Subgroups — C₈₉×#61403 #36439251

Order 22784.

1932 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3402	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3401	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3398	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3397	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3394	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3393	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3153	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3040	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3037	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	2	yes	—
20	C₂×#137×C₈₉	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
23	#559×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#559×C₈₉	C₂²	1	2	yes	complemented
25	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	#556×C₈₉	—	2	1	no	—
27	#556×C₈₉	—	2	1	no	—
28	#556×C₈₉	—	2	2	no	—
29	#556×C₈₉	C₂²	1	2	yes	—
30	#556×C₈₉	C₂²	1	2	yes	—
31	#556×C₈₉	C₂²	1	4	yes	—
32	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#556×C₈₉	C₂²	1	2	yes	complemented
34	#553×C₈₉	—	2	1	no	—
35	#553×C₈₉	—	2	2	no	—
36	#550×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#548×C₈₉	—	2	1	no	—
38	#532×C₈₉	C₂²	1	1	yes	characteristic
39	#532×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#529×C₈₉	—	2	1	no	—
42	#529×C₈₉	—	2	2	no	—
43	C₂×#126×C₈₉	—	2	2	no	—
44	C₂×#124×C₈₉	C₂²	1	2	yes	—
45	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×#41×C₈₉	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₈₉	—	2	1	no	—
53	#497×C₈₉	C₂²	1	4	yes	—
54	#497×C₈₉	C₂²	1	4	yes	complemented
55	#496×C₈₉	C₂²	1	4	yes	—
56	#495×C₈₉	C₂²	1	4	yes	—
57	#495×C₈₉	C₂²	1	4	yes	—
58	#494×C₈₉	C₂²	1	2	yes	complemented
59	#492×C₈₉	C₂²	1	2	yes	complemented
60	#464×C₈₉	C₂²	1	4	yes	—
61	#464×C₈₉	C₂²	1	4	yes	—
62	#464×C₈₉	C₂²	1	4	yes	complemented
63	#464×C₈₉	C₂²	1	4	yes	complemented
64	#463×C₈₉	C₂²	1	4	yes	—
65	#463×C₈₉	C₂²	1	4	yes	—
66	#463×C₈₉	C₂²	1	4	yes	—
67	#462×C₈₉	C₂²	1	2	yes	complemented
68	#462×C₈₉	C₂²	1	4	yes	complemented
69	#462×C₈₉	C₂²	1	2	yes	complemented
70	#461×C₈₉	C₂²	1	2	yes	—
71	#461×C₈₉	C₂²	1	2	yes	complemented
72	#461×C₈₉	C₂²	1	2	yes	complemented
73	#460×C₈₉	C₂²	1	4	yes	complemented
74	#459×C₈₉	C₂²	1	2	yes	—
75	#446×C₈₉	C₂²	1	2	yes	complemented
76	#446×C₈₉	C₂²	1	4	yes	complemented
77	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
78	#442×C₈₉	C₂²	1	2	yes	—
79	#441×C₈₉	C₂²	1	4	yes	complemented
80	#440×C₈₉	C₂²	1	2	yes	—
81	#440×C₈₉	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
85	C₄×D₈×C₈₉	C₂²	1	2	yes	—
86	#428×C₈₉	C₂²	1	1	yes	characteristic
87	#423×C₈₉	C₂²	1	1	yes	characteristic
88	#423×C₈₉	C₂²	1	2	yes	—
89	#419×C₈₉	C₂²	1	2	yes	—
90	#418×C₈₉	C₂²	1	1	yes	characteristic
91	#417×C₈₉	C₂²	1	1	yes	characteristic
92	#417×C₈₉	C₂²	1	2	yes	—
93	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×#41×C₈₉	C₂³	1	2	yes	—
98	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₈₉	—	2	1	no	—
102	#137×C₈₉	—	2	8	no	—
103	#137×C₈₉	—	4	4	no	—
104	#137×C₈₉	—	4	4	no	—
105	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
106	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
107	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
108	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
109	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×D₈×C₈₉	C₂³	1	2	yes	—
116	C₂×D₈×C₈₉	C₂³	1	4	yes	—
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
