Subgroups — C₈₉×#61463 #36439311

Order 22784.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3352	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3327	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3323	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3275	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3183	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3117	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
26	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#556×C₈₉	—	2	1	no	—
28	#556×C₈₉	C₂²	1	1	yes	characteristic
29	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#555×C₈₉	C₂²	1	1	yes	characteristic
31	#554×C₈₉	C₂²	1	1	yes	characteristic
32	#553×C₈₉	—	2	1	no	—
33	#552×C₈₉	—	2	1	no	—
34	#552×C₈₉	—	2	2	no	—
35	#552×C₈₉	C₂²	1	2	yes	—
36	#552×C₈₉	C₂²	1	2	yes	—
37	#551×C₈₉	—	2	2	no	—
38	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#548×C₈₉	C₂²	1	2	yes	—
40	#547×C₈₉	—	2	1	no	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#546×C₈₉	C₂²	1	2	yes	—
44	#533×C₈₉	—	2	1	no	—
45	#533×C₈₉	C₂²	1	1	yes	characteristic
46	#533×C₈₉	C₂²	1	1	yes	characteristic
47	#529×C₈₉	—	2	2	no	—
48	#529×C₈₉	—	2	2	no	—
49	#529×C₈₉	C₂²	1	2	yes	—
50	#529×C₈₉	C₂²	1	2	yes	complemented
51	#525×C₈₉	—	2	1	no	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	2	yes	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#117×C₈₉	—	2	1	no	—
59	#499×C₈₉	C₂²	1	2	yes	complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#495×C₈₉	C₂²	1	2	yes	—
62	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#488×C₈₉	C₂²	1	2	yes	—
64	#488×C₈₉	C₂²	1	2	yes	complemented
65	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
66	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	—
68	#485×C₈₉	C₂²	1	2	yes	complemented
69	#484×C₈₉	C₂²	1	2	yes	—
70	#484×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	2	yes	complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	complemented
74	#479×C₈₉	C₂²	1	2	yes	complemented
75	#479×C₈₉	C₂²	1	2	yes	complemented
76	#478×C₈₉	C₂²	1	2	yes	—
77	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#474×C₈₉	C₂²	1	1	yes	characteristic
80	#474×C₈₉	C₂²	1	1	yes	characteristic
81	#470×C₈₉	C₂²	1	2	yes	—
82	#470×C₈₉	C₂²	1	2	yes	—
83	#470×C₈₉	C₂²	1	2	yes	complemented
84	#469×C₈₉	C₂²	1	2	yes	—
85	#468×C₈₉	C₂²	1	2	yes	—
86	#468×C₈₉	C₂²	1	2	yes	complemented
87	#464×C₈₉	C₂²	1	2	yes	—
88	#464×C₈₉	C₂²	1	2	yes	—
89	#464×C₈₉	C₂²	1	2	yes	complemented
90	#463×C₈₉	C₂²	1	2	yes	—
91	#462×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	#461×C₈₉	C₂²	1	1	yes	characteristic
93	#461×C₈₉	C₂²	1	1	yes	characteristic
94	#461×C₈₉	C₂²	1	1	yes	characteristic, complemented
95	#452×C₈₉	C₂²	1	2	yes	—
96	#452×C₈₉	C₂²	1	2	yes	—
97	#451×C₈₉	C₂²	1	2	yes	complemented
98	#450×C₈₉	C₂²	1	2	yes	—
99	#449×C₈₉	C₂²	1	2	yes	—
100	#448×C₈₉	C₂²	1	2	yes	—
101	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#442×C₈₉	C₂²	1	1	yes	characteristic
104	#442×C₈₉	C₂²	1	1	yes	characteristic
105	#441×C₈₉	C₂²	1	2	yes	complemented
106	#441×C₈₉	C₂²	1	2	yes	complemented
107	#441×C₈₉	C₂²	1	2	yes	complemented
108	#440×C₈₉	C₂²	1	2	yes	—
109	#440×C₈₉	C₂²	1	2	yes	—
110	#440×C₈₉	C₂²	1	1	yes	characteristic
111	#440×C₈₉	C₂²	1	1	yes	characteristic
112	#440×C₈₉	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
