Subgroups — C₈₉×#62179 #36440027

Order 22784.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3354	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3348	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3323	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3306	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3263	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3244	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3118	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3081	C₂	1	2	yes	maximal, complemented
22	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₈₉	—	2	2	no	—
25	#559×C₈₉	C₂²	1	1	yes	characteristic
26	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	#556×C₈₉	C₂²	1	1	yes	characteristic
28	#555×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	#552×C₈₉	—	2	1	no	—
33	#552×C₈₉	C₂²	1	2	yes	complemented
34	#551×C₈₉	—	2	2	no	—
35	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	#548×C₈₉	—	2	1	no	—
37	#547×C₈₉	—	2	1	no	—
38	#547×C₈₉	C₂²	1	2	yes	complemented
39	#546×C₈₉	—	2	1	no	—
40	#546×C₈₉	C₂²	1	2	yes	—
41	D₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#544×C₈₉	—	2	1	no	—
43	#544×C₈₉	C₂²	1	2	yes	complemented
44	#542×C₈₉	—	2	1	no	—
45	#542×C₈₉	C₂²	1	2	yes	—
46	#542×C₈₉	C₂²	1	2	yes	complemented
47	#538×C₈₉	—	2	2	no	—
48	#536×C₈₉	—	2	2	no	—
49	#532×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#529×C₈₉	—	2	1	no	—
52	#529×C₈₉	C₂²	1	1	yes	characteristic
53	#529×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#124×C₈₉	—	2	1	no	—
55	#518×C₈₉	C₂²	1	2	yes	—
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	#501×C₈₉	C₂²	1	2	yes	complemented
58	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#498×C₈₉	C₂²	1	2	yes	complemented
60	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#489×C₈₉	C₂²	1	2	yes	complemented
62	#488×C₈₉	C₂²	1	2	yes	complemented
63	#486×C₈₉	C₂²	1	1	yes	characteristic
64	#486×C₈₉	C₂²	1	1	yes	characteristic
65	#485×C₈₉	C₂²	1	2	yes	complemented
66	#485×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#485×C₈₉	C₂²	1	2	yes	complemented
68	#483×C₈₉	C₂²	1	2	yes	complemented
69	#482×C₈₉	C₂²	1	2	yes	—
70	#482×C₈₉	C₂²	1	2	yes	complemented
71	#482×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#481×C₈₉	C₂²	1	2	yes	—
73	#481×C₈₉	C₂²	1	2	yes	complemented
74	#481×C₈₉	C₂²	1	2	yes	complemented
75	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#478×C₈₉	C₂²	1	2	yes	—
77	#478×C₈₉	C₂²	1	1	yes	characteristic
78	#478×C₈₉	C₂²	1	2	yes	complemented
79	#478×C₈₉	C₂²	1	2	yes	complemented
80	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#476×C₈₉	C₂²	1	1	yes	characteristic
83	#476×C₈₉	C₂²	1	1	yes	characteristic
84	#476×C₈₉	C₂²	1	2	yes	—
85	#476×C₈₉	C₂²	1	2	yes	complemented
86	#476×C₈₉	C₂²	1	2	yes	complemented
87	#476×C₈₉	C₂²	1	2	yes	complemented
88	#475×C₈₉	C₂²	1	2	yes	complemented
89	#475×C₈₉	C₂²	1	2	yes	complemented
90	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#474×C₈₉	C₂²	1	2	yes	—
92	#474×C₈₉	C₂²	1	2	yes	complemented
93	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	#470×C₈₉	C₂²	1	2	yes	complemented
95	#469×C₈₉	C₂²	1	2	yes	—
96	#469×C₈₉	C₂²	1	2	yes	complemented
97	#468×C₈₉	C₂²	1	2	yes	complemented
98	#465×C₈₉	C₂²	1	2	yes	—
99	#465×C₈₉	C₂²	1	2	yes	complemented
100	#464×C₈₉	C₂²	1	2	yes	complemented
101	#464×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#463×C₈₉	C₂²	1	1	yes	characteristic
103	#463×C₈₉	C₂²	1	2	yes	complemented
104	#463×C₈₉	C₂²	1	2	yes	complemented
105	#460×C₈₉	C₂²	1	1	yes	characteristic
106	#459×C₈₉	C₂²	1	1	yes	characteristic
