Subgroups — C₈₉×#61493 #36439341

Order 22784.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3348	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3303	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3296	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3267	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3178	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3125	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3123	C₂	1	2	yes	maximal, complemented
19	C₈₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
25	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
26	#559×C₈₉	C₂²	1	1	yes	characteristic
27	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	#556×C₈₉	C₂²	1	1	yes	characteristic
29	#555×C₈₉	C₂²	1	2	yes	—
30	#554×C₈₉	C₂²	1	1	yes	characteristic
31	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	#553×C₈₉	—	2	1	no	—
33	#552×C₈₉	—	2	2	no	—
34	#552×C₈₉	—	2	1	no	—
35	#552×C₈₉	C₂²	1	2	yes	complemented
36	#551×C₈₉	—	2	2	no	—
37	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	#548×C₈₉	—	2	1	no	—
39	#547×C₈₉	C₂²	1	1	yes	characteristic
40	#547×C₈₉	C₂²	1	2	yes	complemented
41	#546×C₈₉	—	2	1	no	—
42	#546×C₈₉	C₂²	1	2	yes	—
43	D₄²×C₈₉	C₂²	1	1	yes	characteristic
44	#542×C₈₉	C₂²	1	2	yes	—
45	#541×C₈₉	C₂²	1	2	yes	complemented
46	#539×C₈₉	—	2	2	no	—
47	#538×C₈₉	—	2	2	no	—
48	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#532×C₈₉	C₂²	1	1	yes	characteristic
50	#529×C₈₉	—	2	1	no	—
51	#529×C₈₉	—	2	1	no	—
52	#529×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#125×C₈₉	—	2	1	no	—
54	C₂×#124×C₈₉	—	2	1	no	—
55	#520×C₈₉	C₂²	1	2	yes	complemented
56	#518×C₈₉	C₂²	1	2	yes	—
57	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#501×C₈₉	C₂²	1	2	yes	complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#497×C₈₉	C₂²	1	2	yes	complemented
62	#492×C₈₉	C₂²	1	1	yes	characteristic
63	#488×C₈₉	C₂²	1	2	yes	complemented
64	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#487×C₈₉	C₂²	1	2	yes	complemented
66	#486×C₈₉	C₂²	1	1	yes	characteristic
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#485×C₈₉	C₂²	1	2	yes	complemented
70	#483×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#478×C₈₉	C₂²	1	2	yes	—
74	#478×C₈₉	C₂²	1	2	yes	complemented
75	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#476×C₈₉	C₂²	1	1	yes	characteristic
77	#476×C₈₉	C₂²	1	2	yes	complemented
78	#475×C₈₉	C₂²	1	2	yes	complemented
79	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#470×C₈₉	C₂²	1	2	yes	complemented
82	#468×C₈₉	C₂²	1	2	yes	—
83	#467×C₈₉	C₂²	1	2	yes	complemented
84	#465×C₈₉	C₂²	1	2	yes	—
85	#465×C₈₉	C₂²	1	2	yes	complemented
86	#465×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	complemented
88	#463×C₈₉	C₂²	1	2	yes	complemented
89	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#461×C₈₉	C₂²	1	1	yes	characteristic
91	#461×C₈₉	C₂²	1	2	yes	—
92	#461×C₈₉	C₂²	1	2	yes	complemented
93	#460×C₈₉	C₂²	1	1	yes	characteristic
94	#459×C₈₉	C₂²	1	1	yes	characteristic
95	#452×C₈₉	C₂²	1	2	yes	—
96	#452×C₈₉	C₂²	1	2	yes	complemented
97	#450×C₈₉	C₂²	1	2	yes	—
98	#450×C₈₉	C₂²	1	2	yes	—
99	#449×C₈₉	C₂²	1	2	yes	—
100	#449×C₈₉	C₂²	1	2	yes	complemented
101	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#442×C₈₉	C₂²	1	2	yes	—
104	#442×C₈₉	C₂²	1	2	yes	complemented
105	#441×C₈₉	C₂²	1	2	yes	complemented
106	#440×C₈₉	C₂²	1	2	yes	—
107	#440×C₈₉	C₂²	1	2	yes	complemented
108	#440×C₈₉	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
