Subgroups — #1379×D₈₉ #36469295

Order 22784.

606 conjugacy classes of subgroups.

The subgroup lattice has 382 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	C₂²×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#405×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26018342	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018341	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₈₉	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
10	#117×D₈₉	C₄	1	1	yes	characteristic
11	C₂×#15667952	C₂²	1	1	yes	characteristic
12	C₂×#15667951	—	2	1	no	—
13	M₃₂×D₈₉	—	2	2	no	—
14	M₃₂×D₈₉	C₄	1	4	yes	complemented
15	C₂²×#13083549	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×D₈₉	—	2	2	no	—
17	C₂×C₁₆×D₈₉	—	2	1	no	—
18	C₂×C₁₆×D₈₉	—	2	1	no	—
19	C₂×C₁₆×D₈₉	—	2	1	no	—
20	C₂×C₁₆×D₈₉	C₄	1	4	yes	complemented
21	#19151556	C₄	1	1	yes	characteristic
22	#19151555	—	2	1	no	—
23	#19151554	C₄	1	1	yes	characteristic
24	#19151553	C₂²	1	1	yes	characteristic
25	#19151552	—	2	1	no	—
26	#97×D₈₉	—	2	1	no	—
27	C₄×C₈×D₈₉	—	2	1	no	—
28	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	#405×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
33	C₂×#13083557	—	2	1	no	—
34	M₁₆×D₈₉	—	2	2	no	—
35	M₁₆×D₈₉	C₈	1	4	yes	—
36	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₈₉	—	2	1	no	—
38	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₈₉	D₄	1	2	yes	—
41	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
42	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
43	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
44	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
45	C₂×C₈×D₈₉	Q₈	1	2	yes	—
46	#15667971	C₂×C₄	1	1	yes	characteristic
47	#15667970	C₈	1	2	yes	—
48	#15667969	—	2	1	no	—
49	#15667968	—	2	1	no	—
50	C₄⋊C₄×D₈₉	C₈	1	2	yes	—
51	C₂²⋊C₄×D₈₉	—	2	1	no	—
52	C₄²×D₈₉	—	2	1	no	—
53	#15667952	—	2	1	no	—
54	#15667952	C₂×C₄	1	2	yes	complemented
55	#15667951	—	2	4	no	—
56	C₂×#13083549	—	2	1	no	—
57	C₂×#13083549	—	2	1	no	—
58	C₂×#13083549	—	2	1	no	—
59	C₂×#13083549	C₂×C₄	1	2	yes	complemented
60	C₁₆×D₈₉	—	2	4	no	—
61	C₁₆×D₈₉	—	2	4	no	—
62	C₁₆×D₈₉	—	2	4	no	—
63	#15667923	—	2	1	no	—
64	#15667922	—	2	1	no	—
65	#15667922	—	2	1	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₈×Dic₈₉	—	2	1	no	—
68	C₈×Dic₈₉	—	2	1	no	—
69	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
72	M₃₂×C₈₉	—	2	1	no	—
73	M₃₂×C₈₉	C₂×C₄	1	2	yes	complemented
74	C₂×C₁₆×C₈₉	—	2	1	no	—
75	C₂×C₁₆×C₈₉	—	2	1	no	—
76	C₂×C₁₆×C₈₉	—	2	1	no	—
77	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
78	#97×C₈₉	—	2	1	no	—
79	C₄×C₈×C₈₉	—	2	1	no	—
80	C₂³×D₈₉	M₁₆	1	1	yes	characteristic
81	C₂²×Dic₈₉	M₁₆	1	1	yes	characteristic
82	C₂×C₄×D₈₉	—	2	2	no	—
83	C₂×C₄×D₈₉	C₄²	1	2	yes	—
84	C₂×C₄×D₈₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₈₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₈₉	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₈₉	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₈₉	M₁₆	1	2	yes	—
