Subgroups — C₈₉×#26258 #36404106

Order 22784.

960 conjugacy classes of subgroups.

The subgroup lattice has 750 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×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₈₉	—	2	1	no	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	#496×C₈₉	—	2	4	no	—
26	C₄×D₈×C₈₉	—	2	4	no	—
27	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×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×#102×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×#102×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	#397×C₈₉	—	2	1	no	—
42	#397×C₈₉	—	2	1	no	—
43	#394×C₈₉	—	2	1	no	—
44	#394×C₈₉	—	2	1	no	—
45	#391×C₈₉	C₂²	1	1	yes	characteristic
46	#391×C₈₉	C₂²	1	1	yes	characteristic
47	#390×C₈₉	C₂²	1	1	yes	characteristic
48	#390×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#389×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#386×C₈₉	—	2	1	no	—
54	#385×C₈₉	—	2	1	no	—
55	#381×C₈₉	—	2	1	no	—
56	C₄×C₄⋊C₄×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	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₈₉	—	2	1	no	—
63	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₈₉	—	2	1	no	—
68	C₂³×C₄×C₈₉	—	2	1	no	—
69	C₂×SD₁₆×C₈₉	—	2	2	no	—
70	C₂×SD₁₆×C₈₉	—	2	2	no	—
71	C₂×SD₁₆×C₈₉	—	2	2	no	—
72	C₂×SD₁₆×C₈₉	—	2	2	no	—
73	C₂×SD₁₆×C₈₉	—	2	2	no	—
74	C₂×SD₁₆×C₈₉	—	4	1	no	—
75	C₂×D₈×C₈₉	—	2	2	no	—
76	C₂×D₈×C₈₉	—	2	2	no	—
77	C₂×D₈×C₈₉	—	2	2	no	—
78	C₂×D₈×C₈₉	—	2	2	no	—
79	C₂×D₈×C₈₉	—	4	1	no	—
80	C₂×D₈×C₈₉	D₄	1	4	yes	—
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	#127×C₈₉	—	2	2	no	—
86	#127×C₈₉	—	4	1	no	—
87	#124×C₈₉	—	2	2	no	—
88	#124×C₈₉	—	4	1	no	—
89	#123×C₈₉	—	4	4	no	—
90	C₄×D₄×C₈₉	—	2	2	no	—
91	C₄×D₄×C₈₉	—	2	2	no	—
92	C₄×D₄×C₈₉	—	4	1	no	—
93	C₄×D₄×C₈₉	—	4	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₈₉	D₄	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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
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×C₄²×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	#107×C₈₉	—	2	2	no	—
118	#106×C₈₉	—	2	2	no	—
119	C₄⋊C₈×C₈₉	—	2	2	no	—
120	#103×C₈₉	—	4	1	no	—
121	#103×C₈₉	—	4	1	no	—
122	#102×C₈₉	—	2	2	no	—
123	#102×C₈₉	—	2	2	no	—
124	#102×C₈₉	—	4	1	no	—
125	#102×C₈₉	—	4	1	no	—
126	#102×C₈₉	—	4	1	no	—
127	#102×C₈₉	—	4	1	no	—
128	#97×C₈₉	—	2	2	no	—
129	#97×C₈₉	—	2	2	no	—
130	C₄×C₈×C₈₉	—	2	2	no	—
131	#95×C₈₉	—	2	1	no	—
132	#95×C₈₉	—	2	1	no	—
133	#95×C₈₉	—	2	1	no	—
134	#95×C₈₉	—	2	1	no	—
135	#95×C₈₉	—	2	1	no	—
136	#95×C₈₉	—	2	1	no	—
137	#95×C₈₉	D₄	1	1	yes	characteristic
138	#95×C₈₉	D₄	1	1	yes	characteristic
139	C₂⁴×C₈₉	—	2	1	no	—
140	C₂⁴×C₈₉	—	2	1	no	—
141	C₂⁴×C₈₉	—	2	1	no	—
142	C₂×Q₈×C₈₉	—	2	1	no	—
143	C₂×Q₈×C₈₉	—	2	1	no	—
144	C₂×Q₈×C₈₉	—	2	1	no	—
145	C₂×Q₈×C₈₉	—	2	1	no	—
146	C₂×Q₈×C₈₉	—	2	1	no	—
147	C₂×Q₈×C₈₉	—	2	1	no	—
