Subgroups — C₁₁×#60718 #14637911

Order 2816.

1942 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×#3511	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3182	C₂	1	4	yes	maximal, complemented
3	C₁₁×#3175	C₂	1	8	yes	maximal, complemented
4	C₁₁×#3170	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3169	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3141	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3061	C₂	1	4	yes	maximal, complemented
10	C₁₁×#2951	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	4	yes	—
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₁₁×#556	—	2	2	no	—
15	C₁₁×#555	—	2	2	no	—
16	C₁₁×#554	—	2	2	no	—
17	C₁₁×#553	—	2	4	no	—
18	C₁₁×#548	—	2	4	no	—
19	C₁₁×#547	—	2	2	no	—
20	C₁₁×#542	C₂²	1	8	yes	—
21	C₁₁×#537	C₂²	1	4	yes	—
22	C₁₁×#533	C₂²	1	4	yes	—
23	C₁₁×#532	C₂²	1	2	yes	—
24	C₁₁×#532	C₂²	1	4	yes	—
25	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₁₁×#520	C₂²	1	4	yes	—
27	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
28	C₁₁×#500	C₂²	1	2	yes	—
29	C₁₁×#500	C₂²	1	4	yes	—
30	C₁₁×#500	C₂²	1	2	yes	—
31	C₁₁×#495	C₂²	1	4	yes	—
32	C₁₁×#494	C₂²	1	1	yes	characteristic
33	C₁₁×#493	C₂²	1	1	yes	characteristic
34	C₁₁×#492	C₂²	1	2	yes	—
35	C₁₁×#489	C₂²	1	8	yes	—
36	C₁₁×#487	C₂²	1	4	yes	—
37	C₁₁×#486	C₂²	1	4	yes	—
38	C₁₁×#468	C₂²	1	16	yes	—
39	C₁₁×#467	C₂²	1	8	yes	—
40	C₁₁×#466	C₂²	1	8	yes	—
41	C₁₁×#440	C₂²	1	16	yes	—
42	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	—
43	C₄×C₁₁×D₈	C₂²	1	8	yes	—
44	C₂×C₁₁×#107	C₂²	1	4	yes	—
45	C₁₁×#417	C₂²	1	8	yes	—
46	C₁₁×#405	C₂²	1	4	yes	—
47	C₁₁×#405	C₂²	1	2	yes	—
48	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
49	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
52	C₂×C₁₁×#41	—	2	4	no	—
53	C₂×C₁₁×#41	C₂³	1	4	yes	—
54	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₁	—	2	2	no	—
56	C₁₁×#135	—	2	16	no	—
57	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
58	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
59	C₂×C₁₁×D₈	C₂³	1	4	yes	—
60	C₁₁×#131	—	2	8	no	—
61	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
63	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
64	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
65	C₁₁×C₄⋊Q₈	—	2	2	no	—
66	C₁₁×C₄⋊Q₈	—	2	2	no	—
67	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
70	C₁₁×#127	C₂³	1	2	yes	—
71	C₁₁×#126	—	2	8	no	—
72	C₁₁×#125	—	2	4	no	—
73	C₁₁×#124	—	2	8	no	—
74	C₁₁×#124	—	2	4	no	—
75	C₁₁×#124	C₂³	1	4	yes	—
76	C₁₁×#123	—	2	8	no	—
77	C₁₁×C₂²⋊Q₈	—	2	4	no	—
78	C₁₁×C₂²⋊Q₈	—	2	4	no	—
79	C₁₁×C₂²⋊Q₈	—	2	8	no	—
80	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
81	C₁₁×#121	—	2	4	no	—
82	C₁₁×#121	—	2	8	no	—
83	C₁₁×#121	—	2	2	no	—
84	C₁₁×#121	—	2	2	no	—
85	C₁₁×#121	—	2	4	no	—
86	C₁₁×#121	C₂³	1	8	yes	—
87	C₄×Q₈×C₁₁	—	2	4	no	—
88	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
91	C₄×D₄×C₁₁	—	2	8	no	—
92	C₄×D₄×C₁₁	—	2	2	no	—
93	C₄×D₄×C₁₁	—	2	4	no	—
94	C₄×D₄×C₁₁	—	2	2	no	—
95	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
96	C₄×D₄×C₁₁	D₄	1	2	yes	—
97	C₄×D₄×C₁₁	D₄	1	2	yes	—
98	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₁	C₂³	1	8	yes	—
100	C₁₁×#117	—	2	4	no	—
101	C₁₁×#117	—	2	4	no	—
102	C₁₁×#117	C₂³	1	1	yes	characteristic
103	C₁₁×#117	C₂³	1	2	yes	—
104	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
106	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
109	C₁₁×#107	C₂³	1	8	yes	—
110	C₁₁×#107	C₂³	1	8	yes	—
111	C₁₁×#103	C₂³	1	16	yes	—
112	C₁₁×#102	C₂³	1	16	yes	—
113	C₁₁×#97	C₂³	1	2	yes	—
114	C₁₁×#97	C₂³	1	4	yes	—
115	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
