Subgroups — C₈×#66972 #14723151

Order 2816.

750 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	C₈×#4343	C₂	1	2	yes	maximal, complemented
2	C₄×#66972	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#4325	C₂	1	2	yes	maximal, complemented
5	#13067413	C₂	1	2	yes	maximal, complemented
6	C₈×D₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067410	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067363	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066997	C₂	1	2	yes	maximal, complemented
10	C₈²×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66972	C₄	1	1	yes	characteristic
13	C₄×#4343	C₂²	1	2	yes	—
14	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
15	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
16	Q₁₆×Dic₁₁	C₄	1	1	yes	characteristic
17	C₄×#4325	C₂²	1	2	yes	—
18	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
19	#10622493	C₄	1	1	yes	characteristic
20	#10622485	C₄	1	1	yes	characteristic
21	#10622447	—	2	2	no	—
22	#10622447	C₂²	1	2	yes	—
23	#10622446	—	2	2	no	—
24	#10622446	C₂²	1	2	yes	—
25	#10622417	C₄	1	2	yes	—
26	#10622401	C₄	1	2	yes	—
27	C₄×D₈₈	C₂²	1	1	yes	characteristic
28	C₈×D₄₄	—	2	2	no	—
29	C₈×D₄₄	C₂²	1	2	yes	—
30	C₄×C₈×D₁₁	—	2	2	no	—
31	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#335	C₂²	1	1	yes	characteristic
35	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₈²×C₁₁	C₂²	1	1	yes	characteristic
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	#10622121	C₂²	1	2	yes	—
39	#10622118	C₂²	1	2	yes	—
40	#10622097	C₂²	1	2	yes	—
41	#10622096	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×#4343	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
48	Q₈×Dic₁₁	C₂×C₄	1	2	yes	—
49	C₂×#4325	C₂×C₄	1	2	yes	—
50	#66972	C₈	1	8	yes	direct product factor
51	C₂×D₈₈	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₁	—	2	1	no	—
53	C₂×C₈×D₁₁	—	2	2	no	—
54	C₂×C₈×D₁₁	—	2	2	no	—
55	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₁	D₄	1	1	yes	characteristic
58	C₂×C₈×D₁₁	D₄	1	1	yes	characteristic
59	#66946	—	2	2	no	—
60	#66946	C₂×C₄	1	2	yes	—
61	#66945	—	2	2	no	—
62	#66945	C₂×C₄	1	2	yes	—
63	C₄×D₄₄	—	2	2	no	—
64	C₄×D₄₄	C₂³	1	2	yes	—
65	C₄²×D₁₁	—	2	2	no	—
66	C₄²×D₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₁×#103	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₁	—	2	2	no	—
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	#66899	C₂×C₄	1	2	yes	—
76	#66885	C₂×C₄	1	2	yes	—
77	(C₂×D₁₁)⋊C₈	—	2	2	no	—
78	(C₂×D₁₁)⋊C₈	—	2	2	no	—
79	(C₂×D₁₁)⋊C₈	—	2	2	no	—
80	#66882	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₁	—	2	2	no	—
82	C₈×Dic₁₁	—	2	1	no	—
83	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₁	D₄	1	1	yes	characteristic
86	C₈×Dic₁₁	D₄	1	1	yes	characteristic
87	#66873	C₂×C₄	1	2	yes	—
88	#66872	C₂×C₄	1	2	yes	—
89	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
90	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
91	C₄×C₁₁⋊C₈	—	2	2	no	—
92	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
95	C₈×#135	—	11	1	no	maximal, Sylow
