Subgroups — C₈₉×#25089 #36402937

Order 22784.

1078 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#467×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2432	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
27	#467×C₈₉	—	2	4	no	—
28	#464×C₈₉	—	2	4	no	—
29	#452×C₈₉	—	2	4	no	—
30	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
33	#416×C₈₉	—	2	4	no	—
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×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×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#103×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×C₂²⋊C₈×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	#391×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#389×C₈₉	C₂²	1	1	yes	characteristic
51	#388×C₈₉	—	2	1	no	—
52	#388×C₈₉	—	2	1	no	—
53	#387×C₈₉	—	2	1	no	—
54	#385×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	C₂×#41×C₈₉	—	2	2	no	—
64	C₂×#41×C₈₉	—	2	2	no	—
65	C₂×#41×C₈₉	—	2	2	no	—
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	4	1	no	—
68	C₂×#41×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₈₉	—	2	2	no	—
77	C₂×Q₁₆×C₈₉	—	2	2	no	—
78	C₂×Q₁₆×C₈₉	—	2	2	no	—
79	C₂×Q₁₆×C₈₉	—	2	2	no	—
80	C₂×Q₁₆×C₈₉	—	4	1	no	—
81	C₂×Q₁₆×C₈₉	—	4	1	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	4	1	no	—
85	C₂²×C₈×C₈₉	—	2	2	no	—
86	C₂²×C₈×C₈₉	—	2	2	no	—
87	C₂²×C₈×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	C₄⋊Q₈×C₈₉	—	2	2	no	—
93	C₄⋊Q₈×C₈₉	—	4	1	no	—
94	#124×C₈₉	—	2	2	no	—
95	#124×C₈₉	—	4	1	no	—
96	C₂²⋊Q₈×C₈₉	—	2	2	no	—
97	C₂²⋊Q₈×C₈₉	—	2	2	no	—
98	C₂²⋊Q₈×C₈₉	—	2	2	no	—
99	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	—
100	C₄×Q₈×C₈₉	—	2	2	no	—
101	C₄×Q₈×C₈₉	—	4	1	no	—
102	#117×C₈₉	—	2	2	no	—
103	#117×C₈₉	—	4	1	no	—
104	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	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	D₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₈₉	—	2	1	no	—
124	C₂×C₄²×C₈₉	—	2	1	no	—
125	C₂×C₄²×C₈₉	—	2	1	no	—
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	#107×C₈₉	—	2	2	no	—
129	C₄⋊C₈×C₈₉	—	2	2	no	—
130	C₄⋊C₈×C₈₉	—	4	1	no	—
131	#103×C₈₉	—	2	2	no	—
132	#103×C₈₉	—	2	2	no	—
133	#103×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	4	1	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	D₄	1	4	yes	—
141	C₂²⋊C₈×C₈₉	—	2	2	no	—
142	#95×C₈₉	—	2	1	no	—
143	#95×C₈₉	—	2	1	no	—
144	#95×C₈₉	—	2	1	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	C₂×D₄	1	1	yes	characteristic
152	#41×C₈₉	—	2	8	no	—
153	#41×C₈₉	—	4	4	no	—
154	#41×C₈₉	—	4	4	no	—
155	#41×C₈₉	—	4	4	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	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	—	2	1	no	—
166	C₂×Q₈×C₈₉	—	2	1	no	—
167	C₂×Q₈×C₈₉	—	2	1	no	—
168	C₂×Q₈×C₈₉	—	2	1	no	—
169	C₂×Q₈×C₈₉	—	2	1	no	—
170	C₂×Q₈×C₈₉	—	2	1	no	—
171	C₂×Q₈×C₈₉	—	2	1	no	—
172	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₈₉	#41	1	2	yes	—
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	—	4	2	no	—
180	C₂×D₄×C₈₉	—	4	2	no	—
181	C₂×D₄×C₈₉	—	4	2	no	—
182	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
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	—	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	—	4	2	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	2	yes	—
