Subgroups — C₂×#13066455 #14643296

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#13066455	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₁	—	2	1	no	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₁	C₄	1	2	yes	—
8	C₂²×C₄×Dic₁₁	—	2	1	no	—
9	C₂³×C₁₁⋊C₈	—	2	1	no	—
10	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
12	C₂×C₁₁×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁⋊#95	—	2	1	no	—
15	C₄×C₄⋊Dic₁₁	—	2	1	no	—
16	C₄×C₄⋊Dic₁₁	—	2	1	no	—
17	C₄×C₄⋊Dic₁₁	C₄	1	2	yes	—
18	C₄×C₄⋊Dic₁₁	C₂²	1	2	yes	—
19	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
20	C₂×C₄×C₁₁⋊C₈	—	2	2	no	—
21	C₂×C₄×C₁₁⋊C₈	C₄	1	4	yes	complemented
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
26	C₂³×Dic₁₁	—	2	2	no	—
27	C₂²×C₈×C₁₁	—	2	4	no	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	—	4	2	no	—
30	C₂²×C₈×C₁₁	—	4	2	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	2	yes	—
37	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
38	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₁	—	2	2	no	—
40	C₂×C₄⋊Dic₁₁	—	2	4	no	—
41	C₂×C₄⋊Dic₁₁	C₈	1	8	yes	complemented
42	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
43	C₂×C₄×Dic₁₁	—	2	2	no	—
44	C₂×C₄×Dic₁₁	—	2	2	no	—
45	C₂×C₄×Dic₁₁	—	4	2	no	—
46	C₂×C₄×Dic₁₁	—	4	2	no	—
47	C₂²×C₁₁⋊C₈	—	2	8	no	—
48	C₂²×C₁₁⋊C₈	—	2	4	no	—
49	C₂²×C₁₁⋊C₈	—	2	2	no	—
50	C₁₁×C₄⋊C₈	—	2	4	no	—
51	C₁₁×C₄⋊C₈	—	2	2	no	—
52	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
53	C₁₁⋊#95	—	2	2	no	—
54	C₁₁⋊#95	—	2	2	no	—
55	C₄×C₁₁⋊C₈	—	2	4	no	—
56	C₄×C₁₁⋊C₈	—	2	2	no	—
57	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	complemented
58	C₂×#1279	—	11	1	no	maximal, Sylow
59	C₂⁴×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	—	2	4	no	—
61	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
62	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
71	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
72	C₂²×C₄×C₁₁	D₈	1	2	yes	—
73	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₁₁	—	2	8	no	—
80	C₂²×Dic₁₁	—	2	4	no	—
81	C₂²×Dic₁₁	—	4	4	no	—
82	C₂²×Dic₁₁	—	4	4	no	—
83	C₂×C₈×C₁₁	—	2	4	no	—
84	C₂×C₈×C₁₁	—	4	8	no	—
85	C₂×C₈×C₁₁	—	4	2	no	—
86	C₂×C₈×C₁₁	—	4	2	no	—
87	C₄²×C₁₁	C₄²	1	2	yes	—
88	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
89	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
90	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
91	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
92	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
93	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
97	C₄⋊Dic₁₁	—	2	8	no	—
98	C₄⋊Dic₁₁	—	2	4	no	—
99	C₄⋊Dic₁₁	C₂×C₈	1	8	yes	complemented
100	C₄×Dic₁₁	—	4	4	no	—
101	C₄×Dic₁₁	—	4	2	no	—
102	C₄×Dic₁₁	—	4	2	no	—
103	C₂×C₁₁⋊C₈	—	2	16	no	—
104	C₂×C₁₁⋊C₈	—	2	8	no	—
105	C₂×C₁₁⋊C₈	—	2	4	no	—
106	C₂²×C₄⋊C₈	D₁₁	1	1	yes	characteristic
107	C₂²×C₄×C₈	—	11	1	no	—
