Subgroups — #1694×D₈₉ #36537052

Order 22784.

682 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	#500×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#462×D₈₉	C₂	1	2	yes	maximal
3	#446×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019771	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019770	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019769	C₂	1	2	yes	maximal, complemented
7	#26019768	C₂	1	2	yes	maximal, complemented
8	#26019767	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₈₉	C₂	1	1	yes	maximal, characteristic
10	#332×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#1694	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	—	2	2	no	—
13	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
14	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
15	#19152003	C₂²	1	1	yes	characteristic
16	#19152002	—	2	1	no	—
17	#19152002	—	2	1	no	—
18	#19152001	C₂²	1	2	yes	—
19	#19151809	C₂²	1	2	yes	—
20	#19151808	C₂²	1	2	yes	—
21	#19151807	—	2	2	no	—
22	#19151806	—	2	2	no	—
23	#19151805	C₂²	1	2	yes	—
24	#19151729	C₂²	1	1	yes	characteristic
25	#19151728	C₂²	1	1	yes	characteristic
26	#19151727	—	2	1	no	—
27	#19151726	—	2	1	no	—
28	#19151725	C₂²	1	1	yes	characteristic
29	#107×D₈₉	—	2	1	no	—
30	#107×D₈₉	—	2	1	no	—
31	C₄⋊C₈×D₈₉	—	2	1	no	—
32	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
34	#103×D₈₉	—	2	2	no	—
35	#97×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151349	C₂²	1	1	yes	characteristic
38	#19151348	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151344	C₂²	1	2	yes	—
41	#19151343	C₂²	1	2	yes	—
42	#500×C₈₉	C₂²	1	1	yes	characteristic
43	#462×C₈₉	C₂²	1	2	yes	—
44	#446×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	2	yes	—
47	C₂×Q₈×D₈₉	—	2	2	no	—
48	C₂×Q₈×D₈₉	D₄	1	1	yes	characteristic
49	C₂×Dic₃₅₆	—	2	2	no	—
50	C₂×#13083564	—	2	2	no	—
51	C₂×#13083564	—	2	2	no	—
52	Q₁₆×D₈₉	—	4	8	no	—
53	C₂×C₈×D₈₉	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
56	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
57	#15668012	C₂³	1	2	yes	—
58	#15668011	—	2	2	no	—
59	#15668011	—	2	2	no	—
60	#15668010	—	2	2	no	—
61	Q₈×Dic₈₉	D₄	1	1	yes	characteristic
62	C₄×Dic₁₇₈	—	2	1	no	—
63	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	#15667977	—	2	1	no	—
65	#15667977	D₄	1	1	yes	characteristic
66	C₄⋊C₄×D₈₉	—	2	1	no	—
67	C₄⋊C₄×D₈₉	—	2	2	no	—
68	C₄⋊C₄×D₈₉	—	2	2	no	—
69	C₄⋊C₄×D₈₉	D₄	1	1	yes	characteristic
70	C₄²×D₈₉	—	2	1	no	—
71	C₄²×D₈₉	C₂³	1	1	yes	characteristic
72	#15667946	—	2	1	no	—
73	#15667946	—	2	1	no	—
74	#15667945	—	2	2	no	—
75	#15667945	—	2	2	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	#15667941	—	2	1	no	—
80	#15667941	—	2	1	no	—
81	#15667941	—	2	2	no	—
82	#15667941	—	2	1	no	—
83	#15667937	—	2	2	no	—
84	#15667936	—	2	2	no	—
85	#15667935	—	2	2	no	—
86	#15667923	—	2	1	no	—
87	#15667922	—	2	1	no	—
88	#15667922	—	2	1	no	—
89	C₄×#10623494	C₂³	1	1	yes	characteristic
90	C₈×Dic₈₉	D₄	1	1	yes	characteristic
91	C₈×Dic₈₉	D₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₈₉	—	2	2	no	—
