Subgroups — C₈₉×#25336 #36403184

Order 22784.

840 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2367	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2071	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic
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	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	#489×C₈₉	—	2	4	no	—
24	#464×C₈₉	—	2	4	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
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×#97×C₈₉	C₂²	1	1	yes	characteristic
37	#395×C₈₉	—	2	1	no	—
38	#395×C₈₉	—	2	1	no	—
39	#391×C₈₉	C₂²	1	1	yes	characteristic
40	#391×C₈₉	C₂²	1	1	yes	characteristic
41	#391×C₈₉	C₂²	1	1	yes	characteristic
42	#390×C₈₉	C₂²	1	1	yes	characteristic
43	#389×C₈₉	—	2	1	no	—
44	#389×C₈₉	—	2	1	no	—
45	#388×C₈₉	—	2	1	no	—
46	#388×C₈₉	—	2	1	no	—
47	#385×C₈₉	—	2	1	no	—
48	#384×C₈₉	C₂²	1	1	yes	characteristic
49	#384×C₈₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
53	#340×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#340×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	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₈₉	—	2	1	no	—
62	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂×Q₁₆×C₈₉	—	2	2	no	—
67	C₂×Q₁₆×C₈₉	—	2	2	no	—
68	C₂×Q₁₆×C₈₉	—	4	1	no	—
69	C₂×SD₁₆×C₈₉	—	2	2	no	—
70	C₂×SD₁₆×C₈₉	—	2	2	no	—
71	C₂×SD₁₆×C₈₉	—	4	1	no	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₈₉	—	2	2	no	—
77	C₄⋊Q₈×C₈₉	—	2	2	no	—
78	#124×C₈₉	—	2	2	no	—
79	#124×C₈₉	D₄	1	4	yes	—
80	C₄×Q₈×C₈₉	—	2	2	no	—
81	C₄×Q₈×C₈₉	—	2	2	no	—
82	C₄×Q₈×C₈₉	—	2	2	no	—
83	C₄×Q₈×C₈₉	—	4	1	no	—
84	C₄×D₄×C₈₉	—	2	2	no	—
85	C₄×D₄×C₈₉	—	4	1	no	—
86	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₄²×C₈₉	—	2	1	no	—
106	C₂×C₄²×C₈₉	—	2	1	no	—
107	C₂×C₄²×C₈₉	—	2	1	no	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₈₉	—	2	2	no	—
112	C₄⋊C₈×C₈₉	—	4	1	no	—
113	C₄⋊C₈×C₈₉	—	4	1	no	—
114	#103×C₈₉	—	2	2	no	—
115	#103×C₈₉	—	2	2	no	—
116	#103×C₈₉	—	2	2	no	—
117	#103×C₈₉	—	2	2	no	—
118	#103×C₈₉	—	2	2	no	—
119	#102×C₈₉	—	2	2	no	—
120	#102×C₈₉	—	2	2	no	—
121	#102×C₈₉	—	2	2	no	—
122	#97×C₈₉	—	2	2	no	—
123	#95×C₈₉	—	2	1	no	—
124	#95×C₈₉	—	2	1	no	—
125	#95×C₈₉	—	2	1	no	—
126	#95×C₈₉	—	2	1	no	—
127	#95×C₈₉	—	2	1	no	—
128	#95×C₈₉	—	2	1	no	—
129	#95×C₈₉	—	2	1	no	—
130	#95×C₈₉	D₄	1	1	yes	characteristic
131	#95×C₈₉	D₄	1	1	yes	characteristic
132	C₂⁴×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×Q₈×C₈₉	—	2	1	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×Q₈×C₈₉	—	2	1	no	—
141	C₂×Q₈×C₈₉	—	2	1	no	—
142	C₂×Q₈×C₈₉	—	2	1	no	—
143	C₂×Q₈×C₈₉	—	4	2	no	—
144	C₂×Q₈×C₈₉	—	8	1	no	—
145	C₂×Q₈×C₈₉	—	8	1	no	—
146	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₂×Q₈×C₈₉	#41	1	2	yes	—
148	C₂×D₄×C₈₉	—	2	1	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	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	—	2	1	no	—
157	C₂²×C₄×C₈₉	—	2	1	no	—
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	4	2	no	—
162	C₂²×C₄×C₈₉	—	4	2	no	—
163	C₂²×C₄×C₈₉	—	8	1	no	—
164	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	Q₁₆×C₈₉	—	4	4	no	—
172	SD₁₆×C₈₉	—	4	4	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	2	2	no	—
186	C₄⋊C₄×C₈₉	—	2	2	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	4	2	no	—
