Subgroups — #14724314

Order 2816.

630 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	#13077592	C₂	1	2	yes	maximal, complemented
2	#13067513	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067507	C₂	1	2	yes	maximal, complemented
4	#13067501	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
7	D₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067076	C₂	1	2	yes	maximal, complemented
10	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3168	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#529	C₂²	1	2	yes	—
13	C₁₁×#499	C₄	1	1	yes	characteristic
14	C₁₁×#495	C₄	1	1	yes	characteristic
15	C₁₁×#488	C₄	1	2	yes	—
16	C₁₁×#467	C₄	1	1	yes	characteristic
17	C₁₁×#466	C₄	1	1	yes	characteristic
18	C₁₁×#465	C₄	1	2	yes	—
19	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	#10622637	C₂²	1	2	yes	—
24	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
25	#10622625	C₂²	1	2	yes	—
26	#10622624	—	2	2	no	—
27	D₄×C₁₁⋊C₈	—	2	2	no	—
28	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
29	#10622613	—	2	2	no	—
30	#10622610	—	2	2	no	—
31	#10622539	C₂²	1	2	yes	—
32	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
34	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
37	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	#10622096	C₂²	1	1	yes	characteristic
39	#10622096	C₂²	1	1	yes	characteristic
40	#10622095	C₂²	1	2	yes	—
41	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
42	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
43	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
44	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₁₁×#126	—	2	2	no	—
51	C₁₁×#125	C₂×C₄	1	2	yes	—
52	C₁₁×#124	C₂×C₄	1	2	yes	—
53	C₁₁×#123	—	2	2	no	—
54	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
55	C₁₁×#121	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
57	C₄×D₄×C₁₁	—	2	2	no	—
58	C₄×D₄×C₁₁	C₂³	1	2	yes	—
59	C₁₁×#117	—	2	2	no	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₂×#4318	—	2	2	no	—
62	C₂²×C₁₁⋊C₈	—	2	1	no	—
63	C₂²×C₁₁⋊C₈	—	2	2	no	—
64	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
65	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
66	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
67	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
68	C₁₁×#106	C₂×C₄	1	2	yes	—
69	C₁₁×#103	C₂×C₄	1	2	yes	—
70	C₁₁×#103	C₂×C₄	1	2	yes	—
71	C₁₁×#102	C₂×C₄	1	2	yes	—
72	C₁₁×#102	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
80	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
81	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
82	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
83	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
84	#66867	—	2	2	no	—
85	#66867	—	2	2	no	—
86	C₄×C₁₁⋊C₈	—	2	1	no	—
87	C₄×C₁₁⋊C₈	—	2	2	no	—
88	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
89	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	#17959	—	11	1	no	maximal, Sylow
95	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
102	C₁₁×Q₁₆	—	2	2	no	—
103	C₁₁×SD₁₆	—	2	4	no	—
104	C₁₁×D₈	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₁₁×C₄⋊C₄	—	2	2	no	—
112	C₁₁×C₄⋊C₄	—	2	2	no	—
113	C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₁₁×C₄⋊C₄	—	2	2	no	—
115	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
116	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
117	C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	2	no	—
119	C₁₁×C₂²⋊C₄	—	2	2	no	—
120	C₁₁×C₂²⋊C₄	—	2	2	no	—
121	C₁₁×C₂²⋊C₄	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₁	#41	1	1	yes	characteristic
