Subgroups — #2178×D₈₉ #36707824

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#443×D₈₉	C₂	1	2	yes	maximal, complemented
3	#26022134	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022133	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022132	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022131	C₂	1	2	yes	maximal, complemented
7	#26022130	C₂	1	2	yes	maximal, complemented
8	#368×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#359×D₈₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₂²	1	2	yes	—
13	#131×D₈₉	—	2	2	no	—
14	#19152031	C₄	1	1	yes	characteristic, complemented
15	#19152030	C₂²	1	1	yes	characteristic
16	#19152029	C₄	1	2	yes	complemented
17	#19152028	C₂²	1	2	yes	—
18	#19152027	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₈₉	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₈₉	C₄	1	2	yes	complemented
21	D₁₆×D₈₉	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
24	#19151716	C₂²	1	2	yes	complemented
25	#19151715	C₂²	1	2	yes	complemented
26	#19151714	C₂²	1	2	yes	complemented
27	#19151713	—	2	2	no	—
28	#19151712	—	2	2	no	—
29	#108×D₈₉	C₂²	1	2	yes	—
30	#104×D₈₉	—	2	2	no	—
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151428	C₂²	1	1	yes	characteristic, complemented
33	#19151427	C₂²	1	2	yes	complemented
34	#19151406	C₂²	1	2	yes	complemented
35	#19151405	C₂²	1	2	yes	complemented
36	#19151404	C₂²	1	2	yes	complemented
37	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
40	#508×C₈₉	C₂²	1	1	yes	characteristic
41	#443×C₈₉	C₂²	1	2	yes	complemented
42	#368×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#359×C₈₉	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#41×D₈₉	—	2	2	no	—
46	#15668035	C₂×C₄	1	2	yes	—
47	#15668034	C₂³	1	2	yes	—
48	#15668033	—	2	2	no	—
49	#15668032	—	2	2	no	—
50	#15668031	C₂×C₄	1	2	yes	—
51	Q₁₆×D₈₉	C₂×C₄	1	2	yes	—
52	SD₁₆×D₈₉	—	2	2	no	—
53	D₈×D₈₉	C₂×C₄	1	2	yes	—
54	#15668020	—	2	2	no	—
55	#15668020	—	4	2	no	—
56	#15668019	—	2	2	no	—
57	#15668018	—	2	2	no	—
58	#15668018	—	4	2	no	—
59	M₁₆×D₈₉	—	2	2	no	—
60	M₁₆×D₈₉	—	4	2	no	—
61	C₂×C₈×D₈₉	—	4	2	no	—
62	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
63	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
64	C₄²×D₈₉	D₄	1	1	yes	characteristic
65	Dic₇₁₂	C₂×C₄	1	1	yes	characteristic, complemented
66	#15667958	C₂×C₄	1	2	yes	complemented
67	#15667957	C₂×C₄	1	2	yes	complemented
68	#15667956	C₂×C₄	1	2	yes	complemented
69	#15667955	C₂×C₄	1	2	yes	complemented
70	D₁₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
71	#15667953	C₂×C₄	1	2	yes	complemented
72	C₂×#13083549	C₂³	1	1	yes	characteristic
73	C₂×#13083549	C₂³	1	1	yes	characteristic
74	C₁₆×D₈₉	—	2	1	no	—
75	C₁₆×D₈₉	—	2	1	no	—
