Subgroups — C₈₉×#26201 #36404049

Order 22784.

794 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2415	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2352	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1869	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
32	#397×C₈₉	—	2	1	no	—
33	#394×C₈₉	—	2	1	no	—
34	#391×C₈₉	C₂²	1	1	yes	characteristic
35	#389×C₈₉	—	2	1	no	—
36	#389×C₈₉	C₂²	1	1	yes	characteristic
37	#388×C₈₉	—	2	1	no	—
38	#388×C₈₉	—	2	1	no	—
39	#387×C₈₉	—	2	1	no	—
40	#386×C₈₉	—	2	1	no	—
41	#382×C₈₉	C₂²	1	1	yes	characteristic
42	#380×C₈₉	C₂²	1	1	yes	characteristic
43	#380×C₈₉	C₂²	1	1	yes	characteristic
44	#380×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
47	#340×C₈₉	C₂²	1	1	yes	characteristic
48	#340×C₈₉	C₂²	1	1	yes	characteristic
49	#340×C₈₉	C₂²	1	1	yes	characteristic
50	#340×C₈₉	C₂²	1	1	yes	characteristic
51	#340×C₈₉	C₂²	1	1	yes	characteristic
52	#340×C₈₉	C₂²	1	1	yes	characteristic
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	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	—	2	1	no	—
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	—	2	2	no	—
65	C₂²×C₈×C₈₉	—	4	1	no	—
66	C₂²×C₈×C₈₉	—	4	1	no	—
67	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²⋊Q₈×C₈₉	—	2	2	no	—
72	C₂²⋊Q₈×C₈₉	—	2	2	no	—
73	C₂²⋊Q₈×C₈₉	—	2	2	no	—
74	C₂²⋊Q₈×C₈₉	—	4	1	no	—
75	C₄×D₄×C₈₉	—	2	2	no	—
76	C₄×D₄×C₈₉	—	2	2	no	—
77	#117×C₈₉	—	2	2	no	—
78	#117×C₈₉	—	2	2	no	—
79	#117×C₈₉	—	4	1	no	—
80	#117×C₈₉	—	4	1	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₈₉	—	2	1	no	—
105	C₂×C₄²×C₈₉	—	2	1	no	—
106	C₂×C₄²×C₈₉	—	2	1	no	—
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	#107×C₈₉	—	4	1	no	—
109	#106×C₈₉	—	2	2	no	—
110	#103×C₈₉	—	2	2	no	—
111	#103×C₈₉	—	4	1	no	—
112	#103×C₈₉	—	4	1	no	—
113	#103×C₈₉	—	4	1	no	—
114	C₂²⋊C₈×C₈₉	—	2	2	no	—
115	C₂²⋊C₈×C₈₉	—	4	1	no	—
116	C₂²⋊C₈×C₈₉	—	4	1	no	—
117	#95×C₈₉	—	2	1	no	—
118	#95×C₈₉	—	2	1	no	—
119	#95×C₈₉	—	2	1	no	—
120	#95×C₈₉	—	2	1	no	—
121	#95×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	1	no	—
123	#95×C₈₉	—	2	1	no	—
124	#95×C₈₉	—	2	1	no	—
125	#95×C₈₉	—	2	1	no	—
126	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₈₉	—	2	1	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	2	2	no	—
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	—	4	1	no	—
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	—	2	1	no	—
140	C₂²×C₄×C₈₉	—	2	1	no	—
141	C₂²×C₄×C₈₉	—	2	1	no	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	4	2	no	—
156	C₂²×C₄×C₈₉	—	4	2	no	—
157	C₂²×C₄×C₈₉	—	8	1	no	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	#41	1	2	yes	—
163	C₂²×C₄×C₈₉	#41	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	—	2	1	no	—
167	C₂×C₈×C₈₉	—	2	1	no	—
168	C₂×C₈×C₈₉	—	2	1	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	—	2	1	no	—
172	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
178	C₄⋊C₄×C₈₉	—	2	2	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	2	1	no	—
186	C₄⋊C₄×C₈₉	—	2	1	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	—	4	2	no	—
192	C₄⋊C₄×C₈₉	—	4	2	no	—
