Subgroups — C₈₉×#24136 #36401984

Order 22784.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#478×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
17	#553×C₈₉	—	2	4	no	—
18	#553×C₈₉	—	2	4	no	—
19	C₂×#126×C₈₉	—	2	1	no	—
20	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#123×C₈₉	—	2	1	no	—
22	C₂×#121×C₈₉	—	2	1	no	—
23	C₂×#121×C₈₉	—	2	1	no	—
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	—	2	1	no	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#478×C₈₉	—	2	4	no	—
35	#442×C₈₉	—	2	4	no	—
36	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×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×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
51	#394×C₈₉	—	2	1	no	—
52	#394×C₈₉	—	2	1	no	—
53	#384×C₈₉	C₂²	1	1	yes	characteristic
54	#380×C₈₉	—	2	1	no	—
55	#380×C₈₉	C₂²	1	1	yes	characteristic
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×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	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂²×D₄×C₈₉	—	2	1	no	—
65	C₂²×D₄×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	—	2	1	no	—
67	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₈₉	—	2	1	no	—
71	C₂³×C₄×C₈₉	—	2	1	no	—
72	C₂³×C₄×C₈₉	—	2	1	no	—
73	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×D₈×C₈₉	—	2	2	no	—
76	C₂×D₈×C₈₉	—	2	2	no	—
77	C₂×D₈×C₈₉	—	2	2	no	—
78	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	#126×C₈₉	—	2	8	no	—
83	#125×C₈₉	—	2	2	no	—
84	#125×C₈₉	D₄	1	4	yes	complemented
85	#123×C₈₉	—	2	8	no	—
86	#121×C₈₉	—	2	8	no	—
87	#121×C₈₉	—	2	2	no	—
88	#121×C₈₉	—	2	2	no	—
89	#121×C₈₉	—	2	2	no	—
90	#121×C₈₉	—	2	2	no	—
91	#121×C₈₉	—	2	2	no	—
92	#121×C₈₉	—	2	2	no	—
93	#121×C₈₉	—	4	1	no	—
94	#121×C₈₉	—	4	1	no	—
95	#121×C₈₉	—	4	4	no	—
96	C₄×D₄×C₈₉	—	2	8	no	—
97	C₄×D₄×C₈₉	—	2	2	no	—
98	C₄×D₄×C₈₉	—	2	2	no	—
99	C₄×D₄×C₈₉	—	2	2	no	—
100	C₄×D₄×C₈₉	—	2	2	no	—
101	C₄×D₄×C₈₉	—	2	2	no	—
102	C₄×D₄×C₈₉	D₄	1	4	yes	complemented
103	#117×C₈₉	—	2	2	no	—
104	#117×C₈₉	—	2	2	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	2	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	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	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	—	2	2	no	—
133	#106×C₈₉	—	2	2	no	—
134	#106×C₈₉	—	2	2	no	—
135	C₄⋊C₈×C₈₉	—	2	2	no	—
136	#102×C₈₉	—	2	2	no	—
137	#102×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	2	2	no	—
139	#102×C₈₉	—	2	2	no	—
140	#102×C₈₉	—	4	1	no	—
141	#102×C₈₉	—	4	1	no	—
142	C₂²⋊C₈×C₈₉	—	2	2	no	—
143	C₂²⋊C₈×C₈₉	—	2	2	no	—
144	C₂²⋊C₈×C₈₉	—	4	1	no	—
145	C₂²⋊C₈×C₈₉	—	4	1	no	—
146	#97×C₈₉	—	2	2	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	—	2	1	no	—
149	C₂⁴×C₈₉	—	2	1	no	—
150	C₂⁴×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂×D₄×C₈₉	—	2	4	no	—
156	C₂×D₄×C₈₉	—	2	2	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	—	2	1	no	—
165	C₂×D₄×C₈₉	—	2	1	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	—	4	1	no	—
168	C₂×D₄×C₈₉	—	4	2	no	—
169	C₂×D₄×C₈₉	—	4	2	no	—
170	C₂×D₄×C₈₉	—	4	2	no	—
171	C₂×D₄×C₈₉	—	4	2	no	—
172	C₂×D₄×C₈₉	—	4	2	no	—
173	C₂×D₄×C₈₉	—	4	2	no	—
174	C₂×D₄×C₈₉	—	8	1	no	—
175	C₂×D₄×C₈₉	—	8	1	no	—
176	C₂×D₄×C₈₉	—	8	1	no	—
177	C₂×D₄×C₈₉	—	8	1	no	—
178	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₈₉	#41	1	2	yes	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	4	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	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	2	no	—
203	C₂²×C₄×C₈₉	—	8	1	no	—
204	C₂²×C₄×C₈₉	—	8	1	no	—
205	C₂²×C₄×C₈₉	—	8	1	no	—
206	C₂²×C₄×C₈₉	—	8	1	no	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
212	D₈×C₈₉	—	2	8	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	—	2	1	no	—