91	#13083558	—	2	1	no	—
92	#13083558	C₂×C₈	1	2	yes	—
93	#13083557	—	2	4	no	—
94	C₂×#10623494	—	2	1	no	—
95	C₂×#10623494	C₄²	1	2	yes	—
96	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×#10623494	C₄⋊C₄	1	2	yes	—
99	C₈×D₈₉	—	2	4	no	—
100	C₈×D₈₉	C₂²⋊C₄	1	2	yes	—
101	C₈×D₈₉	C₂²⋊C₄	1	2	yes	—
102	C₈×D₈₉	C₂²⋊C₄	1	2	yes	—
103	C₈×D₈₉	C₂²⋊C₄	1	2	yes	—
104	C₈×D₈₉	C₄⋊C₄	1	2	yes	—
105	C₈×D₈₉	C₄⋊C₄	1	2	yes	—
106	C₈×D₈₉	C₄⋊C₄	1	2	yes	—
107	C₈×D₈₉	C₄⋊C₄	1	2	yes	—
108	C₄⋊Dic₈₉	C₂×C₈	1	2	yes	—
109	#13083553	—	2	2	no	—
110	C₂²⋊Dic₈₉	—	2	1	no	—
111	#13083551	—	2	2	no	—
112	C₄×Dic₈₉	—	2	1	no	—
113	C₄×Dic₈₉	—	2	2	no	—
114	#13083549	—	2	2	no	—
115	#13083549	—	2	2	no	—
116	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₈₉	—	2	1	no	—
118	M₁₆×C₈₉	C₂×C₈	1	2	yes	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
126	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
127	C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₄²×C₈₉	—	2	1	no	—
129	C₁₆×C₈₉	—	2	2	no	—
130	C₁₆×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	C₂×M₁₆	1	1	yes	characteristic
132	C₂²×D₈₉	—	2	4	no	—
133	C₂²×D₈₉	#97	1	2	yes	—
134	C₂²×D₈₉	C₂²⋊C₈	1	1	yes	characteristic
135	C₂²×D₈₉	C₂²⋊C₈	1	1	yes	characteristic
136	C₂²×D₈₉	C₄⋊C₈	1	2	yes	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×Dic₈₉	—	2	2	no	—
145	C₂×Dic₈₉	#97	1	2	yes	—
146	C₂×Dic₈₉	C₂²⋊C₈	1	1	yes	characteristic
147	C₂×Dic₈₉	C₂²⋊C₈	1	1	yes	characteristic
148	C₂×Dic₈₉	C₄⋊C₈	1	2	yes	—
149	C₄×D₈₉	—	4	4	no	—
150	C₄×D₈₉	#95	1	2	yes	—
151	C₄×D₈₉	#95	1	2	yes	—
152	C₄×D₈₉	C₄×C₈	1	2	yes	—
153	C₄×D₈₉	C₄×C₈	1	2	yes	—
154	C₄×D₈₉	C₂²⋊C₈	1	2	yes	—
155	C₄×D₈₉	C₂²⋊C₈	1	2	yes	—
156	C₄×D₈₉	C₄⋊C₈	1	2	yes	—
157	C₄×D₈₉	C₄⋊C₈	1	2	yes	—
158	C₈×C₈₉	—	2	2	no	—
159	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	#10623494	—	2	2	no	—
164	#10623494	#95	1	2	yes	—
165	#10623494	#95	1	2	yes	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	C₂×#97	1	1	yes	characteristic
168	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
170	C₂×D₈₉	—	2	2	no	—
171	C₂×D₈₉	—	2	4	no	—
172	C₂×D₈₉	—	2	4	no	—
173	C₂×D₈₉	#336	1	2	yes	—
174	C₂×D₈₉	#336	1	2	yes	—
175	C₂×D₈₉	#350	1	4	yes	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
178	C₄×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
179	C₄×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
180	C₄×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
181	Dic₈₉	—	4	2	no	—
182	Dic₈₉	#336	1	2	yes	—
183	Dic₈₉	#336	1	2	yes	—
184	C₂×#1379	—	89	1	no	maximal, Sylow
185	C₂×C₈₉	—	2	1	no	—
186	C₂×C₈₉	—	2	1	no	—
187	C₂×C₈₉	C₂×#336	1	1	yes	characteristic
188	C₂×C₈₉	C₂×#350	1	2	yes	—
189	D₈₉	—	2	2	no	—
190	D₈₉	#1379	1	4	yes	direct product factor
191	C₂²×M₃₂	—	89	1	no	—
192	C₂³×C₁₆	—	89	1	no	—
193	C₂×#405	—	89	1	no	—
194	#1379	—	89	1	no	—
195	#1379	—	89	1	no	—
196	#1379	—	89	1	no	—
197	#1379	D₈₉	1	1	yes	characteristic, direct product factor
198	C₈₉	C₂×#1379	1	1	yes	characteristic, complemented, Sylow