193	C₄⋊C₄×C₈₉	—	4	2	no	—
194	C₄⋊C₄×C₈₉	—	4	2	no	—
195	C₄⋊C₄×C₈₉	#41	1	2	yes	—
196	C₄⋊C₄×C₈₉	#41	1	2	yes	—
197	C₂²⋊C₄×C₈₉	—	2	2	no	—
198	C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂²⋊C₄×C₈₉	—	4	2	no	—
200	C₂²⋊C₄×C₈₉	—	4	2	no	—
201	C₂²⋊C₄×C₈₉	—	4	2	no	—
202	C₂²⋊C₄×C₈₉	—	4	2	no	—
203	C₂²⋊C₄×C₈₉	—	4	2	no	—
204	C₂²⋊C₄×C₈₉	—	4	2	no	—
205	C₂²⋊C₄×C₈₉	—	8	1	no	—
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	4	2	no	—
209	C₄²×C₈₉	—	4	2	no	—
210	C₄²×C₈₉	—	8	1	no	—
211	C₂³×C₈₉	—	2	1	no	—
212	C₂³×C₈₉	—	2	1	no	—
213	C₂³×C₈₉	—	2	1	no	—
214	C₂³×C₈₉	—	2	1	no	—
215	C₂³×C₈₉	—	2	1	no	—
216	C₂³×C₈₉	—	2	1	no	—
217	C₂³×C₈₉	—	2	1	no	—
218	C₂³×C₈₉	—	2	1	no	—
219	C₂³×C₈₉	—	2	1	no	—
220	C₂³×C₈₉	—	2	1	no	—
221	C₂³×C₈₉	—	2	1	no	—
222	C₂³×C₈₉	—	2	1	no	—
223	C₂³×C₈₉	#123	1	2	yes	—
224	C₂³×C₈₉	#135	1	2	yes	—
225	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₈₉	—	4	1	no	—
227	Q₈×C₈₉	—	4	1	no	—
228	Q₈×C₈₉	—	4	1	no	—
229	Q₈×C₈₉	—	4	1	no	—
230	D₄×C₈₉	—	4	4	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	2	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	1	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	—	4	1	no	—
250	C₂×C₄×C₈₉	—	4	1	no	—
251	C₂×C₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	—	4	1	no	—
253	C₂×C₄×C₈₉	—	4	1	no	—
254	C₂×C₄×C₈₉	—	4	1	no	—
255	C₂×C₄×C₈₉	—	4	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	#123	1	2	yes	—
276	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
282	C₈×C₈₉	—	4	1	no	—
283	C₈×C₈₉	—	4	1	no	—
284	C₈×C₈₉	—	4	1	no	—
285	C₈×C₈₉	—	4	1	no	—
286	C₂²×C₈₉	—	2	2	no	—
287	C₂²×C₈₉	—	2	2	no	—
288	C₂²×C₈₉	—	2	2	no	—
289	C₂²×C₈₉	—	2	2	no	—
290	C₂²×C₈₉	—	2	2	no	—
291	C₂²×C₈₉	—	2	2	no	—
292	C₂²×C₈₉	—	4	1	no	—
293	C₂²×C₈₉	—	4	1	no	—
294	C₂²×C₈₉	—	4	1	no	—
295	C₂²×C₈₉	—	4	1	no	—
296	C₂²×C₈₉	—	4	1	no	—
297	C₂²×C₈₉	—	4	1	no	—
298	C₂²×C₈₉	—	4	1	no	—
299	C₂²×C₈₉	—	4	1	no	—
300	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
301	C₂²×C₈₉	#546	1	1	yes	characteristic
302	C₂²×C₈₉	#546	1	1	yes	characteristic
303	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
304	C₂²×C₈₉	#575	1	1	yes	characteristic
305	C₂²×C₈₉	#577	1	1	yes	characteristic
306	C₂²×C₈₉	#578	1	1	yes	characteristic
307	C₄×C₈₉	—	2	2	no	—
308	C₄×C₈₉	—	4	1	no	—
309	C₄×C₈₉	—	4	1	no	—
310	C₄×C₈₉	—	4	1	no	—
311	C₄×C₈₉	—	4	2	no	—
312	C₄×C₈₉	—	4	2	no	—
313	C₄×C₈₉	—	8	1	no	—
314	C₄×C₈₉	—	8	1	no	—
315	C₄×C₈₉	—	8	1	no	—
316	C₄×C₈₉	—	8	1	no	—
317	C₄×C₈₉	—	8	1	no	—
318	C₄×C₈₉	—	8	1	no	—
319	C₄×C₈₉	#529	1	1	yes	characteristic
320	C₄×C₈₉	#538	1	1	yes	characteristic
321	C₄×C₈₉	#553	1	1	yes	characteristic
322	C₄×C₈₉	#553	1	1	yes	characteristic
323	#26201	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂×C₈₉	—	4	2	no	—
325	C₂×C₈₉	—	4	2	no	—
326	C₂×C₈₉	#2444	1	1	yes	characteristic
327	C₂×C₈₉	#3091	1	1	yes	characteristic
328	C₂×C₈₉	#3097	1	1	yes	characteristic
329	C₂×C₈₉	#3300	1	1	yes	characteristic
330	C₂×C₈₉	#3301	1	1	yes	characteristic
331	C₂×C₈₉	#3311	1	1	yes	characteristic
332	C₂×C₈₉	#3315	1	1	yes	characteristic
333	#2415	C₂×C₈₉	1	1	yes	characteristic