118	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#435×C₈₉	C₂²	1	2	yes	complemented
123	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
125	#433×C₈₉	C₂²	1	2	yes	complemented
126	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₉	C₂²	1	2	yes	complemented
128	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
129	#416×C₈₉	C₂²	1	1	yes	characteristic
130	#416×C₈₉	C₂²	1	1	yes	characteristic, complemented
131	#416×C₈₉	C₂²	1	2	yes	complemented
132	C₂×#102×C₈₉	C₂²	1	2	yes	—
133	#405×C₈₉	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	2	yes	—
138	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₈₉	—	2	1	no	—
140	C₂²×D₄×C₈₉	—	2	1	no	—
141	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
142	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
143	#135×C₈₉	—	2	4	no	—
144	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×D₈×C₈₉	C₂³	1	2	yes	—
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
155	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	#127×C₈₉	C₂³	1	1	yes	characteristic
164	#126×C₈₉	—	2	2	no	—
165	#126×C₈₉	—	2	2	no	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	D₄	1	2	yes	—
170	#125×C₈₉	—	2	2	no	—
171	#125×C₈₉	—	2	2	no	—
172	#125×C₈₉	—	2	1	no	—
173	#125×C₈₉	—	2	1	no	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	—	2	2	no	—
176	#125×C₈₉	—	2	1	no	—
177	#125×C₈₉	D₄	1	1	yes	characteristic
178	#125×C₈₉	C₂³	1	2	yes	—
179	#124×C₈₉	—	2	1	no	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	—	2	2	no	—
184	#124×C₈₉	—	2	1	no	—
185	#124×C₈₉	D₄	1	1	yes	characteristic
186	#124×C₈₉	C₂³	1	2	yes	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	#123×C₈₉	—	2	2	no	—
191	#123×C₈₉	—	2	2	no	—
192	#123×C₈₉	—	2	2	no	—
193	#123×C₈₉	—	2	2	no	—
194	#123×C₈₉	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₈₉	—	2	1	no	—
196	C₂²⋊Q₈×C₈₉	—	2	1	no	—
197	C₂²⋊Q₈×C₈₉	—	2	1	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	—	2	2	no	—
200	C₂²⋊Q₈×C₈₉	—	2	2	no	—
201	C₂²⋊Q₈×C₈₉	—	2	2	no	—
202	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
203	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
207	#121×C₈₉	—	2	1	no	—
208	#121×C₈₉	—	2	2	no	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	2	no	—
213	#121×C₈₉	D₄	1	1	yes	characteristic
214	#121×C₈₉	C₂³	1	2	yes	—
215	#121×C₈₉	C₂³	1	2	yes	—
216	#120×C₈₉	—	2	2	no	—
217	#120×C₈₉	—	2	2	no	—
218	C₄×Q₈×C₈₉	—	2	1	no	—
219	C₄×Q₈×C₈₉	—	2	1	no	—
220	C₄×Q₈×C₈₉	—	2	1	no	—
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
224	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
225	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	1	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	1	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	2	no	—
234	C₄×D₄×C₈₉	—	2	2	no	—
235	C₄×D₄×C₈₉	—	2	1	no	—
236	C₄×D₄×C₈₉	—	2	2	no	—
237	C₄×D₄×C₈₉	—	2	2	no	—
238	C₄×D₄×C₈₉	—	2	1	no	—
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	2	yes	—
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₈₉	C₂³	1	2	yes	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	2	no	—
253	#117×C₈₉	—	2	1	no	—
254	#117×C₈₉	—	2	1	no	—
255	#117×C₈₉	C₂³	1	1	yes	characteristic
256	#117×C₈₉	C₂³	1	1	yes	characteristic
257	#117×C₈₉	C₂³	1	2	yes	—
258	#117×C₈₉	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
267	C₂×C₄²×C₈₉	—	2	1	no	—
268	C₂×C₄²×C₈₉	—	2	1	no	—
269	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#107×C₈₉	C₂³	1	1	yes	characteristic
272	#107×C₈₉	C₂³	1	2	yes	—
273	#107×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	1	yes	characteristic
