Subgroups — #1706×D₈₉ #36542067

Order 22784.

1046 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	#500×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#493×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#492×D₈₉	C₂	1	2	yes	maximal, complemented
4	#486×D₈₉	C₂	1	2	yes	maximal, complemented
5	#26019845	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019844	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019843	C₂	1	2	yes	maximal, complemented
8	#26019842	C₂	1	2	yes	maximal, complemented
9	#26019841	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈²×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₈₉	—	2	4	no	—
13	C₂×D₈×D₈₉	—	2	2	no	—
14	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
15	#127×D₈₉	C₂²	1	2	yes	—
16	#19152003	C₂²	1	1	yes	characteristic, complemented
17	#19152002	—	2	2	no	—
18	#19152001	C₂²	1	2	yes	complemented
19	#19151975	C₂²	1	1	yes	characteristic
20	#19151974	C₂²	1	2	yes	—
21	#19151973	—	2	2	no	—
22	#19151972	C₂²	1	2	yes	complemented
23	#19151971	C₂²	1	2	yes	complemented
24	#19151970	C₂²	1	2	yes	complemented
25	#19151969	—	2	4	no	—
26	#19151946	C₂²	1	2	yes	complemented
27	#19151945	C₂²	1	2	yes	complemented
28	#19151944	C₂²	1	2	yes	complemented
29	#19151943	—	2	4	no	—
30	#107×D₈₉	—	2	2	no	—
31	#102×D₈₉	—	2	4	no	—
32	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
35	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
36	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
37	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
38	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#493×C₈₉	C₂²	1	1	yes	characteristic
40	#492×C₈₉	C₂²	1	2	yes	complemented
41	#486×C₈₉	C₂²	1	2	yes	complemented
42	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×Q₈×D₈₉	—	2	2	no	—
44	C₂×D₄×D₈₉	—	2	2	no	—
45	C₂×D₄×D₈₉	—	2	2	no	—
46	C₂×D₄×D₈₉	—	2	2	no	—
47	C₂×#13083563	—	2	4	no	—
48	C₂×#13083562	—	2	4	no	—
49	C₂×#13083561	—	2	4	no	—
50	SD₁₆×D₈₉	—	4	16	no	—
51	C₂×D₇₁₂	—	2	2	no	—
52	C₂×#13083559	—	2	4	no	—
53	D₈×D₈₉	—	4	8	no	—
54	C₂×C₈×D₈₉	D₄	1	2	yes	—
55	C₂×C₈×D₈₉	D₄	1	2	yes	—
56	C₂×C₈×D₈₉	D₄	1	2	yes	—
57	#15668012	C₂³	1	2	yes	—
58	#15668011	—	2	2	no	—
59	#15668011	—	2	2	no	—
60	#15668010	—	2	2	no	—
61	#15668009	C₂³	1	2	yes	—
62	#15668008	—	2	2	no	—
63	#15668008	—	2	2	no	—
64	#15668008	—	2	2	no	—
65	C₄⋊C₄×D₈₉	—	2	2	no	—
66	C₄⋊C₄×D₈₉	—	2	2	no	—
67	C₄²×D₈₉	C₂³	1	1	yes	characteristic
68	#15667946	—	2	2	no	—
69	#15667945	—	2	4	no	—
