Subgroups — C₈₉×#26984 #36404832

Order 22784.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2422	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#123×C₈₉	—	2	1	no	—
21	C₂×#121×C₈₉	—	2	1	no	—
22	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	#469×C₈₉	—	2	4	no	—
28	#442×C₈₉	—	2	4	no	—
29	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
42	#397×C₈₉	—	2	1	no	—
43	#394×C₈₉	—	2	1	no	—
44	#394×C₈₉	—	2	1	no	—
45	#392×C₈₉	—	2	1	no	—
46	#390×C₈₉	C₂²	1	1	yes	characteristic
47	#390×C₈₉	C₂²	1	1	yes	characteristic
48	#389×C₈₉	C₂²	1	1	yes	characteristic
49	#389×C₈₉	C₂²	1	1	yes	characteristic
50	#386×C₈₉	—	2	1	no	—
51	#385×C₈₉	—	2	1	no	—
52	#384×C₈₉	C₂²	1	1	yes	characteristic
53	#380×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	#340×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₈₉	—	2	1	no	—
62	C₂²×D₄×C₈₉	—	2	1	no	—
63	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂²×D₄×C₈₉	—	2	1	no	—
65	C₂²×D₄×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₈₉	—	2	1	no	—
70	C₂³×C₄×C₈₉	—	2	1	no	—
71	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×D₈×C₈₉	—	2	2	no	—
73	C₂×D₈×C₈₉	—	2	2	no	—
74	C₂×D₈×C₈₉	—	2	2	no	—
75	C₂×D₈×C₈₉	—	2	2	no	—
76	C₂×D₈×C₈₉	—	2	2	no	—
77	C₂×D₈×C₈₉	—	4	1	no	—
78	C₂×M₁₆×C₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	—	2	2	no	—
80	C₂×M₁₆×C₈₉	—	4	1	no	—
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	#127×C₈₉	—	2	2	no	—
86	#127×C₈₉	—	4	1	no	—
87	#123×C₈₉	—	4	4	no	—
88	#121×C₈₉	—	2	2	no	—
89	#121×C₈₉	—	2	2	no	—
90	#121×C₈₉	—	2	2	no	—
91	#121×C₈₉	—	4	4	no	—
92	#121×C₈₉	—	4	1	no	—
93	#121×C₈₉	—	4	1	no	—
94	#121×C₈₉	—	4	1	no	—
95	C₄×D₄×C₈₉	—	2	2	no	—
96	C₄×D₄×C₈₉	—	2	2	no	—
97	C₄×D₄×C₈₉	—	4	1	no	—
98	C₄×D₄×C₈₉	—	4	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	#106×C₈₉	—	2	2	no	—
123	#106×C₈₉	—	2	2	no	—
124	#102×C₈₉	—	2	2	no	—
125	#102×C₈₉	—	2	2	no	—
126	#102×C₈₉	—	2	2	no	—
127	#102×C₈₉	—	2	2	no	—
128	#102×C₈₉	—	4	1	no	—
129	#102×C₈₉	—	4	1	no	—
130	#102×C₈₉	—	4	1	no	—
131	#102×C₈₉	D₄	1	4	yes	complemented
132	C₂²⋊C₈×C₈₉	—	2	2	no	—
133	#97×C₈₉	—	2	2	no	—
134	C₄×C₈×C₈₉	—	4	1	no	—
135	#95×C₈₉	—	2	1	no	—
136	#95×C₈₉	—	2	1	no	—
137	#95×C₈₉	—	2	1	no	—
138	#95×C₈₉	D₄	1	1	yes	characteristic
139	#95×C₈₉	D₄	1	1	yes	characteristic
140	C₂⁴×C₈₉	—	2	1	no	—
141	C₂⁴×C₈₉	—	2	1	no	—
142	C₂⁴×C₈₉	—	2	1	no	—
143	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₈₉	—	2	1	no	—
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	—	2	1	no	—
147	C₂×D₄×C₈₉	—	2	1	no	—
148	C₂×D₄×C₈₉	—	2	1	no	—
149	C₂×D₄×C₈₉	—	2	1	no	—
150	C₂×D₄×C₈₉	—	2	1	no	—
151	C₂×D₄×C₈₉	—	2	1	no	—
152	C₂×D₄×C₈₉	—	2	1	no	—
153	C₂×D₄×C₈₉	—	2	1	no	—
154	C₂×D₄×C₈₉	—	2	1	no	—
155	C₂×D₄×C₈₉	—	2	1	no	—
156	C₂×D₄×C₈₉	—	2	1	no	—
157	C₂×D₄×C₈₉	—	2	1	no	—
158	C₂×D₄×C₈₉	—	2	1	no	—
159	C₂×D₄×C₈₉	—	2	1	no	—
160	C₂×D₄×C₈₉	—	4	2	no	—
161	C₂×D₄×C₈₉	—	4	2	no	—