76	C₁₆×D₈₉	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₈₉	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₈₉	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₈₉	C₂×C₄	1	1	yes	characteristic
80	#15667948	C₂³	1	2	yes	—
81	#15667947	—	2	2	no	—
82	#15667940	—	2	2	no	—
83	#15667939	—	2	2	no	—
84	#15667938	—	2	2	no	—
85	C₄×#10623494	D₄	1	1	yes	characteristic
86	C₈×Dic₈₉	D₄	1	1	yes	characteristic
87	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
88	#135×C₈₉	C₂³	1	2	yes	—
89	#131×C₈₉	—	2	2	no	—
90	Q₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₈₉	C₂×C₄	1	2	yes	complemented
92	D₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
95	#108×C₈₉	C₂³	1	2	yes	—
96	#104×C₈₉	—	2	2	no	—
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#13083575	—	2	2	no	—
99	#13083574	—	2	2	no	—
100	#13083574	—	4	2	no	—
101	#13083573	—	2	2	no	—
102	#13083573	—	4	2	no	—
103	Q₈×D₈₉	—	2	2	no	—
104	D₄×D₈₉	—	2	2	no	—
105	D₄×D₈₉	—	4	2	no	—
106	C₂×C₄×D₈₉	—	2	1	no	—
107	C₂×C₄×D₈₉	—	4	2	no	—
108	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
109	Dic₃₅₆	C₂²×C₄	1	2	yes	—
110	#13083564	—	2	2	no	—
111	#13083563	—	2	2	no	—
112	#13083562	—	2	2	no	—
113	#13083561	—	2	2	no	—
114	D₇₁₂	C₂²×C₄	1	2	yes	—
115	#13083559	—	2	2	no	—
116	#13083558	—	2	2	no	—
117	#13083558	—	4	2	no	—
118	#13083557	—	4	2	no	—
119	#13083557	—	4	2	no	—
120	#13083557	—	4	2	no	—
121	C₂×#10623494	—	4	2	no	—
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₈×D₈₉	—	4	2	no	—
125	C₈×D₈₉	—	4	2	no	—
126	C₈×D₈₉	—	4	2	no	—
127	C₈×D₈₉	D₈	1	1	yes	characteristic
128	C₈×D₈₉	D₈	1	1	yes	characteristic
129	C₈×D₈₉	D₈	1	1	yes	characteristic
130	C₈×D₈₉	D₈	1	1	yes	characteristic
131	C₈×D₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₈₉	#41	1	1	yes	characteristic
134	C₈×D₈₉	#41	1	1	yes	characteristic
135	C₄×Dic₈₉	—	2	1	no	—
136	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	#13083549	—	2	1	no	—
138	#13083549	C₂²×C₄	1	1	yes	characteristic
139	#13083549	C₂²×C₄	1	1	yes	characteristic
140	#41×C₈₉	—	2	2	no	—
141	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	—
142	SD₁₆×C₈₉	—	2	2	no	—
143	D₈×C₈₉	C₂²×C₄	1	2	yes	—
144	M₁₆×C₈₉	—	2	2	no	—
145	M₁₆×C₈₉	—	4	2	no	—
146	C₂×C₈×C₈₉	—	4	2	no	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₈₉	—	2	1	no	—
151	C₁₆×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₁₆×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×D₈₉	—	4	2	no	—
154	C₂²×D₈₉	#135	1	1	yes	characteristic
155	Q₈×C₈₉	—	2	2	no	—
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₈₉	—	4	2	no	—
162	C₂²⋊D₈₉	—	4	2	no	—
163	C₂²⋊D₈₉	—	4	2	no	—
164	C₂×Dic₈₉	—	2	1	no	—
165	C₂×Dic₈₉	—	4	2	no	—
166	C₂×Dic₈₉	#135	1	1	yes	characteristic
167	D₃₅₆	—	2	2	no	—
168	D₃₅₆	—	4	2	no	—
169	C₄×D₈₉	—	2	4	no	—
170	C₄×D₈₉	—	4	2	no	—