107	#452×C₈₉	C₂²	1	1	yes	characteristic
108	#450×C₈₉	C₂²	1	2	yes	—
109	#449×C₈₉	C₂²	1	1	yes	characteristic
110	#447×C₈₉	C₂²	1	2	yes	—
111	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#442×C₈₉	C₂²	1	2	yes	—
114	#440×C₈₉	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	#436×C₈₉	C₂²	1	2	yes	complemented
123	#435×C₈₉	C₂²	1	2	yes	complemented
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
125	#433×C₈₉	C₂²	1	2	yes	complemented
126	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
127	#428×C₈₉	C₂²	1	2	yes	complemented
128	#428×C₈₉	C₂²	1	2	yes	complemented
129	#427×C₈₉	C₂²	1	2	yes	complemented
130	#424×C₈₉	C₂²	1	2	yes	complemented
131	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
132	#418×C₈₉	C₂²	1	2	yes	—
133	#417×C₈₉	C₂²	1	2	yes	—
134	C₂×#102×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	2	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₈₉	—	2	1	no	—
139	C₂²×Q₈×C₈₉	—	2	1	no	—
140	C₂²×D₄×C₈₉	—	2	1	no	—
141	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₈₉	C₂³	1	2	yes	—
148	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
151	C₄⋊Q₈×C₈₉	—	2	2	no	—
152	C₄⋊Q₈×C₈₉	—	2	2	no	—
153	C₄⋊Q₈×C₈₉	—	2	1	no	—
154	C₄⋊Q₈×C₈₉	—	2	1	no	—
155	C₄⋊Q₈×C₈₉	—	2	1	no	—
156	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	#127×C₈₉	C₂³	1	1	yes	characteristic
163	#126×C₈₉	—	2	2	no	—
164	#126×C₈₉	—	2	2	no	—
165	#126×C₈₉	—	2	2	no	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	1	no	—
168	#126×C₈₉	D₄	1	2	yes	—
169	#125×C₈₉	—	2	1	no	—
170	#125×C₈₉	—	2	2	no	—
171	#125×C₈₉	—	2	2	no	—
172	#125×C₈₉	D₄	1	1	yes	characteristic
173	#125×C₈₉	C₂³	1	1	yes	characteristic
174	#125×C₈₉	C₂³	1	2	yes	—
175	#124×C₈₉	—	2	1	no	—
176	#124×C₈₉	—	2	1	no	—
177	#124×C₈₉	—	2	2	no	—
178	#124×C₈₉	—	2	2	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	2	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	—	2	1	no	—
183	#124×C₈₉	D₄	1	1	yes	characteristic
184	#124×C₈₉	C₂³	1	1	yes	characteristic
185	#124×C₈₉	C₂³	1	2	yes	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	1	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	2	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	—	2	2	no	—
203	C₂²⋊Q₈×C₈₉	—	2	2	no	—
204	C₂²⋊Q₈×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
209	#121×C₈₉	—	2	2	no	—
210	#121×C₈₉	—	2	1	no	—
211	#121×C₈₉	—	2	1	no	—
212	#121×C₈₉	—	2	1	no	—
213	#121×C₈₉	—	2	2	no	—
214	#121×C₈₉	D₄	1	1	yes	characteristic
215	#121×C₈₉	C₂³	1	2	yes	—
216	#121×C₈₉	C₂³	1	1	yes	characteristic
217	#121×C₈₉	C₂³	1	2	yes	—
218	#121×C₈₉	C₂³	1	2	yes	—
219	#120×C₈₉	—	2	2	no	—
220	#120×C₈₉	—	2	2	no	—
221	C₄×Q₈×C₈₉	—	2	1	no	—
222	C₄×Q₈×C₈₉	—	2	1	no	—
223	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
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	2	no	—
233	C₄×D₄×C₈₉	—	2	2	no	—
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	1	no	—
236	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₈₉	C₂³	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	2	yes	—
240	C₄×D₄×C₈₉	C₂³	1	2	yes	—
241	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	C₂³	1	2	yes	—
243	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	#117×C₈₉	—	2	2	no	—
246	#117×C₈₉	—	2	1	no	—
247	#117×C₈₉	—	2	2	no	—
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	C₂³	1	2	yes	—
251	#117×C₈₉	C₂³	1	2	yes	—
252	#117×C₈₉	C₂³	1	1	yes	characteristic
253	#117×C₈₉	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
255	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
256	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
261	C₂×C₄²×C₈₉	—	2	1	no	—
