Subgroups — C₈₉×#24402 #36402250

Order 22784.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#472×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#471×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3006	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1900	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	#575×C₈₉	—	2	4	no	—
19	#575×C₈₉	—	2	4	no	—
20	C₂×#137×C₈₉	—	2	1	no	—
21	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#135×C₈₉	—	2	1	no	—
29	C₂×#135×C₈₉	—	2	1	no	—
30	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
36	#472×C₈₉	—	2	4	no	—
37	#471×C₈₉	—	2	4	no	—
38	#449×C₈₉	—	2	1	no	—
39	#449×C₈₉	—	2	1	no	—
40	#449×C₈₉	—	2	1	no	—
41	#449×C₈₉	—	2	1	no	—
42	#449×C₈₉	—	2	1	no	—
43	#449×C₈₉	—	2	1	no	—
44	#448×C₈₉	—	2	1	no	—
45	#447×C₈₉	—	2	1	no	—
46	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#417×C₈₉	C₂²	1	1	yes	characteristic
49	#417×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#408×C₈₉	—	2	1	no	—
59	#408×C₈₉	—	2	1	no	—
60	#408×C₈₉	C₂²	1	1	yes	characteristic
61	#408×C₈₉	C₂²	1	1	yes	characteristic
62	#407×C₈₉	—	2	1	no	—
63	#407×C₈₉	C₂²	1	1	yes	characteristic
64	#407×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
66	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
67	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#343×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	#341×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₈₉	—	2	1	no	—
72	C₂×#41×C₈₉	—	2	1	no	—
73	C₂×#41×C₈₉	—	2	2	no	—
74	C₂×#41×C₈₉	—	2	2	no	—
75	C₂×#41×C₈₉	—	2	2	no	—
76	C₂×#41×C₈₉	—	2	2	no	—
77	C₂×#41×C₈₉	—	2	1	no	—
78	C₂×#41×C₈₉	—	2	1	no	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	4	1	no	—
82	C₂×#41×C₈₉	—	4	1	no	—
83	C₂×#41×C₈₉	—	4	1	no	—
84	C₂×#41×C₈₉	—	4	1	no	—
85	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
86	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
87	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₈₉	—	2	1	no	—
92	C₂²×D₄×C₈₉	—	2	1	no	—
93	C₂²×D₄×C₈₉	—	2	1	no	—
94	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	—	2	1	no	—
98	C₂³×C₄×C₈₉	—	2	1	no	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	#137×C₈₉	—	2	8	no	—
101	#137×C₈₉	—	2	2	no	—
102	#137×C₈₉	—	2	2	no	—
103	#137×C₈₉	—	2	2	no	—
104	#137×C₈₉	D₄	1	4	yes	complemented
105	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
106	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
107	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
108	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
109	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
110	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
111	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
112	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
113	AGL(1,ℤ/8)×C₈₉	D₄	1	4	yes	complemented
114	#135×C₈₉	—	2	8	no	—
115	#135×C₈₉	—	2	8	no	—
116	C₂×Q₁₆×C₈₉	—	2	1	no	—
117	C₂×Q₁₆×C₈₉	—	2	1	no	—
118	C₂×SD₁₆×C₈₉	—	2	1	no	—
119	C₂×SD₁₆×C₈₉	—	2	1	no	—
120	C₂×SD₁₆×C₈₉	—	2	1	no	—
121	C₂×SD₁₆×C₈₉	—	2	1	no	—
122	C₂×SD₁₆×C₈₉	—	2	1	no	—