114	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	2	yes	—
122	#436×C₈₉	C₂²	1	2	yes	—
123	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
125	#432×C₈₉	C₂²	1	1	yes	characteristic
126	#432×C₈₉	C₂²	1	2	yes	complemented
127	#428×C₈₉	C₂²	1	1	yes	characteristic
128	#428×C₈₉	C₂²	1	2	yes	complemented
129	#419×C₈₉	C₂²	1	2	yes	complemented
130	#418×C₈₉	C₂²	1	1	yes	characteristic
131	#417×C₈₉	C₂²	1	2	yes	—
132	#417×C₈₉	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	D₄	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	C₂³	1	2	yes	—
140	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₈₉	—	2	1	no	—
142	#137×C₈₉	—	2	8	no	—
143	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
144	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₈₉	—	2	1	no	—
159	C₄⋊Q₈×C₈₉	—	2	1	no	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×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	—	2	2	no	—
170	#125×C₈₉	—	2	2	no	—
171	#125×C₈₉	—	2	2	no	—
172	#125×C₈₉	—	2	2	no	—
173	#125×C₈₉	—	2	1	no	—
174	#125×C₈₉	—	2	1	no	—
175	#125×C₈₉	C₂³	1	2	yes	—
176	#125×C₈₉	C₂³	1	2	yes	—
177	#124×C₈₉	—	2	2	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	C₂³	1	2	yes	—
180	#124×C₈₉	C₂³	1	2	yes	—
181	#123×C₈₉	—	2	2	no	—
182	#123×C₈₉	—	2	2	no	—
183	#123×C₈₉	—	2	2	no	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	2	no	—
188	C₂²⋊Q₈×C₈₉	—	2	1	no	—
189	C₂²⋊Q₈×C₈₉	—	2	1	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	1	no	—
192	C₂²⋊Q₈×C₈₉	—	2	1	no	—
193	C₂²⋊Q₈×C₈₉	—	2	2	no	—
194	C₂²⋊Q₈×C₈₉	—	2	1	no	—
195	C₂²⋊Q₈×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	2	no	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
201	#121×C₈₉	—	2	1	no	—
202	#121×C₈₉	—	2	1	no	—
203	#121×C₈₉	—	2	2	no	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	C₂³	1	2	yes	—
206	#121×C₈₉	C₂³	1	2	yes	—
207	#120×C₈₉	—	2	2	no	—
208	C₄×Q₈×C₈₉	—	2	1	no	—
209	C₄×Q₈×C₈₉	—	2	2	no	—
210	C₄×Q₈×C₈₉	—	2	2	no	—
211	C₄×Q₈×C₈₉	—	2	1	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
216	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
217	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₈₉	—	2	1	no	—
223	C₄×D₄×C₈₉	—	2	2	no	—
224	C₄×D₄×C₈₉	—	2	2	no	—
225	C₄×D₄×C₈₉	—	2	1	no	—
226	C₄×D₄×C₈₉	—	2	1	no	—
227	C₄×D₄×C₈₉	—	2	2	no	—
228	C₄×D₄×C₈₉	—	2	2	no	—
229	C₄×D₄×C₈₉	—	2	2	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	1	no	—
232	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
233	C₄×D₄×C₈₉	D₄	1	2	yes	—
234	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₉	C₂³	1	2	yes	—
238	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	C₂³	1	2	yes	—
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	#117×C₈₉	—	2	1	no	—
244	#117×C₈₉	—	2	1	no	—
245	#117×C₈₉	—	2	1	no	—
246	#117×C₈₉	—	2	1	no	—
247	#117×C₈₉	—	2	1	no	—
248	#117×C₈₉	—	2	2	no	—
249	#117×C₈₉	—	2	2	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	2	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	—	2	2	no	—
254	#117×C₈₉	D₄	1	1	yes	characteristic
255	#117×C₈₉	D₄	1	2	yes	—
256	#117×C₈₉	C₂³	1	1	yes	characteristic
257	#117×C₈₉	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	—	2	2	no	—
266	C₂×C₄²×C₈₉	—	2	2	no	—
267	C₂×C₄²×C₈₉	—	2	1	no	—
268	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
