Subgroups — C₈₉×#61261 #36439109

Order 22784.

1782 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3493	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3350	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3348	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3342	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3341	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3339	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3336	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3099	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3093	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3084	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	#556×C₈₉	—	2	2	no	—
22	#556×C₈₉	C₂²	1	4	yes	—
23	#555×C₈₉	—	2	2	no	—
24	#555×C₈₉	C₂²	1	4	yes	—
25	#553×C₈₉	—	2	2	no	—
26	#553×C₈₉	C₂²	1	4	yes	—
27	#552×C₈₉	—	2	2	no	—
28	#552×C₈₉	C₂²	1	4	yes	—
29	#544×C₈₉	C₂²	1	2	yes	—
30	#538×C₈₉	—	2	4	no	—
31	#537×C₈₉	C₂²	1	2	yes	—
32	#529×C₈₉	—	2	4	no	—
33	#525×C₈₉	C₂²	1	2	yes	—
34	#525×C₈₉	C₂²	1	1	yes	characteristic
35	#520×C₈₉	C₂²	1	2	yes	—
36	#520×C₈₉	C₂²	1	2	yes	—
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	#501×C₈₉	C₂²	1	4	yes	complemented
39	#500×C₈₉	C₂²	1	2	yes	complemented
40	#499×C₈₉	C₂²	1	2	yes	complemented
41	#485×C₈₉	C₂²	1	4	yes	—
42	#485×C₈₉	C₂²	1	4	yes	—
43	#485×C₈₉	C₂²	1	4	yes	complemented
44	#483×C₈₉	C₂²	1	4	yes	complemented
45	#482×C₈₉	C₂²	1	4	yes	—
46	#482×C₈₉	C₂²	1	4	yes	—
47	#482×C₈₉	C₂²	1	4	yes	complemented
48	#481×C₈₉	C₂²	1	4	yes	complemented
49	#479×C₈₉	C₂²	1	4	yes	complemented
50	#478×C₈₉	C₂²	1	4	yes	complemented
51	#476×C₈₉	C₂²	1	4	yes	complemented
52	#475×C₈₉	C₂²	1	4	yes	complemented
53	#468×C₈₉	C₂²	1	4	yes	complemented
54	#467×C₈₉	C₂²	1	1	yes	characteristic
55	#467×C₈₉	C₂²	1	1	yes	characteristic
56	#467×C₈₉	C₂²	1	2	yes	complemented
57	#466×C₈₉	C₂²	1	1	yes	characteristic
58	#466×C₈₉	C₂²	1	1	yes	characteristic
59	#466×C₈₉	C₂²	1	2	yes	complemented
60	#465×C₈₉	C₂²	1	2	yes	—
61	#465×C₈₉	C₂²	1	2	yes	—
62	#440×C₈₉	C₂²	1	4	yes	complemented
63	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
64	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
65	#435×C₈₉	C₂²	1	2	yes	—
66	#435×C₈₉	C₂²	1	2	yes	—
67	C₈×D₄×C₈₉	C₂²	1	2	yes	—
68	C₈×D₄×C₈₉	C₂²	1	2	yes	—
69	#428×C₈₉	C₂²	1	2	yes	—
70	#428×C₈₉	C₂²	1	2	yes	—
71	#428×C₈₉	C₂²	1	4	yes	complemented
72	#427×C₈₉	C₂²	1	2	yes	—
73	#427×C₈₉	C₂²	1	2	yes	—
74	#427×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	2	yes	—
76	#427×C₈₉	C₂²	1	1	yes	characteristic
77	#427×C₈₉	C₂²	1	2	yes	complemented
78	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
79	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
80	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
81	C₂×#106×C₈₉	C₂²	1	2	yes	—
82	#424×C₈₉	C₂²	1	1	yes	characteristic
83	#417×C₈₉	C₂²	1	2	yes	—
84	#417×C₈₉	C₂²	1	2	yes	—
85	#416×C₈₉	C₂²	1	2	yes	—