119	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₈₉	—	2	1	no	—
121	C₄⋊Q₈×C₈₉	—	2	1	no	—
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
124	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
126	#127×C₈₉	C₂³	1	1	yes	characteristic
127	#127×C₈₉	C₂³	1	2	yes	—
128	#126×C₈₉	—	2	4	no	—
129	#126×C₈₉	—	2	4	no	—
130	#126×C₈₉	—	2	4	no	—
131	#126×C₈₉	—	2	4	no	—
132	#126×C₈₉	—	2	2	no	—
133	#126×C₈₉	—	2	2	no	—
134	#126×C₈₉	—	2	2	no	—
135	#125×C₈₉	—	2	1	no	—
136	#125×C₈₉	—	2	2	no	—
137	#124×C₈₉	—	2	1	no	—
138	#124×C₈₉	—	2	2	no	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	—	2	2	no	—
141	#124×C₈₉	C₂³	1	2	yes	—
142	#124×C₈₉	C₂³	1	4	yes	—
143	#124×C₈₉	C₂³	1	4	yes	—
144	#124×C₈₉	C₂³	1	2	yes	—
145	#124×C₈₉	C₂³	1	2	yes	—
146	#123×C₈₉	—	2	2	no	—
147	#123×C₈₉	—	2	2	no	—
148	#123×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	—	2	4	no	—
152	C₂²⋊Q₈×C₈₉	—	2	1	no	—
153	C₂²⋊Q₈×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	—	2	2	no	—
160	C₄×Q₈×C₈₉	—	2	1	no	—
161	C₄×Q₈×C₈₉	—	2	2	no	—
162	C₄×Q₈×C₈₉	—	2	2	no	—
163	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₈₉	D₄	1	2	yes	—
166	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	1	no	—
182	C₄×D₄×C₈₉	—	2	1	no	—
183	C₄×D₄×C₈₉	—	2	1	no	—
184	C₄×D₄×C₈₉	—	2	2	no	—
185	C₄×D₄×C₈₉	—	2	1	no	—
186	C₄×D₄×C₈₉	—	2	2	no	—
187	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	2	yes	—
191	C₄×D₄×C₈₉	C₂³	1	2	yes	—
192	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
193	#117×C₈₉	—	2	2	no	—
194	#117×C₈₉	—	2	2	no	—
195	#117×C₈₉	—	2	4	no	—
196	#117×C₈₉	—	2	1	no	—
197	#117×C₈₉	—	2	2	no	—
198	#117×C₈₉	—	2	1	no	—
199	#117×C₈₉	—	2	2	no	—
200	#117×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
203	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
204	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
206	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
209	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
210	C₂×C₄²×C₈₉	—	2	2	no	—
211	C₂×C₄²×C₈₉	—	2	1	no	—
212	C₂×C₄²×C₈₉	—	2	2	no	—
213	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
215	#107×C₈₉	C₂³	1	2	yes	—
216	#106×C₈₉	C₂³	1	2	yes	—
217	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
219	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
220	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
221	#103×C₈₉	C₂³	1	2	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#103×C₈₉	C₂³	1	4	yes	—
224	#103×C₈₉	C₂³	1	4	yes	—
225	#102×C₈₉	C₂³	1	2	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	#102×C₈₉	C₂³	1	2	yes	—
228	#102×C₈₉	C₂³	1	2	yes	—
229	#97×C₈₉	C₂³	1	2	yes	—
230	#97×C₈₉	C₂³	1	4	yes	—
231	C₄×C₈×C₈₉	C₂³	1	2	yes	—
232	C₄×C₈×C₈₉	C₂³	1	4	yes	—
233	C₂⁴×C₈₉	—	2	1	no	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	2	4	no	—
236	#41×C₈₉	—	2	4	no	—
237	#41×C₈₉	—	2	2	no	—
238	#41×C₈₉	—	4	4	no	—
239	C₂×Q₈×C₈₉	—	2	2	no	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	2	4	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
249	C₂×D₄×C₈₉	—	2	1	no	—
250	C₂×D₄×C₈₉	—	2	2	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	1	no	—
253	C₂×D₄×C₈₉	—	2	1	no	—
254	C₂×D₄×C₈₉	—	2	2	no	—
255	C₂×D₄×C₈₉	—	2	1	no	—
256	C₂×D₄×C₈₉	—	2	2	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₈₉	—	2	1	no	—
262	C₂²×C₄×C₈₉	—	2	2	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	2	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	1	no	—
267	C₂²×C₄×C₈₉	—	2	2	no	—