96	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
97	#4343	—	2	4	no	—
98	#4343	C₂×C₈	1	8	yes	complemented
99	C₂×D₄₄	—	2	2	no	—
100	C₂×D₄₄	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₁₁	—	2	2	no	—
102	C₂×C₄×D₁₁	—	2	2	no	—
103	C₂×C₄×D₁₁	—	2	2	no	—
104	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	#41	1	1	yes	characteristic
107	C₁₁×Q₁₆	C₂×C₈	1	4	yes	complemented
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₁₁×C₄⋊C₄	—	2	2	no	—
115	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₁	—	2	2	no	—
117	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
118	#4325	C₂×C₈	1	8	yes	complemented
119	(C₂×D₁₁)⋊C₄	—	2	2	no	—
120	(C₂×D₁₁)⋊C₄	—	2	2	no	—
121	(C₂×D₁₁)⋊C₄	—	2	2	no	—
122	C₄⋊Dic₁₁	—	2	2	no	—
123	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
124	C₄×Dic₁₁	—	2	2	no	—
125	C₄×Dic₁₁	—	2	2	no	—
126	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₁₁	#41	1	1	yes	characteristic
129	C₂×C₁₁⋊C₈	—	2	2	no	—
130	C₂×C₁₁⋊C₈	—	2	1	no	—
131	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
135	D₈₈	C₂×C₈	1	4	yes	complemented
136	C₈×D₁₁	—	2	4	no	—
137	C₈×D₁₁	—	2	2	no	—
138	C₈×D₁₁	—	2	2	no	—
139	C₈×D₁₁	—	2	2	no	—
140	C₈×D₁₁	—	4	4	no	—
141	C₈×D₁₁	—	4	4	no	—
142	C₈×D₁₁	C₂×C₈	1	4	yes	complemented
143	C₈×#41	—	11	2	no	—
144	C₄×#135	—	11	1	no	—
145	C₈×Q₁₆	—	11	1	no	—
146	C₈×Q₁₆	D₁₁	1	1	yes	characteristic, complemented
147	C₈×SD₁₆	—	11	2	no	—
148	C₈×SD₁₆	—	11	2	no	—
149	C₈×D₈	—	11	1	no	—
150	C₈×D₈	—	11	1	no	—
151	#1564	—	11	1	no	—
152	#1476	—	11	2	no	—
153	C₂×C₈²	—	11	1	no	—
154	C₂²×D₁₁	—	2	2	no	—
155	C₂²×D₁₁	C₄×D₄	1	1	yes	characteristic
156	Q₈×C₁₁	—	2	2	no	—
157	Q₈×C₁₁	C₂²×C₈	1	4	yes	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₁₁	—	2	2	no	—
164	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
165	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₁₁	C₄×D₄	1	1	yes	characteristic
167	D₄₄	—	2	8	no	—
168	D₄₄	—	2	2	no	—
169	D₄₄	C₂²×C₈	1	4	yes	—
170	C₄×D₁₁	—	2	1	no	—
171	C₄×D₁₁	—	2	1	no	—
172	C₄×D₁₁	—	2	8	no	—
173	C₄×D₁₁	—	2	2	no	—
174	C₄×D₁₁	—	4	2	no	—
175	C₄×D₁₁	—	4	2	no	—
176	C₄×D₁₁	—	4	4	no	—
177	C₄×D₁₁	C₂²×C₈	1	2	yes	—
178	C₄×D₁₁	#131	1	2	yes	—
179	C₈×C₁₁	—	2	2	no	—
180	C₈×C₁₁	—	2	1	no	—
181	C₈×C₁₁	—	2	1	no	—
182	C₈×C₁₁	—	4	2	no	—
183	C₈×C₁₁	C₂²×C₈	1	2	yes	—
184	C₈×C₁₁	#135	1	2	yes	complemented
185	C₁₁⋊C₈	—	2	2	no	—
186	C₁₁⋊C₈	—	2	1	no	—
187	C₁₁⋊C₈	—	2	1	no	—
188	C₁₁⋊C₈	—	4	2	no	—
189	C₁₁⋊C₈	C₂²×C₈	1	2	yes	—
190	C₁₁⋊C₈	#135	1	2	yes	complemented
191	C₂×#135	—	11	1	no	—
192	C₄×#41	—	11	2	no	—
193	C₈×Q₈	—	11	2	no	—
194	C₈×Q₈	C₂×D₁₁	1	2	yes	—
195	C₄×Q₁₆	—	11	1	no	—
196	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
197	C₄×SD₁₆	—	11	2	no	—
198	C₄×SD₁₆	—	11	2	no	—
199	C₄×D₈	—	11	1	no	—
200	C₄×D₈	—	11	1	no	—
201	C₈×D₄	—	11	2	no	—
202	C₈×D₄	—	11	2	no	—
203	C₈×D₄	—	22	2	no	—
204	C₈×D₄	—	22	2	no	—
205	#431	—	11	2	no	—
206	#431	—	22	2	no	—
207	#427	—	11	1	no	—
208	#416	—	11	2	no	—
209	C₂×C₄×C₈	—	11	1	no	—
210	C₂×C₄×C₈	—	11	1	no	—
211	C₂×C₄×C₈	—	11	1	no	—
212	C₂×C₄×C₈	—	22	2	no	—
213	#335	—	11	1	no	—