86	#408×C₈₉	C₂²	1	1	yes	characteristic
87	#407×C₈₉	C₂²	1	1	yes	characteristic
88	#405×C₈₉	C₂²	1	1	yes	characteristic
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	#135×C₈₉	—	2	4	no	—
93	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
95	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
96	#131×C₈₉	—	2	4	no	—
97	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂²×C₈×C₈₉	—	2	4	no	—
101	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₈₉	—	2	2	no	—
109	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
110	#126×C₈₉	—	2	4	no	—
111	#126×C₈₉	—	2	4	no	—
112	#126×C₈₉	—	2	4	no	—
113	#126×C₈₉	—	2	4	no	—
114	#125×C₈₉	—	2	4	no	—
115	#125×C₈₉	—	2	2	no	—
116	#125×C₈₉	C₂³	1	4	yes	—
117	#124×C₈₉	—	2	4	no	—
118	#124×C₈₉	—	2	4	no	—
119	#124×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	4	no	—
121	#123×C₈₉	—	2	2	no	—
122	#123×C₈₉	—	2	4	no	—
123	#123×C₈₉	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₈₉	—	2	2	no	—
125	C₂²⋊Q₈×C₈₉	—	2	4	no	—
126	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
127	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
128	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
130	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
131	#121×C₈₉	—	2	4	no	—
132	#121×C₈₉	—	2	2	no	—
133	#121×C₈₉	—	2	4	no	—
134	#121×C₈₉	—	2	4	no	—
135	#121×C₈₉	D₄	1	1	yes	characteristic
136	#121×C₈₉	D₄	1	1	yes	characteristic
137	#121×C₈₉	C₂³	1	2	yes	—
138	#121×C₈₉	C₂³	1	2	yes	—
139	#121×C₈₉	C₂³	1	4	yes	—
140	#120×C₈₉	—	2	2	no	—
141	#120×C₈₉	D₄	1	2	yes	—
142	C₄×Q₈×C₈₉	—	2	2	no	—
143	C₄×Q₈×C₈₉	—	2	4	no	—
144	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
145	C₄×D₄×C₈₉	—	2	4	no	—
146	C₄×D₄×C₈₉	—	2	2	no	—
147	C₄×D₄×C₈₉	—	2	2	no	—
148	C₄×D₄×C₈₉	—	2	2	no	—
149	C₄×D₄×C₈₉	—	2	4	no	—
150	C₄×D₄×C₈₉	—	2	4	no	—
151	C₄×D₄×C₈₉	C₂³	1	4	yes	—
152	C₄×D₄×C₈₉	C₂³	1	2	yes	—
153	C₄×D₄×C₈₉	C₂³	1	2	yes	—
154	#117×C₈₉	—	2	2	no	—
155	#117×C₈₉	—	2	2	no	—
156	#117×C₈₉	—	2	2	no	—
157	#117×C₈₉	—	2	4	no	—
158	#117×C₈₉	—	2	4	no	—
159	#117×C₈₉	C₂³	1	2	yes	—
160	#117×C₈₉	C₂³	1	4	yes	—
161	#117×C₈₉	C₂³	1	4	yes	—
162	#117×C₈₉	C₂³	1	4	yes	—
163	#117×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
169	C₂×C₄²×C₈₉	—	2	2	no	—
170	#107×C₈₉	C₂³	1	2	yes	—
171	#107×C₈₉	C₂³	1	2	yes	—
172	#107×C₈₉	C₂³	1	2	yes	—
173	#107×C₈₉	C₂³	1	2	yes	—
174	#107×C₈₉	C₂³	1	1	yes	characteristic
175	#107×C₈₉	C₂³	1	4	yes	—
176	#107×C₈₉	C₂³	1	1	yes	characteristic
177	#107×C₈₉	C₂³	1	4	yes	—
178	#106×C₈₉	C₂³	1	4	yes	—
179	#106×C₈₉	C₂³	1	4	yes	—
180	#106×C₈₉	C₂³	1	2	yes	—
181	#106×C₈₉	C₂³	1	4	yes	—
182	#106×C₈₉	C₂³	1	4	yes	—
183	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
184	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
185	#103×C₈₉	C₂³	1	2	yes	—
186	#103×C₈₉	C₂³	1	2	yes	—
187	#103×C₈₉	C₂³	1	4	yes	—
188	#103×C₈₉	C₂³	1	4	yes	—
189	#102×C₈₉	C₂³	1	2	yes	—
190	#102×C₈₉	C₂³	1	2	yes	—
