Subgroups — C₈₉×#61462 #36439310

Order 22784.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3347	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3321	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3309	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3271	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3180	C₂	1	2	yes	maximal, complemented
17	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
18	C₈₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3111	C₂	1	2	yes	maximal, complemented
21	C₈₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2943	C₂	1	2	yes	maximal, complemented
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#135×C₈₉	C₂²	1	2	yes	—
26	#559×C₈₉	—	2	1	no	—
27	#559×C₈₉	C₂²	1	1	yes	characteristic
28	Q₈²×C₈₉	C₂²	1	1	yes	characteristic
29	#557×C₈₉	C₂²	1	1	yes	characteristic
30	#556×C₈₉	—	2	1	no	—
31	#556×C₈₉	C₂²	1	1	yes	characteristic
32	#555×C₈₉	—	2	1	no	—
33	#555×C₈₉	—	2	2	no	—
34	#555×C₈₉	C₂²	1	2	yes	—
35	#555×C₈₉	C₂²	1	1	yes	characteristic
36	#553×C₈₉	—	2	2	no	—
37	#553×C₈₉	C₂²	1	2	yes	—
38	#550×C₈₉	—	2	1	no	—
39	#550×C₈₉	C₂²	1	1	yes	characteristic
40	#550×C₈₉	C₂²	1	2	yes	—
41	#550×C₈₉	C₂²	1	1	yes	characteristic
42	#550×C₈₉	C₂²	1	1	yes	characteristic
43	#548×C₈₉	C₂²	1	2	yes	—
44	#532×C₈₉	—	2	1	no	—
45	#532×C₈₉	—	2	2	no	—
46	#532×C₈₉	—	2	1	no	—
47	#532×C₈₉	C₂²	1	1	yes	characteristic
48	#532×C₈₉	C₂²	1	2	yes	—
49	#532×C₈₉	C₂²	1	1	yes	characteristic
50	#529×C₈₉	—	2	2	no	—
51	#529×C₈₉	C₂²	1	2	yes	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	—	2	1	no	—
54	C₄×#41×C₈₉	C₂²	1	2	yes	—
55	C₄×#41×C₈₉	C₂²	1	2	yes	—
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
59	#501×C₈₉	C₂²	1	2	yes	—
60	#498×C₈₉	C₂²	1	1	yes	characteristic
61	#496×C₈₉	C₂²	1	2	yes	—
62	#493×C₈₉	C₂²	1	1	yes	characteristic
63	#490×C₈₉	C₂²	1	2	yes	—
64	#489×C₈₉	C₂²	1	2	yes	—
65	#486×C₈₉	C₂²	1	1	yes	characteristic
66	#486×C₈₉	C₂²	1	1	yes	characteristic
67	#485×C₈₉	C₂²	1	2	yes	—
68	#482×C₈₉	C₂²	1	2	yes	—
69	#482×C₈₉	C₂²	1	2	yes	—
70	#482×C₈₉	C₂²	1	2	yes	—
71	#482×C₈₉	C₂²	1	2	yes	—
72	#480×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	—
74	#478×C₈₉	C₂²	1	2	yes	—
75	#477×C₈₉	C₂²	1	1	yes	characteristic
76	#477×C₈₉	C₂²	1	1	yes	characteristic
77	#475×C₈₉	C₂²	1	2	yes	—
78	#475×C₈₉	C₂²	1	1	yes	characteristic
79	#474×C₈₉	C₂²	1	1	yes	characteristic
80	#474×C₈₉	C₂²	1	2	yes	—
81	#469×C₈₉	C₂²	1	2	yes	—
82	#469×C₈₉	C₂²	1	2	yes	—
83	#466×C₈₉	C₂²	1	2	yes	—
84	#466×C₈₉	C₂²	1	2	yes	—
85	#465×C₈₉	C₂²	1	2	yes	—
86	#465×C₈₉	C₂²	1	2	yes	—
87	#464×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#460×C₈₉	C₂²	1	1	yes	characteristic
90	#460×C₈₉	C₂²	1	2	yes	—
91	#460×C₈₉	C₂²	1	1	yes	characteristic
92	#460×C₈₉	C₂²	1	1	yes	characteristic
93	#459×C₈₉	C₂²	1	1	yes	characteristic
94	#459×C₈₉	C₂²	1	2	yes	—
95	#452×C₈₉	C₂²	1	2	yes	—
96	#449×C₈₉	C₂²	1	2	yes	—
97	#449×C₈₉	C₂²	1	2	yes	—
98	#449×C₈₉	C₂²	1	2	yes	—
99	#449×C₈₉	C₂²	1	2	yes	—
100	#448×C₈₉	C₂²	1	2	yes	—
101	#446×C₈₉	C₂²	1	1	yes	characteristic
102	#446×C₈₉	C₂²	1	1	yes	characteristic
103	#442×C₈₉	C₂²	1	2	yes	—
104	#442×C₈₉	C₂²	1	2	yes	—
105	#442×C₈₉	C₂²	1	2	yes	—
106	#442×C₈₉	C₂²	1	2	yes	—
107	#441×C₈₉	C₂²	1	1	yes	characteristic
108	#441×C₈₉	C₂²	1	2	yes	—
