Subgroups — #14647697

Order 2816.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄₄	C₂	1	1	yes	maximal, characteristic
2	C₄×#66873	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622118	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10622121	C₂	1	1	yes	maximal, characteristic
5	#13066457	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₁	—	2	1	no	—
9	C₂×C₄×D₄₄	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
15	C₂×#66873	C₄	1	1	yes	characteristic
16	C₂×#66873	C₄	1	1	yes	characteristic
17	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×D₄₄	—	2	2	no	—
21	C₈×D₄₄	—	2	2	no	—
22	C₁₁×#336	—	2	1	no	—
23	#10622167	C₄	1	1	yes	characteristic
24	#10622167	C₄	1	1	yes	characteristic
25	#10622121	—	2	2	no	—
26	#10622118	—	2	2	no	—
27	C₂²×D₄₄	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₁	—	2	1	no	—
29	C₂²×C₈×C₁₁	—	2	1	no	—
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	—	2	1	no	—
35	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₁)⋊C₄	—	2	1	no	—
37	C₂×C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₁₁⋊C₈	—	2	1	no	—
39	C₂²×C₁₁⋊C₈	—	2	1	no	—
40	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₁₁	—	2	4	no	—
43	C₂×C₈×D₁₁	—	4	2	no	—
44	C₂×C₈×D₁₁	—	4	2	no	—
45	C₄×D₄₄	—	2	1	no	—
46	C₄×D₄₄	—	2	1	no	—
47	C₄×D₄₄	D₄	1	2	yes	—
48	C₄×D₄₄	Q₈	1	2	yes	—
49	C₁₁×C₄⋊C₈	—	2	1	no	—
50	C₁₁×C₄⋊C₈	—	2	1	no	—
51	C₁₁×C₄⋊C₈	—	4	2	no	—
52	C₄×C₈×C₁₁	—	2	1	no	—
53	C₄×C₈×C₁₁	—	2	1	no	—
54	C₁₁×#95	—	2	1	no	—
55	(C₂×D₁₁)⋊C₈	—	2	4	no	—
56	#66873	—	2	2	no	—
57	#66873	C₈	1	4	yes	complemented
58	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
60	C₄×C₁₁⋊C₈	—	2	1	no	—
61	C₄×C₁₁⋊C₈	—	2	1	no	—
62	C₄×C₁₁⋊C₈	—	2	1	no	—
63	C₄×C₁₁⋊C₈	—	2	1	no	—
64	#8845	—	11	1	no	maximal, Sylow
65	C₂³×D₁₁	—	2	1	no	—
66	C₂²×C₄×C₁₁	—	2	1	no	—
67	C₂²×C₄×C₁₁	—	2	1	no	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
71	C₂²×Dic₁₁	—	2	1	no	—
72	C₂×D₄₄	—	2	1	no	—
73	C₂×D₄₄	—	2	1	no	—
74	C₂×D₄₄	—	2	1	no	—
75	C₂×D₄₄	C₄⋊C₄	1	2	yes	—
76	C₂×D₄₄	C₂×C₈	1	2	yes	—
77	C₂×D₄₄	M₁₆	1	2	yes	—
78	C₂×C₄×D₁₁	—	2	2	no	—
79	C₂×C₄×D₁₁	—	2	2	no	—
80	C₂×C₄×D₁₁	—	4	1	no	—
81	C₂×C₄×D₁₁	—	4	1	no	—
82	C₂×C₄×D₁₁	—	4	1	no	—
83	C₂×C₄×D₁₁	—	4	1	no	—
84	C₂×C₈×C₁₁	—	2	1	no	—
85	C₂×C₈×C₁₁	—	2	1	no	—
86	C₂×C₈×C₁₁	—	2	1	no	—
87	C₂×C₈×C₁₁	—	2	1	no	—
88	C₂×C₈×C₁₁	—	2	1	no	—
89	C₂×C₈×C₁₁	—	4	1	no	—
90	C₂×C₈×C₁₁	—	4	1	no	—
91	C₂×C₈×C₁₁	—	4	1	no	—
92	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
93	C₁₁×C₄⋊C₄	—	2	1	no	—
94	C₁₁×C₄⋊C₄	—	2	1	no	—
95	C₁₁×C₄⋊C₄	—	2	1	no	—
96	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	complemented
97	C₄²×C₁₁	—	4	1	no	—
98	C₄²×C₁₁	—	4	1	no	—
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
102	C₄²×C₁₁	#41	1	1	yes	characteristic
103	(C₂×D₁₁)⋊C₄	—	2	2	no	—
104	(C₂×D₁₁)⋊C₄	—	2	2	no	—
105	C₄⋊Dic₁₁	—	2	1	no	—
106	C₄⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
107	C₂×C₁₁⋊C₈	—	2	2	no	—
