Subgroups — C₈₉×#60714 #36438562

Order 22784.

2070 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3184	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3176	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3169	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3160	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#493×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3138	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3058	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2948	C₂	1	4	yes	maximal, complemented
10	C₄×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₈×C₈₉	C₂²	1	4	yes	—
12	C₂×#131×C₈₉	C₂²	1	2	yes	—
13	#559×C₈₉	—	2	4	no	—
14	#550×C₈₉	—	2	4	no	—
15	#546×C₈₉	—	2	8	no	—
16	#540×C₈₉	C₂²	1	8	yes	complemented
17	#535×C₈₉	C₂²	1	4	yes	—
18	#533×C₈₉	C₂²	1	2	yes	—
19	#532×C₈₉	C₂²	1	8	yes	complemented
20	C₂×#127×C₈₉	C₂²	1	2	yes	—
21	#518×C₈₉	C₂²	1	4	yes	—
22	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
23	#500×C₈₉	C₂²	1	2	yes	complemented
24	#499×C₈₉	C₂²	1	4	yes	complemented
25	#498×C₈₉	C₂²	1	2	yes	complemented
26	#493×C₈₉	C₂²	1	2	yes	—
27	#493×C₈₉	C₂²	1	4	yes	—
28	#493×C₈₉	C₂²	1	2	yes	—
29	#490×C₈₉	C₂²	1	8	yes	complemented
30	#486×C₈₉	C₂²	1	8	yes	complemented
31	#469×C₈₉	C₂²	1	16	yes	complemented
32	#466×C₈₉	C₂²	1	16	yes	complemented
33	#442×C₈₉	C₂²	1	16	yes	complemented
34	C₄×D₈×C₈₉	C₂²	1	16	yes	complemented
35	#427×C₈₉	C₂²	1	4	yes	—
36	#418×C₈₉	C₂²	1	8	yes	—
37	#405×C₈₉	C₂²	1	2	yes	—
38	#405×C₈₉	C₂²	1	4	yes	complemented
39	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	complemented
43	C₂×#41×C₈₉	—	2	8	no	—
44	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₈₉	—	2	4	no	—
46	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
47	C₂×D₈×C₈₉	—	2	16	no	—
48	C₂×D₈×C₈₉	C₂³	1	8	yes	—
49	C₂×D₈×C₈₉	C₂³	1	8	yes	—
50	#131×C₈₉	—	2	8	no	—
51	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
53	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
54	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
56	#127×C₈₉	—	2	4	no	—
57	#127×C₈₉	—	2	4	no	—
58	#127×C₈₉	C₂³	1	4	yes	—
59	#127×C₈₉	C₂³	1	4	yes	—
60	#125×C₈₉	C₂³	1	4	yes	—
61	#124×C₈₉	—	2	4	no	—
62	#124×C₈₉	—	2	8	no	—
63	#123×C₈₉	—	2	16	no	—
64	C₂²⋊Q₈×C₈₉	—	2	4	no	—
65	#121×C₈₉	—	2	8	no	—
66	#121×C₈₉	—	2	16	no	—
67	#121×C₈₉	C₂³	1	16	yes	—
68	#120×C₈₉	—	2	8	no	—
69	C₄×Q₈×C₈₉	—	2	4	no	—
70	C₄×Q₈×C₈₉	D₄	1	2	yes	—
71	C₄×D₄×C₈₉	—	2	8	no	—
72	C₄×D₄×C₈₉	—	2	8	no	—
73	C₄×D₄×C₈₉	D₄	1	4	yes	—
74	C₄×D₄×C₈₉	D₄	1	2	yes	—
75	C₄×D₄×C₈₉	C₂³	1	16	yes	—
76	#117×C₈₉	C₂³	1	4	yes	—
77	#117×C₈₉	C₂³	1	1	yes	characteristic
78	#117×C₈₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
80	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
82	#107×C₈₉	C₂³	1	8	yes	—
83	#106×C₈₉	C₂³	1	8	yes	—
84	#102×C₈₉	C₂³	1	32	yes	—
85	#97×C₈₉	C₂³	1	2	yes	—
86	#97×C₈₉	C₂³	1	4	yes	—
87	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₈₉	C₂³	1	2	yes	—
90	C₄×C₈×C₈₉	C₂³	1	2	yes	—
91	C₄×C₈×C₈₉	C₂³	1	4	yes	—
92	C₂⁴×C₈₉	—	2	4	no	—
93	#41×C₈₉	—	2	4	no	—
94	#41×C₈₉	—	8	16	no	—
95	C₂×Q₈×C₈₉	—	2	4	no	—
96	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₈₉	—	2	16	no	—
98	C₂×D₄×C₈₉	—	2	4	no	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	8	no	—