262	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
263	#107×C₈₉	C₂³	1	2	yes	—
264	#107×C₈₉	C₂³	1	2	yes	—
265	#107×C₈₉	C₂³	1	2	yes	—
266	#107×C₈₉	C₂³	1	1	yes	characteristic
267	#107×C₈₉	C₂³	1	1	yes	characteristic
268	#106×C₈₉	C₂³	1	1	yes	characteristic
269	#106×C₈₉	C₂³	1	2	yes	—
270	#106×C₈₉	C₂³	1	2	yes	—
271	#106×C₈₉	C₂³	1	2	yes	—
272	#106×C₈₉	C₂³	1	2	yes	—
273	#106×C₈₉	C₂³	1	2	yes	—
274	#106×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	#103×C₈₉	C₂³	1	2	yes	—
285	#103×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
290	#103×C₈₉	C₂³	1	1	yes	characteristic
291	#102×C₈₉	C₂³	1	1	yes	characteristic
292	#102×C₈₉	C₂³	1	2	yes	—
293	#102×C₈₉	C₂³	1	2	yes	—
294	#102×C₈₉	C₂³	1	2	yes	—
295	#102×C₈₉	C₂³	1	2	yes	—
296	#102×C₈₉	C₂³	1	1	yes	characteristic
297	#102×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×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	2	yes	—
312	C₂⁴×C₈₉	—	2	2	no	—
313	#41×C₈₉	—	2	2	no	—
314	#41×C₈₉	—	4	1	no	—
315	#41×C₈₉	—	8	2	no	—
316	#41×C₈₉	—	8	4	no	—
317	C₂×Q₈×C₈₉	—	2	1	no	—
318	C₂×Q₈×C₈₉	—	2	1	no	—
319	C₂×Q₈×C₈₉	—	2	2	no	—
320	C₂×Q₈×C₈₉	—	2	2	no	—
321	C₂×Q₈×C₈₉	—	2	2	no	—
322	C₂×Q₈×C₈₉	—	2	1	no	—
323	C₂×Q₈×C₈₉	—	8	2	no	—
324	C₂×Q₈×C₈₉	—	8	2	no	—
325	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₈₉	—	2	4	no	—
329	C₂×D₄×C₈₉	—	2	1	no	—
330	C₂×D₄×C₈₉	—	2	1	no	—
331	C₂×D₄×C₈₉	—	2	2	no	—
332	C₂×D₄×C₈₉	—	2	2	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	—	2	1	no	—
337	C₂×D₄×C₈₉	—	4	2	no	—
338	C₂×D₄×C₈₉	—	8	2	no	—
339	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
342	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₈₉	—	2	2	no	—
345	C₂²×C₄×C₈₉	—	2	2	no	—
346	C₂²×C₄×C₈₉	—	2	1	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	2	no	—
351	C₂²×C₄×C₈₉	—	2	2	no	—
352	C₂²×C₄×C₈₉	—	2	2	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
358	Q₁₆×C₈₉	—	4	1	no	—
359	SD₁₆×C₈₉	—	2	2	no	—
360	SD₁₆×C₈₉	—	4	1	no	—
361	SD₁₆×C₈₉	—	4	2	no	—
362	D₈×C₈₉	—	2	2	no	—
363	D₈×C₈₉	—	4	2	no	—
364	M₁₆×C₈₉	—	4	2	no	—
365	M₁₆×C₈₉	—	4	2	no	—
366	C₂×C₈×C₈₉	—	4	2	no	—
367	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
372	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₈₉	—	2	1	no	—
374	C₄⋊C₄×C₈₉	—	2	1	no	—
375	C₄⋊C₄×C₈₉	—	2	2	no	—
376	C₄⋊C₄×C₈₉	—	2	2	no	—
377	C₄⋊C₄×C₈₉	—	2	2	no	—
378	C₄⋊C₄×C₈₉	—	2	2	no	—
379	C₄⋊C₄×C₈₉	—	2	1	no	—
380	C₄⋊C₄×C₈₉	—	2	1	no	—
381	C₄⋊C₄×C₈₉	—	2	2	no	—
382	C₄⋊C₄×C₈₉	—	2	2	no	—
383	C₄⋊C₄×C₈₉	—	2	2	no	—
384	C₄⋊C₄×C₈₉	—	2	1	no	—
385	C₄⋊C₄×C₈₉	—	2	1	no	—
386	C₄⋊C₄×C₈₉	—	2	1	no	—
387	C₄⋊C₄×C₈₉	—	2	1	no	—
388	C₄⋊C₄×C₈₉	—	2	2	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	1	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₈₉	—	2	2	no	—
406	C₂²⋊C₄×C₈₉	—	2	2	no	—
407	C₂²⋊C₄×C₈₉	—	2	1	no	—
408	C₂²⋊C₄×C₈₉	—	2	1	no	—
409	C₂²⋊C₄×C₈₉	—	2	2	no	—
410	C₂²⋊C₄×C₈₉	—	2	2	no	—
411	C₂²⋊C₄×C₈₉	—	2	1	no	—
412	C₂²⋊C₄×C₈₉	—	2	2	no	—
413	C₂²⋊C₄×C₈₉	—	2	2	no	—
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	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	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	1	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
431	C₄²×C₈₉	—	2	1	no	—
432	C₄²×C₈₉	—	2	1	no	—
433	C₄²×C₈₉	—	2	1	no	—
434	C₄²×C₈₉	—	2	2	no	—
435	C₄²×C₈₉	—	2	2	no	—
436	C₄²×C₈₉	—	2	1	no	—
437	C₄²×C₈₉	—	2	2	no	—
438	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
441	C₄²×C₈₉	C₂⁴	1	2	yes	—
442	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
443	C₂³×C₈₉	—	2	1	no	—
444	C₂³×C₈₉	—	2	1	no	—
445	C₂³×C₈₉	—	2	2	no	—
446	C₂³×C₈₉	—	4	4	no	—
447	C₂³×C₈₉	—	8	2	no	—
