Subgroups — C₈₉×#60696 #36438544

Order 22784.

1850 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3461	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3178	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3177	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3175	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3172	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3170	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3137	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3063	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3061	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
23	#544×C₈₉	C₂²	1	2	yes	—
24	#542×C₈₉	—	2	2	no	—
25	#542×C₈₉	C₂²	1	4	yes	—
26	#541×C₈₉	—	2	2	no	—
27	#541×C₈₉	C₂²	1	4	yes	—
28	#539×C₈₉	—	2	4	no	—
29	#537×C₈₉	C₂²	1	2	yes	—
30	#536×C₈₉	C₂²	1	2	yes	—
31	#536×C₈₉	C₂²	1	2	yes	—
32	#533×C₈₉	—	2	2	no	—
33	#533×C₈₉	C₂²	1	4	yes	—
34	#529×C₈₉	—	2	4	no	—
35	#529×C₈₉	—	2	2	no	—
36	#529×C₈₉	C₂²	1	4	yes	—
37	C₄×#41×C₈₉	C₂²	1	2	yes	—
38	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
40	#501×C₈₉	C₂²	1	4	yes	—
41	#500×C₈₉	C₂²	1	2	yes	—
42	#499×C₈₉	C₂²	1	2	yes	—
43	#497×C₈₉	C₂²	1	4	yes	—
44	#495×C₈₉	C₂²	1	2	yes	—
45	#494×C₈₉	C₂²	1	2	yes	—
46	#491×C₈₉	C₂²	1	4	yes	—
47	#489×C₈₉	C₂²	1	4	yes	—
48	#488×C₈₉	C₂²	1	4	yes	—
49	#487×C₈₉	C₂²	1	4	yes	—
50	#470×C₈₉	C₂²	1	4	yes	—
51	#470×C₈₉	C₂²	1	4	yes	—
52	#468×C₈₉	C₂²	1	4	yes	—
53	#468×C₈₉	C₂²	1	4	yes	—
54	#467×C₈₉	C₂²	1	4	yes	—
55	#467×C₈₉	C₂²	1	2	yes	—
56	#467×C₈₉	C₂²	1	2	yes	—
57	#467×C₈₉	C₂²	1	2	yes	—
58	#466×C₈₉	C₂²	1	2	yes	—
59	#465×C₈₉	C₂²	1	4	yes	—
60	#441×C₈₉	C₂²	1	4	yes	—
61	#440×C₈₉	C₂²	1	4	yes	—
62	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
63	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
65	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
66	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
67	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
69	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
72	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
73	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
74	#428×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
77	#419×C₈₉	C₂²	1	2	yes	—
78	#417×C₈₉	C₂²	1	2	yes	—
79	#416×C₈₉	C₂²	1	2	yes	—
80	C₂×#103×C₈₉	C₂²	1	2	yes	—
81	#405×C₈₉	C₂²	1	1	yes	characteristic
82	#405×C₈₉	C₂²	1	1	yes	characteristic
83	#405×C₈₉	C₂²	1	2	yes	—
84	#405×C₈₉	C₂²	1	2	yes	—
85	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
86	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
87	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
92	#137×C₈₉	—	2	8	no	—
93	#135×C₈₉	—	2	4	no	—
94	C₂×Q₁₆×C₈₉	—	2	4	no	—
95	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
102	#131×C₈₉	—	2	4	no	—
103	#131×C₈₉	—	2	4	no	—
104	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	—	2	2	no	—
113	C₄⋊Q₈×C₈₉	—	2	2	no	—
114	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
116	#126×C₈₉	—	2	4	no	—
117	#126×C₈₉	—	2	4	no	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	4	no	—
120	#125×C₈₉	—	2	4	no	—
121	#125×C₈₉	—	2	2	no	—
122	#125×C₈₉	—	2	4	no	—
123	#125×C₈₉	—	2	4	no	—
124	#125×C₈₉	C₂³	1	4	yes	—
125	#124×C₈₉	—	2	2	no	—
126	#124×C₈₉	—	2	4	no	—
127	#124×C₈₉	C₂³	1	4	yes	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	4	no	—
130	#123×C₈₉	—	2	4	no	—
131	#123×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	2	no	—
133	C₂²⋊Q₈×C₈₉	—	2	4	no	—
134	C₂²⋊Q₈×C₈₉	—	2	2	no	—
135	C₂²⋊Q₈×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	—	2	4	no	—
138	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
139	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	—	2	2	no	—
143	#121×C₈₉	C₂³	1	4	yes	—
144	C₄×Q₈×C₈₉	—	2	2	no	—
145	C₄×Q₈×C₈₉	—	2	2	no	—