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	2	yes	—
278	#106×C₈₉	C₂³	1	2	yes	—
279	#106×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	2	yes	—
287	#103×C₈₉	C₂³	1	1	yes	characteristic
288	#103×C₈₉	C₂³	1	1	yes	characteristic
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	1	yes	characteristic
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	2	yes	—
297	#102×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	C₂⁴×C₈₉	—	2	2	no	—
315	#41×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	2	4	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	1	no	—
320	#41×C₈₉	—	4	1	no	—
321	#41×C₈₉	—	8	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	2	no	—
325	C₂×Q₈×C₈₉	—	8	2	no	—
326	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₈₉	—	2	4	no	—
331	C₂×D₄×C₈₉	—	2	1	no	—
332	C₂×D₄×C₈₉	—	2	2	no	—
333	C₂×D₄×C₈₉	—	2	1	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	1	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	4	2	no	—
340	C₂×D₄×C₈₉	—	8	2	no	—
341	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
344	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₈₉	—	2	2	no	—
347	C₂²×C₄×C₈₉	—	2	1	no	—
348	C₂²×C₄×C₈₉	—	2	1	no	—
349	C₂²×C₄×C₈₉	—	2	1	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	2	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	1	no	—
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	—	2	2	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
362	Q₁₆×C₈₉	—	2	2	no	—
363	Q₁₆×C₈₉	—	4	2	no	—
364	SD₁₆×C₈₉	—	2	2	no	—
365	SD₁₆×C₈₉	—	2	2	no	—
366	SD₁₆×C₈₉	—	2	4	no	—
367	SD₁₆×C₈₉	—	2	4	no	—
368	SD₁₆×C₈₉	—	4	2	no	—
369	SD₁₆×C₈₉	—	4	2	no	—
370	D₈×C₈₉	—	2	4	no	—
371	D₈×C₈₉	#41	1	4	yes	complemented
372	M₁₆×C₈₉	—	2	4	no	—
373	C₂×C₈×C₈₉	—	2	2	no	—
374	C₂×C₈×C₈₉	—	4	1	no	—
375	C₂×C₈×C₈₉	—	4	2	no	—
376	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
380	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
381	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₈₉	—	2	2	no	—
383	C₄⋊C₄×C₈₉	—	2	1	no	—
384	C₄⋊C₄×C₈₉	—	2	1	no	—
385	C₄⋊C₄×C₈₉	—	2	2	no	—
386	C₄⋊C₄×C₈₉	—	2	2	no	—
387	C₄⋊C₄×C₈₉	—	2	2	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	1	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	1	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₈₉	—	2	2	no	—
415	C₂²⋊C₄×C₈₉	—	2	2	no	—
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	1	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	1	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	2	no	—
432	C₂²⋊C₄×C₈₉	—	2	2	no	—
433	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
438	C₄²×C₈₉	—	2	1	no	—
439	C₄²×C₈₉	—	2	1	no	—
440	C₄²×C₈₉	—	2	1	no	—
441	C₄²×C₈₉	—	2	1	no	—
442	C₄²×C₈₉	—	2	1	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	2	no	—
447	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
451	C₄²×C₈₉	C₂⁴	1	2	yes	—
452	C₂³×C₈₉	—	2	1	no	—
453	C₂³×C₈₉	—	2	1	no	—
454	C₂³×C₈₉	—	2	2	no	—
455	C₂³×C₈₉	—	4	4	no	—
456	C₂³×C₈₉	—	8	2	no	—
457	C₂³×C₈₉	—	8	2	no	—
458	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
459	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	2	2	no	—
462	Q₈×C₈₉	—	2	1	no	—
463	Q₈×C₈₉	—	2	1	no	—
464	Q₈×C₈₉	—	2	1	no	—
465	Q₈×C₈₉	—	2	2	no	—
466	Q₈×C₈₉	—	2	1	no	—
467	Q₈×C₈₉	—	4	2	no	—
468	Q₈×C₈₉	—	8	1	no	—
469	Q₈×C₈₉	—	8	2	no	—
470	D₄×C₈₉	—	2	2	no	—
471	D₄×C₈₉	—	2	2	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	4	2	no	—
476	D₄×C₈₉	—	4	4	no	—
477	D₄×C₈₉	—	4	2	no	—
478	D₄×C₈₉	—	4	2	no	—
