Subgroups — C₈₉×#22878 #36400726

Order 22784.

1218 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2361	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	—	2	1	no	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	#449×C₈₉	C₄	1	8	yes	complemented
27	C₄×D₈×C₈₉	—	2	4	no	—
28	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
30	#417×C₈₉	—	2	4	no	—
31	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#103×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	#391×C₈₉	C₂²	1	1	yes	characteristic
43	#391×C₈₉	C₂²	1	1	yes	characteristic
44	#390×C₈₉	C₂²	1	1	yes	characteristic
45	#389×C₈₉	C₂²	1	1	yes	characteristic
46	#388×C₈₉	—	2	1	no	—
47	#386×C₈₉	—	2	1	no	—
48	#386×C₈₉	—	2	1	no	—
49	#386×C₈₉	—	2	1	no	—
50	#385×C₈₉	—	2	1	no	—
51	#381×C₈₉	—	2	1	no	—
52	#380×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#95×C₈₉	—	2	1	no	—
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	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×#41×C₈₉	—	2	2	no	—
63	C₂×#41×C₈₉	—	2	2	no	—
64	C₂×#41×C₈₉	—	2	2	no	—
65	C₂×#41×C₈₉	—	4	1	no	—
66	C₂×#41×C₈₉	—	4	1	no	—
67	C₂×#41×C₈₉	C₂×C₄	1	4	yes	complemented
68	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	—	2	1	no	—
70	C₂²×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	—	2	1	no	—
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	—	2	1	no	—
77	C₂³×C₄×C₈₉	—	2	1	no	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	—	4	1	no	—
80	C₂×SD₁₆×C₈₉	—	4	1	no	—
81	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
82	C₂×D₈×C₈₉	—	2	2	no	—
83	C₂×D₈×C₈₉	—	2	2	no	—
84	C₂×D₈×C₈₉	C₂×C₄	1	4	yes	complemented
85	C₂×M₁₆×C₈₉	—	2	2	no	—
86	C₂×M₁₆×C₈₉	—	2	2	no	—
87	C₂×M₁₆×C₈₉	—	4	1	no	—
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	#121×C₈₉	—	2	2	no	—
93	#121×C₈₉	C₂×C₄	1	4	yes	complemented
94	C₄×D₄×C₈₉	—	2	2	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	C₄×D₄×C₈₉	—	4	1	no	—
100	C₄×D₄×C₈₉	—	4	4	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₈₉	—	2	1	no	—
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	#107×C₈₉	—	2	2	no	—
123	#107×C₈₉	—	4	1	no	—
124	#103×C₈₉	—	2	2	no	—
125	#103×C₈₉	—	2	2	no	—
126	#103×C₈₉	C₂×C₄	1	4	yes	complemented
127	#102×C₈₉	—	2	2	no	—
128	#102×C₈₉	—	2	2	no	—
129	#102×C₈₉	—	4	1	no	—
130	#102×C₈₉	C₂×C₄	1	4	yes	complemented
131	#102×C₈₉	D₄	1	4	yes	complemented
132	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
133	#97×C₈₉	—	4	1	no	—
134	C₄×C₈×C₈₉	—	2	2	no	—
135	#95×C₈₉	—	2	1	no	—
136	#95×C₈₉	—	2	1	no	—
137	#95×C₈₉	—	2	1	no	—
138	#95×C₈₉	—	2	1	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	—	2	1	no	—
142	#95×C₈₉	D₄	1	1	yes	characteristic
143	#95×C₈₉	D₄	1	1	yes	characteristic
144	C₂⁴×C₈₉	—	2	1	no	—
145	C₂⁴×C₈₉	—	2	1	no	—
146	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
147	#41×C₈₉	—	2	8	no	—
148	#41×C₈₉	—	4	4	no	—
149	#41×C₈₉	—	4	4	no	—
150	#41×C₈₉	—	4	4	no	—
151	C₂×Q₈×C₈₉	—	2	1	no	—
152	C₂×Q₈×C₈₉	—	2	1	no	—
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	1	no	—
156	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
157	C₂×D₄×C₈₉	—	2	4	no	—
158	C₂×D₄×C₈₉	—	2	4	no	—
159	C₂×D₄×C₈₉	—	2	1	no	—
160	C₂×D₄×C₈₉	—	2	1	no	—
161	C₂×D₄×C₈₉	—	2	1	no	—
