Subgroups — #14907366

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 384 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	#13070449	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070447	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070441	C₂	1	2	yes	maximal, complemented
5	#13070438	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070418	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070413	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070225	C₂	1	2	yes	maximal, complemented
10	C₂×(C₂×D₁₁)⋊C₁₆	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₁	C₂²	1	2	yes	—
13	C₄×D₄×D₁₁	C₄	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	complemented
15	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
17	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
18	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
19	C₂×#66862	C₂²	1	2	yes	complemented
20	C₂×#66862	C₂²	1	2	yes	complemented
21	#10622447	C₄	1	1	yes	characteristic
22	D₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
23	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
24	D₁₁×C₂²⋊C₈	C₄	1	2	yes	—
25	C₈×D₄₄	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
29	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
31	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
32	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
33	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
34	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
35	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
36	#10622140	C₂²	1	2	yes	complemented
37	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₁₁	C₈	1	1	yes	characteristic
42	C₂²×C₄×D₁₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	D₄×Dic₁₁	C₈	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
47	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₁₁	—	4	2	no	—
49	C₂×C₈×D₁₁	—	4	2	no	—
50	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
51	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₁	C₂³	1	2	yes	—
54	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
55	#66946	C₈	1	1	yes	characteristic
56	C₄⋊C₄×D₁₁	C₈	1	1	yes	characteristic
57	(C₂²⋊D₁₁)⋊C₄	C₈	1	2	yes	—
58	C₂²⋊C₄×D₁₁	C₈	1	2	yes	—
59	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₁×C₁₆	—	4	2	no	—
62	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
69	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
70	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
72	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
74	C₂×C₁₁⋊C₁₆	—	4	2	no	—
75	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
78	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
80	#66862	—	4	2	no	—
81	#66862	—	4	2	no	—
82	#33488	—	11	1	no	maximal, Sylow
83	C₂³×D₁₁	C₂×C₈	1	2	yes	—
84	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
86	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
87	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
88	D₄×D₁₁	—	2	4	no	—
89	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₁₁	—	4	2	no	—
91	C₂×C₄×D₁₁	—	4	2	no	—