268	C₂²×C₄×C₈₉	—	2	2	no	—
269	C₂²×C₄×C₈₉	—	2	2	no	—
270	C₂²×C₄×C₈₉	—	2	1	no	—
271	C₂²×C₄×C₈₉	—	4	4	no	—
272	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₈₉	—	2	8	no	—
278	Q₁₆×C₈₉	—	4	4	no	—
279	Q₁₆×C₈₉	—	4	4	no	—
280	SD₁₆×C₈₉	—	2	4	no	—
281	SD₁₆×C₈₉	—	2	8	no	—
282	SD₁₆×C₈₉	—	4	4	no	—
283	SD₁₆×C₈₉	—	4	4	no	—
284	SD₁₆×C₈₉	—	4	4	no	—
285	D₈×C₈₉	—	2	4	no	—
286	D₈×C₈₉	—	4	4	no	—
287	M₁₆×C₈₉	—	2	4	no	—
288	M₁₆×C₈₉	—	2	2	no	—
289	M₁₆×C₈₉	#41	1	4	yes	complemented
290	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
291	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
292	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	4	no	—
296	C₄⋊C₄×C₈₉	—	2	4	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	1	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	1	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	1	no	—
304	C₄⋊C₄×C₈₉	—	2	2	no	—
305	C₄⋊C₄×C₈₉	—	2	1	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	1	no	—
308	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂²⋊C₄×C₈₉	—	2	1	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	4	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	4	no	—
324	C₂²⋊C₄×C₈₉	—	2	4	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	—	2	2	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	1	no	—
330	C₂²⋊C₄×C₈₉	—	2	2	no	—
331	C₂²⋊C₄×C₈₉	—	2	1	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	2	no	—
335	C₄²×C₈₉	—	2	1	no	—
336	C₄²×C₈₉	—	2	2	no	—
337	C₄²×C₈₉	—	2	1	no	—
338	C₄²×C₈₉	—	2	4	no	—
339	C₄²×C₈₉	—	2	4	no	—
340	C₄²×C₈₉	—	2	2	no	—
341	C₄²×C₈₉	—	2	1	no	—
342	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₈₉	C₂×D₄	1	2	yes	—
344	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₈₉	C₂×D₄	1	2	yes	—
346	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
347	C₄²×C₈₉	C₂⁴	1	2	yes	—
348	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₄²×C₈₉	C₂⁴	1	2	yes	—
350	C₂³×C₈₉	—	2	2	no	—
351	C₂³×C₈₉	—	2	1	no	—
352	C₂³×C₈₉	—	2	2	no	—
353	C₂³×C₈₉	—	4	2	no	—
354	C₂³×C₈₉	—	4	2	no	—
355	C₂³×C₈₉	—	4	2	no	—
356	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₈₉	—	2	2	no	—
358	Q₈×C₈₉	—	2	2	no	—
359	Q₈×C₈₉	—	2	1	no	—
360	Q₈×C₈₉	—	2	4	no	—
361	Q₈×C₈₉	—	2	2	no	—
362	Q₈×C₈₉	—	2	4	no	—
363	Q₈×C₈₉	—	2	2	no	—
364	Q₈×C₈₉	—	2	1	no	—
365	Q₈×C₈₉	—	4	2	no	—
366	Q₈×C₈₉	—	4	4	no	—
367	D₄×C₈₉	—	2	1	no	—
368	D₄×C₈₉	—	2	2	no	—
369	D₄×C₈₉	—	2	2	no	—
370	D₄×C₈₉	—	2	2	no	—
371	D₄×C₈₉	—	2	2	no	—
372	D₄×C₈₉	—	2	1	no	—
373	D₄×C₈₉	—	4	4	no	—
374	D₄×C₈₉	—	4	2	no	—
375	D₄×C₈₉	—	4	4	no	—
376	D₄×C₈₉	—	4	2	no	—
377	D₄×C₈₉	—	4	2	no	—
378	D₄×C₈₉	—	8	2	no	—
379	D₄×C₈₉	—	8	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	1	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	4	no	—
387	C₂×C₄×C₈₉	—	4	2	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	—	4	2	no	—
390	C₂×C₄×C₈₉	—	4	4	no	—
391	C₂×C₄×C₈₉	—	4	4	no	—
392	C₂×C₄×C₈₉	—	4	2	no	—
393	C₂×C₄×C₈₉	—	4	4	no	—
394	C₂×C₄×C₈₉	—	4	2	no	—
395	C₂×C₄×C₈₉	—	4	4	no	—
396	C₂×C₄×C₈₉	—	4	4	no	—
397	C₂×C₄×C₈₉	—	4	2	no	—
398	C₂×C₄×C₈₉	—	8	2	no	—
399	C₂×C₄×C₈₉	—	8	1	no	—
400	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
411	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
412	C₈×C₈₉	—	2	4	no	—
413	C₈×C₈₉	—	2	2	no	—
414	C₈×C₈₉	C₂×#41	1	4	yes	—
415	C₂²×C₈₉	—	2	1	no	—
416	C₂²×C₈₉	—	2	1	no	—
417	C₂²×C₈₉	—	4	1	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	—	4	2	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	2	no	—
423	C₂²×C₈₉	—	4	2	no	—