479	D₄×C₈₉	—	4	4	no	—
480	D₄×C₈₉	—	4	2	no	—
481	D₄×C₈₉	—	8	1	no	—
482	D₄×C₈₉	—	8	2	no	—
483	D₄×C₈₉	—	8	2	no	—
484	D₄×C₈₉	C₂×#41	1	2	yes	—
485	D₄×C₈₉	C₂×#41	1	2	yes	—
486	C₂×C₄×C₈₉	—	2	2	no	—
487	C₂×C₄×C₈₉	—	2	1	no	—
488	C₂×C₄×C₈₉	—	2	2	no	—
489	C₂×C₄×C₈₉	—	2	2	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	2	no	—
499	C₂×C₄×C₈₉	—	2	2	no	—
500	C₂×C₄×C₈₉	—	4	1	no	—
501	C₂×C₄×C₈₉	—	4	2	no	—
502	C₂×C₄×C₈₉	—	4	2	no	—
503	C₂×C₄×C₈₉	—	4	4	no	—
504	C₂×C₄×C₈₉	—	4	2	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	8	1	no	—
507	C₂×C₄×C₈₉	—	8	1	no	—
508	C₂×C₄×C₈₉	—	8	2	no	—
509	C₂×C₄×C₈₉	—	8	2	no	—
510	C₂×C₄×C₈₉	—	8	2	no	—
511	C₂×C₄×C₈₉	—	8	2	no	—
512	C₂×C₄×C₈₉	—	8	2	no	—
513	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
522	C₈×C₈₉	—	2	1	no	—
523	C₈×C₈₉	—	2	2	no	—
524	C₈×C₈₉	—	2	1	no	—
525	C₈×C₈₉	—	2	1	no	—
526	C₈×C₈₉	—	2	2	no	—
527	C₈×C₈₉	C₂×#41	1	2	yes	—
528	C₂²×C₈₉	—	2	1	no	—
529	C₂²×C₈₉	—	2	2	no	—
530	C₂²×C₈₉	—	2	1	no	—
531	C₂²×C₈₉	—	2	2	no	—
532	C₂²×C₈₉	—	2	2	no	—
533	C₂²×C₈₉	—	2	2	no	—
534	C₂²×C₈₉	—	2	1	no	—
535	C₂²×C₈₉	—	2	2	no	—
536	C₂²×C₈₉	—	4	1	no	—
537	C₂²×C₈₉	—	4	1	no	—
538	C₂²×C₈₉	—	4	1	no	—
539	C₂²×C₈₉	—	4	1	no	—
540	C₂²×C₈₉	—	4	2	no	—
541	C₂²×C₈₉	—	4	2	no	—
542	C₂²×C₈₉	—	4	2	no	—
543	C₂²×C₈₉	—	16	4	no	—
544	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₈₉	—	2	1	no	—
546	C₄×C₈₉	—	2	1	no	—
547	C₄×C₈₉	—	2	2	no	—
548	C₄×C₈₉	—	2	1	no	—
549	C₄×C₈₉	—	2	2	no	—
550	C₄×C₈₉	—	2	1	no	—
551	C₄×C₈₉	—	2	2	no	—
552	C₄×C₈₉	—	4	1	no	—
553	C₄×C₈₉	—	4	1	no	—
554	C₄×C₈₉	—	4	2	no	—
555	C₄×C₈₉	—	4	1	no	—
556	C₄×C₈₉	—	4	2	no	—
557	C₄×C₈₉	—	4	1	no	—
558	C₄×C₈₉	—	4	1	no	—
559	C₄×C₈₉	—	4	1	no	—
560	C₄×C₈₉	—	4	2	no	—
561	C₄×C₈₉	#577	1	2	yes	—
562	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
563	C₄×C₈₉	#585	1	1	yes	characteristic
564	#61493	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
565	C₂×C₈₉	—	4	1	no	—
566	C₂×C₈₉	—	4	2	no	—
567	C₂×C₈₉	—	4	2	no	—
568	C₂×C₈₉	—	4	2	no	—
569	C₂×C₈₉	—	8	2	no	—
570	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
571	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
572	C₂×C₈₉	#3584	1	1	yes	characteristic
573	#3515	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3514	C₂×C₈₉	1	1	yes	characteristic, complemented
575	#3400	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#3384	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#3361	C₂×C₈₉	1	1	yes	characteristic, complemented
578	#3359	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3356	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3348	C₂×C₈₉	1	2	yes	complemented
581	#3303	C₂×C₈₉	1	2	yes	complemented
582	#3302	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3296	C₂×C₈₉	1	2	yes	complemented
584	#3295	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3272	C₂×C₈₉	1	1	yes	characteristic, complemented
586	#3267	C₂×C₈₉	1	2	yes	complemented
587	#3178	C₂×C₈₉	1	2	yes	complemented
588	#3167	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3125	C₂×C₈₉	1	2	yes	complemented
590	#3123	C₂×C₈₉	1	2	yes	complemented
591	#3116	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3115	C₂×C₈₉	1	1	yes	characteristic, complemented
593	#2966	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#2946	C₂×C₈₉	1	2	yes	complemented
595	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
596	C₈₉	#61493	1	1	yes	characteristic, direct product factor, Sylow
597	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
598	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