92	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
104	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
105	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
107	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
108	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
109	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
110	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
111	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
112	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
113	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₁₁⋊C₈	—	4	2	no	—
115	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
118	C₈×D₁₁	—	2	2	no	—
119	C₈×D₁₁	—	2	2	no	—
120	C₈×D₁₁	—	2	1	no	—
121	C₈×D₁₁	—	2	1	no	—
122	C₈×D₁₁	—	4	2	no	—
123	C₈×D₁₁	—	4	2	no	—
124	C₈×D₁₁	—	4	1	no	—
125	C₁₁×C₁₆	—	2	1	no	—
126	C₁₁×C₁₆	—	2	2	no	—
127	C₁₁×C₁₆	—	2	1	no	—
128	C₁₁⋊C₁₆	—	2	1	no	—
129	C₁₁⋊C₁₆	—	2	2	no	—
130	C₁₁⋊C₁₆	—	2	1	no	—
131	C₂×C₈×D₄	—	11	1	no	—
132	#2169	—	11	1	no	—
133	#2169	—	11	1	no	—
134	#2168	—	11	2	no	—
135	#2168	—	11	2	no	—
136	D₄×C₁₆	—	11	1	no	—
137	D₄×C₁₆	D₁₁	1	1	yes	characteristic, complemented
138	#2163	—	11	1	no	—
139	#2162	—	11	1	no	—
140	#2112	—	11	2	no	—
141	C₂×C₂²⋊C₁₆	—	11	2	no	—
142	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
143	C₂²×D₁₁	—	2	4	no	—
144	C₂²×D₁₁	—	2	4	no	—
145	C₂²×D₁₁	—	4	2	no	—
146	C₂²×D₁₁	C₂²×C₈	1	2	yes	—
147	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
148	D₄×C₁₁	M₃₂	1	4	yes	complemented
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
155	C₂²⋊D₁₁	—	2	4	no	—
156	C₂×Dic₁₁	—	4	2	no	—
157	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
158	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
159	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
160	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
161	D₄₄	—	2	2	no	—
162	C₄×D₁₁	—	2	2	no	—
163	C₄×D₁₁	—	2	1	no	—
164	C₄×D₁₁	—	2	2	no	—
165	C₄×D₁₁	—	2	1	no	—
166	C₄×D₁₁	—	2	2	no	—
167	C₄×D₁₁	—	2	2	no	—
168	C₄×D₁₁	—	4	2	no	—
169	C₄×D₁₁	—	4	2	no	—
170	C₈×C₁₁	—	2	2	no	—
171	C₈×C₁₁	—	2	1	no	—
172	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₁₁⋊C₈	—	2	1	no	—
175	C₁₁⋊C₈	—	2	2	no	—
176	C₁₁⋊C₈	—	2	1	no	—
177	C₂³×C₈	—	11	2	no	—
178	C₂×C₄×D₄	—	11	1	no	—
179	C₂×M₃₂	—	11	2	no	—
180	C₂×M₃₂	—	11	2	no	—
181	C₂²×C₁₆	—	11	2	no	—
182	C₂²×C₁₆	C₂×D₁₁	1	2	yes	complemented
183	C₈×D₄	—	11	2	no	—
184	C₈×D₄	—	11	1	no	—
185	C₈×D₄	—	11	1	no	—
186	C₈×D₄	—	11	2	no	—
187	C₈×D₄	—	11	1	no	—
188	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
189	C₂×C₄⋊C₈	—	11	1	no	—
190	C₂×C₂²⋊C₈	—	11	2	no	—
191	C₂×C₄×C₈	—	11	1	no	—
192	C₄⋊C₁₆	—	11	1	no	—
193	C₄⋊C₁₆	—	11	1	no	—
194	C₄⋊C₁₆	—	11	1	no	—
195	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
196	C₂²⋊C₁₆	—	11	2	no	—
197	C₂²⋊C₁₆	—	11	1	no	—
198	C₂²⋊C₁₆	—	11	2	no	—
199	C₂²⋊C₁₆	—	11	2	no	—
200	C₂²⋊C₁₆	—	11	2	no	—
201	C₂²⋊C₁₆	—	11	1	no	—
202	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	complemented
203	#346	—	11	2	no	—
204	C₄×C₁₆	—	11	1	no	—
205	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic, complemented
206	C₂²×C₁₁	—	2	2	no	—