123	C₂×SD₁₆×C₈₉	—	2	1	no	—
124	C₂×SD₁₆×C₈₉	—	2	2	no	—
125	C₂×SD₁₆×C₈₉	—	2	1	no	—
126	C₂×SD₁₆×C₈₉	—	2	1	no	—
127	C₂×SD₁₆×C₈₉	—	4	1	no	—
128	C₂×D₈×C₈₉	—	2	1	no	—
129	C₂×D₈×C₈₉	—	2	1	no	—
130	C₂×D₈×C₈₉	—	2	1	no	—
131	C₂×D₈×C₈₉	—	2	1	no	—
132	C₂×D₈×C₈₉	—	2	2	no	—
133	C₂×D₈×C₈₉	—	2	1	no	—
134	C₂×D₈×C₈₉	—	2	1	no	—
135	C₂×D₈×C₈₉	—	4	1	no	—
136	#131×C₈₉	—	2	2	no	—
137	#131×C₈₉	—	2	2	no	—
138	#131×C₈₉	—	4	1	no	—
139	#131×C₈₉	—	4	1	no	—
140	C₂×M₁₆×C₈₉	—	2	1	no	—
141	C₂×M₁₆×C₈₉	—	2	2	no	—
142	C₂×M₁₆×C₈₉	—	2	2	no	—
143	C₂×M₁₆×C₈₉	—	2	1	no	—
144	C₂×M₁₆×C₈₉	—	2	1	no	—
145	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₈₉	—	2	1	no	—
152	C₂²×C₈×C₈₉	—	2	1	no	—
153	C₂²×C₈×C₈₉	—	2	1	no	—
154	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	—	2	1	no	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
162	#108×C₈₉	—	2	2	no	—
163	#108×C₈₉	—	2	2	no	—
164	#103×C₈₉	—	2	1	no	—
165	#103×C₈₉	—	2	1	no	—
166	#103×C₈₉	—	2	1	no	—
167	#103×C₈₉	—	2	1	no	—
168	#102×C₈₉	—	2	1	no	—
169	#102×C₈₉	—	2	1	no	—
170	#102×C₈₉	—	2	1	no	—
171	#102×C₈₉	—	2	1	no	—
172	#101×C₈₉	—	2	2	no	—
173	#101×C₈₉	—	4	1	no	—
174	#100×C₈₉	—	2	2	no	—
175	#100×C₈₉	—	2	2	no	—
176	#100×C₈₉	—	2	2	no	—
177	#100×C₈₉	—	4	1	no	—
178	C₂²⋊C₈×C₈₉	—	2	1	no	—
179	C₂²⋊C₈×C₈₉	—	2	1	no	—
180	C₂²⋊C₈×C₈₉	—	2	1	no	—
181	C₂²⋊C₈×C₈₉	—	2	1	no	—
182	C₂²⋊C₈×C₈₉	—	2	1	no	—
183	C₂²⋊C₈×C₈₉	—	2	1	no	—
184	C₂²⋊C₈×C₈₉	—	2	1	no	—
185	C₂²⋊C₈×C₈₉	—	2	1	no	—
186	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
187	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
188	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
189	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
190	C₂⁴×C₈₉	—	2	1	no	—
191	C₂⁴×C₈₉	—	2	1	no	—
192	C₂⁴×C₈₉	—	2	1	no	—
193	C₂⁴×C₈₉	#41	1	1	yes	characteristic
194	#41×C₈₉	—	2	1	no	—
195	#41×C₈₉	—	2	1	no	—
196	#41×C₈₉	—	2	4	no	—
197	#41×C₈₉	—	2	4	no	—
198	#41×C₈₉	—	2	2	no	—
199	#41×C₈₉	—	2	2	no	—
200	#41×C₈₉	—	2	1	no	—
201	#41×C₈₉	—	2	1	no	—
202	#41×C₈₉	—	2	1	no	—
203	#41×C₈₉	—	2	1	no	—
204	#41×C₈₉	—	4	2	no	—
205	#41×C₈₉	—	4	2	no	—
206	#41×C₈₉	—	4	1	no	—
207	#41×C₈₉	—	4	1	no	—
208	#41×C₈₉	—	4	2	no	—
209	#41×C₈₉	—	4	2	no	—
210	#41×C₈₉	—	4	2	no	—
211	#41×C₈₉	—	4	2	no	—
212	#41×C₈₉	—	4	2	no	—
213	#41×C₈₉	—	4	2	no	—
214	#41×C₈₉	—	4	2	no	—
215	#41×C₈₉	—	4	2	no	—
216	#41×C₈₉	C₂×D₄	1	2	yes	—
217	#41×C₈₉	C₂×D₄	1	2	yes	—
218	C₂×Q₈×C₈₉	—	2	1	no	—
219	C₂×Q₈×C₈₉	—	2	1	no	—
220	C₂×Q₈×C₈₉	—	2	2	no	—
221	C₂×Q₈×C₈₉	—	2	1	no	—
222	C₂×Q₈×C₈₉	—	2	1	no	—
223	C₂×Q₈×C₈₉	—	2	1	no	—
224	C₂×Q₈×C₈₉	—	2	1	no	—
225	C₂×Q₈×C₈₉	—	4	1	no	—
226	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂×D₄×C₈₉	—	2	1	no	—
230	C₂×D₄×C₈₉	—	2	2	no	—
231	C₂×D₄×C₈₉	—	2	1	no	—
232	C₂×D₄×C₈₉	—	2	1	no	—
233	C₂×D₄×C₈₉	—	2	1	no	—
234	C₂×D₄×C₈₉	—	2	1	no	—
235	C₂×D₄×C₈₉	—	2	1	no	—
236	C₂×D₄×C₈₉	—	2	1	no	—
237	C₂×D₄×C₈₉	—	2	1	no	—
238	C₂×D₄×C₈₉	—	2	1	no	—
239	C₂×D₄×C₈₉	—	2	1	no	—
240	C₂×D₄×C₈₉	—	2	1	no	—
241	C₂×D₄×C₈₉	—	2	1	no	—
242	C₂×D₄×C₈₉	—	2	1	no	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	—	2	1	no	—
245	C₂×D₄×C₈₉	—	2	1	no	—