126	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
127	#4318	—	4	4	no	—
128	C₂×C₁₁⋊C₈	—	2	4	no	—
129	C₂×C₁₁⋊C₈	—	2	2	no	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	—	2	2	no	—
132	C₂×C₁₁⋊C₈	—	2	2	no	—
133	C₂×C₁₁⋊C₈	—	2	1	no	—
134	C₂×C₁₁⋊C₈	—	2	1	no	—
135	C₂×C₁₁⋊C₈	—	4	4	no	—
136	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
140	#3168	D₁₁	1	1	yes	characteristic
141	#2966	—	11	2	no	—
142	#1591	—	11	1	no	—
143	#1590	—	11	2	no	—
144	#1589	—	11	1	no	—
145	C₈×Q₁₆	—	11	1	no	—
146	C₈×SD₁₆	—	11	2	no	—
147	C₈×D₈	—	11	1	no	—
148	#1568	—	11	1	no	—
149	#1494	—	11	2	no	—
150	C₂×C₈²	—	11	1	no	—
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
153	Q₈×C₁₁	—	2	2	no	—
154	Q₈×C₁₁	—	2	2	no	—
155	D₄×C₁₁	—	2	2	no	—
156	D₄×C₁₁	—	2	2	no	—
157	D₄×C₁₁	—	4	4	no	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₁	—	2	1	no	—
175	C₈×C₁₁	—	2	1	no	—
176	C₈×C₁₁	#131	1	2	yes	—
177	C₈×C₁₁	#131	1	2	yes	—
178	C₁₁⋊C₈	—	2	2	no	—
179	C₁₁⋊C₈	—	2	2	no	—
180	C₁₁⋊C₈	—	2	1	no	—
181	C₁₁⋊C₈	—	2	1	no	—
182	C₁₁⋊C₈	—	4	2	no	—
183	C₁₁⋊C₈	—	4	2	no	—
184	C₁₁⋊C₈	#135	1	2	yes	—
185	C₁₁⋊C₈	#135	1	2	yes	—
186	#529	C₂×D₁₁	1	2	yes	—
187	#499	Dic₁₁	1	1	yes	characteristic
188	#495	Dic₁₁	1	1	yes	characteristic
189	#488	Dic₁₁	1	2	yes	—
190	#467	Dic₁₁	1	1	yes	characteristic
191	#466	Dic₁₁	1	1	yes	characteristic
192	#465	Dic₁₁	1	2	yes	—
193	#446	—	11	2	no	—
194	C₈×Q₈	—	11	2	no	—
195	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
196	C₄×SD₁₆	C₂×D₁₁	1	2	yes	—
197	C₄×D₈	C₂×D₁₁	1	1	yes	characteristic
198	#436	—	11	2	no	—
199	#435	—	22	2	no	—
200	C₈×D₄	—	11	2	no	—
201	C₈×D₄	—	22	2	no	—
202	#433	—	22	2	no	—
203	#432	—	11	2	no	—
204	#405	—	22	2	no	—
205	C₂×C₄×C₈	—	11	1	no	—
206	C₂×C₄×C₈	—	11	1	no	—
207	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
208	#335	—	11	1	no	—
209	#335	—	11	1	no	—
210	#334	—	11	2	no	—
211	Q₈⋊C₈	—	11	2	no	—
212	Q₈⋊C₈	—	11	2	no	—
213	D₄⋊C₈	—	11	2	no	—
214	D₄⋊C₈	—	11	2	no	—
215	C₈²	—	11	1	no	—
216	C₈²	—	11	1	no	—
217	C₈²	—	11	1	no	—
218	C₈²	—	11	1	no	—
219	C₂²×C₁₁	—	2	1	no	—
220	C₂²×C₁₁	—	2	1	no	—
221	C₂²×C₁₁	—	4	2	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	—	4	2	no	—
224	C₂²×C₁₁	#443	1	2	yes	—
225	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₁₁	—	2	1	no	—
227	C₄×C₁₁	—	2	1	no	—
228	C₄×C₁₁	—	2	1	no	—
229	C₄×C₁₁	—	2	1	no	—
230	C₄×C₁₁	—	4	2	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	—	4	2	no	—
233	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
234	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
235	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
236	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
237	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
238	C₂×SD₁₆	C₂×Dic₁₁	1	2	yes	—
239	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
240	C₂×M₁₆	—	22	2	no	—
241	C₂²×C₈	—	11	1	no	—
242	C₂²×C₈	—	11	1	no	—
243	C₂²×C₈	—	22	2	no	—
244	C₂²×C₈	—	22	1	no	—
245	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
246	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
247	#126	—	2	2	no	—
248	#125	C₂×Dic₁₁	1	2	yes	—
249	#124	C₂×Dic₁₁	1	2	yes	—
250	#123	—	2	2	no	—
251	C₂²⋊Q₈	C₂×Dic₁₁	1	2	yes	—
252	#121	C₂×Dic₁₁	1	2	yes	—
253	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	C₂²×D₁₁	1	2	yes	—
256	#117	—	2	2	no	—
257	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
258	#107	C₂×Dic₁₁	1	1	yes	characteristic
259	#107	C₂×Dic₁₁	1	1	yes	characteristic
260	#106	C₂×Dic₁₁	1	2	yes	—
261	C₄⋊C₈	—	11	2	no	—
262	C₄⋊C₈	—	11	2	no	—
263	C₄⋊C₈	—	22	2	no	—