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	#107×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
288	#103×C₈₉	C₂³	1	2	yes	—
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	#103×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	1	yes	characteristic
296	#102×C₈₉	C₂³	1	1	yes	characteristic
297	#102×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	2	yes	—
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
308	#97×C₈₉	C₂³	1	1	yes	characteristic
309	#97×C₈₉	C₂³	1	2	yes	—
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	2	yes	—
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	C₂⁴×C₈₉	—	2	1	no	—
315	#41×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	4	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	1	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	4	no	—
321	C₂×Q₈×C₈₉	—	2	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	4	no	—
325	C₂×Q₈×C₈₉	—	4	2	no	—
326	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₈₉	—	2	2	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	1	no	—
333	C₂×D₄×C₈₉	—	2	2	no	—
334	C₂×D₄×C₈₉	—	2	2	no	—
335	C₂×D₄×C₈₉	—	2	1	no	—
336	C₂×D₄×C₈₉	—	4	1	no	—
337	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	—	2	2	no	—
343	C₂²×C₄×C₈₉	—	2	2	no	—
344	C₂²×C₄×C₈₉	—	2	1	no	—
345	C₂²×C₄×C₈₉	—	2	1	no	—
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	1	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	4	4	no	—
355	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₈₉	—	2	4	no	—
362	Q₁₆×C₈₉	—	2	4	no	—
363	Q₁₆×C₈₉	—	4	2	no	—
364	SD₁₆×C₈₉	—	2	2	no	—
365	SD₁₆×C₈₉	—	2	4	no	—
366	SD₁₆×C₈₉	—	4	2	no	—
367	SD₁₆×C₈₉	—	4	2	no	—
368	SD₁₆×C₈₉	#41	1	4	yes	complemented
369	D₈×C₈₉	—	2	2	no	—
370	D₈×C₈₉	—	2	2	no	—
371	M₁₆×C₈₉	—	2	2	no	—
372	M₁₆×C₈₉	—	2	4	no	—
373	M₁₆×C₈₉	—	4	2	no	—
374	M₁₆×C₈₉	—	4	1	no	—
375	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
378	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
379	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₈₉	—	2	1	no	—
382	C₄⋊C₄×C₈₉	—	2	1	no	—
383	C₄⋊C₄×C₈₉	—	2	1	no	—
384	C₄⋊C₄×C₈₉	—	2	2	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	1	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	1	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	1	no	—
398	C₄⋊C₄×C₈₉	—	2	2	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	1	no	—
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	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	1	no	—
424	C₂²⋊C₄×C₈₉	—	2	1	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	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	C₄²×C₈₉	—	2	1	no	—
437	C₄²×C₈₉	—	2	2	no	—
438	C₄²×C₈₉	—	2	1	no	—
439	C₄²×C₈₉	—	2	2	no	—
440	C₄²×C₈₉	—	2	2	no	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	C₂×D₄	1	2	yes	—
446	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₈₉	C₂×D₄	1	2	yes	—
448	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₈₉	C₂⁴	1	2	yes	—
451	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
452	C₂³×C₈₉	—	2	1	no	—
453	C₂³×C₈₉	—	2	1	no	—
454	C₂³×C₈₉	—	2	1	no	—
455	C₂³×C₈₉	—	4	2	no	—
456	C₂³×C₈₉	—	4	2	no	—
457	C₂³×C₈₉	—	8	1	no	—
458	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	2	1	no	—
462	Q₈×C₈₉	—	2	2	no	—
463	Q₈×C₈₉	—	2	2	no	—
464	Q₈×C₈₉	—	2	2	no	—
465	Q₈×C₈₉	—	2	2	no	—
466	Q₈×C₈₉	—	4	4	no	—
