Subgroups — C₈₉×#24762 #36402610

Order 22784.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 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×#466×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2619	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1804	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	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	#469×C₈₉	—	2	4	no	—
27	#466×C₈₉	—	2	4	no	—
28	#459×C₈₉	—	2	4	no	—
29	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
31	#424×C₈₉	—	2	4	no	—
32	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
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×#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×#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	#394×C₈₉	—	2	1	no	—
45	#394×C₈₉	—	2	1	no	—
46	#392×C₈₉	—	2	1	no	—
47	#392×C₈₉	—	2	1	no	—
48	#390×C₈₉	—	2	1	no	—
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#388×C₈₉	—	2	1	no	—
54	#386×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	#382×C₈₉	C₂²	1	1	yes	characteristic
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#340×C₈₉	C₂²	1	1	yes	characteristic
62	#340×C₈₉	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
67	C₂²×D₄×C₈₉	—	2	1	no	—
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	—	2	1	no	—
72	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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×D₈×C₈₉	—	4	1	no	—
79	C₂×M₁₆×C₈₉	—	2	2	no	—
80	C₂×M₁₆×C₈₉	—	2	2	no	—
81	C₂×M₁₆×C₈₉	—	4	1	no	—
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	#127×C₈₉	—	2	2	no	—
90	#127×C₈₉	—	2	2	no	—
91	#121×C₈₉	—	2	2	no	—
92	#121×C₈₉	—	2	2	no	—
93	#121×C₈₉	—	2	2	no	—
94	#121×C₈₉	—	2	2	no	—
95	#121×C₈₉	—	2	2	no	—
96	#121×C₈₉	D₄	1	4	yes	complemented
97	C₄×D₄×C₈₉	—	2	2	no	—
98	C₄×D₄×C₈₉	—	2	2	no	—
99	#117×C₈₉	—	2	2	no	—
100	#117×C₈₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	D₄	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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
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	—	2	2	no	—
126	#106×C₈₉	—	2	2	no	—
127	C₄⋊C₈×C₈₉	—	2	2	no	—
128	C₄⋊C₈×C₈₉	—	2	2	no	—
129	C₄⋊C₈×C₈₉	—	2	2	no	—
130	C₄⋊C₈×C₈₉	D₄	1	4	yes	complemented
131	#102×C₈₉	—	2	2	no	—
132	#102×C₈₉	—	2	2	no	—
133	#102×C₈₉	—	2	2	no	—
134	#102×C₈₉	—	2	2	no	—
135	#102×C₈₉	—	2	2	no	—
136	#102×C₈₉	—	2	2	no	—
137	#102×C₈₉	—	4	1	no	—
138	#102×C₈₉	—	4	1	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	—	2	1	no	—
142	#95×C₈₉	—	2	1	no	—
143	#95×C₈₉	—	2	1	no	—
144	C₂⁴×C₈₉	—	2	1	no	—
145	C₂⁴×C₈₉	—	2	1	no	—
146	C₂⁴×C₈₉	—	2	1	no	—
147	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₈₉	—	2	4	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	—	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	—	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	—	8	1	no	—
176	C₂×D₄×C₈₉	—	8	1	no	—
177	C₂×D₄×C₈₉	—	8	1	no	—
178	C₂×D₄×C₈₉	—	8	1	no	—
179	C₂×D₄×C₈₉	—	8	1	no	—
180	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	4	2	no	—
191	C₂²×C₄×C₈₉	—	8	1	no	—
192	C₂²×C₄×C₈₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₈₉	#41	1	2	yes	—
200	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
201	D₈×C₈₉	—	4	4	no	—
202	D₈×C₈₉	—	4	4	no	—
203	M₁₆×C₈₉	—	4	4	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	—	2	1	no	—
213	C₂×C₈×C₈₉	—	2	1	no	—
214	C₂×C₈×C₈₉	—	4	4	no	—
215	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₈₉	—	2	2	no	—
218	C₄⋊C₄×C₈₉	—	2	2	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	—	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	—	8	1	no	—
