Subgroups — #14722756

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#4318	C₂	1	1	yes	maximal, characteristic
3	#13067369	C₂	1	4	yes	maximal, complemented
4	#13067366	C₂	1	4	yes	maximal, complemented
5	#13067362	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×#4318	C₄	1	1	yes	characteristic
9	C₂²×#4318	C₄	1	1	yes	characteristic
10	C₁₁×#431	—	2	1	no	—
11	C₁₁×#431	—	2	1	no	—
12	C₁₁×#431	C₂²	1	2	yes	—
13	C₁₁×#431	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
16	C₂×C₄×C₈×C₁₁	—	2	1	no	—
17	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
18	#10622538	—	2	1	no	—
19	#10622538	—	2	1	no	—
20	#10622538	C₂²	1	2	yes	—
21	#10622538	C₂²	1	2	yes	—
22	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
23	C₄×#4318	C₄	1	2	yes	—
24	C₄×#4318	C₄	1	2	yes	—
25	C₄×#4318	C₂²	1	2	yes	—
26	C₄×#4318	C₂²	1	2	yes	—
27	C₂×#66867	C₄	1	2	yes	—
28	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
29	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
30	#10622118	C₂²	1	8	yes	complemented
31	#10622117	C₂²	1	8	yes	complemented
32	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	—	2	2	no	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×#4318	—	2	4	no	—
49	C₂×#4318	C₈	1	8	yes	complemented
50	C₂×#4318	C₂×C₄	1	2	yes	—
51	C₂×#4318	C₂×C₄	1	2	yes	—
52	C₂×#4318	C₂×C₄	1	2	yes	—
53	C₂×#4318	C₂×C₄	1	2	yes	—
54	C₂²×C₁₁⋊C₈	—	2	2	no	—
55	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
56	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₁×C₄⋊C₈	—	2	2	no	—
58	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
59	C₁₁×C₂²⋊C₈	—	2	2	no	—
60	C₁₁×C₂²⋊C₈	—	2	2	no	—
61	C₄×C₈×C₁₁	—	2	2	no	—
62	C₄×C₈×C₁₁	—	2	2	no	—
63	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
65	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
66	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
67	#66867	C₂×C₄	1	4	yes	—
68	#66867	C₂×C₄	1	4	yes	—
69	C₄×C₁₁⋊C₈	—	2	2	no	—
70	C₄×C₁₁⋊C₈	—	2	2	no	—
71	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
72	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
73	#17787	—	11	1	no	maximal, Sylow
74	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	—	4	2	no	—
76	C₂²×C₄×C₁₁	—	4	2	no	—
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
87	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	—	4	4	no	—
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
115	#4318	—	2	4	no	—
116	#4318	—	2	4	no	—
117	#4318	C₂×C₈	1	8	yes	complemented
118	#4318	C₂×C₈	1	8	yes	complemented
119	C₂×C₁₁⋊C₈	—	2	4	no	—
120	C₂×C₁₁⋊C₈	—	2	4	no	—
121	C₂×C₁₁⋊C₈	—	4	4	no	—
122	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	complemented
123	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
124	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
125	C₂×#431	—	11	1	no	—
126	C₂×#431	D₁₁	1	1	yes	characteristic
127	C₂×C₄×M₁₆	—	11	1	no	—
128	#1565	—	11	4	no	—
129	#1565	—	11	4	no	—
130	#1564	—	11	4	no	—
131	C₂³×C₁₁	—	4	1	no	—
132	C₂³×C₁₁	—	4	1	no	—
133	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
134	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	2	2	no	—
143	C₂×C₄×C₁₁	—	4	1	no	—
144	C₂×C₄×C₁₁	—	4	1	no	—
145	C₂×C₄×C₁₁	—	4	1	no	—
146	C₂×C₄×C₁₁	—	4	1	no	—
147	C₂×C₄×C₁₁	—	4	1	no	—
148	C₂×C₄×C₁₁	—	4	1	no	—
149	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
150	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
151	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
163	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
165	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
166	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₁₁	—	4	4	no	—
171	C₁₁⋊C₈	—	2	4	no	—
172	C₁₁⋊C₈	—	4	4	no	—
173	C₁₁⋊C₈	C₂²×C₈	1	8	yes	—
174	C₂²×M₁₆	—	11	1	no	—
175	C₂²×M₁₆	—	11	1	no	—
176	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
177	#431	—	2	1	no	—
178	#431	—	2	1	no	—
179	#431	—	11	2	no	—
180	#431	—	11	2	no	—
181	#431	—	22	1	no	—
182	#431	—	22	1	no	—
183	#431	C₂×D₁₁	1	2	yes	—
184	#431	C₂×D₁₁	1	2	yes	—
185	C₂×C₄⋊C₈	—	11	2	no	—
186	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
187	C₂×C₂²⋊C₈	—	2	1	no	—
188	C₂×C₂²⋊C₈	—	22	1	no	—
189	C₄×M₁₆	—	11	2	no	—
190	C₄×M₁₆	—	11	2	no	—
191	C₄×M₁₆	—	11	2	no	—
192	C₄×M₁₆	—	11	2	no	—
193	C₂×#97	—	11	2	no	—
194	C₂×C₄×C₈	—	2	1	no	—
195	C₂×C₄×C₈	—	11	2	no	—
196	C₂×C₄×C₈	—	22	1	no	—
197	#335	—	11	8	no	—
198	#334	—	11	8	no	—
199	C₂²×C₁₁	—	2	1	no	—
200	C₂²×C₁₁	—	2	1	no	—
201	C₂²×C₁₁	—	2	1	no	—
202	C₂²×C₁₁	—	2	1	no	—
203	C₂²×C₁₁	—	2	1	no	—
204	C₂²×C₁₁	—	2	1	no	—
205	C₂²×C₁₁	—	4	4	no	—
206	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