191	#102×C₈₉	C₂³	1	4	yes	—
192	#102×C₈₉	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
197	#97×C₈₉	C₂³	1	2	yes	—
198	C₄×C₈×C₈₉	C₂³	1	2	yes	—
199	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
200	#41×C₈₉	—	2	2	no	—
201	#41×C₈₉	—	2	2	no	—
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	2	4	no	—
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
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	4	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	4	no	—
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₈₉	—	2	2	no	—
231	SD₁₆×C₈₉	—	2	4	no	—
232	D₈×C₈₉	—	2	2	no	—
233	M₁₆×C₈₉	—	2	2	no	—
234	M₁₆×C₈₉	—	2	2	no	—
235	M₁₆×C₈₉	—	2	4	no	—
236	C₂×C₈×C₈₉	—	2	2	no	—
237	C₂×C₈×C₈₉	—	2	2	no	—
238	C₂×C₈×C₈₉	—	2	2	no	—
239	C₂×C₈×C₈₉	—	2	2	no	—
240	C₂×C₈×C₈₉	—	2	2	no	—
241	C₂×C₈×C₈₉	—	2	4	no	—
242	C₂×C₈×C₈₉	#41	1	4	yes	—
243	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
244	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₈₉	—	2	2	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	—	2	4	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	2	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	4	no	—
259	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
264	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	2	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	2	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	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₄²×C₈₉	—	2	4	no	—
284	C₄²×C₈₉	—	2	4	no	—
285	C₄²×C₈₉	—	2	4	no	—
286	C₄²×C₈₉	—	2	4	no	—
287	C₄²×C₈₉	—	2	2	no	—
288	C₄²×C₈₉	C₂⁴	1	2	yes	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	4	1	no	—
293	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
296	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₈₉	—	2	2	no	—
298	Q₈×C₈₉	—	2	2	no	—
299	Q₈×C₈₉	—	2	2	no	—
300	Q₈×C₈₉	—	8	4	no	—
301	D₄×C₈₉	—	2	4	no	—
302	D₄×C₈₉	—	2	2	no	—
303	D₄×C₈₉	—	2	2	no	—
304	D₄×C₈₉	—	2	2	no	—
305	D₄×C₈₉	—	4	2	no	—
306	D₄×C₈₉	—	4	2	no	—
307	D₄×C₈₉	—	4	4	no	—
308	D₄×C₈₉	—	8	2	no	—
309	D₄×C₈₉	—	8	4	no	—
310	D₄×C₈₉	—	8	2	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	1	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	4	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	4	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	4	4	no	—
326	C₂×C₄×C₈₉	—	8	4	no	—
327	C₂×C₄×C₈₉	—	8	2	no	—
328	C₂×C₄×C₈₉	—	8	4	no	—
329	C₂×C₄×C₈₉	—	8	2	no	—
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
339	C₈×C₈₉	—	2	1	no	—
340	C₈×C₈₉	—	2	1	no	—
341	C₈×C₈₉	—	2	2	no	—
342	C₈×C₈₉	—	2	2	no	—
343	C₈×C₈₉	C₂×#41	1	2	yes	—
344	C₈×C₈₉	C₂×#41	1	2	yes	—
345	C₂²×C₈₉	—	2	1	no	—
346	C₂²×C₈₉	—	2	1	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	1	no	—
349	C₂²×C₈₉	—	2	1	no	—
350	C₂²×C₈₉	—	2	2	no	—
351	C₂²×C₈₉	—	2	1	no	—
352	C₂²×C₈₉	—	2	1	no	—
353	C₂²×C₈₉	—	2	1	no	—