220	C₂×C₈×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	#41	1	2	yes	—
225	C₄⋊C₄×C₈₉	—	2	4	no	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	4	no	—
228	C₄⋊C₄×C₈₉	—	2	2	no	—
229	C₄⋊C₄×C₈₉	—	2	1	no	—
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₄⋊C₄×C₈₉	—	2	1	no	—
232	C₄⋊C₄×C₈₉	—	2	1	no	—
233	C₄⋊C₄×C₈₉	—	2	1	no	—
234	C₄⋊C₄×C₈₉	—	2	1	no	—
235	C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₄⋊C₄×C₈₉	—	2	1	no	—
237	C₄⋊C₄×C₈₉	—	2	1	no	—
238	C₄⋊C₄×C₈₉	—	4	2	no	—
239	C₄⋊C₄×C₈₉	—	8	1	no	—
240	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
243	C₂²⋊C₄×C₈₉	—	2	4	no	—
244	C₂²⋊C₄×C₈₉	—	2	4	no	—
245	C₂²⋊C₄×C₈₉	—	2	4	no	—
246	C₂²⋊C₄×C₈₉	—	2	4	no	—
247	C₂²⋊C₄×C₈₉	—	2	2	no	—
248	C₂²⋊C₄×C₈₉	—	2	2	no	—
249	C₂²⋊C₄×C₈₉	—	4	2	no	—
250	C₂²⋊C₄×C₈₉	—	4	2	no	—
251	C₂²⋊C₄×C₈₉	—	4	2	no	—
252	C₂²⋊C₄×C₈₉	—	4	2	no	—
253	C₂²⋊C₄×C₈₉	—	4	2	no	—
254	C₄²×C₈₉	—	2	4	no	—
255	C₄²×C₈₉	C₂×D₄	1	2	yes	—
256	C₄²×C₈₉	C₂×D₄	1	2	yes	—
257	C₂³×C₈₉	—	2	1	no	—
258	C₂³×C₈₉	—	2	1	no	—
259	C₂³×C₈₉	—	2	1	no	—
260	C₂³×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	2	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	—	4	1	no	—
273	C₂³×C₈₉	—	4	1	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	—	4	1	no	—
276	C₂³×C₈₉	—	4	1	no	—
277	C₂³×C₈₉	—	4	1	no	—
278	C₂³×C₈₉	—	4	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	AGL(1,ℤ/8)	1	2	yes	—
285	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
286	D₄×C₈₉	—	2	2	no	—
287	D₄×C₈₉	—	2	2	no	—
288	D₄×C₈₉	—	2	2	no	—
289	D₄×C₈₉	—	2	2	no	—
290	D₄×C₈₉	—	4	4	no	—
291	D₄×C₈₉	—	4	8	no	—
292	D₄×C₈₉	—	4	1	no	—
293	D₄×C₈₉	—	4	1	no	—
294	D₄×C₈₉	—	4	1	no	—
295	D₄×C₈₉	—	4	1	no	—
296	D₄×C₈₉	—	8	4	no	—
297	D₄×C₈₉	—	8	4	no	—
298	D₄×C₈₉	—	8	4	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	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
323	C₂×C₄×C₈₉	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	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	—	8	4	no	—
336	C₂×C₄×C₈₉	—	8	4	no	—
337	C₂×C₄×C₈₉	—	8	4	no	—
338	C₂×C₄×C₈₉	#120	1	2	yes	—
339	C₂×C₄×C₈₉	#120	1	2	yes	—
340	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
346	C₈×C₈₉	—	2	2	no	—
347	C₈×C₈₉	—	4	1	no	—
348	C₈×C₈₉	—	4	1	no	—
349	C₈×C₈₉	—	4	1	no	—
350	C₂²×C₈₉	—	2	2	no	—
351	C₂²×C₈₉	—	2	2	no	—
352	C₂²×C₈₉	—	2	2	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	4	1	no	—
355	C₂²×C₈₉	—	4	1	no	—
356	C₂²×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	4	1	no	—
359	C₂²×C₈₉	—	4	1	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	4	2	no	—
362	C₂²×C₈₉	—	4	1	no	—
363	C₂²×C₈₉	—	4	2	no	—
364	C₂²×C₈₉	—	4	2	no	—
365	C₂²×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	4	1	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	1	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	8	1	no	—
371	C₂²×C₈₉	—	8	1	no	—
372	C₂²×C₈₉	—	8	1	no	—
373	C₂²×C₈₉	—	8	1	no	—
374	C₂²×C₈₉	—	8	1	no	—
375	C₂²×C₈₉	—	8	1	no	—
376	C₂²×C₈₉	—	8	1	no	—
377	C₂²×C₈₉	—	8	1	no	—
378	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
379	C₂²×C₈₉	#546	1	1	yes	characteristic
380	C₂²×C₈₉	#547	1	1	yes	characteristic
381	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂²×C₈₉	#575	1	1	yes	characteristic
383	C₂²×C₈₉	#576	1	1	yes	characteristic
384	C₂²×C₈₉	#577	1	1	yes	characteristic
385	C₄×C₈₉	—	2	2	no	—
386	C₄×C₈₉	—	2	2	no	—
387	C₄×C₈₉	—	4	1	no	—
388	C₄×C₈₉	—	4	1	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	4	2	no	—
391	C₄×C₈₉	—	4	2	no	—
392	C₄×C₈₉	—	8	1	no	—
393	C₄×C₈₉	—	8	1	no	—
394	C₄×C₈₉	—	8	1	no	—
395	C₄×C₈₉	#525	1	1	yes	characteristic
396	C₄×C₈₉	#537	1	1	yes	characteristic
397	C₄×C₈₉	#548	1	1	yes	characteristic
