Subgroups — C₈₉×#25133 #36402981

Order 22784.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 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×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#436×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×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×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#121×C₈₉	—	2	1	no	—
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	#469×C₈₉	—	2	4	no	—
29	#449×C₈₉	—	2	4	no	—
30	#436×C₈₉	—	2	4	no	—
31	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	#417×C₈₉	—	2	4	no	—
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×#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×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
46	#396×C₈₉	—	2	1	no	—
47	#394×C₈₉	—	2	1	no	—
48	#394×C₈₉	—	2	1	no	—
49	#392×C₈₉	—	2	1	no	—
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#386×C₈₉	—	2	1	no	—
55	#386×C₈₉	—	2	1	no	—
56	#385×C₈₉	—	2	1	no	—
57	#380×C₈₉	C₂²	1	1	yes	characteristic
58	#380×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	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×D₄×C₈₉	—	2	1	no	—
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	—	2	1	no	—
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₉	—	2	1	no	—
78	C₂³×C₄×C₈₉	—	2	1	no	—
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₈₉	—	2	2	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	4	1	no	—
84	C₂×D₈×C₈₉	—	2	2	no	—
85	C₂×D₈×C₈₉	—	2	2	no	—
86	C₂×D₈×C₈₉	—	4	1	no	—
87	C₂×M₁₆×C₈₉	—	2	2	no	—
88	C₂×M₁₆×C₈₉	—	2	2	no	—
89	C₂×M₁₆×C₈₉	—	2	2	no	—
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂×M₁₆×C₈₉	—	4	1	no	—
92	C₂×M₁₆×C₈₉	—	4	1	no	—
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²⋊Q₈×C₈₉	—	2	2	no	—
98	C₂²⋊Q₈×C₈₉	—	4	1	no	—
99	#121×C₈₉	—	2	2	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	—	2	2	no	—
103	#121×C₈₉	—	4	1	no	—
104	#121×C₈₉	—	4	1	no	—
105	#121×C₈₉	—	4	4	no	—
106	C₄×D₄×C₈₉	—	2	2	no	—
107	C₄×D₄×C₈₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
113	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	#106×C₈₉	—	2	2	no	—
133	#106×C₈₉	—	4	1	no	—
134	C₄⋊C₈×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	4	1	no	—
142	#102×C₈₉	D₄	1	4	yes	complemented
143	C₂²⋊C₈×C₈₉	—	2	2	no	—
144	C₂²⋊C₈×C₈₉	D₄	1	4	yes	complemented
145	C₄×C₈×C₈₉	—	2	2	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	—	2	1	no	—
149	#95×C₈₉	—	2	1	no	—
150	#95×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×C₈₉	—	2	1	no	—
153	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
155	#41×C₈₉	—	2	8	no	—
156	#41×C₈₉	—	4	4	no	—
157	#41×C₈₉	—	4	4	no	—
158	#41×C₈₉	—	4	4	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	#41	1	2	yes	—
165	C₂×D₄×C₈₉	—	2	2	no	—
166	C₂×D₄×C₈₉	—	2	2	no	—
167	C₂×D₄×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	2	1	no	—
172	C₂×D₄×C₈₉	—	2	1	no	—
173	C₂×D₄×C₈₉	—	2	1	no	—
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	—	4	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	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	4	2	no	—
186	C₂×D₄×C₈₉	—	4	2	no	—
187	C₂×D₄×C₈₉	—	4	2	no	—
188	C₂×D₄×C₈₉	—	4	2	no	—