171	C₄×D₈₉	—	4	2	no	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
174	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
175	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
176	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	—	4	2	no	—
179	C₈×C₈₉	—	4	2	no	—
180	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
181	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
182	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
184	#10623494	—	4	2	no	—
185	#10623494	C₄×D₄	1	1	yes	characteristic
186	#10623494	C₄×D₄	1	1	yes	characteristic
187	#10623494	C₂×D₈	1	1	yes	characteristic
188	#10623494	C₂×D₈	1	1	yes	characteristic
189	C₂²×C₈₉	—	4	2	no	—
190	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
191	C₂×D₈₉	—	2	2	no	—
192	C₂×D₈₉	—	4	2	no	—
193	C₂×D₈₉	—	8	4	no	—
194	C₂×D₈₉	C₄×D₈	1	1	yes	characteristic
195	C₂×D₈₉	C₄×D₈	1	1	yes	characteristic
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
200	Dic₈₉	—	2	2	no	—
201	Dic₈₉	—	4	2	no	—
202	Dic₈₉	C₄×D₈	1	1	yes	characteristic
203	Dic₈₉	C₄×D₈	1	1	yes	characteristic
204	C₂×#2178	—	89	1	no	maximal, Sylow
205	C₂×C₈₉	—	2	1	no	—
206	C₂×C₈₉	—	8	2	no	—
207	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
208	D₈₉	—	2	1	no	—
209	D₈₉	—	8	2	no	—
210	D₈₉	#2178	1	2	yes	direct product factor
211	C₂×#508	—	89	1	no	—
212	C₂×#443	—	89	2	no	—
213	#2178	—	89	1	no	—
214	#2178	—	89	2	no	—
215	#2178	—	89	1	no	—
216	#2178	—	89	2	no	—
217	#2178	—	89	1	no	—
218	#2178	D₈₉	1	1	yes	characteristic, direct product factor
219	C₂×#368	—	89	1	no	—
220	C₂×#359	—	89	2	no	—
221	C₂×C₄×C₁₆	—	89	1	no	—
222	C₈₉	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	89	2	no	—
224	C₂×#131	—	178	2	no	—
225	#508	—	89	2	no	—
226	#508	—	89	1	no	—
227	#508	—	89	2	no	—
228	#508	—	89	1	no	—
229	#508	—	89	1	no	—
230	#508	C₂×D₈₉	1	1	yes	characteristic
231	C₂×Q₃₂	—	89	1	no	—
232	C₂×SD₃₂	—	89	2	no	—
233	C₂×D₁₆	—	89	1	no	—
234	C₂²×C₁₆	—	89	1	no	—
235	C₂²×C₁₆	—	89	1	no	—
236	#443	—	89	2	no	—
237	#443	—	89	2	no	—
238	#443	—	89	2	no	—
239	#443	—	178	2	no	—
240	#443	—	178	2	no	—
241	#443	C₂×D₈₉	1	2	yes	complemented
242	C₂×#108	—	89	2	no	—
243	C₂×#104	—	178	2	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	#368	—	89	1	no	—
246	#368	—	89	2	no	—
247	#368	C₂×D₈₉	1	1	yes	characteristic, complemented
248	#359	—	89	2	no	—
249	#359	—	89	2	no	—
250	#359	—	89	2	no	—
251	#359	C₂×D₈₉	1	2	yes	complemented
252	C₄×C₁₆	—	89	1	no	—
253	C₄×C₁₆	—	89	1	no	—
254	C₄×C₁₆	—	89	1	no	—
255	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
256	C₂×#41	—	178	2	no	—
257	#135	—	89	2	no	—
258	#135	—	89	2	no	—
259	#135	—	89	2	no	—
260	#135	—	178	2	no	—
261	#135	—	178	2	no	—
262	#135	C₂²×D₈₉	1	2	yes	—
263	C₂×Q₁₆	—	89	2	no	—
264	C₂×SD₁₆	—	178	2	no	—
265	C₂×D₈	—	89	2	no	—
266	#131	—	2	2	no	—
