Subgroups — #2159×D₈₉ #36707458

Order 22784.

718 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#427×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#107×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26022041	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022040	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022039	C₂	1	2	yes	maximal, complemented
7	#26022038	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022037	C₂	1	2	yes	maximal, complemented
9	#367×D₈₉	C₂	1	2	yes	maximal, complemented
10	#366×D₈₉	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2159	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
13	#117×D₈₉	—	2	1	no	—
14	C₂×C₄⋊C₄×D₈₉	—	2	1	no	—
15	C₂×#15667952	C₂²	1	1	yes	characteristic
16	C₂×#15667951	C₂²	1	2	yes	—
17	M₃₂×D₈₉	C₄	1	8	yes	complemented
18	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
19	#19151636	C₂²	1	1	yes	characteristic
20	#19151635	C₂²	1	1	yes	characteristic
21	#19151635	C₂²	1	1	yes	characteristic
22	#19151634	—	2	1	no	—
23	#19151633	—	2	1	no	—
24	C₂×#15667946	C₂²	1	1	yes	characteristic
25	C₂×#15667945	—	2	1	no	—
26	#107×D₈₉	—	2	1	no	—
27	#107×D₈₉	—	2	1	no	—
28	#107×D₈₉	C₂²	1	2	yes	—
29	#107×D₈₉	C₂²	1	2	yes	—
30	#107×D₈₉	C₂²	1	1	yes	characteristic
31	#107×D₈₉	C₂²	1	1	yes	characteristic
32	#106×D₈₉	—	2	1	no	—
33	#19151426	C₂²	1	2	yes	complemented
34	#19151425	C₂²	1	2	yes	complemented
35	#19151425	C₂²	1	2	yes	complemented
36	#19151424	C₂²	1	2	yes	complemented
37	#19151423	C₂²	1	2	yes	complemented
38	#19151423	C₂²	1	2	yes	complemented
39	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
42	#367×C₈₉	C₂²	1	2	yes	complemented
43	#366×C₈₉	C₂²	1	2	yes	complemented
44	C₂²×C₄×D₈₉	—	4	1	no	—
45	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
46	C₂²×#10623494	D₄	1	1	yes	characteristic
47	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
48	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
50	C₂×C₈×D₈₉	Q₈	1	4	yes	—
51	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
53	#15667971	—	2	1	no	—
54	#15667970	—	2	1	no	—
55	#15667970	—	2	1	no	—
56	#15667969	—	4	1	no	—
57	#15667968	—	4	1	no	—
58	C₂×C₄⋊Dic₈₉	—	2	1	no	—
59	C₂×#13083553	—	4	1	no	—
60	C₄⋊C₄×D₈₉	—	2	1	no	—
61	C₄⋊C₄×D₈₉	—	2	1	no	—
62	C₄⋊C₄×D₈₉	—	2	2	no	—
63	C₄⋊C₄×D₈₉	—	2	2	no	—
64	C₄⋊C₄×D₈₉	—	4	1	no	—
65	C₄⋊C₄×D₈₉	—	4	1	no	—
66	C₂²⋊C₄×D₈₉	—	4	1	no	—
67	C₄²×D₈₉	—	4	1	no	—
68	#15667952	C₂×C₄	1	4	yes	complemented
69	#15667951	C₂×C₄	1	8	yes	complemented
70	C₂×#13083549	C₂³	1	2	yes	—
71	C₁₆×D₈₉	C₂×C₄	1	8	yes	complemented
72	#15667946	—	2	1	no	—
73	#15667946	C₂³	1	2	yes	—
74	#15667946	C₂³	1	1	yes	characteristic
75	#15667946	C₂³	1	1	yes	characteristic
76	#15667945	—	2	2	no	—
77	#15667945	—	2	2	no	—
78	#15667945	—	2	1	no	—
79	#15667945	—	2	1	no	—
80	#15667944	—	2	1	no	—
81	#15667943	—	2	1	no	—
82	#15667943	—	2	1	no	—
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	#117×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
86	M₃₂×C₈₉	C₂×C₄	1	4	yes	complemented
87	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
88	#107×C₈₉	—	2	1	no	—
89	#107×C₈₉	C₂³	1	2	yes	—
90	#107×C₈₉	C₂³	1	1	yes	characteristic
91	#107×C₈₉	C₂³	1	1	yes	characteristic
92	#106×C₈₉	—	2	1	no	—
93	C₂³×D₈₉	D₈	1	1	yes	characteristic
94	C₂²×Dic₈₉	—	4	1	no	—
95	C₂²×Dic₈₉	D₈	1	1	yes	characteristic
96	C₂×C₄×D₈₉	—	4	2	no	—
97	C₂×C₄×D₈₉	—	4	2	no	—