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	—	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	—	4	2	no	—
165	C₂×D₄×C₈₉	—	4	2	no	—
166	C₂×D₄×C₈₉	—	4	2	no	—
167	C₂×D₄×C₈₉	—	4	2	no	—
168	C₂×D₄×C₈₉	—	8	1	no	—
169	C₂×D₄×C₈₉	—	8	1	no	—
170	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
171	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₈₉	—	2	1	no	—
173	C₂²×C₄×C₈₉	—	2	1	no	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	1	no	—
177	C₂²×C₄×C₈₉	—	4	2	no	—
178	C₂²×C₄×C₈₉	—	4	2	no	—
179	C₂²×C₄×C₈₉	—	4	2	no	—
180	C₂²×C₄×C₈₉	—	4	2	no	—
181	C₂²×C₄×C₈₉	—	8	1	no	—
182	C₂²×C₄×C₈₉	—	8	1	no	—
183	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
190	SD₁₆×C₈₉	—	4	4	no	—
191	SD₁₆×C₈₉	—	4	4	no	—
192	D₈×C₈₉	—	2	8	no	—
193	D₈×C₈₉	—	4	4	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
203	C₂×C₈×C₈₉	#41	1	2	yes	—
204	C₂×C₈×C₈₉	#41	1	2	yes	—
205	C₂×C₈×C₈₉	#41	1	2	yes	—
206	C₄⋊C₄×C₈₉	—	2	2	no	—
207	C₄⋊C₄×C₈₉	—	2	1	no	—
208	C₄⋊C₄×C₈₉	—	2	1	no	—
209	C₄⋊C₄×C₈₉	—	2	1	no	—
210	C₄⋊C₄×C₈₉	—	2	1	no	—
211	C₄⋊C₄×C₈₉	—	2	1	no	—
212	C₄⋊C₄×C₈₉	—	2	1	no	—
213	C₄⋊C₄×C₈₉	—	2	1	no	—
214	C₄⋊C₄×C₈₉	—	2	1	no	—
215	C₄⋊C₄×C₈₉	—	4	1	no	—
216	C₄⋊C₄×C₈₉	—	4	2	no	—
217	C₄⋊C₄×C₈₉	—	8	1	no	—
218	C₂²⋊C₄×C₈₉	—	4	2	no	—
219	C₂²⋊C₄×C₈₉	—	4	2	no	—
220	C₂²⋊C₄×C₈₉	—	4	2	no	—
221	C₂²⋊C₄×C₈₉	—	4	2	no	—
222	C₂²⋊C₄×C₈₉	—	4	2	no	—
223	C₂²⋊C₄×C₈₉	—	4	2	no	—
224	C₂²⋊C₄×C₈₉	—	4	2	no	—
225	C₂²⋊C₄×C₈₉	—	4	2	no	—
226	C₂²⋊C₄×C₈₉	—	8	1	no	—
227	C₂²⋊C₄×C₈₉	—	8	1	no	—
228	C₂²⋊C₄×C₈₉	—	8	1	no	—
229	C₂²⋊C₄×C₈₉	—	8	1	no	—
230	C₄²×C₈₉	—	2	1	no	—
231	C₄²×C₈₉	—	2	1	no	—
232	C₄²×C₈₉	—	2	1	no	—
233	C₄²×C₈₉	—	2	1	no	—
234	C₄²×C₈₉	—	2	1	no	—
235	C₄²×C₈₉	—	2	1	no	—
236	C₂³×C₈₉	—	2	2	no	—
237	C₂³×C₈₉	—	2	2	no	—
238	C₂³×C₈₉	—	4	1	no	—
239	C₂³×C₈₉	—	4	1	no	—
240	C₂³×C₈₉	—	4	1	no	—
241	C₂³×C₈₉	—	4	1	no	—
242	C₂³×C₈₉	—	4	1	no	—
243	C₂³×C₈₉	—	4	1	no	—
244	C₂³×C₈₉	—	4	1	no	—
245	C₂³×C₈₉	—	4	1	no	—
246	C₂³×C₈₉	—	4	1	no	—
247	C₂³×C₈₉	—	4	1	no	—
248	C₂³×C₈₉	—	4	1	no	—
249	C₂³×C₈₉	—	4	1	no	—
250	C₂³×C₈₉	—	4	1	no	—
251	C₂³×C₈₉	—	4	1	no	—
252	C₂³×C₈₉	—	4	1	no	—
253	C₂³×C₈₉	—	4	1	no	—
254	C₂³×C₈₉	—	4	1	no	—
255	C₂³×C₈₉	—	4	1	no	—
256	C₂³×C₈₉	—	4	1	no	—
257	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
258	Q₈×C₈₉	—	4	1	no	—
259	Q₈×C₈₉	—	4	1	no	—
260	Q₈×C₈₉	—	4	1	no	—
261	Q₈×C₈₉	—	4	1	no	—
262	D₄×C₈₉	—	2	2	no	—
263	D₄×C₈₉	—	2	2	no	—
264	D₄×C₈₉	—	2	2	no	—
265	D₄×C₈₉	—	2	2	no	—
266	D₄×C₈₉	—	4	1	no	—
267	D₄×C₈₉	—	4	1	no	—
268	D₄×C₈₉	—	4	1	no	—
269	D₄×C₈₉	—	4	1	no	—
270	D₄×C₈₉	—	4	1	no	—
271	D₄×C₈₉	—	4	1	no	—
272	D₄×C₈₉	—	4	1	no	—
273	D₄×C₈₉	—	4	1	no	—
274	D₄×C₈₉	—	8	4	no	—
275	D₄×C₈₉	—	8	4	no	—
276	C₂×C₄×C₈₉	—	2	1	no	—
277	C₂×C₄×C₈₉	—	2	1	no	—
278	C₂×C₄×C₈₉	—	2	1	no	—
279	C₂×C₄×C₈₉	—	2	1	no	—
280	C₂×C₄×C₈₉	—	2	1	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	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	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	1	no	—