116	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₁	C₂³	1	2	yes	—
118	C₄×C₈×C₁₁	C₂³	1	2	yes	—
119	C₄×C₈×C₁₁	C₂³	1	4	yes	—
120	#60718	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₁₁×#41	—	2	4	no	—
122	C₁₁×#41	—	2	16	no	—
123	C₁₁×#41	—	8	8	no	—
124	C₂×Q₈×C₁₁	—	2	4	no	—
125	C₂×Q₈×C₁₁	—	2	4	no	—
126	C₂×Q₈×C₁₁	—	8	4	no	—
127	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
129	C₂×D₄×C₁₁	—	2	4	no	—
130	C₂×D₄×C₁₁	—	2	8	no	—
131	C₂×D₄×C₁₁	—	2	2	no	—
132	C₂×D₄×C₁₁	—	2	2	no	—
133	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₁	—	2	4	no	—
137	C₂²×C₄×C₁₁	—	2	4	no	—
138	C₂²×C₄×C₁₁	—	2	8	no	—
139	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
145	C₁₁×Q₁₆	—	2	8	no	—
146	C₁₁×SD₁₆	—	2	16	no	—
147	C₁₁×D₈	—	2	8	no	—
148	C₁₁×M₁₆	—	2	8	no	—
149	C₁₁×M₁₆	—	2	4	no	—
150	C₂×C₈×C₁₁	—	2	8	no	—
151	C₂×C₈×C₁₁	#41	1	8	yes	complemented
152	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
153	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
154	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
155	C₁₁×C₄⋊C₄	—	2	4	no	—
156	C₁₁×C₄⋊C₄	—	2	4	no	—
157	C₁₁×C₄⋊C₄	—	2	8	no	—
158	C₁₁×C₄⋊C₄	—	2	4	no	—
159	C₁₁×C₄⋊C₄	—	2	2	no	—
160	C₁₁×C₄⋊C₄	—	2	2	no	—
161	C₁₁×C₄⋊C₄	—	2	8	no	—
162	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
163	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
164	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
167	C₁₁×C₂²⋊C₄	—	2	8	no	—
168	C₁₁×C₂²⋊C₄	—	2	8	no	—
169	C₁₁×C₂²⋊C₄	—	2	8	no	—
170	C₁₁×C₂²⋊C₄	—	2	4	no	—
171	C₁₁×C₂²⋊C₄	—	2	4	no	—
172	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
173	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
174	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
175	C₄²×C₁₁	—	2	8	no	—
176	C₄²×C₁₁	C₂×D₄	1	2	yes	—
177	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₁	C₂×D₄	1	2	yes	—
180	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
181	C₄²×C₁₁	C₂⁴	1	2	yes	—
182	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
183	#3511	C₂×C₁₁	1	2	yes	complemented
184	#3182	C₂×C₁₁	1	4	yes	complemented
185	#3175	C₂×C₁₁	1	8	yes	complemented
186	#3170	C₂×C₁₁	1	2	yes	complemented
187	#3169	C₂×C₁₁	1	2	yes	complemented
188	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#3147	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#3141	C₂×C₁₁	1	2	yes	complemented
191	#3061	C₂×C₁₁	1	4	yes	complemented
192	#2951	C₂×C₁₁	1	4	yes	complemented
193	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
194	C₂³×C₁₁	—	2	4	no	—
195	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
196	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₁	—	2	2	no	—
198	Q₈×C₁₁	—	2	8	no	—
199	Q₈×C₁₁	—	4	8	no	—
200	Q₈×C₁₁	—	8	4	no	—
201	D₄×C₁₁	—	2	4	no	—
202	D₄×C₁₁	—	2	2	no	—
203	D₄×C₁₁	—	2	8	no	—
204	D₄×C₁₁	—	4	8	no	—
205	D₄×C₁₁	—	4	4	no	—
206	D₄×C₁₁	—	4	4	no	—
207	D₄×C₁₁	—	8	8	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	2	4	no	—
210	C₂×C₄×C₁₁	—	2	2	no	—
211	C₂×C₄×C₁₁	—	2	4	no	—
212	C₂×C₄×C₁₁	—	2	4	no	—
213	C₂×C₄×C₁₁	—	2	4	no	—
214	C₂×C₄×C₁₁	—	2	8	no	—
215	C₂×C₄×C₁₁	—	4	8	no	—
216	C₂×C₄×C₁₁	—	8	8	no	—
217	C₂×C₄×C₁₁	—	8	4	no	—
218	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
227	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
228	C₈×C₁₁	—	2	4	no	—
229	C₈×C₁₁	C₂×#41	1	4	yes	—
230	C₈×C₁₁	C₂×#41	1	4	yes	—
231	C₂×#135	C₂²×C₁₁	1	4	yes	—
232	C₂×#131	C₂²×C₁₁	1	2	yes	—
233	#556	—	2	2	no	—
234	#555	—	2	2	no	—
235	#554	—	2	2	no	—
236	#553	—	2	4	no	—
237	#548	—	2	4	no	—
238	#547	—	2	2	no	—
239	#542	C₂²×C₁₁	1	8	yes	—
240	#537	C₂²×C₁₁	1	4	yes	—
241	#533	C₂²×C₁₁	1	4	yes	—