448	C₂³×C₈₉	—	8	2	no	—
449	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
450	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₈₉	—	2	2	no	—
452	Q₈×C₈₉	—	2	1	no	—
453	Q₈×C₈₉	—	2	1	no	—
454	Q₈×C₈₉	—	2	1	no	—
455	Q₈×C₈₉	—	2	1	no	—
456	Q₈×C₈₉	—	4	2	no	—
457	Q₈×C₈₉	—	8	2	no	—
458	Q₈×C₈₉	—	8	1	no	—
459	Q₈×C₈₉	—	8	1	no	—
460	Q₈×C₈₉	—	8	2	no	—
461	Q₈×C₈₉	—	8	2	no	—
462	D₄×C₈₉	—	2	2	no	—
463	D₄×C₈₉	—	2	1	no	—
464	D₄×C₈₉	—	2	2	no	—
465	D₄×C₈₉	—	2	1	no	—
466	D₄×C₈₉	—	2	1	no	—
467	D₄×C₈₉	—	2	2	no	—
468	D₄×C₈₉	—	4	2	no	—
469	D₄×C₈₉	—	4	4	no	—
470	D₄×C₈₉	—	4	2	no	—
471	D₄×C₈₉	—	4	2	no	—
472	D₄×C₈₉	—	4	2	no	—
473	D₄×C₈₉	—	8	1	no	—
474	D₄×C₈₉	—	8	2	no	—
475	D₄×C₈₉	—	8	2	no	—
476	D₄×C₈₉	—	8	2	no	—
477	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
478	C₂×C₄×C₈₉	—	2	2	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	1	no	—
481	C₂×C₄×C₈₉	—	2	2	no	—
482	C₂×C₄×C₈₉	—	2	1	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	1	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	1	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	2	no	—
492	C₂×C₄×C₈₉	—	4	1	no	—
493	C₂×C₄×C₈₉	—	4	2	no	—
494	C₂×C₄×C₈₉	—	4	4	no	—
495	C₂×C₄×C₈₉	—	4	2	no	—
496	C₂×C₄×C₈₉	—	4	2	no	—
497	C₂×C₄×C₈₉	—	8	1	no	—
498	C₂×C₄×C₈₉	—	8	2	no	—
499	C₂×C₄×C₈₉	—	8	2	no	—
500	C₂×C₄×C₈₉	—	8	2	no	—
501	C₂×C₄×C₈₉	—	8	2	no	—
502	C₂×C₄×C₈₉	—	8	2	no	—
503	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
512	C₈×C₈₉	—	2	1	no	—
513	C₈×C₈₉	—	2	1	no	—
514	C₈×C₈₉	—	2	1	no	—
515	C₈×C₈₉	—	2	2	no	—
516	C₈×C₈₉	—	2	2	no	—
517	C₈×C₈₉	—	2	1	no	—
518	C₂²×C₈₉	—	2	1	no	—
519	C₂²×C₈₉	—	2	2	no	—
520	C₂²×C₈₉	—	2	1	no	—
521	C₂²×C₈₉	—	2	2	no	—
522	C₂²×C₈₉	—	2	2	no	—
523	C₂²×C₈₉	—	2	1	no	—
524	C₂²×C₈₉	—	2	2	no	—
525	C₂²×C₈₉	—	4	1	no	—
526	C₂²×C₈₉	—	4	1	no	—
527	C₂²×C₈₉	—	4	1	no	—
528	C₂²×C₈₉	—	4	2	no	—
529	C₂²×C₈₉	—	4	2	no	—
530	C₂²×C₈₉	—	4	1	no	—
531	C₂²×C₈₉	—	4	1	no	—
532	C₂²×C₈₉	—	4	2	no	—
533	C₂²×C₈₉	—	16	4	no	—
534	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₈₉	—	2	1	no	—
536	C₄×C₈₉	—	2	1	no	—
537	C₄×C₈₉	—	2	2	no	—
538	C₄×C₈₉	—	2	1	no	—
539	C₄×C₈₉	—	2	2	no	—
540	C₄×C₈₉	—	2	1	no	—
541	C₄×C₈₉	—	2	2	no	—
542	C₄×C₈₉	—	4	2	no	—
543	C₄×C₈₉	—	4	2	no	—
544	C₄×C₈₉	—	4	1	no	—
545	C₄×C₈₉	—	4	1	no	—
546	C₄×C₈₉	—	4	1	no	—
547	C₄×C₈₉	—	4	1	no	—
548	C₄×C₈₉	—	4	1	no	—
549	C₄×C₈₉	—	4	1	no	—
550	C₄×C₈₉	—	4	2	no	—
551	C₄×C₈₉	#577	1	2	yes	—
552	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₈₉	#585	1	1	yes	characteristic
554	#62179	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₂×C₈₉	—	4	1	no	—
556	C₂×C₈₉	—	4	2	no	—
557	C₂×C₈₉	—	4	2	no	—
558	C₂×C₈₉	—	8	1	no	—
559	C₂×C₈₉	—	8	2	no	—
560	C₂×C₈₉	#3489	1	1	yes	characteristic
561	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
562	C₂×C₈₉	#3585	1	1	yes	characteristic
563	#3544	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#3514	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#3384	C₂×C₈₉	1	1	yes	characteristic, complemented
566	Q₈×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
567	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
568	#3361	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#3356	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#3354	C₂×C₈₉	1	2	yes	complemented
571	#3348	C₂×C₈₉	1	2	yes	complemented
572	#3340	C₂×C₈₉	1	1	yes	characteristic, complemented
573	#3325	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#3323	C₂×C₈₉	1	2	yes	complemented
575	#3306	C₂×C₈₉	1	2	yes	complemented
576	#3295	C₂×C₈₉	1	1	yes	characteristic, complemented
577	#3263	C₂×C₈₉	1	2	yes	complemented
