Subgroups — #14907358

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×D₁₁	C₂	1	1	yes	maximal, characteristic
2	#13070444	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070443	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070442	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070441	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070440	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070439	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070438	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070418	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070417	C₂	1	1	yes	maximal, characteristic, complemented
11	#13070226	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070225	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂×D₁₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₁	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₁₁	C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
26	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
27	C₂×#66862	C₂²	1	1	yes	characteristic, complemented
28	C₂×#66862	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic, complemented
31	#10622447	C₄	1	1	yes	characteristic
32	D₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
33	(C₂²⋊D₁₁)⋊C₈	C₄	1	1	yes	characteristic
34	(C₂²⋊D₁₁)⋊C₈	C₄	1	1	yes	characteristic
35	D₁₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
36	D₁₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
37	C₈×D₄₄	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
39	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₁₁×#346	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
45	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
46	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
48	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
49	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
53	#10622140	C₂²	1	1	yes	characteristic, complemented
54	#10622140	C₂²	1	1	yes	characteristic, complemented
55	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
56	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
58	#10622099	C₂²	1	1	yes	characteristic, complemented
59	C₂×D₄×D₁₁	C₈	1	1	yes	characteristic
60	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
65	D₄×Dic₁₁	C₈	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₁	—	4	1	no	—
71	C₂×C₈×D₁₁	—	4	1	no	—
72	C₂×C₈×D₁₁	—	4	1	no	—
73	C₂×C₈×D₁₁	—	4	1	no	—
74	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
80	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
81	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
82	#66946	C₈	1	1	yes	characteristic
83	C₄⋊C₄×D₁₁	C₈	1	1	yes	characteristic
84	(C₂²⋊D₁₁)⋊C₄	C₈	1	1	yes	characteristic
85	(C₂²⋊D₁₁)⋊C₄	C₈	1	1	yes	characteristic
86	C₂²⋊C₄×D₁₁	C₈	1	1	yes	characteristic
87	C₂²⋊C₄×D₁₁	C₈	1	1	yes	characteristic
88	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
90	C₁₁×M₃₂	—	4	1	no	—
91	C₂×C₁₁×C₁₆	—	4	1	no	—
92	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
96	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
105	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
106	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
107	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
109	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
110	#66876	—	4	1	no	—
111	C₂×C₁₁⋊C₁₆	—	4	1	no	—
112	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
116	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