162	C₂×D₄×C₈₉	—	2	1	no	—
163	C₂×D₄×C₈₉	—	2	1	no	—
164	C₂×D₄×C₈₉	—	2	1	no	—
165	C₂×D₄×C₈₉	—	2	1	no	—
166	C₂×D₄×C₈₉	—	2	1	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	—	4	2	no	—
171	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
172	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₈₉	#41	1	2	yes	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	1	no	—
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	4	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	—	4	2	no	—
187	C₂²×C₄×C₈₉	—	4	2	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	—	4	2	no	—
193	C₂²×C₄×C₈₉	—	4	2	no	—
194	C₂²×C₄×C₈₉	—	4	2	no	—
195	C₂²×C₄×C₈₉	—	4	2	no	—
196	C₂²×C₄×C₈₉	—	8	1	no	—
197	C₂²×C₄×C₈₉	—	8	1	no	—
198	C₂²×C₄×C₈₉	—	8	1	no	—
199	C₂²×C₄×C₈₉	—	8	1	no	—
200	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	#41	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	SD₁₆×C₈₉	—	4	4	no	—
209	D₈×C₈₉	—	2	8	no	—
210	M₁₆×C₈₉	—	4	4	no	—
211	C₂×C₈×C₈₉	—	2	1	no	—
212	C₂×C₈×C₈₉	—	2	1	no	—
213	C₂×C₈×C₈₉	—	2	1	no	—
214	C₂×C₈×C₈₉	—	2	1	no	—
215	C₂×C₈×C₈₉	—	2	1	no	—
216	C₂×C₈×C₈₉	—	2	1	no	—
217	C₂×C₈×C₈₉	—	2	1	no	—
218	C₂×C₈×C₈₉	—	2	1	no	—
219	C₂×C₈×C₈₉	—	2	1	no	—
220	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
221	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
222	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
223	C₄⋊C₄×C₈₉	—	2	1	no	—
224	C₄⋊C₄×C₈₉	—	2	1	no	—
225	C₄⋊C₄×C₈₉	—	2	1	no	—
226	C₄⋊C₄×C₈₉	—	2	1	no	—
227	C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₄⋊C₄×C₈₉	—	2	1	no	—
229	C₄⋊C₄×C₈₉	—	2	1	no	—
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₄⋊C₄×C₈₉	—	4	2	no	—
232	C₄⋊C₄×C₈₉	—	4	2	no	—
233	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
234	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
235	C₂²⋊C₄×C₈₉	—	2	4	no	—
236	C₂²⋊C₄×C₈₉	—	2	2	no	—
237	C₂²⋊C₄×C₈₉	—	4	1	no	—
238	C₂²⋊C₄×C₈₉	—	4	2	no	—
239	C₂²⋊C₄×C₈₉	—	4	2	no	—
240	C₂²⋊C₄×C₈₉	—	4	2	no	—
241	C₂²⋊C₄×C₈₉	—	4	2	no	—
242	C₂²⋊C₄×C₈₉	—	8	1	no	—
243	C₂²⋊C₄×C₈₉	—	8	1	no	—
244	C₄²×C₈₉	—	2	1	no	—
245	C₄²×C₈₉	—	2	1	no	—
246	C₄²×C₈₉	—	2	1	no	—
247	C₄²×C₈₉	—	2	1	no	—
248	C₄²×C₈₉	—	4	2	no	—
249	C₂³×C₈₉	—	2	2	no	—
250	C₂³×C₈₉	—	2	2	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	2	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	1	no	—
255	C₂³×C₈₉	—	2	1	no	—
256	C₂³×C₈₉	—	2	1	no	—
257	C₂³×C₈₉	—	2	1	no	—
258	C₂³×C₈₉	—	2	2	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	C₄×D₄	1	2	yes	—
270	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₈₉	—	2	2	no	—
272	Q₈×C₈₉	—	2	2	no	—
273	Q₈×C₈₉	—	4	1	no	—
274	Q₈×C₈₉	—	4	1	no	—
275	D₄×C₈₉	—	2	2	no	—
276	D₄×C₈₉	—	2	2	no	—
277	D₄×C₈₉	—	2	2	no	—
278	D₄×C₈₉	—	2	2	no	—
279	D₄×C₈₉	—	2	2	no	—
280	D₄×C₈₉	—	4	8	no	—
281	D₄×C₈₉	—	4	8	no	—
282	D₄×C₈₉	—	4	1	no	—
283	D₄×C₈₉	—	4	1	no	—
284	D₄×C₈₉	C₄×D₄	1	4	yes	complemented
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	1	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	8	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	—	8	4	no	—
322	C₂×C₄×C₈₉	—	8	4	no	—
323	C₂×C₄×C₈₉	—	8	4	no	—
324	C₂×C₄×C₈₉	—	8	4	no	—
325	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