578	#3251	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3244	C₂×C₈₉	1	2	yes	complemented
580	#3227	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3118	C₂×C₈₉	1	2	yes	complemented
582	#3102	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3081	C₂×C₈₉	1	2	yes	complemented
584	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
586	C₈₉	#62179	1	1	yes	characteristic, direct product factor, Sylow
587	#563	—	2	2	no	—
588	#559	C₂²×C₈₉	1	1	yes	characteristic
589	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
590	#556	C₂²×C₈₉	1	1	yes	characteristic
591	#555	C₂²×C₈₉	1	1	yes	characteristic
592	#555	C₂²×C₈₉	1	2	yes	—
593	#554	C₂²×C₈₉	1	1	yes	characteristic
594	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
595	#552	—	2	1	no	—
596	#552	C₂²×C₈₉	1	2	yes	complemented
597	#551	—	2	2	no	—
598	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
599	#548	—	2	1	no	—
600	#547	—	2	1	no	—
601	#547	C₂²×C₈₉	1	2	yes	complemented
602	#546	—	2	1	no	—
603	#546	C₂²×C₈₉	1	2	yes	—
604	D₄²	C₂²×C₈₉	1	1	yes	characteristic
605	#544	—	2	1	no	—
606	#544	C₂²×C₈₉	1	2	yes	complemented
607	#542	—	2	1	no	—
608	#542	C₂²×C₈₉	1	2	yes	—
609	#542	C₂²×C₈₉	1	2	yes	complemented
610	#538	—	2	2	no	—
611	#536	—	2	2	no	—
612	#532	C₂²×C₈₉	1	1	yes	characteristic
613	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
614	#529	—	2	1	no	—
615	#529	C₂²×C₈₉	1	1	yes	characteristic
616	#529	C₂²×C₈₉	1	1	yes	characteristic, complemented
617	C₂×#124	—	2	1	no	—
618	#518	C₂²×C₈₉	1	2	yes	—
619	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
620	#501	C₂²×C₈₉	1	2	yes	complemented
621	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
622	#498	C₂²×C₈₉	1	2	yes	complemented
623	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
624	#489	C₂²×C₈₉	1	2	yes	complemented
625	#488	C₂²×C₈₉	1	2	yes	complemented
626	#486	C₂²×C₈₉	1	1	yes	characteristic
627	#486	C₂²×C₈₉	1	1	yes	characteristic
628	#485	C₂²×C₈₉	1	2	yes	complemented
629	#485	C₂²×C₈₉	1	1	yes	characteristic, complemented
630	#485	C₂²×C₈₉	1	2	yes	complemented
631	#483	C₂²×C₈₉	1	2	yes	complemented
632	#482	C₂²×C₈₉	1	2	yes	—
633	#482	C₂²×C₈₉	1	2	yes	complemented
634	#482	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	#481	C₂²×C₈₉	1	2	yes	—
636	#481	C₂²×C₈₉	1	2	yes	complemented
637	#481	C₂²×C₈₉	1	2	yes	complemented
638	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
639	#478	C₂²×C₈₉	1	1	yes	characteristic
640	#478	C₂²×C₈₉	1	2	yes	—
641	#478	C₂²×C₈₉	1	2	yes	complemented
642	#478	C₂²×C₈₉	1	2	yes	complemented
643	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
645	#476	C₂²×C₈₉	1	1	yes	characteristic
646	#476	C₂²×C₈₉	1	1	yes	characteristic
647	#476	C₂²×C₈₉	1	2	yes	—
648	#476	C₂²×C₈₉	1	2	yes	complemented
649	#476	C₂²×C₈₉	1	2	yes	complemented
650	#476	C₂²×C₈₉	1	2	yes	complemented
651	#475	C₂²×C₈₉	1	2	yes	complemented
652	#475	C₂²×C₈₉	1	2	yes	complemented
653	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
654	#474	C₂²×C₈₉	1	2	yes	—
655	#474	C₂²×C₈₉	1	2	yes	complemented
656	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#470	C₂²×C₈₉	1	2	yes	complemented
658	#469	C₂²×C₈₉	1	2	yes	—
659	#469	C₂²×C₈₉	1	2	yes	complemented
660	#468	C₂²×C₈₉	1	2	yes	complemented
661	#465	C₂²×C₈₉	1	2	yes	—
662	#465	C₂²×C₈₉	1	2	yes	complemented
663	#464	C₂²×C₈₉	1	1	yes	characteristic, complemented
664	#464	C₂²×C₈₉	1	2	yes	complemented
665	#463	C₂²×C₈₉	1	1	yes	characteristic
666	#463	C₂²×C₈₉	1	2	yes	complemented
667	#463	C₂²×C₈₉	1	2	yes	complemented
668	#460	C₂²×C₈₉	1	1	yes	characteristic
669	#459	C₂²×C₈₉	1	1	yes	characteristic
670	#452	C₂²×C₈₉	1	1	yes	characteristic
