Subgroups — C₁₁×#22529 #14599722

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1995	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1986	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1806	C₂	1	2	yes	maximal
9	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1759	C₂	1	2	yes	maximal
11	C₄×C₁₁×#104	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₁₁	C₄	1	1	yes	characteristic, complemented
13	C₁₁×#557	C₄	1	2	yes	complemented
14	C₁₁×#557	C₄	1	1	yes	characteristic, complemented
15	C₁₁×#554	—	2	2	no	—
16	C₁₁×#554	—	2	1	no	—
17	C₁₁×#554	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#554	C₄	1	2	yes	complemented
19	D₄×Q₈×C₁₁	—	2	1	no	—
20	D₄×Q₈×C₁₁	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#533	—	2	1	no	—
22	C₁₁×#533	—	2	2	no	—
23	C₁₁×#533	C₂²	1	1	yes	characteristic
24	C₁₁×#533	C₂²	1	2	yes	—
25	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
26	C₄×C₁₁×#41	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#446	—	2	1	no	—
30	C₁₁×#446	—	2	2	no	—
31	C₈×Q₈×C₁₁	—	2	1	no	—
32	C₁₁×#423	C₂²	1	1	yes	characteristic
33	C₁₁×#423	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
37	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
39	C₁₁×#391	—	2	1	no	—
40	C₁₁×#389	—	2	1	no	—
41	C₁₁×#387	—	2	2	no	—
42	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
44	C₁₁×#376	C₂²	1	2	yes	—
45	C₄³×C₁₁	C₂²	1	1	yes	characteristic
46	C₁₁×#339	C₂²	1	1	yes	characteristic
47	C₁₁×#339	C₂²	1	2	yes	—
48	C₁₁×#339	C₂²	1	2	yes	—
49	C₁₁×#339	C₂²	1	2	yes	—
50	C₁₁×#339	C₂²	1	2	yes	—
51	C₁₁×#339	C₂²	1	2	yes	—
52	C₁₁×#339	C₂²	1	1	yes	characteristic
53	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₁	—	2	1	no	—
55	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
56	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊Q₈	—	2	1	no	—
60	C₁₁×C₄⋊Q₈	—	2	2	no	—
61	C₁₁×C₄⋊Q₈	—	2	2	no	—
62	C₁₁×C₄⋊Q₈	—	2	1	no	—
63	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
66	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
67	C₁₁×#125	—	2	2	no	—
68	C₁₁×#125	—	2	2	no	—
69	C₁₁×#125	—	2	2	no	—
70	C₁₁×#125	C₂×C₄	1	2	yes	—
71	C₁₁×#125	C₂×C₄	1	2	yes	—
72	C₁₁×#125	C₂×C₄	1	2	yes	—
73	C₁₁×C₂²⋊Q₈	—	2	1	no	—
74	C₁₁×C₂²⋊Q₈	—	2	2	no	—
75	C₁₁×C₂²⋊Q₈	—	2	1	no	—
76	C₁₁×C₂²⋊Q₈	—	2	2	no	—
77	C₁₁×C₂²⋊Q₈	—	2	1	no	—
78	C₁₁×C₂²⋊Q₈	—	2	2	no	—
79	C₁₁×C₂²⋊Q₈	—	2	2	no	—
80	C₁₁×C₂²⋊Q₈	—	2	1	no	—
81	C₁₁×C₂²⋊Q₈	—	2	2	no	—
82	C₁₁×C₂²⋊Q₈	—	2	2	no	—
83	C₁₁×C₂²⋊Q₈	—	2	2	no	—
84	C₄×Q₈×C₁₁	—	2	1	no	—
85	C₄×Q₈×C₁₁	—	2	2	no	—
86	C₄×Q₈×C₁₁	—	2	1	no	—
87	C₄×Q₈×C₁₁	—	2	1	no	—
88	C₄×Q₈×C₁₁	—	2	2	no	—
89	C₄×Q₈×C₁₁	—	2	2	no	—
90	C₄×Q₈×C₁₁	—	2	1	no	—
91	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
95	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₁	D₄	1	2	yes	—
101	C₄×D₄×C₁₁	—	2	1	no	—
102	C₄×D₄×C₁₁	—	2	2	no	—
103	C₄×D₄×C₁₁	—	2	1	no	—
104	C₄×D₄×C₁₁	—	2	2	no	—
105	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
109	C₁₁×#117	—	2	2	no	—
110	C₁₁×#117	—	2	1	no	—
111	C₁₁×#117	C₂³	1	1	yes	characteristic
112	C₁₁×#117	C₂³	1	2	yes	—
113	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
118	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₁	—	2	1	no	—
120	C₂×C₄²×C₁₁	—	2	2	no	—
121	C₂×C₄²×C₁₁	—	2	1	no	—
122	C₂×C₄²×C₁₁	—	2	1	no	—
123	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
128	C₁₁×C₄⋊C₈	—	2	1	no	—
129	C₁₁×C₄⋊C₈	—	2	2	no	—
130	C₁₁×C₄⋊C₈	—	2	2	no	—
131	C₁₁×C₄⋊C₈	—	2	1	no	—
132	C₁₁×#104	—	2	2	no	—
133	C₁₁×#104	—	2	4	no	—