109	#441×C₈₉	C₂²	1	1	yes	characteristic
110	#440×C₈₉	C₂²	1	2	yes	—
111	#440×C₈₉	C₂²	1	2	yes	—
112	#440×C₈₉	C₂²	1	2	yes	—
113	#440×C₈₉	C₂²	1	2	yes	—
114	#440×C₈₉	C₂²	1	1	yes	characteristic
115	#440×C₈₉	C₂²	1	2	yes	—
116	#440×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
121	#435×C₈₉	C₂²	1	2	yes	—
122	#435×C₈₉	C₂²	1	2	yes	—
123	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
125	#432×C₈₉	C₂²	1	2	yes	—
126	#432×C₈₉	C₂²	1	1	yes	characteristic
127	#428×C₈₉	C₂²	1	1	yes	characteristic
128	#427×C₈₉	C₂²	1	2	yes	—
129	#419×C₈₉	C₂²	1	1	yes	characteristic
130	#417×C₈₉	C₂²	1	1	yes	characteristic
131	#416×C₈₉	C₂²	1	2	yes	—
132	#416×C₈₉	C₂²	1	2	yes	—
133	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
134	C₂×#97×C₈₉	C₂²	1	2	yes	—
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	—	2	1	no	—
137	C₂×#41×C₈₉	—	2	1	no	—
138	C₂×#41×C₈₉	—	2	2	no	—
139	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
140	C₂×#41×C₈₉	C₂³	1	2	yes	—
141	C₂×#41×C₈₉	C₂³	1	2	yes	—
142	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
144	#137×C₈₉	—	2	4	no	—
145	#135×C₈₉	—	2	8	no	—
146	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
153	C₂×D₈×C₈₉	C₂³	1	2	yes	—
154	C₂×D₈×C₈₉	C₂³	1	2	yes	—
155	C₂×D₈×C₈₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
159	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₈₉	—	2	1	no	—
161	C₄⋊Q₈×C₈₉	—	2	1	no	—
162	C₄⋊Q₈×C₈₉	—	2	2	no	—
163	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
166	#127×C₈₉	—	2	1	no	—
167	#127×C₈₉	—	2	2	no	—
168	#127×C₈₉	—	2	1	no	—
169	#127×C₈₉	C₂³	1	1	yes	characteristic
170	#127×C₈₉	C₂³	1	2	yes	—
171	#127×C₈₉	C₂³	1	1	yes	characteristic
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	2	no	—
175	#125×C₈₉	—	2	2	no	—
176	#125×C₈₉	C₂³	1	2	yes	—
177	#124×C₈₉	—	2	1	no	—
178	#124×C₈₉	—	2	1	no	—
179	#124×C₈₉	—	2	2	no	—
180	#124×C₈₉	—	2	2	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	—	2	1	no	—
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	C₂²⋊Q₈×C₈₉	—	2	2	no	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
192	#121×C₈₉	—	2	2	no	—
193	#121×C₈₉	—	2	1	no	—
194	#121×C₈₉	—	2	2	no	—
195	#121×C₈₉	—	2	2	no	—
196	#121×C₈₉	—	2	1	no	—
197	#121×C₈₉	—	2	2	no	—
198	#121×C₈₉	—	2	1	no	—
199	#121×C₈₉	—	2	1	no	—
200	#121×C₈₉	—	2	2	no	—
201	#121×C₈₉	—	2	2	no	—
202	#121×C₈₉	—	2	2	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	#121×C₈₉	C₂³	1	2	yes	—
208	#121×C₈₉	C₂³	1	2	yes	—
209	#121×C₈₉	C₂³	1	2	yes	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	—	2	1	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	—	2	1	no	—
214	C₄×Q₈×C₈₉	—	2	1	no	—
215	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
223	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
224	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₈₉	—	2	2	no	—
226	C₄×D₄×C₈₉	—	2	1	no	—
227	C₄×D₄×C₈₉	—	2	2	no	—
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	2	no	—
230	C₄×D₄×C₈₉	—	2	2	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	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	—	2	2	no	—
237	C₄×D₄×C₈₉	—	2	2	no	—
238	C₄×D₄×C₈₉	—	2	2	no	—
239	C₄×D₄×C₈₉	—	2	1	no	—
240	C₄×D₄×C₈₉	—	2	1	no	—
241	C₄×D₄×C₈₉	D₄	1	2	yes	—