229	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
230	C₂²⋊C₄×C₈₉	—	2	4	no	—
231	C₂²⋊C₄×C₈₉	—	2	2	no	—
232	C₂²⋊C₄×C₈₉	—	2	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	—	8	1	no	—
237	C₂²⋊C₄×C₈₉	—	8	1	no	—
238	C₂²⋊C₄×C₈₉	—	8	1	no	—
239	C₂²⋊C₄×C₈₉	—	8	1	no	—
240	C₂²⋊C₄×C₈₉	—	8	1	no	—
241	C₂²⋊C₄×C₈₉	—	8	1	no	—
242	C₂²⋊C₄×C₈₉	—	8	1	no	—
243	C₄²×C₈₉	—	2	1	no	—
244	C₄²×C₈₉	—	2	1	no	—
245	C₄²×C₈₉	—	8	1	no	—
246	C₄²×C₈₉	C₂×D₄	1	2	yes	—
247	C₄²×C₈₉	#41	1	2	yes	—
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	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
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	#121	1	2	yes	—
276	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
277	D₄×C₈₉	—	2	2	no	—
278	D₄×C₈₉	—	2	2	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	—	4	1	no	—
287	D₄×C₈₉	—	4	1	no	—
288	D₄×C₈₉	—	4	1	no	—
289	D₄×C₈₉	—	8	4	no	—
290	D₄×C₈₉	—	8	4	no	—
291	D₄×C₈₉	—	8	4	no	—
292	D₄×C₈₉	—	8	4	no	—
293	D₄×C₈₉	—	8	4	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	1	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	8	4	no	—
326	C₂×C₄×C₈₉	#121	1	2	yes	—
327	C₂×C₄×C₈₉	#121	1	2	yes	—
328	C₂×C₄×C₈₉	#121	1	2	yes	—
329	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
335	C₈×C₈₉	—	2	2	no	—
336	C₈×C₈₉	—	2	2	no	—
337	C₈×C₈₉	—	4	1	no	—
338	C₈×C₈₉	—	4	1	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	2	2	no	—
341	C₂²×C₈₉	—	2	2	no	—
342	C₂²×C₈₉	—	4	1	no	—
343	C₂²×C₈₉	—	4	1	no	—
344	C₂²×C₈₉	—	4	1	no	—
345	C₂²×C₈₉	—	4	1	no	—
346	C₂²×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	—	4	2	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	—	8	1	no	—
364	C₂²×C₈₉	—	8	1	no	—
365	C₂²×C₈₉	—	8	1	no	—
366	C₂²×C₈₉	—	8	1	no	—
367	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
368	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
369	C₂²×C₈₉	#537	1	1	yes	characteristic
370	C₂²×C₈₉	#576	1	1	yes	characteristic
371	C₂²×C₈₉	#576	1	1	yes	characteristic
372	C₂²×C₈₉	#576	1	1	yes	characteristic
373	C₂²×C₈₉	#577	1	1	yes	characteristic
374	C₄×C₈₉	—	2	2	no	—
375	C₄×C₈₉	—	2	2	no	—
376	C₄×C₈₉	—	2	2	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	—	4	1	no	—
379	C₄×C₈₉	—	4	1	no	—
380	C₄×C₈₉	—	8	1	no	—
381	C₄×C₈₉	—	8	1	no	—
382	C₄×C₈₉	—	8	1	no	—
383	C₄×C₈₉	—	8	1	no	—
384	C₄×C₈₉	D₄²	1	1	yes	characteristic
385	C₄×C₈₉	#547	1	1	yes	characteristic
386	C₄×C₈₉	#548	1	1	yes	characteristic
387	C₄×C₈₉	#553	1	1	yes	characteristic
388	#24762	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂×C₈₉	—	4	2	no	—
390	C₂×C₈₉	—	8	2	no	—
391	C₂×C₈₉	—	16	1	no	—
392	C₂×C₈₉	—	16	1	no	—
393	C₂×C₈₉	#2416	1	1	yes	characteristic
394	C₂×C₈₉	#3041	1	1	yes	characteristic
395	C₂×C₈₉	#3045	1	1	yes	characteristic
396	C₂×C₈₉	#3058	1	1	yes	characteristic
397	C₂×C₈₉	#3062	1	1	yes	characteristic
398	C₂×C₈₉	#3257	1	1	yes	characteristic
399	C₂×C₈₉	#3259	1	1	yes	characteristic
400	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₂×#466	C₂×C₈₉	1	1	yes	characteristic, complemented
402	C₂×#459	C₂×C₈₉	1	1	yes	characteristic, complemented
403	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#2619	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2067	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#2065	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#1982	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#1949	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#1804	C₂×C₈₉	1	1	yes	characteristic, complemented
415	C₈₉	#24762	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