101	C₂×D₄×C₈₉	—	2	16	no	—
102	C₂×D₄×C₈₉	—	8	8	no	—
103	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₈₉	—	2	16	no	—
107	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
111	D₈×C₈₉	—	2	16	no	—
112	D₈×C₈₉	—	2	16	no	—
113	M₁₆×C₈₉	—	2	4	no	—
114	M₁₆×C₈₉	—	2	8	no	—
115	C₂×C₈×C₈₉	—	2	8	no	—
116	C₂×C₈×C₈₉	#41	1	8	yes	complemented
117	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
118	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
119	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
120	C₄⋊C₄×C₈₉	—	2	4	no	—
121	C₄⋊C₄×C₈₉	—	2	8	no	—
122	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
124	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
125	C₂²⋊C₄×C₈₉	—	2	4	no	—
126	C₂²⋊C₄×C₈₉	—	2	16	no	—
127	C₂²⋊C₄×C₈₉	—	2	16	no	—
128	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
130	C₄²×C₈₉	—	2	4	no	—
131	C₄²×C₈₉	C₂×D₄	1	4	yes	—
132	C₄²×C₈₉	C₂×D₄	1	2	yes	—
133	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₄²×C₈₉	C₂⁴	1	2	yes	—
135	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₈₉	—	2	8	no	—
137	C₂³×C₈₉	—	4	8	no	—
138	C₂³×C₈₉	—	8	8	no	—
139	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
140	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₈₉	—	2	2	no	—
142	Q₈×C₈₉	—	4	8	no	—
143	D₄×C₈₉	—	2	4	no	—
144	D₄×C₈₉	—	2	2	no	—
145	D₄×C₈₉	—	2	16	no	—
146	D₄×C₈₉	—	4	8	no	—
147	D₄×C₈₉	—	4	16	no	—
148	D₄×C₈₉	—	8	8	no	—
149	D₄×C₈₉	—	8	16	no	—
150	C₂×C₄×C₈₉	—	2	4	no	—
151	C₂×C₄×C₈₉	—	2	8	no	—
152	C₂×C₄×C₈₉	—	2	4	no	—
153	C₂×C₄×C₈₉	—	2	8	no	—
154	C₂×C₄×C₈₉	—	8	16	no	—
155	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
161	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
162	C₈×C₈₉	—	2	4	no	—
163	C₈×C₈₉	C₂×#41	1	4	yes	—
164	C₈×C₈₉	C₂×#41	1	4	yes	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	2	2	no	—
167	C₂²×C₈₉	—	2	4	no	—
168	C₂²×C₈₉	—	4	8	no	—
169	C₂²×C₈₉	—	4	16	no	—
170	C₂²×C₈₉	—	16	8	no	—
171	C₂²×C₈₉	#532	1	2	yes	—
172	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₈₉	—	2	2	no	—
174	C₄×C₈₉	—	2	4	no	—
175	C₄×C₈₉	—	2	2	no	—
176	C₄×C₈₉	—	4	8	no	—
177	C₄×C₈₉	#532	1	2	yes	—
178	C₄×C₈₉	#576	1	4	yes	—
179	C₄×C₈₉	C₂²×#41	1	2	yes	—
180	#60714	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₈₉	—	2	2	no	—
182	C₂×C₈₉	—	4	2	no	—
183	C₂×C₈₉	—	8	8	no	—
184	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
185	C₂×C₈₉	C₂×#576	1	2	yes	—
186	#3508	C₂×C₈₉	1	2	yes	complemented
187	#3184	C₂×C₈₉	1	4	yes	complemented
188	#3176	C₂×C₈₉	1	8	yes	complemented
189	#3169	C₂×C₈₉	1	4	yes	complemented
190	#3160	C₂×C₈₉	1	1	yes	characteristic, complemented
191	C₂×#493	C₂×C₈₉	1	1	yes	characteristic, complemented
192	#3138	C₂×C₈₉	1	2	yes	complemented
193	#3058	C₂×C₈₉	1	4	yes	complemented
194	#2948	C₂×C₈₉	1	4	yes	complemented
195	C₄×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
196	C₈₉	#60714	1	1	yes	characteristic, direct product factor, Sylow
197	C₂²×D₈	C₂²×C₈₉	1	4	yes	—
198	C₂×#131	C₂²×C₈₉	1	2	yes	—
199	#559	—	2	4	no	—
200	#550	—	2	4	no	—
201	#546	—	2	8	no	—
202	#540	C₂²×C₈₉	1	8	yes	complemented
203	#535	C₂²×C₈₉	1	4	yes	—
204	#533	C₂²×C₈₉	1	2	yes	—
205	#532	C₂²×C₈₉	1	8	yes	complemented
206	C₂×#127	C₂²×C₈₉	1	2	yes	—
207	#518	C₂²×C₈₉	1	4	yes	—