242	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₈₉	C₂³	1	2	yes	—
247	C₄×D₄×C₈₉	C₂³	1	2	yes	—
248	C₄×D₄×C₈₉	C₂³	1	2	yes	—
249	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₈₉	C₂³	1	2	yes	—
251	#117×C₈₉	—	2	1	no	—
252	#117×C₈₉	—	2	2	no	—
253	#117×C₈₉	—	2	2	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	—	2	2	no	—
256	#117×C₈₉	—	2	1	no	—
257	#117×C₈₉	D₄	1	1	yes	characteristic
258	#117×C₈₉	D₄	1	2	yes	—
259	#117×C₈₉	C₂³	1	2	yes	—
260	#117×C₈₉	C₂³	1	2	yes	—
261	#117×C₈₉	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₈₉	—	2	1	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	2	yes	—
269	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
270	#107×C₈₉	C₂³	1	2	yes	—
271	#107×C₈₉	C₂³	1	2	yes	—
272	#107×C₈₉	C₂³	1	1	yes	characteristic
273	#107×C₈₉	C₂³	1	1	yes	characteristic
274	#107×C₈₉	C₂³	1	2	yes	—
275	#106×C₈₉	C₂³	1	1	yes	characteristic
276	#106×C₈₉	C₂³	1	2	yes	—
277	#106×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
289	#103×C₈₉	C₂³	1	1	yes	characteristic
290	#103×C₈₉	C₂³	1	1	yes	characteristic
291	#103×C₈₉	C₂³	1	1	yes	characteristic
292	#103×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	2	yes	—
297	#102×C₈₉	C₂³	1	1	yes	characteristic
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	2	yes	—
300	#102×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
308	#97×C₈₉	C₂³	1	2	yes	—
309	#97×C₈₉	C₂³	1	2	yes	—
310	#97×C₈₉	C₂³	1	2	yes	—
311	#97×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
314	#41×C₈₉	—	2	4	no	—
315	#41×C₈₉	—	2	4	no	—
316	#41×C₈₉	—	2	2	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	2	no	—
319	#41×C₈₉	—	4	2	no	—
320	#41×C₈₉	—	4	1	no	—
321	#41×C₈₉	—	4	4	no	—
322	#41×C₈₉	—	4	4	no	—
323	#41×C₈₉	—	8	4	no	—
324	#41×C₈₉	—	8	2	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	2	1	no	—
327	C₂×Q₈×C₈₉	—	2	2	no	—
328	C₂×Q₈×C₈₉	—	2	1	no	—
329	C₂×Q₈×C₈₉	—	2	2	no	—
330	C₂×Q₈×C₈₉	—	4	1	no	—
331	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	2	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	1	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	2	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	—	2	2	no	—
344	C₂×D₄×C₈₉	—	2	1	no	—
345	C₂×D₄×C₈₉	—	2	1	no	—
346	C₂×D₄×C₈₉	—	2	1	no	—
347	C₂×D₄×C₈₉	—	2	2	no	—
348	C₂×D₄×C₈₉	—	2	1	no	—
349	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
352	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
353	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₈₉	—	2	1	no	—
355	C₂²×C₄×C₈₉	—	2	1	no	—
356	C₂²×C₄×C₈₉	—	2	2	no	—
357	C₂²×C₄×C₈₉	—	2	2	no	—
358	C₂²×C₄×C₈₉	—	2	1	no	—
359	C₂²×C₄×C₈₉	—	2	2	no	—
360	C₂²×C₄×C₈₉	—	2	2	no	—
361	C₂²×C₄×C₈₉	—	2	1	no	—
362	C₂²×C₄×C₈₉	—	2	2	no	—
363	C₂²×C₄×C₈₉	—	2	1	no	—
364	C₂²×C₄×C₈₉	—	2	2	no	—
365	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
371	Q₁₆×C₈₉	—	2	2	no	—
372	Q₁₆×C₈₉	#41	1	4	yes	complemented
373	SD₁₆×C₈₉	—	2	4	no	—
374	SD₁₆×C₈₉	—	2	4	no	—
375	SD₁₆×C₈₉	—	2	2	no	—
376	SD₁₆×C₈₉	—	2	2	no	—
377	SD₁₆×C₈₉	—	4	2	no	—
378	D₈×C₈₉	—	2	4	no	—
379	D₈×C₈₉	—	4	2	no	—
380	D₈×C₈₉	—	4	2	no	—
381	M₁₆×C₈₉	—	2	2	no	—
382	M₁₆×C₈₉	—	4	1	no	—
383	C₂×C₈×C₈₉	—	2	4	no	—
384	C₂×C₈×C₈₉	—	4	2	no	—
385	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