246	C₂×D₄×C₈₉	—	4	1	no	—
247	C₂×D₄×C₈₉	—	4	2	no	—
248	C₂×D₄×C₈₉	—	4	2	no	—
249	C₂×D₄×C₈₉	—	4	2	no	—
250	C₂×D₄×C₈₉	—	4	2	no	—
251	C₂×D₄×C₈₉	—	4	1	no	—
252	C₂×D₄×C₈₉	—	4	1	no	—
253	C₂×D₄×C₈₉	—	4	1	no	—
254	C₂×D₄×C₈₉	—	4	1	no	—
255	C₂×D₄×C₈₉	—	8	2	no	—
256	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	—	2	1	no	—
260	C₂²×C₄×C₈₉	—	2	1	no	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	1	no	—
266	C₂²×C₄×C₈₉	—	2	1	no	—
267	C₂²×C₄×C₈₉	—	2	1	no	—
268	C₂²×C₄×C₈₉	—	2	1	no	—
269	C₂²×C₄×C₈₉	—	2	1	no	—
270	C₂²×C₄×C₈₉	—	4	2	no	—
271	C₂²×C₄×C₈₉	—	4	2	no	—
272	C₂²×C₄×C₈₉	—	4	2	no	—
273	C₂²×C₄×C₈₉	—	4	2	no	—
274	C₂²×C₄×C₈₉	—	4	1	no	—
275	C₂²×C₄×C₈₉	—	4	1	no	—
276	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
281	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	Q₁₆×C₈₉	—	2	4	no	—
283	Q₁₆×C₈₉	—	2	4	no	—
284	SD₁₆×C₈₉	—	2	4	no	—
285	SD₁₆×C₈₉	—	2	4	no	—
286	SD₁₆×C₈₉	—	2	4	no	—
287	SD₁₆×C₈₉	—	2	4	no	—
288	SD₁₆×C₈₉	—	4	2	no	—
289	SD₁₆×C₈₉	—	4	2	no	—
290	SD₁₆×C₈₉	—	4	2	no	—
291	SD₁₆×C₈₉	—	4	2	no	—
292	D₈×C₈₉	—	2	4	no	—
293	D₈×C₈₉	—	2	4	no	—
294	D₈×C₈₉	—	4	2	no	—
295	D₈×C₈₉	—	4	2	no	—
296	D₈×C₈₉	—	4	2	no	—
297	D₈×C₈₉	—	4	2	no	—
298	M₁₆×C₈₉	—	2	4	no	—
299	M₁₆×C₈₉	—	2	1	no	—
300	M₁₆×C₈₉	—	2	1	no	—
301	M₁₆×C₈₉	—	2	1	no	—
302	M₁₆×C₈₉	—	2	1	no	—
303	M₁₆×C₈₉	—	2	1	no	—
304	M₁₆×C₈₉	—	2	1	no	—
305	M₁₆×C₈₉	—	2	1	no	—
306	M₁₆×C₈₉	—	2	1	no	—
307	M₁₆×C₈₉	—	2	1	no	—
308	M₁₆×C₈₉	—	2	1	no	—
309	M₁₆×C₈₉	—	4	2	no	—
310	M₁₆×C₈₉	—	4	2	no	—
311	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
312	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
313	C₂×C₈×C₈₉	—	2	4	no	—
314	C₂×C₈×C₈₉	—	2	1	no	—
315	C₂×C₈×C₈₉	—	2	1	no	—
316	C₂×C₈×C₈₉	—	2	1	no	—
317	C₂×C₈×C₈₉	—	2	1	no	—
318	C₂×C₈×C₈₉	—	2	1	no	—
319	C₂×C₈×C₈₉	—	2	1	no	—
320	C₂×C₈×C₈₉	—	2	1	no	—
321	C₂×C₈×C₈₉	—	2	1	no	—
322	C₂×C₈×C₈₉	—	2	1	no	—
323	C₂×C₈×C₈₉	—	2	1	no	—
324	C₂×C₈×C₈₉	—	4	2	no	—
325	C₂×C₈×C₈₉	—	4	2	no	—
326	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
328	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	—	2	1	no	—
331	C₄⋊C₄×C₈₉	—	2	1	no	—
332	C₂²⋊C₄×C₈₉	—	4	1	no	—
333	C₂²⋊C₄×C₈₉	—	4	1	no	—
334	C₂³×C₈₉	—	2	1	no	—
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	1	no	—
337	C₂³×C₈₉	—	2	1	no	—
338	C₂³×C₈₉	—	2	2	no	—
339	C₂³×C₈₉	—	4	1	no	—
340	C₂³×C₈₉	—	4	1	no	—
341	C₂³×C₈₉	—	4	2	no	—
342	C₂³×C₈₉	—	4	2	no	—
343	C₂³×C₈₉	—	4	1	no	—
344	C₂³×C₈₉	—	4	1	no	—
345	C₂³×C₈₉	—	4	1	no	—
346	C₂³×C₈₉	—	4	1	no	—
347	C₂³×C₈₉	—	4	1	no	—
348	C₂³×C₈₉	—	8	1	no	—
349	C₂³×C₈₉	—	8	1	no	—
350	C₂³×C₈₉	—	8	1	no	—
351	C₂³×C₈₉	—	8	1	no	—
352	C₂³×C₈₉	—	8	1	no	—
353	C₂³×C₈₉	#121	1	1	yes	characteristic
354	C₂³×C₈₉	#121	1	1	yes	characteristic
355	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
356	Q₈×C₈₉	—	2	1	no	—
357	Q₈×C₈₉	—	2	1	no	—
358	Q₈×C₈₉	—	2	2	no	—
359	Q₈×C₈₉	—	2	1	no	—
360	Q₈×C₈₉	—	2	2	no	—
361	Q₈×C₈₉	—	4	2	no	—
362	Q₈×C₈₉	—	4	1	no	—
363	Q₈×C₈₉	—	4	1	no	—
364	Q₈×C₈₉	#120	1	2	yes	—
365	D₄×C₈₉	—	2	2	no	—
366	D₄×C₈₉	—	2	2	no	—
367	D₄×C₈₉	—	2	1	no	—
368	D₄×C₈₉	—	2	2	no	—
369	D₄×C₈₉	—	2	1	no	—