326	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
327	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂²×D₄	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	—	2	2	no	—
338	C₂²×C₈₉	—	2	4	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	2	2	no	—
341	C₂²×C₈₉	—	4	1	no	—
342	C₂²×C₈₉	—	4	2	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	2	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	4	1	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	2	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	C₂×C₄×D₄	1	1	yes	characteristic
359	C₂²×C₈₉	D₄²	1	1	yes	characteristic
360	C₂²×C₈₉	#546	1	1	yes	characteristic
361	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂²×C₈₉	#575	1	1	yes	characteristic
363	C₂²×C₈₉	#576	1	1	yes	characteristic
364	C₂²×C₈₉	#578	1	1	yes	characteristic
365	C₄×C₈₉	—	2	2	no	—
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	4	1	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	2	no	—
371	C₄×C₈₉	—	4	1	no	—
372	C₄×C₈₉	—	4	1	no	—
373	C₄×C₈₉	—	8	1	no	—
374	C₄×C₈₉	—	8	1	no	—
375	C₄×C₈₉	—	8	1	no	—
376	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
377	C₄×C₈₉	#518	1	1	yes	characteristic
378	C₄×C₈₉	#546	1	1	yes	characteristic
379	C₄×C₈₉	#551	1	1	yes	characteristic
380	#22878	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₈₉	—	4	2	no	—
382	C₂×C₈₉	—	4	4	no	—
383	C₂×C₈₉	—	8	2	no	—
384	C₂×C₈₉	#2358	1	1	yes	characteristic
385	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₈₉	#2951	1	1	yes	characteristic
387	C₂×C₈₉	#3264	1	1	yes	characteristic
388	C₂×C₈₉	#3269	1	1	yes	characteristic
389	C₂×C₈₉	#3322	1	1	yes	characteristic
390	C₂×C₈₉	#3330	1	1	yes	characteristic
391	C₂×#449	C₂×C₈₉	1	1	yes	characteristic
392	C₂×C₄×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2361	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2339	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#1973	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#1933	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#1928	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#1862	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#1852	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#1753	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₈₉	#22878	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
417	#449	C₄×C₈₉	1	8	yes	complemented
418	C₄×D₈	—	2	4	no	—
419	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
421	#417	—	2	4	no	—
422	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
433	#391	C₂²×C₈₉	1	1	yes	characteristic
434	#391	C₂²×C₈₉	1	1	yes	characteristic
435	#390	C₂²×C₈₉	1	1	yes	characteristic
436	#389	C₂²×C₈₉	1	1	yes	characteristic
437	#388	—	2	1	no	—
438	#386	—	2	1	no	—
439	#386	—	2	1	no	—
440	#386	—	2	1	no	—
441	#385	—	2	1	no	—
442	#381	—	2	1	no	—
443	#380	C₂²×C₈₉	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×#95	—	2	1	no	—
447	#340	C₂²×C₈₉	1	1	yes	characteristic
448	#340	C₂²×C₈₉	1	1	yes	characteristic
449	#340	C₂²×C₈₉	1	1	yes	characteristic
450	#340	C₂²×C₈₉	1	1	yes	characteristic
451	#336	C₂²×C₈₉	1	1	yes	characteristic
452	#336	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	4	1	no	—