189	C₂×D₄×C₈₉	—	8	1	no	—
190	C₂×D₄×C₈₉	—	8	1	no	—
191	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	2	1	no	—
203	C₂²×C₄×C₈₉	—	2	1	no	—
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	C₂²×C₄×C₈₉	—	2	1	no	—
206	C₂²×C₄×C₈₉	—	2	1	no	—
207	C₂²×C₄×C₈₉	—	2	1	no	—
208	C₂²×C₄×C₈₉	—	4	2	no	—
209	C₂²×C₄×C₈₉	—	4	2	no	—
210	C₂²×C₄×C₈₉	—	4	2	no	—
211	C₂²×C₄×C₈₉	—	4	2	no	—
212	C₂²×C₄×C₈₉	—	4	2	no	—
213	C₂²×C₄×C₈₉	—	8	1	no	—
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	#41	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	SD₁₆×C₈₉	—	4	4	no	—
222	D₈×C₈₉	—	4	4	no	—
223	M₁₆×C₈₉	—	4	4	no	—
224	M₁₆×C₈₉	—	4	4	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	1	no	—
227	C₂×C₈×C₈₉	—	2	1	no	—
228	C₂×C₈×C₈₉	—	2	1	no	—
229	C₂×C₈×C₈₉	—	2	1	no	—
230	C₂×C₈×C₈₉	—	2	1	no	—
231	C₂×C₈×C₈₉	—	2	1	no	—
232	C₂×C₈×C₈₉	—	2	1	no	—
233	C₂×C₈×C₈₉	—	2	1	no	—
234	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
235	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
236	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₈₉	—	2	2	no	—
238	C₄⋊C₄×C₈₉	—	2	1	no	—
239	C₄⋊C₄×C₈₉	—	2	1	no	—
240	C₄⋊C₄×C₈₉	—	2	1	no	—
241	C₄⋊C₄×C₈₉	—	2	1	no	—
242	C₄⋊C₄×C₈₉	—	2	1	no	—
243	C₄⋊C₄×C₈₉	—	2	1	no	—
244	C₄⋊C₄×C₈₉	—	2	1	no	—
245	C₄⋊C₄×C₈₉	—	2	1	no	—
246	C₄⋊C₄×C₈₉	—	2	1	no	—
247	C₄⋊C₄×C₈₉	—	4	2	no	—
248	C₄⋊C₄×C₈₉	—	4	2	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
251	C₂²⋊C₄×C₈₉	—	2	2	no	—
252	C₂²⋊C₄×C₈₉	—	2	2	no	—
253	C₂²⋊C₄×C₈₉	—	4	2	no	—
254	C₂²⋊C₄×C₈₉	—	4	2	no	—
255	C₂²⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	—	4	2	no	—
257	C₂²⋊C₄×C₈₉	—	4	2	no	—
258	C₂²⋊C₄×C₈₉	—	4	2	no	—
259	C₂²⋊C₄×C₈₉	—	4	2	no	—
260	C₂²⋊C₄×C₈₉	—	8	1	no	—
261	C₂²⋊C₄×C₈₉	—	8	1	no	—
262	C₂²⋊C₄×C₈₉	—	8	1	no	—
263	C₄²×C₈₉	—	2	1	no	—
264	C₄²×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	2	1	no	—
267	C₂³×C₈₉	—	2	1	no	—
268	C₂³×C₈₉	—	2	1	no	—
269	C₂³×C₈₉	—	2	1	no	—
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	2	no	—
273	C₂³×C₈₉	—	2	1	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	1	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	1	no	—
278	C₂³×C₈₉	—	2	1	no	—
279	C₂³×C₈₉	—	4	1	no	—
280	C₂³×C₈₉	—	4	1	no	—
281	C₂³×C₈₉	—	4	1	no	—
282	C₂³×C₈₉	—	4	1	no	—
283	C₂³×C₈₉	—	4	1	no	—
284	C₂³×C₈₉	—	4	1	no	—
285	C₂³×C₈₉	—	4	1	no	—
286	C₂³×C₈₉	—	4	1	no	—
287	C₂³×C₈₉	—	4	1	no	—
288	C₂³×C₈₉	—	4	1	no	—
289	C₂³×C₈₉	—	4	1	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	#121	1	2	yes	—
293	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₈₉	—	2	2	no	—
295	Q₈×C₈₉	—	2	2	no	—
296	Q₈×C₈₉	—	4	1	no	—
297	Q₈×C₈₉	—	4	1	no	—
298	D₄×C₈₉	—	2	2	no	—
299	D₄×C₈₉	—	2	2	no	—
300	D₄×C₈₉	—	4	4	no	—
301	D₄×C₈₉	—	4	8	no	—
302	D₄×C₈₉	—	4	1	no	—
303	D₄×C₈₉	—	4	1	no	—
304	D₄×C₈₉	—	4	1	no	—
305	D₄×C₈₉	—	4	1	no	—
306	D₄×C₈₉	—	4	1	no	—
307	D₄×C₈₉	—	4	1	no	—
308	D₄×C₈₉	—	8	4	no	—
309	D₄×C₈₉	—	8	4	no	—
310	D₄×C₈₉	—	8	4	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	1	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	1	no	—
327	C₂×C₄×C₈₉	—	4	8	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	4	1	no	—
330	C₂×C₄×C₈₉	—	4	1	no	—
331	C₂×C₄×C₈₉	—	4	1	no	—
332	C₂×C₄×C₈₉	—	4	1	no	—