389	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	—	2	1	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	1	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	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	1	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	2	no	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	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	1	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	1	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	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	1	no	—
438	C₄²×C₈₉	—	2	2	no	—
439	C₄²×C₈₉	—	2	1	no	—
440	C₄²×C₈₉	—	2	1	no	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	2	no	—
444	C₄²×C₈₉	—	2	1	no	—
445	C₄²×C₈₉	—	2	1	no	—
446	C₄²×C₈₉	—	2	1	no	—
447	C₄²×C₈₉	C₂×D₄	1	2	yes	—
448	C₄²×C₈₉	C₂×D₄	1	2	yes	—
449	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
452	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
453	C₄²×C₈₉	C₂⁴	1	2	yes	—
454	C₂³×C₈₉	—	2	2	no	—
455	C₂³×C₈₉	—	2	2	no	—
456	C₂³×C₈₉	—	2	1	no	—
457	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
458	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₈₉	—	2	2	no	—
460	Q₈×C₈₉	—	2	1	no	—
461	Q₈×C₈₉	—	2	1	no	—
462	Q₈×C₈₉	—	2	1	no	—
463	Q₈×C₈₉	—	2	1	no	—
464	Q₈×C₈₉	—	4	2	no	—
465	Q₈×C₈₉	—	4	2	no	—
466	Q₈×C₈₉	—	8	2	no	—
467	Q₈×C₈₉	—	8	1	no	—
468	Q₈×C₈₉	C₂×#41	1	2	yes	—
469	Q₈×C₈₉	C₂×#41	1	2	yes	—
470	D₄×C₈₉	—	2	2	no	—
471	D₄×C₈₉	—	2	2	no	—
472	D₄×C₈₉	—	2	2	no	—
473	D₄×C₈₉	—	2	1	no	—
474	D₄×C₈₉	—	2	2	no	—
475	D₄×C₈₉	—	2	1	no	—
476	D₄×C₈₉	—	2	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	—	4	4	no	—
482	D₄×C₈₉	—	4	4	no	—
483	D₄×C₈₉	—	4	2	no	—
484	D₄×C₈₉	—	4	2	no	—
485	D₄×C₈₉	—	8	1	no	—
486	D₄×C₈₉	—	8	2	no	—
487	D₄×C₈₉	—	8	1	no	—
488	D₄×C₈₉	—	8	2	no	—
489	D₄×C₈₉	—	8	2	no	—
490	D₄×C₈₉	—	8	2	no	—
491	D₄×C₈₉	—	8	2	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	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	—	2	2	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	2	1	no	—
500	C₂×C₄×C₈₉	—	2	1	no	—
501	C₂×C₄×C₈₉	—	2	1	no	—
502	C₂×C₄×C₈₉	—	2	2	no	—
503	C₂×C₄×C₈₉	—	2	2	no	—
504	C₂×C₄×C₈₉	—	2	1	no	—
505	C₂×C₄×C₈₉	—	2	1	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	4	2	no	—
508	C₂×C₄×C₈₉	—	4	1	no	—
509	C₂×C₄×C₈₉	—	4	4	no	—
510	C₂×C₄×C₈₉	—	4	4	no	—
511	C₂×C₄×C₈₉	—	4	2	no	—
512	C₂×C₄×C₈₉	—	4	2	no	—
513	C₂×C₄×C₈₉	—	4	4	no	—
514	C₂×C₄×C₈₉	—	4	4	no	—
515	C₂×C₄×C₈₉	—	4	4	no	—
516	C₂×C₄×C₈₉	—	4	2	no	—
517	C₂×C₄×C₈₉	—	4	2	no	—
518	C₂×C₄×C₈₉	—	8	2	no	—
519	C₂×C₄×C₈₉	—	8	1	no	—
520	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₈₉	—	2	2	no	—
530	C₈×C₈₉	—	2	1	no	—
531	C₈×C₈₉	—	2	1	no	—
532	C₈×C₈₉	—	2	2	no	—
533	C₈×C₈₉	—	2	1	no	—
534	C₈×C₈₉	C₂×#41	1	2	yes	—
535	C₂²×C₈₉	—	2	1	no	—
536	C₂²×C₈₉	—	2	2	no	—
537	C₂²×C₈₉	—	2	1	no	—
538	C₂²×C₈₉	—	2	2	no	—
539	C₂²×C₈₉	—	2	1	no	—
540	C₂²×C₈₉	—	2	2	no	—
541	C₂²×C₈₉	—	4	1	no	—
542	C₂²×C₈₉	—	4	2	no	—
543	C₂²×C₈₉	—	4	2	no	—
544	C₂²×C₈₉	—	4	2	no	—
545	C₂²×C₈₉	—	4	2	no	—
546	C₂²×C₈₉	—	4	1	no	—
547	C₂²×C₈₉	—	4	2	no	—
548	C₂²×C₈₉	—	4	2	no	—
549	C₂²×C₈₉	—	4	1	no	—
550	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₈₉	—	2	1	no	—
552	C₄×C₈₉	—	2	2	no	—
553	C₄×C₈₉	—	2	1	no	—
554	C₄×C₈₉	—	2	2	no	—