267	#131	—	356	2	no	—
268	#131	—	356	2	no	—
269	#131	—	178	2	no	—
270	#131	—	178	2	no	—
271	#131	—	178	2	no	—
272	C₂×M₁₆	—	356	2	no	—
273	C₂×M₁₆	—	178	2	no	—
274	C₂²×C₈	—	89	1	no	—
275	C₂²×C₈	—	89	1	no	—
276	C₂²×C₈	—	356	2	no	—
277	C₂×C₄²	—	89	1	no	—
278	Q₃₂	—	89	2	no	—
279	Q₃₂	—	89	1	no	—
280	Q₃₂	C₄×D₈₉	1	1	yes	characteristic, complemented
281	SD₃₂	—	89	2	no	—
282	SD₃₂	—	89	2	no	—
283	SD₃₂	—	89	2	no	—
284	SD₃₂	C₄×D₈₉	1	2	yes	complemented
285	D₁₆	—	89	2	no	—
286	D₁₆	—	89	1	no	—
287	D₁₆	C₄×D₈₉	1	1	yes	characteristic, complemented
288	C₂×C₁₆	—	89	1	no	—
289	C₂×C₁₆	—	89	1	no	—
290	C₂×C₁₆	—	89	1	no	—
291	C₂×C₁₆	—	89	1	no	—
292	C₂×C₁₆	—	89	1	no	—
293	C₂×C₁₆	—	89	1	no	—
294	C₂×C₁₆	—	178	1	no	—
295	C₂×C₁₆	—	178	1	no	—
296	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
298	#108	—	89	2	no	—
299	#108	—	178	2	no	—
300	#108	C₂²×D₈₉	1	2	yes	—
301	#104	—	2	2	no	—
302	#104	—	178	2	no	—
303	#104	—	178	2	no	—
304	#104	—	178	2	no	—
305	C₄×C₈	—	89	1	no	—
306	C₄×C₈	—	89	1	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#41	—	2	2	no	—
310	#41	—	356	2	no	—
311	#41	—	356	2	no	—
312	#41	—	178	2	no	—
313	#41	—	178	2	no	—
314	#41	—	178	2	no	—
315	C₂×Q₈	—	178	2	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	356	2	no	—
320	C₂²×C₄	—	178	1	no	—
321	Q₁₆	—	89	2	no	—
322	Q₁₆	—	178	2	no	—
323	Q₁₆	C₂×C₄×D₈₉	1	2	yes	—
324	SD₁₆	—	2	2	no	—
325	SD₁₆	—	178	2	no	—
326	SD₁₆	—	178	2	no	—
327	SD₁₆	—	178	2	no	—
328	D₈	—	89	2	no	—
329	D₈	—	178	2	no	—
330	D₈	C₂×C₄×D₈₉	1	2	yes	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	—	356	2	no	—
334	M₁₆	—	356	2	no	—
335	M₁₆	—	356	2	no	—
336	M₁₆	—	356	2	no	—
337	M₁₆	—	178	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	89	1	no	—
341	C₂×C₈	—	89	1	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	89	1	no	—
344	C₂×C₈	—	89	1	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	1	no	—
347	C₂×C₈	—	89	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	356	2	no	—
350	C₂×C₈	—	356	2	no	—
351	C₂×C₈	—	356	2	no	—
352	C₂×C₈	—	356	2	no	—
353	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
355	C₄²	—	89	1	no	—
356	C₄²	—	178	1	no	—
357	C₄²	D₄×D₈₉	1	1	yes	characteristic
358	C₁₆	—	2	1	no	—
359	C₁₆	—	89	1	no	—
360	C₁₆	—	89	1	no	—
361	C₁₆	—	178	1	no	—
362	C₁₆	C₂×C₄×D₈₉	1	1	yes	characteristic
363	C₁₆	C₂×C₄×D₈₉	1	1	yes	characteristic
364	C₂³	—	89	1	no	—
365	C₂³	—	356	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	356	2	no	—
368	Q₈	—	178	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	356	2	no	—
372	D₄	—	356	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	178	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	89	1	no	—
379	C₂×C₄	—	89	1	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	178	4	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	89	1	no	—