108	C₂×C₁₁⋊C₈	—	2	1	no	—
109	C₂×C₁₁⋊C₈	—	2	1	no	—
110	C₂×C₁₁⋊C₈	—	2	2	no	—
111	C₂×C₁₁⋊C₈	—	2	1	no	—
112	C₂×C₁₁⋊C₈	—	2	1	no	—
113	C₂×C₁₁⋊C₈	—	2	1	no	—
114	C₂×C₁₁⋊C₈	—	4	1	no	—
115	C₂×C₁₁⋊C₈	—	4	1	no	—
116	C₂×C₁₁⋊C₈	—	4	1	no	—
117	C₂×C₁₁⋊C₈	—	4	1	no	—
118	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	complemented
119	C₈×D₁₁	—	4	8	no	—
120	C₂×C₈×D₄	—	11	1	no	—
121	#1939	D₁₁	1	1	yes	characteristic, complemented
122	C₄×#102	—	11	1	no	—
123	C₂×#334	—	11	1	no	—
124	C₂×D₄⋊C₈	—	11	1	no	—
125	#1279	—	11	1	no	—
126	#1273	—	11	1	no	—
127	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
128	C₂²×D₁₁	—	2	2	no	—
129	C₂²×D₁₁	—	2	2	no	—
130	C₂²×D₁₁	—	2	2	no	—
131	C₂²×D₁₁	—	4	1	no	—
132	C₂²×D₁₁	—	4	1	no	—
133	C₂²×D₁₁	—	4	1	no	—
134	C₂²×D₁₁	—	4	1	no	—
135	C₂×C₄×C₁₁	—	2	1	no	—
136	C₂×C₄×C₁₁	—	2	1	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	4	1	no	—
139	C₂×C₄×C₁₁	—	4	1	no	—
140	C₂×C₄×C₁₁	—	4	1	no	—
141	C₂×C₄×C₁₁	—	4	1	no	—
142	C₂×C₄×C₁₁	—	4	1	no	—
143	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
151	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
152	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
155	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×Dic₁₁	—	2	2	no	—
158	C₂×Dic₁₁	—	4	1	no	—
159	C₂×Dic₁₁	—	4	1	no	—
160	D₄₄	—	2	2	no	—
161	D₄₄	—	2	2	no	—
162	D₄₄	—	2	2	no	—
163	D₄₄	C₄⋊C₈	1	4	yes	complemented
164	C₄×D₁₁	—	4	2	no	—
165	C₄×D₁₁	—	4	2	no	—
166	C₄×D₁₁	—	4	2	no	—
167	C₄×D₁₁	—	4	2	no	—
168	C₈×C₁₁	—	2	2	no	—
169	C₈×C₁₁	—	4	1	no	—
170	C₈×C₁₁	—	8	1	no	—
171	C₁₁⋊C₈	—	2	2	no	—
172	C₁₁⋊C₈	—	4	2	no	—
173	C₁₁⋊C₈	—	4	1	no	—
174	C₁₁⋊C₈	—	4	2	no	—
175	C₂³×C₈	—	22	1	no	—
176	C₂×C₄×D₄	—	11	1	no	—
177	C₈×D₄	—	22	2	no	—
178	C₈×D₄	—	22	2	no	—
179	C₂×C₄⋊C₈	—	2	1	no	—
180	C₂×C₄⋊C₈	—	11	1	no	—
181	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
182	C₂×#102	—	11	1	no	—
183	C₂×#102	—	11	1	no	—
184	C₂×C₂²⋊C₈	—	22	1	no	—
185	C₂×C₄×C₈	—	11	1	no	—
186	C₂×C₄×C₈	—	11	1	no	—
187	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
188	C₄×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
189	#340	—	11	1	no	—
190	#340	—	11	1	no	—
191	#336	—	2	1	no	—
192	#334	—	22	2	no	—
193	D₄⋊C₈	—	22	2	no	—
194	C₂²×C₁₁	#385	1	1	yes	characteristic
195	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
196	C₂²×C₁₁	#435	1	1	yes	characteristic
197	C₂²×C₁₁	C₄×SD₁₆	1	1	yes	characteristic
198	C₂²×C₁₁	#442	1	1	yes	characteristic
199	C₂²×C₁₁	#443	1	1	yes	characteristic
200	C₂²×C₁₁	#444	1	1	yes	characteristic
201	C₂×D₁₁	—	2	4	no	—
202	C₂×D₁₁	—	4	2	no	—
203	C₂×D₁₁	—	4	2	no	—
204	C₂×D₁₁	—	4	2	no	—
205	C₂×D₁₁	—	4	2	no	—
206	C₂×D₁₁	—	4	2	no	—
207	C₂×D₁₁	—	4	2	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	—	4	2	no	—
211	C₄×C₁₁	—	8	1	no	—
212	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
213	C₄×C₁₁	#424	1	1	yes	characteristic
214	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