333	C₂×C₄×C₈₉	—	4	1	no	—
334	C₂×C₄×C₈₉	—	4	1	no	—
335	C₂×C₄×C₈₉	—	4	1	no	—
336	C₂×C₄×C₈₉	—	4	1	no	—
337	C₂×C₄×C₈₉	—	4	1	no	—
338	C₂×C₄×C₈₉	—	4	1	no	—
339	C₂×C₄×C₈₉	—	4	1	no	—
340	C₂×C₄×C₈₉	—	4	1	no	—
341	C₂×C₄×C₈₉	—	4	1	no	—
342	C₂×C₄×C₈₉	—	4	1	no	—
343	C₂×C₄×C₈₉	—	4	1	no	—
344	C₂×C₄×C₈₉	—	4	1	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	1	no	—
347	C₂×C₄×C₈₉	—	4	1	no	—
348	C₂×C₄×C₈₉	—	8	4	no	—
349	C₂×C₄×C₈₉	#121	1	2	yes	—
350	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
351	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
357	C₈×C₈₉	—	2	2	no	—
358	C₈×C₈₉	—	2	2	no	—
359	C₈×C₈₉	—	2	2	no	—
360	C₈×C₈₉	—	4	1	no	—
361	C₂²×C₈₉	—	2	2	no	—
362	C₂²×C₈₉	—	2	2	no	—
363	C₂²×C₈₉	—	2	2	no	—
364	C₂²×C₈₉	—	4	1	no	—
365	C₂²×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	4	1	no	—
367	C₂²×C₈₉	—	4	1	no	—
368	C₂²×C₈₉	—	4	1	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	1	no	—
371	C₂²×C₈₉	—	4	1	no	—
372	C₂²×C₈₉	—	4	2	no	—
373	C₂²×C₈₉	—	4	1	no	—
374	C₂²×C₈₉	—	4	2	no	—
375	C₂²×C₈₉	—	4	1	no	—
376	C₂²×C₈₉	—	4	1	no	—
377	C₂²×C₈₉	—	4	1	no	—
378	C₂²×C₈₉	—	8	1	no	—
379	C₂²×C₈₉	—	8	1	no	—
380	C₂²×C₈₉	—	8	1	no	—
381	C₂²×C₈₉	—	8	1	no	—
382	C₂²×C₈₉	—	8	1	no	—
383	C₂²×C₈₉	—	8	1	no	—
384	C₂²×C₈₉	—	8	1	no	—
385	C₂²×C₈₉	—	8	1	no	—
386	C₂²×C₈₉	—	8	1	no	—
387	C₂²×C₈₉	—	8	1	no	—
388	C₂²×C₈₉	—	8	1	no	—
389	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
390	C₂²×C₈₉	D₄²	1	1	yes	characteristic
391	C₂²×C₈₉	#546	1	1	yes	characteristic
392	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂²×C₈₉	#575	1	1	yes	characteristic
394	C₂²×C₈₉	#577	1	1	yes	characteristic
395	C₂²×C₈₉	#577	1	1	yes	characteristic
396	C₄×C₈₉	—	2	2	no	—
397	C₄×C₈₉	—	2	2	no	—
398	C₄×C₈₉	—	4	1	no	—
399	C₄×C₈₉	—	4	2	no	—
400	C₄×C₈₉	—	4	2	no	—
401	C₄×C₈₉	—	4	1	no	—
402	C₄×C₈₉	—	8	1	no	—
403	C₄×C₈₉	—	8	1	no	—
404	C₄×C₈₉	—	8	1	no	—
405	C₄×C₈₉	—	8	1	no	—
406	C₄×C₈₉	#525	1	1	yes	characteristic
407	C₄×C₈₉	#538	1	1	yes	characteristic
408	C₄×C₈₉	D₄²	1	1	yes	characteristic
409	C₄×C₈₉	#546	1	1	yes	characteristic
410	#25133	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₈₉	—	4	2	no	—
412	C₂×C₈₉	—	8	1	no	—
413	C₂×C₈₉	—	8	2	no	—
414	C₂×C₈₉	—	16	1	no	—
415	C₂×C₈₉	#2424	1	1	yes	characteristic
416	C₂×C₈₉	#3055	1	1	yes	characteristic
417	C₂×C₈₉	#3060	1	1	yes	characteristic
418	C₂×C₈₉	#3272	1	1	yes	characteristic
419	C₂×C₈₉	#3275	1	1	yes	characteristic
420	C₂×C₈₉	#3326	1	1	yes	characteristic
421	C₂×C₈₉	#3332	1	1	yes	characteristic
422	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
423	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
424	C₂×#436	C₂×C₈₉	1	1	yes	characteristic, complemented
425	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
426	#2416	C₂×C₈₉	1	1	yes	characteristic, complemented
427	#2407	C₂×C₈₉	1	1	yes	characteristic, complemented
428	#2066	C₂×C₈₉	1	1	yes	characteristic, complemented
429	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
430	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
431	#2000	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
433	#1934	C₂×C₈₉	1	1	yes	characteristic, complemented
434	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