457	C₂×#41	—	4	1	no	—
458	C₂×#41	C₂×C₄×C₈₉	1	4	yes	complemented
459	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂×SD₁₆	—	4	1	no	—
471	C₂×SD₁₆	—	4	1	no	—
472	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	complemented
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	C₂×C₄×C₈₉	1	4	yes	complemented
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	#121	—	2	2	no	—
484	#121	C₂×C₄×C₈₉	1	4	yes	complemented
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	4	1	no	—
489	C₄×D₄	—	4	1	no	—
490	C₄×D₄	—	4	1	no	—
491	C₄×D₄	—	4	4	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	4	1	no	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
513	#107	—	2	2	no	—
514	#107	—	4	1	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	C₂×C₄×C₈₉	1	4	yes	complemented
518	#102	—	2	2	no	—
519	#102	—	2	2	no	—
520	#102	—	4	1	no	—
521	#102	C₂×C₄×C₈₉	1	4	yes	complemented
522	#102	D₄×C₈₉	1	4	yes	complemented
523	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	complemented
524	#97	—	4	1	no	—
525	C₄×C₈	—	2	2	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	—	2	1	no	—
532	#95	—	2	1	no	—
533	#95	D₄×C₈₉	1	1	yes	characteristic
534	#95	D₄×C₈₉	1	1	yes	characteristic
535	C₂⁴	—	2	1	no	—
536	C₂⁴	—	2	1	no	—
537	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
538	#41	—	2	8	no	—
539	#41	—	4	4	no	—
540	#41	—	4	4	no	—
541	#41	—	4	4	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	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	C₂²×C₄×C₈₉	1	2	yes	—
563	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
564	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
565	C₂×D₄	#41×C₈₉	1	2	yes	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	8	1	no	—
588	C₂²×C₄	—	8	1	no	—
589	C₂²×C₄	—	8	1	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
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	#41×C₈₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
599	SD₁₆	—	4	4	no	—
600	D₈	—	2	8	no	—
601	M₁₆	—	4	4	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	—	2	1	no	—
611	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
612	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
613	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
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	C₂²×C₄×C₈₉	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	4	1	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	—	8	1	no	—
634	C₂²⋊C₄	—	8	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	4	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	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	C₄×D₄×C₈₉	1	2	yes	—
661	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	1	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	C₄×D₄×C₈₉	1	4	yes	complemented
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	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	—	4	8	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	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	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
717	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
721	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