370	D₄×C₈₉	—	2	1	no	—
371	D₄×C₈₉	—	2	2	no	—
372	D₄×C₈₉	—	4	2	no	—
373	D₄×C₈₉	—	4	2	no	—
374	D₄×C₈₉	—	4	2	no	—
375	D₄×C₈₉	—	4	4	no	—
376	D₄×C₈₉	—	4	4	no	—
377	D₄×C₈₉	—	4	1	no	—
378	D₄×C₈₉	—	4	1	no	—
379	D₄×C₈₉	—	4	1	no	—
380	D₄×C₈₉	—	4	1	no	—
381	D₄×C₈₉	—	4	1	no	—
382	D₄×C₈₉	—	4	1	no	—
383	D₄×C₈₉	—	4	1	no	—
384	D₄×C₈₉	—	4	1	no	—
385	D₄×C₈₉	—	8	2	no	—
386	D₄×C₈₉	—	8	2	no	—
387	D₄×C₈₉	#120	1	2	yes	—
388	C₂×C₄×C₈₉	—	2	1	no	—
389	C₂×C₄×C₈₉	—	2	1	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	1	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	4	2	no	—
404	C₂×C₄×C₈₉	—	4	2	no	—
405	C₂×C₄×C₈₉	—	4	2	no	—
406	C₂×C₄×C₈₉	—	4	4	no	—
407	C₂×C₄×C₈₉	—	4	4	no	—
408	C₂×C₄×C₈₉	—	4	1	no	—
409	C₂×C₄×C₈₉	—	4	1	no	—
410	C₂×C₄×C₈₉	—	4	1	no	—
411	C₂×C₄×C₈₉	—	4	1	no	—
412	C₂×C₄×C₈₉	—	4	1	no	—
413	C₂×C₄×C₈₉	—	8	1	no	—
414	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
415	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
416	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
421	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
422	C₈×C₈₉	—	2	2	no	—
423	C₈×C₈₉	—	2	2	no	—
424	C₈×C₈₉	—	2	1	no	—
425	C₈×C₈₉	—	2	1	no	—
426	C₈×C₈₉	—	2	1	no	—
427	C₈×C₈₉	—	2	1	no	—
428	C₈×C₈₉	—	4	1	no	—
429	C₈×C₈₉	—	4	1	no	—
430	C₈×C₈₉	—	4	1	no	—
431	C₈×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	2	1	no	—
433	C₂²×C₈₉	—	2	1	no	—
434	C₂²×C₈₉	—	2	1	no	—
435	C₂²×C₈₉	—	2	1	no	—
436	C₂²×C₈₉	—	2	2	no	—
437	C₂²×C₈₉	—	2	1	no	—
438	C₂²×C₈₉	—	2	1	no	—
439	C₂²×C₈₉	—	2	1	no	—
440	C₂²×C₈₉	—	2	1	no	—
441	C₂²×C₈₉	—	4	1	no	—
442	C₂²×C₈₉	—	4	1	no	—
443	C₂²×C₈₉	—	4	1	no	—
444	C₂²×C₈₉	—	4	2	no	—
445	C₂²×C₈₉	—	4	1	no	—
446	C₂²×C₈₉	—	4	1	no	—
447	C₂²×C₈₉	—	8	1	no	—
448	C₂²×C₈₉	—	8	1	no	—
449	C₂²×C₈₉	—	8	2	no	—
450	C₂²×C₈₉	—	8	2	no	—
451	C₂²×C₈₉	—	8	4	no	—
452	C₂²×C₈₉	—	8	1	no	—
453	C₂²×C₈₉	—	8	1	no	—
454	C₂²×C₈₉	—	8	1	no	—
455	C₂²×C₈₉	—	8	1	no	—
456	C₂²×C₈₉	—	8	1	no	—
457	C₂²×C₈₉	—	16	1	no	—
458	C₂²×C₈₉	—	16	1	no	—
459	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
460	C₂²×C₈₉	#546	1	1	yes	characteristic
461	C₂²×C₈₉	#546	1	1	yes	characteristic
462	C₄×C₈₉	—	2	1	no	—
463	C₄×C₈₉	—	2	1	no	—
464	C₄×C₈₉	—	2	2	no	—
465	C₄×C₈₉	—	4	1	no	—
466	C₄×C₈₉	—	4	2	no	—
467	C₄×C₈₉	—	8	1	no	—
468	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
469	C₄×C₈₉	#534	1	1	yes	characteristic
470	C₄×C₈₉	D₄²	1	1	yes	characteristic
471	C₄×C₈₉	D₄²	1	1	yes	characteristic
472	#24402	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
473	C₂×C₈₉	—	2	1	no	—
474	C₂×C₈₉	—	2	1	no	—
475	C₂×C₈₉	—	4	1	no	—
476	C₂×C₈₉	—	4	1	no	—
477	C₂×C₈₉	—	4	2	no	—
478	C₂×C₈₉	—	8	1	no	—
479	C₂×C₈₉	—	8	2	no	—
480	C₂×C₈₉	—	16	1	no	—
481	C₂×C₈₉	#2410	1	1	yes	characteristic
482	C₂×C₈₉	#3067	1	1	yes	characteristic
483	C₂×C₈₉	#3068	1	1	yes	characteristic
484	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
485	C₂×#472	C₂×C₈₉	1	1	yes	characteristic, complemented
486	C₂×#471	C₂×C₈₉	1	1	yes	characteristic, complemented
487	#3006	C₂×C₈₉	1	1	yes	characteristic, complemented
488	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