215	C₄×C₁₁	#435	1	1	yes	characteristic
216	C₄×C₁₁	#449	1	1	yes	characteristic
217	C₄×C₁₁	#450	1	1	yes	characteristic
218	C₄×C₁₁	#476	1	1	yes	characteristic
219	C₄×C₁₁	#478	1	1	yes	characteristic
220	Dic₁₁	—	4	2	no	—
221	C₂²×D₄	—	11	1	no	—
222	C₂³×C₄	—	22	1	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	11	1	no	—
225	C₂²×C₈	—	11	1	no	—
226	C₂²×C₈	—	22	4	no	—
227	C₂²×C₈	—	22	1	no	—
228	C₂²×C₈	—	22	1	no	—
229	C₂²×C₈	—	44	2	no	—
230	C₂²×C₈	—	44	2	no	—
231	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
232	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
233	C₄×D₄	—	11	2	no	—
234	C₄×D₄	—	11	2	no	—
235	C₄×D₄	—	22	1	no	—
236	C₄×D₄	—	22	1	no	—
237	C₂×C₄⋊C₄	—	11	1	no	—
238	C₂×C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	—	22	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	4	2	no	—
246	C₄⋊C₈	—	11	2	no	—
247	C₄⋊C₈	—	22	1	no	—
248	#102	—	11	4	no	—
249	#102	—	22	2	no	—
250	C₂²⋊C₈	—	22	4	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	22	1	no	—
254	C₄×C₈	—	22	1	no	—
255	C₄×C₈	—	22	1	no	—
256	C₄×C₈	—	22	1	no	—
257	#95	—	2	1	no	—
258	C₂×C₁₁	C₈×SD₁₆	1	1	yes	characteristic
259	C₂×C₁₁	#1580	1	1	yes	characteristic
260	C₂×C₁₁	#1582	1	1	yes	characteristic
261	C₂×C₁₁	#1586	1	1	yes	characteristic
262	C₂×C₁₁	#1850	1	1	yes	characteristic
263	C₂×C₁₁	#1864	1	1	yes	characteristic
264	C₂×C₁₁	#1866	1	1	yes	characteristic
265	D₁₁	—	4	4	no	—
266	C₂⁴	—	22	1	no	—
267	C₂×D₄	—	11	2	no	—
268	C₂×D₄	—	11	2	no	—
269	C₂×D₄	—	11	2	no	—
270	C₂×D₄	—	22	1	no	—
271	C₂×D₄	—	22	1	no	—
272	C₂×D₄	—	22	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	22	1	no	—
276	C₂²×C₄	—	22	2	no	—
277	C₂²×C₄	—	22	2	no	—
278	C₂²×C₄	—	44	1	no	—
279	C₂²×C₄	—	44	1	no	—
280	C₂²×C₄	—	44	1	no	—
281	C₂²×C₄	—	44	1	no	—
282	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
283	C₂²×C₄	#4339	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	11	2	no	—
294	C₂×C₈	—	22	1	no	—
295	C₂×C₈	—	22	1	no	—
296	C₂×C₈	—	22	2	no	—
297	C₂×C₈	—	22	1	no	—
298	C₂×C₈	—	22	1	no	—
299	C₂×C₈	—	22	1	no	—
300	C₂×C₈	—	22	2	no	—
301	C₂×C₈	—	44	8	no	—
302	C₂×C₈	—	44	1	no	—
303	C₂×C₈	—	44	1	no	—
304	C₂×C₈	—	44	1	no	—
305	C₂×C₈	—	44	1	no	—
306	C₂×C₈	#4325	1	2	yes	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	11	2	no	—
311	C₄⋊C₄	—	22	1	no	—
312	C₄⋊C₄	C₈×D₁₁	1	2	yes	complemented
313	C₂²⋊C₄	—	22	2	no	—
314	C₂²⋊C₄	—	22	2	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	D₄×D₁₁	1	1	yes	characteristic
318	C₄²	D₄×D₁₁	1	1	yes	characteristic
319	C₄²	Q₈×D₁₁	1	1	yes	characteristic
320	C₄²	#4343	1	1	yes	characteristic
321	C₁₁	#8845	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	22	2	no	—
323	C₂³	—	22	2	no	—
324	C₂³	—	22	2	no	—
325	C₂³	—	44	1	no	—
326	C₂³	—	44	1	no	—
327	C₂³	—	44	1	no	—
328	C₂³	—	44	1	no	—
329	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
330	D₄	—	11	4	no	—
331	D₄	—	22	2	no	—
332	D₄	—	22	2	no	—