467	Q₈×C₈₉	—	4	2	no	—
468	Q₈×C₈₉	—	8	1	no	—
469	Q₈×C₈₉	C₂×#41	1	2	yes	—
470	D₄×C₈₉	—	2	2	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	1	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	4	2	no	—
477	D₄×C₈₉	—	4	2	no	—
478	D₄×C₈₉	—	4	2	no	—
479	D₄×C₈₉	—	4	4	no	—
480	D₄×C₈₉	—	4	4	no	—
481	D₄×C₈₉	—	8	2	no	—
482	D₄×C₈₉	C₂×#41	1	2	yes	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
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	1	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	1	no	—
492	C₂×C₄×C₈₉	—	2	2	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	4	2	no	—
498	C₂×C₄×C₈₉	—	4	1	no	—
499	C₂×C₄×C₈₉	—	4	2	no	—
500	C₂×C₄×C₈₉	—	4	2	no	—
501	C₂×C₄×C₈₉	—	4	4	no	—
502	C₂×C₄×C₈₉	—	4	4	no	—
503	C₂×C₄×C₈₉	—	4	2	no	—
504	C₂×C₄×C₈₉	—	4	2	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	4	no	—
508	C₂×C₄×C₈₉	—	4	2	no	—
509	C₂×C₄×C₈₉	—	4	2	no	—
510	C₂×C₄×C₈₉	—	4	2	no	—
511	C₂×C₄×C₈₉	—	8	2	no	—
512	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
521	C₈×C₈₉	—	2	1	no	—
522	C₈×C₈₉	—	2	2	no	—
523	C₈×C₈₉	—	2	1	no	—
524	C₈×C₈₉	—	2	2	no	—
525	C₈×C₈₉	—	2	1	no	—
526	C₈×C₈₉	C₂×#41	1	2	yes	—
527	C₂²×C₈₉	—	2	2	no	—
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	1	no	—
533	C₂²×C₈₉	—	2	2	no	—
534	C₂²×C₈₉	—	4	1	no	—
535	C₂²×C₈₉	—	4	1	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	1	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	8	4	no	—
543	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₈₉	—	2	1	no	—
545	C₄×C₈₉	—	2	2	no	—
546	C₄×C₈₉	—	2	1	no	—
547	C₄×C₈₉	—	2	1	no	—
548	C₄×C₈₉	—	2	2	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	2	no	—
554	C₄×C₈₉	—	4	2	no	—
555	C₄×C₈₉	—	4	2	no	—
556	C₄×C₈₉	—	4	1	no	—
557	C₄×C₈₉	—	4	1	no	—
558	C₄×C₈₉	—	4	1	no	—
559	C₄×C₈₉	—	4	2	no	—
560	C₄×C₈₉	#575	1	2	yes	—
561	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
562	C₄×C₈₉	#585	1	1	yes	characteristic
563	#61463	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
564	C₂×C₈₉	—	4	2	no	—
565	C₂×C₈₉	—	4	1	no	—
566	C₂×C₈₉	—	4	2	no	—
567	C₂×C₈₉	—	8	1	no	—
568	C₂×C₈₉	—	8	1	no	—
569	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
570	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
571	C₂×C₈₉	#3586	1	1	yes	characteristic
572	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
573	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3393	C₂×C₈₉	1	1	yes	characteristic, complemented
575	#3381	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#3364	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#3360	C₂×C₈₉	1	1	yes	characteristic, complemented
578	#3354	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3352	C₂×C₈₉	1	2	yes	complemented
580	#3330	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3329	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3327	C₂×C₈₉	1	2	yes	complemented
583	#3323	C₂×C₈₉	1	2	yes	complemented
584	#3276	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3275	C₂×C₈₉	1	2	yes	complemented
586	#3185	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3183	C₂×C₈₉	1	2	yes	complemented
588	#3117	C₂×C₈₉	1	2	yes	complemented
589	#3116	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3111	C₂×C₈₉	1	2	yes	complemented
591	#3110	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
593	C₄×#137	C₂×C₈₉	1	2	yes	complemented