207	C₂²×C₁₁	—	2	2	no	—
208	C₂²×C₁₁	C₂×M₃₂	1	4	yes	—
209	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
210	C₂×D₁₁	—	2	1	no	—
211	C₂×D₁₁	—	2	1	no	—
212	C₂×D₁₁	—	2	2	no	—
213	C₂×D₁₁	—	2	2	no	—
214	C₂×D₁₁	—	2	2	no	—
215	C₂×D₁₁	—	4	8	no	—
216	C₂×D₁₁	#504	1	2	yes	—
217	C₄×C₁₁	—	2	1	no	—
218	C₄×C₁₁	—	2	2	no	—
219	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
220	C₄×C₁₁	#518	1	1	yes	characteristic
221	C₄×C₁₁	#568	1	1	yes	characteristic
222	Dic₁₁	—	2	1	no	—
223	Dic₁₁	—	2	1	no	—
224	Dic₁₁	—	2	1	no	—
225	Dic₁₁	—	2	2	no	—
226	C₂²×D₄	—	11	1	no	—
227	C₂³×C₄	—	11	2	no	—
228	C₂²×C₈	—	11	2	no	—
229	C₂²×C₈	—	11	1	no	—
230	C₂²×C₈	—	11	2	no	—
231	C₂²×C₈	—	11	2	no	—
232	C₂²×C₈	—	11	2	no	—
233	C₂²×C₈	—	11	1	no	—
234	C₂²×C₈	—	44	2	no	—
235	C₂²×C₈	—	44	2	no	—
236	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
237	C₄×D₄	—	11	1	no	—
238	C₄×D₄	—	11	2	no	—
239	C₄×D₄	—	11	1	no	—
240	C₄×D₄	—	11	2	no	—
241	C₄×D₄	—	11	1	no	—
242	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	—	11	1	no	—
244	C₂×C₂²⋊C₄	—	11	2	no	—
245	C₂×C₄²	—	11	1	no	—
246	M₃₂	—	44	2	no	—
247	M₃₂	—	44	2	no	—
248	C₂×C₁₆	—	4	2	no	—
249	C₂×C₁₆	—	11	1	no	—
250	C₂×C₁₆	—	11	1	no	—
251	C₂×C₁₆	—	11	2	no	—
252	C₂×C₁₆	—	44	2	no	—
253	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
254	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
255	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
256	C₄⋊C₈	—	11	2	no	—
257	C₄⋊C₈	—	11	1	no	—
258	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
259	C₂²⋊C₈	—	11	2	no	—
260	C₂²⋊C₈	—	11	2	no	—
261	C₂²⋊C₈	—	11	2	no	—
262	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
263	C₄×C₈	—	11	1	no	—
264	C₄×C₈	—	11	1	no	—
265	C₄×C₈	—	11	1	no	—
266	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
267	C₂×C₁₁	—	2	4	no	—
268	C₂×C₁₁	#2972	1	1	yes	characteristic
269	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
270	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
271	D₁₁	—	2	2	no	—
272	D₁₁	—	4	2	no	—
273	C₂⁴	—	11	2	no	—
274	C₂×D₄	—	11	2	no	—
275	C₂×D₄	—	11	1	no	—
276	C₂×D₄	—	22	4	no	—
277	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
278	C₂²×C₄	—	11	2	no	—
279	C₂²×C₄	—	11	1	no	—
280	C₂²×C₄	—	11	1	no	—
281	C₂²×C₄	—	11	2	no	—
282	C₂²×C₄	—	11	1	no	—
283	C₂²×C₄	—	11	2	no	—
284	C₂²×C₄	—	11	2	no	—
285	C₂²×C₄	—	44	2	no	—
286	C₂²×C₄	—	44	2	no	—
287	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	11	1	no	—
291	C₂×C₈	—	11	1	no	—
292	C₂×C₈	—	11	2	no	—
293	C₂×C₈	—	22	2	no	—
294	C₂×C₈	—	22	1	no	—
295	C₂×C₈	—	22	2	no	—
296	C₂×C₈	—	22	1	no	—
297	C₂×C₈	—	44	2	no	—
298	C₂×C₈	—	44	2	no	—
299	C₂×C₈	—	44	1	no	—
300	C₂×C₈	—	44	2	no	—
301	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
303	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
304	C₄⋊C₄	—	11	2	no	—
305	C₄⋊C₄	—	11	1	no	—
306	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
307	C₂²⋊C₄	—	11	2	no	—
308	C₂²⋊C₄	—	11	2	no	—
309	C₂²⋊C₄	—	11	2	no	—
310	C₂²⋊C₄	C₈×D₁₁	1	2	yes	—
311	C₄²	—	11	1	no	—
312	C₄²	—	11	1	no	—
313	C₄²	—	11	1	no	—
314	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
315	C₁₆	—	2	1	no	—