134	C₁₁×#104	Q₈	1	4	yes	complemented
135	C₁₁×#97	—	2	2	no	—
136	C₁₁×#97	—	2	1	no	—
137	C₄×C₈×C₁₁	—	2	1	no	—
138	C₄×C₈×C₁₁	—	2	2	no	—
139	C₁₁×#95	—	2	2	no	—
140	C₁₁×#95	—	2	2	no	—
141	C₁₁×#95	—	2	1	no	—
142	C₁₁×#95	—	2	2	no	—
143	#22529	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₁₁×#41	—	2	1	no	—
145	C₁₁×#41	—	2	1	no	—
146	C₁₁×#41	C₂×Q₈	1	2	yes	—
147	C₁₁×#41	#41	1	2	yes	—
148	C₂×Q₈×C₁₁	—	2	2	no	—
149	C₂×Q₈×C₁₁	—	2	1	no	—
150	C₂×Q₈×C₁₁	—	2	2	no	—
151	C₂×Q₈×C₁₁	—	2	1	no	—
152	C₂×Q₈×C₁₁	—	4	2	no	—
153	C₂×Q₈×C₁₁	—	4	4	no	—
154	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₁	C₂²⋊C₄	1	2	yes	—
157	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₁	—	2	1	no	—
159	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	—	2	1	no	—
161	C₂²×C₄×C₁₁	—	2	1	no	—
162	C₂²×C₄×C₁₁	—	2	1	no	—
163	C₂²×C₄×C₁₁	—	2	2	no	—
164	C₂²×C₄×C₁₁	—	2	1	no	—
165	C₂²×C₄×C₁₁	—	2	1	no	—
166	C₂²×C₄×C₁₁	—	2	2	no	—
167	C₂²×C₄×C₁₁	—	2	2	no	—
168	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
173	C₁₁×M₁₆	—	2	1	no	—
174	C₁₁×M₁₆	—	2	2	no	—
175	C₁₁×M₁₆	—	2	1	no	—
176	C₁₁×M₁₆	—	2	2	no	—
177	C₁₁×M₁₆	—	2	1	no	—
178	C₁₁×M₁₆	C₂×Q₈	1	2	yes	complemented
179	C₂×C₈×C₁₁	—	2	1	no	—
180	C₂×C₈×C₁₁	—	2	1	no	—
181	C₂×C₈×C₁₁	—	2	2	no	—
182	C₁₁×C₄⋊C₄	—	2	2	no	—
183	C₁₁×C₄⋊C₄	—	2	2	no	—
184	C₁₁×C₄⋊C₄	—	2	2	no	—
185	C₁₁×C₄⋊C₄	—	2	2	no	—
186	C₁₁×C₄⋊C₄	—	2	1	no	—
187	C₁₁×C₄⋊C₄	—	2	1	no	—
188	C₁₁×C₄⋊C₄	—	2	2	no	—
189	C₁₁×C₄⋊C₄	—	2	2	no	—
190	C₁₁×C₄⋊C₄	—	2	1	no	—
191	C₁₁×C₄⋊C₄	—	2	2	no	—
192	C₁₁×C₄⋊C₄	—	2	1	no	—
193	C₁₁×C₄⋊C₄	—	2	2	no	—
194	C₁₁×C₄⋊C₄	—	2	2	no	—
195	C₁₁×C₄⋊C₄	—	2	2	no	—
196	C₁₁×C₄⋊C₄	—	4	2	no	—
197	C₁₁×C₄⋊C₄	—	4	4	no	—
198	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
199	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
200	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
201	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
202	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
203	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
204	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
205	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
207	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
208	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
209	C₁₁×C₂²⋊C₄	—	2	1	no	—
210	C₁₁×C₂²⋊C₄	—	2	2	no	—
211	C₁₁×C₂²⋊C₄	—	2	1	no	—
212	C₁₁×C₂²⋊C₄	—	2	2	no	—
213	C₁₁×C₂²⋊C₄	—	2	2	no	—
214	C₁₁×C₂²⋊C₄	—	2	1	no	—
215	C₄²×C₁₁	—	2	1	no	—
216	C₄²×C₁₁	—	2	2	no	—
217	C₄²×C₁₁	—	2	2	no	—
218	C₄²×C₁₁	—	2	1	no	—
219	C₄²×C₁₁	—	2	1	no	—
220	C₄²×C₁₁	—	2	2	no	—
221	C₄²×C₁₁	—	2	1	no	—
222	C₄²×C₁₁	—	2	1	no	—
223	C₄²×C₁₁	—	2	2	no	—
224	C₄²×C₁₁	—	2	1	no	—
225	C₄²×C₁₁	—	2	2	no	—
226	C₄²×C₁₁	—	4	2	no	—
227	C₄²×C₁₁	—	4	2	no	—
228	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
230	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
231	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₁	C₂×D₄	1	2	yes	—
234	C₄²×C₁₁	C₂×D₄	1	2	yes	—
235	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₁	C₂×Q₈	1	2	yes	complemented
237	Q₈×#41	C₂×C₁₁	1	1	yes	characteristic
238	Q₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
239	#2295	C₂×C₁₁	1	1	yes	characteristic, complemented
240	#1995	C₂×C₁₁	1	2	yes	complemented
241	#1994	C₂×C₁₁	1	1	yes	characteristic, complemented
242	#1986	C₂×C₁₁	1	1	yes	characteristic, complemented
243	#1986	C₂×C₁₁	1	2	yes	complemented
244	#1806	C₂×C₁₁	1	1	yes	characteristic
245	#1806	C₂×C₁₁	1	2	yes	—