117	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
118	#66862	—	4	1	no	—
119	#66862	—	4	1	no	—
120	C₁₆×D₁₁	—	4	1	no	—
121	C₁₆×D₁₁	—	4	1	no	—
122	#33487	—	11	1	no	maximal, Sylow
123	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
124	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
125	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
130	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
131	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
132	D₄×D₁₁	—	2	4	no	—
133	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
134	C₂×C₄×D₁₁	—	4	1	no	—
135	C₂×C₄×D₁₁	—	4	1	no	—
136	C₂×C₄×D₁₁	—	4	1	no	—
137	C₂×C₄×D₁₁	—	4	1	no	—
138	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	1	no	—
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
155	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
158	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
161	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
162	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
163	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
164	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
165	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
166	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
167	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
168	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
169	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
170	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₁₁⋊C₈	—	4	1	no	—
172	C₂×C₁₁⋊C₈	—	4	1	no	—
173	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₈×D₁₁	—	2	1	no	—
178	C₈×D₁₁	—	2	1	no	—
179	C₈×D₁₁	—	2	1	no	—
180	C₈×D₁₁	—	2	1	no	—
181	C₈×D₁₁	—	2	1	no	—
182	C₈×D₁₁	—	2	1	no	—
183	C₈×D₁₁	—	4	1	no	—
184	C₈×D₁₁	—	4	1	no	—
185	C₈×D₁₁	—	4	1	no	—
186	C₈×D₁₁	—	4	1	no	—
187	C₈×D₁₁	—	4	1	no	—
188	C₁₁×C₁₆	—	2	1	no	—
189	C₁₁×C₁₆	—	2	1	no	—
190	C₁₁×C₁₆	—	2	1	no	—
191	C₁₁×C₁₆	—	2	1	no	—
192	C₁₁⋊C₁₆	—	2	1	no	—
193	C₁₁⋊C₁₆	—	2	1	no	—
194	C₁₁⋊C₁₆	—	2	1	no	—
195	C₁₁⋊C₁₆	—	2	1	no	—
196	C₂×C₈×D₄	—	11	1	no	—
197	#2168	—	11	1	no	—
198	#2168	—	11	1	no	—
199	#2168	—	11	1	no	—
200	#2168	—	11	1	no	—
201	#2168	—	11	1	no	—
202	#2168	—	11	1	no	—
203	#2168	—	11	1	no	—
204	#2168	D₁₁	1	1	yes	characteristic, complemented
205	#2163	—	11	1	no	—
206	#2163	—	11	1	no	—
207	#2112	—	11	1	no	—
208	#2112	—	11	1	no	—
209	C₂×C₂²⋊C₁₆	—	11	1	no	—
210	C₂×C₂²⋊C₁₆	—	11	1	no	—
211	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
212	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
213	C₂²×D₁₁	—	2	2	no	—
214	C₂²×D₁₁	—	4	1	no	—
215	C₂²×D₁₁	—	4	1	no	—
216	C₂²×D₁₁	—	4	1	no	—
217	C₂²×D₁₁	—	4	1	no	—
218	C₂²×D₁₁	M₃₂	1	4	yes	complemented
219	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
220	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
221	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
222	D₄×C₁₁	—	2	2	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	1	no	—
225	C₂×C₄×C₁₁	—	2	1	no	—
226	C₂×C₄×C₁₁	—	2	1	no	—
227	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
228	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
232	C₂²⋊D₁₁	—	2	2	no	—
233	C₂²⋊D₁₁	—	2	2	no	—
234	C₂×Dic₁₁	—	4	1	no	—
235	C₂×Dic₁₁	—	4	1	no	—
236	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
237	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
238	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
239	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
241	D₄₄	—	2	2	no	—
242	C₄×D₁₁	—	2	2	no	—
243	C₄×D₁₁	—	2	1	no	—