70	#15667934	—	2	4	no	—
71	#15667933	—	2	4	no	—
72	#15667932	—	2	4	no	—
73	C₄×#10623494	C₂³	1	1	yes	characteristic
74	C₄×#10623494	C₂³	1	1	yes	characteristic
75	C₄×#10623494	C₂³	1	1	yes	characteristic
76	C₈×Dic₈₉	D₄	1	2	yes	—
77	C₈×Dic₈₉	D₄	1	2	yes	—
78	C₈×Dic₈₉	D₄	1	2	yes	—
79	C₂×SD₁₆×C₈₉	—	2	4	no	—
80	C₂×D₈×C₈₉	—	2	2	no	—
81	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
82	#127×C₈₉	C₂³	1	2	yes	—
83	#107×C₈₉	—	2	2	no	—
84	#102×C₈₉	—	2	4	no	—
85	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×D₈₉	—	4	2	no	—
89	C₂×Dic₁₇₈	—	2	2	no	—
90	C₂×Dic₁₇₈	—	4	2	no	—
91	Q₈×D₈₉	—	4	8	no	—
92	C₂×D₃₅₆	—	2	2	no	—
93	C₂×D₃₅₆	—	2	2	no	—
94	C₂×D₃₅₆	—	2	2	no	—
95	C₂×C₂²⋊D₈₉	—	4	2	no	—
96	C₂×C₂²⋊D₈₉	—	4	2	no	—
97	C₂×C₂²⋊D₈₉	—	4	2	no	—
98	D₄×D₈₉	—	4	8	no	—
99	D₄×D₈₉	—	4	8	no	—
100	D₄×D₈₉	—	4	8	no	—
101	C₂×C₄×D₈₉	—	4	2	no	—
102	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
105	#13083563	—	4	8	no	—
106	#13083562	—	4	8	no	—
107	#13083561	—	4	8	no	—
108	D₇₁₂	—	4	4	no	—
109	#13083559	—	4	8	no	—
110	C₂×#10623494	C₂×D₄	1	2	yes	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	2	yes	—
113	C₈×D₈₉	—	2	4	no	—
114	C₈×D₈₉	D₈	1	8	yes	complemented
115	C₈×D₈₉	SD₁₆	1	8	yes	complemented
116	C₄⋊Dic₈₉	—	2	2	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	#13083553	—	4	2	no	—
119	#13083553	—	4	2	no	—
120	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₈₉	—	2	2	no	—
124	C₂×D₄×C₈₉	—	2	2	no	—
125	C₂×D₄×C₈₉	—	2	2	no	—
126	C₂×D₄×C₈₉	—	2	2	no	—
127	SD₁₆×C₈₉	—	4	8	no	—
128	D₈×C₈₉	—	4	4	no	—
129	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₈₉	—	2	2	no	—
133	C₄⋊C₄×C₈₉	—	2	2	no	—
134	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
135	C₂³×C₈₉	—	4	2	no	—
136	C₂²×D₈₉	—	4	2	no	—
137	C₂²×D₈₉	—	8	4	no	—
138	C₂²×D₈₉	—	8	4	no	—
139	C₂²×D₈₉	—	8	4	no	—
140	C₂²×D₈₉	#127	1	1	yes	characteristic
141	Q₈×C₈₉	—	4	4	no	—
142	D₄×C₈₉	—	4	4	no	—
143	D₄×C₈₉	—	4	4	no	—
144	D₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₈₉	—	8	4	no	—
150	C₂²⋊D₈₉	—	8	4	no	—
151	C₂²⋊D₈₉	—	8	4	no	—
152	C₂×Dic₈₉	—	4	2	no	—
153	C₂×Dic₈₉	#127	1	1	yes	characteristic
154	C₂×Dic₈₉	#127	1	1	yes	characteristic
155	C₂×Dic₈₉	#127	1	1	yes	characteristic
156	D₃₅₆	—	4	4	no	—
157	D₃₅₆	—	4	4	no	—
158	D₃₅₆	—	4	4	no	—
159	C₄×D₈₉	—	8	4	no	—
160	C₄×D₈₉	C₂×D₈	1	4	yes	—
161	C₄×D₈₉	C₂×SD₁₆	1	4	yes	—
162	C₄×D₈₉	#135	1	4	yes	—
163	Dic₁₇₈	—	4	4	no	—
164	Dic₁₇₈	—	8	4	no	—
165	C₈×C₈₉	—	2	2	no	—
166	C₈×C₈₉	C₂×D₈	1	4	yes	complemented
167	C₈×C₈₉	C₂×SD₁₆	1	4	yes	complemented