417	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
419	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#127	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×#121	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
426	#469	—	2	4	no	—
427	#466	—	2	4	no	—
428	#459	—	2	4	no	—
429	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
431	#424	—	2	4	no	—
432	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×C₄⋊C₈	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×#102	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
444	#394	—	2	1	no	—
445	#394	—	2	1	no	—
446	#392	—	2	1	no	—
447	#392	—	2	1	no	—
448	#390	—	2	1	no	—
449	#390	C₂²×C₈₉	1	1	yes	characteristic
450	#390	C₂²×C₈₉	1	1	yes	characteristic
451	#390	C₂²×C₈₉	1	1	yes	characteristic
452	#389	C₂²×C₈₉	1	1	yes	characteristic
453	#388	—	2	1	no	—
454	#386	—	2	1	no	—
455	#385	—	2	1	no	—
456	#382	C₂²×C₈₉	1	1	yes	characteristic
457	#380	C₂²×C₈₉	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
459	#340	C₂²×C₈₉	1	1	yes	characteristic
460	#340	C₂²×C₈₉	1	1	yes	characteristic
461	#340	C₂²×C₈₉	1	1	yes	characteristic
462	#340	C₂²×C₈₉	1	1	yes	characteristic
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	2	2	no	—
476	C₂×D₈	—	2	2	no	—
477	C₂×D₈	—	4	1	no	—
478	C₂×D₈	—	4	1	no	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	2	2	no	—
481	C₂×M₁₆	—	4	1	no	—
482	C₂²×C₈	—	2	2	no	—
483	C₂²×C₈	—	2	2	no	—
484	C₂²×C₈	—	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	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	D₄×C₈₉	1	4	yes	complemented
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	#117	—	2	2	no	—
500	#117	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×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×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	—	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	D₄×C₈₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
522	C₂×C₄²	—	2	1	no	—
523	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
525	#107	—	2	2	no	—
526	#106	—	2	2	no	—
527	C₄⋊C₈	—	2	2	no	—
528	C₄⋊C₈	—	2	2	no	—
529	C₄⋊C₈	—	2	2	no	—
530	C₄⋊C₈	D₄×C₈₉	1	4	yes	complemented
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	4	1	no	—
538	#102	—	4	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	1	no	—
546	C₂⁴	—	2	1	no	—
547	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
548	C₂×D₄	—	2	4	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	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	—	8	1	no	—
572	C₂×D₄	—	8	1	no	—
573	C₂×D₄	—	8	1	no	—
574	C₂×D₄	—	8	1	no	—
575	C₂×D₄	—	8	1	no	—
576	C₂×D₄	—	8	1	no	—
577	C₂×D₄	—	8	1	no	—
578	C₂×D₄	—	8	1	no	—
579	C₂×D₄	—	8	1	no	—
580	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
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	—	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	—	8	1	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	2	yes	—
599	C₂²×C₄	#41×C₈₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
601	D₈	—	4	4	no	—
602	D₈	—	4	4	no	—
603	M₁₆	—	4	4	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	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	4	4	no	—
615	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
616	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	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	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	8	1	no	—
629	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	—	8	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	8	1	no	—
