Subgroups — #2209×D₈₉ #36708674

Order 22784.

702 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×D₈₉	C₂	1	2	yes	maximal
2	#494×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26022303	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022302	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022301	C₂	1	2	yes	maximal, complemented
7	#26022300	C₂	1	2	yes	maximal, complemented
8	#26022299	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
10	#358×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	—	2	1	no	—
13	C₂×Q₁₆×D₈₉	C₂²	1	2	yes	—
14	C₂×Q₁₆×D₈₉	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×D₈₉	—	2	1	no	—
16	C₄×Q₈×D₈₉	—	2	1	no	—
17	C₂×Dic₇₁₂	C₂²	1	2	yes	—
18	C₂×#15667958	C₂²	1	2	yes	—
19	C₂×#15667958	C₂²	1	2	yes	—
20	Q₃₂×D₈₉	—	2	8	no	—
21	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
22	#19151978	C₂²	1	1	yes	characteristic
23	#19151977	—	2	1	no	—
24	#19151976	—	2	1	no	—
25	#19151976	C₂²	1	2	yes	—
26	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
27	Q₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
28	#19151692	C₂²	1	1	yes	characteristic
29	C₄×#13083564	—	2	1	no	—
30	#19151690	—	2	1	no	—
31	#107×D₈₉	C₂²	1	1	yes	characteristic
32	#103×D₈₉	—	2	1	no	—
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄⋊#13083549	C₂²	1	1	yes	characteristic
35	#19151416	C₂²	1	2	yes	—
36	#19151403	C₂²	1	2	yes	—
37	#19151402	C₂²	1	2	yes	—
38	#19151401	C₂²	1	2	yes	—
39	C₂×Q₃₂×C₈₉	C₂²	1	2	yes	—
40	#494×C₈₉	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
43	#358×C₈₉	C₂²	1	2	yes	—
44	C₂×Q₈×D₈₉	—	2	1	no	—
45	C₂×Q₈×D₈₉	—	2	2	no	—
46	C₂×Dic₃₅₆	—	2	1	no	—
47	C₂×Dic₃₅₆	C₂³	1	2	yes	—
48	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
49	C₂×#13083564	—	2	1	no	—
50	C₂×#13083564	—	2	2	no	—
51	C₂×#13083564	—	2	2	no	—
52	Q₁₆×D₈₉	—	2	4	no	—
53	Q₁₆×D₈₉	—	2	2	no	—
54	Q₁₆×D₈₉	—	2	4	no	—
55	Q₁₆×D₈₉	—	4	4	no	—
56	Q₁₆×D₈₉	D₄	1	4	yes	—
57	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
59	#15668012	—	2	1	no	—
60	#15668011	—	4	1	no	—
61	#15668011	—	4	1	no	—
62	#15668010	—	2	2	no	—
63	Q₈×Dic₈₉	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	—	4	1	no	—
66	#15667977	—	2	1	no	—
67	#15667977	—	4	1	no	—
68	C₄⋊C₄×D₈₉	—	2	1	no	—
69	C₄⋊C₄×D₈₉	—	4	1	no	—
70	C₄⋊C₄×D₈₉	—	4	1	no	—
71	C₄⋊C₄×D₈₉	—	4	1	no	—
72	C₄²×D₈₉	—	4	1	no	—
73	C₄²×D₈₉	D₄	1	1	yes	characteristic
74	Dic₇₁₂	—	2	4	no	—
75	#15667958	—	2	4	no	—
76	#15667958	—	2	4	no	—
77	C₂×#13083549	C₂³	1	2	yes	—
78	C₁₆×D₈₉	—	2	4	no	—
79	#15667946	C₂³	1	1	yes	characteristic
80	#15667945	—	2	1	no	—
81	#15667937	—	2	1	no	—
82	#15667936	—	2	1	no	—
83	#15667935	—	2	1	no	—
84	C₄×#10623494	D₄	1	1	yes	characteristic
85	C₈×Dic₈₉	D₄	1	1	yes	characteristic
86	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₈₉	—	2	1	no	—
88	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	—	2	1	no	—
92	Q₃₂×C₈₉	—	2	4	no	—
93	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
94	#107×C₈₉	C₂³	1	1	yes	characteristic
95	#103×C₈₉	—	2	1	no	—
96	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×Dic₁₇₈	—	2	1	no	—
98	C₂×Dic₁₇₈	—	2	2	no	—