197	C₄⋊C₄×C₈₉	—	4	2	no	—
198	C₄⋊C₄×C₈₉	—	4	2	no	—
199	C₄⋊C₄×C₈₉	—	8	1	no	—
200	C₄⋊C₄×C₈₉	—	8	1	no	—
201	C₄⋊C₄×C₈₉	—	8	1	no	—
202	C₄⋊C₄×C₈₉	—	8	1	no	—
203	C₄⋊C₄×C₈₉	#41	1	2	yes	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	4	2	no	—
207	C₂²⋊C₄×C₈₉	—	4	2	no	—
208	C₂²⋊C₄×C₈₉	—	8	1	no	—
209	C₄²×C₈₉	—	2	1	no	—
210	C₄²×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	—	2	1	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	—	4	2	no	—
214	C₄²×C₈₉	—	4	2	no	—
215	C₄²×C₈₉	—	8	1	no	—
216	C₄²×C₈₉	C₂×D₄	1	2	yes	—
217	C₄²×C₈₉	#41	1	2	yes	—
218	C₂³×C₈₉	—	2	2	no	—
219	C₂³×C₈₉	—	4	1	no	—
220	C₂³×C₈₉	—	4	1	no	—
221	C₂³×C₈₉	—	4	1	no	—
222	C₂³×C₈₉	—	4	1	no	—
223	C₂³×C₈₉	—	4	1	no	—
224	C₂³×C₈₉	—	4	1	no	—
225	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₈₉	—	2	2	no	—
227	Q₈×C₈₉	—	2	2	no	—
228	Q₈×C₈₉	—	2	2	no	—
229	Q₈×C₈₉	—	2	2	no	—
230	Q₈×C₈₉	—	4	1	no	—
231	Q₈×C₈₉	—	4	1	no	—
232	Q₈×C₈₉	—	4	1	no	—
233	Q₈×C₈₉	—	4	1	no	—
234	Q₈×C₈₉	—	8	4	no	—
235	D₄×C₈₉	—	2	2	no	—
236	D₄×C₈₉	—	2	2	no	—
237	D₄×C₈₉	—	4	1	no	—
238	D₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	1	no	—
242	C₂×C₄×C₈₉	—	2	1	no	—
243	C₂×C₄×C₈₉	—	2	1	no	—
244	C₂×C₄×C₈₉	—	2	1	no	—
245	C₂×C₄×C₈₉	—	2	1	no	—
246	C₂×C₄×C₈₉	—	2	1	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	1	no	—
249	C₂×C₄×C₈₉	—	2	1	no	—
250	C₂×C₄×C₈₉	—	2	2	no	—
251	C₂×C₄×C₈₉	—	2	2	no	—
252	C₂×C₄×C₈₉	—	2	1	no	—
253	C₂×C₄×C₈₉	—	2	1	no	—
254	C₂×C₄×C₈₉	—	2	1	no	—
255	C₂×C₄×C₈₉	—	2	1	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	1	no	—
258	C₂×C₄×C₈₉	—	4	1	no	—
259	C₂×C₄×C₈₉	—	4	1	no	—
260	C₂×C₄×C₈₉	—	4	1	no	—
261	C₂×C₄×C₈₉	—	4	1	no	—
262	C₂×C₄×C₈₉	—	4	1	no	—
263	C₂×C₄×C₈₉	—	4	1	no	—
264	C₂×C₄×C₈₉	—	4	1	no	—
265	C₂×C₄×C₈₉	—	4	1	no	—
266	C₂×C₄×C₈₉	—	4	1	no	—
267	C₂×C₄×C₈₉	—	4	1	no	—
268	C₂×C₄×C₈₉	—	4	1	no	—
269	C₂×C₄×C₈₉	—	4	1	no	—
270	C₂×C₄×C₈₉	—	4	1	no	—
271	C₂×C₄×C₈₉	—	4	1	no	—
272	C₂×C₄×C₈₉	—	4	1	no	—
273	C₂×C₄×C₈₉	—	4	1	no	—
274	C₂×C₄×C₈₉	—	8	4	no	—
275	C₂×C₄×C₈₉	#121	1	2	yes	—
276	C₂×C₄×C₈₉	#121	1	2	yes	—
277	C₂×C₄×C₈₉	#137	1	2	yes	—
278	C₂×C₄×C₈₉	#137	1	2	yes	—
279	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
284	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
285	C₈×C₈₉	—	4	1	no	—
286	C₈×C₈₉	—	4	1	no	—
287	C₈×C₈₉	—	4	1	no	—
288	C₈×C₈₉	—	4	1	no	—
289	C₂²×C₈₉	—	4	2	no	—
290	C₂²×C₈₉	—	4	2	no	—
291	C₂²×C₈₉	—	4	2	no	—
292	C₂²×C₈₉	—	8	1	no	—
293	C₂²×C₈₉	—	8	1	no	—
294	C₂²×C₈₉	—	8	1	no	—
295	C₂²×C₈₉	—	8	1	no	—
296	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
297	C₂²×C₈₉	#546	1	1	yes	characteristic
298	C₂²×C₈₉	#548	1	1	yes	characteristic
299	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
300	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
301	C₂²×C₈₉	#576	1	1	yes	characteristic
302	C₂²×C₈₉	#577	1	1	yes	characteristic
303	C₄×C₈₉	—	2	2	no	—
304	C₄×C₈₉	—	2	2	no	—
305	C₄×C₈₉	—	2	2	no	—
306	C₄×C₈₉	—	2	2	no	—
307	C₄×C₈₉	—	4	2	no	—
308	C₄×C₈₉	—	4	2	no	—
309	C₄×C₈₉	—	4	1	no	—
310	C₄×C₈₉	—	4	2	no	—
311	C₄×C₈₉	—	4	1	no	—
312	C₄×C₈₉	—	8	1	no	—
313	C₄×C₈₉	—	8	1	no	—
314	C₄×C₈₉	—	8	1	no	—
315	C₄×C₈₉	—	8	1	no	—
316	C₄×C₈₉	#529	1	1	yes	characteristic
317	C₄×C₈₉	#542	1	1	yes	characteristic
318	C₄×C₈₉	#546	1	1	yes	characteristic
319	C₄×C₈₉	#547	1	1	yes	characteristic