199	C₂²×M₁₆	—	89	1	no	—
200	C₂³×C₈	—	89	1	no	—
201	C₂×#117	—	89	1	no	—
202	C₂×M₃₂	—	89	1	no	—
203	C₂×M₃₂	—	89	4	no	—
204	C₂×M₃₂	—	178	1	no	—
205	C₂×M₃₂	—	178	2	no	—
206	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
207	C₂²×C₁₆	—	89	1	no	—
208	C₂²×C₁₆	—	89	4	no	—
209	C₂²×C₁₆	—	178	1	no	—
210	C₂²×C₁₆	—	178	1	no	—
211	C₂²×C₁₆	—	178	2	no	—
212	C₂²×C₁₆	—	178	1	no	—
213	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
214	#405	—	89	1	no	—
215	#405	—	89	1	no	—
216	#405	—	89	1	no	—
217	#405	—	178	1	no	—
218	#405	—	178	1	no	—
219	#405	C₂×D₈₉	1	1	yes	characteristic
220	C₂×#97	—	178	1	no	—
221	C₂×C₄×C₈	—	178	1	no	—
222	C₂³×C₄	—	89	1	no	—
223	C₂×M₁₆	—	89	1	no	—
224	C₂×M₁₆	—	89	4	no	—
225	C₂×M₁₆	—	178	1	no	—
226	C₂×M₁₆	—	178	2	no	—
227	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
228	C₂²×C₈	—	89	1	no	—
229	C₂²×C₈	—	89	2	no	—
230	C₂²×C₈	—	89	2	no	—
231	C₂²×C₈	—	89	1	no	—
232	C₂²×C₈	—	89	1	no	—
233	C₂²×C₈	—	89	2	no	—
234	C₂²×C₈	—	89	1	no	—
235	C₂²×C₈	—	89	1	no	—
236	C₂²×C₈	—	89	2	no	—
237	C₂²×C₈	—	178	1	no	—
238	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
239	#117	—	89	1	no	—
240	#117	—	89	2	no	—
241	#117	—	178	1	no	—
242	#117	—	178	1	no	—
243	#117	C₄×D₈₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	89	2	no	—
245	C₂×C₂²⋊C₄	—	178	1	no	—
246	C₂×C₄²	—	178	1	no	—
247	M₃₂	—	2	1	no	—
248	M₃₂	—	89	2	no	—
249	M₃₂	—	178	4	no	—
250	M₃₂	—	178	1	no	—
251	M₃₂	C₄×D₈₉	1	2	yes	complemented
252	C₂×C₁₆	—	2	1	no	—
253	C₂×C₁₆	—	2	1	no	—
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	89	2	no	—
256	C₂×C₁₆	—	178	4	no	—
257	C₂×C₁₆	—	178	4	no	—
258	C₂×C₁₆	—	178	4	no	—
259	C₂×C₁₆	—	178	1	no	—
260	C₂×C₁₆	—	178	1	no	—
261	C₂×C₁₆	—	178	1	no	—
262	C₂×C₁₆	C₄×D₈₉	1	2	yes	complemented
263	#97	—	2	1	no	—
264	#97	—	178	1	no	—
265	#97	—	178	1	no	—
266	#97	—	178	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	178	1	no	—
269	C₄×C₈	—	178	1	no	—
270	C₄×C₈	—	178	1	no	—
271	C₂⁴	—	89	1	no	—
272	C₂²×C₄	—	89	1	no	—
273	C₂²×C₄	—	89	1	no	—
274	C₂²×C₄	—	89	1	no	—
275	C₂²×C₄	—	89	2	no	—
276	C₂²×C₄	—	89	2	no	—
277	C₂²×C₄	—	89	2	no	—
278	C₂²×C₄	—	89	1	no	—
279	C₂²×C₄	—	89	1	no	—
280	C₂²×C₄	—	89	2	no	—
281	C₂²×C₄	—	178	2	no	—
282	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
283	M₁₆	—	2	1	no	—
284	M₁₆	—	89	2	no	—
285	M₁₆	—	178	4	no	—
286	M₁₆	—	178	1	no	—
287	M₁₆	C₈×D₈₉	1	2	yes	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	89	2	no	—
290	C₂×C₈	—	89	1	no	—
291	C₂×C₈	—	89	1	no	—
292	C₂×C₈	—	89	2	no	—
293	C₂×C₈	—	89	2	no	—
294	C₂×C₈	—	89	2	no	—
295	C₂×C₈	—	89	2	no	—
296	C₂×C₈	—	89	2	no	—
297	C₂×C₈	—	89	2	no	—
298	C₂×C₈	—	89	2	no	—
299	C₂×C₈	—	89	2	no	—
300	C₂×C₈	—	89	2	no	—
301	C₂×C₈	—	178	4	no	—
302	C₂×C₈	—	178	1	no	—
303	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
305	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
306	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
307	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