599	#559	C₂²×C₈₉	1	1	yes	characteristic
600	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
601	#556	C₂²×C₈₉	1	1	yes	characteristic
602	#555	C₂²×C₈₉	1	2	yes	—
603	#554	C₂²×C₈₉	1	1	yes	characteristic
604	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
605	#553	—	2	1	no	—
606	#552	—	2	2	no	—
607	#552	—	2	1	no	—
608	#552	C₂²×C₈₉	1	2	yes	complemented
609	#551	—	2	2	no	—
610	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
611	#548	—	2	1	no	—
612	#547	C₂²×C₈₉	1	1	yes	characteristic
613	#547	C₂²×C₈₉	1	2	yes	complemented
614	#546	—	2	1	no	—
615	#546	C₂²×C₈₉	1	2	yes	—
616	D₄²	C₂²×C₈₉	1	1	yes	characteristic
617	#542	C₂²×C₈₉	1	2	yes	—
618	#541	C₂²×C₈₉	1	2	yes	complemented
619	#539	—	2	2	no	—
620	#538	—	2	2	no	—
621	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#532	C₂²×C₈₉	1	1	yes	characteristic
623	#529	—	2	1	no	—
624	#529	—	2	1	no	—
625	#529	C₂²×C₈₉	1	1	yes	characteristic
626	C₂×#125	—	2	1	no	—
627	C₂×#124	—	2	1	no	—
628	#520	C₂²×C₈₉	1	2	yes	complemented
629	#518	C₂²×C₈₉	1	2	yes	—
630	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
631	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
632	#501	C₂²×C₈₉	1	2	yes	complemented
633	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
634	#497	C₂²×C₈₉	1	2	yes	complemented
635	#492	C₂²×C₈₉	1	1	yes	characteristic
636	#488	C₂²×C₈₉	1	2	yes	complemented
637	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	#487	C₂²×C₈₉	1	2	yes	complemented
639	#486	C₂²×C₈₉	1	1	yes	characteristic
640	#485	C₂²×C₈₉	1	2	yes	complemented
641	#485	C₂²×C₈₉	1	2	yes	complemented
642	#485	C₂²×C₈₉	1	2	yes	complemented
643	#483	C₂²×C₈₉	1	2	yes	complemented
644	#482	C₂²×C₈₉	1	2	yes	complemented
645	#481	C₂²×C₈₉	1	2	yes	—
646	#478	C₂²×C₈₉	1	2	yes	—
647	#478	C₂²×C₈₉	1	2	yes	complemented
648	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#476	C₂²×C₈₉	1	1	yes	characteristic
650	#476	C₂²×C₈₉	1	2	yes	complemented
651	#475	C₂²×C₈₉	1	2	yes	complemented
652	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
654	#470	C₂²×C₈₉	1	2	yes	complemented
655	#468	C₂²×C₈₉	1	2	yes	—
656	#467	C₂²×C₈₉	1	2	yes	complemented
657	#465	C₂²×C₈₉	1	2	yes	—
658	#465	C₂²×C₈₉	1	2	yes	complemented
659	#465	C₂²×C₈₉	1	2	yes	complemented
660	#464	C₂²×C₈₉	1	2	yes	complemented
661	#463	C₂²×C₈₉	1	2	yes	complemented
662	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#461	C₂²×C₈₉	1	1	yes	characteristic
664	#461	C₂²×C₈₉	1	2	yes	—
665	#461	C₂²×C₈₉	1	2	yes	complemented
666	#460	C₂²×C₈₉	1	1	yes	characteristic
667	#459	C₂²×C₈₉	1	1	yes	characteristic
668	#452	C₂²×C₈₉	1	2	yes	—
669	#452	C₂²×C₈₉	1	2	yes	complemented
670	#450	C₂²×C₈₉	1	2	yes	—
671	#450	C₂²×C₈₉	1	2	yes	—
672	#449	C₂²×C₈₉	1	2	yes	—
673	#449	C₂²×C₈₉	1	2	yes	complemented
674	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
675	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
676	#442	C₂²×C₈₉	1	2	yes	—
677	#442	C₂²×C₈₉	1	2	yes	complemented
678	#441	C₂²×C₈₉	1	2	yes	complemented
679	#440	C₂²×C₈₉	1	2	yes	—
680	#440	C₂²×C₈₉	1	2	yes	complemented
681	#440	C₂²×C₈₉	1	2	yes	complemented
682	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
683	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
688	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
691	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
693	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
694	#436	C₂²×C₈₉	1	1	yes	characteristic
695	#435	C₂²×C₈₉	1	2	yes	complemented
696	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
