (N × H)
457. Q₈	C₂×C₁₁×SD₁₆	semidirect
458. Q₈	C₁₁×H(5,𝔽₂)	semidirect
467. D₄	C₂×C₁₁×SD₁₆	semidirect
479. C₂×C₄	C₂×C₁₁×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3498	2
Q₈×C₁₁×#41	2
C₁₁×#3392	2
C₁₁×#3362	2
C₁₁×#3295	2
D₄×C₁₁×SD₁₆	2
C₁₁×#3246	2
C₁₁×#3208	2
C₁₁×#3103	2
C₂×C₁₁×#460	2
C₁₁×#2988	2
#61951	11

Subgroups — C11×#61951 #14639144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#61951 #14639144