146	C₄×Q₈×C₈₉	—	2	4	no	—
147	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
149	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
150	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
151	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
152	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	2	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
157	C₄×D₄×C₈₉	D₄	1	2	yes	—
158	C₄×D₄×C₈₉	D₄	1	2	yes	—
159	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
160	C₄×D₄×C₈₉	C₂³	1	2	yes	—
161	C₄×D₄×C₈₉	C₂³	1	2	yes	—
162	#117×C₈₉	—	2	4	no	—
163	#117×C₈₉	—	2	2	no	—
164	#117×C₈₉	—	2	4	no	—
165	#117×C₈₉	C₂³	1	2	yes	—
166	#117×C₈₉	C₂³	1	1	yes	characteristic
167	#117×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₈₉	—	2	2	no	—
171	C₂×C₄²×C₈₉	—	2	2	no	—
172	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
174	#107×C₈₉	C₂³	1	2	yes	—
175	#107×C₈₉	C₂³	1	2	yes	—
176	#107×C₈₉	C₂³	1	1	yes	characteristic
177	#107×C₈₉	C₂³	1	1	yes	characteristic
178	#107×C₈₉	C₂³	1	4	yes	—
179	#106×C₈₉	C₂³	1	2	yes	—
180	#106×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	4	yes	—
182	#103×C₈₉	C₂³	1	4	yes	—
183	#103×C₈₉	C₂³	1	2	yes	—
184	#103×C₈₉	C₂³	1	2	yes	—
185	#103×C₈₉	C₂³	1	4	yes	—
186	#103×C₈₉	C₂³	1	4	yes	—
187	#103×C₈₉	C₂³	1	4	yes	—
188	#102×C₈₉	C₂³	1	2	yes	—
189	#102×C₈₉	C₂³	1	2	yes	—
190	#102×C₈₉	C₂³	1	4	yes	—
191	#97×C₈₉	C₂³	1	2	yes	—
192	#97×C₈₉	C₂³	1	2	yes	—
193	#97×C₈₉	C₂³	1	2	yes	—
194	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₈₉	C₂³	1	2	yes	—
196	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₈₉	C₂³	1	2	yes	—
200	C₄×C₈×C₈₉	C₂³	1	2	yes	—
201	#41×C₈₉	—	2	2	no	—
202	#41×C₈₉	—	2	2	no	—
203	#41×C₈₉	—	2	4	no	—
204	#41×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	—	2	2	no	—
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	—	2	4	no	—
208	C₂×Q₈×C₈₉	—	2	4	no	—
209	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
211	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₈₉	—	2	4	no	—
229	Q₁₆×C₈₉	—	2	4	no	—
230	Q₁₆×C₈₉	—	2	2	no	—
231	Q₁₆×C₈₉	—	2	8	no	—
232	SD₁₆×C₈₉	—	2	4	no	—
233	SD₁₆×C₈₉	—	2	8	no	—
234	D₈×C₈₉	—	2	2	no	—
235	M₁₆×C₈₉	—	2	2	no	—
236	M₁₆×C₈₉	—	2	4	no	—
237	M₁₆×C₈₉	—	2	4	no	—
238	M₁₆×C₈₉	#41	1	4	yes	—
239	C₂×C₈×C₈₉	—	2	2	no	—
240	C₂×C₈×C₈₉	—	2	4	no	—
241	C₂×C₈×C₈₉	—	2	4	no	—
242	C₂×C₈×C₈₉	#41	1	4	yes	—
243	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
246	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	—	2	2	no	—
253	C₄⋊C₄×C₈₉	—	2	2	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	2	4	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	4	no	—
271	C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	2	no	—
274	C₂²⋊C₄×C₈₉	—	2	2	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
281	C₄²×C₈₉	—	2	2	no	—
282	C₄²×C₈₉	—	2	2	no	—
283	C₄²×C₈₉	—	2	4	no	—
284	C₄²×C₈₉	—	2	4	no	—
285	C₄²×C₈₉	—	2	2	no	—
286	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₈₉	C₂×D₄	1	2	yes	—
288	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₈₉	C₂×D₄	1	2	yes	—
290	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₄²×C₈₉	C₂⁴	1	2	yes	—
292	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₂³×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
295	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₈₉	—	2	2	no	—
297	Q₈×C₈₉	—	2	4	no	—
298	Q₈×C₈₉	—	2	2	no	—
299	Q₈×C₈₉	—	2	4	no	—
300	Q₈×C₈₉	—	2	2	no	—
301	Q₈×C₈₉	—	4	4	no	—
302	Q₈×C₈₉	—	8	4	no	—
303	D₄×C₈₉	—	2	4	no	—
304	D₄×C₈₉	—	2	2	no	—
305	D₄×C₈₉	—	2	2	no	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	4	4	no	—
308	D₄×C₈₉	—	8	4	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	4	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	4	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	2	no	—
320	C₂×C₄×C₈₉	—	4	4	no	—