202	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	#41	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	Q₁₆×C₈₉	—	4	4	no	—
206	Q₁₆×C₈₉	—	4	4	no	—
207	SD₁₆×C₈₉	—	4	4	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	—	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	—	4	4	no	—
220	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₈₉	—	2	4	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	—	4	2	no	—
229	C₄⋊C₄×C₈₉	—	4	2	no	—
230	C₄⋊C₄×C₈₉	—	4	2	no	—
231	C₄⋊C₄×C₈₉	—	4	2	no	—
232	C₄⋊C₄×C₈₉	—	4	2	no	—
233	C₄⋊C₄×C₈₉	C₂×D₄	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	—	4	2	no	—
243	C₂²⋊C₄×C₈₉	—	4	2	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	C₄²×C₈₉	—	4	2	no	—
250	C₄²×C₈₉	—	4	2	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	1	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	2	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	#121	1	2	yes	—
265	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
266	Q₈×C₈₉	—	2	2	no	—
267	Q₈×C₈₉	—	2	2	no	—
268	Q₈×C₈₉	—	2	2	no	—
269	Q₈×C₈₉	—	2	2	no	—
270	Q₈×C₈₉	—	4	1	no	—
271	Q₈×C₈₉	—	4	1	no	—
272	Q₈×C₈₉	—	4	1	no	—
273	Q₈×C₈₉	—	4	1	no	—
274	Q₈×C₈₉	—	4	1	no	—
275	Q₈×C₈₉	—	4	1	no	—
276	Q₈×C₈₉	—	4	1	no	—
277	Q₈×C₈₉	—	4	1	no	—
278	D₄×C₈₉	—	2	2	no	—
279	D₄×C₈₉	—	2	2	no	—
280	D₄×C₈₉	—	4	8	no	—
281	D₄×C₈₉	—	4	1	no	—
282	D₄×C₈₉	—	4	1	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	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	1	no	—
294	C₂×C₄×C₈₉	—	2	1	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	—	2	1	no	—
304	C₂×C₄×C₈₉	—	4	8	no	—
305	C₂×C₄×C₈₉	—	4	1	no	—
306	C₂×C₄×C₈₉	—	4	1	no	—
307	C₂×C₄×C₈₉	—	4	1	no	—
308	C₂×C₄×C₈₉	—	4	1	no	—
309	C₂×C₄×C₈₉	—	4	1	no	—
310	C₂×C₄×C₈₉	—	4	1	no	—
311	C₂×C₄×C₈₉	—	4	1	no	—
312	C₂×C₄×C₈₉	—	4	1	no	—
313	C₂×C₄×C₈₉	—	4	1	no	—
314	C₂×C₄×C₈₉	—	4	1	no	—
315	C₂×C₄×C₈₉	—	4	1	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	#121	1	2	yes	—
323	C₂×C₄×C₈₉	#135	1	2	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
330	C₈×C₈₉	—	2	2	no	—
331	C₈×C₈₉	—	4	1	no	—
332	C₈×C₈₉	—	4	1	no	—
333	C₈×C₈₉	—	4	1	no	—
334	C₂²×C₈₉	—	2	2	no	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	4	1	no	—
338	C₂²×C₈₉	—	4	1	no	—
339	C₂²×C₈₉	—	4	1	no	—
340	C₂²×C₈₉	—	4	1	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	C₂×#121	1	1	yes	characteristic
349	C₂²×C₈₉	D₄²	1	1	yes	characteristic
350	C₂²×C₈₉	#546	1	1	yes	characteristic
351	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
352	C₂²×C₈₉	#575	1	1	yes	characteristic
353	C₂²×C₈₉	#578	1	1	yes	characteristic
354	C₂²×C₈₉	#578	1	1	yes	characteristic
355	C₄×C₈₉	—	2	2	no	—
356	C₄×C₈₉	—	2	2	no	—
357	C₄×C₈₉	—	4	2	no	—
358	C₄×C₈₉	—	4	2	no	—
359	C₄×C₈₉	—	4	1	no	—
360	C₄×C₈₉	—	4	1	no	—
361	C₄×C₈₉	—	4	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	1	no	—
364	C₄×C₈₉	—	8	1	no	—
365	C₄×C₈₉	—	8	1	no	—
366	C₄×C₈₉	—	8	1	no	—
367	C₄×C₈₉	#525	1	1	yes	characteristic
368	C₄×C₈₉	#538	1	1	yes	characteristic
369	C₄×C₈₉	D₄²	1	1	yes	characteristic
370	C₄×C₈₉	#546	1	1	yes	characteristic
371	#25089	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₈₉	—	4	2	no	—
373	C₂×C₈₉	—	8	2	no	—
374	C₂×C₈₉	#2424	1	1	yes	characteristic
375	C₂×C₈₉	#3035	1	1	yes	characteristic
376	C₂×C₈₉	#3044	1	1	yes	characteristic
377	C₂×C₈₉	#3269	1	1	yes	characteristic
378	C₂×C₈₉	#3283	1	1	yes	characteristic
379	C₂×C₈₉	#3300	1	1	yes	characteristic