555	C₄×C₈₉	—	2	1	no	—
556	C₄×C₈₉	—	2	2	no	—
557	C₄×C₈₉	—	2	2	no	—
558	C₄×C₈₉	—	2	1	no	—
559	C₄×C₈₉	—	2	2	no	—
560	C₄×C₈₉	—	4	2	no	—
561	C₄×C₈₉	—	4	1	no	—
562	C₄×C₈₉	—	4	1	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	1	no	—
566	C₄×C₈₉	—	4	2	no	—
567	C₄×C₈₉	#575	1	2	yes	—
568	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
569	C₄×C₈₉	#585	1	1	yes	characteristic
570	#61462	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
571	C₂×C₈₉	—	4	1	no	—
572	C₂×C₈₉	—	4	2	no	—
573	C₂×C₈₉	—	8	2	no	—
574	C₂×C₈₉	—	8	1	no	—
575	C₂×C₈₉	—	8	2	no	—
576	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
577	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
578	C₂×C₈₉	#3585	1	1	yes	characteristic
579	#3483	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3399	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3387	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3375	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#3368	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3347	C₂×C₈₉	1	2	yes	complemented
586	#3340	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3321	C₂×C₈₉	1	2	yes	complemented
588	#3309	C₂×C₈₉	1	2	yes	complemented
589	#3305	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3304	C₂×C₈₉	1	1	yes	characteristic, complemented
591	#3287	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#3271	C₂×C₈₉	1	2	yes	complemented
593	#3184	C₂×C₈₉	1	1	yes	characteristic, complemented
594	#3180	C₂×C₈₉	1	2	yes	complemented
595	#3115	C₂×C₈₉	1	2	yes	complemented
596	#3115	C₂×C₈₉	1	1	yes	characteristic, complemented
597	#3112	C₂×C₈₉	1	1	yes	characteristic, complemented
598	#3111	C₂×C₈₉	1	2	yes	complemented
599	#2970	C₂×C₈₉	1	1	yes	characteristic, complemented
600	C₄×#137	C₂×C₈₉	1	1	yes	characteristic, complemented
601	#2943	C₂×C₈₉	1	2	yes	complemented
602	C₈₉	#61462	1	1	yes	characteristic, direct product factor, Sylow
603	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
604	C₂×#135	C₂²×C₈₉	1	2	yes	—
605	#559	—	2	1	no	—
606	#559	C₂²×C₈₉	1	1	yes	characteristic
607	Q₈²	C₂²×C₈₉	1	1	yes	characteristic
608	#557	C₂²×C₈₉	1	1	yes	characteristic
609	#556	—	2	1	no	—
610	#556	C₂²×C₈₉	1	1	yes	characteristic
611	#555	—	2	1	no	—
612	#555	—	2	2	no	—
613	#555	C₂²×C₈₉	1	1	yes	characteristic
614	#555	C₂²×C₈₉	1	2	yes	—
615	#553	—	2	2	no	—
616	#553	C₂²×C₈₉	1	2	yes	—
617	#550	—	2	1	no	—
618	#550	C₂²×C₈₉	1	1	yes	characteristic
619	#550	C₂²×C₈₉	1	2	yes	—
620	#550	C₂²×C₈₉	1	1	yes	characteristic
621	#550	C₂²×C₈₉	1	1	yes	characteristic
622	#548	C₂²×C₈₉	1	2	yes	—
623	#532	—	2	1	no	—
624	#532	—	2	2	no	—
625	#532	—	2	1	no	—
626	#532	C₂²×C₈₉	1	1	yes	characteristic
627	#532	C₂²×C₈₉	1	2	yes	—
628	#532	C₂²×C₈₉	1	1	yes	characteristic
629	#529	—	2	2	no	—
630	#529	C₂²×C₈₉	1	2	yes	—
631	C₄×#41	—	2	1	no	—
632	C₄×#41	—	2	1	no	—
633	C₄×#41	C₂²×C₈₉	1	2	yes	—
634	C₄×#41	C₂²×C₈₉	1	2	yes	—
635	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
636	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
637	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
638	#501	C₂²×C₈₉	1	2	yes	—
639	#498	C₂²×C₈₉	1	1	yes	characteristic
640	#496	C₂²×C₈₉	1	2	yes	—
641	#493	C₂²×C₈₉	1	1	yes	characteristic
642	#490	C₂²×C₈₉	1	2	yes	—