162	C₂×D₄×C₈₉	—	4	2	no	—
163	C₂×D₄×C₈₉	—	4	2	no	—
164	C₂×D₄×C₈₉	—	4	2	no	—
165	C₂×D₄×C₈₉	—	4	2	no	—
166	C₂×D₄×C₈₉	—	4	2	no	—
167	C₂×D₄×C₈₉	—	4	2	no	—
168	C₂×D₄×C₈₉	—	4	2	no	—
169	C₂×D₄×C₈₉	—	4	2	no	—
170	C₂×D₄×C₈₉	—	8	1	no	—
171	C₂×D₄×C₈₉	—	8	1	no	—
172	C₂×D₄×C₈₉	—	8	1	no	—
173	C₂×D₄×C₈₉	—	8	1	no	—
174	C₂×D₄×C₈₉	—	8	1	no	—
175	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₈₉	#41	1	2	yes	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	1	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	1	no	—
184	C₂²×C₄×C₈₉	—	2	1	no	—
185	C₂²×C₄×C₈₉	—	2	1	no	—
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	—	4	2	no	—
189	C₂²×C₄×C₈₉	—	4	2	no	—
190	C₂²×C₄×C₈₉	—	4	2	no	—
191	C₂²×C₄×C₈₉	—	4	2	no	—
192	C₂²×C₄×C₈₉	—	8	1	no	—
193	C₂²×C₄×C₈₉	—	8	1	no	—
194	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
200	D₈×C₈₉	—	2	8	no	—
201	D₈×C₈₉	—	4	4	no	—
202	M₁₆×C₈₉	—	4	4	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	2	1	no	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	2	1	no	—
210	C₂×C₈×C₈₉	—	2	1	no	—
211	C₂×C₈×C₈₉	—	2	1	no	—
212	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₈₉	#41	1	2	yes	—
214	C₂×C₈×C₈₉	#41	1	2	yes	—
215	C₄⋊C₄×C₈₉	—	2	1	no	—
216	C₄⋊C₄×C₈₉	—	2	1	no	—
217	C₄⋊C₄×C₈₉	—	2	1	no	—
218	C₄⋊C₄×C₈₉	—	2	1	no	—
219	C₄⋊C₄×C₈₉	—	2	1	no	—
220	C₄⋊C₄×C₈₉	—	2	1	no	—
221	C₄⋊C₄×C₈₉	—	2	1	no	—
222	C₄⋊C₄×C₈₉	—	2	1	no	—
223	C₄⋊C₄×C₈₉	—	2	1	no	—
224	C₄⋊C₄×C₈₉	—	4	2	no	—
225	C₄⋊C₄×C₈₉	—	4	2	no	—
226	C₄⋊C₄×C₈₉	—	4	2	no	—
227	C₄⋊C₄×C₈₉	—	8	1	no	—
228	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
229	C₂²⋊C₄×C₈₉	—	2	2	no	—
230	C₂²⋊C₄×C₈₉	—	2	2	no	—
231	C₂²⋊C₄×C₈₉	—	4	2	no	—
232	C₂²⋊C₄×C₈₉	—	4	2	no	—
233	C₂²⋊C₄×C₈₉	—	4	2	no	—
234	C₂²⋊C₄×C₈₉	—	4	2	no	—
235	C₂²⋊C₄×C₈₉	—	4	2	no	—
236	C₂²⋊C₄×C₈₉	—	4	2	no	—
237	C₂²⋊C₄×C₈₉	—	4	2	no	—
238	C₂²⋊C₄×C₈₉	—	4	2	no	—
239	C₂²⋊C₄×C₈₉	—	4	2	no	—
240	C₂²⋊C₄×C₈₉	—	8	1	no	—
241	C₄²×C₈₉	—	2	1	no	—
242	C₄²×C₈₉	—	2	1	no	—
243	C₄²×C₈₉	—	2	1	no	—
244	C₄²×C₈₉	—	2	1	no	—
245	C₂³×C₈₉	—	2	1	no	—
246	C₂³×C₈₉	—	2	2	no	—
247	C₂³×C₈₉	—	2	1	no	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	2	1	no	—
250	C₂³×C₈₉	—	2	1	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	4	1	no	—
255	C₂³×C₈₉	—	4	1	no	—
256	C₂³×C₈₉	—	4	1	no	—
257	C₂³×C₈₉	—	4	1	no	—
258	C₂³×C₈₉	—	4	1	no	—
259	C₂³×C₈₉	—	4	1	no	—
260	C₂³×C₈₉	—	4	1	no	—
261	C₂³×C₈₉	—	4	1	no	—
262	C₂³×C₈₉	—	4	1	no	—
263	C₂³×C₈₉	—	4	1	no	—
264	C₂³×C₈₉	—	4	1	no	—
265	C₂³×C₈₉	—	4	1	no	—
266	C₂³×C₈₉	—	4	1	no	—
267	C₂³×C₈₉	—	4	1	no	—
268	C₂³×C₈₉	—	4	1	no	—
269	C₂³×C₈₉	—	4	1	no	—
270	C₂³×C₈₉	—	4	1	no	—
271	C₂³×C₈₉	—	4	1	no	—
272	C₂³×C₈₉	—	4	1	no	—
273	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
274	D₄×C₈₉	—	2	2	no	—
275	D₄×C₈₉	—	2	2	no	—
276	D₄×C₈₉	—	2	2	no	—
277	D₄×C₈₉	—	2	2	no	—
278	D₄×C₈₉	—	4	1	no	—
279	D₄×C₈₉	—	4	1	no	—
280	D₄×C₈₉	—	4	1	no	—
281	D₄×C₈₉	—	4	1	no	—
282	D₄×C₈₉	—	4	1	no	—