380	C₂×C₈₉	#3313	1	1	yes	characteristic
381	C₂×#467	C₂×C₈₉	1	1	yes	characteristic, complemented
382	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
383	C₂×#452	C₂×C₈₉	1	1	yes	characteristic
384	C₂×#416	C₂×C₈₉	1	1	yes	characteristic
385	#2432	C₂×C₈₉	1	1	yes	characteristic
386	#2362	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2068	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2042	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#2016	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#1981	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#1925	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#1850	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₈₉	#25089	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
398	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
399	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
400	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
401	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
402	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
408	#467	—	2	4	no	—
409	#464	—	2	4	no	—
410	#452	—	2	4	no	—
411	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄⋊C₈	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×#103	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
426	#394	—	2	1	no	—
427	#394	—	2	1	no	—
428	#391	C₂²×C₈₉	1	1	yes	characteristic
429	#391	C₂²×C₈₉	1	1	yes	characteristic
430	#390	C₂²×C₈₉	1	1	yes	characteristic
431	#389	C₂²×C₈₉	1	1	yes	characteristic
432	#388	—	2	1	no	—
433	#388	—	2	1	no	—
434	#387	—	2	1	no	—
435	#385	—	2	1	no	—
436	#385	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
440	#340	C₂²×C₈₉	1	1	yes	characteristic
441	#340	C₂²×C₈₉	1	1	yes	characteristic
442	#336	C₂²×C₈₉	1	1	yes	characteristic
443	#336	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	4	1	no	—
449	C₂×#41	—	4	1	no	—
450	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
451	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
457	C₂×Q₁₆	—	2	2	no	—
458	C₂×Q₁₆	—	2	2	no	—
459	C₂×Q₁₆	—	2	2	no	—
460	C₂×Q₁₆	—	2	2	no	—
461	C₂×Q₁₆	—	4	1	no	—
462	C₂×Q₁₆	—	4	1	no	—
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	4	1	no	—
466	C₂²×C₈	—	2	2	no	—
467	C₂²×C₈	—	2	2	no	—
468	C₂²×C₈	—	4	1	no	—
469	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	—	4	1	no	—
475	#124	—	2	2	no	—
476	#124	—	4	1	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	4	1	no	—
483	#117	—	2	2	no	—
484	#117	—	4	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
509	#107	—	2	2	no	—
510	C₄⋊C₈	—	2	2	no	—
511	C₄⋊C₈	—	4	1	no	—
512	#103	—	2	2	no	—
513	#103	—	2	2	no	—
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#103	—	4	1	no	—
519	#102	—	2	2	no	—
520	#102	—	2	2	no	—
521	#102	D₄×C₈₉	1	4	yes	—
522	C₂²⋊C₈	—	2	2	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	D₄×C₈₉	1	1	yes	characteristic
530	#95	D₄×C₈₉	1	1	yes	characteristic
531	C₂⁴	—	2	1	no	—
532	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
533	#41	—	2	8	no	—
534	#41	—	4	4	no	—
535	#41	—	4	4	no	—
536	#41	—	4	4	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	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	—	2	1	no	—
548	C₂×Q₈	—	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	C₂×D₄×C₈₉	1	2	yes	—
554	C₂×Q₈	#41×C₈₉	1	2	yes	—
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	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