643	#489	C₂²×C₈₉	1	2	yes	—
644	#486	C₂²×C₈₉	1	1	yes	characteristic
645	#486	C₂²×C₈₉	1	1	yes	characteristic
646	#485	C₂²×C₈₉	1	2	yes	—
647	#482	C₂²×C₈₉	1	2	yes	—
648	#482	C₂²×C₈₉	1	2	yes	—
649	#482	C₂²×C₈₉	1	2	yes	—
650	#482	C₂²×C₈₉	1	2	yes	—
651	#480	C₂²×C₈₉	1	2	yes	—
652	#479	C₂²×C₈₉	1	2	yes	—
653	#478	C₂²×C₈₉	1	2	yes	—
654	#477	C₂²×C₈₉	1	1	yes	characteristic
655	#477	C₂²×C₈₉	1	1	yes	characteristic
656	#475	C₂²×C₈₉	1	1	yes	characteristic
657	#475	C₂²×C₈₉	1	2	yes	—
658	#474	C₂²×C₈₉	1	1	yes	characteristic
659	#474	C₂²×C₈₉	1	2	yes	—
660	#469	C₂²×C₈₉	1	2	yes	—
661	#469	C₂²×C₈₉	1	2	yes	—
662	#466	C₂²×C₈₉	1	2	yes	—
663	#466	C₂²×C₈₉	1	2	yes	—
664	#465	C₂²×C₈₉	1	2	yes	—
665	#465	C₂²×C₈₉	1	2	yes	—
666	#464	C₂²×C₈₉	1	2	yes	—
667	#463	C₂²×C₈₉	1	2	yes	—
668	#460	C₂²×C₈₉	1	1	yes	characteristic
669	#460	C₂²×C₈₉	1	1	yes	characteristic
670	#460	C₂²×C₈₉	1	2	yes	—
671	#460	C₂²×C₈₉	1	1	yes	characteristic
672	#459	C₂²×C₈₉	1	1	yes	characteristic
673	#459	C₂²×C₈₉	1	2	yes	—
674	#452	C₂²×C₈₉	1	2	yes	—
675	#449	C₂²×C₈₉	1	2	yes	—
676	#449	C₂²×C₈₉	1	2	yes	—
677	#449	C₂²×C₈₉	1	2	yes	—
678	#449	C₂²×C₈₉	1	2	yes	—
679	#448	C₂²×C₈₉	1	2	yes	—
680	#446	C₂²×C₈₉	1	1	yes	characteristic
681	#446	C₂²×C₈₉	1	1	yes	characteristic
682	#442	C₂²×C₈₉	1	2	yes	—
683	#442	C₂²×C₈₉	1	2	yes	—
684	#442	C₂²×C₈₉	1	2	yes	—
685	#442	C₂²×C₈₉	1	2	yes	—
686	#441	C₂²×C₈₉	1	1	yes	characteristic
687	#441	C₂²×C₈₉	1	2	yes	—
688	#441	C₂²×C₈₉	1	1	yes	characteristic
689	#440	C₂²×C₈₉	1	2	yes	—
690	#440	C₂²×C₈₉	1	2	yes	—
691	#440	C₂²×C₈₉	1	2	yes	—
692	#440	C₂²×C₈₉	1	2	yes	—
693	#440	C₂²×C₈₉	1	1	yes	characteristic
694	#440	C₂²×C₈₉	1	2	yes	—
695	#440	C₂²×C₈₉	1	1	yes	characteristic
696	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
697	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
698	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
700	#435	C₂²×C₈₉	1	2	yes	—
701	#435	C₂²×C₈₉	1	2	yes	—
702	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
703	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
704	#432	C₂²×C₈₉	1	2	yes	—
705	#432	C₂²×C₈₉	1	1	yes	characteristic
706	#428	C₂²×C₈₉	1	1	yes	characteristic
707	#427	C₂²×C₈₉	1	2	yes	—
708	#419	C₂²×C₈₉	1	1	yes	characteristic
709	#417	C₂²×C₈₉	1	1	yes	characteristic
710	#416	C₂²×C₈₉	1	2	yes	—
711	#416	C₂²×C₈₉	1	2	yes	—
712	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
713	C₂×#97	C₂²×C₈₉	1	2	yes	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	2	no	—
718	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
719	C₂×#41	C₂³×C₈₉	1	2	yes	—
720	C₂×#41	C₂³×C₈₉	1	2	yes	—
721	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
723	#137	—	2	4	no	—
724	#135	—	2	8	no	—
725	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
732	C₂×D₈	C₂³×C₈₉	1	2	yes	—
733	C₂×D₈	C₂³×C₈₉	1	2	yes	—
734	C₂×D₈	C₂³×C₈₉	1	2	yes	—
735	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
737	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
738	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
743	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
745	#127	—	2	1	no	—
746	#127	—	2	2	no	—
747	#127	—	2	1	no	—
748	#127	C₂³×C₈₉	1	2	yes	—
749	#127	C₂³×C₈₉	1	1	yes	characteristic
750	#127	C₂³×C₈₉	1	1	yes	characteristic