334	#2352	C₂×C₈₉	1	1	yes	characteristic
335	#2101	C₂×C₈₉	1	1	yes	characteristic, complemented
336	#2075	C₂×C₈₉	1	1	yes	characteristic, complemented
337	#2074	C₂×C₈₉	1	1	yes	characteristic, complemented
338	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
339	#1928	C₂×C₈₉	1	1	yes	characteristic, complemented
340	#1920	C₂×C₈₉	1	1	yes	characteristic, complemented
341	#1892	C₂×C₈₉	1	1	yes	characteristic, complemented
342	#1873	C₂×C₈₉	1	1	yes	characteristic, complemented
343	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
344	#1869	C₂×C₈₉	1	1	yes	characteristic
345	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
346	#1824	C₂×C₈₉	1	1	yes	characteristic, complemented
347	#1735	C₂×C₈₉	1	1	yes	characteristic, complemented
348	C₈₉	#26201	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
350	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
353	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
354	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
356	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
357	C₂×#106	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×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
363	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
365	#397	—	2	1	no	—
366	#394	—	2	1	no	—
367	#391	C₂²×C₈₉	1	1	yes	characteristic
368	#389	—	2	1	no	—
369	#389	C₂²×C₈₉	1	1	yes	characteristic
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#387	—	2	1	no	—
373	#386	—	2	1	no	—
374	#382	C₂²×C₈₉	1	1	yes	characteristic
375	#380	C₂²×C₈₉	1	1	yes	characteristic
376	#380	C₂²×C₈₉	1	1	yes	characteristic
377	#380	C₂²×C₈₉	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	—	2	1	no	—
380	#340	C₂²×C₈₉	1	1	yes	characteristic
381	#340	C₂²×C₈₉	1	1	yes	characteristic
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	#340	C₂²×C₈₉	1	1	yes	characteristic
389	#340	C₂²×C₈₉	1	1	yes	characteristic
390	#336	C₂²×C₈₉	1	1	yes	characteristic
391	#336	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
393	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	4	1	no	—
399	C₂²×C₈	—	4	1	no	—
400	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
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⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	—	4	1	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	4	1	no	—
413	#117	—	4	1	no	—
414	C₂×C₄⋊C₄	—	2	2	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	—	4	1	no	—
420	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
441	#107	—	4	1	no	—
442	#106	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	4	1	no	—
445	#103	—	4	1	no	—
446	#103	—	4	1	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	4	1	no	—
449	C₂²⋊C₈	—	4	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	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	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
460	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
461	C₂×Q₈	—	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×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	8	1	no	—