207	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
208	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
209	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
210	C₄×C₁₁	—	2	1	no	—
211	C₄×C₁₁	—	2	1	no	—
212	C₄×C₁₁	—	2	1	no	—
213	C₄×C₁₁	—	2	1	no	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
217	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
218	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
219	C₄×C₁₁	#430	1	2	yes	—
220	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
221	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
222	C₄×C₁₁	#575	1	2	yes	—
223	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
224	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
226	C₂×M₁₆	—	11	8	no	—
227	C₂×M₁₆	—	11	2	no	—
228	C₂×M₁₆	—	11	2	no	—
229	C₂×M₁₆	—	11	2	no	—
230	C₂×M₁₆	—	11	2	no	—
231	C₂×M₁₆	—	22	4	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	11	2	no	—
234	C₂²×C₈	—	11	2	no	—
235	C₂²×C₈	—	22	2	no	—
236	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
237	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
238	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	11	4	no	—
250	C₄⋊C₈	—	22	2	no	—
251	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	22	2	no	—
255	C₂²⋊C₈	—	22	2	no	—
256	#97	—	11	4	no	—
257	#97	—	11	4	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	11	4	no	—
261	C₄×C₈	—	11	4	no	—
262	C₄×C₈	—	22	2	no	—
263	C₄×C₈	—	22	2	no	—
264	C₂×C₁₁	—	2	2	no	—
265	C₂×C₁₁	—	2	2	no	—
266	C₂×C₁₁	—	2	2	no	—
267	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
268	C₂×C₁₁	#2911	1	1	yes	characteristic
269	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
270	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₈×D₁₁	1	4	yes	—
274	C₂²×C₄	#4313	1	4	yes	—
275	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
286	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
293	M₁₆	—	11	8	no	—
294	M₁₆	—	11	8	no	—
295	M₁₆	—	22	4	no	—
296	M₁₆	—	22	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	4	4	no	—
299	C₂×C₈	—	11	8	no	—
300	C₂×C₈	—	11	4	no	—
301	C₂×C₈	—	11	4	no	—
302	C₂×C₈	—	22	4	no	—
303	C₂×C₈	—	22	4	no	—
304	C₂×C₈	—	44	4	no	—
305	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
306	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
308	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
309	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
310	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
311	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
312	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
313	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
317	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
320	C₄²	C₂³×D₁₁	1	1	yes	characteristic
321	C₁₁	#17787	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	Dic₁₁⋊C₈	1	4	yes	—
325	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
326	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
327	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
341	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
342	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
343	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
346	C₂×C₄	C₂×#4313	1	2	yes	—
347	C₂×C₄	C₂×#4313	1	2	yes	—
348	C₂×C₄	C₂×#4313	1	2	yes	—
349	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	11	8	no	—
363	C₈	—	22	4	no	—
364	C₈	—	44	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	4	no	—
372	C₂²	C₂×Dic₁₁⋊C₈	1	2	yes	—
373	C₂²	C₂×Dic₁₁⋊C₈	1	2	yes	—
374	C₂²	C₂×Dic₁₁⋊C₈	1	2	yes	—
375	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	C₂×Dic₁₁⋊C₈	1	2	yes	—
383	C₄	C₂×Dic₁₁⋊C₈	1	2	yes	—
384	C₄	C₂×Dic₁₁⋊C₈	1	2	yes	—
385	C₄	#10622737	1	2	yes	—
386	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
387	C₄	C₂²×#4313	1	1	yes	characteristic
388	C₄	#10623353	1	2	yes	—
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	2	2	no	—
392	C₂	C₂²×Dic₁₁⋊C₈	1	1	yes	characteristic
393	C₂	#13077205	1	1	yes	characteristic
394	C₂	C₂×#10622737	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#17787
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13067369	C₂	semidirect
4. #13067366	C₂	semidirect
5. #13067362	C₂	semidirect
30. #10622118	C₂²	semidirect
31. #10622117	C₂²	semidirect
49. C₂×#4318	C₈	semidirect
117. #4318	C₂×C₈	semidirect
118. #4318	C₂×C₈	semidirect
122. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
321. C₁₁	#17787	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622538	2
C₂×C₄×#4318	2
#13067369	2
#13067366	2
#13067362	2
C₂×C₁₁×#431	2
#17787	11