Subgroups — C₈₉×#22877 #36400725

Order 22784.

1158 conjugacy classes of subgroups.

The subgroup lattice has 770 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×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₈₉	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	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	#449×C₈₉	C₄	1	8	yes	complemented
26	C₄×SD₁₆×C₈₉	—	2	4	no	—
27	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
29	#416×C₈₉	—	2	4	no	—
30	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#103×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×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	#390×C₈₉	—	2	1	no	—
42	#390×C₈₉	—	2	1	no	—
43	#390×C₈₉	—	2	1	no	—
44	#390×C₈₉	C₂²	1	1	yes	characteristic
45	#390×C₈₉	C₂²	1	1	yes	characteristic
46	#390×C₈₉	C₂²	1	1	yes	characteristic
47	#389×C₈₉	C₂²	1	1	yes	characteristic
48	#388×C₈₉	—	2	1	no	—
49	#386×C₈₉	—	2	1	no	—
50	#380×C₈₉	—	2	1	no	—
51	#380×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×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	#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	C₂³	1	1	yes	characteristic
76	C₂×SD₁₆×C₈₉	—	2	2	no	—
77	C₂×SD₁₆×C₈₉	—	2	2	no	—
78	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	—
79	C₂×D₈×C₈₉	—	4	1	no	—
80	C₂×D₈×C₈₉	—	4	1	no	—
81	C₂×D₈×C₈₉	C₂×C₄	1	4	yes	—
82	C₂²×C₈×C₈₉	—	2	2	no	—
83	C₂²×C₈×C₈₉	—	2	2	no	—
84	C₂²×C₈×C₈₉	—	4	1	no	—
85	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	#121×C₈₉	—	2	2	no	—
90	#121×C₈₉	C₂×C₄	1	4	yes	—
91	C₄×Q₈×C₈₉	—	2	2	no	—
92	C₄×Q₈×C₈₉	—	2	2	no	—
93	C₄×Q₈×C₈₉	—	4	1	no	—
94	C₄×Q₈×C₈₉	—	4	1	no	—
95	C₄×D₄×C₈₉	—	2	2	no	—
96	C₄×D₄×C₈₉	—	4	1	no	—
97	#117×C₈₉	—	2	2	no	—
98	#117×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	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	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	—	2	1	no	—
121	C₂×C₄²×C₈₉	—	2	1	no	—
122	C₂×C₄²×C₈₉	—	2	1	no	—
123	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
125	#107×C₈₉	—	4	1	no	—
126	#106×C₈₉	—	2	2	no	—
127	#103×C₈₉	—	2	2	no	—
128	#103×C₈₉	C₂×C₄	1	4	yes	complemented
129	#103×C₈₉	D₄	1	4	yes	complemented
130	#102×C₈₉	—	2	2	no	—
131	#102×C₈₉	—	2	2	no	—
132	#102×C₈₉	—	2	2	no	—
133	#102×C₈₉	—	4	1	no	—
134	#102×C₈₉	C₂×C₄	1	4	yes	complemented
135	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
136	C₄×C₈×C₈₉	—	2	2	no	—
137	C₄×C₈×C₈₉	—	4	1	no	—
138	#95×C₈₉	—	2	1	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	D₄	1	1	yes	characteristic
142	#95×C₈₉	D₄	1	1	yes	characteristic
143	C₂⁴×C₈₉	—	2	1	no	—
144	C₂⁴×C₈₉	—	2	1	no	—
145	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
146	#41×C₈₉	—	2	8	no	—
147	#41×C₈₉	—	4	4	no	—
148	#41×C₈₉	—	4	4	no	—
149	#41×C₈₉	—	4	4	no	—
150	C₂×Q₈×C₈₉	—	2	1	no	—
151	C₂×Q₈×C₈₉	—	2	1	no	—
152	C₂×Q₈×C₈₉	—	2	1	no	—
153	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
154	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
155	C₂×Q₈×C₈₉	#41	1	2	yes	—
156	C₂×D₄×C₈₉	—	2	4	no	—
157	C₂×D₄×C₈₉	—	2	4	no	—
158	C₂×D₄×C₈₉	—	2	1	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	—	2	1	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	C₂²×C₄	1	2	yes	—
173	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
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	4	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	—	4	2	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	—	8	1	no	—
190	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	#41	1	2	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₈₉	—	2	8	no	—
199	D₈×C₈₉	—	4	4	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
210	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
211	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
213	C₄⋊C₄×C₈₉	—	2	1	no	—