491	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
495	C₂²×C₄	#41×C₈₉	1	2	yes	—
496	C₂²×C₄	#41×C₈₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	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	—	4	4	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	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	—	4	2	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	#41×C₈₉	1	2	yes	—
529	C₄⋊C₄	#41×C₈₉	1	2	yes	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	8	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	4	2	no	—
542	C₄²	—	4	2	no	—
543	C₄²	—	8	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	#123×C₈₉	1	2	yes	—
557	C₂³	#135×C₈₉	1	2	yes	—
558	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	D₄	—	4	4	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	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	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	8	4	no	—
608	C₂×C₄	#123×C₈₉	1	2	yes	—
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	C₂×#41×C₈₉	1	1	yes	characteristic
613	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
614	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
634	C₂²	#546×C₈₉	1	1	yes	characteristic
635	C₂²	#546×C₈₉	1	1	yes	characteristic
636	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
637	C₂²	#575×C₈₉	1	1	yes	characteristic
638	C₂²	#577×C₈₉	1	1	yes	characteristic
639	C₂²	#578×C₈₉	1	1	yes	characteristic
640	C₄	—	2	2	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	#529×C₈₉	1	1	yes	characteristic
653	C₄	#538×C₈₉	1	1	yes	characteristic
654	C₄	#553×C₈₉	1	1	yes	characteristic
655	C₄	#553×C₈₉	1	1	yes	characteristic
656	C₂	—	4	2	no	—
657	C₂	—	4	2	no	—
658	C₂	C₈₉×#2444	1	1	yes	characteristic
659	C₂	C₈₉×#3091	1	1	yes	characteristic
660	C₂	C₈₉×#3097	1	1	yes	characteristic
661	C₂	C₈₉×#3300	1	1	yes	characteristic
662	C₂	C₈₉×#3301	1	1	yes	characteristic
663	C₂	C₈₉×#3311	1	1	yes	characteristic
664	C₂	C₈₉×#3315	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₉×#2101	C₂	semidirect
4. C₈₉×#2075	C₂	semidirect
5. C₈₉×#2074	C₂	semidirect
6. C₈₉×#2035	C₂	semidirect
7. C₈₉×#1928	C₂	semidirect
8. C₈₉×#1920	C₂	semidirect
9. C₈₉×#1892	C₂	semidirect
10. C₈₉×#1873	C₂	semidirect
11. C₈₉×#1872	C₂	semidirect
13. C₈₉×#1854	C₂	semidirect
14. C₈₉×#1824	C₂	semidirect
15. C₈₉×#1735	C₂	semidirect
323. #26201	C₈₉	direct (N × H)
335. #2101	C₂×C₈₉	semidirect
336. #2075	C₂×C₈₉	semidirect
337. #2074	C₂×C₈₉	semidirect
338. #2035	C₂×C₈₉	semidirect
339. #1928	C₂×C₈₉	semidirect
340. #1920	C₂×C₈₉	semidirect
341. #1892	C₂×C₈₉	semidirect
342. #1873	C₂×C₈₉	semidirect
343. #1872	C₂×C₈₉	semidirect
345. #1854	C₂×C₈₉	semidirect
346. #1824	C₂×C₈₉	semidirect
347. #1735	C₂×C₈₉	semidirect
348. C₈₉	#26201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2415	2
C₈₉×#2352	2
C₈₉×#2101	2
C₈₉×#2075	2
C₈₉×#2074	2
C₈₉×#2035	2
C₈₉×#1928	2
C₈₉×#1920	2
C₈₉×#1892	2
C₈₉×#1873	2
C₈₉×#1872	2
C₈₉×#1869	2
C₈₉×#1854	2
C₈₉×#1824	2
C₈₉×#1735	2
#26201	89

Subgroups — C89×#26201 #36404049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26201 #36404049