489	#2880	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#2052	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#2051	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
493	#2018	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#1908	C₂×C₈₉	1	1	yes	characteristic, complemented
495	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
496	#1900	C₂×C₈₉	1	1	yes	characteristic, complemented
497	#1855	C₂×C₈₉	1	1	yes	characteristic, complemented
498	#1785	C₂×C₈₉	1	1	yes	characteristic, complemented
499	C₈₉	#24402	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
501	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
502	#575	—	2	4	no	—
503	#575	—	2	4	no	—
504	C₂×#137	—	2	1	no	—
505	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×AGL(1,ℤ/8)	—	2	1	no	—
508	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×#135	—	2	1	no	—
513	C₂×#135	—	2	1	no	—
514	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
515	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
516	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
517	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
518	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
519	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
520	#472	—	2	4	no	—
521	#471	—	2	4	no	—
522	#449	—	2	1	no	—
523	#449	—	2	1	no	—
524	#449	—	2	1	no	—
525	#449	—	2	1	no	—
526	#449	—	2	1	no	—
527	#449	—	2	1	no	—
528	#448	—	2	1	no	—
529	#447	—	2	1	no	—
530	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
531	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic, complemented
532	#417	C₂²×C₈₉	1	1	yes	characteristic
533	#417	C₂²×C₈₉	1	1	yes	characteristic
534	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
535	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
537	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
539	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
540	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic, complemented
542	#408	—	2	1	no	—
543	#408	—	2	1	no	—
544	#408	C₂²×C₈₉	1	1	yes	characteristic
545	#408	C₂²×C₈₉	1	1	yes	characteristic
546	#407	—	2	1	no	—
547	#407	C₂²×C₈₉	1	1	yes	characteristic
548	#407	C₂²×C₈₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₈	—	2	1	no	—
550	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
551	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
552	#343	C₂²×C₈₉	1	1	yes	characteristic, complemented
553	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
554	#341	C₂²×C₈₉	1	1	yes	characteristic, complemented
555	C₂×#41	—	2	1	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	2	1	no	—
562	C₂×#41	—	2	1	no	—
563	C₂×#41	—	2	1	no	—
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	4	1	no	—
566	C₂×#41	—	4	1	no	—
567	C₂×#41	—	4	1	no	—
568	C₂×#41	—	4	1	no	—
569	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
570	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
571	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
573	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
