Subgroups — C₈₉×#25383 #36403231

Order 22784.

1048 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#496×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	#496×C₈₉	—	2	4	no	—
30	#464×C₈₉	—	2	4	no	—
31	#464×C₈₉	—	2	4	no	—
32	#463×C₈₉	—	2	4	no	—
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
45	#394×C₈₉	—	2	1	no	—
46	#394×C₈₉	—	2	1	no	—
47	#391×C₈₉	C₂²	1	1	yes	characteristic
48	#390×C₈₉	—	2	1	no	—
49	#390×C₈₉	—	2	1	no	—
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#388×C₈₉	—	2	1	no	—
54	#388×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	#336×C₈₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	—	2	1	no	—
67	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₈₉	—	2	1	no	—
71	C₂×Q₁₆×C₈₉	—	2	2	no	—
72	C₂×Q₁₆×C₈₉	—	2	2	no	—
73	C₂×Q₁₆×C₈₉	—	4	1	no	—
74	C₂×SD₁₆×C₈₉	—	2	2	no	—
75	C₂×SD₁₆×C₈₉	—	2	2	no	—
76	C₂×SD₁₆×C₈₉	—	2	2	no	—
77	C₂×SD₁₆×C₈₉	—	2	2	no	—
78	C₂×SD₁₆×C₈₉	—	2	2	no	—
79	C₂×SD₁₆×C₈₉	—	2	2	no	—
80	C₂×SD₁₆×C₈₉	—	4	1	no	—
81	C₂×SD₁₆×C₈₉	—	4	1	no	—
82	C₂×SD₁₆×C₈₉	—	4	1	no	—
83	C₂×D₈×C₈₉	—	2	2	no	—
84	C₂×D₈×C₈₉	—	2	2	no	—
85	C₂×D₈×C₈₉	—	2	2	no	—
86	C₂×D₈×C₈₉	—	2	2	no	—
87	C₂×D₈×C₈₉	—	4	1	no	—
88	C₂×D₈×C₈₉	—	4	1	no	—
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	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	#127×C₈₉	—	2	2	no	—
94	#127×C₈₉	—	2	2	no	—
95	#124×C₈₉	—	2	2	no	—
96	#124×C₈₉	—	2	2	no	—
97	#124×C₈₉	—	2	2	no	—
98	#124×C₈₉	—	4	1	no	—
99	#124×C₈₉	—	4	1	no	—
100	#124×C₈₉	D₄	1	4	yes	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	2	2	no	—
103	C₄×Q₈×C₈₉	—	2	2	no	—
104	C₄×Q₈×C₈₉	—	4	1	no	—
105	C₄×D₄×C₈₉	—	2	2	no	—
106	C₄×D₄×C₈₉	—	4	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₄²×C₈₉	—	2	1	no	—
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	—	2	2	no	—
134	C₄⋊C₈×C₈₉	—	2	2	no	—
135	C₄⋊C₈×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	D₄	1	4	yes	complemented
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	4	1	no	—
143	#102×C₈₉	—	4	1	no	—
144	#97×C₈₉	—	2	2	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	D₄	1	1	yes	characteristic
149	#95×C₈₉	D₄	1	1	yes	characteristic
150	C₂⁴×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×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	—	2	1	no	—
157	C₂×Q₈×C₈₉	—	2	1	no	—
158	C₂×Q₈×C₈₉	—	2	1	no	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
164	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	—	2	1	no	—
176	C₂×D₄×C₈₉	—	2	1	no	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	4	2	no	—
186	C₂×D₄×C₈₉	—	8	1	no	—
187	C₂×D₄×C₈₉	—	8	1	no	—
188	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
204	Q₁₆×C₈₉	—	4	4	no	—
205	SD₁₆×C₈₉	—	4	4	no	—
206	SD₁₆×C₈₉	—	4	4	no	—
207	SD₁₆×C₈₉	—	4	4	no	—
208	D₈×C₈₉	—	4	4	no	—
209	D₈×C₈₉	—	4	4	no	—
210	C₂×C₈×C₈₉	—	2	1	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	C₂×D₄	1	2	yes	—
221	C₂×C₈×C₈₉	#41	1	2	yes	—
222	C₄⋊C₄×C₈₉	—	2	1	no	—
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	—	4	1	no	—
228	C₄⋊C₄×C₈₉	—	4	1	no	—
229	C₄⋊C₄×C₈₉	—	4	2	no	—
230	C₄⋊C₄×C₈₉	—	4	2	no	—