214	C₄⋊C₄×C₈₉	—	2	1	no	—
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	—	4	2	no	—
222	C₄⋊C₄×C₈₉	—	4	2	no	—
223	C₄⋊C₄×C₈₉	—	8	1	no	—
224	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
225	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₈₉	—	2	4	no	—
227	C₂²⋊C₄×C₈₉	—	2	2	no	—
228	C₂²⋊C₄×C₈₉	—	2	2	no	—
229	C₂²⋊C₄×C₈₉	—	4	2	no	—
230	C₂²⋊C₄×C₈₉	—	4	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	—	8	1	no	—
235	C₂²⋊C₄×C₈₉	—	8	1	no	—
236	C₂²⋊C₄×C₈₉	—	8	1	no	—
237	C₂²⋊C₄×C₈₉	—	8	1	no	—
238	C₄²×C₈₉	—	2	1	no	—
239	C₄²×C₈₉	—	2	1	no	—
240	C₄²×C₈₉	—	2	1	no	—
241	C₄²×C₈₉	—	2	1	no	—
242	C₄²×C₈₉	—	4	2	no	—
243	C₄²×C₈₉	—	4	2	no	—
244	C₄²×C₈₉	—	4	2	no	—
245	C₄²×C₈₉	—	8	1	no	—
246	C₂³×C₈₉	—	2	1	no	—
247	C₂³×C₈₉	—	2	1	no	—
248	C₂³×C₈₉	—	2	1	no	—
249	C₂³×C₈₉	—	2	1	no	—
250	C₂³×C₈₉	—	2	1	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	2	no	—
253	C₂³×C₈₉	—	2	2	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	C₄×D₄	1	2	yes	—
267	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₈₉	—	2	2	no	—
269	Q₈×C₈₉	—	2	2	no	—
270	Q₈×C₈₉	—	2	2	no	—
271	Q₈×C₈₉	C₄×D₄	1	4	yes	—
272	D₄×C₈₉	—	2	2	no	—
273	D₄×C₈₉	—	2	2	no	—
274	D₄×C₈₉	—	2	2	no	—
275	D₄×C₈₉	—	2	2	no	—
276	D₄×C₈₉	—	4	8	no	—
277	D₄×C₈₉	—	4	1	no	—
278	D₄×C₈₉	—	4	1	no	—
279	D₄×C₈₉	—	4	1	no	—
280	D₄×C₈₉	—	4	1	no	—
281	D₄×C₈₉	—	8	4	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	1	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	2	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	2	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	—	4	8	no	—
304	C₂×C₄×C₈₉	—	4	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	—	8	4	no	—
318	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₈₉	#135	1	2	yes	—
320	C₂×C₄×C₈₉	#135	1	2	yes	—
321	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
327	C₈×C₈₉	—	2	2	no	—
328	C₈×C₈₉	—	2	2	no	—
329	C₈×C₈₉	—	2	2	no	—
330	C₈×C₈₉	—	4	1	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	2	no	—
333	C₂²×C₈₉	—	2	2	no	—
334	C₂²×C₈₉	—	4	1	no	—
335	C₂²×C₈₉	—	4	1	no	—
336	C₂²×C₈₉	—	4	1	no	—
337	C₂²×C₈₉	—	4	1	no	—
338	C₂²×C₈₉	—	4	2	no	—
339	C₂²×C₈₉	—	4	2	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	8	1	no	—
345	C₂²×C₈₉	—	8	1	no	—
346	C₂²×C₈₉	—	8	1	no	—
347	C₂²×C₈₉	—	8	1	no	—
348	C₂²×C₈₉	—	8	1	no	—
349	C₂²×C₈₉	—	8	1	no	—
350	C₂²×C₈₉	—	8	1	no	—
351	C₂²×C₈₉	—	8	1	no	—
352	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₈₉	D₄²	1	1	yes	characteristic
354	C₂²×C₈₉	#546	1	1	yes	characteristic
355	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
356	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
357	C₂²×C₈₉	#576	1	1	yes	characteristic
358	C₂²×C₈₉	#577	1	1	yes	characteristic
359	C₄×C₈₉	—	2	2	no	—
360	C₄×C₈₉	—	2	4	no	—
361	C₄×C₈₉	—	2	2	no	—
362	C₄×C₈₉	—	2	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	—	4	1	no	—
366	C₄×C₈₉	—	4	1	no	—
367	C₄×C₈₉	—	8	1	no	—
368	C₄×C₈₉	—	8	1	no	—
369	C₄×C₈₉	—	8	1	no	—
370	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
371	C₄×C₈₉	#518	1	1	yes	characteristic
372	C₄×C₈₉	#546	1	1	yes	characteristic
373	C₄×C₈₉	#551	1	1	yes	characteristic
374	#22877	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂×C₈₉	—	4	2	no	—
376	C₂×C₈₉	—	8	2	no	—
377	C₂×C₈₉	—	8	2	no	—
378	C₂×C₈₉	#2358	1	1	yes	characteristic
379	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
380	C₂×C₈₉	#2946	1	1	yes	characteristic
381	C₂×C₈₉	#3282	1	1	yes	characteristic
382	C₂×C₈₉	#3287	1	1	yes	characteristic
383	C₂×C₈₉	#3301	1	1	yes	characteristic
384	C₂×C₈₉	#3305	1	1	yes	characteristic
385	C₂×#449	C₂×C₈₉	1	1	yes	characteristic
386	C₂×C₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