594	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	1	yes	characteristic, complemented
595	C₈₉	#61463	1	1	yes	characteristic, direct product factor, Sylow
596	C₂×#137	C₂²×C₈₉	1	2	yes	—
597	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
598	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
599	#556	—	2	1	no	—
600	#556	C₂²×C₈₉	1	1	yes	characteristic
601	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
602	#555	C₂²×C₈₉	1	1	yes	characteristic
603	#554	C₂²×C₈₉	1	1	yes	characteristic
604	#553	—	2	1	no	—
605	#552	—	2	1	no	—
606	#552	—	2	2	no	—
607	#552	C₂²×C₈₉	1	2	yes	—
608	#552	C₂²×C₈₉	1	2	yes	—
609	#551	—	2	2	no	—
610	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
611	#548	C₂²×C₈₉	1	2	yes	—
612	#547	—	2	1	no	—
613	#547	C₂²×C₈₉	1	1	yes	characteristic
614	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
615	#546	C₂²×C₈₉	1	2	yes	—
616	#533	—	2	1	no	—
617	#533	C₂²×C₈₉	1	1	yes	characteristic
618	#533	C₂²×C₈₉	1	1	yes	characteristic
619	#529	—	2	2	no	—
620	#529	—	2	2	no	—
621	#529	C₂²×C₈₉	1	2	yes	—
622	#529	C₂²×C₈₉	1	2	yes	complemented
623	#525	—	2	1	no	—
624	C₄×#41	—	2	1	no	—
625	C₄×#41	C₂²×C₈₉	1	2	yes	—
626	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
627	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
628	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
629	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
630	C₂×#117	—	2	1	no	—
631	#499	C₂²×C₈₉	1	2	yes	complemented
632	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
633	#495	C₂²×C₈₉	1	2	yes	—
634	#494	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	#488	C₂²×C₈₉	1	2	yes	—
636	#488	C₂²×C₈₉	1	2	yes	complemented
637	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
638	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#485	C₂²×C₈₉	1	2	yes	—
640	#485	C₂²×C₈₉	1	2	yes	complemented
641	#484	C₂²×C₈₉	1	2	yes	—
642	#484	C₂²×C₈₉	1	2	yes	complemented
643	#482	C₂²×C₈₉	1	2	yes	complemented
644	#481	C₂²×C₈₉	1	2	yes	—
645	#479	C₂²×C₈₉	1	2	yes	complemented
646	#479	C₂²×C₈₉	1	2	yes	complemented
647	#479	C₂²×C₈₉	1	2	yes	complemented
648	#478	C₂²×C₈₉	1	2	yes	—
649	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
650	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
651	#474	C₂²×C₈₉	1	1	yes	characteristic
652	#474	C₂²×C₈₉	1	1	yes	characteristic
653	#470	C₂²×C₈₉	1	2	yes	—
654	#470	C₂²×C₈₉	1	2	yes	—
655	#470	C₂²×C₈₉	1	2	yes	complemented
656	#469	C₂²×C₈₉	1	2	yes	—
657	#468	C₂²×C₈₉	1	2	yes	—
658	#468	C₂²×C₈₉	1	2	yes	complemented
659	#464	C₂²×C₈₉	1	2	yes	—
660	#464	C₂²×C₈₉	1	2	yes	—
661	#464	C₂²×C₈₉	1	2	yes	complemented
662	#463	C₂²×C₈₉	1	2	yes	—
663	#462	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#461	C₂²×C₈₉	1	1	yes	characteristic
665	#461	C₂²×C₈₉	1	1	yes	characteristic
666	#461	C₂²×C₈₉	1	1	yes	characteristic, complemented
667	#452	C₂²×C₈₉	1	2	yes	—
668	#452	C₂²×C₈₉	1	2	yes	—
669	#451	C₂²×C₈₉	1	2	yes	complemented
670	#450	C₂²×C₈₉	1	2	yes	—
671	#449	C₂²×C₈₉	1	2	yes	—
672	#448	C₂²×C₈₉	1	2	yes	—
673	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
675	#442	C₂²×C₈₉	1	1	yes	characteristic
676	#442	C₂²×C₈₉	1	1	yes	characteristic
677	#441	C₂²×C₈₉	1	2	yes	complemented
678	#441	C₂²×C₈₉	1	2	yes	complemented
679	#441	C₂²×C₈₉	1	2	yes	complemented