246	#1759	C₂×C₁₁	1	2	yes	—
247	C₄×#104	C₂×C₁₁	1	1	yes	characteristic
248	C₂³×C₁₁	—	2	1	no	—
249	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
250	Q₈×C₁₁	—	2	1	no	—
251	Q₈×C₁₁	—	2	2	no	—
252	Q₈×C₁₁	—	2	2	no	—
253	Q₈×C₁₁	—	4	2	no	—
254	Q₈×C₁₁	—	4	4	no	—
255	Q₈×C₁₁	—	4	2	no	—
256	Q₈×C₁₁	—	8	1	no	—
257	Q₈×C₁₁	—	8	2	no	—
258	Q₈×C₁₁	C₄×Q₈	1	2	yes	—
259	D₄×C₁₁	—	2	2	no	—
260	D₄×C₁₁	—	2	2	no	—
261	D₄×C₁₁	—	2	1	no	—
262	D₄×C₁₁	C₄×Q₈	1	2	yes	—
263	C₂×C₄×C₁₁	—	2	1	no	—
264	C₂×C₄×C₁₁	—	2	2	no	—
265	C₂×C₄×C₁₁	—	2	2	no	—
266	C₂×C₄×C₁₁	—	2	2	no	—
267	C₂×C₄×C₁₁	—	2	2	no	—
268	C₂×C₄×C₁₁	—	2	2	no	—
269	C₂×C₄×C₁₁	—	2	1	no	—
270	C₂×C₄×C₁₁	—	2	2	no	—
271	C₂×C₄×C₁₁	—	2	1	no	—
272	C₂×C₄×C₁₁	—	2	2	no	—
273	C₂×C₄×C₁₁	—	4	1	no	—
274	C₂×C₄×C₁₁	—	4	2	no	—
275	C₂×C₄×C₁₁	—	4	2	no	—
276	C₂×C₄×C₁₁	—	4	4	no	—
277	C₂×C₄×C₁₁	—	4	1	no	—
278	C₂×C₄×C₁₁	—	4	1	no	—
279	C₂×C₄×C₁₁	—	4	1	no	—
280	C₂×C₄×C₁₁	—	4	1	no	—
281	C₂×C₄×C₁₁	—	4	2	no	—
282	C₂×C₄×C₁₁	—	4	2	no	—
283	C₂×C₄×C₁₁	—	4	2	no	—
284	C₂×C₄×C₁₁	—	4	2	no	—
285	C₂×C₄×C₁₁	—	8	1	no	—
286	C₂×C₄×C₁₁	—	8	2	no	—
287	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
296	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
298	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
300	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
301	C₈×C₁₁	—	2	2	no	—
302	C₈×C₁₁	—	4	1	no	—
303	C₈×C₁₁	—	4	2	no	—
304	Q₈²	C₄×C₁₁	1	1	yes	characteristic, complemented
305	#557	C₄×C₁₁	1	2	yes	complemented
306	#557	C₄×C₁₁	1	1	yes	characteristic, complemented
307	#554	—	2	2	no	—
308	#554	—	2	1	no	—
309	#554	C₄×C₁₁	1	1	yes	characteristic, complemented
310	#554	C₄×C₁₁	1	2	yes	complemented
311	D₄×Q₈	—	2	1	no	—
312	D₄×Q₈	C₄×C₁₁	1	1	yes	characteristic, complemented
313	#533	—	2	1	no	—
314	#533	—	2	2	no	—
315	#533	C₂²×C₁₁	1	1	yes	characteristic
316	#533	C₂²×C₁₁	1	2	yes	—
317	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
318	C₄×#41	C₂²×C₁₁	1	2	yes	—
319	C₂×C₄×Q₈	—	2	1	no	—
320	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
321	#446	—	2	1	no	—
322	#446	—	2	2	no	—
323	C₈×Q₈	—	2	1	no	—
324	#423	C₂²×C₁₁	1	1	yes	characteristic
325	#423	C₂²×C₁₁	1	2	yes	—
326	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
327	C₂×#104	C₂²×C₁₁	1	2	yes	—
328	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
329	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
330	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
331	#391	—	2	1	no	—
332	#389	—	2	1	no	—
333	#387	—	2	2	no	—
334	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
336	#376	C₂²×C₁₁	1	2	yes	—
337	C₄³	C₂²×C₁₁	1	1	yes	characteristic
338	#339	C₂²×C₁₁	1	2	yes	—
339	#339	C₂²×C₁₁	1	2	yes	—
340	#339	C₂²×C₁₁	1	2	yes	—
341	#339	C₂²×C₁₁	1	1	yes	characteristic
342	#339	C₂²×C₁₁	1	2	yes	—
343	#339	C₂²×C₁₁	1	2	yes	—
344	#339	C₂²×C₁₁	1	1	yes	characteristic
345	C₂²×C₁₁	—	2	1	no	—
346	C₂²×C₁₁	—	2	1	no	—
347	C₂²×C₁₁	—	2	2	no	—
348	C₂²×C₁₁	—	4	1	no	—
349	C₂²×C₁₁	—	4	1	no	—
350	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₁₁	#548	1	1	yes	characteristic
352	C₂²×C₁₁	D₄×Q₈	1	1	yes	characteristic
353	C₄×C₁₁	—	2	2	no	—
354	C₄×C₁₁	—	2	1	no	—
355	C₄×C₁₁	—	2	2	no	—
356	C₄×C₁₁	—	2	2	no	—
357	C₄×C₁₁	—	2	1	no	—
358	C₄×C₁₁	—	2	2	no	—
359	C₄×C₁₁	—	2	1	no	—
360	C₄×C₁₁	—	2	2	no	—
361	C₄×C₁₁	—	4	2	no	—
362	C₄×C₁₁	—	4	2	no	—
363	C₄×C₁₁	—	4	2	no	—
364	C₄×C₁₁	—	4	1	no	—
365	C₄×C₁₁	—	4	2	no	—
366	C₄×C₁₁	—	4	1	no	—
367	C₄×C₁₁	—	8	2	no	—
368	C₄×C₁₁	#421	1	2	yes	—