321	C₂×C₄×C₈₉	—	4	4	no	—
322	C₂×C₄×C₈₉	—	4	4	no	—
323	C₂×C₄×C₈₉	—	8	2	no	—
324	C₂×C₄×C₈₉	—	8	2	no	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
334	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
335	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
336	C₈×C₈₉	—	2	1	no	—
337	C₈×C₈₉	—	2	1	no	—
338	C₈×C₈₉	—	2	2	no	—
339	C₈×C₈₉	C₂×#41	1	2	yes	—
340	C₈×C₈₉	C₂×#41	1	4	yes	—
341	C₈×C₈₉	C₂×#41	1	2	yes	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	1	no	—
344	C₂²×C₈₉	—	2	2	no	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	—	4	2	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	#532	1	2	yes	—
351	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₈₉	—	2	1	no	—
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	2	no	—
355	C₄×C₈₉	—	2	2	no	—
356	C₄×C₈₉	—	2	1	no	—
357	C₄×C₈₉	—	2	2	no	—
358	C₄×C₈₉	—	4	4	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	2	no	—
361	C₄×C₈₉	—	4	4	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	#532	1	2	yes	—
364	C₄×C₈₉	#578	1	2	yes	—
365	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
366	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
367	#60696	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂×C₈₉	—	2	2	no	—
369	C₂×C₈₉	—	4	2	no	—
370	C₂×C₈₉	—	8	2	no	—
371	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
372	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
373	C₂×C₈₉	#3584	1	1	yes	characteristic
374	#3461	C₂×C₈₉	1	2	yes	complemented
375	#3178	C₂×C₈₉	1	4	yes	complemented
376	#3177	C₂×C₈₉	1	2	yes	complemented
377	#3175	C₂×C₈₉	1	2	yes	complemented
378	#3172	C₂×C₈₉	1	4	yes	complemented
379	#3170	C₂×C₈₉	1	2	yes	complemented
380	#3168	C₂×C₈₉	1	2	yes	complemented
381	#3164	C₂×C₈₉	1	1	yes	characteristic, complemented
382	#3156	C₂×C₈₉	1	1	yes	characteristic, complemented
383	#3137	C₂×C₈₉	1	2	yes	complemented
384	#3063	C₂×C₈₉	1	2	yes	complemented
385	#3061	C₂×C₈₉	1	1	yes	characteristic
386	#3059	C₂×C₈₉	1	1	yes	characteristic, complemented
387	C₄×#137	C₂×C₈₉	1	2	yes	complemented
388	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
389	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₄×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₈₉	#60696	1	1	yes	characteristic, direct product factor, Sylow
392	C₂×#137	C₂²×C₈₉	1	2	yes	—
393	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
394	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
396	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
397	#544	C₂²×C₈₉	1	2	yes	—
398	#542	—	2	2	no	—
399	#542	C₂²×C₈₉	1	4	yes	—
400	#541	—	2	2	no	—
401	#541	C₂²×C₈₉	1	4	yes	—
402	#539	—	2	4	no	—
403	#537	C₂²×C₈₉	1	2	yes	—
404	#536	C₂²×C₈₉	1	2	yes	—
405	#536	C₂²×C₈₉	1	2	yes	—
406	#533	—	2	2	no	—
407	#533	C₂²×C₈₉	1	4	yes	—
408	#529	—	2	4	no	—
409	#529	—	2	2	no	—
410	#529	C₂²×C₈₉	1	4	yes	—
411	C₄×#41	C₂²×C₈₉	1	2	yes	—
412	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
414	#501	C₂²×C₈₉	1	4	yes	—
415	#500	C₂²×C₈₉	1	2	yes	—
416	#499	C₂²×C₈₉	1	2	yes	—
417	#497	C₂²×C₈₉	1	4	yes	—
418	#495	C₂²×C₈₉	1	2	yes	—
419	#494	C₂²×C₈₉	1	2	yes	—
420	#491	C₂²×C₈₉	1	4	yes	—
421	#489	C₂²×C₈₉	1	4	yes	—
422	#488	C₂²×C₈₉	1	4	yes	—
423	#487	C₂²×C₈₉	1	4	yes	—
424	#470	C₂²×C₈₉	1	4	yes	—
425	#470	C₂²×C₈₉	1	4	yes	—
426	#468	C₂²×C₈₉	1	4	yes	—
427	#468	C₂²×C₈₉	1	4	yes	—
428	#467	C₂²×C₈₉	1	2	yes	—
429	#467	C₂²×C₈₉	1	2	yes	—
430	#467	C₂²×C₈₉	1	2	yes	—
431	#467	C₂²×C₈₉	1	4	yes	—
432	#466	C₂²×C₈₉	1	2	yes	—
433	#465	C₂²×C₈₉	1	4	yes	—
434	#441	C₂²×C₈₉	1	4	yes	—
435	#440	C₂²×C₈₉	1	4	yes	—
436	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
437	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
438	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
439	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