214	#335	C₂×D₁₁	1	1	yes	characteristic
215	#334	—	11	2	no	—
216	Q₈⋊C₈	—	11	2	no	—
217	Q₈⋊C₈	C₂×D₁₁	1	2	yes	—
218	D₄⋊C₈	—	11	2	no	—
219	D₄⋊C₈	—	11	2	no	—
220	C₈²	—	11	1	no	—
221	C₈²	—	11	1	no	—
222	C₈²	—	11	1	no	—
223	C₈²	C₂×D₁₁	1	1	yes	characteristic
224	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂×D₁₁	—	2	1	no	—
226	C₂×D₁₁	—	2	1	no	—
227	C₂×D₁₁	—	2	4	no	—
228	C₂×D₁₁	—	4	2	no	—
229	C₂×D₁₁	—	4	2	no	—
230	C₂×D₁₁	C₈×D₄	1	2	yes	—
231	C₄×C₁₁	—	2	4	no	—
232	C₄×C₁₁	—	2	1	no	—
233	C₄×C₁₁	—	4	2	no	—
234	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
235	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
236	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
237	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
238	Dic₁₁	—	2	1	no	—
239	Dic₁₁	—	4	2	no	—
240	Dic₁₁	C₈×D₄	1	2	yes	—
241	Dic₁₁	#443	1	2	yes	—
242	C₂×#41	—	11	2	no	—
243	#135	—	11	8	no	—
244	C₂×Q₁₆	C₄×D₁₁	1	1	yes	characteristic
245	C₂×SD₁₆	—	11	2	no	—
246	C₂×D₈	—	11	1	no	—
247	C₂²×C₈	—	11	1	no	—
248	C₂²×C₈	—	11	1	no	—
249	C₂²×C₈	—	11	1	no	—
250	C₂²×C₈	—	11	1	no	—
251	C₂²×C₈	—	22	2	no	—
252	C₂²×C₈	—	22	1	no	—
253	C₂²×C₈	—	22	2	no	—
254	C₄×Q₈	—	11	2	no	—
255	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
256	C₄×D₄	—	11	2	no	—
257	C₄×D₄	—	11	2	no	—
258	C₄×D₄	—	22	2	no	—
259	C₄×D₄	—	22	2	no	—
260	#117	—	11	2	no	—
261	#117	—	22	2	no	—
262	C₂×C₄²	—	11	1	no	—
263	C₂×C₄²	—	22	2	no	—
264	#107	—	11	1	no	—
265	#107	C₄×D₁₁	1	1	yes	characteristic
266	#106	—	11	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	11	2	no	—
269	C₄⋊C₈	—	22	2	no	—
270	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
271	#103	—	11	2	no	—
272	#103	C₄×D₁₁	1	2	yes	—
273	#102	—	11	2	no	—
274	#102	—	11	2	no	—
275	C₂²⋊C₈	—	22	2	no	—
276	C₂²⋊C₈	—	22	2	no	—
277	C₂²⋊C₈	—	22	2	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	11	1	no	—
280	C₄×C₈	—	11	1	no	—
281	C₄×C₈	—	11	1	no	—
282	C₄×C₈	—	11	1	no	—
283	C₄×C₈	—	11	1	no	—
284	C₄×C₈	—	11	1	no	—
285	C₄×C₈	—	11	1	no	—
286	C₄×C₈	—	22	2	no	—
287	C₄×C₈	—	22	1	no	—
288	C₄×C₈	—	22	2	no	—
289	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
292	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
293	C₂×C₁₁	C₄×#135	1	1	yes	characteristic
294	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
295	D₁₁	—	2	2	no	—
296	D₁₁	—	4	4	no	—
297	#41	—	11	8	no	—
298	#41	—	22	4	no	—
299	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
300	C₂×D₄	—	11	2	no	—
301	C₂×D₄	—	22	2	no	—
302	C₂²×C₄	—	11	1	no	—
303	C₂²×C₄	—	11	1	no	—
304	C₂²×C₄	—	11	1	no	—
305	C₂²×C₄	—	22	2	no	—
306	C₂²×C₄	—	22	2	no	—
307	C₂²×C₄	—	22	2	no	—
308	Q₁₆	C₈×D₁₁	1	4	yes	complemented
309	SD₁₆	—	11	8	no	—
310	D₈	—	11	4	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	11	1	no	—
314	C₂×C₈	—	11	1	no	—
315	C₂×C₈	—	11	4	no	—
316	C₂×C₈	—	11	1	no	—
317	C₂×C₈	—	11	1	no	—
318	C₂×C₈	—	22	2	no	—
319	C₂×C₈	—	22	2	no	—
320	C₂×C₈	—	22	4	no	—
321	C₂×C₈	—	22	1	no	—
322	C₂×C₈	—	22	2	no	—
323	C₂×C₈	—	22	2	no	—
324	C₂×C₈	—	44	4	no	—
325	C₂×C₈	—	44	4	no	—
326	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