98	C₂×C₄×D₈₉	—	4	1	no	—
99	C₂×C₄×D₈₉	—	4	1	no	—
100	C₂×C₄×D₈₉	—	8	4	no	—
101	C₂×C₄×D₈₉	C₄⋊C₄	1	4	yes	—
102	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
103	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
104	C₂×C₄×D₈₉	Q₁₆	1	4	yes	—
105	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂×#10623494	C₄⋊C₄	1	4	yes	—
108	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
109	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
110	C₈×D₈₉	C₄⋊C₄	1	4	yes	—
111	C₈×D₈₉	C₄⋊C₄	1	4	yes	—
112	C₈×D₈₉	C₂²×C₄	1	2	yes	—
113	C₈×D₈₉	C₂²×C₄	1	2	yes	—
114	C₈×D₈₉	C₂×Q₈	1	2	yes	—
115	C₈×D₈₉	C₂×Q₈	1	2	yes	—
116	C₄⋊Dic₈₉	—	2	1	no	—
117	C₄⋊Dic₈₉	—	2	1	no	—
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	—	4	1	no	—
120	#13083553	—	4	1	no	—
121	#13083553	—	4	1	no	—
122	#13083553	—	4	2	no	—
123	#13083553	—	4	2	no	—
124	C₂²⋊Dic₈₉	—	4	1	no	—
125	#13083551	—	4	1	no	—
126	#13083551	—	4	1	no	—
127	C₄×Dic₈₉	—	4	1	no	—
128	C₄×Dic₈₉	—	4	1	no	—
129	C₄×Dic₈₉	—	4	1	no	—
130	#13083549	C₂²×C₄	1	4	yes	complemented
131	C₂²×C₄×C₈₉	—	4	1	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
136	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	4	1	no	—
141	C₂²⋊C₄×C₈₉	—	4	1	no	—
142	C₄²×C₈₉	—	4	1	no	—
143	C₁₆×C₈₉	C₂²×C₄	1	4	yes	complemented
144	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
145	C₂²×D₈₉	—	2	2	no	—
146	C₂²×D₈₉	—	2	2	no	—
147	C₂²×D₈₉	#107	1	4	yes	—
148	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
149	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	8	2	no	—
154	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×Dic₈₉	—	4	1	no	—
159	C₂×Dic₈₉	—	4	1	no	—
160	C₂×Dic₈₉	—	4	2	no	—
161	C₂×Dic₈₉	—	8	2	no	—
162	C₂×Dic₈₉	#107	1	4	yes	—
163	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
164	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
165	C₄×D₈₉	—	8	4	no	—
166	C₄×D₈₉	—	8	2	no	—
167	C₄×D₈₉	—	8	4	no	—
168	C₄×D₈₉	—	8	2	no	—
169	C₄×D₈₉	#107	1	4	yes	—
170	C₄×D₈₉	#107	1	4	yes	—
171	C₄×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
172	C₄×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
173	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
174	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
175	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
176	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
177	C₈×C₈₉	C₂²×Q₈	1	1	yes	characteristic
178	#10623494	C₂×C₄⋊C₄	1	2	yes	—
179	#10623494	C₂×C₄⋊C₄	1	2	yes	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	C₂×#107	1	2	yes	—
183	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	1	no	—
186	C₂×D₈₉	—	2	8	no	—
187	C₂×D₈₉	C₂×#107	1	2	yes	—
188	C₂×D₈₉	C₂×#107	1	2	yes	—
189	C₂×D₈₉	#509	1	2	yes	—
190	C₂×D₈₉	#510	1	2	yes	—
191	C₄×C₈₉	—	8	2	no	—
192	C₄×C₈₉	—	8	1	no	—
193	C₄×C₈₉	—	8	1	no	—
194	C₄×C₈₉	C₂×#107	1	2	yes	—
195	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
197	Dic₈₉	—	8	2	no	—
198	Dic₈₉	—	8	1	no	—
199	Dic₈₉	—	8	1	no	—
200	Dic₈₉	C₂×#107	1	2	yes	—
201	Dic₈₉	C₂×#107	1	2	yes	—
202	C₂×#2159	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	—	2	2	no	—
204	C₂×C₈₉	C₂²×#107	1	1	yes	characteristic
205	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
206	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
207	D₈₉	—	2	2	no	—
208	D₈₉	#2159	1	4	yes	direct product factor
209	C₂²×M₃₂	—	89	1	no	—
210	C₂×#427	—	89	1	no	—
211	C₂²×#107	—	89	1	no	—