697	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
698	#433	C₂²×C₈₉	1	2	yes	complemented
699	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
700	#428	C₂²×C₈₉	1	2	yes	complemented
701	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
702	#416	C₂²×C₈₉	1	1	yes	characteristic
703	#416	C₂²×C₈₉	1	1	yes	characteristic, complemented
704	#416	C₂²×C₈₉	1	2	yes	complemented
705	C₂×#102	C₂²×C₈₉	1	2	yes	—
706	#405	C₂²×C₈₉	1	2	yes	complemented
707	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
710	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
711	C₂×#41	C₂³×C₈₉	1	2	yes	—
712	C₂²×Q₈	—	2	1	no	—
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
715	AGL(1,ℤ/8)	—	2	8	no	—
716	#135	—	2	4	no	—
717	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
718	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
725	C₂×D₈	C₂³×C₈₉	1	2	yes	—
726	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
736	#127	C₂³×C₈₉	1	1	yes	characteristic
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	D₄×C₈₉	1	2	yes	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	D₄×C₈₉	1	1	yes	characteristic
751	#125	C₂³×C₈₉	1	2	yes	—
752	#124	—	2	1	no	—
753	#124	—	2	1	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	1	no	—
758	#124	D₄×C₈₉	1	1	yes	characteristic
759	#124	C₂³×C₈₉	1	2	yes	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	D₄×C₈₉	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₈₉	1	1	yes	characteristic
787	#121	C₂³×C₈₉	1	2	yes	—
788	#121	C₂³×C₈₉	1	2	yes	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
799	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
800	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₈₉	1	2	yes	—
817	C₄×D₄	C₂³×C₈₉	1	2	yes	—
818	C₄×D₄	C₂³×C₈₉	1	2	yes	—
819	C₄×D₄	C₂³×C₈₉	1	2	yes	—
820	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₈₉	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	C₂³×C₈₉	1	1	yes	characteristic
829	#117	C₂³×C₈₉	1	1	yes	characteristic
830	#117	C₂³×C₈₉	1	2	yes	—
831	#117	C₂³×C₈₉	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	2	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
843	#107	C₂³×C₈₉	1	1	yes	characteristic
844	#107	C₂³×C₈₉	1	1	yes	characteristic
845	#107	C₂³×C₈₉	1	2	yes	—
846	#107	C₂³×C₈₉	1	2	yes	—
847	#106	C₂³×C₈₉	1	1	yes	characteristic
848	#106	C₂³×C₈₉	1	1	yes	characteristic
849	#106	C₂³×C₈₉	1	2	yes	—
850	#106	C₂³×C₈₉	1	2	yes	—
851	#106	C₂³×C₈₉	1	2	yes	—
852	#106	C₂³×C₈₉	1	2	yes	—
853	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
856	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
857	#103	C₂³×C₈₉	1	1	yes	characteristic
858	#103	C₂³×C₈₉	1	1	yes	characteristic
859	#103	C₂³×C₈₉	1	2	yes	—
860	#103	C₂³×C₈₉	1	1	yes	characteristic
861	#103	C₂³×C₈₉	1	1	yes	characteristic
862	#103	C₂³×C₈₉	1	2	yes	—
863	#103	C₂³×C₈₉	1	2	yes	—
864	#103	C₂³×C₈₉	1	2	yes	—
865	#103	C₂³×C₈₉	1	2	yes	—
866	#103	C₂³×C₈₉	1	2	yes	—
867	#102	C₂³×C₈₉	1	1	yes	characteristic
868	#102	C₂³×C₈₉	1	2	yes	—
869	#102	C₂³×C₈₉	1	2	yes	—
870	#102	C₂³×C₈₉	1	2	yes	—
871	#102	C₂³×C₈₉	1	1	yes	characteristic
872	#102	C₂³×C₈₉	1	1	yes	characteristic
873	#102	C₂³×C₈₉	1	1	yes	characteristic
874	#102	C₂³×C₈₉	1	2	yes	—
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
880	#97	C₂³×C₈₉	1	2	yes	—
881	#97	C₂³×C₈₉	1	2	yes	—
882	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₈₉	1	2	yes	—
887	C₂⁴	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	2	4	no	—
891	#41	—	4	2	no	—
892	#41	—	4	1	no	—