108	C₂×C₄×C₄⋊C₄	—	11	1	no	—
109	#1279	—	11	4	no	—
110	C₂³×C₁₁	#95	1	2	yes	—
111	C₂³×C₁₁	C₂²⋊C₈	1	4	yes	—
112	C₂³×C₁₁	#102	1	2	yes	—
113	C₂³×C₁₁	#103	1	2	yes	—
114	C₂³×C₁₁	#104	1	4	yes	—
115	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₁	—	2	4	no	—
117	C₂×C₄×C₁₁	—	2	4	no	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	2	2	no	—
120	C₂×C₄×C₁₁	#95	1	2	yes	—
121	C₂×C₄×C₁₁	#95	1	2	yes	—
122	C₂×C₄×C₁₁	#95	1	2	yes	—
123	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
124	C₂×C₄×C₁₁	#97	1	4	yes	—
125	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
126	C₂×C₄×C₁₁	#102	1	2	yes	—
127	C₂×C₄×C₁₁	#102	1	4	yes	—
128	C₂×C₄×C₁₁	#103	1	2	yes	—
129	C₂×C₄×C₁₁	#103	1	4	yes	—
130	C₂×C₄×C₁₁	C₄⋊C₈	1	8	yes	—
131	C₂×C₄×C₁₁	#106	1	4	yes	—
132	C₂×C₄×C₁₁	#107	1	4	yes	—
133	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
141	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
145	C₂×Dic₁₁	—	2	8	no	—
146	C₂×Dic₁₁	—	4	16	no	—
147	C₂×Dic₁₁	—	4	4	no	—
148	C₂×Dic₁₁	—	4	4	no	—
149	C₈×C₁₁	—	4	4	no	—
150	C₁₁⋊C₈	—	2	8	no	—
151	C₂³×C₈	—	2	1	no	—
152	C₂³×C₈	—	22	1	no	—
153	C₂²×C₄⋊C₄	—	11	2	no	—
154	C₂²×C₄²	—	22	1	no	—
155	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
156	C₂×C₄⋊C₈	—	2	1	no	—
157	C₂×C₄⋊C₈	—	2	2	no	—
158	C₂×C₄⋊C₈	Dic₁₁	1	4	yes	complemented
159	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
160	C₂×C₄×C₈	—	11	2	no	—
161	C₂×C₄×C₈	—	11	4	no	—
162	C₂×C₄×C₈	—	22	1	no	—
163	C₂×C₄×C₈	—	22	2	no	—
164	C₄×C₄⋊C₄	—	11	2	no	—
165	C₄×C₄⋊C₄	—	11	2	no	—
166	C₄×C₄⋊C₄	—	22	1	no	—
167	C₄×C₄⋊C₄	—	22	1	no	—
168	C₂×#95	—	22	1	no	—
169	C₂²×C₁₁	D₄⋊C₈	1	8	yes	—
170	C₂²×C₁₁	Q₈⋊C₈	1	8	yes	—
171	C₂²×C₁₁	#336	1	4	yes	—
172	C₂²×C₁₁	#339	1	4	yes	—
173	C₂²×C₁₁	#340	1	4	yes	—
174	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
175	C₂²×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
176	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
177	C₂²×C₁₁	C₂×#103	1	1	yes	characteristic
178	C₂²×C₁₁	C₂×#104	1	2	yes	—
179	C₄×C₁₁	—	2	2	no	—
180	C₄×C₁₁	—	2	1	no	—
181	C₄×C₁₁	—	2	1	no	—
182	C₄×C₁₁	#336	1	4	yes	—
183	C₄×C₁₁	#340	1	4	yes	—
184	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
185	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
186	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
187	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
188	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
189	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
190	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
191	Dic₁₁	—	4	8	no	—
192	C₂³×C₄	—	22	2	no	—
193	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
194	C₂³×C₄	D₄₄	1	1	yes	characteristic
195	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
196	C₂²×C₈	—	2	4	no	—
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	4	2	no	—
199	C₂²×C₈	—	4	2	no	—
200	C₂²×C₈	—	22	8	no	—