242	#532	C₂²×C₁₁	1	2	yes	—
243	#532	C₂²×C₁₁	1	4	yes	—
244	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
245	#520	C₂²×C₁₁	1	4	yes	—
246	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
247	#500	C₂²×C₁₁	1	2	yes	—
248	#500	C₂²×C₁₁	1	4	yes	—
249	#500	C₂²×C₁₁	1	2	yes	—
250	#495	C₂²×C₁₁	1	4	yes	—
251	#494	C₂²×C₁₁	1	1	yes	characteristic
252	#493	C₂²×C₁₁	1	1	yes	characteristic
253	#492	C₂²×C₁₁	1	2	yes	—
254	#489	C₂²×C₁₁	1	8	yes	—
255	#487	C₂²×C₁₁	1	4	yes	—
256	#486	C₂²×C₁₁	1	4	yes	—
257	#468	C₂²×C₁₁	1	16	yes	—
258	#467	C₂²×C₁₁	1	8	yes	—
259	#466	C₂²×C₁₁	1	8	yes	—
260	#440	C₂²×C₁₁	1	16	yes	—
261	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	—
262	C₄×D₈	C₂²×C₁₁	1	8	yes	—
263	C₂×#107	C₂²×C₁₁	1	4	yes	—
264	#417	C₂²×C₁₁	1	8	yes	—
265	#405	C₂²×C₁₁	1	4	yes	—
266	#405	C₂²×C₁₁	1	2	yes	—
267	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
268	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
269	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
271	C₂²×C₁₁	—	2	1	no	—
272	C₂²×C₁₁	—	2	1	no	—
273	C₂²×C₁₁	—	2	2	no	—
274	C₂²×C₁₁	—	2	2	no	—
275	C₂²×C₁₁	—	2	2	no	—
276	C₂²×C₁₁	—	4	4	no	—
277	C₂²×C₁₁	—	4	4	no	—
278	C₂²×C₁₁	—	4	4	no	—
279	C₂²×C₁₁	#532	1	2	yes	—
280	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
281	C₄×C₁₁	—	2	2	no	—
282	C₄×C₁₁	—	2	2	no	—
283	C₄×C₁₁	—	2	1	no	—
284	C₄×C₁₁	—	2	2	no	—
285	C₄×C₁₁	—	2	1	no	—
286	C₄×C₁₁	—	4	4	no	—
287	C₄×C₁₁	—	4	8	no	—
288	C₄×C₁₁	#532	1	2	yes	—
289	C₄×C₁₁	#576	1	2	yes	—
290	C₄×C₁₁	#578	1	2	yes	—
291	C₄×C₁₁	C₂²×#41	1	2	yes	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	C₂³×C₁₁	1	4	yes	—
294	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
295	C₂²×Q₈	—	2	2	no	—
296	#135	—	2	16	no	—
297	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
298	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
299	C₂×D₈	C₂³×C₁₁	1	4	yes	—
300	#131	—	2	8	no	—
301	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
302	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
303	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
304	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
309	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
310	#127	C₂³×C₁₁	1	2	yes	—
311	#126	—	2	8	no	—
312	#125	—	2	4	no	—
313	#124	—	2	8	no	—
314	#124	—	2	4	no	—
315	#124	C₂³×C₁₁	1	4	yes	—
316	#123	—	2	8	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
321	#121	—	2	4	no	—
322	#121	—	2	8	no	—
323	#121	—	2	2	no	—
324	#121	—	2	2	no	—
325	#121	—	2	4	no	—
326	#121	C₂³×C₁₁	1	8	yes	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
329	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
330	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
331	C₄×D₄	—	2	8	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
336	C₄×D₄	D₄×C₁₁	1	2	yes	—
337	C₄×D₄	D₄×C₁₁	1	2	yes	—
338	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
339	C₄×D₄	C₂³×C₁₁	1	8	yes	—
340	#117	—	2	4	no	—
341	#117	—	2	4	no	—
342	#117	C₂³×C₁₁	1	1	yes	characteristic
343	#117	C₂³×C₁₁	1	2	yes	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
347	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
349	#107	C₂³×C₁₁	1	8	yes	—
350	#107	C₂³×C₁₁	1	8	yes	—
351	#103	C₂³×C₁₁	1	16	yes	—
352	#102	C₂³×C₁₁	1	16	yes	—
353	#97	C₂³×C₁₁	1	4	yes	—
354	#97	C₂³×C₁₁	1	2	yes	—
355	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
356	C₄×C₈	C₂³×C₁₁	1	2	yes	—
357	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
358	C₄×C₈	C₂³×C₁₁	1	4	yes	—
359	C₄×C₈	C₂³×C₁₁	1	2	yes	—
360	C₂×C₁₁	—	2	2	no	—
361	C₂×C₁₁	—	4	2	no	—
362	C₂×C₁₁	—	8	4	no	—