208	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
209	#500	C₂²×C₈₉	1	2	yes	complemented
210	#499	C₂²×C₈₉	1	4	yes	complemented
211	#498	C₂²×C₈₉	1	2	yes	complemented
212	#493	C₂²×C₈₉	1	2	yes	—
213	#493	C₂²×C₈₉	1	4	yes	—
214	#493	C₂²×C₈₉	1	2	yes	—
215	#490	C₂²×C₈₉	1	8	yes	complemented
216	#486	C₂²×C₈₉	1	8	yes	complemented
217	#469	C₂²×C₈₉	1	16	yes	complemented
218	#466	C₂²×C₈₉	1	16	yes	complemented
219	#442	C₂²×C₈₉	1	16	yes	complemented
220	C₄×D₈	C₂²×C₈₉	1	16	yes	complemented
221	#427	C₂²×C₈₉	1	4	yes	—
222	#418	C₂²×C₈₉	1	8	yes	—
223	#405	C₂²×C₈₉	1	2	yes	—
224	#405	C₂²×C₈₉	1	4	yes	complemented
225	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
226	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
227	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
229	C₂×#41	—	2	8	no	—
230	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
233	C₂×D₈	—	2	16	no	—
234	C₂×D₈	C₂³×C₈₉	1	8	yes	—
235	C₂×D₈	C₂³×C₈₉	1	8	yes	—
236	#131	—	2	8	no	—
237	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
238	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
239	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
240	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
241	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
242	#127	—	2	4	no	—
243	#127	—	2	4	no	—
244	#127	C₂³×C₈₉	1	4	yes	—
245	#127	C₂³×C₈₉	1	4	yes	—
246	#125	C₂³×C₈₉	1	4	yes	—
247	#124	—	2	4	no	—
248	#124	—	2	8	no	—
249	#123	—	2	16	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	#121	—	2	8	no	—
252	#121	—	2	16	no	—
253	#121	C₂³×C₈₉	1	16	yes	—
254	#120	—	2	8	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	D₄×C₈₉	1	2	yes	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	D₄×C₈₉	1	4	yes	—
260	C₄×D₄	D₄×C₈₉	1	2	yes	—
261	C₄×D₄	C₂³×C₈₉	1	16	yes	—
262	#117	C₂³×C₈₉	1	4	yes	—
263	#117	C₂³×C₈₉	1	1	yes	characteristic
264	#117	C₂³×C₈₉	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	8	no	—
266	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
268	#107	C₂³×C₈₉	1	8	yes	—
269	#106	C₂³×C₈₉	1	8	yes	—
270	#102	C₂³×C₈₉	1	32	yes	—
271	#97	C₂³×C₈₉	1	2	yes	—
272	#97	C₂³×C₈₉	1	4	yes	—
273	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₈₉	1	2	yes	—
276	C₄×C₈	C₂³×C₈₉	1	2	yes	—
277	C₄×C₈	C₂³×C₈₉	1	4	yes	—
278	C₂⁴	—	2	4	no	—
279	#41	—	2	4	no	—
280	#41	—	8	16	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
283	C₂×D₄	—	2	16	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	8	8	no	—
289	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
290	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
291	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
292	C₂²×C₄	—	2	16	no	—
293	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
297	D₈	—	2	16	no	—
298	D₈	—	2	16	no	—
299	M₁₆	—	2	4	no	—
300	M₁₆	—	2	8	no	—
301	C₂×C₈	—	2	8	no	—
302	C₂×C₈	#41×C₈₉	1	8	yes	complemented
303	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
304	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
305	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
309	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
310	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
315	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