201	C₂²×C₈	—	22	4	no	—
202	C₂²×C₈	—	22	2	no	—
203	C₂×C₄⋊C₄	—	11	8	no	—
204	C₂×C₄⋊C₄	—	11	4	no	—
205	C₂×C₄⋊C₄	—	22	4	no	—
206	C₂×C₄⋊C₄	—	22	2	no	—
207	C₂×C₄²	—	22	2	no	—
208	C₂×C₄²	—	22	2	no	—
209	C₂×C₄²	—	44	2	no	—
210	C₂×C₄²	—	44	2	no	—
211	C₂×C₄²	Dic₂₂	1	2	yes	—
212	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
213	C₂×C₄²	C₄×D₁₁	1	2	yes	—
214	C₂×C₄²	D₄₄	1	1	yes	characteristic
215	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
216	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
217	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
218	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
219	C₄⋊C₈	—	2	4	no	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	complemented
222	C₄×C₈	—	11	4	no	—
223	C₄×C₈	—	22	4	no	—
224	C₄×C₈	—	22	2	no	—
225	#95	—	22	2	no	—
226	#95	—	22	2	no	—
227	C₂×C₁₁	#1279	1	8	yes	complemented
228	C₂×C₁₁	C₂×D₄⋊C₈	1	2	yes	—
229	C₂×C₁₁	C₂×Q₈⋊C₈	1	2	yes	—
230	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
231	C₂×C₁₁	C₂×#339	1	1	yes	characteristic
232	C₂×C₁₁	C₂×#340	1	1	yes	characteristic
233	C₂⁴	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	22	8	no	—
236	C₂²×C₄	—	22	4	no	—
237	C₂²×C₄	—	44	4	no	—
238	C₂²×C₄	—	44	4	no	—
239	C₂²×C₄	C₈×D₁₁	1	4	yes	—
240	C₂²×C₄	#4313	1	4	yes	—
241	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
242	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
243	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
244	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
245	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
246	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
247	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	#4323	1	2	yes	—
250	C₂²×C₄	#4324	1	2	yes	—
251	C₂²×C₄	#4325	1	2	yes	—
252	C₂²×C₄	#4326	1	2	yes	—
253	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
254	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	4	8	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	22	8	no	—
262	C₂×C₈	—	22	16	no	—
263	C₂×C₈	—	22	4	no	—
264	C₄⋊C₄	—	11	8	no	—
265	C₄⋊C₄	—	22	8	no	—
266	C₄⋊C₄	—	22	4	no	—
267	C₄²	—	44	4	no	—
268	C₄²	—	44	2	no	—
269	C₄²	—	44	2	no	—
270	C₄²	C₄×Dic₁₁	1	2	yes	—
271	C₄²	Dic₁₁⋊C₄	1	2	yes	—
272	C₄²	Dic₁₁⋊C₄	1	2	yes	—
273	C₄²	C₄⋊Dic₁₁	1	2	yes	—
274	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
275	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
276	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
277	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
278	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
279	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
280	C₁₁	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
281	C₂³	#66873	1	2	yes	—
282	C₂³	#66874	1	2	yes	—
283	C₂³	(C₂×D₁₁)⋊C₈	1	4	yes	—
284	C₂³	#66889	1	4	yes	—
285	C₂³	C₁₁⋊#95	1	2	yes	—
286	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	22	8	no	—