244	C₄×D₁₁	—	2	1	no	—
245	C₄×D₁₁	—	2	1	no	—
246	C₄×D₁₁	—	2	1	no	—
247	C₄×D₁₁	—	2	1	no	—
248	C₄×D₁₁	—	2	1	no	—
249	C₄×D₁₁	—	4	1	no	—
250	C₄×D₁₁	—	4	1	no	—
251	C₄×D₁₁	—	4	1	no	—
252	C₄×D₁₁	—	4	1	no	—
253	C₄×D₁₁	—	4	1	no	—
254	C₈×C₁₁	—	2	1	no	—
255	C₈×C₁₁	—	2	1	no	—
256	C₈×C₁₁	—	2	1	no	—
257	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
259	C₁₁⋊C₈	—	2	1	no	—
260	C₁₁⋊C₈	—	2	1	no	—
261	C₁₁⋊C₈	—	2	1	no	—
262	C₁₁⋊C₈	—	2	1	no	—
263	C₂³×C₈	—	11	1	no	—
264	C₂³×C₈	—	11	1	no	—
265	C₂×C₄×D₄	—	11	1	no	—
266	C₂×M₃₂	—	11	1	no	—
267	C₂×M₃₂	—	11	1	no	—
268	C₂×M₃₂	—	11	1	no	—
269	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic, complemented
270	C₂²×C₁₆	—	11	1	no	—
271	C₂²×C₁₆	—	11	1	no	—
272	C₂²×C₁₆	—	11	1	no	—
273	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
274	C₈×D₄	—	11	1	no	—
275	C₈×D₄	—	11	1	no	—
276	C₈×D₄	—	11	1	no	—
277	C₈×D₄	—	11	1	no	—
278	C₈×D₄	—	11	1	no	—
279	C₈×D₄	—	11	1	no	—
280	C₈×D₄	—	11	1	no	—
281	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
282	C₂×C₄⋊C₈	—	11	1	no	—
283	C₂×C₂²⋊C₈	—	11	1	no	—
284	C₂×C₂²⋊C₈	—	11	1	no	—
285	C₂×C₄×C₈	—	11	1	no	—
286	C₄⋊C₁₆	—	11	1	no	—
287	C₄⋊C₁₆	—	11	1	no	—
288	C₄⋊C₁₆	—	11	1	no	—
289	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
290	C₂²⋊C₁₆	—	11	1	no	—
291	C₂²⋊C₁₆	—	11	1	no	—
292	C₂²⋊C₁₆	—	11	1	no	—
293	C₂²⋊C₁₆	—	11	1	no	—
294	C₂²⋊C₁₆	—	11	1	no	—
295	C₂²⋊C₁₆	—	11	1	no	—
296	C₂²⋊C₁₆	—	11	1	no	—
297	C₂²⋊C₁₆	—	11	1	no	—
298	C₂²⋊C₁₆	—	11	1	no	—
299	C₂²⋊C₁₆	—	11	1	no	—
300	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
301	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
302	#346	—	11	1	no	—
303	#346	—	11	1	no	—
304	#346	—	11	1	no	—
305	#346	C₂×D₁₁	1	1	yes	characteristic, complemented
306	C₂²×C₁₁	—	2	1	no	—
307	C₂²×C₁₁	—	2	1	no	—
308	C₂²×C₁₁	—	2	1	no	—
309	C₂²×C₁₁	—	2	1	no	—
310	C₂²×C₁₁	—	2	1	no	—
311	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
312	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
313	C₂×D₁₁	—	2	1	no	—
314	C₂×D₁₁	—	2	1	no	—
315	C₂×D₁₁	—	2	1	no	—
316	C₂×D₁₁	—	2	1	no	—
317	C₂×D₁₁	—	2	1	no	—
318	C₂×D₁₁	—	2	1	no	—
319	C₂×D₁₁	—	2	1	no	—
320	C₂×D₁₁	—	4	4	no	—
321	C₂×D₁₁	—	4	4	no	—
322	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
323	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
324	C₄×C₁₁	—	2	1	no	—
325	C₄×C₁₁	—	2	1	no	—
326	C₄×C₁₁	—	2	1	no	—
327	C₄×C₁₁	—	2	1	no	—
328	C₄×C₁₁	#518	1	1	yes	characteristic
329	C₄×C₁₁	#568	1	1	yes	characteristic
330	Dic₁₁	—	2	1	no	—
331	Dic₁₁	—	2	1	no	—
332	Dic₁₁	—	2	1	no	—
333	Dic₁₁	—	2	1	no	—
334	Dic₁₁	—	2	1	no	—
335	C₂²×D₄	—	11	1	no	—
336	C₂³×C₄	—	11	1	no	—
337	C₂³×C₄	—	11	1	no	—
338	C₂²×C₈	—	11	1	no	—
339	C₂²×C₈	—	11	1	no	—
340	C₂²×C₈	—	11	1	no	—
341	C₂²×C₈	—	11	1	no	—
342	C₂²×C₈	—	11	1	no	—
343	C₂²×C₈	—	11	1	no	—
344	C₂²×C₈	—	11	1	no	—
345	C₂²×C₈	—	11	1	no	—
346	C₂²×C₈	—	11	1	no	—
347	C₂²×C₈	—	11	1	no	—
348	C₂²×C₈	—	44	1	no	—
349	C₂²×C₈	—	44	1	no	—
350	C₂²×C₈	—	44	1	no	—
351	C₂²×C₈	—	44	1	no	—
352	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
354	C₄×D₄	—	11	1	no	—
355	C₄×D₄	—	11	1	no	—
356	C₄×D₄	—	11	1	no	—
357	C₄×D₄	—	11	1	no	—
358	C₄×D₄	—	11	1	no	—
359	C₄×D₄	—	11	1	no	—
360	C₄×D₄	—	11	1	no	—
361	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
362	C₂×C₄⋊C₄	—	11	1	no	—
363	C₂×C₂²⋊C₄	—	11	1	no	—
364	C₂×C₂²⋊C₄	—	11	1	no	—
365	C₂×C₄²	—	11	1	no	—
366	M₃₂	—	4	1	no	—
367	M₃₂	—	44	1	no	—
368	M₃₂	—	44	1	no	—
369	M₃₂	—	44	1	no	—
370	C₂×C₁₆	—	4	1	no	—
371	C₂×C₁₆	—	11	1	no	—
372	C₂×C₁₆	—	11	1	no	—