354	C₂²×C₈₉	—	2	1	no	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	4	4	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	#547	1	2	yes	—
361	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₈₉	—	2	2	no	—
363	C₄×C₈₉	—	2	2	no	—
364	C₄×C₈₉	—	2	1	no	—
365	C₄×C₈₉	—	2	1	no	—
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	4	4	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	4	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	#547	1	2	yes	—
373	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
374	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
375	#61261	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₂×C₈₉	—	2	2	no	—
377	C₂×C₈₉	—	4	2	no	—
378	C₂×C₈₉	—	4	1	no	—
379	C₂×C₈₉	—	4	1	no	—
380	C₂×C₈₉	—	8	2	no	—
381	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
382	C₂×C₈₉	#3584	1	1	yes	characteristic
383	C₂×C₈₉	#3584	1	1	yes	characteristic
384	#3493	C₂×C₈₉	1	2	yes	complemented
385	#3350	C₂×C₈₉	1	4	yes	complemented
386	#3348	C₂×C₈₉	1	4	yes	complemented
387	#3342	C₂×C₈₉	1	2	yes	complemented
388	#3341	C₂×C₈₉	1	2	yes	complemented
389	#3339	C₂×C₈₉	1	2	yes	complemented
390	#3336	C₂×C₈₉	1	2	yes	complemented
391	#3164	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#3099	C₂×C₈₉	1	2	yes	complemented
393	#3093	C₂×C₈₉	1	2	yes	complemented
394	#3084	C₂×C₈₉	1	2	yes	complemented
395	#3061	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#3050	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2951	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#2929	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#2913	C₂×C₈₉	1	1	yes	characteristic, complemented
400	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₈₉	#61261	1	1	yes	characteristic, direct product factor, Sylow
402	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
404	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
405	#556	—	2	2	no	—
406	#556	C₂²×C₈₉	1	4	yes	—
407	#555	—	2	2	no	—
408	#555	C₂²×C₈₉	1	4	yes	—
409	#553	—	2	2	no	—
410	#553	C₂²×C₈₉	1	4	yes	—
411	#552	—	2	2	no	—
412	#552	C₂²×C₈₉	1	4	yes	—
413	#544	C₂²×C₈₉	1	2	yes	—
414	#538	—	2	4	no	—
415	#537	C₂²×C₈₉	1	2	yes	—
416	#529	—	2	4	no	—
417	#525	C₂²×C₈₉	1	2	yes	—
418	#525	C₂²×C₈₉	1	1	yes	characteristic
419	#520	C₂²×C₈₉	1	2	yes	—
420	#520	C₂²×C₈₉	1	2	yes	—
421	C₂×#117	C₂²×C₈₉	1	2	yes	—
422	#501	C₂²×C₈₉	1	4	yes	complemented
423	#500	C₂²×C₈₉	1	2	yes	complemented
424	#499	C₂²×C₈₉	1	2	yes	complemented
425	#485	C₂²×C₈₉	1	4	yes	—
426	#485	C₂²×C₈₉	1	4	yes	—
427	#485	C₂²×C₈₉	1	4	yes	complemented
428	#483	C₂²×C₈₉	1	4	yes	complemented
429	#482	C₂²×C₈₉	1	4	yes	—
430	#482	C₂²×C₈₉	1	4	yes	—
431	#482	C₂²×C₈₉	1	4	yes	complemented
432	#481	C₂²×C₈₉	1	4	yes	complemented
433	#479	C₂²×C₈₉	1	4	yes	complemented
434	#478	C₂²×C₈₉	1	4	yes	complemented
435	#476	C₂²×C₈₉	1	4	yes	complemented
436	#475	C₂²×C₈₉	1	4	yes	complemented
437	#468	C₂²×C₈₉	1	4	yes	complemented
438	#467	C₂²×C₈₉	1	1	yes	characteristic