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	C₂³×C₈₉	1	2	yes	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	C₂³×C₈₉	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	C₂³×C₈₉	1	2	yes	—
785	#121	C₂³×C₈₉	1	2	yes	—
786	#121	C₂³×C₈₉	1	2	yes	—
787	#121	C₂³×C₈₉	1	2	yes	—
788	#121	C₂³×C₈₉	1	2	yes	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	D₄×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	1	yes	characteristic
799	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
801	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
803	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	D₄×C₈₉	1	2	yes	—
821	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₉	1	2	yes	—
823	C₄×D₄	C₂³×C₈₉	1	2	yes	—
824	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₈₉	1	2	yes	—
827	C₄×D₄	C₂³×C₈₉	1	2	yes	—
828	C₄×D₄	C₂³×C₈₉	1	2	yes	—
829	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	—	2	1	no	—
836	#117	D₄×C₈₉	1	1	yes	characteristic
837	#117	D₄×C₈₉	1	2	yes	—
838	#117	C₂³×C₈₉	1	2	yes	—
839	#117	C₂³×C₈₉	1	2	yes	—
840	#117	C₂³×C₈₉	1	1	yes	characteristic
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	2	2	no	—
845	C₂×C₄²	—	2	2	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
849	#107	C₂³×C₈₉	1	2	yes	—
850	#107	C₂³×C₈₉	1	2	yes	—
851	#107	C₂³×C₈₉	1	1	yes	characteristic
852	#107	C₂³×C₈₉	1	1	yes	characteristic
853	#107	C₂³×C₈₉	1	2	yes	—
854	#106	C₂³×C₈₉	1	1	yes	characteristic
855	#106	C₂³×C₈₉	1	2	yes	—
856	#106	C₂³×C₈₉	1	1	yes	characteristic
857	#106	C₂³×C₈₉	1	2	yes	—
858	#106	C₂³×C₈₉	1	2	yes	—
859	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
862	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
863	#103	C₂³×C₈₉	1	1	yes	characteristic
864	#103	C₂³×C₈₉	1	1	yes	characteristic
865	#103	C₂³×C₈₉	1	2	yes	—
866	#103	C₂³×C₈₉	1	2	yes	—
867	#103	C₂³×C₈₉	1	1	yes	characteristic
868	#103	C₂³×C₈₉	1	1	yes	characteristic
869	#103	C₂³×C₈₉	1	1	yes	characteristic
870	#103	C₂³×C₈₉	1	1	yes	characteristic
871	#103	C₂³×C₈₉	1	2	yes	—
872	#102	C₂³×C₈₉	1	2	yes	—
873	#102	C₂³×C₈₉	1	2	yes	—
874	#102	C₂³×C₈₉	1	2	yes	—
875	#102	C₂³×C₈₉	1	2	yes	—
876	#102	C₂³×C₈₉	1	1	yes	characteristic
877	#102	C₂³×C₈₉	1	1	yes	characteristic
878	#102	C₂³×C₈₉	1	2	yes	—
879	#102	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	2	yes	—
882	#102	C₂³×C₈₉	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
886	#97	C₂³×C₈₉	1	1	yes	characteristic
887	#97	C₂³×C₈₉	1	2	yes	—
888	#97	C₂³×C₈₉	1	2	yes	—
889	#97	C₂³×C₈₉	1	2	yes	—
890	#97	C₂³×C₈₉	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
893	#41	—	2	4	no	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	1	no	—
900	#41	—	4	4	no	—
901	#41	—	4	4	no	—
902	#41	—	8	4	no	—
903	#41	—	8	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
929	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
930	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
931	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
932	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
945	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
947	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
950	Q₁₆	—	2	2	no	—
951	Q₁₆	#41×C₈₉	1	4	yes	complemented