99	C₂×Dic₁₇₈	—	4	1	no	—
100	C₂×Dic₁₇₈	—	4	2	no	—
101	Q₈×D₈₉	—	2	4	no	—
102	Q₈×D₈₉	—	4	2	no	—
103	Q₈×D₈₉	—	4	4	no	—
104	Q₈×D₈₉	—	4	4	no	—
105	C₂×C₄×D₈₉	—	4	1	no	—
106	C₂×C₄×D₈₉	—	4	2	no	—
107	C₂×C₄×D₈₉	—	4	1	no	—
108	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
109	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
111	Dic₃₅₆	—	2	2	no	—
112	Dic₃₅₆	—	2	1	no	—
113	Dic₃₅₆	—	2	2	no	—
114	Dic₃₅₆	—	4	2	no	—
115	Dic₃₅₆	C₂×D₄	1	2	yes	—
116	#13083564	—	2	4	no	—
117	#13083564	—	4	4	no	—
118	#13083564	—	4	4	no	—
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₈×D₈₉	—	2	2	no	—
122	C₈×D₈₉	C₂×D₄	1	2	yes	—
123	C₈×D₈₉	#41	1	2	yes	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	—	4	1	no	—
126	C₄⋊Dic₈₉	—	4	1	no	—
127	C₄⋊Dic₈₉	—	4	1	no	—
128	#13083553	—	4	1	no	—
129	#13083553	—	4	1	no	—
130	#13083553	—	4	1	no	—
131	#13083553	—	4	2	no	—
132	#13083553	—	4	2	no	—
133	C₄×Dic₈₉	—	4	1	no	—
134	C₄×Dic₈₉	—	4	1	no	—
135	C₄×Dic₈₉	—	4	1	no	—
136	C₄×Dic₈₉	D₈	1	1	yes	characteristic
137	C₄×Dic₈₉	D₈	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
139	#13083549	—	2	2	no	—
140	C₂×Q₈×C₈₉	—	2	1	no	—
141	C₂×Q₈×C₈₉	—	2	2	no	—
142	Q₁₆×C₈₉	—	2	2	no	—
143	Q₁₆×C₈₉	—	2	1	no	—
144	Q₁₆×C₈₉	—	2	2	no	—
145	Q₁₆×C₈₉	—	4	2	no	—
146	Q₁₆×C₈₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	4	1	no	—
151	C₄⋊C₄×C₈₉	—	4	1	no	—
152	C₄⋊C₄×C₈₉	—	4	1	no	—
153	C₄²×C₈₉	—	4	1	no	—
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₁₆×C₈₉	—	2	2	no	—
156	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
157	Q₈×C₈₉	—	2	2	no	—
158	Q₈×C₈₉	—	4	1	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	Q₈×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×Dic₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	4	2	no	—
170	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
171	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
172	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
173	C₄×D₈₉	—	2	2	no	—
174	C₄×D₈₉	—	4	4	no	—
175	C₄×D₈₉	—	8	4	no	—
176	C₄×D₈₉	—	8	2	no	—
177	C₄×D₈₉	Q₃₂	1	4	yes	complemented
178	C₄×D₈₉	#121	1	2	yes	—
179	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
180	Dic₁₇₈	—	2	2	no	—
181	Dic₁₇₈	—	4	1	no	—
182	Dic₁₇₈	—	4	4	no	—
183	Dic₁₇₈	—	4	2	no	—
184	Dic₁₇₈	—	4	2	no	—
185	Dic₁₇₈	—	8	4	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
189	#10623494	—	2	1	no	—
190	#10623494	#121	1	2	yes	—
191	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
192	C₂×D₈₉	#459	1	2	yes	—
193	C₂×D₈₉	C₂×Q₃₂	1	2	yes	—
194	C₂×D₈₉	#510	1	2	yes	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	—	8	1	no	—
198	C₄×C₈₉	—	8	2	no	—
199	C₄×C₈₉	C₂×Q₃₂	1	2	yes	complemented
200	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
201	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	Dic₈₉	—	2	1	no	—
203	Dic₈₉	—	4	2	no	—
204	Dic₈₉	—	8	1	no	—
205	Dic₈₉	—	8	2	no	—
206	Dic₈₉	#459	1	2	yes	—
207	Dic₈₉	C₂×Q₃₂	1	2	yes	complemented
208	C₂×#2209	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
210	C₂×C₈₉	C₂²×Q₃₂	1	1	yes	characteristic
211	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
212	D₈₉	#2209	1	4	yes	direct product factor