440	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
441	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
442	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
443	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
444	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
445	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
446	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
447	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
448	#428	C₂²×C₈₉	1	2	yes	—
449	#427	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
451	#419	C₂²×C₈₉	1	2	yes	—
452	#417	C₂²×C₈₉	1	2	yes	—
453	#416	C₂²×C₈₉	1	2	yes	—
454	C₂×#103	C₂²×C₈₉	1	2	yes	—
455	#405	C₂²×C₈₉	1	1	yes	characteristic
456	#405	C₂²×C₈₉	1	1	yes	characteristic
457	#405	C₂²×C₈₉	1	2	yes	—
458	#405	C₂²×C₈₉	1	2	yes	—
459	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
460	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
462	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#41	C₂³×C₈₉	1	2	yes	—
464	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
466	#137	—	2	8	no	—
467	#135	—	2	4	no	—
468	C₂×Q₁₆	—	2	4	no	—
469	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
470	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
471	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
472	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
473	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
475	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
476	#131	—	2	4	no	—
477	#131	—	2	4	no	—
478	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
480	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
481	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
484	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
485	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
489	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
490	#126	—	2	4	no	—
491	#126	—	2	4	no	—
492	#126	—	2	4	no	—
493	#126	—	2	4	no	—
494	#125	—	2	4	no	—
495	#125	—	2	2	no	—
496	#125	—	2	4	no	—
497	#125	—	2	4	no	—
498	#125	C₂³×C₈₉	1	4	yes	—
499	#124	—	2	2	no	—
500	#124	—	2	4	no	—
501	#124	C₂³×C₈₉	1	4	yes	—
502	#123	—	2	4	no	—
503	#123	—	2	4	no	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
513	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
514	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
515	#121	—	2	4	no	—
516	#121	—	2	2	no	—
517	#121	C₂³×C₈₉	1	4	yes	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
522	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
523	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
524	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
525	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
526	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
531	C₄×D₄	D₄×C₈₉	1	2	yes	—
532	C₄×D₄	D₄×C₈₉	1	2	yes	—
533	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
534	C₄×D₄	C₂³×C₈₉	1	2	yes	—
535	C₄×D₄	C₂³×C₈₉	1	2	yes	—
536	#117	—	2	4	no	—
537	#117	—	2	2	no	—
538	#117	—	2	4	no	—
539	#117	C₂³×C₈₉	1	2	yes	—
540	#117	C₂³×C₈₉	1	1	yes	characteristic
541	#117	C₂³×C₈₉	1	2	yes	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₄²	—	2	2	no	—
545	C₂×C₄²	—	2	2	no	—
546	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
548	#107	C₂³×C₈₉	1	2	yes	—
549	#107	C₂³×C₈₉	1	2	yes	—
550	#107	C₂³×C₈₉	1	1	yes	characteristic
551	#107	C₂³×C₈₉	1	1	yes	characteristic
552	#107	C₂³×C₈₉	1	4	yes	—
553	#106	C₂³×C₈₉	1	2	yes	—
554	#106	C₂³×C₈₉	1	4	yes	—
555	#103	C₂³×C₈₉	1	4	yes	—
556	#103	C₂³×C₈₉	1	4	yes	—
557	#103	C₂³×C₈₉	1	2	yes	—
558	#103	C₂³×C₈₉	1	2	yes	—
559	#103	C₂³×C₈₉	1	4	yes	—
560	#103	C₂³×C₈₉	1	4	yes	—
561	#103	C₂³×C₈₉	1	4	yes	—
562	#102	C₂³×C₈₉	1	2	yes	—
563	#102	C₂³×C₈₉	1	2	yes	—
564	#102	C₂³×C₈₉	1	4	yes	—