363	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
364	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
365	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
366	#41	—	2	4	no	—
367	#41	—	2	16	no	—
368	#41	—	8	8	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	8	4	no	—
372	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
379	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
380	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
390	Q₁₆	—	2	8	no	—
391	SD₁₆	—	2	16	no	—
392	D₈	—	2	8	no	—
393	M₁₆	—	2	4	no	—
394	M₁₆	—	2	8	no	—
395	C₂×C₈	—	2	8	no	—
396	C₂×C₈	C₁₁×#41	1	8	yes	complemented
397	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
398	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
399	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
410	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
411	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
418	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
419	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
420	C₄²	—	2	8	no	—
421	C₄²	C₂×D₄×C₁₁	1	2	yes	—
422	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₁₁	1	2	yes	—
425	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
426	C₄²	C₂⁴×C₁₁	1	2	yes	—
427	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
428	C₁₁	#60718	1	1	yes	characteristic, direct product factor, Sylow
429	C₂³	—	2	4	no	—
430	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
431	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	8	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	8	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	4	no	—
442	D₄	—	8	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	8	8	no	—
452	C₂×C₄	—	8	4	no	—
453	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
461	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
462	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
463	C₈	—	2	4	no	—
464	C₈	C₂×C₁₁×#41	1	4	yes	—
465	C₈	C₂×C₁₁×#41	1	4	yes	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	C₁₁×#532	1	2	yes	—
475	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	1	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	8	no	—
483	C₄	C₁₁×#532	1	2	yes	—
484	C₄	C₁₁×#576	1	2	yes	—
485	C₄	C₁₁×#578	1	2	yes	—
486	C₄	C₂²×C₁₁×#41	1	2	yes	—
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	8	4	no	—
490	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
491	C₂	C₂×C₁₁×#576	1	1	yes	characteristic
492	C₂	C₂×C₁₁×#578	1	1	yes	characteristic

	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. C₁₁×#3511	C₂	semidirect
2. C₁₁×#3182	C₂	semidirect
3. C₁₁×#3175	C₂	semidirect
4. C₁₁×#3170	C₂	semidirect
5. C₁₁×#3169	C₂	semidirect
6. C₂×C₁₁×#500	C₂	semidirect
7. C₁₁×#3147	C₂	semidirect
8. C₁₁×#3141	C₂	semidirect
9. C₁₁×#3061	C₂	semidirect
10. C₁₁×#2951	C₂	semidirect
11. C₄×C₁₁×#131	C₂	semidirect
120. #60718	C₁₁	direct (N × H)
151. C₂×C₈×C₁₁	#41	semidirect
183. #3511	C₂×C₁₁	semidirect
184. #3182	C₂×C₁₁	semidirect
185. #3175	C₂×C₁₁	semidirect
186. #3170	C₂×C₁₁	semidirect
187. #3169	C₂×C₁₁	semidirect
188. C₂×#500	C₂×C₁₁	semidirect
189. #3147	C₂×C₁₁	semidirect
190. #3141	C₂×C₁₁	semidirect
191. #3061	C₂×C₁₁	semidirect
192. #2951	C₂×C₁₁	semidirect
193. C₄×#131	C₂×C₁₁	semidirect
396. C₂×C₈	C₁₁×#41	semidirect
428. C₁₁	#60718	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×#3511	2
C₁₁×#3182	2
C₁₁×#3175	2
C₁₁×#3170	2
C₁₁×#3169	2
C₂×C₁₁×#500	2
C₁₁×#3147	2
C₁₁×#3141	2
C₁₁×#3061	2
C₁₁×#2951	2
C₄×C₁₁×#131	2
#60718	11

Subgroups — C11×#60718 #14637911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60718 #14637911