680	#440	C₂²×C₈₉	1	2	yes	—
681	#440	C₂²×C₈₉	1	2	yes	—
682	#440	C₂²×C₈₉	1	1	yes	characteristic
683	#440	C₂²×C₈₉	1	1	yes	characteristic
684	#440	C₂²×C₈₉	1	2	yes	complemented
685	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
686	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
691	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
693	#436	C₂²×C₈₉	1	2	yes	—
694	#436	C₂²×C₈₉	1	2	yes	—
695	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
696	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
697	#432	C₂²×C₈₉	1	1	yes	characteristic
698	#432	C₂²×C₈₉	1	2	yes	complemented
699	#428	C₂²×C₈₉	1	1	yes	characteristic
700	#428	C₂²×C₈₉	1	2	yes	complemented
701	#419	C₂²×C₈₉	1	2	yes	complemented
702	#418	C₂²×C₈₉	1	1	yes	characteristic
703	#417	C₂²×C₈₉	1	2	yes	—
704	#417	C₂²×C₈₉	1	1	yes	characteristic
705	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
706	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
707	C₂×#41	—	2	1	no	—
708	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
709	C₂×#41	C₂³×C₈₉	1	2	yes	—
710	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
711	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
712	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	#137	—	2	8	no	—
715	AGL(1,ℤ/8)	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
736	#126	—	2	2	no	—
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	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	1	no	—
747	#125	C₂³×C₈₉	1	2	yes	—
748	#125	C₂³×C₈₉	1	2	yes	—
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	C₂³×C₈₉	1	2	yes	—
752	#124	C₂³×C₈₉	1	2	yes	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	C₂³×C₈₉	1	2	yes	—
778	#121	C₂³×C₈₉	1	2	yes	—
779	#120	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	2	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
788	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
789	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
791	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
793	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
805	C₄×D₄	D₄×C₈₉	1	2	yes	—
806	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₈₉	1	2	yes	—
812	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₈₉	1	2	yes	—
814	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	—	2	2	no	—
826	#117	D₄×C₈₉	1	1	yes	characteristic
827	#117	D₄×C₈₉	1	2	yes	—
828	#117	C₂³×C₈₉	1	1	yes	characteristic
829	#117	C₂³×C₈₉	1	2	yes	—
830	C₂×C₄⋊C₄	—	2	2	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
834	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₄²	—	2	2	no	—
838	C₂×C₄²	—	2	2	no	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
842	#107	C₂³×C₈₉	1	1	yes	characteristic
843	#107	C₂³×C₈₉	1	1	yes	characteristic
844	#107	C₂³×C₈₉	1	2	yes	—
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	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
855	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
856	#103	C₂³×C₈₉	1	1	yes	characteristic
857	#103	C₂³×C₈₉	1	1	yes	characteristic
858	#103	C₂³×C₈₉	1	2	yes	—
859	#103	C₂³×C₈₉	1	2	yes	—
860	#103	C₂³×C₈₉	1	2	yes	—
861	#103	C₂³×C₈₉	1	2	yes	—
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	1	yes	characteristic
869	#102	C₂³×C₈₉	1	1	yes	characteristic