893	#41	—	4	1	no	—
894	#41	—	8	2	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	8	2	no	—
899	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
903	C₂×D₄	—	2	4	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	8	2	no	—
914	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
915	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
916	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
917	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
918	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	4	2	no	—
937	SD₁₆	—	2	2	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	D₈	—	2	4	no	—
944	D₈	#41×C₈₉	1	4	yes	complemented
945	M₁₆	—	2	4	no	—
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
953	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
954	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
979	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₈₉	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1032	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	C₂×#41×C₈₉	1	2	yes	—
1058	D₄	C₂×#41×C₈₉	1	2	yes	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1094	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	C₂×#41×C₈₉	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	16	4	no	—
1117	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	#577×C₈₉	1	2	yes	—
1135	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1136	C₄	#585×C₈₉	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	8	2	no	—
1142	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1143	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1144	C₂	C₈₉×#3584	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 ◁ #529×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3515	C₂	semidirect
2. C₈₉×#3514	C₂	semidirect
3. C₈₉×#3400	C₂	semidirect
4. C₈₉×#3384	C₂	semidirect
5. C₈₉×#3361	C₂	semidirect
6. C₈₉×#3359	C₂	semidirect
7. C₈₉×#3356	C₂	semidirect
8. C₈₉×#3348	C₂	semidirect
9. C₈₉×#3303	C₂	semidirect
10. C₈₉×#3302	C₂	semidirect
11. C₈₉×#3296	C₂	semidirect
12. C₈₉×#3295	C₂	semidirect
13. C₈₉×#3272	C₂	semidirect
14. C₈₉×#3267	C₂	semidirect
15. C₈₉×#3178	C₂	semidirect
16. C₈₉×#3167	C₂	semidirect
17. C₈₉×#3125	C₂	semidirect
18. C₈₉×#3123	C₂	semidirect
19. C₈₉×#3116	C₂	semidirect
20. C₈₉×#3115	C₂	semidirect
21. C₈₉×#2966	C₂	semidirect
22. C₈₉×#2946	C₂	semidirect
23. C₄×#135×C₈₉	C₂	semidirect
27. #557×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
35. #552×C₈₉	C₂²	semidirect
40. #547×C₈₉	C₂²	semidirect
45. #541×C₈₉	C₂²	semidirect
48. #533×C₈₉	C₂²	semidirect
55. #520×C₈₉	C₂²	semidirect
58. C₄×#41×C₈₉	C₂²	semidirect
59. #501×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
61. #497×C₈₉	C₂²	semidirect
63. #488×C₈₉	C₂²	semidirect
64. #487×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
69. #485×C₈₉	C₂²	semidirect
70. #483×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
74. #478×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #475×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
80. #474×C₈₉	C₂²	semidirect
81. #470×C₈₉	C₂²	semidirect
83. #467×C₈₉	C₂²	semidirect
85. #465×C₈₉	C₂²	semidirect
86. #465×C₈₉	C₂²	semidirect
87. #464×C₈₉	C₂²	semidirect
88. #463×C₈₉	C₂²	semidirect
89. #462×C₈₉	C₂²	semidirect
92. #461×C₈₉	C₂²	semidirect
96. #452×C₈₉	C₂²	semidirect
100. #449×C₈₉	C₂²	semidirect
101. #446×C₈₉	C₂²	semidirect
102. C₈×Q₈×C₈₉	C₂²	semidirect
104. #442×C₈₉	C₂²	semidirect
105. #441×C₈₉	C₂²	semidirect
107. #440×C₈₉	C₂²	semidirect
108. #440×C₈₉	C₂²	semidirect