424	C₂²×C₈₉	—	4	2	no	—
425	C₂²×C₈₉	—	4	1	no	—
426	C₂²×C₈₉	—	8	4	no	—
427	C₂²×C₈₉	#550	1	2	yes	—
428	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
429	C₄×C₈₉	—	2	2	no	—
430	C₄×C₈₉	—	2	1	no	—
431	C₄×C₈₉	—	2	2	no	—
432	C₄×C₈₉	—	2	1	no	—
433	C₄×C₈₉	—	2	1	no	—
434	C₄×C₈₉	—	2	2	no	—
435	C₄×C₈₉	—	2	2	no	—
436	C₄×C₈₉	—	4	1	no	—
437	C₄×C₈₉	—	4	1	no	—
438	C₄×C₈₉	—	4	2	no	—
439	C₄×C₈₉	—	4	4	no	—
440	C₄×C₈₉	—	4	1	no	—
441	C₄×C₈₉	—	4	2	no	—
442	C₄×C₈₉	#550	1	2	yes	—
443	C₄×C₈₉	#575	1	2	yes	—
444	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
445	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	#61403	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂×C₈₉	—	2	2	no	—
448	C₂×C₈₉	—	8	1	no	—
449	C₂×C₈₉	—	8	2	no	—
450	C₂×C₈₉	—	8	2	no	—
451	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
452	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
453	C₂×C₈₉	#3586	1	1	yes	characteristic
454	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
455	C₂×#556	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#3402	C₂×C₈₉	1	4	yes	complemented
457	#3401	C₂×C₈₉	1	4	yes	complemented
458	#3398	C₂×C₈₉	1	2	yes	complemented
459	#3397	C₂×C₈₉	1	2	yes	complemented
460	#3394	C₂×C₈₉	1	2	yes	complemented
461	#3393	C₂×C₈₉	1	2	yes	complemented
462	#3153	C₂×C₈₉	1	2	yes	complemented
463	#3152	C₂×C₈₉	1	1	yes	characteristic, complemented
464	#3040	C₂×C₈₉	1	2	yes	complemented
465	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
466	#3037	C₂×C₈₉	1	2	yes	complemented
467	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
468	Q₈×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
469	C₄×#137	C₂×C₈₉	1	2	yes	complemented
470	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
471	C₈₉	#61403	1	1	yes	characteristic, direct product factor, Sylow
472	C₂×#137	C₂²×C₈₉	1	2	yes	—
473	C₂×#137	C₂²×C₈₉	1	2	yes	—
474	C₂×#137	C₂²×C₈₉	1	2	yes	—
475	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
476	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
477	#559	C₂²×C₈₉	1	1	yes	characteristic, complemented
478	#559	C₂²×C₈₉	1	2	yes	complemented
479	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
480	#556	—	2	1	no	—
481	#556	—	2	1	no	—
482	#556	—	2	2	no	—
483	#556	C₂²×C₈₉	1	2	yes	—
484	#556	C₂²×C₈₉	1	2	yes	—
485	#556	C₂²×C₈₉	1	4	yes	—
486	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
487	#556	C₂²×C₈₉	1	2	yes	complemented
488	#553	—	2	1	no	—
489	#553	—	2	2	no	—
490	#550	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#548	—	2	1	no	—
492	#532	C₂²×C₈₉	1	1	yes	characteristic
493	#532	C₂²×C₈₉	1	2	yes	—
494	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
495	#529	—	2	1	no	—
496	#529	—	2	2	no	—
497	C₂×#126	—	2	2	no	—
498	C₂×#124	C₂²×C₈₉	1	2	yes	—
499	C₂×C₂²⋊Q₈	—	2	1	no	—
500	C₄×#41	—	2	1	no	—
501	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
502	C₄×#41	C₂²×C₈₉	1	2	yes	—
503	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
504	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×#117	—	2	1	no	—
507	#497	C₂²×C₈₉	1	4	yes	—
508	#497	C₂²×C₈₉	1	4	yes	complemented
509	#496	C₂²×C₈₉	1	4	yes	—
510	#495	C₂²×C₈₉	1	4	yes	—
511	#495	C₂²×C₈₉	1	4	yes	—
512	#494	C₂²×C₈₉	1	2	yes	complemented
513	#492	C₂²×C₈₉	1	2	yes	complemented
514	#464	C₂²×C₈₉	1	4	yes	—
515	#464	C₂²×C₈₉	1	4	yes	—
516	#464	C₂²×C₈₉	1	4	yes	complemented
517	#464	C₂²×C₈₉	1	4	yes	complemented
518	#463	C₂²×C₈₉	1	4	yes	—
519	#463	C₂²×C₈₉	1	4	yes	—
520	#463	C₂²×C₈₉	1	4	yes	—