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	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
879	#97	C₂³×C₈₉	1	1	yes	characteristic
880	#97	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
885	C₄×C₈	C₂³×C₈₉	1	2	yes	—
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	2	no	—
892	#41	—	4	4	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
901	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	4	1	no	—
909	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
911	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	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	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	4	4	no	—
927	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
928	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
929	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
933	Q₁₆	—	2	4	no	—
934	Q₁₆	—	2	4	no	—
935	Q₁₆	—	4	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	#41×C₈₉	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	—	4	2	no	—
946	M₁₆	—	4	1	no	—
947	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
950	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
951	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	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	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1018	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1020	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₈₉	1	2	yes	—
1023	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	4	4	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	1	no	—
1041	Q₈	C₂×#41×C₈₉	1	2	yes	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	8	2	no	—
1054	D₄	C₂×#41×C₈₉	1	2	yes	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×#41×C₈₉	1	2	yes	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
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	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	#575×C₈₉	1	2	yes	—
1133	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1134	C₄	#585×C₈₉	1	1	yes	characteristic
1135	C₂	—	4	2	no	—
1136	C₂	—	4	1	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1141	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1142	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3482	C₂	semidirect
2. C₈₉×#3475	C₂	semidirect
3. C₈₉×#3393	C₂	semidirect
4. C₈₉×#3381	C₂	semidirect
5. C₈₉×#3364	C₂	semidirect
6. C₈₉×#3360	C₂	semidirect
7. C₈₉×#3354	C₂	semidirect
8. C₈₉×#3352	C₂	semidirect
9. C₈₉×#3330	C₂	semidirect
10. C₈₉×#3329	C₂	semidirect
11. C₈₉×#3327	C₂	semidirect
12. C₈₉×#3323	C₂	semidirect
13. C₈₉×#3276	C₂	semidirect
14. C₈₉×#3275	C₂	semidirect
15. C₈₉×#3185	C₂	semidirect
16. C₈₉×#3183	C₂	semidirect
17. C₈₉×#3117	C₂	semidirect
18. C₈₉×#3116	C₂	semidirect
19. C₈₉×#3111	C₂	semidirect
20. C₈₉×#3110	C₂	semidirect
21. C₈₉×#2971	C₂	semidirect
22. C₄×#137×C₈₉	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
26. #557×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
42. #547×C₈₉	C₂²	semidirect
50. #529×C₈₉	C₂²	semidirect
56. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
59. #499×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
62. #494×C₈₉	C₂²	semidirect
64. #488×C₈₉	C₂²	semidirect
65. #487×C₈₉	C₂²	semidirect
66. #487×C₈₉	C₂²	semidirect
68. #485×C₈₉	C₂²	semidirect