398	C₄×C₈₉	#550	1	1	yes	characteristic
399	#24136	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂×C₈₉	—	4	2	no	—
401	C₂×C₈₉	—	8	1	no	—
402	C₂×C₈₉	—	8	2	no	—
403	C₂×C₈₉	—	8	2	no	—
404	C₂×C₈₉	#2407	1	1	yes	characteristic
405	C₂×C₈₉	#3006	1	1	yes	characteristic
406	C₂×C₈₉	#3012	1	1	yes	characteristic
407	C₂×C₈₉	#3307	1	1	yes	characteristic
408	C₂×C₈₉	#3318	1	1	yes	characteristic
409	C₂×C₈₉	#3345	1	1	yes	characteristic
410	C₂×C₈₉	#3347	1	1	yes	characteristic
411	C₂×#553	C₂×C₈₉	1	1	yes	characteristic, complemented
412	C₂×#478	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#2537	C₂×C₈₉	1	1	yes	characteristic, complemented
415	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
416	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
417	#1999	C₂×C₈₉	1	1	yes	characteristic, complemented
418	#1999	C₂×C₈₉	1	1	yes	characteristic, complemented
419	#1992	C₂×C₈₉	1	1	yes	characteristic, complemented
420	#1955	C₂×C₈₉	1	1	yes	characteristic, complemented
421	#1875	C₂×C₈₉	1	1	yes	characteristic, complemented
422	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
423	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
424	#1853	C₂×C₈₉	1	1	yes	characteristic, complemented
425	#1802	C₂×C₈₉	1	1	yes	characteristic, complemented
426	C₈₉	#24136	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
428	#553	—	2	4	no	—
429	#553	—	2	4	no	—
430	C₂×#126	—	2	1	no	—
431	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#123	—	2	1	no	—
433	C₂×#121	—	2	1	no	—
434	C₂×#121	—	2	1	no	—
435	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
437	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
443	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
445	#478	—	2	4	no	—
446	#442	—	2	4	no	—
447	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
448	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
449	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
450	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
452	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
453	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
462	#394	—	2	1	no	—
463	#394	—	2	1	no	—
464	#384	C₂²×C₈₉	1	1	yes	characteristic
465	#380	—	2	1	no	—
466	#380	C₂²×C₈₉	1	1	yes	characteristic
467	#380	C₂²×C₈₉	1	1	yes	characteristic
468	#340	C₂²×C₈₉	1	1	yes	characteristic
469	#340	C₂²×C₈₉	1	1	yes	characteristic
470	#340	C₂²×C₈₉	1	1	yes	characteristic
471	#340	C₂²×C₈₉	1	1	yes	characteristic
472	#340	C₂²×C₈₉	1	1	yes	characteristic
473	#340	C₂²×C₈₉	1	1	yes	characteristic
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
480	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	2	2	no	—
488	C₂×D₈	—	2	2	no	—
489	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
493	#126	—	2	8	no	—
494	#125	—	2	2	no	—
495	#125	D₄×C₈₉	1	4	yes	complemented
496	#123	—	2	8	no	—
497	#121	—	2	8	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	4	1	no	—
505	#121	—	4	1	no	—
506	#121	—	4	4	no	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	D₄×C₈₉	1	4	yes	complemented
514	#117	—	2	2	no	—
515	#117	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
543	#107	—	2	2	no	—
544	#106	—	2	2	no	—
545	#106	—	2	2	no	—
546	C₄⋊C₈	—	2	2	no	—
547	#102	—	2	2	no	—
548	#102	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	#102	—	4	1	no	—
552	#102	—	4	1	no	—
553	C₂²⋊C₈	—	2	2	no	—
554	C₂²⋊C₈	—	2	2	no	—
555	C₂²⋊C₈	—	4	1	no	—
556	C₂²⋊C₈	—	4	1	no	—
557	#97	—	2	2	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	C₂⁴	—	2	1	no	—
561	C₂⁴	—	2	1	no	—
562	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
563	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	8	1	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	1	no	—