231	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	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	C₂²⋊C₄×C₈₉	—	8	1	no	—
242	C₂²⋊C₄×C₈₉	—	8	1	no	—
243	C₂²⋊C₄×C₈₉	—	8	1	no	—
244	C₂²⋊C₄×C₈₉	—	8	1	no	—
245	C₄²×C₈₉	—	2	1	no	—
246	C₄²×C₈₉	—	2	1	no	—
247	C₄²×C₈₉	—	2	1	no	—
248	C₄²×C₈₉	—	2	1	no	—
249	C₄²×C₈₉	—	4	2	no	—
250	C₄²×C₈₉	—	4	2	no	—
251	C₄²×C₈₉	—	8	1	no	—
252	C₄²×C₈₉	C₂×D₄	1	2	yes	—
253	C₄²×C₈₉	#41	1	2	yes	—
254	C₂³×C₈₉	—	2	2	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	—	4	1	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₈₉	—	2	2	no	—
277	Q₈×C₈₉	—	2	2	no	—
278	Q₈×C₈₉	—	2	2	no	—
279	Q₈×C₈₉	—	2	2	no	—
280	Q₈×C₈₉	—	4	1	no	—
281	Q₈×C₈₉	—	4	1	no	—
282	Q₈×C₈₉	—	4	1	no	—
283	Q₈×C₈₉	—	4	1	no	—
284	D₄×C₈₉	—	2	2	no	—
285	D₄×C₈₉	—	2	2	no	—
286	D₄×C₈₉	—	4	1	no	—
287	D₄×C₈₉	—	4	1	no	—
288	D₄×C₈₉	—	4	1	no	—
289	D₄×C₈₉	—	4	1	no	—
290	D₄×C₈₉	—	4	1	no	—
291	D₄×C₈₉	—	4	1	no	—
292	D₄×C₈₉	—	4	1	no	—
293	D₄×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	4	1	no	—
295	D₄×C₈₉	—	4	1	no	—
296	D₄×C₈₉	—	8	4	no	—
297	D₄×C₈₉	—	8	4	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	2	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	#121	1	2	yes	—
331	C₂×C₄×C₈₉	#121	1	2	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
338	C₈×C₈₉	—	2	2	no	—
339	C₈×C₈₉	—	2	2	no	—
340	C₈×C₈₉	—	4	1	no	—
341	C₈×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	—	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	—	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	C₂×#121	1	1	yes	characteristic
364	C₂²×C₈₉	D₄²	1	1	yes	characteristic
365	C₂²×C₈₉	#550	1	1	yes	characteristic
366	C₂²×C₈₉	#575	1	1	yes	characteristic
367	C₂²×C₈₉	#575	1	1	yes	characteristic
368	C₂²×C₈₉	#576	1	1	yes	characteristic
369	C₂²×C₈₉	#577	1	1	yes	characteristic
370	C₄×C₈₉	—	2	2	no	—
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	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	—	4	1	no	—
379	C₄×C₈₉	—	8	1	no	—
380	C₄×C₈₉	—	8	1	no	—
381	C₄×C₈₉	#532	1	1	yes	characteristic
382	C₄×C₈₉	#540	1	1	yes	characteristic
383	C₄×C₈₉	D₄²	1	1	yes	characteristic
384	C₄×C₈₉	#546	1	1	yes	characteristic
385	#25383	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂×C₈₉	—	8	2	no	—
387	C₂×C₈₉	—	16	1	no	—
388	C₂×C₈₉	—	16	1	no	—
389	C₂×C₈₉	#2428	1	1	yes	characteristic
390	C₂×C₈₉	#3040	1	1	yes	characteristic
391	C₂×C₈₉	#3045	1	1	yes	characteristic
392	C₂×C₈₉	#3268	1	1	yes	characteristic
393	C₂×C₈₉	#3271	1	1	yes	characteristic
394	C₂×C₈₉	#3401	1	1	yes	characteristic
395	C₂×C₈₉	#3403	1	1	yes	characteristic
396	C₂×#496	C₂×C₈₉	1	1	yes	characteristic
397	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
398	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2548	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#2367	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#2015	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#1982	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#1940	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#1763	C₂×C₈₉	1	1	yes	characteristic, complemented
411	C₈₉	#25383	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