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	4	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	2	no	—
960	M₁₆	—	2	2	no	—
961	M₁₆	—	4	1	no	—
962	C₂×C₈	—	2	4	no	—
963	C₂×C₈	—	4	2	no	—
964	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
968	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
969	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1027	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1028	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₈₉	1	2	yes	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1037	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	2	no	—
1046	Q₈	—	8	1	no	—
1047	Q₈	C₂×#41×C₈₉	1	2	yes	—
1048	Q₈	C₂×#41×C₈₉	1	2	yes	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	8	1	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1108	C₈	—	2	2	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	C₂×#41×C₈₉	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	#575×C₈₉	1	2	yes	—
1147	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1148	C₄	#585×C₈₉	1	1	yes	characteristic
1149	C₂	—	4	1	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	2	no	—
1154	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1155	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1156	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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3483	C₂	semidirect
2. C₈₉×#3480	C₂	semidirect
3. C₈₉×#3399	C₂	semidirect
4. C₈₉×#3387	C₂	semidirect
5. C₈₉×#3375	C₂	semidirect
6. C₈₉×#3368	C₂	semidirect
7. C₈₉×#3347	C₂	semidirect
8. C₈₉×#3340	C₂	semidirect
9. C₈₉×#3321	C₂	semidirect
10. C₈₉×#3309	C₂	semidirect
11. C₈₉×#3305	C₂	semidirect
12. C₈₉×#3304	C₂	semidirect
13. C₈₉×#3287	C₂	semidirect
14. C₈₉×#3271	C₂	semidirect
15. C₈₉×#3184	C₂	semidirect
16. C₈₉×#3180	C₂	semidirect
17. C₈₉×#3115	C₂	semidirect
18. C₈₉×#3115	C₂	semidirect
19. C₈₉×#3112	C₂	semidirect
20. C₈₉×#3111	C₂	semidirect
21. C₈₉×#2970	C₂	semidirect
22. C₄×#137×C₈₉	C₂	semidirect
23. C₈₉×#2943	C₂	semidirect
372. Q₁₆×C₈₉	#41	semidirect
570. #61462	C₈₉	direct (N × H)
579. #3483	C₂×C₈₉	semidirect
580. #3480	C₂×C₈₉	semidirect
581. #3399	C₂×C₈₉	semidirect
582. #3387	C₂×C₈₉	semidirect
583. #3375	C₂×C₈₉	semidirect
584. #3368	C₂×C₈₉	semidirect
585. #3347	C₂×C₈₉	semidirect
586. #3340	C₂×C₈₉	semidirect
587. #3321	C₂×C₈₉	semidirect
588. #3309	C₂×C₈₉	semidirect
589. #3305	C₂×C₈₉	semidirect
590. #3304	C₂×C₈₉	semidirect
591. #3287	C₂×C₈₉	semidirect
592. #3271	C₂×C₈₉	semidirect
593. #3184	C₂×C₈₉	semidirect
594. #3180	C₂×C₈₉	semidirect
595. #3115	C₂×C₈₉	semidirect
596. #3115	C₂×C₈₉	semidirect
597. #3112	C₂×C₈₉	semidirect
598. #3111	C₂×C₈₉	semidirect
599. #2970	C₂×C₈₉	semidirect
600. C₄×#137	C₂×C₈₉	semidirect
601. #2943	C₂×C₈₉	semidirect
602. C₈₉	#61462	direct (N × H)
951. Q₁₆	#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×#3483	2
C₈₉×#3480	2
C₈₉×#3399	2
C₈₉×#3387	2
C₈₉×#3375	2
C₈₉×#3368	2
C₈₉×#3347	2
C₈₉×#3340	2
C₈₉×#3321	2
C₈₉×#3309	2
C₈₉×#3305	2
C₈₉×#3304	2
C₈₉×#3287	2
C₈₉×#3271	2
C₈₉×#3184	2
C₈₉×#3180	2
C₈₉×#3115	2
C₈₉×#3112	2
C₈₉×#3111	2
C₈₉×#2970	2
C₄×#137×C₈₉	2
C₈₉×#2943	2
#61462	89

Subgroups — C89×#61462 #36439310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61462 #36439310