439	#467	C₂²×C₈₉	1	1	yes	characteristic
440	#467	C₂²×C₈₉	1	2	yes	complemented
441	#466	C₂²×C₈₉	1	1	yes	characteristic
442	#466	C₂²×C₈₉	1	1	yes	characteristic
443	#466	C₂²×C₈₉	1	2	yes	complemented
444	#465	C₂²×C₈₉	1	2	yes	—
445	#465	C₂²×C₈₉	1	2	yes	—
446	#440	C₂²×C₈₉	1	4	yes	complemented
447	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
448	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
449	#435	C₂²×C₈₉	1	2	yes	—
450	#435	C₂²×C₈₉	1	2	yes	—
451	C₈×D₄	C₂²×C₈₉	1	2	yes	—
452	C₈×D₄	C₂²×C₈₉	1	2	yes	—
453	#428	C₂²×C₈₉	1	2	yes	—
454	#428	C₂²×C₈₉	1	2	yes	—
455	#428	C₂²×C₈₉	1	4	yes	complemented
456	#427	C₂²×C₈₉	1	2	yes	—
457	#427	C₂²×C₈₉	1	2	yes	—
458	#427	C₂²×C₈₉	1	2	yes	—
459	#427	C₂²×C₈₉	1	2	yes	—
460	#427	C₂²×C₈₉	1	1	yes	characteristic
461	#427	C₂²×C₈₉	1	2	yes	complemented
462	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
465	C₂×#106	C₂²×C₈₉	1	2	yes	—
466	#424	C₂²×C₈₉	1	1	yes	characteristic
467	#417	C₂²×C₈₉	1	2	yes	—
468	#417	C₂²×C₈₉	1	2	yes	—
469	#416	C₂²×C₈₉	1	2	yes	—
470	#408	C₂²×C₈₉	1	1	yes	characteristic
471	#407	C₂²×C₈₉	1	1	yes	characteristic
472	#405	C₂²×C₈₉	1	1	yes	characteristic
473	C₂×#41	C₂³×C₈₉	1	2	yes	—
474	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
476	#135	—	2	4	no	—
477	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
478	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
479	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
480	#131	—	2	4	no	—
481	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
482	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
483	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
484	C₂²×C₈	—	2	4	no	—
485	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
491	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
494	#126	—	2	4	no	—
495	#126	—	2	4	no	—
496	#126	—	2	4	no	—
497	#126	—	2	4	no	—
498	#125	—	2	4	no	—
499	#125	—	2	2	no	—
500	#125	C₂³×C₈₉	1	4	yes	—
501	#124	—	2	4	no	—
502	#124	—	2	4	no	—
503	#124	—	2	4	no	—
504	#123	—	2	4	no	—
505	#123	—	2	2	no	—
506	#123	—	2	4	no	—
507	#123	D₄×C₈₉	1	2	yes	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
511	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
512	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
513	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
514	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
515	#121	—	2	4	no	—
516	#121	—	2	2	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	D₄×C₈₉	1	1	yes	characteristic
520	#121	D₄×C₈₉	1	1	yes	characteristic
521	#121	C₂³×C₈₉	1	2	yes	—
522	#121	C₂³×C₈₉	1	2	yes	—
523	#121	C₂³×C₈₉	1	4	yes	—
524	#120	—	2	2	no	—
525	#120	D₄×C₈₉	1	2	yes	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	4	no	—
528	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	C₂³×C₈₉	1	4	yes	—
536	C₄×D₄	C₂³×C₈₉	1	2	yes	—
537	C₄×D₄	C₂³×C₈₉	1	2	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	4	no	—