413	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
417	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
425	#496	—	2	4	no	—
426	#464	—	2	4	no	—
427	#464	—	2	4	no	—
428	#463	—	2	4	no	—
429	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#103	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×#102	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
441	#394	—	2	1	no	—
442	#394	—	2	1	no	—
443	#391	C₂²×C₈₉	1	1	yes	characteristic
444	#390	—	2	1	no	—
445	#390	—	2	1	no	—
446	#390	C₂²×C₈₉	1	1	yes	characteristic
447	#390	C₂²×C₈₉	1	1	yes	characteristic
448	#390	C₂²×C₈₉	1	1	yes	characteristic
449	#388	—	2	1	no	—
450	#388	—	2	1	no	—
451	#385	—	2	1	no	—
452	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	—	2	1	no	—
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×Q₈	C₂³×C₈₉	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
466	C₂³×C₄	—	2	1	no	—
467	C₂×Q₁₆	—	2	2	no	—
468	C₂×Q₁₆	—	2	2	no	—
469	C₂×Q₁₆	—	4	1	no	—
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	2	2	no	—
472	C₂×SD₁₆	—	2	2	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	4	1	no	—
477	C₂×SD₁₆	—	4	1	no	—
478	C₂×SD₁₆	—	4	1	no	—
479	C₂×D₈	—	2	2	no	—
480	C₂×D₈	—	2	2	no	—
481	C₂×D₈	—	2	2	no	—
482	C₂×D₈	—	2	2	no	—
483	C₂×D₈	—	4	1	no	—
484	C₂×D₈	—	4	1	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	#127	—	2	2	no	—
490	#127	—	2	2	no	—
491	#124	—	2	2	no	—
492	#124	—	2	2	no	—
493	#124	—	2	2	no	—
494	#124	—	4	1	no	—
495	#124	—	4	1	no	—
496	#124	D₄×C₈₉	1	4	yes	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	4	1	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	4	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
529	C₄⋊C₈	—	2	2	no	—
530	C₄⋊C₈	—	2	2	no	—
531	C₄⋊C₈	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	2	2	no	—
534	#103	D₄×C₈₉	1	4	yes	complemented
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	4	1	no	—
539	#102	—	4	1	no	—
540	#97	—	2	2	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	D₄×C₈₉	1	1	yes	characteristic
545	#95	D₄×C₈₉	1	1	yes	characteristic
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
560	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	8	1	no	—
583	C₂×D₄	—	8	1	no	—
584	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	8	1	no	—
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	C₂×D₄×C₈₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	SD₁₆	—	4	4	no	—
603	SD₁₆	—	4	4	no	—
604	D₈	—	4	4	no	—
605	D₈	—	4	4	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	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
617	C₂×C₈	#41×C₈₉	1	2	yes	—
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	—	2	1	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	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	—	8	1	no	—
637	C₂²⋊C₄	—	8	1	no	—
638	C₂²⋊C₄	—	8	1	no	—
639	C₂²⋊C₄	—	8	1	no	—
640	C₂²⋊C₄	—	8	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	8	1	no	—
648	C₄²	C₂×D₄×C₈₉	1	2	yes	—
649	C₄²	#41×C₈₉	1	2	yes	—