387	C₂×#416	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#2363	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2341	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#1970	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#1934	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#1926	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#1863	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
398	C₄×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
400	C₈₉	#22877	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
402	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
403	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
404	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
410	#449	C₄×C₈₉	1	8	yes	complemented
411	C₄×SD₁₆	—	2	4	no	—
412	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
414	#416	—	2	4	no	—
415	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
426	#390	—	2	1	no	—
427	#390	—	2	1	no	—
428	#390	—	2	1	no	—
429	#390	C₂²×C₈₉	1	1	yes	characteristic
430	#390	C₂²×C₈₉	1	1	yes	characteristic
431	#390	C₂²×C₈₉	1	1	yes	characteristic
432	#389	C₂²×C₈₉	1	1	yes	characteristic
433	#388	—	2	1	no	—
434	#386	—	2	1	no	—
435	#380	—	2	1	no	—
436	#380	C₂²×C₈₉	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	—	2	1	no	—
440	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
441	#340	C₂²×C₈₉	1	1	yes	characteristic
442	#340	C₂²×C₈₉	1	1	yes	characteristic
443	#340	C₂²×C₈₉	1	1	yes	characteristic
444	#340	C₂²×C₈₉	1	1	yes	characteristic
445	#336	C₂²×C₈₉	1	1	yes	characteristic
446	#336	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	4	1	no	—
451	C₂×#41	—	4	1	no	—
452	C₂×#41	C₂×C₄×C₈₉	1	4	yes	complemented
453	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
461	C₂×SD₁₆	—	2	2	no	—
462	C₂×SD₁₆	—	2	2	no	—
463	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	—
464	C₂×D₈	—	4	1	no	—
465	C₂×D₈	—	4	1	no	—
466	C₂×D₈	C₂×C₄×C₈₉	1	4	yes	—
467	C₂²×C₈	—	2	2	no	—
468	C₂²×C₈	—	2	2	no	—
469	C₂²×C₈	—	4	1	no	—
470	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
474	#121	—	2	2	no	—
475	#121	C₂×C₄×C₈₉	1	4	yes	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	—	4	1	no	—
479	C₄×Q₈	—	4	1	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	4	1	no	—
482	#117	—	2	2	no	—
483	#117	—	4	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	—	2	1	no	—
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
510	#107	—	4	1	no	—
511	#106	—	2	2	no	—
512	#103	—	2	2	no	—
513	#103	C₂×C₄×C₈₉	1	4	yes	complemented
514	#103	D₄×C₈₉	1	4	yes	complemented
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	2	2	no	—
518	#102	—	4	1	no	—
519	#102	C₂×C₄×C₈₉	1	4	yes	complemented
520	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	complemented
521	C₄×C₈	—	2	2	no	—
522	C₄×C₈	—	4	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	D₄×C₈₉	1	1	yes	characteristic
527	#95	D₄×C₈₉	1	1	yes	characteristic
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
531	#41	—	2	8	no	—
532	#41	—	4	4	no	—
533	#41	—	4	4	no	—
534	#41	—	4	4	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
539	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
540	C₂×Q₈	#41×C₈₉	1	2	yes	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	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	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	8	1	no	—
556	C₂×D₄	—	8	1	no	—
557	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
558	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	8	1	no	—
575	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
581	C₂²×C₄	#41×C₈₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
583	SD₁₆	—	2	8	no	—
584	D₈	—	4	4	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	4	4	no	—
595	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
596	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