283	D₄×C₈₉	—	4	1	no	—
284	D₄×C₈₉	—	4	1	no	—
285	D₄×C₈₉	—	4	1	no	—
286	D₄×C₈₉	—	8	4	no	—
287	D₄×C₈₉	—	8	4	no	—
288	D₄×C₈₉	—	8	4	no	—
289	D₄×C₈₉	—	8	4	no	—
290	D₄×C₈₉	—	8	4	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	1	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	1	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	4	1	no	—
306	C₂×C₄×C₈₉	—	4	1	no	—
307	C₂×C₄×C₈₉	—	4	1	no	—
308	C₂×C₄×C₈₉	—	4	1	no	—
309	C₂×C₄×C₈₉	—	4	1	no	—
310	C₂×C₄×C₈₉	—	4	1	no	—
311	C₂×C₄×C₈₉	—	4	1	no	—
312	C₂×C₄×C₈₉	—	4	1	no	—
313	C₂×C₄×C₈₉	—	4	1	no	—
314	C₂×C₄×C₈₉	—	4	1	no	—
315	C₂×C₄×C₈₉	—	4	1	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	1	no	—
323	C₂×C₄×C₈₉	—	8	4	no	—
324	C₂×C₄×C₈₉	—	8	4	no	—
325	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
326	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
333	C₈×C₈₉	—	2	2	no	—
334	C₈×C₈₉	—	2	2	no	—
335	C₈×C₈₉	—	2	2	no	—
336	C₈×C₈₉	—	4	1	no	—
337	C₂²×C₈₉	—	4	1	no	—
338	C₂²×C₈₉	—	4	1	no	—
339	C₂²×C₈₉	—	4	1	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	1	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	4	2	no	—
345	C₂²×C₈₉	—	4	1	no	—
346	C₂²×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	—	4	1	no	—
348	C₂²×C₈₉	—	4	1	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	8	1	no	—
351	C₂²×C₈₉	—	8	1	no	—
352	C₂²×C₈₉	—	8	1	no	—
353	C₂²×C₈₉	—	8	1	no	—
354	C₂²×C₈₉	—	8	1	no	—
355	C₂²×C₈₉	—	8	1	no	—
356	C₂²×C₈₉	—	8	1	no	—
357	C₂²×C₈₉	—	8	1	no	—
358	C₂²×C₈₉	—	8	1	no	—
359	C₂²×C₈₉	—	8	1	no	—
360	C₂²×C₈₉	—	8	1	no	—
361	C₂²×C₈₉	—	8	1	no	—
362	C₂²×C₈₉	—	8	1	no	—
363	C₂²×C₈₉	—	8	1	no	—
364	C₂²×C₈₉	—	8	1	no	—
365	C₂²×C₈₉	#532	1	1	yes	characteristic
366	C₂²×C₈₉	D₄²	1	1	yes	characteristic
367	C₂²×C₈₉	#546	1	1	yes	characteristic
368	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂²×C₈₉	#576	1	1	yes	characteristic
371	C₂²×C₈₉	#577	1	1	yes	characteristic
372	C₄×C₈₉	—	2	2	no	—
373	C₄×C₈₉	—	2	2	no	—
374	C₄×C₈₉	—	4	1	no	—
375	C₄×C₈₉	—	4	1	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	1	no	—
378	C₄×C₈₉	—	8	1	no	—
379	C₄×C₈₉	—	8	1	no	—
380	C₄×C₈₉	—	8	1	no	—
381	C₄×C₈₉	—	8	1	no	—
382	C₄×C₈₉	#525	1	1	yes	characteristic
383	C₄×C₈₉	#540	1	1	yes	characteristic
384	C₄×C₈₉	#546	1	1	yes	characteristic
385	C₄×C₈₉	#553	1	1	yes	characteristic
386	#26984	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂×C₈₉	—	8	1	no	—
388	C₂×C₈₉	—	8	2	no	—
389	C₂×C₈₉	—	8	2	no	—
390	C₂×C₈₉	—	16	1	no	—
391	C₂×C₈₉	#2464	1	1	yes	characteristic
392	C₂×C₈₉	#3179	1	1	yes	characteristic
393	C₂×C₈₉	#3184	1	1	yes	characteristic
394	C₂×C₈₉	#3272	1	1	yes	characteristic
395	C₂×C₈₉	#3274	1	1	yes	characteristic
396	C₂×C₈₉	#3306	1	1	yes	characteristic
397	C₂×C₈₉	#3318	1	1	yes	characteristic