316	C₄²	—	2	4	no	—
317	C₄²	C₂×D₄×C₈₉	1	4	yes	—
318	C₄²	C₂×D₄×C₈₉	1	2	yes	—
319	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
320	C₄²	C₂⁴×C₈₉	1	2	yes	—
321	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
322	C₂³	—	2	8	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	8	8	no	—
325	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
326	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
327	Q₈	—	2	2	no	—
328	Q₈	—	4	8	no	—
329	D₄	—	2	4	no	—
330	D₄	—	2	2	no	—
331	D₄	—	2	16	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	16	no	—
334	D₄	—	8	8	no	—
335	D₄	—	8	16	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	8	16	no	—
341	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
343	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
346	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
347	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	C₂×#41×C₈₉	1	4	yes	—
350	C₈	C₂×#41×C₈₉	1	4	yes	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	16	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	16	8	no	—
357	C₂²	#532×C₈₉	1	2	yes	—
358	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	8	no	—
363	C₄	#532×C₈₉	1	2	yes	—
364	C₄	#576×C₈₉	1	4	yes	—
365	C₄	C₂²×#41×C₈₉	1	2	yes	—
366	C₂	—	2	2	no	—
367	C₂	—	4	2	no	—
368	C₂	—	8	8	no	—
369	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
370	C₂	C₂×#576×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3508	C₂	semidirect
2. C₈₉×#3184	C₂	semidirect
3. C₈₉×#3176	C₂	semidirect
4. C₈₉×#3169	C₂	semidirect
5. C₈₉×#3160	C₂	semidirect
6. C₂×#493×C₈₉	C₂	semidirect
7. C₈₉×#3138	C₂	semidirect
8. C₈₉×#3058	C₂	semidirect
9. C₈₉×#2948	C₂	semidirect
10. C₄×#131×C₈₉	C₂	semidirect
16. #540×C₈₉	C₂²	semidirect
19. #532×C₈₉	C₂²	semidirect
23. #500×C₈₉	C₂²	semidirect
24. #499×C₈₉	C₂²	semidirect
25. #498×C₈₉	C₂²	semidirect
29. #490×C₈₉	C₂²	semidirect
30. #486×C₈₉	C₂²	semidirect
31. #469×C₈₉	C₂²	semidirect
32. #466×C₈₉	C₂²	semidirect
33. #442×C₈₉	C₂²	semidirect
34. C₄×D₈×C₈₉	C₂²	semidirect
38. #405×C₈₉	C₂²	semidirect
40. C₄×M₁₆×C₈₉	C₂²	semidirect
42. C₂×C₄×C₈×C₈₉	C₂²	semidirect
116. C₂×C₈×C₈₉	#41	semidirect
180. #60714	C₈₉	direct (N × H)
186. #3508	C₂×C₈₉	semidirect
187. #3184	C₂×C₈₉	semidirect
188. #3176	C₂×C₈₉	semidirect
189. #3169	C₂×C₈₉	semidirect
190. #3160	C₂×C₈₉	semidirect
191. C₂×#493	C₂×C₈₉	semidirect
192. #3138	C₂×C₈₉	semidirect
193. #3058	C₂×C₈₉	semidirect
194. #2948	C₂×C₈₉	semidirect
195. C₄×#131	C₂×C₈₉	semidirect
196. C₈₉	#60714	direct (N × H)
202. #540	C₂²×C₈₉	semidirect
205. #532	C₂²×C₈₉	semidirect
209. #500	C₂²×C₈₉	semidirect
210. #499	C₂²×C₈₉	semidirect
211. #498	C₂²×C₈₉	semidirect
215. #490	C₂²×C₈₉	semidirect
216. #486	C₂²×C₈₉	semidirect
217. #469	C₂²×C₈₉	semidirect
218. #466	C₂²×C₈₉	semidirect
219. #442	C₂²×C₈₉	semidirect
220. C₄×D₈	C₂²×C₈₉	semidirect
224. #405	C₂²×C₈₉	semidirect
226. C₄×M₁₆	C₂²×C₈₉	semidirect
228. C₂×C₄×C₈	C₂²×C₈₉	semidirect
302. C₂×C₈	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3184	2
C₈₉×#3176	2
C₈₉×#3169	2
C₈₉×#3160	2
C₂×#493×C₈₉	2
C₈₉×#3138	2
C₈₉×#3058	2
C₈₉×#2948	2
C₄×#131×C₈₉	2
#60714	89

Subgroups — C89×#60714 #36438562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60714 #36438562