Subgroups — #14722786

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	2	yes	maximal
2	#13067379	C₂	1	4	yes	maximal, complemented
3	#13067375	C₂	1	2	yes	maximal, complemented
4	#13067372	C₂	1	2	yes	maximal, complemented
5	#13067364	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₁	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
18	#10622820	—	2	2	no	—
19	#10622539	—	2	2	no	—
20	#10622539	C₂²	1	4	yes	—
21	#10622538	—	2	2	no	—
22	#10622538	C₂²	1	4	yes	—
23	#10622537	C₂²	1	4	yes	—
24	C₄×#4318	—	2	2	no	—
25	#10622096	C₂²	1	8	yes	complemented
26	#10622095	C₂²	1	8	yes	complemented
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	8	no	—
31	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	C₂×C₄	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	D₄	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	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×#4318	—	2	4	no	—
50	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
53	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
54	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
58	C₄×C₈×C₁₁	C₂³	1	2	yes	—
59	C₄×C₈×C₁₁	C₂³	1	2	yes	—
60	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
61	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
62	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
63	C₄⋊(C₁₁⋊C₈)	C₂³	1	8	yes	—
64	#66867	—	2	4	no	—
65	C₄×C₁₁⋊C₈	—	2	4	no	—
66	#17793	—	11	1	no	maximal, Sylow
67	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	—	2	4	no	—
69	C₂²×C₄×C₁₁	—	2	4	no	—
70	C₂²×C₄×C₁₁	—	2	4	no	—
71	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₁₁	—	2	4	no	—
90	C₂×C₈×C₁₁	—	2	4	no	—
91	C₂×C₈×C₁₁	—	2	4	no	—
92	C₂×C₈×C₁₁	—	2	4	no	—
93	C₂×C₈×C₁₁	—	2	4	no	—
94	C₂×C₈×C₁₁	M₁₆	1	8	yes	complemented
95	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
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	—	4	8	no	—
116	C₂×C₁₁⋊C₈	—	2	8	no	—
117	#2920	—	11	2	no	—
118	C₂²×C₄×C₈	D₁₁	1	1	yes	characteristic
119	#1568	—	11	4	no	—
120	#1567	—	11	2	no	—
121	#1566	—	11	2	no	—
122	#1564	—	11	4	no	—
123	C₂³×C₁₁	—	2	2	no	—
124	C₂³×C₁₁	—	2	2	no	—
125	C₂³×C₁₁	—	2	2	no	—
126	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
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	—	2	2	no	—
144	C₂×C₄×C₁₁	#108	1	4	yes	—
145	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
155	C₂×C₄×C₁₁	#135	1	4	yes	—
156	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
159	C₈×C₁₁	—	2	2	no	—
160	C₈×C₁₁	—	2	2	no	—
161	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
162	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
163	C₁₁⋊C₈	—	4	8	no	—
164	C₂³×C₈	Dic₁₁	1	2	yes	—
165	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
166	#432	—	11	4	no	—
167	#432	—	22	2	no	—
168	#431	—	11	4	no	—
169	#431	—	22	2	no	—
170	#423	—	11	4	no	—
171	#407	—	22	2	no	—
172	C₄×M₁₆	—	22	2	no	—
173	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
174	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
175	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
176	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
177	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
179	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
180	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
182	#335	—	11	8	no	—
183	#334	—	11	8	no	—
184	C₂²×C₁₁	—	2	8	no	—
185	C₂²×C₁₁	—	2	1	no	—
186	C₂²×C₁₁	—	2	1	no	—
187	C₂²×C₁₁	—	2	1	no	—
188	C₂²×C₁₁	—	2	1	no	—
189	C₂²×C₁₁	—	2	1	no	—
190	C₂²×C₁₁	—	2	1	no	—
191	C₂²×C₁₁	#423	1	2	yes	—
192	C₂²×C₁₁	#427	1	2	yes	—
193	C₂²×C₁₁	C₂×#108	1	2	yes	—
194	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₄×C₁₁	—	2	1	no	—
196	C₄×C₁₁	—	2	1	no	—
197	C₄×C₁₁	—	2	1	no	—
198	C₄×C₁₁	—	2	1	no	—
199	C₄×C₁₁	—	2	1	no	—
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	#423	1	2	yes	—
202	C₄×C₁₁	#427	1	2	yes	—
203	C₄×C₁₁	C₂×#108	1	2	yes	—
204	C₄×C₁₁	C₂×#108	1	2	yes	—
205	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
206	C₄×C₁₁	C₂×#135	1	2	yes	—
207	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
208	C₂³×C₄	D₄₄	1	1	yes	characteristic
209	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
210	C₂×M₁₆	—	22	4	no	—
211	C₂²×C₈	—	2	8	no	—