168	#10623494	—	2	2	no	—
169	#10623494	C₂×D₈	1	4	yes	complemented
170	#10623494	C₂×SD₁₆	1	4	yes	complemented
171	C₂²×C₈₉	—	8	2	no	—
172	C₂²×C₈₉	—	8	2	no	—
173	C₂²×C₈₉	—	8	2	no	—
174	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
175	C₂×D₈₉	—	8	2	no	—
176	C₂×D₈₉	—	8	2	no	—
177	C₂×D₈₉	—	8	2	no	—
178	C₂×D₈₉	—	16	8	no	—
179	C₂×D₈₉	#492	1	2	yes	—
180	C₂×D₈₉	#493	1	2	yes	—
181	C₂×D₈₉	#495	1	2	yes	—
182	C₄×C₈₉	—	8	2	no	—
183	C₄×C₈₉	C₂²×D₈	1	2	yes	—
184	C₄×C₈₉	C₂²×SD₁₆	1	2	yes	—
185	C₄×C₈₉	C₂×#135	1	2	yes	—
186	Dic₈₉	—	8	2	no	—
187	Dic₈₉	#492	1	2	yes	—
188	Dic₈₉	#493	1	2	yes	—
189	Dic₈₉	#495	1	2	yes	—
190	C₂×#1706	—	89	1	no	maximal, Sylow
191	C₂×C₈₉	—	16	2	no	—
192	C₂×C₈₉	C₂×#492	1	1	yes	characteristic
193	C₂×C₈₉	C₂×#493	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#495	1	1	yes	characteristic
195	D₈₉	—	16	2	no	—
196	D₈₉	#1706	1	4	yes	direct product factor
197	C₂×#500	—	89	1	no	—
198	C₂×#493	—	89	1	no	—
199	C₂×#492	—	89	2	no	—
200	C₂×#486	—	89	2	no	—
201	#1706	—	89	1	no	—
202	#1706	—	89	1	no	—
203	#1706	—	89	2	no	—
204	#1706	—	89	2	no	—
205	#1706	—	89	1	no	—
206	#1706	D₈₉	1	1	yes	characteristic, direct product factor
207	C₂×C₈²	—	89	1	no	—
208	C₈₉	C₂×#1706	1	1	yes	characteristic, complemented, Sylow
209	C₂²×SD₁₆	—	178	4	no	—
210	C₂²×D₈	—	178	2	no	—
211	C₂×C₄⋊Q₈	—	89	2	no	—
212	C₂×#127	—	89	2	no	—
213	#500	—	89	2	no	—
214	#500	—	89	1	no	—
215	#500	—	178	2	no	—
216	#500	C₂×D₈₉	1	1	yes	characteristic, complemented
217	#493	—	89	2	no	—
218	#493	—	89	1	no	—
219	#493	—	178	2	no	—
220	#493	C₂×D₈₉	1	1	yes	characteristic
221	#492	—	89	2	no	—
222	#492	—	89	2	no	—
223	#492	—	89	2	no	—
224	#492	—	178	4	no	—
225	#492	C₂×D₈₉	1	2	yes	complemented
226	#486	—	89	2	no	—
227	#486	—	89	2	no	—
228	#486	—	89	2	no	—
229	#486	—	178	4	no	—
230	#486	C₂×D₈₉	1	2	yes	complemented
231	C₂×#107	—	178	2	no	—
232	C₂×#102	—	178	4	no	—
233	C₂×C₄×C₈	—	89	1	no	—
234	C₂×C₄×C₈	—	89	1	no	—
235	C₂×C₄×C₈	—	89	1	no	—
236	C₈²	—	89	1	no	—
237	C₈²	—	89	1	no	—
238	C₈²	—	89	1	no	—
239	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
240	C₂²×Q₈	—	178	2	no	—
241	C₂²×D₄	—	178	2	no	—
242	C₂²×D₄	—	178	2	no	—
243	C₂²×D₄	—	178	2	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	356	16	no	—
246	C₂×SD₁₆	—	178	4	no	—
247	C₂×SD₁₆	—	178	4	no	—
248	C₂×SD₁₆	—	178	4	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	356	8	no	—
251	C₂×D₈	—	178	4	no	—
252	C₂×D₈	—	178	2	no	—
253	C₂²×C₈	—	89	2	no	—
254	C₂²×C₈	—	89	2	no	—