521	#462	C₂²×C₈₉	1	2	yes	complemented
522	#462	C₂²×C₈₉	1	4	yes	complemented
523	#462	C₂²×C₈₉	1	2	yes	complemented
524	#461	C₂²×C₈₉	1	2	yes	—
525	#461	C₂²×C₈₉	1	2	yes	complemented
526	#461	C₂²×C₈₉	1	2	yes	complemented
527	#460	C₂²×C₈₉	1	4	yes	complemented
528	#459	C₂²×C₈₉	1	2	yes	—
529	#446	C₂²×C₈₉	1	2	yes	complemented
530	#446	C₂²×C₈₉	1	4	yes	complemented
531	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
532	#442	C₂²×C₈₉	1	2	yes	—
533	#441	C₂²×C₈₉	1	4	yes	complemented
534	#440	C₂²×C₈₉	1	2	yes	—
535	#440	C₂²×C₈₉	1	4	yes	complemented
536	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
537	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
538	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
539	C₄×D₈	C₂²×C₈₉	1	2	yes	—
540	#428	C₂²×C₈₉	1	1	yes	characteristic
541	#423	C₂²×C₈₉	1	1	yes	characteristic
542	#423	C₂²×C₈₉	1	2	yes	—
543	#419	C₂²×C₈₉	1	2	yes	—
544	#418	C₂²×C₈₉	1	1	yes	characteristic
545	#417	C₂²×C₈₉	1	1	yes	characteristic
546	#417	C₂²×C₈₉	1	2	yes	—
547	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
548	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
549	C₂×#41	—	2	1	no	—
550	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×#41	C₂³×C₈₉	1	2	yes	—
552	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
553	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
554	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂³×C₄	—	2	1	no	—
556	#137	—	2	8	no	—
557	#137	—	4	4	no	—
558	#137	—	4	4	no	—
559	AGL(1,ℤ/8)	—	2	4	no	—
560	AGL(1,ℤ/8)	—	4	4	no	—
561	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
562	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
563	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
568	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
569	C₂×D₈	C₂³×C₈₉	1	2	yes	—
570	C₂×D₈	C₂³×C₈₉	1	4	yes	—
571	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
572	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
573	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
574	C₄⋊Q₈	—	2	1	no	—
575	C₄⋊Q₈	—	2	1	no	—
576	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
577	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
578	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
579	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
580	#127	C₂³×C₈₉	1	1	yes	characteristic
581	#127	C₂³×C₈₉	1	2	yes	—
582	#126	—	2	4	no	—
583	#126	—	2	4	no	—
584	#126	—	2	4	no	—
585	#126	—	2	4	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#125	—	2	1	no	—
590	#125	—	2	2	no	—
591	#124	—	2	1	no	—
592	#124	—	2	2	no	—
593	#124	—	2	2	no	—
594	#124	—	2	2	no	—
595	#124	C₂³×C₈₉	1	4	yes	—
596	#124	C₂³×C₈₉	1	4	yes	—
597	#124	C₂³×C₈₉	1	2	yes	—
598	#124	C₂³×C₈₉	1	2	yes	—
599	#124	C₂³×C₈₉	1	2	yes	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	4	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	2	no	—
616	C₄×Q₈	—	2	2	no	—
617	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
618	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
619	C₄×Q₈	D₄×C₈₉	1	2	yes	—
620	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
621	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
622	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
623	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
625	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
626	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
627	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	C₂³×C₈₉	1	2	yes	—