650	C₂³	—	2	2	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	—	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	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	2	2	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	Q₈	—	4	1	no	—
679	Q₈	—	4	1	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	8	4	no	—
693	D₄	—	8	4	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	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	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	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	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	#121×C₈₉	1	2	yes	—
727	C₂×C₄	#121×C₈₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
730	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
732	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
733	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	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	C₂×#121×C₈₉	1	1	yes	characteristic
760	C₂²	D₄²×C₈₉	1	1	yes	characteristic
761	C₂²	#550×C₈₉	1	1	yes	characteristic
762	C₂²	#575×C₈₉	1	1	yes	characteristic
763	C₂²	#575×C₈₉	1	1	yes	characteristic
764	C₂²	#576×C₈₉	1	1	yes	characteristic
765	C₂²	#577×C₈₉	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	8	1	no	—
776	C₄	—	8	1	no	—
777	C₄	#532×C₈₉	1	1	yes	characteristic
778	C₄	#540×C₈₉	1	1	yes	characteristic
779	C₄	D₄²×C₈₉	1	1	yes	characteristic
780	C₄	#546×C₈₉	1	1	yes	characteristic
781	C₂	—	8	2	no	—
782	C₂	—	16	1	no	—
783	C₂	—	16	1	no	—
784	C₂	C₈₉×#2428	1	1	yes	characteristic
785	C₂	C₈₉×#3040	1	1	yes	characteristic
786	C₂	C₈₉×#3045	1	1	yes	characteristic
787	C₂	C₈₉×#3268	1	1	yes	characteristic
788	C₂	C₈₉×#3271	1	1	yes	characteristic
789	C₂	C₈₉×#3401	1	1	yes	characteristic
790	C₂	C₈₉×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#496×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₄⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#464×C₈₉	C₂	semidirect
3. C₂×#464×C₈₉	C₂	semidirect
4. C₂×#463×C₈₉	C₂	semidirect
5. C₈₉×#2548	C₂	semidirect
6. C₈₉×#2367	C₂	semidirect
7. C₈₉×#2055	C₂	semidirect
8. C₈₉×#2054	C₂	semidirect
9. C₈₉×#2015	C₂	semidirect
10. C₈₉×#2012	C₂	semidirect
11. C₈₉×#1982	C₂	semidirect
12. C₈₉×#1940	C₂	semidirect
13. C₈₉×#1880	C₂	semidirect
14. C₈₉×#1879	C₂	semidirect
15. C₈₉×#1763	C₂	semidirect
138. #103×C₈₉	D₄	semidirect
385. #25383	C₈₉	direct (N × H)
397. C₂×#464	C₂×C₈₉	semidirect
398. C₂×#464	C₂×C₈₉	semidirect
399. C₂×#463	C₂×C₈₉	semidirect
400. #2548	C₂×C₈₉	semidirect
401. #2367	C₂×C₈₉	semidirect
402. #2055	C₂×C₈₉	semidirect
403. #2054	C₂×C₈₉	semidirect
404. #2015	C₂×C₈₉	semidirect
405. #2012	C₂×C₈₉	semidirect
406. #1982	C₂×C₈₉	semidirect
407. #1940	C₂×C₈₉	semidirect
408. #1880	C₂×C₈₉	semidirect
409. #1879	C₂×C₈₉	semidirect
410. #1763	C₂×C₈₉	semidirect
411. C₈₉	#25383	direct (N × H)
534. #103	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×#496×C₈₉	2
C₂×#464×C₈₉	2
C₂×#463×C₈₉	2
C₈₉×#2548	2
C₈₉×#2367	2
C₈₉×#2055	2
C₈₉×#2054	2
C₈₉×#2015	2
C₈₉×#2012	2
C₈₉×#1982	2
C₈₉×#1940	2
C₈₉×#1880	2
C₈₉×#1879	2
C₈₉×#1763	2
#25383	89

Subgroups — C89×#25383 #36403231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25383 #36403231