Subgroups — #1591×D₈₉ #36524166

Order 22784.

670 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₈₉	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019150	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019149	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019148	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019147	C₂	1	2	yes	maximal, complemented
7	#26019146	C₂	1	2	yes	maximal, complemented
8	#335×D₈₉	C₂	1	1	yes	maximal, characteristic
9	Q₈⋊C₈×D₈₉	C₂	1	2	yes	maximal
10	C₈²×D₈₉	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1591	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₈₉	C₂²	1	2	yes	—
14	#19151729	C₂²	1	2	yes	—
15	#19151728	C₂²	1	2	yes	—
16	#19151727	—	2	2	no	—
17	#19151726	—	2	2	no	—
18	#19151725	C₂²	1	2	yes	—
19	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic
21	#19151692	C₄	1	1	yes	characteristic
22	C₄×#13083564	C₂²	1	2	yes	—
23	#19151690	C₄	1	2	yes	—
24	#107×D₈₉	C₄	1	1	yes	characteristic
25	C₄⋊C₈×D₈₉	—	2	2	no	—
26	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
27	#103×D₈₉	C₄	1	2	yes	—
28	#97×D₈₉	—	2	2	no	—
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	—
34	#19151330	C₂²	1	2	yes	—
35	Q₈⋊#10623494	C₂²	1	2	yes	—
36	#19151328	C₂²	1	2	yes	—
37	C₈×#10623494	C₂²	1	1	yes	characteristic
38	C₈×#10623494	C₂²	1	1	yes	characteristic
39	C₈×#10623494	C₂²	1	1	yes	characteristic
40	#446×C₈₉	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	#335×C₈₉	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₈₉	C₂×C₄	1	2	yes	—
46	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083564	C₂×C₄	1	2	yes	—
48	Q₁₆×D₈₉	—	2	4	no	—
49	C₂×C₈×D₈₉	—	2	1	no	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
55	Q₈×Dic₈₉	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₇₈	—	2	2	no	—
57	C₄×Dic₁₇₈	C₂³	1	2	yes	—
58	#15667977	—	2	2	no	—
59	#15667977	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×D₈₉	—	2	2	no	—
61	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
62	C₄²×D₈₉	—	2	2	no	—
63	C₄²×D₈₉	C₂³	1	1	yes	characteristic
64	#15667946	C₂×C₄	1	1	yes	characteristic
65	#15667945	C₂×C₄	1	2	yes	—
66	C₄⋊#10623494	—	2	2	no	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	#15667941	—	2	2	no	—
69	#15667941	—	2	2	no	—
70	#15667941	—	2	2	no	—
71	#15667937	C₂×C₄	1	2	yes	—
72	#15667936	C₂×C₄	1	2	yes	—
73	#15667935	C₂×C₄	1	2	yes	—
74	#15667923	—	2	2	no	—
75	#15667922	—	2	2	no	—
76	#15667922	—	2	2	no	—
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₈×Dic₈₉	—	2	1	no	—
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₉	D₄	1	1	yes	characteristic
84	C₈×Dic₈₉	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
87	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	—	2	2	no	—
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	#103×C₈₉	C₂×C₄	1	2	yes	—
91	#97×C₈₉	—	2	2	no	—
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×Dic₁₇₈	—	2	2	no	—
96	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
97	Q₈×D₈₉	—	2	4	no	—
98	Q₈×D₈₉	—	2	4	no	—
99	C₂×C₄×D₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
104	Dic₃₅₆	—	2	2	no	—
105	#13083564	—	2	4	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
109	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
110	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
111	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
112	C₈×D₈₉	—	2	4	no	—
113	C₈×D₈₉	—	2	2	no	—
114	C₈×D₈₉	—	2	2	no	—
115	C₈×D₈₉	—	4	4	no	—
116	C₈×D₈₉	M₁₆	1	4	yes	—
117	C₈×D₈₉	Q₁₆	1	4	yes	complemented
118	C₄⋊Dic₈₉	—	2	2	no	—
119	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
120	#13083553	—	2	2	no	—
121	#13083553	—	2	2	no	—
122	#13083553	—	2	2	no	—
123	C₄×Dic₈₉	—	2	2	no	—
124	C₄×Dic₈₉	—	2	2	no	—
125	C₄×Dic₈₉	—	2	2	no	—
126	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₈₉	#41	1	1	yes	characteristic