212	#2159	—	89	1	no	—
213	#2159	—	89	1	no	—
214	#2159	—	89	1	no	—
215	#2159	—	89	2	no	—
216	#2159	—	89	2	no	—
217	#2159	D₈₉	1	1	yes	characteristic, direct product factor
218	C₂×#367	—	89	2	no	—
219	C₂×#366	—	89	2	no	—
220	C₈₉	C₂×#2159	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₈	—	89	1	no	—
222	C₂×#117	—	178	1	no	—
223	C₂²×C₄⋊C₄	—	178	1	no	—
224	C₂×M₃₂	—	89	1	no	—
225	C₂×M₃₂	—	89	8	no	—
226	C₂×M₃₂	—	89	2	no	—
227	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
228	C₂²×C₁₆	—	89	2	no	—
229	#427	—	89	1	no	—
230	#427	—	89	1	no	—
231	#427	—	89	1	no	—
232	#427	—	178	1	no	—
233	#427	—	178	1	no	—
234	#427	C₂×D₈₉	1	1	yes	characteristic
235	C₂×#107	—	89	1	no	—
236	C₂×#107	—	89	2	no	—
237	C₂×#107	—	89	2	no	—
238	C₂×#107	—	89	1	no	—
239	C₂×#107	—	89	1	no	—
240	C₂×#107	—	178	1	no	—
241	C₂×#107	—	178	1	no	—
242	C₂×#107	—	178	1	no	—
243	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
244	C₂×#106	—	178	1	no	—
245	#367	—	89	2	no	—
246	#367	—	89	2	no	—
247	#367	—	89	2	no	—
248	#367	C₂×D₈₉	1	2	yes	complemented
249	#366	—	89	2	no	—
250	#366	—	89	2	no	—
251	#366	—	89	2	no	—
252	#366	C₂×D₈₉	1	2	yes	complemented
253	C₂³×C₄	—	89	1	no	—
254	C₂³×C₄	—	356	1	no	—
255	C₂²×C₈	—	89	1	no	—
256	C₂²×C₈	—	89	4	no	—
257	C₂²×C₈	—	89	1	no	—
258	C₂²×C₈	—	89	1	no	—
259	C₂²×C₈	—	89	4	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
263	#117	—	2	1	no	—
264	#117	—	356	1	no	—
265	#117	—	356	1	no	—
266	#117	—	178	1	no	—
267	#117	—	178	1	no	—
268	#117	—	178	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	356	1	no	—
271	C₂×C₄⋊C₄	—	356	1	no	—
272	C₂×C₄⋊C₄	—	356	1	no	—
273	C₂×C₄⋊C₄	—	178	2	no	—
274	C₂×C₄⋊C₄	—	178	2	no	—
275	C₂×C₄⋊C₄	—	178	1	no	—
276	C₂×C₄⋊C₄	—	178	1	no	—
277	C₂×C₄⋊C₄	—	178	1	no	—
278	C₂×C₂²⋊C₄	—	356	1	no	—
279	C₂×C₄²	—	356	1	no	—
280	M₃₂	—	89	4	no	—
281	M₃₂	—	89	8	no	—
282	M₃₂	C₄×D₈₉	1	4	yes	complemented
283	C₂×C₁₆	—	89	2	no	—
284	C₂×C₁₆	—	89	8	no	—
285	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
286	#107	—	2	1	no	—
287	#107	—	89	1	no	—
288	#107	—	89	2	no	—
289	#107	—	89	1	no	—
290	#107	—	178	2	no	—
291	#107	—	178	2	no	—
292	#107	—	178	1	no	—
293	#107	—	178	1	no	—
294	#107	—	178	1	no	—
295	#107	C₂²×D₈₉	1	1	yes	characteristic
296	#107	C₂²×D₈₉	1	2	yes	—
297	#107	C₂²×D₈₉	1	1	yes	characteristic
298	#106	—	2	1	no	—
299	#106	—	178	1	no	—
300	#106	—	178	1	no	—
301	#106	—	178	1	no	—
302	C₂⁴	—	89	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	89	1	no	—
305	C₂²×C₄	—	89	1	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	4	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	89	4	no	—
311	C₂²×C₄	—	356	1	no	—
312	C₂²×C₄	—	356	1	no	—
313	C₂²×C₄	—	356	2	no	—
314	C₂²×C₄	—	356	2	no	—
315	C₂²×C₄	—	356	1	no	—
316	C₂²×C₄	—	712	4	no	—
317	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	89	1	no	—
320	C₂×C₈	—	89	4	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	89	4	no	—
326	C₂×C₈	—	89	4	no	—
327	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
328	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
329	C₂×C₈	Q₈×D₈₉	1	2	yes	—
330	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	356	2	no	—
336	C₄⋊C₄	—	356	2	no	—
337	C₄⋊C₄	—	356	1	no	—
338	C₄⋊C₄	—	356	1	no	—
339	C₄⋊C₄	—	356	1	no	—
340	C₄⋊C₄	—	178	1	no	—
341	C₄⋊C₄	—	178	1	no	—
342	C₄⋊C₄	—	178	2	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	356	1	no	—