373	C₂×C₁₆	—	11	1	no	—
374	C₂×C₁₆	—	11	1	no	—
375	C₂×C₁₆	—	44	1	no	—
376	C₂×C₁₆	—	44	1	no	—
377	C₂×C₁₆	—	44	1	no	—
378	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
379	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
380	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
381	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
382	C₄⋊C₈	—	11	1	no	—
383	C₄⋊C₈	—	11	1	no	—
384	C₄⋊C₈	—	11	1	no	—
385	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
386	C₂²⋊C₈	—	11	1	no	—
387	C₂²⋊C₈	—	11	1	no	—
388	C₂²⋊C₈	—	11	1	no	—
389	C₂²⋊C₈	—	11	1	no	—
390	C₂²⋊C₈	—	11	1	no	—
391	C₂²⋊C₈	—	11	1	no	—
392	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
393	C₂²⋊C₈	C₄×D₁₁	1	1	yes	characteristic
394	C₄×C₈	—	11	1	no	—
395	C₄×C₈	—	11	1	no	—
396	C₄×C₈	—	11	1	no	—
397	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
398	C₂×C₁₁	—	2	2	no	—
399	C₂×C₁₁	—	4	1	no	—
400	C₂×C₁₁	#2972	1	1	yes	characteristic
401	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
402	C₂×C₁₁	#3407	1	1	yes	characteristic
403	D₁₁	—	2	2	no	—
404	D₁₁	—	2	2	no	—
405	D₁₁	—	4	1	no	—
406	C₂⁴	—	11	1	no	—
407	C₂⁴	—	11	1	no	—
408	C₂×D₄	—	11	1	no	—
409	C₂×D₄	—	11	1	no	—
410	C₂×D₄	—	11	1	no	—
411	C₂×D₄	—	22	4	no	—
412	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
413	C₂²×C₄	—	11	1	no	—
414	C₂²×C₄	—	11	1	no	—
415	C₂²×C₄	—	11	1	no	—
416	C₂²×C₄	—	11	1	no	—
417	C₂²×C₄	—	11	1	no	—
418	C₂²×C₄	—	11	1	no	—
419	C₂²×C₄	—	11	1	no	—
420	C₂²×C₄	—	11	1	no	—
421	C₂²×C₄	—	11	1	no	—
422	C₂²×C₄	—	11	1	no	—
423	C₂²×C₄	—	11	1	no	—
424	C₂²×C₄	—	44	1	no	—
425	C₂²×C₄	—	44	1	no	—
426	C₂²×C₄	—	44	1	no	—
427	C₂²×C₄	—	44	1	no	—
428	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	11	1	no	—
435	C₂×C₈	—	11	1	no	—
436	C₂×C₈	—	11	1	no	—
437	C₂×C₈	—	11	1	no	—
438	C₂×C₈	—	22	1	no	—
439	C₂×C₈	—	22	1	no	—
440	C₂×C₈	—	22	1	no	—
441	C₂×C₈	—	22	1	no	—
442	C₂×C₈	—	22	1	no	—
443	C₂×C₈	—	22	1	no	—
444	C₂×C₈	—	44	1	no	—
445	C₂×C₈	—	44	1	no	—
446	C₂×C₈	—	44	1	no	—
447	C₂×C₈	—	44	1	no	—
448	C₂×C₈	—	44	1	no	—
449	C₂×C₈	—	44	1	no	—
450	C₂×C₈	—	44	1	no	—
451	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
452	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
453	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
454	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
455	C₄⋊C₄	—	11	1	no	—
456	C₄⋊C₄	—	11	1	no	—
457	C₄⋊C₄	—	11	1	no	—
458	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
459	C₂²⋊C₄	—	11	1	no	—
460	C₂²⋊C₄	—	11	1	no	—
461	C₂²⋊C₄	—	11	1	no	—
462	C₂²⋊C₄	—	11	1	no	—
463	C₂²⋊C₄	—	11	1	no	—
464	C₂²⋊C₄	—	11	1	no	—
465	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
466	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
467	C₄²	—	11	1	no	—
468	C₄²	—	11	1	no	—
469	C₄²	—	11	1	no	—
470	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
471	C₁₆	—	2	1	no	—
472	C₁₆	—	2	1	no	—
473	C₁₆	—	2	1	no	—
474	C₁₆	—	2	1	no	—
475	C₁₆	—	22	1	no	—
476	C₁₆	—	22	1	no	—
477	C₁₆	—	22	1	no	—
478	C₁₆	—	22	1	no	—
479	C₁₁	#33487	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	11	1	no	—
481	C₂³	—	11	1	no	—
482	C₂³	—	11	4	no	—
483	C₂³	—	11	1	no	—
484	C₂³	—	22	2	no	—
485	C₂³	—	44	1	no	—
486	C₂³	—	44	1	no	—
487	C₂³	—	44	1	no	—
488	C₂³	—	44	1	no	—
489	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
490	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
491	D₄	—	2	2	no	—
492	D₄	—	22	2	no	—
493	D₄	—	22	2	no	—
494	D₄	—	22	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	11	1	no	—
500	C₂×C₄	—	11	1	no	—