212	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
213	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
214	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
215	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
216	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
217	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
218	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
219	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
220	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
221	C₂×C₄²	D₄₄	1	1	yes	characteristic
222	C₂×C₄²	D₄₄	1	1	yes	characteristic
223	C₂×C₄²	D₄₄	1	1	yes	characteristic
224	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
227	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
228	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
230	C₄⋊C₈	—	11	8	no	—
231	C₄⋊C₈	—	22	4	no	—
232	C₂²⋊C₈	—	22	4	no	—
233	C₂²⋊C₈	—	22	4	no	—
234	#97	—	22	4	no	—
235	C₄×C₈	—	22	4	no	—
236	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
237	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
238	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
239	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
240	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
241	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
242	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
243	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
244	C₄×C₈	C₂²×D₁₁	1	2	yes	—
245	C₄×C₈	C₂²×D₁₁	1	2	yes	—
246	C₂×C₁₁	—	2	2	no	—
247	C₂×C₁₁	—	2	2	no	—
248	C₂×C₁₁	—	2	2	no	—
249	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
250	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
251	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
252	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
274	M₁₆	—	44	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	22	8	no	—
281	C₂×C₈	#4318	1	8	yes	complemented
282	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
283	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
284	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
285	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
286	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
287	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
292	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
293	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
294	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
295	C₄²	C₂×D₄₄	1	1	yes	characteristic
296	C₄²	C₂×D₄₄	1	1	yes	characteristic
297	C₄²	C₂×D₄₄	1	1	yes	characteristic
298	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
299	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
300	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
301	C₄²	C₂³×D₁₁	1	1	yes	characteristic
302	C₁₁	#17793	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
307	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	#66883	1	4	yes	—
325	C₂×C₄	#66957	1	4	yes	—
326	C₂×C₄	C₂×#4318	1	4	yes	—
327	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
338	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	44	8	no	—
342	C₈	C₂×#4318	1	4	yes	—
343	C₈	C₂×#4318	1	4	yes	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	#10622537	1	2	yes	—
352	C₂²	#10622719	1	2	yes	—
353	C₂²	C₂×#66883	1	2	yes	—
354	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	#10622537	1	2	yes	—
362	C₄	#10622719	1	2	yes	—
363	C₄	C₂×#66883	1	2	yes	—
364	C₄	C₂×#66883	1	2	yes	—
365	C₄	C₂×#66957	1	2	yes	—
366	C₄	C₂²×#4318	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	C₂×#10622537	1	1	yes	characteristic
371	C₂	C₂×#10622719	1	1	yes	characteristic
372	C₂	C₂²×#66883	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂²×C₄×C₈×C₁₁	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₁
hypocenter	C₁₁	#17793
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13067379	C₂	semidirect
3. #13067375	C₂	semidirect
4. #13067372	C₂	semidirect
5. #13067364	C₂	semidirect
25. #10622096	C₂²	semidirect
26. #10622095	C₂²	semidirect
94. C₂×C₈×C₁₁	M₁₆	semidirect
281. C₂×C₈	#4318	semidirect
302. C₁₁	#17793	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
#13067379	2
#13067375	2
#13067372	2
#13067364	2
C₂²×C₄×C₈×C₁₁	2
#17793	11