213	C₂²×Q₃₂	—	89	2	no	—
214	C₂×#494	—	89	1	no	—
215	C₂×C₄×Q₁₆	—	89	1	no	—
216	#2209	—	89	2	no	—
217	#2209	—	89	1	no	—
218	#2209	—	89	1	no	—
219	#2209	—	89	1	no	—
220	#2209	—	89	2	no	—
221	#2209	D₈₉	1	1	yes	characteristic, direct product factor
222	C₂×C₄⋊C₁₆	—	89	1	no	—
223	C₂×#358	—	89	2	no	—
224	C₈₉	C₂×#2209	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₁₆	—	89	1	no	—
226	C₂²×Q₁₆	—	89	2	no	—
227	C₂²×Q₁₆	—	178	1	no	—
228	C₂×C₄⋊Q₈	—	178	1	no	—
229	C₂×C₄×Q₈	—	178	1	no	—
230	C₂×Q₃₂	—	89	2	no	—
231	C₂×Q₃₂	—	89	2	no	—
232	C₂×Q₃₂	—	89	2	no	—
233	C₂×Q₃₂	—	178	8	no	—
234	C₂×Q₃₂	C₂×D₈₉	1	2	yes	—
235	C₂²×C₁₆	—	89	2	no	—
236	#494	—	89	2	no	—
237	#494	—	89	1	no	—
238	#494	—	178	1	no	—
239	#494	—	178	1	no	—
240	#494	C₂×D₈₉	1	1	yes	characteristic
241	C₄×Q₁₆	—	89	1	no	—
242	C₄×Q₁₆	—	89	1	no	—
243	C₄×Q₁₆	—	89	1	no	—
244	C₄×Q₁₆	—	178	1	no	—
245	C₄×Q₁₆	—	178	1	no	—
246	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
247	C₂×#107	—	89	1	no	—
248	C₂×#103	—	178	1	no	—
249	C₂×C₄×C₈	—	89	1	no	—
250	C₄⋊C₁₆	—	89	2	no	—
251	C₄⋊C₁₆	—	89	1	no	—
252	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
253	#358	—	89	2	no	—
254	#358	—	89	2	no	—
255	#358	—	89	2	no	—
256	#358	C₂×D₈₉	1	2	yes	—
257	C₂²×Q₈	—	178	2	no	—
258	C₂²×Q₈	—	178	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	89	4	no	—
261	C₂×Q₁₆	—	89	1	no	—
262	C₂×Q₁₆	—	89	2	no	—
263	C₂×Q₁₆	—	356	4	no	—
264	C₂×Q₁₆	—	178	4	no	—
265	C₂×Q₁₆	—	178	4	no	—
266	C₂×Q₁₆	—	178	2	no	—
267	C₂×Q₁₆	—	178	2	no	—
268	C₂×Q₁₆	—	178	2	no	—
269	C₂×Q₁₆	—	178	1	no	—
270	C₂×Q₁₆	—	178	1	no	—
271	C₂×Q₁₆	C₂²×D₈₉	1	2	yes	—
272	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
273	C₂²×C₈	—	89	1	no	—
274	C₂²×C₈	—	89	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	356	1	no	—
277	C₄⋊Q₈	—	356	1	no	—
278	C₄⋊Q₈	—	178	2	no	—
279	C₄⋊Q₈	—	178	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	356	1	no	—
282	C₄×Q₈	—	356	1	no	—
283	C₄×Q₈	—	178	1	no	—
284	C₄×Q₈	—	178	1	no	—
285	C₄×Q₈	—	178	1	no	—
286	C₂×C₄⋊C₄	—	356	1	no	—
287	C₂×C₄⋊C₄	—	356	1	no	—
288	C₂×C₄⋊C₄	—	356	1	no	—
289	C₂×C₄⋊C₄	—	178	1	no	—
290	C₂×C₄²	—	89	1	no	—
291	C₂×C₄²	—	356	1	no	—
292	Q₃₂	—	2	4	no	—
293	Q₃₂	—	178	4	no	—
294	Q₃₂	—	178	4	no	—
295	Q₃₂	—	178	4	no	—
296	C₂×C₁₆	—	89	2	no	—
297	C₂×C₁₆	—	178	4	no	—
298	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
299	#107	—	89	1	no	—
300	#107	—	178	1	no	—
301	#107	C₂²×D₈₉	1	1	yes	characteristic
302	#103	—	2	1	no	—
303	#103	—	178	1	no	—
304	#103	—	178	1	no	—
305	#103	—	178	1	no	—
306	C₄×C₈	—	89	1	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	—	89	1	no	—
309	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	356	1	no	—
313	C₂×Q₈	—	356	2	no	—
314	C₂×Q₈	—	356	2	no	—
315	C₂×Q₈	—	356	4	no	—
316	C₂×Q₈	—	356	4	no	—
317	C₂×Q₈	—	178	4	no	—
318	C₂×Q₈	—	178	2	no	—
319	C₂×Q₈	—	178	1	no	—
320	C₂²×C₄	—	89	1	no	—
321	C₂²×C₄	—	89	1	no	—
322	C₂²×C₄	—	89	1	no	—
323	C₂²×C₄	—	356	1	no	—
324	C₂²×C₄	—	356	1	no	—
325	C₂²×C₄	—	356	2	no	—
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	4	2	no	—
330	Q₁₆	—	89	2	no	—
331	Q₁₆	—	356	2	no	—
332	Q₁₆	—	356	4	no	—