597	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	8	1	no	—
609	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
610	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	4	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	8	1	no	—
620	C₂²⋊C₄	—	8	1	no	—
621	C₂²⋊C₄	—	8	1	no	—
622	C₂²⋊C₄	—	8	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	4	2	no	—
628	C₄²	—	4	2	no	—
629	C₄²	—	4	2	no	—
630	C₄²	—	8	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	C₄×D₄×C₈₉	1	2	yes	—
652	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	C₄×D₄×C₈₉	1	4	yes	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	8	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	8	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	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	—	8	4	no	—
703	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
704	C₂×C₄	#135×C₈₉	1	2	yes	—
705	C₂×C₄	#135×C₈₉	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
709	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
710	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
711	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	2	no	—
715	C₈	—	4	1	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
738	C₂²	D₄²×C₈₉	1	1	yes	characteristic
739	C₂²	#546×C₈₉	1	1	yes	characteristic
740	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
741	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
742	C₂²	#576×C₈₉	1	1	yes	characteristic
743	C₂²	#577×C₈₉	1	1	yes	characteristic
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
756	C₄	#518×C₈₉	1	1	yes	characteristic
757	C₄	#546×C₈₉	1	1	yes	characteristic
758	C₄	#551×C₈₉	1	1	yes	characteristic
759	C₂	—	4	2	no	—
760	C₂	—	8	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₈₉×#2358	1	1	yes	characteristic
763	C₂	C₄×#135×C₈₉	1	1	yes	characteristic
764	C₂	C₈₉×#2946	1	1	yes	characteristic
765	C₂	C₈₉×#3282	1	1	yes	characteristic
766	C₂	C₈₉×#3287	1	1	yes	characteristic
767	C₂	C₈₉×#3301	1	1	yes	characteristic
768	C₂	C₈₉×#3305	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×SD₁₆×C₈₉	C₂	semidirect
3. C₂×#416×C₈₉	C₂	semidirect
4. C₈₉×#2363	C₂	semidirect
5. C₈₉×#2341	C₂	semidirect
6. C₈₉×#1970	C₂	semidirect
7. C₈₉×#1934	C₂	semidirect
8. C₈₉×#1926	C₂	semidirect
9. C₈₉×#1893	C₂	semidirect
10. C₈₉×#1880	C₂	semidirect
11. C₈₉×#1879	C₂	semidirect
12. C₈₉×#1863	C₂	semidirect
13. C₈₉×#1854	C₂	semidirect
14. C₄×#103×C₈₉	C₂	semidirect
15. C₈×C₂²⋊C₄×C₈₉	C₂	semidirect
25. #449×C₈₉	C₄	semidirect
67. C₂×#41×C₈₉	C₂×C₄	semidirect
128. #103×C₈₉	C₂×C₄	semidirect
129. #103×C₈₉	D₄	semidirect
134. #102×C₈₉	C₂×C₄	semidirect
135. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
374. #22877	C₈₉	direct (N × H)
386. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
387. C₂×#416	C₂×C₈₉	semidirect
388. #2363	C₂×C₈₉	semidirect
389. #2341	C₂×C₈₉	semidirect
390. #1970	C₂×C₈₉	semidirect
391. #1934	C₂×C₈₉	semidirect
392. #1926	C₂×C₈₉	semidirect
393. #1893	C₂×C₈₉	semidirect
394. #1880	C₂×C₈₉	semidirect
395. #1879	C₂×C₈₉	semidirect
396. #1863	C₂×C₈₉	semidirect
397. #1854	C₂×C₈₉	semidirect
398. C₄×#103	C₂×C₈₉	semidirect
399. C₈×C₂²⋊C₄	C₂×C₈₉	semidirect
400. C₈₉	#22877	direct (N × H)
410. #449	C₄×C₈₉	semidirect
452. C₂×#41	C₂×C₄×C₈₉	semidirect
513. #103	C₂×C₄×C₈₉	semidirect
514. #103	D₄×C₈₉	semidirect
519. #102	C₂×C₄×C₈₉	semidirect
520. C₂²⋊C₈	C₂×C₄×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×SD₁₆×C₈₉	2
C₂×#416×C₈₉	2
C₈₉×#2363	2
C₈₉×#2341	2
C₈₉×#1970	2
C₈₉×#1934	2
C₈₉×#1926	2
C₈₉×#1893	2
C₈₉×#1880	2
C₈₉×#1879	2
C₈₉×#1863	2
C₈₉×#1854	2
C₄×#103×C₈₉	2
C₈×C₂²⋊C₄×C₈₉	2
#22877	89

Subgroups — C89×#22877 #36400725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22877 #36400725