565	#97	C₂³×C₈₉	1	2	yes	—
566	#97	C₂³×C₈₉	1	2	yes	—
567	#97	C₂³×C₈₉	1	2	yes	—
568	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₈₉	1	2	yes	—
570	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₈₉	1	2	yes	—
574	C₄×C₈	C₂³×C₈₉	1	2	yes	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	4	no	—
578	#41	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
584	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
585	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
589	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
602	Q₁₆	—	2	4	no	—
603	Q₁₆	—	2	4	no	—
604	Q₁₆	—	2	2	no	—
605	Q₁₆	—	2	8	no	—
606	SD₁₆	—	2	4	no	—
607	SD₁₆	—	2	8	no	—
608	D₈	—	2	2	no	—
609	M₁₆	—	2	2	no	—
610	M₁₆	—	2	4	no	—
611	M₁₆	—	2	4	no	—
612	M₁₆	#41×C₈₉	1	4	yes	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	4	no	—
615	C₂×C₈	—	2	4	no	—
616	C₂×C₈	#41×C₈₉	1	4	yes	—
617	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
620	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
622	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
642	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
662	C₄²	C₂×D₄×C₈₉	1	2	yes	—
663	C₄²	C₂×D₄×C₈₉	1	2	yes	—
664	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
665	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
666	C₄²	C₂⁴×C₈₉	1	2	yes	—
667	C₂³	—	2	2	no	—
668	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
669	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	8	4	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	8	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
709	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	1	no	—
712	C₈	—	2	2	no	—
713	C₈	C₂×#41×C₈₉	1	2	yes	—
714	C₈	C₂×#41×C₈₉	1	4	yes	—
715	C₈	C₂×#41×C₈₉	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	#532×C₈₉	1	2	yes	—
725	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	4	no	—
737	C₄	#532×C₈₉	1	2	yes	—
738	C₄	#578×C₈₉	1	2	yes	—
739	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
740	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
741	C₂	—	2	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
745	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
746	C₂	C₈₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
prime radical	C₈₉×#3061	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3461	C₂	semidirect
2. C₈₉×#3178	C₂	semidirect
3. C₈₉×#3177	C₂	semidirect
4. C₈₉×#3175	C₂	semidirect
5. C₈₉×#3172	C₂	semidirect
6. C₈₉×#3170	C₂	semidirect
7. C₈₉×#3168	C₂	semidirect
8. C₈₉×#3164	C₂	semidirect
9. C₈₉×#3156	C₂	semidirect
10. C₈₉×#3137	C₂	semidirect
11. C₈₉×#3063	C₂	semidirect
13. C₈₉×#3059	C₂	semidirect
14. C₄×#137×C₈₉	C₂	semidirect
15. C₄×#135×C₈₉	C₂	semidirect
16. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
17. C₄×#131×C₈₉	C₂	semidirect
367. #60696	C₈₉	direct (N × H)
374. #3461	C₂×C₈₉	semidirect
375. #3178	C₂×C₈₉	semidirect
376. #3177	C₂×C₈₉	semidirect
377. #3175	C₂×C₈₉	semidirect
378. #3172	C₂×C₈₉	semidirect
379. #3170	C₂×C₈₉	semidirect
380. #3168	C₂×C₈₉	semidirect
381. #3164	C₂×C₈₉	semidirect
382. #3156	C₂×C₈₉	semidirect
383. #3137	C₂×C₈₉	semidirect
384. #3063	C₂×C₈₉	semidirect
386. #3059	C₂×C₈₉	semidirect
387. C₄×#137	C₂×C₈₉	semidirect
388. C₄×#135	C₂×C₈₉	semidirect
389. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
390. C₄×#131	C₂×C₈₉	semidirect
391. C₈₉	#60696	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3461	2
C₈₉×#3178	2
C₈₉×#3177	2
C₈₉×#3175	2
C₈₉×#3172	2
C₈₉×#3170	2
C₈₉×#3168	2
C₈₉×#3164	2
C₈₉×#3156	2
C₈₉×#3137	2
C₈₉×#3063	2
C₈₉×#3061	2
C₈₉×#3059	2
C₄×#137×C₈₉	2
C₄×#135×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₄×#131×C₈₉	2
#60696	89

Subgroups — C89×#60696 #36438544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60696 #36438544