642	C₄×D₄	C₂³×C₈₉	1	2	yes	—
643	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₈₉	1	2	yes	—
645	C₄×D₄	C₂³×C₈₉	1	2	yes	—
646	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
647	#117	—	2	2	no	—
648	#117	—	2	2	no	—
649	#117	—	2	4	no	—
650	#117	—	2	1	no	—
651	#117	—	2	2	no	—
652	#117	—	2	1	no	—
653	#117	—	2	2	no	—
654	#117	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₄²	—	2	2	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	2	no	—
667	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
669	#107	C₂³×C₈₉	1	2	yes	—
670	#106	C₂³×C₈₉	1	2	yes	—
671	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
672	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
673	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
674	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
675	#103	C₂³×C₈₉	1	2	yes	—
676	#103	C₂³×C₈₉	1	4	yes	—
677	#103	C₂³×C₈₉	1	4	yes	—
678	#103	C₂³×C₈₉	1	4	yes	—
679	#102	C₂³×C₈₉	1	2	yes	—
680	#102	C₂³×C₈₉	1	4	yes	—
681	#102	C₂³×C₈₉	1	2	yes	—
682	#102	C₂³×C₈₉	1	2	yes	—
683	#97	C₂³×C₈₉	1	2	yes	—
684	#97	C₂³×C₈₉	1	4	yes	—
685	C₄×C₈	C₂³×C₈₉	1	2	yes	—
686	C₄×C₈	C₂³×C₈₉	1	4	yes	—
687	C₂⁴	—	2	1	no	—
688	#41	—	2	2	no	—
689	#41	—	2	4	no	—
690	#41	—	2	4	no	—
691	#41	—	2	2	no	—
692	#41	—	4	4	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
698	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
699	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
701	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
702	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
713	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
731	Q₁₆	—	2	8	no	—
732	Q₁₆	—	4	4	no	—
733	Q₁₆	—	4	4	no	—
734	SD₁₆	—	2	4	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	4	4	no	—
737	SD₁₆	—	4	4	no	—
738	SD₁₆	—	4	4	no	—
739	D₈	—	2	4	no	—
740	D₈	—	4	4	no	—
741	M₁₆	—	2	4	no	—
742	M₁₆	—	2	2	no	—
743	M₁₆	#41×C₈₉	1	4	yes	complemented
744	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
745	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
746	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
763	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
764	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
766	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
771	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	1	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	1	no	—
796	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
797	C₄²	C₂×D₄×C₈₉	1	2	yes	—
798	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₈₉	1	2	yes	—
800	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
801	C₄²	C₂⁴×C₈₉	1	2	yes	—
802	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
803	C₄²	C₂⁴×C₈₉	1	2	yes	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
811	Q₈	—	2	2	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	2	4	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	2	1	no	—
819	Q₈	—	4	2	no	—
820	Q₈	—	4	4	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	1	no	—
827	D₄	—	4	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	2	no	—
833	D₄	—	8	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
863	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
864	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
865	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
866	C₈	—	2	4	no	—
867	C₈	—	2	2	no	—
868	C₈	C₂×#41×C₈₉	1	4	yes	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	8	4	no	—