542	#117	—	2	4	no	—
543	#117	C₂³×C₈₉	1	4	yes	—
544	#117	C₂³×C₈₉	1	4	yes	—
545	#117	C₂³×C₈₉	1	2	yes	—
546	#117	C₂³×C₈₉	1	4	yes	—
547	#117	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
552	C₂×C₂²⋊C₄	—	2	2	no	—
553	C₂×C₄²	—	2	2	no	—
554	#107	C₂³×C₈₉	1	2	yes	—
555	#107	C₂³×C₈₉	1	2	yes	—
556	#107	C₂³×C₈₉	1	2	yes	—
557	#107	C₂³×C₈₉	1	2	yes	—
558	#107	C₂³×C₈₉	1	1	yes	characteristic
559	#107	C₂³×C₈₉	1	4	yes	—
560	#107	C₂³×C₈₉	1	1	yes	characteristic
561	#107	C₂³×C₈₉	1	4	yes	—
562	#106	C₂³×C₈₉	1	4	yes	—
563	#106	C₂³×C₈₉	1	4	yes	—
564	#106	C₂³×C₈₉	1	2	yes	—
565	#106	C₂³×C₈₉	1	4	yes	—
566	#106	C₂³×C₈₉	1	4	yes	—
567	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
568	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
569	#103	C₂³×C₈₉	1	2	yes	—
570	#103	C₂³×C₈₉	1	2	yes	—
571	#103	C₂³×C₈₉	1	4	yes	—
572	#103	C₂³×C₈₉	1	4	yes	—
573	#102	C₂³×C₈₉	1	2	yes	—
574	#102	C₂³×C₈₉	1	2	yes	—
575	#102	C₂³×C₈₉	1	4	yes	—
576	#102	C₂³×C₈₉	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
581	#97	C₂³×C₈₉	1	2	yes	—
582	C₄×C₈	C₂³×C₈₉	1	2	yes	—
583	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
584	#41	—	2	2	no	—
585	#41	—	2	2	no	—
586	#41	—	2	4	no	—
587	#41	—	2	4	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
596	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
599	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	SD₁₆	—	2	4	no	—
616	D₈	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	2	no	—
619	M₁₆	—	2	4	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	4	no	—
626	C₂×C₈	#41×C₈₉	1	4	yes	—
627	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
628	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
631	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
648	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
649	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
663	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
664	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	C₂⁴×C₈₉	1	2	yes	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
678	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
679	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
680	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	8	4	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	4	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	—	8	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
721	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
722	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
723	C₈	—	2	1	no	—
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×#41×C₈₉	1	2	yes	—
728	C₈	C₂×#41×C₈₉	1	2	yes	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	#547×C₈₉	1	2	yes	—
745	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	#547×C₈₉	1	2	yes	—
757	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