398	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2428	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#2422	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2084	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#2011	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#1999	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#1957	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#1936	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#1934	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#1864	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#1753	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₈₉	#26984	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
416	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#123	—	2	1	no	—
419	C₂×#121	—	2	1	no	—
420	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
425	#469	—	2	4	no	—
426	#442	—	2	4	no	—
427	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
440	#397	—	2	1	no	—
441	#394	—	2	1	no	—
442	#394	—	2	1	no	—
443	#392	—	2	1	no	—
444	#390	C₂²×C₈₉	1	1	yes	characteristic
445	#390	C₂²×C₈₉	1	1	yes	characteristic
446	#389	C₂²×C₈₉	1	1	yes	characteristic
447	#389	C₂²×C₈₉	1	1	yes	characteristic
448	#386	—	2	1	no	—
449	#385	—	2	1	no	—
450	#384	C₂²×C₈₉	1	1	yes	characteristic
451	#380	C₂²×C₈₉	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
453	#340	C₂²×C₈₉	1	1	yes	characteristic
454	#340	C₂²×C₈₉	1	1	yes	characteristic
455	#340	C₂²×C₈₉	1	1	yes	characteristic
456	#340	C₂²×C₈₉	1	1	yes	characteristic
457	#336	C₂²×C₈₉	1	1	yes	characteristic
458	#336	C₂²×C₈₉	1	1	yes	characteristic
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂×D₈	—	2	2	no	—
471	C₂×D₈	—	2	2	no	—
472	C₂×D₈	—	2	2	no	—
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	4	1	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	4	1	no	—
479	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
483	#127	—	2	2	no	—
484	#127	—	4	1	no	—
485	#123	—	4	4	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	4	4	no	—
490	#121	—	4	1	no	—
491	#121	—	4	1	no	—
492	#121	—	4	1	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	4	1	no	—
496	C₄×D₄	—	4	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
520	#106	—	2	2	no	—
521	#106	—	2	2	no	—
522	#102	—	2	2	no	—
523	#102	—	2	2	no	—
524	#102	—	2	2	no	—
525	#102	—	2	2	no	—
526	#102	—	4	1	no	—
527	#102	—	4	1	no	—
528	#102	—	4	1	no	—
529	#102	D₄×C₈₉	1	4	yes	complemented
530	C₂²⋊C₈	—	2	2	no	—
531	#97	—	2	2	no	—
532	C₄×C₈	—	4	1	no	—
533	#95	—	2	1	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	D₄×C₈₉	1	1	yes	characteristic
537	#95	D₄×C₈₉	1	1	yes	characteristic
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂×D₄	—	8	1	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	—	8	1	no	—
573	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
574	C₂×D₄	#41×C₈₉	1	2	yes	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	—	8	1	no	—
592	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
598	D₈	—	2	8	no	—