93	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
94	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
95	#107×C₈₉	—	2	1	no	—
96	#107×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	—	2	1	no	—
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	#103×C₈₉	—	2	2	no	—
101	#97×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×Dic₁₇₈	—	2	1	no	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×Dic₁₇₈	—	4	2	no	—
106	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
107	Q₈×D₈₉	—	2	4	no	—
108	Q₈×D₈₉	—	4	4	no	—
109	Q₈×D₈₉	—	4	4	no	—
110	C₂×C₄×D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	C₂×C₄×D₈₉	—	4	2	no	—
113	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
116	Dic₃₅₆	—	4	4	no	—
117	#13083564	—	4	4	no	—
118	#13083564	—	4	4	no	—
119	C₂×#10623494	—	2	2	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₈×D₈₉	—	2	2	no	—
124	C₈×D₈₉	—	4	4	no	—
125	C₈×D₈₉	—	4	2	no	—
126	C₈×D₈₉	Q₁₆	1	4	yes	complemented
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	—	2	2	no	—
129	C₄⋊Dic₈₉	—	2	2	no	—
130	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
131	#13083553	—	2	1	no	—
132	#13083553	—	2	1	no	—
133	#13083553	—	2	1	no	—
134	#13083553	—	4	2	no	—
135	#13083553	—	4	2	no	—
136	C₄×Dic₈₉	—	2	1	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₈₉	#41	1	1	yes	characteristic
142	C₂×Q₈×C₈₉	—	2	2	no	—
143	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	Q₁₆×C₈₉	—	4	4	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂²×D₈₉	#121	1	1	yes	characteristic
156	Q₈×C₈₉	—	2	2	no	—
157	Q₈×C₈₉	—	4	2	no	—
158	Q₈×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₈₉	—	2	1	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	4	2	no	—
168	C₂×Dic₈₉	#121	1	1	yes	characteristic
169	C₂×Dic₈₉	#121	1	1	yes	characteristic
170	C₂×Dic₈₉	#121	1	1	yes	characteristic
171	C₄×D₈₉	—	2	2	no	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	8	4	no	—
175	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
176	C₄×D₈₉	AGL(1,ℤ/8)	1	4	yes	—
177	C₄×D₈₉	#137	1	2	yes	—
178	Dic₁₇₈	—	2	2	no	—
179	Dic₁₇₈	—	4	2	no	—
180	Dic₁₇₈	—	4	2	no	—
181	Dic₁₇₈	—	4	2	no	—
182	Dic₁₇₈	—	8	4	no	—
183	C₈×C₈₉	—	2	1	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₈×C₈₉	—	4	1	no	—
186	C₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
187	#10623494	—	2	1	no	—
188	#10623494	—	4	2	no	—
189	#10623494	—	4	1	no	—
190	#10623494	C₂×Q₁₆	1	2	yes	complemented
191	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
192	C₂×D₈₉	#462	1	2	yes	—
193	C₂×D₈₉	#469	1	2	yes	—
194	C₂×D₈₉	#473	1	2	yes	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	4	1	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	—	8	2	no	—
199	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
200	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
201	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
202	Dic₈₉	—	2	1	no	—
203	Dic₈₉	—	4	1	no	—
204	Dic₈₉	—	4	1	no	—
205	Dic₈₉	—	8	2	no	—
206	Dic₈₉	#462	1	2	yes	—
207	Dic₈₉	#469	1	2	yes	—