435	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
436	#1853	C₂×C₈₉	1	1	yes	characteristic, complemented
437	C₈₉	#25133	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
440	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
441	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
442	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×#121	—	2	1	no	—
445	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
446	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
447	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
449	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
450	#469	—	2	4	no	—
451	#449	—	2	4	no	—
452	#436	—	2	4	no	—
453	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
456	#417	—	2	4	no	—
457	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
468	#396	—	2	1	no	—
469	#394	—	2	1	no	—
470	#394	—	2	1	no	—
471	#392	—	2	1	no	—
472	#391	C₂²×C₈₉	1	1	yes	characteristic
473	#390	C₂²×C₈₉	1	1	yes	characteristic
474	#390	C₂²×C₈₉	1	1	yes	characteristic
475	#389	C₂²×C₈₉	1	1	yes	characteristic
476	#386	—	2	1	no	—
477	#386	—	2	1	no	—
478	#385	—	2	1	no	—
479	#380	C₂²×C₈₉	1	1	yes	characteristic
480	#380	C₂²×C₈₉	1	1	yes	characteristic
481	#340	C₂²×C₈₉	1	1	yes	characteristic
482	#340	C₂²×C₈₉	1	1	yes	characteristic
483	#340	C₂²×C₈₉	1	1	yes	characteristic
484	#340	C₂²×C₈₉	1	1	yes	characteristic
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	4	1	no	—
490	C₂×#41	—	4	1	no	—
491	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	4	1	no	—
506	C₂×D₈	—	2	2	no	—
507	C₂×D₈	—	2	2	no	—
508	C₂×D₈	—	4	1	no	—
509	C₂×M₁₆	—	2	2	no	—
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	2	2	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	4	1	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	4	1	no	—
526	#121	—	4	1	no	—
527	#121	—	4	4	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	4	1	no	—
535	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
554	#106	—	2	2	no	—
555	#106	—	4	1	no	—
556	C₄⋊C₈	—	2	2	no	—
557	#103	—	2	2	no	—
558	#103	—	2	2	no	—
559	#103	—	2	2	no	—
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	2	2	no	—
563	#102	—	4	1	no	—
564	#102	D₄×C₈₉	1	4	yes	complemented
565	C₂²⋊C₈	—	2	2	no	—
566	C₂²⋊C₈	D₄×C₈₉	1	4	yes	complemented
567	C₄×C₈	—	2	2	no	—
568	#95	—	2	1	no	—
569	#95	—	2	1	no	—
570	#95	—	2	1	no	—
571	#95	—	2	1	no	—
572	#95	—	2	1	no	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
576	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
577	#41	—	2	8	no	—
578	#41	—	4	4	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	#41×C₈₉	1	2	yes	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	4	1	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	8	1	no	—
612	C₂×D₄	—	8	1	no	—
613	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	8	1	no	—
636	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
640	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	#41×C₈₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
643	SD₁₆	—	4	4	no	—
644	D₈	—	4	4	no	—
645	M₁₆	—	4	4	no	—
646	M₁₆	—	4	4	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
657	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