316	C₁₆	—	2	2	no	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	22	1	no	—
319	C₁₆	—	22	1	no	—
320	C₁₆	—	22	2	no	—
321	C₁₁	#33488	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	11	1	no	—
323	C₂³	—	11	2	no	—
324	C₂³	—	22	4	no	—
325	C₂³	—	22	4	no	—
326	C₂³	—	44	2	no	—
327	C₂³	C₂×C₈×D₁₁	1	2	yes	—
328	D₄	—	22	4	no	—
329	D₄	—	22	2	no	—
330	D₄	#66862	1	4	yes	complemented
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	11	1	no	—
334	C₂×C₄	—	11	1	no	—
335	C₂×C₄	—	11	1	no	—
336	C₂×C₄	—	11	2	no	—
337	C₂×C₄	—	22	2	no	—
338	C₂×C₄	—	22	2	no	—
339	C₂×C₄	—	22	1	no	—
340	C₂×C₄	—	22	2	no	—
341	C₂×C₄	—	22	1	no	—
342	C₂×C₄	—	22	2	no	—
343	C₂×C₄	—	44	2	no	—
344	C₂×C₄	—	44	2	no	—
345	C₂×C₄	—	44	2	no	—
346	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
348	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	2	no	—
352	C₈	—	22	1	no	—
353	C₈	—	22	1	no	—
354	C₈	—	22	2	no	—
355	C₈	#67037	1	1	yes	characteristic
356	C₈	#67042	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	11	2	no	—
360	C₂²	—	22	1	no	—
361	C₂²	—	22	1	no	—
362	C₂²	—	22	2	no	—
363	C₂²	—	22	2	no	—
364	C₂²	—	22	2	no	—
365	C₂²	—	44	8	no	—
366	C₂²	C₂×#66862	1	4	yes	—
367	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	22	1	no	—
371	C₄	—	22	1	no	—
372	C₄	—	22	1	no	—
373	C₄	—	22	2	no	—
374	C₄	C₂×#66862	1	2	yes	—
375	C₄	#10623076	1	1	yes	characteristic
376	C₄	#10623281	1	1	yes	characteristic
377	C₂	—	2	4	no	—
378	C₂	—	22	2	no	—
379	C₂	—	44	2	no	—
380	C₂	#13077637	1	1	yes	characteristic
381	C₂	C₂²×#66862	1	1	yes	characteristic
382	C₂	D₁₁×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	D₄×C₁₁×C₁₆	C₂
prime radical	C₂×D₄×D₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	D₄×C₁₆	D₁₁
hypocenter	C₁₁	#33488
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13070449	C₂	semidirect
3. #13070447	C₂	semidirect
4. #13070441	C₂	semidirect
5. #13070438	C₂	semidirect
6. D₄×C₁₁⋊C₁₆	C₂	semidirect
7. #13070418	C₂	semidirect
8. #13070413	C₂	semidirect
9. #13070225	C₂	semidirect
10. C₂×(C₂×D₁₁)⋊C₁₆	C₂	semidirect
11. D₄×C₁₁×C₁₆	C₂	semidirect
14. C₂²×C₁₁×C₁₆	C₂²	semidirect
17. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
19. C₂×#66862	C₂²	semidirect
20. C₂×#66862	C₂²	semidirect
27. C₁₁×C₄⋊C₁₆	C₂²	semidirect
28. C₁₁×C₂²⋊C₁₆	C₂²	semidirect
29. C₄×C₁₁×C₁₆	C₂²	semidirect
30. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
34. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
35. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
36. #10622140	C₂²	semidirect
37. Dic₁₁⋊C₁₆	C₂²	semidirect
38. Dic₁₁⋊C₁₆	C₂²	semidirect
39. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
40. C₄×C₁₁⋊C₁₆	C₂²	semidirect
137. D₄×C₁₆	D₁₁	semidirect
148. D₄×C₁₁	M₃₂	semidirect
182. C₂²×C₁₆	C₂×D₁₁	semidirect
195. C₄⋊C₁₆	C₂×D₁₁	semidirect
202. C₂²⋊C₁₆	C₂×D₁₁	semidirect
205. C₄×C₁₆	C₂×D₁₁	semidirect
321. C₁₁	#33488	semidirect
330. D₄	#66862	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
#13070449	2
#13070447	2
#13070441	2
#13070438	2
D₄×C₁₁⋊C₁₆	2
#13070418	2
#13070413	2
#13070225	2
C₂×(C₂×D₁₁)⋊C₁₆	2
D₄×C₁₁×C₁₆	2
#33488	11