599	D₈	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
611	C₂×C₈	#41×C₈₉	1	2	yes	—
612	C₂×C₈	#41×C₈₉	1	2	yes	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	8	1	no	—
626	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	4	no	—
688	D₄	—	8	4	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
724	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
726	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
729	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
730	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	#532×C₈₉	1	1	yes	characteristic
764	C₂²	D₄²×C₈₉	1	1	yes	characteristic
765	C₂²	#546×C₈₉	1	1	yes	characteristic
766	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
767	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
768	C₂²	#576×C₈₉	1	1	yes	characteristic
769	C₂²	#577×C₈₉	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	8	1	no	—
777	C₄	—	8	1	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	#525×C₈₉	1	1	yes	characteristic
781	C₄	#540×C₈₉	1	1	yes	characteristic
782	C₄	#546×C₈₉	1	1	yes	characteristic
783	C₄	#553×C₈₉	1	1	yes	characteristic
784	C₂	—	8	1	no	—
785	C₂	—	8	2	no	—
786	C₂	—	8	2	no	—
787	C₂	—	16	1	no	—
788	C₂	C₈₉×#2464	1	1	yes	characteristic
789	C₂	C₈₉×#3179	1	1	yes	characteristic
790	C₂	C₈₉×#3184	1	1	yes	characteristic
791	C₂	C₈₉×#3272	1	1	yes	characteristic
792	C₂	C₈₉×#3274	1	1	yes	characteristic
793	C₂	C₈₉×#3306	1	1	yes	characteristic
794	C₂	C₈₉×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#469×C₈₉	C₂	semidirect
2. C₂×#442×C₈₉	C₂	semidirect
3. C₈₉×#2428	C₂	semidirect
4. C₈₉×#2422	C₂	semidirect
5. C₈₉×#2084	C₂	semidirect
6. C₈₉×#2034	C₂	semidirect
7. C₈₉×#2011	C₂	semidirect
8. C₈₉×#1999	C₂	semidirect
9. C₈₉×#1957	C₂	semidirect
10. C₈₉×#1936	C₂	semidirect
11. C₈₉×#1934	C₂	semidirect
12. C₈₉×#1895	C₂	semidirect
13. C₈₉×#1879	C₂	semidirect
14. C₈₉×#1864	C₂	semidirect
15. C₈₉×#1753	C₂	semidirect
131. #102×C₈₉	D₄	semidirect
386. #26984	C₈₉	direct (N × H)
398. C₂×#469	C₂×C₈₉	semidirect
399. C₂×#442	C₂×C₈₉	semidirect
400. #2428	C₂×C₈₉	semidirect
401. #2422	C₂×C₈₉	semidirect
402. #2084	C₂×C₈₉	semidirect
403. #2034	C₂×C₈₉	semidirect
404. #2011	C₂×C₈₉	semidirect
405. #1999	C₂×C₈₉	semidirect
406. #1957	C₂×C₈₉	semidirect
407. #1936	C₂×C₈₉	semidirect
408. #1934	C₂×C₈₉	semidirect
409. #1895	C₂×C₈₉	semidirect
410. #1879	C₂×C₈₉	semidirect
411. #1864	C₂×C₈₉	semidirect
412. #1753	C₂×C₈₉	semidirect
413. C₈₉	#26984	direct (N × H)
529. #102	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#469×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×#2428	2
C₈₉×#2422	2
C₈₉×#2084	2
C₈₉×#2034	2
C₈₉×#2011	2
C₈₉×#1999	2
C₈₉×#1957	2
C₈₉×#1936	2
C₈₉×#1934	2
C₈₉×#1895	2
C₈₉×#1879	2
C₈₉×#1864	2
C₈₉×#1753	2
#26984	89

Subgroups — C89×#26984 #36404832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26984 #36404832