671	#450	C₂²×C₈₉	1	2	yes	—
672	#449	C₂²×C₈₉	1	1	yes	characteristic
673	#447	C₂²×C₈₉	1	2	yes	—
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	#440	C₂²×C₈₉	1	2	yes	complemented
678	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
679	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
682	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
684	#436	C₂²×C₈₉	1	1	yes	characteristic
685	#436	C₂²×C₈₉	1	2	yes	complemented
686	#435	C₂²×C₈₉	1	2	yes	complemented
687	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
688	#433	C₂²×C₈₉	1	2	yes	complemented
689	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
690	#428	C₂²×C₈₉	1	2	yes	complemented
691	#428	C₂²×C₈₉	1	2	yes	complemented
692	#427	C₂²×C₈₉	1	2	yes	complemented
693	#424	C₂²×C₈₉	1	2	yes	complemented
694	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
695	#418	C₂²×C₈₉	1	2	yes	—
696	#417	C₂²×C₈₉	1	2	yes	—
697	C₂×#102	C₂²×C₈₉	1	2	yes	—
698	C₂×#41	—	2	2	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
709	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₈₉	1	2	yes	—
711	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
712	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
713	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
725	#127	C₂³×C₈₉	1	1	yes	characteristic
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	1	no	—
731	#126	D₄×C₈₉	1	2	yes	—
732	#125	—	2	1	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	D₄×C₈₉	1	1	yes	characteristic
736	#125	C₂³×C₈₉	1	1	yes	characteristic
737	#125	C₂³×C₈₉	1	2	yes	—
738	#124	—	2	1	no	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	D₄×C₈₉	1	1	yes	characteristic
747	#124	C₂³×C₈₉	1	1	yes	characteristic
748	#124	C₂³×C₈₉	1	2	yes	—
749	#123	—	2	2	no	—
750	#123	—	2	1	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₈₉	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	D₄×C₈₉	1	1	yes	characteristic
778	#121	C₂³×C₈₉	1	1	yes	characteristic
779	#121	C₂³×C₈₉	1	2	yes	—
780	#121	C₂³×C₈₉	1	2	yes	—
781	#121	C₂³×C₈₉	1	2	yes	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
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	C₂³×C₈₉	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₈₉	1	2	yes	—
802	C₄×D₄	C₂³×C₈₉	1	2	yes	—
803	C₄×D₄	C₂³×C₈₉	1	2	yes	—
804	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₈₉	1	2	yes	—
806	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₈₉	1	2	yes	—
808	#117	—	2	2	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	C₂³×C₈₉	1	1	yes	characteristic
814	#117	C₂³×C₈₉	1	2	yes	—
815	#117	C₂³×C₈₉	1	2	yes	—
816	#117	C₂³×C₈₉	1	2	yes	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
826	#107	C₂³×C₈₉	1	2	yes	—
827	#107	C₂³×C₈₉	1	2	yes	—
828	#107	C₂³×C₈₉	1	2	yes	—
829	#107	C₂³×C₈₉	1	1	yes	characteristic
830	#107	C₂³×C₈₉	1	1	yes	characteristic
831	#106	C₂³×C₈₉	1	1	yes	characteristic
832	#106	C₂³×C₈₉	1	2	yes	—
833	#106	C₂³×C₈₉	1	2	yes	—
834	#106	C₂³×C₈₉	1	2	yes	—
835	#106	C₂³×C₈₉	1	2	yes	—
836	#106	C₂³×C₈₉	1	2	yes	—
837	#106	C₂³×C₈₉	1	2	yes	—
838	#106	C₂³×C₈₉	1	1	yes	characteristic
839	#106	C₂³×C₈₉	1	2	yes	—
840	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
841	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
845	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
846	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
847	#103	C₂³×C₈₉	1	2	yes	—
848	#103	C₂³×C₈₉	1	2	yes	—
849	#103	C₂³×C₈₉	1	2	yes	—
850	#103	C₂³×C₈₉	1	1	yes	characteristic
851	#103	C₂³×C₈₉	1	1	yes	characteristic
852	#103	C₂³×C₈₉	1	1	yes	characteristic
853	#103	C₂³×C₈₉	1	1	yes	characteristic