581	C₂³×C₄	—	2	1	no	—
582	C₂³×C₄	—	2	1	no	—
583	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
584	#137	—	2	8	no	—
585	#137	—	2	2	no	—
586	#137	—	2	2	no	—
587	#137	—	2	2	no	—
588	#137	D₄×C₈₉	1	4	yes	complemented
589	AGL(1,ℤ/8)	—	2	8	no	—
590	AGL(1,ℤ/8)	—	2	2	no	—
591	AGL(1,ℤ/8)	—	2	2	no	—
592	AGL(1,ℤ/8)	—	2	2	no	—
593	AGL(1,ℤ/8)	—	2	2	no	—
594	AGL(1,ℤ/8)	—	2	2	no	—
595	AGL(1,ℤ/8)	—	4	1	no	—
596	AGL(1,ℤ/8)	—	4	1	no	—
597	AGL(1,ℤ/8)	D₄×C₈₉	1	4	yes	complemented
598	#135	—	2	8	no	—
599	#135	—	2	8	no	—
600	C₂×Q₁₆	—	2	1	no	—
601	C₂×Q₁₆	—	2	1	no	—
602	C₂×SD₁₆	—	2	1	no	—
603	C₂×SD₁₆	—	2	1	no	—
604	C₂×SD₁₆	—	2	1	no	—
605	C₂×SD₁₆	—	2	1	no	—
606	C₂×SD₁₆	—	2	2	no	—
607	C₂×SD₁₆	—	2	1	no	—
608	C₂×SD₁₆	—	2	1	no	—
609	C₂×SD₁₆	—	2	1	no	—
610	C₂×SD₁₆	—	2	1	no	—
611	C₂×SD₁₆	—	4	1	no	—
612	C₂×D₈	—	2	1	no	—
613	C₂×D₈	—	2	1	no	—
614	C₂×D₈	—	2	2	no	—
615	C₂×D₈	—	2	1	no	—
616	C₂×D₈	—	2	1	no	—
617	C₂×D₈	—	2	1	no	—
618	C₂×D₈	—	2	1	no	—
619	C₂×D₈	—	4	1	no	—
620	#131	—	2	2	no	—
621	#131	—	2	2	no	—
622	#131	—	4	1	no	—
623	#131	—	4	1	no	—
624	C₂×M₁₆	—	2	1	no	—
625	C₂×M₁₆	—	2	2	no	—
626	C₂×M₁₆	—	2	2	no	—
627	C₂×M₁₆	—	2	1	no	—
628	C₂×M₁₆	—	2	1	no	—
629	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
631	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
634	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
635	C₂²×C₈	—	2	1	no	—
636	C₂²×C₈	—	2	1	no	—
637	C₂²×C₈	—	2	1	no	—
638	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
640	#121	—	2	1	no	—
641	#121	—	2	1	no	—
642	#121	—	2	1	no	—
643	#121	—	2	1	no	—
644	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	#108	—	2	2	no	—
647	#108	—	2	2	no	—
648	#103	—	2	1	no	—
649	#103	—	2	1	no	—
650	#103	—	2	1	no	—
651	#103	—	2	1	no	—
652	#102	—	2	1	no	—
653	#102	—	2	1	no	—
654	#102	—	2	1	no	—
655	#102	—	2	1	no	—
656	#101	—	2	2	no	—
657	#101	—	4	1	no	—
658	#100	—	2	2	no	—
659	#100	—	2	2	no	—
660	#100	—	2	2	no	—
661	#100	—	4	1	no	—
662	C₂²⋊C₈	—	2	1	no	—
663	C₂²⋊C₈	—	2	1	no	—
664	C₂²⋊C₈	—	2	1	no	—
665	C₂²⋊C₈	—	2	1	no	—
666	C₂²⋊C₈	—	2	1	no	—
667	C₂²⋊C₈	—	2	1	no	—
668	C₂²⋊C₈	—	2	1	no	—
669	C₂²⋊C₈	—	2	1	no	—
670	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
671	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
672	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
673	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
674	C₂⁴	—	2	1	no	—
675	C₂⁴	—	2	1	no	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	#41×C₈₉	1	1	yes	characteristic
678	#41	—	2	1	no	—
679	#41	—	2	1	no	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	2	no	—
683	#41	—	2	2	no	—
684	#41	—	2	1	no	—
685	#41	—	2	1	no	—
686	#41	—	2	1	no	—
687	#41	—	2	1	no	—
688	#41	—	4	2	no	—
689	#41	—	4	2	no	—
690	#41	—	4	1	no	—
691	#41	—	4	1	no	—
692	#41	—	4	2	no	—
693	#41	—	4	2	no	—
694	#41	—	4	2	no	—
695	#41	—	4	2	no	—
696	#41	—	4	2	no	—
697	#41	—	4	2	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	C₂×D₄×C₈₉	1	2	yes	—
701	#41	C₂×D₄×C₈₉	1	2	yes	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	4	1	no	—