658	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	8	1	no	—
683	C₂²⋊C₄	—	8	1	no	—
684	C₂²⋊C₄	—	8	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	#121×C₈₉	1	2	yes	—
715	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	1	no	—
719	Q₈	—	4	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	4	4	no	—
723	D₄	—	4	8	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	8	4	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	#121×C₈₉	1	2	yes	—
772	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
775	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
776	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
777	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
778	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	—	4	1	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
812	C₂²	D₄²×C₈₉	1	1	yes	characteristic
813	C₂²	#546×C₈₉	1	1	yes	characteristic
814	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
815	C₂²	#575×C₈₉	1	1	yes	characteristic
816	C₂²	#577×C₈₉	1	1	yes	characteristic
817	C₂²	#577×C₈₉	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	8	1	no	—
825	C₄	—	8	1	no	—
826	C₄	—	8	1	no	—
827	C₄	—	8	1	no	—
828	C₄	#525×C₈₉	1	1	yes	characteristic
829	C₄	#538×C₈₉	1	1	yes	characteristic
830	C₄	D₄²×C₈₉	1	1	yes	characteristic
831	C₄	#546×C₈₉	1	1	yes	characteristic
832	C₂	—	4	2	no	—
833	C₂	—	8	1	no	—
834	C₂	—	8	2	no	—
835	C₂	—	16	1	no	—
836	C₂	C₈₉×#2424	1	1	yes	characteristic
837	C₂	C₈₉×#3055	1	1	yes	characteristic
838	C₂	C₈₉×#3060	1	1	yes	characteristic
839	C₂	C₈₉×#3272	1	1	yes	characteristic
840	C₂	C₈₉×#3275	1	1	yes	characteristic
841	C₂	C₈₉×#3326	1	1	yes	characteristic
842	C₂	C₈₉×#3332	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×C₄×D₄×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×#449×C₈₉	C₂	semidirect
3. C₂×#436×C₈₉	C₂	semidirect
4. C₂×#417×C₈₉	C₂	semidirect
5. C₈₉×#2416	C₂	semidirect
6. C₈₉×#2407	C₂	semidirect
7. C₈₉×#2066	C₂	semidirect
8. C₈₉×#2054	C₂	semidirect
9. C₈₉×#2034	C₂	semidirect
10. C₈₉×#2000	C₂	semidirect
11. C₈₉×#1968	C₂	semidirect
12. C₈₉×#1934	C₂	semidirect
13. C₈₉×#1895	C₂	semidirect
14. C₈₉×#1894	C₂	semidirect
15. C₈₉×#1853	C₂	semidirect
142. #102×C₈₉	D₄	semidirect
144. C₂²⋊C₈×C₈₉	D₄	semidirect
410. #25133	C₈₉	direct (N × H)
422. C₂×#469	C₂×C₈₉	semidirect
423. C₂×#449	C₂×C₈₉	semidirect
424. C₂×#436	C₂×C₈₉	semidirect
425. C₂×#417	C₂×C₈₉	semidirect
426. #2416	C₂×C₈₉	semidirect
427. #2407	C₂×C₈₉	semidirect
428. #2066	C₂×C₈₉	semidirect
429. #2054	C₂×C₈₉	semidirect
430. #2034	C₂×C₈₉	semidirect
431. #2000	C₂×C₈₉	semidirect
432. #1968	C₂×C₈₉	semidirect
433. #1934	C₂×C₈₉	semidirect
434. #1895	C₂×C₈₉	semidirect
435. #1894	C₂×C₈₉	semidirect
436. #1853	C₂×C₈₉	semidirect
437. C₈₉	#25133	direct (N × H)
564. #102	D₄×C₈₉	semidirect
566. C₂²⋊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×#449×C₈₉	2
C₂×#436×C₈₉	2
C₂×#417×C₈₉	2
C₈₉×#2416	2
C₈₉×#2407	2
C₈₉×#2066	2
C₈₉×#2054	2
C₈₉×#2034	2
C₈₉×#2000	2
C₈₉×#1968	2
C₈₉×#1934	2
C₈₉×#1895	2
C₈₉×#1894	2
C₈₉×#1853	2
#25133	89

Subgroups — C89×#25133 #36402981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25133 #36402981