255	C₂²×C₈	—	89	2	no	—
256	C₄⋊Q₈	—	89	2	no	—
257	C₄⋊Q₈	—	178	2	no	—
258	C₄⋊Q₈	—	178	2	no	—
259	C₄⋊Q₈	—	178	2	no	—
260	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
261	#127	—	89	2	no	—
262	#127	—	178	2	no	—
263	#127	—	178	2	no	—
264	#127	—	178	2	no	—
265	#127	C₂²×D₈₉	1	2	yes	—
266	C₂×C₄⋊C₄	—	178	2	no	—
267	C₂×C₄⋊C₄	—	178	2	no	—
268	C₂×C₄²	—	89	1	no	—
269	#107	—	2	2	no	—
270	#107	—	178	4	no	—
271	#107	—	178	2	no	—
272	#102	—	2	4	no	—
273	#102	—	178	4	no	—
274	#102	—	178	4	no	—
275	#102	—	178	4	no	—
276	C₄×C₈	—	89	2	no	—
277	C₄×C₈	—	89	2	no	—
278	C₄×C₈	—	89	2	no	—
279	C₄×C₈	—	89	1	no	—
280	C₄×C₈	—	89	1	no	—
281	C₄×C₈	—	89	1	no	—
282	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₂⁴	—	356	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	356	2	no	—
288	C₂×Q₈	—	356	8	no	—
289	C₂×Q₈	—	178	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	356	8	no	—
294	C₂×D₄	—	356	8	no	—
295	C₂×D₄	—	356	8	no	—
296	C₂×D₄	—	356	2	no	—
297	C₂×D₄	—	356	2	no	—
298	C₂×D₄	—	356	2	no	—
299	C₂×D₄	—	178	2	no	—
300	C₂×D₄	—	178	2	no	—
301	C₂×D₄	—	178	2	no	—
302	C₂²×C₄	—	89	1	no	—
303	C₂²×C₄	—	89	1	no	—
304	C₂²×C₄	—	89	1	no	—
305	C₂²×C₄	—	356	2	no	—
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	356	8	no	—
308	SD₁₆	—	356	8	no	—
309	SD₁₆	—	356	8	no	—
310	D₈	—	4	4	no	—
311	D₈	—	356	8	no	—
312	D₈	—	356	4	no	—
313	C₂×C₈	—	89	2	no	—
314	C₂×C₈	—	89	2	no	—
315	C₂×C₈	—	89	8	no	—
316	C₂×C₈	—	89	8	no	—
317	C₂×C₈	—	89	2	no	—
318	C₂×C₈	—	178	4	no	—
319	C₂×C₈	D₄×D₈₉	1	2	yes	—
320	C₂×C₈	D₄×D₈₉	1	2	yes	—
321	C₂×C₈	D₄×D₈₉	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	356	2	no	—
325	C₄⋊C₄	—	356	2	no	—
326	C₄⋊C₄	—	178	2	no	—
327	C₄⋊C₄	—	178	2	no	—
328	C₄²	—	89	1	no	—
329	C₄²	—	89	1	no	—
330	C₄²	—	89	1	no	—
331	C₄²	C₂³×D₈₉	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	89	1	no	—
334	C₂³	—	356	2	no	—
335	C₂³	—	712	4	no	—
336	C₂³	—	712	4	no	—
337	C₂³	—	712	4	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	356	4	no	—
340	Q₈	—	712	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	356	4	no	—
345	D₄	—	356	4	no	—
346	D₄	—	356	4	no	—
347	D₄	—	712	4	no	—
348	D₄	—	712	4	no	—
349	D₄	—	712	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	89	1	no	—
352	C₂×C₄	—	89	1	no	—
353	C₂×C₄	—	89	1	no	—
354	C₂×C₄	—	89	4	no	—
355	C₂×C₄	—	89	4	no	—
356	C₂×C₄	—	89	4	no	—
357	C₂×C₄	—	356	2	no	—
358	C₂×C₄	—	712	4	no	—
359	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