710	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
711	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	1	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	8	2	no	—
740	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
741	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
742	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
766	Q₁₆	—	2	4	no	—
767	Q₁₆	—	2	4	no	—
768	SD₁₆	—	2	4	no	—
769	SD₁₆	—	2	4	no	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	2	4	no	—
772	SD₁₆	—	4	2	no	—
773	SD₁₆	—	4	2	no	—
774	SD₁₆	—	4	2	no	—
775	SD₁₆	—	4	2	no	—
776	D₈	—	2	4	no	—
777	D₈	—	2	4	no	—
778	D₈	—	4	2	no	—
779	D₈	—	4	2	no	—
780	D₈	—	4	2	no	—
781	D₈	—	4	2	no	—
782	M₁₆	—	2	4	no	—
783	M₁₆	—	2	1	no	—
784	M₁₆	—	2	1	no	—
785	M₁₆	—	2	1	no	—
786	M₁₆	—	2	1	no	—
787	M₁₆	—	2	1	no	—
788	M₁₆	—	2	1	no	—
789	M₁₆	—	2	1	no	—
790	M₁₆	—	2	1	no	—
791	M₁₆	—	2	1	no	—
792	M₁₆	—	2	1	no	—
793	M₁₆	—	4	2	no	—
794	M₁₆	—	4	2	no	—
795	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
796	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
797	C₂×C₈	—	2	4	no	—
798	C₂×C₈	—	2	1	no	—
799	C₂×C₈	—	2	1	no	—
800	C₂×C₈	—	2	1	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	2	1	no	—
806	C₂×C₈	—	2	1	no	—
807	C₂×C₈	—	2	1	no	—
808	C₂×C₈	—	4	2	no	—
809	C₂×C₈	—	4	2	no	—
810	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
811	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
812	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
813	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	4	1	no	—
817	C₂²⋊C₄	—	4	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	1	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	8	1	no	—
833	C₂³	—	8	1	no	—
834	C₂³	—	8	1	no	—
835	C₂³	—	8	1	no	—
836	C₂³	—	8	1	no	—
837	C₂³	#121×C₈₉	1	1	yes	characteristic
838	C₂³	#121×C₈₉	1	1	yes	characteristic
839	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
840	Q₈	—	2	1	no	—
841	Q₈	—	2	1	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	1	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	4	1	no	—
847	Q₈	—	4	1	no	—
848	Q₈	#120×C₈₉	1	2	yes	—
849	D₄	—	2	2	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	1	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	1	no	—
854	D₄	—	2	1	no	—
855	D₄	—	2	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	1	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	1	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	#120×C₈₉	1	2	yes	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
899	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
904	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
905	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	1	no	—
909	C₈	—	2	1	no	—
910	C₈	—	2	1	no	—
911	C₈	—	2	1	no	—
912	C₈	—	4	1	no	—
913	C₈	—	4	1	no	—
914	C₈	—	4	1	no	—
915	C₈	—	4	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	—	8	2	no	—
934	C₂²	—	8	2	no	—
935	C₂²	—	8	4	no	—
936	C₂²	—	8	1	no	—
937	C₂²	—	8	1	no	—
938	C₂²	—	8	1	no	—
939	C₂²	—	8	1	no	—
940	C₂²	—	8	1	no	—
941	C₂²	—	16	1	no	—
942	C₂²	—	16	1	no	—