109. C₄×Q₁₆×C₈₉	C₂²	semidirect
110. C₄×Q₁₆×C₈₉	C₂²	semidirect
114. C₄×SD₁₆×C₈₉	C₂²	semidirect
115. C₄×SD₁₆×C₈₉	C₂²	semidirect
116. C₄×SD₁₆×C₈₉	C₂²	semidirect
117. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
122. #435×C₈₉	C₂²	semidirect
124. C₈×D₄×C₈₉	C₂²	semidirect
125. #433×C₈₉	C₂²	semidirect
126. #432×C₈₉	C₂²	semidirect
127. #428×C₈₉	C₂²	semidirect
128. #427×C₈₉	C₂²	semidirect
130. #416×C₈₉	C₂²	semidirect
131. #416×C₈₉	C₂²	semidirect
133. #405×C₈₉	C₂²	semidirect
134. C₂×C₄×C₈×C₈₉	C₂²	semidirect
371. D₈×C₈₉	#41	semidirect
564. #61493	C₈₉	direct (N × H)
573. #3515	C₂×C₈₉	semidirect
574. #3514	C₂×C₈₉	semidirect
575. #3400	C₂×C₈₉	semidirect
576. #3384	C₂×C₈₉	semidirect
577. #3361	C₂×C₈₉	semidirect
578. #3359	C₂×C₈₉	semidirect
579. #3356	C₂×C₈₉	semidirect
580. #3348	C₂×C₈₉	semidirect
581. #3303	C₂×C₈₉	semidirect
582. #3302	C₂×C₈₉	semidirect
583. #3296	C₂×C₈₉	semidirect
584. #3295	C₂×C₈₉	semidirect
585. #3272	C₂×C₈₉	semidirect
586. #3267	C₂×C₈₉	semidirect
587. #3178	C₂×C₈₉	semidirect
588. #3167	C₂×C₈₉	semidirect
589. #3125	C₂×C₈₉	semidirect
590. #3123	C₂×C₈₉	semidirect
591. #3116	C₂×C₈₉	semidirect
592. #3115	C₂×C₈₉	semidirect
593. #2966	C₂×C₈₉	semidirect
594. #2946	C₂×C₈₉	semidirect
595. C₄×#135	C₂×C₈₉	semidirect
596. C₈₉	#61493	direct (N × H)
600. #557	C₂²×C₈₉	semidirect
604. #554	C₂²×C₈₉	semidirect
608. #552	C₂²×C₈₉	semidirect
613. #547	C₂²×C₈₉	semidirect
618. #541	C₂²×C₈₉	semidirect
621. #533	C₂²×C₈₉	semidirect
628. #520	C₂²×C₈₉	semidirect
631. C₄×#41	C₂²×C₈₉	semidirect
632. #501	C₂²×C₈₉	semidirect
633. #498	C₂²×C₈₉	semidirect
634. #497	C₂²×C₈₉	semidirect
636. #488	C₂²×C₈₉	semidirect
637. #487	C₂²×C₈₉	semidirect
638. #487	C₂²×C₈₉	semidirect
640. #485	C₂²×C₈₉	semidirect
641. #485	C₂²×C₈₉	semidirect
642. #485	C₂²×C₈₉	semidirect
643. #483	C₂²×C₈₉	semidirect
644. #482	C₂²×C₈₉	semidirect
647. #478	C₂²×C₈₉	semidirect
648. #477	C₂²×C₈₉	semidirect
650. #476	C₂²×C₈₉	semidirect
651. #475	C₂²×C₈₉	semidirect
652. #475	C₂²×C₈₉	semidirect
653. #474	C₂²×C₈₉	semidirect
654. #470	C₂²×C₈₉	semidirect
656. #467	C₂²×C₈₉	semidirect
658. #465	C₂²×C₈₉	semidirect
659. #465	C₂²×C₈₉	semidirect
660. #464	C₂²×C₈₉	semidirect
661. #463	C₂²×C₈₉	semidirect
662. #462	C₂²×C₈₉	semidirect
665. #461	C₂²×C₈₉	semidirect
669. #452	C₂²×C₈₉	semidirect
673. #449	C₂²×C₈₉	semidirect
674. #446	C₂²×C₈₉	semidirect
675. C₈×Q₈	C₂²×C₈₉	semidirect
677. #442	C₂²×C₈₉	semidirect
678. #441	C₂²×C₈₉	semidirect
680. #440	C₂²×C₈₉	semidirect
681. #440	C₂²×C₈₉	semidirect
682. C₄×Q₁₆	C₂²×C₈₉	semidirect
683. C₄×Q₁₆	C₂²×C₈₉	semidirect
687. C₄×SD₁₆	C₂²×C₈₉	semidirect
688. C₄×SD₁₆	C₂²×C₈₉	semidirect
689. C₄×SD₁₆	C₂²×C₈₉	semidirect
690. C₄×SD₁₆	C₂²×C₈₉	semidirect
693. C₄×D₈	C₂²×C₈₉	semidirect
695. #435	C₂²×C₈₉	semidirect
697. C₈×D₄	C₂²×C₈₉	semidirect
698. #433	C₂²×C₈₉	semidirect
699. #432	C₂²×C₈₉	semidirect
700. #428	C₂²×C₈₉	semidirect
701. #427	C₂²×C₈₉	semidirect
703. #416	C₂²×C₈₉	semidirect
704. #416	C₂²×C₈₉	semidirect
706. #405	C₂²×C₈₉	semidirect
707. C₂×C₄×C₈	C₂²×C₈₉	semidirect
944. D₈	#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×#3515	2
C₈₉×#3514	2
C₈₉×#3400	2
C₈₉×#3384	2
C₈₉×#3361	2
C₈₉×#3359	2
C₈₉×#3356	2
C₈₉×#3348	2
C₈₉×#3303	2
C₈₉×#3302	2
C₈₉×#3296	2
C₈₉×#3295	2
C₈₉×#3272	2
C₈₉×#3267	2
C₈₉×#3178	2
C₈₉×#3167	2
C₈₉×#3125	2
C₈₉×#3123	2
C₈₉×#3116	2
C₈₉×#3115	2
C₈₉×#2966	2
C₈₉×#2946	2
C₄×#135×C₈₉	2
#61493	89

Subgroups — C89×#61493 #36439341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61493 #36439341