129	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
130	Q₁₆×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
139	C₄²×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₈₉	—	2	2	no	—
143	Q₈×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₈₉	—	2	2	no	—
150	C₂×Dic₈₉	—	2	2	no	—
151	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
154	C₄×D₈₉	—	2	2	no	—
155	C₄×D₈₉	—	4	4	no	—
156	C₄×D₈₉	—	4	4	no	—
157	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
158	C₄×D₈₉	#131	1	2	yes	—
159	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
160	C₄×D₈₉	#135	1	2	yes	—
161	Dic₁₇₈	—	2	2	no	—
162	Dic₁₇₈	—	2	2	no	—
163	Dic₁₇₈	—	4	4	no	—
164	C₈×C₈₉	—	2	2	no	—
165	C₈×C₈₉	—	2	1	no	—
166	C₈×C₈₉	—	2	1	no	—
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
169	C₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
170	#10623494	—	2	2	no	—
171	#10623494	—	2	1	no	—
172	#10623494	—	2	1	no	—
173	#10623494	—	4	2	no	—
174	#10623494	C₂×M₁₆	1	2	yes	—
175	#10623494	C₂×Q₁₆	1	2	yes	complemented
176	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×D₈₉	#436	1	2	yes	—
178	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
179	C₂×D₈₉	#443	1	2	yes	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	4	2	no	—
182	C₄×C₈₉	—	4	2	no	—
183	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
184	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
185	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
186	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
187	Dic₈₉	—	2	1	no	—
188	Dic₈₉	—	4	2	no	—
189	Dic₈₉	—	4	2	no	—
190	Dic₈₉	#436	1	2	yes	—
191	Dic₈₉	C₄×Q₁₆	1	2	yes	—
192	C₂×#1591	—	89	1	no	maximal, Sylow
193	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
194	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
195	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
196	D₈₉	#1591	1	4	yes	direct product factor
197	C₂×#446	—	89	2	no	—
198	C₂×C₄×Q₁₆	—	89	1	no	—
199	#1591	—	89	2	no	—
200	#1591	—	89	1	no	—
201	#1591	—	89	1	no	—
202	#1591	—	89	2	no	—
203	#1591	—	89	1	no	—
204	#1591	D₈₉	1	1	yes	characteristic, direct product factor
205	C₂×#335	—	89	1	no	—
206	C₂×Q₈⋊C₈	—	89	2	no	—
207	C₂×C₈²	—	89	1	no	—
208	C₈₉	C₂×#1591	1	1	yes	characteristic, complemented, Sylow
209	C₂²×Q₁₆	—	89	1	no	—
210	C₂×C₄×Q₈	—	89	2	no	—
211	#446	—	89	2	no	—
212	#446	—	89	2	no	—
213	#446	—	89	2	no	—
214	#446	—	178	2	no	—
215	#446	—	178	2	no	—
216	#446	C₂×D₈₉	1	2	yes	—
217	C₄×Q₁₆	—	89	1	no	—
218	C₄×Q₁₆	—	89	2	no	—
219	C₄×Q₁₆	—	89	1	no	—
220	C₄×Q₁₆	—	89	2	no	—
221	C₄×Q₁₆	—	89	1	no	—
222	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
223	C₂×#107	—	89	1	no	—
224	C₂×C₄⋊C₈	—	89	2	no	—
225	C₂×C₄⋊C₈	—	178	2	no	—
226	C₂×#103	—	89	2	no	—
227	C₂×#97	—	178	2	no	—
228	C₂×C₄×C₈	—	89	1	no	—
229	C₂×C₄×C₈	—	89	1	no	—
230	C₂×C₄×C₈	—	89	1	no	—
231	#335	—	89	2	no	—
232	#335	—	89	1	no	—
233	#335	C₂×D₈₉	1	1	yes	characteristic
234	Q₈⋊C₈	—	89	2	no	—
235	Q₈⋊C₈	—	89	2	no	—
236	Q₈⋊C₈	—	89	2	no	—
237	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
238	C₈²	—	89	1	no	—
239	C₈²	—	89	1	no	—
240	C₈²	—	89	1	no	—
241	C₈²	C₂×D₈₉	1	1	yes	characteristic
242	C₂²×Q₈	—	89	2	no	—
243	C₂×Q₁₆	—	89	2	no	—
244	C₂×Q₁₆	—	89	1	no	—
245	C₂×Q₁₆	—	178	4	no	—
246	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
247	C₂²×C₈	—	89	1	no	—
248	C₂²×C₈	—	89	1	no	—
249	C₂²×C₈	—	89	1	no	—
250	C₂²×C₈	—	89	1	no	—
251	C₂²×C₈	—	178	2	no	—
252	C₂²×C₈	—	178	1	no	—
253	C₄×Q₈	—	89	2	no	—
254	C₄×Q₈	—	89	2	no	—
255	C₄×Q₈	—	89	2	no	—
256	C₄×Q₈	—	178	2	no	—
257	C₄×Q₈	—	178	2	no	—
258	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
259	C₂×C₄⋊C₄	—	89	2	no	—
260	C₂×C₄⋊C₄	—	178	2	no	—
261	C₂×C₄²	—	89	1	no	—
262	C₂×C₄²	—	178	2	no	—
263	#107	—	89	1	no	—
264	#107	—	89	2	no	—
265	#107	C₄×D₈₉	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	89	2	no	—
268	C₄⋊C₈	—	178	2	no	—