264	C₄⋊C₈	—	22	2	no	—
265	#103	C₂×Dic₁₁	1	2	yes	—
266	#103	C₂×Dic₁₁	1	2	yes	—
267	#102	C₂×Dic₁₁	1	2	yes	—
268	#102	C₂×Dic₁₁	1	2	yes	—
269	C₂²⋊C₈	—	22	2	no	—
270	C₂²⋊C₈	—	22	2	no	—
271	C₂²⋊C₈	—	22	2	no	—
272	#97	—	22	2	no	—
273	#97	—	22	2	no	—
274	C₄×C₈	—	11	1	no	—
275	C₄×C₈	—	11	1	no	—
276	C₄×C₈	—	11	1	no	—
277	C₄×C₈	—	11	1	no	—
278	C₄×C₈	—	11	1	no	—
279	C₄×C₈	—	11	1	no	—
280	C₄×C₈	—	22	2	no	—
281	C₄×C₈	—	22	1	no	—
282	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
283	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
286	C₂×C₁₁	—	2	2	no	—
287	C₂×C₁₁	—	8	2	no	—
288	C₂×C₁₁	#2931	1	1	yes	characteristic
289	C₂×C₁₁	C₄×#135	1	1	yes	characteristic
290	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
291	C₂×Q₈	C₂²×Dic₁₁	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	C₂²×Dic₁₁	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
296	C₂²×C₄	#4341	1	1	yes	characteristic
297	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
298	Q₁₆	—	2	2	no	—
299	SD₁₆	—	2	4	no	—
300	D₈	—	2	2	no	—
301	M₁₆	—	44	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	11	1	no	—
305	C₂×C₈	—	11	1	no	—
306	C₂×C₈	—	11	1	no	—
307	C₂×C₈	—	11	1	no	—
308	C₂×C₈	—	22	2	no	—
309	C₂×C₈	—	22	2	no	—
310	C₂×C₈	—	22	4	no	—
311	C₂×C₈	—	22	1	no	—
312	C₂×C₈	—	22	1	no	—
313	C₂×C₈	—	22	2	no	—
314	C₂×C₈	—	22	2	no	—
315	C₂×C₈	—	44	4	no	—
316	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
317	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
318	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
319	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
325	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	D₄×D₁₁	1	1	yes	characteristic
333	C₄²	#4341	1	1	yes	characteristic
334	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
335	C₄²	C₂³×D₁₁	1	1	yes	characteristic
336	C₁₁	#17959	1	1	yes	characteristic, complemented, Sylow
337	C₂³	—	2	2	no	—
338	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
356	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
358	C₂×C₄	C₂×#4341	1	1	yes	characteristic
359	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	11	2	no	—
363	C₈	—	11	2	no	—
364	C₈	—	22	2	no	—
365	C₈	—	22	2	no	—
366	C₈	—	22	1	no	—
367	C₈	—	22	1	no	—
368	C₈	—	44	2	no	—
369	C₈	—	44	2	no	—
370	C₈	#67001	1	2	yes	—
371	C₈	#67001	1	2	yes	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	#10622809	1	2	yes	—
378	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	D₁₁×#135	1	1	yes	characteristic
387	C₄	D₁₁×#135	1	1	yes	characteristic
388	C₄	C₂×#67001	1	1	yes	characteristic
389	C₄	C₂×#67001	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	#13077328	1	1	yes	characteristic
393	C₂	#135×Dic₁₁	1	1	yes	characteristic
394	C₂	C₂×#10622809	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#3168	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#466	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#3168	D₁₁
hypocenter	C₁₁	#17959
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #13077592	C₂	semidirect
2. #13067513	C₂	semidirect
3. #13067507	C₂	semidirect
4. #13067501	C₂	semidirect
5. Q₁₆×C₁₁⋊C₈	C₂	semidirect
6. SD₁₆×C₁₁⋊C₈	C₂	semidirect
7. D₈×C₁₁⋊C₈	C₂	semidirect
8. #13067379	C₂	semidirect
9. #13067076	C₂	semidirect
10. C₂×C₈×C₁₁⋊C₈	C₂	semidirect
336. C₁₁	#17959	semidirect

Maximal subgroups

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

subgroup	index
#13077592	2
#13067513	2
#13067507	2
#13067501	2
Q₁₆×C₁₁⋊C₈	2
SD₁₆×C₁₁⋊C₈	2
D₈×C₁₁⋊C₈	2
#13067379	2
#13067076	2
C₂×C₈×C₁₁⋊C₈	2
C₁₁×#3168	2
#17959	11