854	#102	C₂³×C₈₉	1	1	yes	characteristic
855	#102	C₂³×C₈₉	1	2	yes	—
856	#102	C₂³×C₈₉	1	2	yes	—
857	#102	C₂³×C₈₉	1	2	yes	—
858	#102	C₂³×C₈₉	1	2	yes	—
859	#102	C₂³×C₈₉	1	1	yes	characteristic
860	#102	C₂³×C₈₉	1	2	yes	—
861	#102	C₂³×C₈₉	1	2	yes	—
862	#102	C₂³×C₈₉	1	1	yes	characteristic
863	#102	C₂³×C₈₉	1	1	yes	characteristic
864	#102	C₂³×C₈₉	1	2	yes	—
865	#102	C₂³×C₈₉	1	2	yes	—
866	#102	C₂³×C₈₉	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
871	#97	C₂³×C₈₉	1	2	yes	—
872	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₈₉	1	2	yes	—
875	C₂⁴	—	2	2	no	—
876	#41	—	2	2	no	—
877	#41	—	4	1	no	—
878	#41	—	8	2	no	—
879	#41	—	8	4	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	8	2	no	—
902	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
904	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
905	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
935	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1002	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₈₉	1	2	yes	—
1005	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	8	2	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1013	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	—	8	2	no	—
1022	Q₈	—	8	1	no	—
1023	Q₈	—	8	1	no	—
1024	Q₈	—	8	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	1	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	2	no	—
1040	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	16	4	no	—
1097	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	#577×C₈₉	1	2	yes	—
1115	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1116	C₄	#585×C₈₉	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	1	no	—
1121	C₂	—	8	2	no	—
1122	C₂	C₈₉×#3489	1	1	yes	characteristic
1123	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
1124	C₂	C₈₉×#3585	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×#3544	C₂	semidirect
2. C₈₉×#3514	C₂	semidirect
3. C₈₉×#3384	C₂	semidirect
4. Q₈×SD₁₆×C₈₉	C₂	semidirect
5. C₈₉×#3375	C₂	semidirect
6. C₈₉×#3361	C₂	semidirect
7. C₈₉×#3356	C₂	semidirect
8. C₈₉×#3354	C₂	semidirect
9. C₈₉×#3348	C₂	semidirect
10. C₈₉×#3340	C₂	semidirect
11. C₈₉×#3325	C₂	semidirect
12. C₈₉×#3323	C₂	semidirect
13. C₈₉×#3306	C₂	semidirect
14. C₈₉×#3295	C₂	semidirect
15. C₈₉×#3263	C₂	semidirect
16. C₈₉×#3251	C₂	semidirect
17. C₈₉×#3244	C₂	semidirect
18. C₈₉×#3227	C₂	semidirect
19. C₈₉×#3118	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#3081	C₂	semidirect
22. C₈₉×#3079	C₂	semidirect
23. C₈₉×#2993	C₂	semidirect
26. Q₈²×C₈₉	C₂²	semidirect
31. #554×C₈₉	C₂²	semidirect
33. #552×C₈₉	C₂²	semidirect
38. #547×C₈₉	C₂²	semidirect
43. #544×C₈₉	C₂²	semidirect
46. #542×C₈₉	C₂²	semidirect
50. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
53. #529×C₈₉	C₂²	semidirect
57. #501×C₈₉	C₂²	semidirect
58. #498×C₈₉	C₂²	semidirect
59. #498×C₈₉	C₂²	semidirect
60. #498×C₈₉	C₂²	semidirect
61. #489×C₈₉	C₂²	semidirect
62. #488×C₈₉	C₂²	semidirect
65. #485×C₈₉	C₂²	semidirect
66. #485×C₈₉	C₂²	semidirect
67. #485×C₈₉	C₂²	semidirect
68. #483×C₈₉	C₂²	semidirect
70. #482×C₈₉	C₂²	semidirect
71. #482×C₈₉	C₂²	semidirect
73. #481×C₈₉	C₂²	semidirect
74. #481×C₈₉	C₂²	semidirect
75. #479×C₈₉	C₂²	semidirect
78. #478×C₈₉	C₂²	semidirect
79. #478×C₈₉	C₂²	semidirect
80. #477×C₈₉	C₂²	semidirect
81. #477×C₈₉	C₂²	semidirect
85. #476×C₈₉	C₂²	semidirect
86. #476×C₈₉	C₂²	semidirect
87. #476×C₈₉	C₂²	semidirect
88. #475×C₈₉	C₂²	semidirect
89. #475×C₈₉	C₂²	semidirect
90. #475×C₈₉	C₂²	semidirect
92. #474×C₈₉	C₂²	semidirect
93. #474×C₈₉	C₂²	semidirect
94. #470×C₈₉	C₂²	semidirect