293	C₂×C₄×C₈₉	—	4	1	no	—
294	C₂×C₄×C₈₉	—	4	1	no	—
295	C₂×C₄×C₈₉	—	4	1	no	—
296	C₂×C₄×C₈₉	—	4	1	no	—
297	C₂×C₄×C₈₉	—	4	1	no	—
298	C₂×C₄×C₈₉	—	4	1	no	—
299	C₂×C₄×C₈₉	—	4	1	no	—
300	C₂×C₄×C₈₉	—	4	1	no	—
301	C₂×C₄×C₈₉	—	4	1	no	—
302	C₂×C₄×C₈₉	—	4	1	no	—
303	C₂×C₄×C₈₉	—	4	1	no	—
304	C₂×C₄×C₈₉	—	4	1	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	—	8	4	no	—
309	C₂×C₄×C₈₉	—	8	4	no	—
310	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
311	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
317	C₈×C₈₉	—	2	2	no	—
318	C₈×C₈₉	—	4	1	no	—
319	C₈×C₈₉	—	4	1	no	—
320	C₈×C₈₉	#123	1	4	yes	complemented
321	C₂²×C₈₉	—	4	2	no	—
322	C₂²×C₈₉	—	4	2	no	—
323	C₂²×C₈₉	—	4	2	no	—
324	C₂²×C₈₉	—	4	2	no	—
325	C₂²×C₈₉	—	4	2	no	—
326	C₂²×C₈₉	—	4	2	no	—
327	C₂²×C₈₉	—	8	1	no	—
328	C₂²×C₈₉	—	8	1	no	—
329	C₂²×C₈₉	—	8	1	no	—
330	C₂²×C₈₉	—	8	1	no	—
331	C₂²×C₈₉	—	8	1	no	—
332	C₂²×C₈₉	—	8	1	no	—
333	C₂²×C₈₉	—	8	1	no	—
334	C₂²×C₈₉	—	8	1	no	—
335	C₂²×C₈₉	—	8	1	no	—
336	C₂²×C₈₉	—	8	1	no	—
337	C₂²×C₈₉	—	8	1	no	—
338	C₂²×C₈₉	—	8	1	no	—
339	C₂²×C₈₉	—	8	1	no	—
340	C₂²×C₈₉	—	8	1	no	—
341	C₂²×C₈₉	—	8	1	no	—
342	C₂²×C₈₉	#532	1	1	yes	characteristic
343	C₂²×C₈₉	D₄²	1	1	yes	characteristic
344	C₂²×C₈₉	#550	1	1	yes	characteristic
345	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂²×C₈₉	#575	1	1	yes	characteristic
347	C₂²×C₈₉	#576	1	1	yes	characteristic
348	C₂²×C₈₉	#577	1	1	yes	characteristic
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	4	1	no	—
351	C₄×C₈₉	—	4	1	no	—
352	C₄×C₈₉	—	4	1	no	—
353	C₄×C₈₉	—	4	1	no	—
354	C₄×C₈₉	—	4	1	no	—
355	C₄×C₈₉	—	8	1	no	—
356	C₄×C₈₉	—	8	1	no	—
357	C₄×C₈₉	—	8	1	no	—
358	C₄×C₈₉	—	8	1	no	—
359	C₄×C₈₉	—	8	1	no	—
360	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
361	C₄×C₈₉	#540	1	1	yes	characteristic
362	C₄×C₈₉	#546	1	1	yes	characteristic
363	C₄×C₈₉	#559	1	1	yes	characteristic
364	#26258	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂×C₈₉	—	8	2	no	—
366	C₂×C₈₉	—	8	2	no	—
367	C₂×C₈₉	—	16	1	no	—
368	C₂×C₈₉	#2445	1	1	yes	characteristic
369	C₂×C₈₉	#3171	1	1	yes	characteristic
370	C₂×C₈₉	#3179	1	1	yes	characteristic
371	C₂×C₈₉	#3264	1	1	yes	characteristic
372	C₂×C₈₉	#3267	1	1	yes	characteristic
373	C₂×C₈₉	#3397	1	1	yes	characteristic
374	C₂×C₈₉	#3403	1	1	yes	characteristic
375	C₂×#496	C₂×C₈₉	1	1	yes	characteristic
376	C₂×C₄×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
377	#2447	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#2445	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#2042	C₂×C₈₉	1	1	yes	characteristic, complemented
382	#2041	C₂×C₈₉	1	1	yes	characteristic, complemented
383	#1973	C₂×C₈₉	1	1	yes	characteristic, complemented
384	#1972	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#1944	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#1771	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₈₉	#26258	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