392	C₈	—	89	1	no	—
393	C₈	—	89	1	no	—
394	C₈	—	89	1	no	—
395	C₈	—	356	2	no	—
396	C₈	D₈×D₈₉	1	1	yes	characteristic
397	C₈	D₈×D₈₉	1	1	yes	characteristic
398	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
399	C₈	#41×D₈₉	1	1	yes	characteristic
400	C₂²	—	4	2	no	—
401	C₂²	—	89	1	no	—
402	C₂²	—	89	1	no	—
403	C₂²	—	356	2	no	—
404	C₂²	—	178	2	no	—
405	C₂²	—	712	4	no	—
406	C₂²	#135×D₈₉	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	89	1	no	—
410	C₄	—	89	1	no	—
411	C₄	—	356	2	no	—
412	C₄	—	178	2	no	—
413	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
414	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	—	89	2	no	—
418	C₂	—	178	1	no	—
419	C₂	—	712	2	no	—
420	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2178	C₂
socle	C₂×C₈₉	C₂×C₄×D₈
prime radical	#508×D₈₉	C₂
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2178	D₈₉
hypocenter	C₈₉	C₂×#2178
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #443×D₈₉	C₂	semidirect
3. #26022134	C₂	semidirect
4. #26022133	C₂	semidirect
5. #26022132	C₂	semidirect
6. #26022131	C₂	semidirect
7. #26022130	C₂	semidirect
8. #368×D₈₉	C₂	semidirect
9. #359×D₈₉	C₂	semidirect
10. C₄×C₁₆×D₈₉	C₂	semidirect
11. C₈₉×#2178	C₂	semidirect
14. #19152031	C₄	semidirect
16. #19152029	C₄	semidirect
18. #19152027	C₄	semidirect
19. Q₃₂×D₈₉	C₄	semidirect
20. SD₃₂×D₈₉	C₄	semidirect
21. D₁₆×D₈₉	C₄	semidirect
24. #19151716	C₂²	semidirect
25. #19151715	C₂²	semidirect
26. #19151714	C₂²	semidirect
32. #19151428	C₂²	semidirect
33. #19151427	C₂²	semidirect
34. #19151406	C₂²	semidirect
35. #19151405	C₂²	semidirect
36. #19151404	C₂²	semidirect
37. C₄×#13083549	C₂²	semidirect
38. C₁₆×Dic₈₉	C₂²	semidirect
39. C₁₆×Dic₈₉	C₂²	semidirect
41. #443×C₈₉	C₂²	semidirect
42. #368×C₈₉	C₂²	semidirect
43. #359×C₈₉	C₂²	semidirect
44. C₄×C₁₆×C₈₉	C₂²	semidirect
65. Dic₇₁₂	C₂×C₄	semidirect
66. #15667958	C₂×C₄	semidirect
67. #15667957	C₂×C₄	semidirect
68. #15667956	C₂×C₄	semidirect
69. #15667955	C₂×C₄	semidirect
70. D₁₄₂₄	C₂×C₄	semidirect
71. #15667953	C₂×C₄	semidirect
90. Q₃₂×C₈₉	C₂×C₄	semidirect
91. SD₃₂×C₈₉	C₂×C₄	semidirect
92. D₁₆×C₈₉	C₂×C₄	semidirect
210. D₈₉	#2178	direct (N × H)
218. #2178	D₈₉	direct (N × H)
222. C₈₉	C₂×#2178	semidirect
241. #443	C₂×D₈₉	semidirect
247. #368	C₂×D₈₉	semidirect
251. #359	C₂×D₈₉	semidirect
255. C₄×C₁₆	C₂×D₈₉	semidirect
280. Q₃₂	C₄×D₈₉	semidirect
284. SD₃₂	C₄×D₈₉	semidirect
287. D₁₆	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#508×D₈₉	2
#443×D₈₉	2
#26022134	2
#26022133	2
#26022132	2
#26022131	2
#26022130	2
#368×D₈₉	2
#359×D₈₉	2
C₄×C₁₆×D₈₉	2
C₈₉×#2178	2
C₂×#2178	89

Subgroups — #2178×D89 #36707824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2178×D₈₉ #36707824