333	Q₁₆	—	356	4	no	—
334	Q₁₆	—	178	4	no	—
335	Q₁₆	—	178	2	no	—
336	Q₁₆	—	178	2	no	—
337	Q₁₆	—	178	1	no	—
338	Q₁₆	D₄×D₈₉	1	2	yes	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	89	2	no	—
341	C₂×C₈	—	89	2	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	178	2	no	—
344	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
345	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	356	1	no	—
351	C₄⋊C₄	—	356	1	no	—
352	C₄⋊C₄	—	356	2	no	—
353	C₄⋊C₄	—	356	2	no	—
354	C₄⋊C₄	—	356	1	no	—
355	C₄⋊C₄	—	356	1	no	—
356	C₄⋊C₄	—	356	1	no	—
357	C₄⋊C₄	—	356	1	no	—
358	C₄⋊C₄	—	178	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	89	1	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	356	1	no	—
364	C₄²	—	356	1	no	—
365	C₄²	—	356	1	no	—
366	C₄²	D₄×D₈₉	1	1	yes	characteristic
367	C₁₆	—	2	2	no	—
368	C₁₆	—	178	2	no	—
369	C₂³	—	89	1	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	356	4	no	—
375	Q₈	—	356	1	no	—
376	Q₈	—	356	2	no	—
377	Q₈	—	356	2	no	—
378	Q₈	—	178	2	no	—
379	Q₈	—	712	4	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	89	1	no	—
384	C₂×C₄	—	89	1	no	—
385	C₂×C₄	—	89	4	no	—
386	C₂×C₄	—	89	2	no	—
387	C₂×C₄	—	89	2	no	—
388	C₂×C₄	—	89	1	no	—
389	C₂×C₄	—	356	4	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	356	1	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	178	2	no	—
394	C₂×C₄	—	712	2	no	—
395	C₂×C₄	—	712	4	no	—
396	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
397	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
399	C₈	—	2	1	no	—
400	C₈	—	89	2	no	—
401	C₈	—	178	1	no	—
402	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
403	C₈	#41×D₈₉	1	1	yes	characteristic
404	C₂²	—	89	2	no	—
405	C₂²	—	89	2	no	—
406	C₂²	—	89	2	no	—
407	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	89	2	no	—
413	C₄	—	89	2	no	—
414	C₄	—	356	2	no	—
415	C₄	—	178	1	no	—
416	C₄	—	712	2	no	—
417	C₄	—	712	1	no	—
418	C₄	Q₃₂×D₈₉	1	2	yes	complemented
419	C₄	#121×D₈₉	1	1	yes	characteristic
420	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
421	C₂	—	89	4	no	—
422	C₂	#459×D₈₉	1	1	yes	characteristic
423	C₂	C₂×Q₃₂×D₈₉	1	1	yes	characteristic
424	C₂	#510×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2209	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂²×D₈₉	C₂×D₈
hypercenter	#2209	D₈₉
hypocenter	C₈₉	C₂×#2209
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2209

Complements

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

N	H ≅ G/N	type
4. #26022303	C₂	semidirect
5. #26022302	C₂	semidirect
6. #26022301	C₂	semidirect
7. #26022300	C₂	semidirect
8. #26022299	C₂	semidirect
11. C₈₉×#2209	C₂	semidirect
177. C₄×D₈₉	Q₃₂	semidirect
199. C₄×C₈₉	C₂×Q₃₂	semidirect
207. Dic₈₉	C₂×Q₃₂	semidirect
212. D₈₉	#2209	direct (N × H)
221. #2209	D₈₉	direct (N × H)
224. C₈₉	C₂×#2209	semidirect
418. C₄	Q₃₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₈₉	2
#494×D₈₉	2
C₄×Q₁₆×D₈₉	2
#26022303	2
#26022302	2
#26022301	2
#26022300	2
#26022299	2
C₄⋊C₁₆×D₈₉	2
#358×D₈₉	2
C₈₉×#2209	2
C₂×#2209	89

Subgroups — #2209×D89 #36708674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2209×D₈₉ #36708674