308	C₂×C₈	Q₈×D₈₉	1	1	yes	characteristic
309	C₄⋊C₄	—	89	2	no	—
310	C₄⋊C₄	—	178	2	no	—
311	C₄⋊C₄	C₈×D₈₉	1	2	yes	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	178	2	no	—
314	C₂²⋊C₄	—	178	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	178	2	no	—
317	C₄²	—	178	1	no	—
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	178	2	no	—
321	C₁₆	—	178	2	no	—
322	C₂³	—	89	1	no	—
323	C₂³	—	89	2	no	—
324	C₂³	—	89	2	no	—
325	C₂³	—	89	1	no	—
326	C₂³	—	178	4	no	—
327	C₂³	M₁₆×D₈₉	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	89	2	no	—
330	C₂×C₄	—	89	2	no	—
331	C₂×C₄	—	89	1	no	—
332	C₂×C₄	—	89	1	no	—
333	C₂×C₄	—	89	2	no	—
334	C₂×C₄	—	89	2	no	—
335	C₂×C₄	—	89	2	no	—
336	C₂×C₄	—	89	2	no	—
337	C₂×C₄	—	89	2	no	—
338	C₂×C₄	—	89	2	no	—
339	C₂×C₄	—	89	2	no	—
340	C₂×C₄	—	89	2	no	—
341	C₂×C₄	—	356	4	no	—
342	C₂×C₄	—	178	2	no	—
343	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
344	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
345	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
348	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	89	2	no	—
351	C₈	—	89	2	no	—
352	C₈	—	178	2	no	—
353	C₈	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
354	C₈	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
355	C₈	C₄⋊C₄×D₈₉	1	1	yes	characteristic
356	C₈	C₄⋊C₄×D₈₉	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	89	2	no	—
359	C₂²	—	89	4	no	—
360	C₂²	—	89	2	no	—
361	C₂²	—	178	4	no	—
362	C₂²	—	178	4	no	—
363	C₂²	—	178	2	no	—
364	C₂²	#97×D₈₉	1	1	yes	characteristic
365	C₂²	C₂²⋊C₈×D₈₉	1	1	yes	characteristic
366	C₂²	C₄⋊C₈×D₈₉	1	1	yes	characteristic
367	C₄	—	4	2	no	—
368	C₄	—	89	2	no	—
369	C₄	—	89	2	no	—
370	C₄	—	356	2	no	—
371	C₄	#95×D₈₉	1	1	yes	characteristic
372	C₄	C₄×C₈×D₈₉	1	1	yes	characteristic
373	C₄	C₂²⋊C₈×D₈₉	1	1	yes	characteristic
374	C₄	C₄⋊C₈×D₈₉	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	89	4	no	—
378	C₂	—	178	2	no	—
379	C₂	#336×D₈₉	1	1	yes	characteristic
380	C₂	#350×D₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₈₉
commutator	C₄×C₈₉	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1379	C₂
socle	C₂²×C₈₉	C₂×C₂²⋊C₈
prime radical	C₂³×D₈₉	M₁₆
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1379	D₈₉
hypocenter	C₈₉	C₂×#1379
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
4. #26018342	C₂	semidirect
5. #26018341	C₂	semidirect
6. #26018340	C₂	semidirect
7. C₈₉×#1379	C₂	semidirect
14. M₃₂×D₈₉	C₄	semidirect
20. C₂×C₁₆×D₈₉	C₄	semidirect
54. #15667952	C₂×C₄	semidirect
59. C₂×#13083549	C₂×C₄	semidirect
73. M₃₂×C₈₉	C₂×C₄	semidirect
77. C₂×C₁₆×C₈₉	C₂×C₄	semidirect
190. D₈₉	#1379	direct (N × H)
197. #1379	D₈₉	direct (N × H)
198. C₈₉	C₂×#1379	semidirect
251. M₃₂	C₄×D₈₉	semidirect
262. C₂×C₁₆	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
C₂²×C₁₆×D₈₉	2
#405×D₈₉	2
#26018342	2
#26018341	2
#26018340	2
C₈₉×#1379	2
C₂×#1379	89

Subgroups — #1379×D89 #36469295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1379×D₈₉ #36469295