501	C₂×C₄	—	11	1	no	—
502	C₂×C₄	—	11	1	no	—
503	C₂×C₄	—	11	1	no	—
504	C₂×C₄	—	22	2	no	—
505	C₂×C₄	—	22	1	no	—
506	C₂×C₄	—	22	1	no	—
507	C₂×C₄	—	22	1	no	—
508	C₂×C₄	—	22	1	no	—
509	C₂×C₄	—	22	1	no	—
510	C₂×C₄	—	22	1	no	—
511	C₂×C₄	—	44	1	no	—
512	C₂×C₄	—	44	1	no	—
513	C₂×C₄	—	44	1	no	—
514	C₂×C₄	—	44	1	no	—
515	C₂×C₄	—	44	1	no	—
516	C₂×C₄	—	44	1	no	—
517	C₂×C₄	—	44	1	no	—
518	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
519	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	22	1	no	—
527	C₈	—	22	1	no	—
528	C₈	—	22	1	no	—
529	C₈	—	22	1	no	—
530	C₈	#67037	1	1	yes	characteristic
531	C₈	#67042	1	1	yes	characteristic
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	11	2	no	—
538	C₂²	—	11	2	no	—
539	C₂²	—	22	1	no	—
540	C₂²	—	22	1	no	—
541	C₂²	—	22	1	no	—
542	C₂²	—	22	1	no	—
543	C₂²	—	22	1	no	—
544	C₂²	—	22	1	no	—
545	C₂²	—	22	1	no	—
546	C₂²	—	44	4	no	—
547	C₂²	—	44	4	no	—
548	C₂²	D₁₁×M₃₂	1	2	yes	—
549	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	22	1	no	—
555	C₄	—	22	1	no	—
556	C₄	—	22	1	no	—
557	C₄	—	22	1	no	—
558	C₄	—	22	1	no	—
559	C₄	#10623076	1	1	yes	characteristic
560	C₄	#10623281	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	22	2	no	—
564	C₂	—	22	2	no	—
565	C₂	—	44	1	no	—
566	C₂	#13077637	1	1	yes	characteristic
567	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
568	C₂	#13081717	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2168	C₂
prime radical	C₂×D₄×D₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2168	D₁₁
hypocenter	C₁₁	#33487
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #13070444	C₂	semidirect
3. #13070443	C₂	semidirect
4. #13070442	C₂	semidirect
5. #13070441	C₂	semidirect
6. #13070440	C₂	semidirect
7. #13070439	C₂	semidirect
8. #13070438	C₂	semidirect
9. #13070418	C₂	semidirect
10. #13070417	C₂	semidirect
11. #13070226	C₂	semidirect
12. #13070225	C₂	semidirect
13. C₂×(C₂×D₁₁)⋊C₁₆	C₂	semidirect
14. D₁₁×C₂²⋊C₁₆	C₂	semidirect
15. C₁₁×#2168	C₂	semidirect
19. C₂×C₁₁×M₃₂	C₂²	semidirect
20. C₂²×C₁₁×C₁₆	C₂²	semidirect
24. C₂×#66876	C₂²	semidirect
25. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
27. C₂×#66862	C₂²	semidirect
28. C₂×#66862	C₂²	semidirect
29. C₂×C₁₆×D₁₁	C₂²	semidirect
30. C₂×C₁₆×D₁₁	C₂²	semidirect
39. C₁₁×C₄⋊C₁₆	C₂²	semidirect
40. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
41. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
42. C₁₁×#346	C₂²	semidirect
43. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
44. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
49. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
50. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
51. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
52. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
53. #10622140	C₂²	semidirect
54. #10622140	C₂²	semidirect
55. Dic₁₁⋊C₁₆	C₂²	semidirect
56. Dic₁₁⋊C₁₆	C₂²	semidirect
57. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
58. #10622099	C₂²	semidirect
204. #2168	D₁₁	semidirect
218. C₂²×D₁₁	M₃₂	semidirect
269. C₂×M₃₂	C₂×D₁₁	semidirect
273. C₂²×C₁₆	C₂×D₁₁	semidirect
289. C₄⋊C₁₆	C₂×D₁₁	semidirect
300. C₂²⋊C₁₆	C₂×D₁₁	semidirect
301. C₂²⋊C₁₆	C₂×D₁₁	semidirect
305. #346	C₂×D₁₁	semidirect
479. C₁₁	#33487	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₁₁	2
#13070444	2
#13070443	2
#13070442	2
#13070441	2
#13070440	2
#13070439	2
#13070438	2
#13070418	2
#13070417	2
#13070226	2
#13070225	2
C₂×(C₂×D₁₁)⋊C₁₆	2
D₁₁×C₂²⋊C₁₆	2
C₁₁×#2168	2
#33487	11