345	C₂²⋊C₄	—	356	1	no	—
346	C₂²⋊C₄	—	356	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	356	1	no	—
349	C₄²	—	356	1	no	—
350	C₄²	—	356	1	no	—
351	C₁₆	—	89	4	no	—
352	C₁₆	C₂×C₄×D₈₉	1	4	yes	complemented
353	C₂³	—	89	1	no	—
354	C₂³	—	89	4	no	—
355	C₂³	—	89	1	no	—
356	C₂³	—	178	2	no	—
357	C₂³	—	178	2	no	—
358	C₂³	D₈×D₈₉	1	1	yes	characteristic
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	89	4	no	—
364	C₂×C₄	—	89	1	no	—
365	C₂×C₄	—	89	1	no	—
366	C₂×C₄	—	89	4	no	—
367	C₂×C₄	—	89	4	no	—
368	C₂×C₄	—	89	2	no	—
369	C₂×C₄	—	89	2	no	—
370	C₂×C₄	—	89	2	no	—
371	C₂×C₄	—	89	2	no	—
372	C₂×C₄	—	356	1	no	—
373	C₂×C₄	—	356	1	no	—
374	C₂×C₄	—	356	2	no	—
375	C₂×C₄	—	712	2	no	—
376	C₂×C₄	—	712	2	no	—
377	C₂×C₄	—	712	4	no	—
378	C₂×C₄	—	712	4	no	—
379	C₂×C₄	—	712	2	no	—
380	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
381	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
382	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
383	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
384	C₈	—	89	2	no	—
385	C₈	—	89	2	no	—
386	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
387	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
388	C₈	C₂×Q₈×D₈₉	1	1	yes	characteristic
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	89	2	no	—
392	C₂²	—	89	2	no	—
393	C₂²	—	89	2	no	—
394	C₂²	—	89	2	no	—
395	C₂²	—	178	8	no	—
396	C₂²	—	178	1	no	—
397	C₂²	—	178	1	no	—
398	C₂²	#107×D₈₉	1	2	yes	—
399	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	89	2	no	—
404	C₄	—	89	2	no	—
405	C₄	—	712	2	no	—
406	C₄	—	712	1	no	—
407	C₄	—	712	1	no	—
408	C₄	#107×D₈₉	1	2	yes	—
409	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
410	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	89	4	no	—
413	C₂	—	178	2	no	—
414	C₂	C₂×#107×D₈₉	1	1	yes	characteristic
415	C₂	#509×D₈₉	1	1	yes	characteristic
416	C₂	#510×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2159	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂³×D₈₉	D₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2159	D₈₉
hypocenter	C₈₉	C₂×#2159
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2159

Complements

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

N	H ≅ G/N	type
4. #26022041	C₂	semidirect
5. #26022040	C₂	semidirect
6. #26022039	C₂	semidirect
7. #26022038	C₂	semidirect
8. #26022037	C₂	semidirect
9. #367×D₈₉	C₂	semidirect
10. #366×D₈₉	C₂	semidirect
11. C₈₉×#2159	C₂	semidirect
17. M₃₂×D₈₉	C₄	semidirect
33. #19151426	C₂²	semidirect
34. #19151425	C₂²	semidirect
35. #19151425	C₂²	semidirect
36. #19151424	C₂²	semidirect
37. #19151423	C₂²	semidirect
38. #19151423	C₂²	semidirect
42. #367×C₈₉	C₂²	semidirect
43. #366×C₈₉	C₂²	semidirect
68. #15667952	C₂×C₄	semidirect
69. #15667951	C₂×C₄	semidirect
71. C₁₆×D₈₉	C₂×C₄	semidirect
86. M₃₂×C₈₉	C₂×C₄	semidirect
130. #13083549	C₂²×C₄	semidirect
143. C₁₆×C₈₉	C₂²×C₄	semidirect
208. D₈₉	#2159	direct (N × H)
217. #2159	D₈₉	direct (N × H)
220. C₈₉	C₂×#2159	semidirect
248. #367	C₂×D₈₉	semidirect
252. #366	C₂×D₈₉	semidirect
282. M₃₂	C₄×D₈₉	semidirect
352. C₁₆	C₂×C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₈₉	2
#427×D₈₉	2
C₂×#107×D₈₉	2
#26022041	2
#26022040	2
#26022039	2
#26022038	2
#26022037	2
#367×D₈₉	2
#366×D₈₉	2
C₈₉×#2159	2
C₂×#2159	89

Subgroups — #2159×D89 #36707458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2159×D₈₉ #36707458