320	#25336	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂×C₈₉	—	8	2	no	—
322	C₂×C₈₉	#2427	1	1	yes	characteristic
323	C₂×C₈₉	#3039	1	1	yes	characteristic
324	C₂×C₈₉	#3045	1	1	yes	characteristic
325	C₂×C₈₉	#3314	1	1	yes	characteristic
326	C₂×C₈₉	#3316	1	1	yes	characteristic
327	C₂×C₈₉	#3369	1	1	yes	characteristic
328	C₂×C₈₉	#3375	1	1	yes	characteristic
329	C₂×#489	C₂×C₈₉	1	1	yes	characteristic
330	C₂×#464	C₂×C₈₉	1	1	yes	characteristic
331	#2567	C₂×C₈₉	1	1	yes	characteristic, complemented
332	#2367	C₂×C₈₉	1	1	yes	characteristic
333	#2072	C₂×C₈₉	1	1	yes	characteristic, complemented
334	#2071	C₂×C₈₉	1	1	yes	characteristic
335	#2056	C₂×C₈₉	1	1	yes	characteristic, complemented
336	#2055	C₂×C₈₉	1	1	yes	characteristic
337	#1988	C₂×C₈₉	1	1	yes	characteristic, complemented
338	#1940	C₂×C₈₉	1	1	yes	characteristic, complemented
339	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
340	#1877	C₂×C₈₉	1	1	yes	characteristic
341	#1803	C₂×C₈₉	1	1	yes	characteristic, complemented
342	#1802	C₂×C₈₉	1	1	yes	characteristic
343	#1763	C₂×C₈₉	1	1	yes	characteristic, complemented
344	C₈₉	#25336	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
347	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
348	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
349	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
352	#489	—	2	4	no	—
353	#464	—	2	4	no	—
354	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
355	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
356	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
358	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
359	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
360	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
361	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
362	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
363	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
364	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
365	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
366	#395	—	2	1	no	—
367	#395	—	2	1	no	—
368	#391	C₂²×C₈₉	1	1	yes	characteristic
369	#391	C₂²×C₈₉	1	1	yes	characteristic
370	#391	C₂²×C₈₉	1	1	yes	characteristic
371	#390	C₂²×C₈₉	1	1	yes	characteristic
372	#389	—	2	1	no	—
373	#389	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#385	—	2	1	no	—
377	#384	C₂²×C₈₉	1	1	yes	characteristic
378	#384	C₂²×C₈₉	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	—	2	1	no	—
382	#340	C₂²×C₈₉	1	1	yes	characteristic
383	#340	C₂²×C₈₉	1	1	yes	characteristic
384	#340	C₂²×C₈₉	1	1	yes	characteristic
385	#340	C₂²×C₈₉	1	1	yes	characteristic
386	#340	C₂²×C₈₉	1	1	yes	characteristic
387	#340	C₂²×C₈₉	1	1	yes	characteristic
388	#336	C₂²×C₈₉	1	1	yes	characteristic
389	#336	C₂²×C₈₉	1	1	yes	characteristic
390	C₂²×Q₈	—	2	1	no	—
391	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂×Q₁₆	—	2	2	no	—
396	C₂×Q₁₆	—	2	2	no	—
397	C₂×Q₁₆	—	4	1	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	4	1	no	—
401	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
405	C₄⋊Q₈	—	2	2	no	—
406	C₄⋊Q₈	—	2	2	no	—
407	#124	—	2	2	no	—