646	C₄²	C₂×D₄×C₈₉	1	2	yes	—
647	C₄²	#41×C₈₉	1	2	yes	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	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	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	#121×C₈₉	1	2	yes	—
676	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
677	D₄	—	2	2	no	—
678	D₄	—	2	2	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	—	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	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	4	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	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	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	—	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	—	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	#121×C₈₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
731	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
732	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
733	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
734	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	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	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
768	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
769	C₂²	#537×C₈₉	1	1	yes	characteristic
770	C₂²	#576×C₈₉	1	1	yes	characteristic
771	C₂²	#576×C₈₉	1	1	yes	characteristic
772	C₂²	#576×C₈₉	1	1	yes	characteristic
773	C₂²	#577×C₈₉	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	8	1	no	—
781	C₄	—	8	1	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	D₄²×C₈₉	1	1	yes	characteristic
785	C₄	#547×C₈₉	1	1	yes	characteristic
786	C₄	#548×C₈₉	1	1	yes	characteristic
787	C₄	#553×C₈₉	1	1	yes	characteristic
788	C₂	—	4	2	no	—
789	C₂	—	8	2	no	—
790	C₂	—	16	1	no	—
791	C₂	—	16	1	no	—
792	C₂	C₈₉×#2416	1	1	yes	characteristic
793	C₂	C₈₉×#3041	1	1	yes	characteristic
794	C₂	C₈₉×#3045	1	1	yes	characteristic
795	C₂	C₈₉×#3058	1	1	yes	characteristic
796	C₂	C₈₉×#3062	1	1	yes	characteristic
797	C₂	C₈₉×#3257	1	1	yes	characteristic
798	C₂	C₈₉×#3259	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 ◁ C₂×#117×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×#466×C₈₉	C₂	semidirect
3. C₂×#459×C₈₉	C₂	semidirect
4. C₂×#424×C₈₉	C₂	semidirect
5. C₈₉×#2619	C₂	semidirect
6. C₈₉×#2324	C₂	semidirect
7. C₈₉×#2067	C₂	semidirect
8. C₈₉×#2065	C₂	semidirect
9. C₈₉×#2054	C₂	semidirect
10. C₈₉×#2054	C₂	semidirect
11. C₈₉×#1982	C₂	semidirect
12. C₈₉×#1949	C₂	semidirect
13. C₈₉×#1895	C₂	semidirect
14. C₈₉×#1893	C₂	semidirect
15. C₈₉×#1804	C₂	semidirect
96. #121×C₈₉	D₄	semidirect
130. C₄⋊C₈×C₈₉	D₄	semidirect
388. #24762	C₈₉	direct (N × H)
400. C₂×#469	C₂×C₈₉	semidirect
401. C₂×#466	C₂×C₈₉	semidirect
402. C₂×#459	C₂×C₈₉	semidirect
403. C₂×#424	C₂×C₈₉	semidirect
404. #2619	C₂×C₈₉	semidirect
405. #2324	C₂×C₈₉	semidirect
406. #2067	C₂×C₈₉	semidirect
407. #2065	C₂×C₈₉	semidirect
408. #2054	C₂×C₈₉	semidirect
409. #2054	C₂×C₈₉	semidirect
410. #1982	C₂×C₈₉	semidirect
411. #1949	C₂×C₈₉	semidirect
412. #1895	C₂×C₈₉	semidirect
413. #1893	C₂×C₈₉	semidirect
414. #1804	C₂×C₈₉	semidirect
415. C₈₉	#24762	direct (N × H)
496. #121	D₄×C₈₉	semidirect
530. C₄⋊C₈	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×#466×C₈₉	2
C₂×#459×C₈₉	2
C₂×#424×C₈₉	2
C₈₉×#2619	2
C₈₉×#2324	2
C₈₉×#2067	2
C₈₉×#2065	2
C₈₉×#2054	2
C₈₉×#1982	2
C₈₉×#1949	2
C₈₉×#1895	2
C₈₉×#1893	2
C₈₉×#1804	2
#24762	89

Subgroups — C89×#24762 #36402610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24762 #36402610