208	C₂×#1694	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	C₂×#462	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#469	1	1	yes	characteristic
211	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
212	D₈₉	#1694	1	4	yes	direct product factor
213	C₂×#500	—	89	1	no	—
214	C₂×#462	—	89	2	no	—
215	C₂×#446	—	89	1	no	—
216	#1694	—	89	1	no	—
217	#1694	—	89	2	no	—
218	#1694	—	89	1	no	—
219	#1694	—	89	1	no	—
220	#1694	—	89	2	no	—
221	#1694	D₈₉	1	1	yes	characteristic, direct product factor
222	C₂×#334	—	89	1	no	—
223	C₂×#332	—	89	2	no	—
224	C₈₉	C₂×#1694	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₁₆	—	178	2	no	—
226	C₂×C₄⋊Q₈	—	89	2	no	—
227	C₂×C₄×Q₈	—	89	1	no	—
228	#500	—	89	2	no	—
229	#500	—	89	1	no	—
230	#500	—	178	1	no	—
231	#500	—	178	1	no	—
232	#500	C₂×D₈₉	1	1	yes	characteristic
233	#462	—	89	2	no	—
234	#462	—	89	2	no	—
235	#462	—	89	2	no	—
236	#462	—	178	2	no	—
237	#462	—	178	2	no	—
238	#462	C₂×D₈₉	1	2	yes	—
239	#446	—	89	1	no	—
240	#446	—	89	1	no	—
241	#446	—	89	1	no	—
242	#446	—	178	1	no	—
243	#446	—	178	1	no	—
244	#446	C₂×D₈₉	1	1	yes	characteristic
245	C₂×#107	—	178	1	no	—
246	C₂×#107	—	178	1	no	—
247	C₂×C₄⋊C₈	—	89	1	no	—
248	C₂×C₄⋊C₈	—	89	2	no	—
249	C₂×C₄⋊C₈	—	178	1	no	—
250	C₂×#103	—	178	2	no	—
251	C₂×#97	—	178	1	no	—
252	C₂×C₄×C₈	—	89	1	no	—
253	#334	—	89	2	no	—
254	#334	—	89	1	no	—
255	#334	C₂×D₈₉	1	1	yes	characteristic
256	#332	—	89	2	no	—
257	#332	—	89	2	no	—
258	#332	—	89	2	no	—
259	#332	C₂×D₈₉	1	2	yes	—
260	C₂²×Q₈	—	89	1	no	—
261	C₂²×Q₈	—	178	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	356	8	no	—
264	C₂×Q₁₆	—	178	2	no	—
265	C₂×Q₁₆	—	178	2	no	—
266	C₂×Q₁₆	—	178	2	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	178	2	no	—
270	C₂²×C₈	—	178	1	no	—
271	C₄⋊Q₈	—	89	2	no	—
272	C₄⋊Q₈	—	178	2	no	—
273	C₄⋊Q₈	—	178	2	no	—
274	C₄⋊Q₈	—	178	2	no	—
275	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
276	C₄×Q₈	—	89	1	no	—
277	C₄×Q₈	—	89	1	no	—
278	C₄×Q₈	—	89	1	no	—
279	C₄×Q₈	—	178	1	no	—
280	C₄×Q₈	—	178	1	no	—
281	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	89	1	no	—
283	C₂×C₄⋊C₄	—	178	2	no	—
284	C₂×C₄⋊C₄	—	178	2	no	—
285	C₂×C₄⋊C₄	—	178	1	no	—
286	C₂×C₄²	—	89	1	no	—
287	C₂×C₄²	—	178	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	1	no	—
290	#107	—	178	2	no	—
291	#107	—	178	2	no	—
292	#107	—	178	1	no	—
293	#107	—	178	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	89	1	no	—
296	C₄⋊C₈	—	89	2	no	—
297	C₄⋊C₈	—	178	1	no	—
298	C₄⋊C₈	—	178	1	no	—
299	C₄⋊C₈	—	178	2	no	—
300	C₄⋊C₈	—	178	1	no	—
301	C₄⋊C₈	—	178	1	no	—
302	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
304	#103	—	2	2	no	—
305	#103	—	178	2	no	—
306	#103	—	178	2	no	—
307	#103	—	178	2	no	—
308	#97	—	2	1	no	—
309	#97	—	178	1	no	—
310	#97	—	178	1	no	—
311	#97	—	178	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	1	no	—
315	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	89	1	no	—
318	C₂×Q₈	—	356	2	no	—
319	C₂×Q₈	—	356	4	no	—
320	C₂×Q₈	—	356	4	no	—
321	C₂×Q₈	—	178	1	no	—
322	C₂×Q₈	—	178	4	no	—
323	C₂×Q₈	—	178	2	no	—
324	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