722	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
723	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
724	C₈	—	2	2	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	4	1	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
750	C₂²	D₄²×C₈₉	1	1	yes	characteristic
751	C₂²	#546×C₈₉	1	1	yes	characteristic
752	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
753	C₂²	#575×C₈₉	1	1	yes	characteristic
754	C₂²	#576×C₈₉	1	1	yes	characteristic
755	C₂²	#578×C₈₉	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	8	1	no	—
765	C₄	—	8	1	no	—
766	C₄	—	8	1	no	—
767	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
768	C₄	#518×C₈₉	1	1	yes	characteristic
769	C₄	#546×C₈₉	1	1	yes	characteristic
770	C₄	#551×C₈₉	1	1	yes	characteristic
771	C₂	—	4	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	8	2	no	—
774	C₂	C₈₉×#2358	1	1	yes	characteristic
775	C₂	C₄×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
776	C₂	C₈₉×#2951	1	1	yes	characteristic
777	C₂	C₈₉×#3264	1	1	yes	characteristic
778	C₂	C₈₉×#3269	1	1	yes	characteristic
779	C₂	C₈₉×#3322	1	1	yes	characteristic
780	C₂	C₈₉×#3330	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#449×C₈₉	C₂
LCS	G ▷ C₂×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
2. C₂×C₄×D₈×C₈₉	C₂	semidirect
3. C₂×#417×C₈₉	C₂	semidirect
4. C₈₉×#2361	C₂	semidirect
5. C₈₉×#2339	C₂	semidirect
6. C₈₉×#1973	C₂	semidirect
7. C₈₉×#1933	C₂	semidirect
8. C₈₉×#1928	C₂	semidirect
9. C₈₉×#1895	C₂	semidirect
10. C₈₉×#1879	C₂	semidirect
11. C₈₉×#1877	C₂	semidirect
12. C₈₉×#1862	C₂	semidirect
13. C₈₉×#1852	C₂	semidirect
14. C₈₉×#1762	C₂	semidirect
15. C₈₉×#1753	C₂	semidirect
26. #449×C₈₉	C₄	semidirect
67. C₂×#41×C₈₉	C₂×C₄	semidirect
81. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
84. C₂×D₈×C₈₉	C₂×C₄	semidirect
93. #121×C₈₉	C₂×C₄	semidirect
126. #103×C₈₉	C₂×C₄	semidirect
130. #102×C₈₉	C₂×C₄	semidirect
131. #102×C₈₉	D₄	semidirect
132. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
284. D₄×C₈₉	C₄×D₄	semidirect
380. #22878	C₈₉	direct (N × H)
392. C₂×C₄×D₈	C₂×C₈₉	semidirect
393. C₂×#417	C₂×C₈₉	semidirect
394. #2361	C₂×C₈₉	semidirect
395. #2339	C₂×C₈₉	semidirect
396. #1973	C₂×C₈₉	semidirect
397. #1933	C₂×C₈₉	semidirect
398. #1928	C₂×C₈₉	semidirect
399. #1895	C₂×C₈₉	semidirect
400. #1879	C₂×C₈₉	semidirect
401. #1877	C₂×C₈₉	semidirect
402. #1862	C₂×C₈₉	semidirect
403. #1852	C₂×C₈₉	semidirect
404. #1762	C₂×C₈₉	semidirect
405. #1753	C₂×C₈₉	semidirect
406. C₈₉	#22878	direct (N × H)
417. #449	C₄×C₈₉	semidirect
458. C₂×#41	C₂×C₄×C₈₉	semidirect
472. C₂×SD₁₆	C₂×C₄×C₈₉	semidirect
475. C₂×D₈	C₂×C₄×C₈₉	semidirect
484. #121	C₂×C₄×C₈₉	semidirect
517. #103	C₂×C₄×C₈₉	semidirect
521. #102	C₂×C₄×C₈₉	semidirect
522. #102	D₄×C₈₉	semidirect
523. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect
675. D₄	C₄×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×#449×C₈₉	2
C₂×C₄×D₈×C₈₉	2
C₂×#417×C₈₉	2
C₈₉×#2361	2
C₈₉×#2339	2
C₈₉×#1973	2
C₈₉×#1933	2
C₈₉×#1928	2
C₈₉×#1895	2
C₈₉×#1879	2
C₈₉×#1877	2
C₈₉×#1862	2
C₈₉×#1852	2
C₈₉×#1762	2
C₈₉×#1753	2
#22878	89

Subgroups — C89×#22878 #36400726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22878 #36400726