588	C₂×D₄	—	8	1	no	—
589	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
590	C₂×D₄	#41×C₈₉	1	2	yes	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	8	1	no	—
615	C₂²×C₄	—	8	1	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	—	8	1	no	—
618	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
623	D₈	—	2	8	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	#41×C₈₉	1	2	yes	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	8	1	no	—
651	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₄²	—	2	4	no	—
666	C₄²	C₂×D₄×C₈₉	1	2	yes	—
667	C₄²	C₂×D₄×C₈₉	1	2	yes	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
696	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	—	8	4	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	8	4	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	#120×C₈₉	1	2	yes	—
750	C₂×C₄	#120×C₈₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
753	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
754	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
755	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
756	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	4	1	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	—	8	1	no	—
786	C₂²	—	8	1	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
790	C₂²	#546×C₈₉	1	1	yes	characteristic
791	C₂²	#547×C₈₉	1	1	yes	characteristic
792	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
793	C₂²	#575×C₈₉	1	1	yes	characteristic
794	C₂²	#576×C₈₉	1	1	yes	characteristic
795	C₂²	#577×C₈₉	1	1	yes	characteristic
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	8	1	no	—
804	C₄	—	8	1	no	—
805	C₄	—	8	1	no	—
806	C₄	#525×C₈₉	1	1	yes	characteristic
807	C₄	#537×C₈₉	1	1	yes	characteristic
808	C₄	#548×C₈₉	1	1	yes	characteristic
809	C₄	#550×C₈₉	1	1	yes	characteristic
810	C₂	—	4	2	no	—
811	C₂	—	8	1	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	2	no	—
814	C₂	C₈₉×#2407	1	1	yes	characteristic
815	C₂	C₈₉×#3006	1	1	yes	characteristic
816	C₂	C₈₉×#3012	1	1	yes	characteristic
817	C₂	C₈₉×#3307	1	1	yes	characteristic
818	C₂	C₈₉×#3318	1	1	yes	characteristic
819	C₂	C₈₉×#3345	1	1	yes	characteristic
820	C₂	C₈₉×#3347	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×#553×C₈₉	C₂	semidirect
2. C₂×#478×C₈₉	C₂	semidirect
3. C₂×#442×C₈₉	C₂	semidirect
4. C₈₉×#2537	C₂	semidirect
5. C₈₉×#2034	C₂	semidirect
6. C₈₉×#2033	C₂	semidirect
7. C₈₉×#1999	C₂	semidirect
8. C₈₉×#1999	C₂	semidirect
9. C₈₉×#1992	C₂	semidirect
10. C₈₉×#1955	C₂	semidirect
11. C₈₉×#1875	C₂	semidirect
12. C₈₉×#1874	C₂	semidirect
13. C₈₉×#1854	C₂	semidirect
14. C₈₉×#1853	C₂	semidirect
15. C₈₉×#1802	C₂	semidirect
84. #125×C₈₉	D₄	semidirect
102. C₄×D₄×C₈₉	D₄	semidirect
399. #24136	C₈₉	direct (N × H)
411. C₂×#553	C₂×C₈₉	semidirect
412. C₂×#478	C₂×C₈₉	semidirect
413. C₂×#442	C₂×C₈₉	semidirect
414. #2537	C₂×C₈₉	semidirect
415. #2034	C₂×C₈₉	semidirect
416. #2033	C₂×C₈₉	semidirect
417. #1999	C₂×C₈₉	semidirect
418. #1999	C₂×C₈₉	semidirect
419. #1992	C₂×C₈₉	semidirect
420. #1955	C₂×C₈₉	semidirect
421. #1875	C₂×C₈₉	semidirect
422. #1874	C₂×C₈₉	semidirect
423. #1854	C₂×C₈₉	semidirect
424. #1853	C₂×C₈₉	semidirect
425. #1802	C₂×C₈₉	semidirect
426. C₈₉	#24136	direct (N × H)
495. #125	D₄×C₈₉	semidirect
513. C₄×D₄	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×#553×C₈₉	2
C₂×#478×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×#2537	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#1999	2
C₈₉×#1992	2
C₈₉×#1955	2
C₈₉×#1875	2
C₈₉×#1874	2
C₈₉×#1854	2
C₈₉×#1853	2
C₈₉×#1802	2
#24136	89

Subgroups — C89×#24136 #36401984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24136 #36401984