881	C₂²	#550×C₈₉	1	2	yes	—
882	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	4	no	—
896	C₄	#550×C₈₉	1	2	yes	—
897	C₄	#575×C₈₉	1	2	yes	—
898	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
899	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
900	C₂	—	2	2	no	—
901	C₂	—	8	2	no	—
902	C₂	—	8	1	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
905	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
906	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3480	C₂	semidirect
2. C₂×#556×C₈₉	C₂	semidirect
3. C₈₉×#3402	C₂	semidirect
4. C₈₉×#3401	C₂	semidirect
5. C₈₉×#3398	C₂	semidirect
6. C₈₉×#3397	C₂	semidirect
7. C₈₉×#3394	C₂	semidirect
8. C₈₉×#3393	C₂	semidirect
9. C₈₉×#3153	C₂	semidirect
10. C₈₉×#3152	C₂	semidirect
11. C₈₉×#3040	C₂	semidirect
12. C₈₉×#3039	C₂	semidirect
13. C₈₉×#3037	C₂	semidirect
14. C₈₉×#3036	C₂	semidirect
15. Q₈×M₁₆×C₈₉	C₂	semidirect
16. C₄×#137×C₈₉	C₂	semidirect
17. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
23. #559×C₈₉	C₂²	semidirect
24. #559×C₈₉	C₂²	semidirect
25. #557×C₈₉	C₂²	semidirect
32. #556×C₈₉	C₂²	semidirect
33. #556×C₈₉	C₂²	semidirect
36. #550×C₈₉	C₂²	semidirect
54. #497×C₈₉	C₂²	semidirect
58. #494×C₈₉	C₂²	semidirect
59. #492×C₈₉	C₂²	semidirect
62. #464×C₈₉	C₂²	semidirect
63. #464×C₈₉	C₂²	semidirect
67. #462×C₈₉	C₂²	semidirect
68. #462×C₈₉	C₂²	semidirect
69. #462×C₈₉	C₂²	semidirect
71. #461×C₈₉	C₂²	semidirect
72. #461×C₈₉	C₂²	semidirect
73. #460×C₈₉	C₂²	semidirect
75. #446×C₈₉	C₂²	semidirect
76. #446×C₈₉	C₂²	semidirect
77. C₈×Q₈×C₈₉	C₂²	semidirect
79. #441×C₈₉	C₂²	semidirect
81. #440×C₈₉	C₂²	semidirect
82. C₄×Q₁₆×C₈₉	C₂²	semidirect
84. C₄×SD₁₆×C₈₉	C₂²	semidirect
289. M₁₆×C₈₉	#41	semidirect
446. #61403	C₈₉	direct (N × H)
454. #3480	C₂×C₈₉	semidirect
455. C₂×#556	C₂×C₈₉	semidirect
456. #3402	C₂×C₈₉	semidirect
457. #3401	C₂×C₈₉	semidirect
458. #3398	C₂×C₈₉	semidirect
459. #3397	C₂×C₈₉	semidirect
460. #3394	C₂×C₈₉	semidirect
461. #3393	C₂×C₈₉	semidirect
462. #3153	C₂×C₈₉	semidirect
463. #3152	C₂×C₈₉	semidirect
464. #3040	C₂×C₈₉	semidirect
465. #3039	C₂×C₈₉	semidirect
466. #3037	C₂×C₈₉	semidirect
467. #3036	C₂×C₈₉	semidirect
468. Q₈×M₁₆	C₂×C₈₉	semidirect
469. C₄×#137	C₂×C₈₉	semidirect
470. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
471. C₈₉	#61403	direct (N × H)
477. #559	C₂²×C₈₉	semidirect
478. #559	C₂²×C₈₉	semidirect
479. #557	C₂²×C₈₉	semidirect
486. #556	C₂²×C₈₉	semidirect
487. #556	C₂²×C₈₉	semidirect
490. #550	C₂²×C₈₉	semidirect
508. #497	C₂²×C₈₉	semidirect
512. #494	C₂²×C₈₉	semidirect
513. #492	C₂²×C₈₉	semidirect
516. #464	C₂²×C₈₉	semidirect
517. #464	C₂²×C₈₉	semidirect
521. #462	C₂²×C₈₉	semidirect
522. #462	C₂²×C₈₉	semidirect
523. #462	C₂²×C₈₉	semidirect
525. #461	C₂²×C₈₉	semidirect
526. #461	C₂²×C₈₉	semidirect
527. #460	C₂²×C₈₉	semidirect
529. #446	C₂²×C₈₉	semidirect
530. #446	C₂²×C₈₉	semidirect
531. C₈×Q₈	C₂²×C₈₉	semidirect
533. #441	C₂²×C₈₉	semidirect
535. #440	C₂²×C₈₉	semidirect
536. C₄×Q₁₆	C₂²×C₈₉	semidirect
538. C₄×SD₁₆	C₂²×C₈₉	semidirect
743. M₁₆	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3480	2
C₂×#556×C₈₉	2
C₈₉×#3402	2
C₈₉×#3401	2
C₈₉×#3398	2
C₈₉×#3397	2
C₈₉×#3394	2
C₈₉×#3393	2
C₈₉×#3153	2
C₈₉×#3152	2
C₈₉×#3040	2
C₈₉×#3039	2
C₈₉×#3037	2
C₈₉×#3036	2
Q₈×M₁₆×C₈₉	2
C₄×#137×C₈₉	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#61403	89

Subgroups — C89×#61403 #36439251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61403 #36439251