325	C₂²×C₄	—	89	1	no	—
326	C₂²×C₄	—	89	1	no	—
327	C₂²×C₄	—	89	1	no	—
328	C₂²×C₄	—	356	2	no	—
329	C₂²×C₄	—	178	1	no	—
330	C₂²×C₄	—	178	1	no	—
331	Q₁₆	—	4	4	no	—
332	Q₁₆	—	356	4	no	—
333	Q₁₆	—	356	4	no	—
334	Q₁₆	—	356	4	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	89	1	no	—
338	C₂×C₈	—	89	4	no	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	356	4	no	—
341	C₂×C₈	—	356	2	no	—
342	C₂×C₈	—	178	2	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	—	178	2	no	—
345	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	89	1	no	—
351	C₄⋊C₄	—	356	2	no	—
352	C₄⋊C₄	—	356	2	no	—
353	C₄⋊C₄	—	178	1	no	—
354	C₄⋊C₄	—	178	1	no	—
355	C₄⋊C₄	—	178	1	no	—
356	C₄⋊C₄	—	178	2	no	—
357	C₄⋊C₄	—	178	2	no	—
358	C₄⋊C₄	—	178	1	no	—
359	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
360	C₄²	—	2	1	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	89	1	no	—
364	C₄²	—	178	1	no	—
365	C₄²	—	178	1	no	—
366	C₄²	—	178	1	no	—
367	C₄²	C₂³×D₈₉	1	1	yes	characteristic
368	C₂³	—	89	1	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	356	2	no	—
373	Q₈	—	356	2	no	—
374	Q₈	—	356	2	no	—
375	Q₈	—	178	2	no	—
376	Q₈	—	712	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	2	no	—
383	C₂×C₄	—	89	2	no	—
384	C₂×C₄	—	89	4	no	—
385	C₂×C₄	—	89	1	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	356	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	1	no	—
391	C₂×C₄	—	178	1	no	—
392	C₂×C₄	—	712	4	no	—
393	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	89	2	no	—
400	C₈	—	356	1	no	—
401	C₈	—	356	2	no	—
402	C₈	—	178	1	no	—
403	C₈	Q₁₆×D₈₉	1	2	yes	complemented
404	C₂²	—	89	2	no	—
405	C₂²	—	89	2	no	—
406	C₂²	—	89	2	no	—
407	C₂²	#121×D₈₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	89	2	no	—
413	C₄	—	89	2	no	—
414	C₄	—	356	1	no	—
415	C₄	—	356	1	no	—
416	C₄	—	178	1	no	—
417	C₄	—	712	2	no	—
418	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
419	C₄	AGL(1,ℤ/8)×D₈₉	1	2	yes	—
420	C₄	#137×D₈₉	1	1	yes	characteristic
421	C₂	—	89	4	no	—
422	C₂	#462×D₈₉	1	1	yes	characteristic
423	C₂	#469×D₈₉	1	1	yes	characteristic
424	C₂	#473×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1694	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₈₉	#121
hypercenter	#1694	D₈₉
hypocenter	C₈₉	C₂×#1694
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1694

Complements

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

N	H ≅ G/N	type
4. #26019771	C₂	semidirect
5. #26019770	C₂	semidirect
6. #26019769	C₂	semidirect
7. #26019768	C₂	semidirect
8. #26019767	C₂	semidirect
11. C₈₉×#1694	C₂	semidirect
126. C₈×D₈₉	Q₁₆	semidirect
186. C₈×C₈₉	C₂×Q₁₆	semidirect
190. #10623494	C₂×Q₁₆	semidirect
212. D₈₉	#1694	direct (N × H)
221. #1694	D₈₉	direct (N × H)
224. C₈₉	C₂×#1694	semidirect
403. 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
#500×D₈₉	2
#462×D₈₉	2
#446×D₈₉	2
#26019771	2
#26019770	2
#26019769	2
#26019768	2
#26019767	2
#334×D₈₉	2
#332×D₈₉	2
C₈₉×#1694	2
C₂×#1694	89

Subgroups — #1694×D89 #36537052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1694×D₈₉ #36537052