96. #469×C₈₉	C₂²	semidirect
97. #468×C₈₉	C₂²	semidirect
99. #465×C₈₉	C₂²	semidirect
100. #464×C₈₉	C₂²	semidirect
101. #464×C₈₉	C₂²	semidirect
103. #463×C₈₉	C₂²	semidirect
104. #463×C₈₉	C₂²	semidirect
111. #446×C₈₉	C₂²	semidirect
112. C₈×Q₈×C₈₉	C₂²	semidirect
114. #440×C₈₉	C₂²	semidirect
115. C₄×Q₁₆×C₈₉	C₂²	semidirect
118. C₄×SD₁₆×C₈₉	C₂²	semidirect
120. C₄×D₈×C₈₉	C₂²	semidirect
122. #436×C₈₉	C₂²	semidirect
123. #435×C₈₉	C₂²	semidirect
125. #433×C₈₉	C₂²	semidirect
126. #431×C₈₉	C₂²	semidirect
127. #428×C₈₉	C₂²	semidirect
128. #428×C₈₉	C₂²	semidirect
129. #427×C₈₉	C₂²	semidirect
130. #424×C₈₉	C₂²	semidirect
131. #423×C₈₉	C₂²	semidirect
554. #62179	C₈₉	direct (N × H)
563. #3544	C₂×C₈₉	semidirect
564. #3514	C₂×C₈₉	semidirect
565. #3384	C₂×C₈₉	semidirect
566. Q₈×SD₁₆	C₂×C₈₉	semidirect
567. #3375	C₂×C₈₉	semidirect
568. #3361	C₂×C₈₉	semidirect
569. #3356	C₂×C₈₉	semidirect
570. #3354	C₂×C₈₉	semidirect
571. #3348	C₂×C₈₉	semidirect
572. #3340	C₂×C₈₉	semidirect
573. #3325	C₂×C₈₉	semidirect
574. #3323	C₂×C₈₉	semidirect
575. #3306	C₂×C₈₉	semidirect
576. #3295	C₂×C₈₉	semidirect
577. #3263	C₂×C₈₉	semidirect
578. #3251	C₂×C₈₉	semidirect
579. #3244	C₂×C₈₉	semidirect
580. #3227	C₂×C₈₉	semidirect
581. #3118	C₂×C₈₉	semidirect
582. #3102	C₂×C₈₉	semidirect
583. #3081	C₂×C₈₉	semidirect
584. #3079	C₂×C₈₉	semidirect
585. #2993	C₂×C₈₉	semidirect
586. C₈₉	#62179	direct (N × H)
589. Q₈²	C₂²×C₈₉	semidirect
594. #554	C₂²×C₈₉	semidirect
596. #552	C₂²×C₈₉	semidirect
601. #547	C₂²×C₈₉	semidirect
606. #544	C₂²×C₈₉	semidirect
609. #542	C₂²×C₈₉	semidirect
613. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
616. #529	C₂²×C₈₉	semidirect
620. #501	C₂²×C₈₉	semidirect
621. #498	C₂²×C₈₉	semidirect
622. #498	C₂²×C₈₉	semidirect
623. #498	C₂²×C₈₉	semidirect
624. #489	C₂²×C₈₉	semidirect
625. #488	C₂²×C₈₉	semidirect
628. #485	C₂²×C₈₉	semidirect
629. #485	C₂²×C₈₉	semidirect
630. #485	C₂²×C₈₉	semidirect
631. #483	C₂²×C₈₉	semidirect
633. #482	C₂²×C₈₉	semidirect
634. #482	C₂²×C₈₉	semidirect
636. #481	C₂²×C₈₉	semidirect
637. #481	C₂²×C₈₉	semidirect
638. #479	C₂²×C₈₉	semidirect
641. #478	C₂²×C₈₉	semidirect
642. #478	C₂²×C₈₉	semidirect
643. #477	C₂²×C₈₉	semidirect
644. #477	C₂²×C₈₉	semidirect
648. #476	C₂²×C₈₉	semidirect
649. #476	C₂²×C₈₉	semidirect
650. #476	C₂²×C₈₉	semidirect
651. #475	C₂²×C₈₉	semidirect
652. #475	C₂²×C₈₉	semidirect
653. #475	C₂²×C₈₉	semidirect
655. #474	C₂²×C₈₉	semidirect
656. #474	C₂²×C₈₉	semidirect
657. #470	C₂²×C₈₉	semidirect
659. #469	C₂²×C₈₉	semidirect
660. #468	C₂²×C₈₉	semidirect
662. #465	C₂²×C₈₉	semidirect
663. #464	C₂²×C₈₉	semidirect
664. #464	C₂²×C₈₉	semidirect
666. #463	C₂²×C₈₉	semidirect
667. #463	C₂²×C₈₉	semidirect
674. #446	C₂²×C₈₉	semidirect
675. C₈×Q₈	C₂²×C₈₉	semidirect
677. #440	C₂²×C₈₉	semidirect
678. C₄×Q₁₆	C₂²×C₈₉	semidirect
681. C₄×SD₁₆	C₂²×C₈₉	semidirect
683. C₄×D₈	C₂²×C₈₉	semidirect
685. #436	C₂²×C₈₉	semidirect
686. #435	C₂²×C₈₉	semidirect
688. #433	C₂²×C₈₉	semidirect
689. #431	C₂²×C₈₉	semidirect
690. #428	C₂²×C₈₉	semidirect
691. #428	C₂²×C₈₉	semidirect
692. #427	C₂²×C₈₉	semidirect
693. #424	C₂²×C₈₉	semidirect
694. #423	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3544	2
C₈₉×#3514	2
C₈₉×#3384	2
Q₈×SD₁₆×C₈₉	2
C₈₉×#3375	2
C₈₉×#3361	2
C₈₉×#3356	2
C₈₉×#3354	2
C₈₉×#3348	2
C₈₉×#3340	2
C₈₉×#3325	2
C₈₉×#3323	2
C₈₉×#3306	2
C₈₉×#3295	2
C₈₉×#3263	2
C₈₉×#3251	2
C₈₉×#3244	2
C₈₉×#3227	2
C₈₉×#3118	2
C₈₉×#3102	2
C₈₉×#3081	2
C₈₉×#3079	2
C₈₉×#2993	2
#62179	89

Subgroups — C89×#62179 #36440027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62179 #36440027