333	D₄	—	22	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	22	2	no	—
343	C₂×C₄	—	44	1	no	—
344	C₂×C₄	—	44	1	no	—
345	C₂×C₄	—	44	2	no	—
346	C₂×C₄	—	44	2	no	—
347	C₂×C₄	—	44	2	no	—
348	C₂×C₄	—	44	2	no	—
349	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
350	C₂×C₄	#66946	1	1	yes	characteristic
351	C₂×C₄	#66947	1	1	yes	characteristic
352	C₂×C₄	#66949	1	1	yes	characteristic
353	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
354	C₂×C₄	#66954	1	1	yes	characteristic
355	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
356	C₂×C₄	#66960	1	1	yes	characteristic
357	C₂×C₄	#66985	1	1	yes	characteristic
358	C₂×C₄	#66990	1	1	yes	characteristic
359	C₂×C₄	C₂×#4325	1	1	yes	characteristic
360	C₂×C₄	#66999	1	1	yes	characteristic
361	C₂×C₄	#67002	1	1	yes	characteristic
362	C₂×C₄	#67003	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	4	1	no	—
365	C₈	—	8	1	no	—
366	C₈	—	22	2	no	—
367	C₈	—	44	2	no	—
368	C₈	—	44	2	no	—
369	C₈	—	44	1	no	—
370	C₂²	—	22	4	no	—
371	C₂²	—	44	2	no	—
372	C₂²	—	44	2	no	—
373	C₂²	—	44	2	no	—
374	C₂²	—	44	2	no	—
375	C₂²	—	44	2	no	—
376	C₂²	—	44	2	no	—
377	C₂²	#10622602	1	1	yes	characteristic
378	C₂²	#10622627	1	1	yes	characteristic
379	C₂²	C₄×#4325	1	1	yes	characteristic
380	C₂²	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
381	C₂²	#10622740	1	1	yes	characteristic
382	C₂²	#10622757	1	1	yes	characteristic
383	C₂²	#10622758	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	44	2	no	—
389	C₄	D₁₁×C₄⋊C₈	1	1	yes	characteristic
390	C₄	#10622447	1	1	yes	characteristic
391	C₄	#10622449	1	1	yes	characteristic
392	C₄	#10622452	1	1	yes	characteristic
393	C₄	#10622650	1	1	yes	characteristic
394	C₄	#10622659	1	1	yes	characteristic
395	C₄	#10622679	1	1	yes	characteristic
396	C₄	#10622697	1	1	yes	characteristic
397	C₂	—	44	4	no	—
398	C₂	C₈×#4325	1	1	yes	characteristic
399	C₂	#13067438	1	1	yes	characteristic
400	C₂	#13067450	1	1	yes	characteristic
401	C₂	#13067478	1	1	yes	characteristic
402	C₂	#13068792	1	1	yes	characteristic
403	C₂	#13068876	1	1	yes	characteristic
404	C₂	#13068890	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1939	C₂
socle	C₂³×C₁₁	C₄×D₄
prime radical	C₂²×D₄₄	C₂×C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1939	D₁₁
hypocenter	C₁₁	#8845
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1939

Complements

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

N	H ≅ G/N	type
3. C₂×#10622118	C₂	semidirect
5. #13066457	C₂	semidirect
6. C₁₁⋊#1273	C₂	semidirect
7. C₁₁×#1939	C₂	semidirect
57. #66873	C₈	semidirect
96. C₁₁×C₄⋊C₄	C₂×C₈	semidirect
118. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
121. #1939	D₁₁	semidirect
163. D₄₄	C₄⋊C₈	semidirect
312. C₄⋊C₄	C₈×D₁₁	semidirect
321. C₁₁	#8845	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄₄	2
C₄×#66873	2
C₂×#10622118	2
C₂×#10622121	2
#13066457	2
C₁₁⋊#1273	2
C₁₁×#1939	2
#8845	11