292	C₂×C₄	—	44	4	no	—
293	C₂×C₄	—	44	4	no	—
294	C₂×C₄	—	44	16	no	—
295	C₂×C₄	#66871	1	4	yes	—
296	C₂×C₄	#66872	1	4	yes	—
297	C₂×C₄	#66873	1	2	yes	—
298	C₂×C₄	#66874	1	2	yes	—
299	C₂×C₄	C₈×Dic₁₁	1	4	yes	—
300	C₂×C₄	Dic₁₁⋊C₈	1	8	yes	—
301	C₂×C₄	#66879	1	4	yes	—
302	C₂×C₄	(C₂×D₁₁)⋊C₈	1	4	yes	—
303	C₂×C₄	C₁₁⋊#95	1	2	yes	—
304	C₂×C₄	C₁₁⋊#95	1	2	yes	—
305	C₂×C₄	C₁₁⋊#95	1	2	yes	—
306	C₂×C₄	#66896	1	4	yes	—
307	C₂×C₄	#66899	1	4	yes	—
308	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
309	C₂×C₄	C₂×#4313	1	2	yes	—
310	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
311	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
312	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
314	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
315	C₂×C₄	C₂×#4323	1	1	yes	characteristic
316	C₂×C₄	C₂×#4324	1	1	yes	characteristic
317	C₂×C₄	C₂×#4325	1	1	yes	characteristic
318	C₂×C₄	C₂×#4326	1	1	yes	characteristic
319	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
320	C₈	—	4	4	no	—
321	C₈	—	22	8	no	—
322	C₂²	#10622121	1	8	yes	—
323	C₂²	#10622122	1	8	yes	—
324	C₂²	#10622167	1	4	yes	—
325	C₂²	#10622188	1	4	yes	—
326	C₂²	#10622193	1	4	yes	—
327	C₂²	C₂×#66873	1	1	yes	characteristic
328	C₂²	C₂×#66874	1	1	yes	characteristic
329	C₂²	C₂×(C₂×D₁₁)⋊C₈	1	2	yes	—
330	C₂²	C₂×#66889	1	2	yes	—
331	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
332	C₄	—	2	1	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	44	8	no	—
336	C₄	#10622167	1	4	yes	—
337	C₄	#10622188	1	4	yes	—
338	C₄	C₂×#66871	1	1	yes	characteristic
339	C₄	C₂×#66872	1	1	yes	characteristic
340	C₄	C₂×C₈×Dic₁₁	1	1	yes	characteristic
341	C₄	C₂×Dic₁₁⋊C₈	1	2	yes	—
342	C₄	C₂×#66879	1	1	yes	characteristic
343	C₄	C₂×#66896	1	1	yes	characteristic
344	C₄	C₂×#66899	1	1	yes	characteristic
345	C₂	#13066455	1	8	yes	direct product factor
346	C₂	C₂×#10622121	1	2	yes	—
347	C₂	C₂×#10622122	1	2	yes	—
348	C₂	C₂×#10622188	1	1	yes	characteristic
349	C₂	C₂×#10622193	1	1	yes	characteristic
350	C₂	C₂×#10622167	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂²×C₁₁×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₁₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂²×C₄⋊C₈	D₁₁
hypocenter	C₁₁	C₂×#1279
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13066455	C₂	direct (N × H)
12. C₂×C₁₁×C₄⋊C₈	C₄	semidirect
21. C₂×C₄×C₁₁⋊C₈	C₄	semidirect
41. C₂×C₄⋊Dic₁₁	C₈	semidirect
52. C₁₁×C₄⋊C₈	C₂×C₄	semidirect
57. C₄×C₁₁⋊C₈	C₂×C₄	semidirect
99. C₄⋊Dic₁₁	C₂×C₈	semidirect
158. C₂×C₄⋊C₈	Dic₁₁	semidirect
221. C₄⋊C₈	C₂×Dic₁₁	semidirect
227. C₂×C₁₁	#1279	semidirect
280. C₁₁	C₂×#1279	semidirect
345. C₂	#13066455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₁⋊C₈	2
C₂×C₄×C₄⋊Dic₁₁	2
#13066455	2
C₂²×C₁₁×C₄⋊C₈	2
C₂×#1279	11

Subgroups — C2×#13066455 #14643296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066455 #14643296