393	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
394	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
396	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
397	C₂×#123	—	2	1	no	—
398	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
400	#496	—	2	4	no	—
401	C₄×D₈	—	2	4	no	—
402	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
416	#397	—	2	1	no	—
417	#397	—	2	1	no	—
418	#394	—	2	1	no	—
419	#394	—	2	1	no	—
420	#391	C₂²×C₈₉	1	1	yes	characteristic
421	#391	C₂²×C₈₉	1	1	yes	characteristic
422	#390	C₂²×C₈₉	1	1	yes	characteristic
423	#390	C₂²×C₈₉	1	1	yes	characteristic
424	#390	C₂²×C₈₉	1	1	yes	characteristic
425	#390	C₂²×C₈₉	1	1	yes	characteristic
426	#389	C₂²×C₈₉	1	1	yes	characteristic
427	#389	C₂²×C₈₉	1	1	yes	characteristic
428	#386	—	2	1	no	—
429	#385	—	2	1	no	—
430	#381	—	2	1	no	—
431	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
432	#340	C₂²×C₈₉	1	1	yes	characteristic
433	#340	C₂²×C₈₉	1	1	yes	characteristic
434	#336	C₂²×C₈₉	1	1	yes	characteristic
435	#336	C₂²×C₈₉	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
440	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×SD₁₆	—	4	1	no	—
450	C₂×D₈	—	2	2	no	—
451	C₂×D₈	—	2	2	no	—
452	C₂×D₈	—	2	2	no	—
453	C₂×D₈	—	2	2	no	—
454	C₂×D₈	—	4	1	no	—
455	C₂×D₈	D₄×C₈₉	1	4	yes	—
456	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
460	#127	—	2	2	no	—
461	#127	—	4	1	no	—
462	#124	—	2	2	no	—
463	#124	—	4	1	no	—
464	#123	—	4	4	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	4	1	no	—
468	C₄×D₄	—	4	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
492	#107	—	2	2	no	—
493	#106	—	2	2	no	—
494	C₄⋊C₈	—	2	2	no	—
495	#103	—	4	1	no	—
496	#103	—	4	1	no	—
497	#102	—	2	2	no	—
498	#102	—	2	2	no	—
499	#102	—	4	1	no	—
500	#102	—	4	1	no	—
501	#102	—	4	1	no	—
502	#102	—	4	1	no	—
503	#97	—	2	2	no	—
504	#97	—	2	2	no	—
505	C₄×C₈	—	2	2	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	D₄×C₈₉	1	1	yes	characteristic
513	#95	D₄×C₈₉	1	1	yes	characteristic
514	C₂⁴	—	2	1	no	—
515	C₂⁴	—	2	1	no	—
516	C₂⁴	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	8	1	no	—
544	C₂×D₄	—	8	1	no	—
545	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
546	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	8	1	no	—
557	C₂²×C₄	—	8	1	no	—
558	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
565	SD₁₆	—	4	4	no	—
566	SD₁₆	—	4	4	no	—
567	D₈	—	2	8	no	—
568	D₈	—	4	4	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
578	C₂×C₈	#41×C₈₉	1	2	yes	—
579	C₂×C₈	#41×C₈₉	1	2	yes	—
580	C₂×C₈	#41×C₈₉	1	2	yes	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	8	1	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	8	1	no	—
602	C₂²⋊C₄	—	8	1	no	—
603	C₂²⋊C₄	—	8	1	no	—