943	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
944	C₂²	#546×C₈₉	1	1	yes	characteristic
945	C₂²	#546×C₈₉	1	1	yes	characteristic
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	8	1	no	—
952	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
953	C₄	#534×C₈₉	1	1	yes	characteristic
954	C₄	D₄²×C₈₉	1	1	yes	characteristic
955	C₄	D₄²×C₈₉	1	1	yes	characteristic
956	C₂	—	2	1	no	—
957	C₂	—	2	1	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	2	no	—
961	C₂	—	8	1	no	—
962	C₂	—	8	2	no	—
963	C₂	—	16	1	no	—
964	C₂	C₈₉×#2410	1	1	yes	characteristic
965	C₂	C₈₉×#3067	1	1	yes	characteristic
966	C₂	C₈₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₈₉	C₂	semidirect
2. C₂×#472×C₈₉	C₂	semidirect
3. C₂×#471×C₈₉	C₂	semidirect
4. C₈₉×#3006	C₂	semidirect
5. C₂×#449×C₈₉	C₂	semidirect
6. C₈₉×#2880	C₂	semidirect
7. C₈₉×#2052	C₂	semidirect
8. C₈₉×#2051	C₂	semidirect
9. C₈₉×#2019	C₂	semidirect
10. C₈₉×#2018	C₂	semidirect
11. C₈₉×#1908	C₂	semidirect
12. C₈₉×#1907	C₂	semidirect
13. C₈₉×#1900	C₂	semidirect
14. C₈₉×#1855	C₂	semidirect
15. C₈₉×#1785	C₂	semidirect
30. C₂²×SD₁₆×C₈₉	C₂²	semidirect
31. C₂²×D₈×C₈₉	C₂²	semidirect
46. C₂×#108×C₈₉	C₂²	semidirect
47. C₂×#108×C₈₉	C₂²	semidirect
50. C₂×#103×C₈₉	C₂²	semidirect
51. C₂×#102×C₈₉	C₂²	semidirect
52. C₂×#101×C₈₉	C₂²	semidirect
53. C₂×#101×C₈₉	C₂²	semidirect
54. C₂×#100×C₈₉	C₂²	semidirect
55. C₂×#100×C₈₉	C₂²	semidirect
56. C₂×#100×C₈₉	C₂²	semidirect
57. C₂×#100×C₈₉	C₂²	semidirect
67. #343×C₈₉	C₂²	semidirect
68. #343×C₈₉	C₂²	semidirect
69. #341×C₈₉	C₂²	semidirect
70. #341×C₈₉	C₂²	semidirect
104. #137×C₈₉	D₄	semidirect
113. AGL(1,ℤ/8)×C₈₉	D₄	semidirect
472. #24402	C₈₉	direct (N × H)
484. C₂×#575	C₂×C₈₉	semidirect
485. C₂×#472	C₂×C₈₉	semidirect
486. C₂×#471	C₂×C₈₉	semidirect
487. #3006	C₂×C₈₉	semidirect
488. C₂×#449	C₂×C₈₉	semidirect
489. #2880	C₂×C₈₉	semidirect
490. #2052	C₂×C₈₉	semidirect
491. #2051	C₂×C₈₉	semidirect
492. #2019	C₂×C₈₉	semidirect
493. #2018	C₂×C₈₉	semidirect
494. #1908	C₂×C₈₉	semidirect
495. #1907	C₂×C₈₉	semidirect
496. #1900	C₂×C₈₉	semidirect
497. #1855	C₂×C₈₉	semidirect
498. #1785	C₂×C₈₉	semidirect
499. C₈₉	#24402	direct (N × H)
514. C₂²×SD₁₆	C₂²×C₈₉	semidirect
515. C₂²×D₈	C₂²×C₈₉	semidirect
530. C₂×#108	C₂²×C₈₉	semidirect
531. C₂×#108	C₂²×C₈₉	semidirect
534. C₂×#103	C₂²×C₈₉	semidirect
535. C₂×#102	C₂²×C₈₉	semidirect
536. C₂×#101	C₂²×C₈₉	semidirect
537. C₂×#101	C₂²×C₈₉	semidirect
538. C₂×#100	C₂²×C₈₉	semidirect
539. C₂×#100	C₂²×C₈₉	semidirect
540. C₂×#100	C₂²×C₈₉	semidirect
541. C₂×#100	C₂²×C₈₉	semidirect
551. #343	C₂²×C₈₉	semidirect
552. #343	C₂²×C₈₉	semidirect
553. #341	C₂²×C₈₉	semidirect
554. #341	C₂²×C₈₉	semidirect
588. #137	D₄×C₈₉	semidirect
597. AGL(1,ℤ/8)	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×#575×C₈₉	2
C₂×#472×C₈₉	2
C₂×#471×C₈₉	2
C₈₉×#3006	2
C₂×#449×C₈₉	2
C₈₉×#2880	2
C₈₉×#2052	2
C₈₉×#2051	2
C₈₉×#2019	2
C₈₉×#2018	2
C₈₉×#1908	2
C₈₉×#1907	2
C₈₉×#1900	2
C₈₉×#1855	2
C₈₉×#1785	2
#24402	89

Subgroups — C89×#24402 #36402250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24402 #36402250