70. #484×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
73. #479×C₈₉	C₂²	semidirect
74. #479×C₈₉	C₂²	semidirect
75. #479×C₈₉	C₂²	semidirect
77. #477×C₈₉	C₂²	semidirect
78. #476×C₈₉	C₂²	semidirect
83. #470×C₈₉	C₂²	semidirect
86. #468×C₈₉	C₂²	semidirect
89. #464×C₈₉	C₂²	semidirect
91. #462×C₈₉	C₂²	semidirect
94. #461×C₈₉	C₂²	semidirect
97. #451×C₈₉	C₂²	semidirect
101. C₈×Q₈×C₈₉	C₂²	semidirect
102. C₈×Q₈×C₈₉	C₂²	semidirect
105. #441×C₈₉	C₂²	semidirect
106. #441×C₈₉	C₂²	semidirect
107. #441×C₈₉	C₂²	semidirect
112. #440×C₈₉	C₂²	semidirect
113. C₄×Q₁₆×C₈₉	C₂²	semidirect
114. C₄×Q₁₆×C₈₉	C₂²	semidirect
123. #436×C₈₉	C₂²	semidirect
124. #436×C₈₉	C₂²	semidirect
126. #432×C₈₉	C₂²	semidirect
128. #428×C₈₉	C₂²	semidirect
129. #419×C₈₉	C₂²	semidirect
134. C₄×M₁₆×C₈₉	C₂²	semidirect
368. SD₁₆×C₈₉	#41	semidirect
563. #61463	C₈₉	direct (N × H)
572. #3482	C₂×C₈₉	semidirect
573. #3475	C₂×C₈₉	semidirect
574. #3393	C₂×C₈₉	semidirect
575. #3381	C₂×C₈₉	semidirect
576. #3364	C₂×C₈₉	semidirect
577. #3360	C₂×C₈₉	semidirect
578. #3354	C₂×C₈₉	semidirect
579. #3352	C₂×C₈₉	semidirect
580. #3330	C₂×C₈₉	semidirect
581. #3329	C₂×C₈₉	semidirect
582. #3327	C₂×C₈₉	semidirect
583. #3323	C₂×C₈₉	semidirect
584. #3276	C₂×C₈₉	semidirect
585. #3275	C₂×C₈₉	semidirect
586. #3185	C₂×C₈₉	semidirect
587. #3183	C₂×C₈₉	semidirect
588. #3117	C₂×C₈₉	semidirect
589. #3116	C₂×C₈₉	semidirect
590. #3111	C₂×C₈₉	semidirect
591. #3110	C₂×C₈₉	semidirect
592. #2971	C₂×C₈₉	semidirect
593. C₄×#137	C₂×C₈₉	semidirect
594. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
595. C₈₉	#61463	direct (N × H)
598. #557	C₂²×C₈₉	semidirect
601. #556	C₂²×C₈₉	semidirect
610. D₄×Q₈	C₂²×C₈₉	semidirect
614. #547	C₂²×C₈₉	semidirect
622. #529	C₂²×C₈₉	semidirect
628. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
631. #499	C₂²×C₈₉	semidirect
632. #498	C₂²×C₈₉	semidirect
634. #494	C₂²×C₈₉	semidirect
636. #488	C₂²×C₈₉	semidirect
637. #487	C₂²×C₈₉	semidirect
638. #487	C₂²×C₈₉	semidirect
640. #485	C₂²×C₈₉	semidirect
642. #484	C₂²×C₈₉	semidirect
643. #482	C₂²×C₈₉	semidirect
645. #479	C₂²×C₈₉	semidirect
646. #479	C₂²×C₈₉	semidirect
647. #479	C₂²×C₈₉	semidirect
649. #477	C₂²×C₈₉	semidirect
650. #476	C₂²×C₈₉	semidirect
655. #470	C₂²×C₈₉	semidirect
658. #468	C₂²×C₈₉	semidirect
661. #464	C₂²×C₈₉	semidirect
663. #462	C₂²×C₈₉	semidirect
666. #461	C₂²×C₈₉	semidirect
669. #451	C₂²×C₈₉	semidirect
673. C₈×Q₈	C₂²×C₈₉	semidirect
674. C₈×Q₈	C₂²×C₈₉	semidirect
677. #441	C₂²×C₈₉	semidirect
678. #441	C₂²×C₈₉	semidirect
679. #441	C₂²×C₈₉	semidirect
684. #440	C₂²×C₈₉	semidirect
685. C₄×Q₁₆	C₂²×C₈₉	semidirect
686. C₄×Q₁₆	C₂²×C₈₉	semidirect
695. #436	C₂²×C₈₉	semidirect
696. #436	C₂²×C₈₉	semidirect
698. #432	C₂²×C₈₉	semidirect
700. #428	C₂²×C₈₉	semidirect
701. #419	C₂²×C₈₉	semidirect
706. C₄×M₁₆	C₂²×C₈₉	semidirect
940. SD₁₆	#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×#3482	2
C₈₉×#3475	2
C₈₉×#3393	2
C₈₉×#3381	2
C₈₉×#3364	2
C₈₉×#3360	2
C₈₉×#3354	2
C₈₉×#3352	2
C₈₉×#3330	2
C₈₉×#3329	2
C₈₉×#3327	2
C₈₉×#3323	2
C₈₉×#3276	2
C₈₉×#3275	2
C₈₉×#3185	2
C₈₉×#3183	2
C₈₉×#3117	2
C₈₉×#3116	2
C₈₉×#3111	2
C₈₉×#3110	2
C₈₉×#2971	2
C₄×#137×C₈₉	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#61463	89

Subgroups — C89×#61463 #36439311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61463 #36439311