604	C₂²⋊C₄	—	8	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	8	4	no	—
650	D₄	—	8	4	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	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	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
687	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
689	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
690	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
691	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
692	C₈	—	2	2	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	#123×C₈₉	1	4	yes	complemented
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	#532×C₈₉	1	1	yes	characteristic
718	C₂²	D₄²×C₈₉	1	1	yes	characteristic
719	C₂²	#550×C₈₉	1	1	yes	characteristic
720	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
721	C₂²	#575×C₈₉	1	1	yes	characteristic
722	C₂²	#576×C₈₉	1	1	yes	characteristic
723	C₂²	#577×C₈₉	1	1	yes	characteristic
724	C₄	—	2	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	8	1	no	—
731	C₄	—	8	1	no	—
732	C₄	—	8	1	no	—
733	C₄	—	8	1	no	—
734	C₄	—	8	1	no	—
735	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
736	C₄	#540×C₈₉	1	1	yes	characteristic
737	C₄	#546×C₈₉	1	1	yes	characteristic
738	C₄	#559×C₈₉	1	1	yes	characteristic
739	C₂	—	8	2	no	—
740	C₂	—	8	2	no	—
741	C₂	—	16	1	no	—
742	C₂	C₈₉×#2445	1	1	yes	characteristic
743	C₂	C₈₉×#3171	1	1	yes	characteristic
744	C₂	C₈₉×#3179	1	1	yes	characteristic
745	C₂	C₈₉×#3264	1	1	yes	characteristic
746	C₂	C₈₉×#3267	1	1	yes	characteristic
747	C₂	C₈₉×#3397	1	1	yes	characteristic
748	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×C₄×D₈×C₈₉	C₂	semidirect
3. C₈₉×#2447	C₂	semidirect
4. C₈₉×#2445	C₂	semidirect
5. C₈₉×#2055	C₂	semidirect
6. C₈₉×#2054	C₂	semidirect
7. C₈₉×#2042	C₂	semidirect
8. C₈₉×#2041	C₂	semidirect
9. C₈₉×#1973	C₂	semidirect
10. C₈₉×#1972	C₂	semidirect
11. C₈₉×#1968	C₂	semidirect
12. C₈₉×#1944	C₂	semidirect
13. C₈₉×#1879	C₂	semidirect
14. C₈₉×#1877	C₂	semidirect
15. C₈₉×#1771	C₂	semidirect
320. C₈×C₈₉	#123	semidirect
364. #26258	C₈₉	direct (N × H)
376. C₂×C₄×D₈	C₂×C₈₉	semidirect
377. #2447	C₂×C₈₉	semidirect
378. #2445	C₂×C₈₉	semidirect
379. #2055	C₂×C₈₉	semidirect
380. #2054	C₂×C₈₉	semidirect
381. #2042	C₂×C₈₉	semidirect
382. #2041	C₂×C₈₉	semidirect
383. #1973	C₂×C₈₉	semidirect
384. #1972	C₂×C₈₉	semidirect
385. #1968	C₂×C₈₉	semidirect
386. #1944	C₂×C₈₉	semidirect
387. #1879	C₂×C₈₉	semidirect
388. #1877	C₂×C₈₉	semidirect
389. #1771	C₂×C₈₉	semidirect
390. C₈₉	#26258	direct (N × H)
695. C₈	#123×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×C₄×D₈×C₈₉	2
C₈₉×#2447	2
C₈₉×#2445	2
C₈₉×#2055	2
C₈₉×#2054	2
C₈₉×#2042	2
C₈₉×#2041	2
C₈₉×#1973	2
C₈₉×#1972	2
C₈₉×#1968	2
C₈₉×#1944	2
C₈₉×#1879	2
C₈₉×#1877	2
C₈₉×#1771	2
#26258	89

Subgroups — C89×#26258 #36404106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26258 #36404106