369	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
370	C₄×C₁₁	#519	1	1	yes	characteristic
371	C₄×C₁₁	#548	1	1	yes	characteristic
372	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
373	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
376	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
377	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
378	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	—	2	2	no	—
381	C₄⋊Q₈	—	2	2	no	—
382	C₄⋊Q₈	—	2	1	no	—
383	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
384	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
385	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
386	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
387	#125	—	2	2	no	—
388	#125	—	2	2	no	—
389	#125	—	2	2	no	—
390	#125	C₂×C₄×C₁₁	1	2	yes	—
391	#125	C₂×C₄×C₁₁	1	2	yes	—
392	#125	C₂×C₄×C₁₁	1	2	yes	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
412	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
413	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
414	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
415	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
416	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
417	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
418	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
419	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
420	C₄×Q₈	D₄×C₁₁	1	2	yes	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	1	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
426	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
427	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
428	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
429	#117	—	2	2	no	—
430	#117	—	2	1	no	—
431	#117	C₂³×C₁₁	1	1	yes	characteristic
432	#117	C₂³×C₁₁	1	2	yes	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
438	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	2	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
445	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
448	C₄⋊C₈	—	2	1	no	—
449	C₄⋊C₈	—	2	2	no	—
450	C₄⋊C₈	—	2	2	no	—
451	C₄⋊C₈	—	2	1	no	—
452	#104	—	2	2	no	—
453	#104	—	2	4	no	—
454	#104	Q₈×C₁₁	1	4	yes	complemented
455	#97	—	2	2	no	—
456	#97	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	2	no	—
459	#95	—	2	2	no	—
460	#95	—	2	2	no	—
461	#95	—	2	1	no	—
462	#95	—	2	2	no	—
463	C₂×C₁₁	—	2	1	no	—
464	C₂×C₁₁	—	2	1	no	—
465	C₂×C₁₁	—	4	2	no	—
466	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₁₁	C₂×#421	1	1	yes	characteristic
468	C₂×C₁₁	#2901	1	1	yes	characteristic
469	#41	—	2	1	no	—
470	#41	—	2	1	no	—
471	#41	C₂×Q₈×C₁₁	1	2	yes	—
472	#41	C₁₁×#41	1	2	yes	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	—	4	4	no	—
479	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×Q₈	C₁₁×C₂²⋊C₄	1	2	yes	—
482	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
495	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	2	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	C₂×Q₈×C₁₁	1	2	yes	complemented
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	4	4	no	—
523	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
524	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
525	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
526	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
527	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
528	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