269	C₄⋊C₈	—	178	2	no	—
270	C₄⋊C₈	—	178	2	no	—
271	C₄⋊C₈	—	178	2	no	—
272	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
273	#103	—	89	2	no	—
274	#103	—	89	2	no	—
275	#103	—	89	2	no	—
276	#103	C₄×D₈₉	1	2	yes	—
277	#97	—	2	2	no	—
278	#97	—	178	2	no	—
279	#97	—	178	2	no	—
280	#97	—	178	2	no	—
281	C₄×C₈	—	89	1	no	—
282	C₄×C₈	—	89	1	no	—
283	C₄×C₈	—	89	1	no	—
284	C₄×C₈	—	89	1	no	—
285	C₄×C₈	—	89	1	no	—
286	C₄×C₈	—	89	1	no	—
287	C₄×C₈	—	89	1	no	—
288	C₄×C₈	—	178	1	no	—
289	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₂×Q₈	—	89	2	no	—
293	C₂×Q₈	—	178	2	no	—
294	C₂×Q₈	—	178	4	no	—
295	C₂×Q₈	—	178	4	no	—
296	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
297	C₂²×C₄	—	89	1	no	—
298	C₂²×C₄	—	89	1	no	—
299	C₂²×C₄	—	89	1	no	—
300	C₂²×C₄	—	178	2	no	—
301	C₂²×C₄	—	178	2	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	178	4	no	—
304	Q₁₆	—	178	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	89	1	no	—
308	C₂×C₈	—	89	1	no	—
309	C₂×C₈	—	89	4	no	—
310	C₂×C₈	—	89	4	no	—
311	C₂×C₈	—	89	1	no	—
312	C₂×C₈	—	89	1	no	—
313	C₂×C₈	—	356	4	no	—
314	C₂×C₈	—	178	2	no	—
315	C₂×C₈	—	178	2	no	—
316	C₂×C₈	—	178	4	no	—
317	C₂×C₈	—	178	2	no	—
318	C₂×C₈	—	178	1	no	—
319	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
321	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
322	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	89	2	no	—
325	C₄⋊C₄	—	178	2	no	—
326	C₄⋊C₄	—	178	2	no	—
327	C₄⋊C₄	—	178	2	no	—
328	C₄⋊C₄	—	178	2	no	—
329	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	89	1	no	—
332	C₄²	—	89	1	no	—
333	C₄²	—	89	1	no	—
334	C₄²	—	178	2	no	—
335	C₄²	—	178	2	no	—
336	C₄²	—	178	2	no	—
337	C₄²	C₂³×D₈₉	1	1	yes	characteristic
338	C₂³	—	89	1	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	356	4	no	—
342	Q₈	—	178	2	no	—
343	Q₈	—	178	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	89	1	no	—
347	C₂×C₄	—	89	1	no	—
348	C₂×C₄	—	89	2	no	—
349	C₂×C₄	—	89	2	no	—
350	C₂×C₄	—	89	2	no	—
351	C₂×C₄	—	89	2	no	—
352	C₂×C₄	—	89	1	no	—
353	C₂×C₄	—	356	4	no	—
354	C₂×C₄	—	356	4	no	—
355	C₂×C₄	—	178	2	no	—
356	C₂×C₄	—	178	2	no	—
357	C₂×C₄	—	178	2	no	—
358	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
360	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	89	2	no	—
366	C₈	—	89	2	no	—
367	C₈	—	356	2	no	—
368	C₈	—	178	2	no	—
369	C₈	—	178	1	no	—
370	C₈	—	178	1	no	—
371	C₈	M₁₆×D₈₉	1	2	yes	—
372	C₈	Q₁₆×D₈₉	1	2	yes	complemented
373	C₂²	—	89	2	no	—
374	C₂²	—	89	2	no	—
375	C₂²	—	89	2	no	—
376	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	89	2	no	—
381	C₄	—	89	2	no	—
382	C₄	—	356	2	no	—
383	C₄	—	356	2	no	—
384	C₄	—	178	1	no	—
385	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
386	C₄	#131×D₈₉	1	1	yes	characteristic
387	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
388	C₄	#135×D₈₉	1	1	yes	characteristic
389	C₂	—	89	4	no	—
390	C₂	#436×D₈₉	1	1	yes	characteristic
391	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
392	C₂	#443×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1591	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1591	D₈₉
hypocenter	C₈₉	C₂×#1591
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
3. #26019150	C₂	semidirect
4. #26019149	C₂	semidirect
5. #26019148	C₂	semidirect
6. #26019147	C₂	semidirect
7. #26019146	C₂	semidirect
11. C₈₉×#1591	C₂	semidirect
117. C₈×D₈₉	Q₁₆	semidirect
169. C₈×C₈₉	C₂×Q₁₆	semidirect
175. #10623494	C₂×Q₁₆	semidirect
196. D₈₉	#1591	direct (N × H)
204. #1591	D₈₉	direct (N × H)
208. C₈₉	C₂×#1591	semidirect
372. C₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#446×D₈₉	2
C₄×Q₁₆×D₈₉	2
#26019150	2
#26019149	2
#26019148	2
#26019147	2
#26019146	2
#335×D₈₉	2
Q₈⋊C₈×D₈₉	2
C₈²×D₈₉	2
C₈₉×#1591	2
C₂×#1591	89

Subgroups — #1591×D89 #36524166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1591×D₈₉ #36524166