361	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	89	4	no	—
364	C₈	—	89	4	no	—
365	C₈	—	178	2	no	—
366	C₈	D₈×D₈₉	1	4	yes	complemented
367	C₈	SD₁₆×D₈₉	1	4	yes	complemented
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	89	2	no	—
372	C₂²	—	89	2	no	—
373	C₂²	—	89	2	no	—
374	C₂²	—	1424	8	no	—
375	C₂²	—	712	2	no	—
376	C₂²	—	712	2	no	—
377	C₂²	—	712	2	no	—
378	C₂²	#127×D₈₉	1	1	yes	characteristic
379	C₄	—	8	2	no	—
380	C₄	—	89	2	no	—
381	C₄	—	89	2	no	—
382	C₄	—	89	2	no	—
383	C₄	—	712	2	no	—
384	C₄	C₂×D₈×D₈₉	1	2	yes	—
385	C₄	C₂×SD₁₆×D₈₉	1	2	yes	—
386	C₄	#135×D₈₉	1	2	yes	—
387	C₂	—	16	2	no	—
388	C₂	—	89	4	no	—
389	C₂	—	1424	2	no	—
390	C₂	#492×D₈₉	1	1	yes	characteristic
391	C₂	#493×D₈₉	1	1	yes	characteristic
392	C₂	#495×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1706	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	#493×D₈₉	C₂
hypercenter	#1706	D₈₉
hypocenter	C₈₉	C₂×#1706
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1706

Complements

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

N	H ≅ G/N	type
1. #500×D₈₉	C₂	semidirect
3. #492×D₈₉	C₂	semidirect
4. #486×D₈₉	C₂	semidirect
5. #26019845	C₂	semidirect
6. #26019844	C₂	semidirect
7. #26019843	C₂	semidirect
8. #26019842	C₂	semidirect
9. #26019841	C₂	semidirect
10. C₈²×D₈₉	C₂	semidirect
11. C₈₉×#1706	C₂	semidirect
16. #19152003	C₂²	semidirect
18. #19152001	C₂²	semidirect
22. #19151972	C₂²	semidirect
23. #19151971	C₂²	semidirect
24. #19151970	C₂²	semidirect
26. #19151946	C₂²	semidirect
27. #19151945	C₂²	semidirect
28. #19151944	C₂²	semidirect
35. C₈×#10623494	C₂²	semidirect
36. C₈×#10623494	C₂²	semidirect
37. C₈×#10623494	C₂²	semidirect
38. #500×C₈₉	C₂²	semidirect
40. #492×C₈₉	C₂²	semidirect
41. #486×C₈₉	C₂²	semidirect
42. C₈²×C₈₉	C₂²	semidirect
114. C₈×D₈₉	D₈	semidirect
115. C₈×D₈₉	SD₁₆	semidirect
166. C₈×C₈₉	C₂×D₈	semidirect
167. C₈×C₈₉	C₂×SD₁₆	semidirect
169. #10623494	C₂×D₈	semidirect
170. #10623494	C₂×SD₁₆	semidirect
196. D₈₉	#1706	direct (N × H)
206. #1706	D₈₉	direct (N × H)
208. C₈₉	C₂×#1706	semidirect
216. #500	C₂×D₈₉	semidirect
225. #492	C₂×D₈₉	semidirect
230. #486	C₂×D₈₉	semidirect
239. C₈²	C₂×D₈₉	semidirect
366. C₈	D₈×D₈₉	semidirect
367. C₈	SD₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₈₉	2
#493×D₈₉	2
#492×D₈₉	2
#486×D₈₉	2
#26019845	2
#26019844	2
#26019843	2
#26019842	2
#26019841	2
C₈²×D₈₉	2
C₈₉×#1706	2
C₂×#1706	89

Subgroups — #1706×D89 #36542067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1706×D₈₉ #36542067