529	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
532	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	4	2	no	—
552	C₄²	—	4	2	no	—
553	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
554	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
555	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
556	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
557	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
558	C₄²	C₂×D₄×C₁₁	1	2	yes	—
559	C₄²	C₂×D₄×C₁₁	1	2	yes	—
560	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
561	C₄²	C₂×Q₈×C₁₁	1	2	yes	complemented
562	C₁₁	#22529	1	1	yes	characteristic, direct product factor, Sylow
563	C₂³	—	2	1	no	—
564	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
565	Q₈	—	2	1	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	4	4	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	8	1	no	—
572	Q₈	—	8	2	no	—
573	Q₈	C₄×Q₈×C₁₁	1	2	yes	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	1	no	—
577	D₄	C₄×Q₈×C₁₁	1	2	yes	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	—	8	2	no	—
602	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
604	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
605	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
607	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
608	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
609	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
610	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
612	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
613	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
614	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
625	C₂²	C₁₁×#548	1	1	yes	characteristic
626	C₂²	D₄×Q₈×C₁₁	1	1	yes	characteristic
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	8	2	no	—
642	C₄	C₁₁×#421	1	2	yes	—
643	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
644	C₄	C₁₁×#519	1	1	yes	characteristic
645	C₄	C₁₁×#548	1	1	yes	characteristic
646	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	4	2	no	—
650	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
651	C₂	C₂×C₁₁×#421	1	1	yes	characteristic
652	C₂	C₁₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₁×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₁×M₁₆	C₂	semidirect
3. C₁₁×#2295	C₂	semidirect
4. C₁₁×#1995	C₂	semidirect
5. C₁₁×#1994	C₂	semidirect
6. C₁₁×#1986	C₂	semidirect
7. C₁₁×#1986	C₂	semidirect
12. Q₈²×C₁₁	C₄	semidirect
13. C₁₁×#557	C₄	semidirect
14. C₁₁×#557	C₄	semidirect
17. C₁₁×#554	C₄	semidirect
18. C₁₁×#554	C₄	semidirect
20. D₄×Q₈×C₁₁	C₄	semidirect
134. C₁₁×#104	Q₈	semidirect
143. #22529	C₁₁	direct (N × H)
178. C₁₁×M₁₆	C₂×Q₈	semidirect
236. C₄²×C₁₁	C₂×Q₈	semidirect
238. Q₈×M₁₆	C₂×C₁₁	semidirect
239. #2295	C₂×C₁₁	semidirect
240. #1995	C₂×C₁₁	semidirect
241. #1994	C₂×C₁₁	semidirect
242. #1986	C₂×C₁₁	semidirect
243. #1986	C₂×C₁₁	semidirect
304. Q₈²	C₄×C₁₁	semidirect
305. #557	C₄×C₁₁	semidirect
306. #557	C₄×C₁₁	semidirect
309. #554	C₄×C₁₁	semidirect
310. #554	C₄×C₁₁	semidirect
312. D₄×Q₈	C₄×C₁₁	semidirect
454. #104	Q₈×C₁₁	semidirect
503. M₁₆	C₂×Q₈×C₁₁	semidirect
561. C₄²	C₂×Q₈×C₁₁	semidirect
562. C₁₁	#22529	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×#41	2
Q₈×C₁₁×M₁₆	2
C₁₁×#2295	2
C₁₁×#1995	2
C₁₁×#1994	2
C₁₁×#1986	2
C₁₁×#1806	2
C₁₁×#1759	2
C₄×C₁₁×#104	2
#22529	11

Subgroups — C11×#22529 #14599722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22529 #14599722