408	#124	D₄×C₈₉	1	4	yes	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	4	1	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	4	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	4	1	no	—
442	C₄⋊C₈	—	4	1	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#97	—	2	2	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	D₄×C₈₉	1	1	yes	characteristic
460	#95	D₄×C₈₉	1	1	yes	characteristic
461	C₂⁴	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	8	1	no	—
474	C₂×Q₈	—	8	1	no	—
475	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
476	C₂×Q₈	#41×C₈₉	1	2	yes	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	8	1	no	—
493	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
500	Q₁₆	—	4	4	no	—
501	SD₁₆	—	4	4	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	8	1	no	—
529	C₄⋊C₄	—	8	1	no	—
530	C₄⋊C₄	—	8	1	no	—
531	C₄⋊C₄	—	8	1	no	—
532	C₄⋊C₄	#41×C₈₉	1	2	yes	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	8	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	4	2	no	—
543	C₄²	—	4	2	no	—
544	C₄²	—	8	1	no	—
545	C₄²	C₂×D₄×C₈₉	1	2	yes	—
546	C₄²	#41×C₈₉	1	2	yes	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	8	4	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	8	4	no	—
604	C₂×C₄	#121×C₈₉	1	2	yes	—
605	C₂×C₄	#121×C₈₉	1	2	yes	—
606	C₂×C₄	#137×C₈₉	1	2	yes	—
607	C₂×C₄	#137×C₈₉	1	2	yes	—
608	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
610	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
612	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
613	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
626	C₂²	#546×C₈₉	1	1	yes	characteristic
627	C₂²	#548×C₈₉	1	1	yes	characteristic
628	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
629	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
630	C₂²	#576×C₈₉	1	1	yes	characteristic
631	C₂²	#577×C₈₉	1	1	yes	characteristic
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	#529×C₈₉	1	1	yes	characteristic
646	C₄	#542×C₈₉	1	1	yes	characteristic
647	C₄	#546×C₈₉	1	1	yes	characteristic
648	C₄	#547×C₈₉	1	1	yes	characteristic
649	C₂	—	8	2	no	—
650	C₂	C₈₉×#2427	1	1	yes	characteristic
651	C₂	C₈₉×#3039	1	1	yes	characteristic
652	C₂	C₈₉×#3045	1	1	yes	characteristic
653	C₂	C₈₉×#3314	1	1	yes	characteristic
654	C₂	C₈₉×#3316	1	1	yes	characteristic
655	C₂	C₈₉×#3369	1	1	yes	characteristic
656	C₂	C₈₉×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
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
3. C₈₉×#2567	C₂	semidirect
5. C₈₉×#2072	C₂	semidirect
7. C₈₉×#2056	C₂	semidirect
9. C₈₉×#1988	C₂	semidirect
10. C₈₉×#1940	C₂	semidirect
11. C₈₉×#1878	C₂	semidirect
13. C₈₉×#1803	C₂	semidirect
15. C₈₉×#1763	C₂	semidirect
320. #25336	C₈₉	direct (N × H)
331. #2567	C₂×C₈₉	semidirect
333. #2072	C₂×C₈₉	semidirect
335. #2056	C₂×C₈₉	semidirect
337. #1988	C₂×C₈₉	semidirect
338. #1940	C₂×C₈₉	semidirect
339. #1878	C₂×C₈₉	semidirect
341. #1803	C₂×C₈₉	semidirect
343. #1763	C₂×C₈₉	semidirect
344. C₈₉	#25336	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×#489×C₈₉	2
C₂×#464×C₈₉	2
C₈₉×#2567	2
C₈₉×#2367	2
C₈₉×#2072	2
C₈₉×#2071	2
C₈₉×#2056	2
C₈₉×#2055	2
C₈₉×#1988	2
C₈₉×#1940	2
C₈₉×#1878	2
C₈₉×#1877	2
C₈₉×#1803	2
C₈₉×#1802	2
C₈₉×#1763	2
#25336	89

Subgroups — C89×#25336 #36403184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25336 #36403184