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	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	2	no	—
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	C₂×D₄×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
584	C₂²×C₄	#41×C₈₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
586	Q₁₆	—	4	4	no	—
587	Q₁₆	—	4	4	no	—
588	SD₁₆	—	4	4	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	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	4	2	no	—
630	C₄²	—	4	2	no	—
631	C₄²	—	4	2	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	1	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	#121×C₈₉	1	2	yes	—
646	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
647	Q₈	—	2	2	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	2	2	no	—
650	Q₈	—	2	2	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	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	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	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	—	4	1	no	—
703	C₂×C₄	#121×C₈₉	1	2	yes	—
704	C₂×C₄	#135×C₈₉	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
709	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
710	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	4	1	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
730	C₂²	D₄²×C₈₉	1	1	yes	characteristic
731	C₂²	#546×C₈₉	1	1	yes	characteristic
732	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
733	C₂²	#575×C₈₉	1	1	yes	characteristic
734	C₂²	#578×C₈₉	1	1	yes	characteristic
735	C₂²	#578×C₈₉	1	1	yes	characteristic
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	8	1	no	—
746	C₄	—	8	1	no	—
747	C₄	—	8	1	no	—
748	C₄	#525×C₈₉	1	1	yes	characteristic
749	C₄	#538×C₈₉	1	1	yes	characteristic
750	C₄	D₄²×C₈₉	1	1	yes	characteristic
751	C₄	#546×C₈₉	1	1	yes	characteristic
752	C₂	—	4	2	no	—
753	C₂	—	8	2	no	—
754	C₂	C₈₉×#2424	1	1	yes	characteristic
755	C₂	C₈₉×#3035	1	1	yes	characteristic
756	C₂	C₈₉×#3044	1	1	yes	characteristic
757	C₂	C₈₉×#3269	1	1	yes	characteristic
758	C₂	C₈₉×#3283	1	1	yes	characteristic
759	C₂	C₈₉×#3300	1	1	yes	characteristic
760	C₂	C₈₉×#3313	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#467×C₈₉	C₂	semidirect
2. C₂×#464×C₈₉	C₂	semidirect
6. C₈₉×#2362	C₂	semidirect
7. C₈₉×#2068	C₂	semidirect
8. C₈₉×#2055	C₂	semidirect
9. C₈₉×#2042	C₂	semidirect
10. C₈₉×#2016	C₂	semidirect
11. C₈₉×#1981	C₂	semidirect
12. C₈₉×#1925	C₂	semidirect
13. C₈₉×#1878	C₂	semidirect
14. C₈₉×#1873	C₂	semidirect
15. C₈₉×#1850	C₂	semidirect
371. #25089	C₈₉	direct (N × H)
381. C₂×#467	C₂×C₈₉	semidirect
382. C₂×#464	C₂×C₈₉	semidirect
386. #2362	C₂×C₈₉	semidirect
387. #2068	C₂×C₈₉	semidirect
388. #2055	C₂×C₈₉	semidirect
389. #2042	C₂×C₈₉	semidirect
390. #2016	C₂×C₈₉	semidirect
391. #1981	C₂×C₈₉	semidirect
392. #1925	C₂×C₈₉	semidirect
393. #1878	C₂×C₈₉	semidirect
394. #1873	C₂×C₈₉	semidirect
395. #1850	C₂×C₈₉	semidirect
396. C₈₉	#25089	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#467×C₈₉	2
C₂×#464×C₈₉	2
C₂×#452×C₈₉	2
C₂×#416×C₈₉	2
C₈₉×#2432	2
C₈₉×#2362	2
C₈₉×#2068	2
C₈₉×#2055	2
C₈₉×#2042	2
C₈₉×#2016	2
C₈₉×#1981	2
C₈₉×#1925	2
C₈₉×#1878	2
C₈₉×#1873	2
C₈₉×#1850	2
#25089	89

Subgroups — C89×#25089 #36402937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25089 #36402937