328	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
329	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	11	2	no	—
332	C₄⋊C₄	—	22	2	no	—
333	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
334	C₂²⋊C₄	—	22	2	no	—
335	C₂²⋊C₄	—	22	2	no	—
336	C₂²⋊C₄	—	22	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	11	1	no	—
339	C₄²	—	11	1	no	—
340	C₄²	—	11	1	no	—
341	C₄²	—	22	2	no	—
342	C₄²	—	22	2	no	—
343	C₄²	C₂³×D₁₁	1	1	yes	characteristic
344	C₁₁	C₈×#135	1	1	yes	characteristic, complemented, Sylow
345	C₂³	—	11	1	no	—
346	C₂³	—	22	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	C₂×C₈×D₁₁	1	4	yes	—
349	D₄	—	11	4	no	—
350	D₄	—	22	8	no	—
351	D₄	—	22	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	11	1	no	—
355	C₂×C₄	—	11	1	no	—
356	C₂×C₄	—	11	2	no	—
357	C₂×C₄	—	11	2	no	—
358	C₂×C₄	—	11	1	no	—
359	C₂×C₄	—	22	2	no	—
360	C₂×C₄	—	22	8	no	—
361	C₂×C₄	—	22	1	no	—
362	C₂×C₄	—	22	1	no	—
363	C₂×C₄	—	22	2	no	—
364	C₂×C₄	—	44	4	no	—
365	C₂×C₄	—	44	2	no	—
366	C₂×C₄	—	44	2	no	—
367	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
369	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	11	2	no	—
375	C₈	—	11	2	no	—
376	C₈	—	22	2	no	—
377	C₈	—	22	1	no	—
378	C₈	—	22	1	no	—
379	C₈	—	44	2	no	—
380	C₈	C₂×C₈×D₁₁	1	2	yes	—
381	C₈	#66972	1	2	yes	direct product factor
382	C₂²	—	11	2	no	—
383	C₂²	—	22	1	no	—
384	C₂²	—	22	1	no	—
385	C₂²	—	22	4	no	—
386	C₂²	—	44	2	no	—
387	C₂²	—	44	2	no	—
388	C₂²	C₄×D₄×D₁₁	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	11	2	no	—
393	C₄	—	11	2	no	—
394	C₄	—	22	1	no	—
395	C₄	—	44	2	no	—
396	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
397	C₄	D₁₁×#131	1	1	yes	characteristic
398	C₄	C₂×#66972	1	1	yes	characteristic
399	C₄	D₁₁×#135	1	1	yes	characteristic
400	C₂	—	22	2	no	—
401	C₂	—	44	4	no	—
402	C₂	C₈×D₄×D₁₁	1	1	yes	characteristic
403	C₂	C₄×#66972	1	1	yes	characteristic
404	C₂	D₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₈×C₁₁×Q₁₆	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#66972	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×Q₁₆	D₁₁
hypocenter	C₁₁	C₈×#135
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×#4343	C₂	semidirect
3. Q₁₆×C₁₁⋊C₈	C₂	semidirect
4. C₈×#4325	C₂	semidirect
5. #13067413	C₂	semidirect
6. C₈×D₈₈	C₂	semidirect
7. #13067410	C₂	semidirect
8. #13067363	C₂	semidirect
9. #13066997	C₂	semidirect
10. C₈²×D₁₁	C₂	semidirect
11. C₈×C₁₁×Q₁₆	C₂	semidirect
50. #66972	C₈	direct (N × H)
98. #4343	C₂×C₈	semidirect
107. C₁₁×Q₁₆	C₂×C₈	semidirect
118. #4325	C₂×C₈	semidirect
135. D₈₈	C₂×C₈	semidirect
142. C₈×D₁₁	C₂×C₈	semidirect
146. C₈×Q₁₆	D₁₁	semidirect
184. C₈×C₁₁	#135	semidirect
190. C₁₁⋊C₈	#135	semidirect
308. Q₁₆	C₈×D₁₁	semidirect
344. C₁₁	C₈×#135	semidirect
381. C₈	#66972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#4343	2
C₄×#66972	2
Q₁₆×C₁₁⋊C₈	2
C₈×#4325	2
#13067413	2
C₈×D₈₈	2
#13067410	2
#13067363	2
#13066997	2
C₈²×D₁₁	2
C₈×C₁₁×Q₁₆	2
C₈×#135	11

Subgroups — C8×#66972 #14723151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#66972 #14723151