758	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
759	C₂	—	2	2	no	—
760	C₂	—	4	2	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
765	C₂	C₈₉×#3584	1	1	yes	characteristic
766	C₂	C₈₉×#3584	1	1	yes	characteristic

	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 ◁ #525×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3493	C₂	semidirect
2. C₈₉×#3350	C₂	semidirect
3. C₈₉×#3348	C₂	semidirect
4. C₈₉×#3342	C₂	semidirect
5. C₈₉×#3341	C₂	semidirect
6. C₈₉×#3339	C₂	semidirect
7. C₈₉×#3336	C₂	semidirect
8. C₈₉×#3164	C₂	semidirect
9. C₈₉×#3099	C₂	semidirect
10. C₈₉×#3093	C₂	semidirect
11. C₈₉×#3084	C₂	semidirect
12. C₈₉×#3061	C₂	semidirect
13. C₈₉×#3050	C₂	semidirect
14. C₈₉×#2951	C₂	semidirect
15. C₈₉×#2929	C₂	semidirect
16. C₈₉×#2913	C₂	semidirect
17. C₂×#427×C₈₉	C₂	semidirect
38. #501×C₈₉	C₂²	semidirect
39. #500×C₈₉	C₂²	semidirect
40. #499×C₈₉	C₂²	semidirect
43. #485×C₈₉	C₂²	semidirect
44. #483×C₈₉	C₂²	semidirect
47. #482×C₈₉	C₂²	semidirect
48. #481×C₈₉	C₂²	semidirect
49. #479×C₈₉	C₂²	semidirect
50. #478×C₈₉	C₂²	semidirect
51. #476×C₈₉	C₂²	semidirect
52. #475×C₈₉	C₂²	semidirect
53. #468×C₈₉	C₂²	semidirect
56. #467×C₈₉	C₂²	semidirect
59. #466×C₈₉	C₂²	semidirect
62. #440×C₈₉	C₂²	semidirect
63. C₄×Q₁₆×C₈₉	C₂²	semidirect
64. C₄×D₈×C₈₉	C₂²	semidirect
71. #428×C₈₉	C₂²	semidirect
77. #427×C₈₉	C₂²	semidirect
80. C₂×#107×C₈₉	C₂²	semidirect
375. #61261	C₈₉	direct (N × H)
384. #3493	C₂×C₈₉	semidirect
385. #3350	C₂×C₈₉	semidirect
386. #3348	C₂×C₈₉	semidirect
387. #3342	C₂×C₈₉	semidirect
388. #3341	C₂×C₈₉	semidirect
389. #3339	C₂×C₈₉	semidirect
390. #3336	C₂×C₈₉	semidirect
391. #3164	C₂×C₈₉	semidirect
392. #3099	C₂×C₈₉	semidirect
393. #3093	C₂×C₈₉	semidirect
394. #3084	C₂×C₈₉	semidirect
395. #3061	C₂×C₈₉	semidirect
396. #3050	C₂×C₈₉	semidirect
397. #2951	C₂×C₈₉	semidirect
398. #2929	C₂×C₈₉	semidirect
399. #2913	C₂×C₈₉	semidirect
400. C₂×#427	C₂×C₈₉	semidirect
401. C₈₉	#61261	direct (N × H)
422. #501	C₂²×C₈₉	semidirect
423. #500	C₂²×C₈₉	semidirect
424. #499	C₂²×C₈₉	semidirect
427. #485	C₂²×C₈₉	semidirect
428. #483	C₂²×C₈₉	semidirect
431. #482	C₂²×C₈₉	semidirect
432. #481	C₂²×C₈₉	semidirect
433. #479	C₂²×C₈₉	semidirect
434. #478	C₂²×C₈₉	semidirect
435. #476	C₂²×C₈₉	semidirect
436. #475	C₂²×C₈₉	semidirect
437. #468	C₂²×C₈₉	semidirect
440. #467	C₂²×C₈₉	semidirect
443. #466	C₂²×C₈₉	semidirect
446. #440	C₂²×C₈₉	semidirect
447. C₄×Q₁₆	C₂²×C₈₉	semidirect
448. C₄×D₈	C₂²×C₈₉	semidirect
455. #428	C₂²×C₈₉	semidirect
461. #427	C₂²×C₈₉	semidirect
464. C₂×#107	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3493	2
C₈₉×#3350	2
C₈₉×#3348	2
C₈₉×#3342	2
C₈₉×#3341	2
C₈₉×#3339	2
C₈₉×#3336	2
C₈₉×#3164	2
C₈₉×#3099	2
C₈₉×#3093	2
C₈₉×#3084	2
C₈₉×#3061	2
C₈₉×#3050	2
C₈₉×#2951	2
C₈₉×#2929	2
C₈₉×#2913	2
C₂×#427×C₈₉	2
#61261	89

Subgroups — C89×#61261 #36439109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61261 #36439109