Subgroups — C₈₉×#62582 #36440430

Order 22784.

1770 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3514	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3375	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3369	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3316	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3314	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3299	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3295	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3239	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3215	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3181	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#489×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₂²	1	1	yes	characteristic
19	Q₈²×C₈₉	C₂²	1	2	yes	complemented
20	#557×C₈₉	—	2	1	no	—
21	#556×C₈₉	C₂²	1	1	yes	characteristic
22	#555×C₈₉	—	2	1	no	—
23	#554×C₈₉	C₂²	1	2	yes	—
24	#554×C₈₉	C₂²	1	4	yes	complemented
25	#551×C₈₉	—	2	2	no	—
26	D₄×Q₈×C₈₉	—	2	1	no	—
27	D₄×Q₈×C₈₉	—	2	2	no	—
28	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	#548×C₈₉	C₂²	1	2	yes	—
30	#546×C₈₉	—	2	1	no	—
31	#546×C₈₉	C₂²	1	2	yes	—
32	D₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#544×C₈₉	—	2	2	no	—
34	#544×C₈₉	—	2	1	no	—
35	#542×C₈₉	—	2	1	no	—
36	#538×C₈₉	—	2	2	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	#533×C₈₉	C₂²	1	2	yes	complemented
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
41	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#529×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	C₂²	1	2	yes	—
44	C₂×#124×C₈₉	C₂²	1	2	yes	—
45	#520×C₈₉	—	2	1	no	—
46	#518×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	#501×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#501×C₈₉	C₂²	1	2	yes	complemented
50	#497×C₈₉	C₂²	1	1	yes	characteristic
51	#497×C₈₉	C₂²	1	2	yes	complemented
52	#491×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	#489×C₈₉	C₂²	1	4	yes	—
54	#489×C₈₉	C₂²	1	1	yes	characteristic
55	#489×C₈₉	C₂²	1	2	yes	—
56	#489×C₈₉	C₂²	1	4	yes	complemented
57	#489×C₈₉	C₂²	1	2	yes	complemented
58	#489×C₈₉	C₂²	1	2	yes	complemented
59	#489×C₈₉	C₂²	1	2	yes	complemented
60	#487×C₈₉	C₂²	1	2	yes	complemented
61	#486×C₈₉	C₂²	1	2	yes	—
62	#484×C₈₉	C₂²	1	4	yes	complemented
63	#483×C₈₉	C₂²	1	2	yes	complemented
64	#481×C₈₉	C₂²	1	4	yes	—
65	#480×C₈₉	C₂²	1	2	yes	—
66	#477×C₈₉	C₂²	1	2	yes	complemented
67	#476×C₈₉	C₂²	1	2	yes	—
68	#475×C₈₉	C₂²	1	4	yes	complemented
69	#474×C₈₉	C₂²	1	4	yes	complemented
70	#470×C₈₉	C₂²	1	2	yes	complemented
71	#468×C₈₉	C₂²	1	2	yes	—
72	#467×C₈₉	C₂²	1	4	yes	complemented
73	#465×C₈₉	C₂²	1	4	yes	—
74	#464×C₈₉	C₂²	1	4	yes	—
75	#464×C₈₉	C₂²	1	4	yes	complemented
76	#462×C₈₉	C₂²	1	2	yes	complemented
77	#460×C₈₉	C₂²	1	2	yes	—
78	#452×C₈₉	C₂²	1	4	yes	complemented
79	#451×C₈₉	C₂²	1	4	yes	complemented
80	#450×C₈₉	C₂²	1	4	yes	—
81	#446×C₈₉	C₂²	1	2	yes	complemented
82	#441×C₈₉	C₂²	1	4	yes	complemented
83	#440×C₈₉	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
86	#435×C₈₉	C₂²	1	4	yes	complemented
87	C₈×D₄×C₈₉	C₂²	1	2	yes	—
88	#432×C₈₉	C₂²	1	2	yes	complemented
89	#432×C₈₉	C₂²	1	1	yes	characteristic, complemented
90	#417×C₈₉	C₂²	1	4	yes	complemented
91	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
92	C₂×#102×C₈₉	C₂²	1	4	yes	—
93	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×#97×C₈₉	C₂²	1	2	yes	complemented
95	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
96	C₂×#41×C₈₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₈₉	—	2	2	no	—
98	C₂²×Q₈×C₈₉	—	2	1	no	—
99	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₈₉	—	2	1	no	—
109	C₄⋊Q₈×C₈₉	—	2	2	no	—
110	C₄⋊Q₈×C₈₉	—	2	4	no	—
111	C₄⋊Q₈×C₈₉	—	2	2	no	—
112	C₄⋊Q₈×C₈₉	—	2	1	no	—
113	C₄⋊Q₈×C₈₉	—	2	1	no	—
114	C₄⋊Q₈×C₈₉	—	2	2	no	—
115	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
121	#127×C₈₉	C₂³	1	1	yes	characteristic
122	#126×C₈₉	—	2	2	no	—
123	#126×C₈₉	—	2	2	no	—
124	#126×C₈₉	—	2	1	no	—
125	#125×C₈₉	—	2	2	no	—
126	#125×C₈₉	—	2	4	no	—
127	#125×C₈₉	—	2	2	no	—
128	#125×C₈₉	—	2	1	no	—
129	#125×C₈₉	C₂³	1	1	yes	characteristic
130	#124×C₈₉	—	2	1	no	—
131	#124×C₈₉	—	2	2	no	—
132	#124×C₈₉	—	2	2	no	—
133	#124×C₈₉	—	2	2	no	—
134	#124×C₈₉	C₂³	1	2	yes	—
135	#124×C₈₉	C₂³	1	2	yes	—
136	#124×C₈₉	C₂³	1	1	yes	characteristic
137	#124×C₈₉	C₂³	1	2	yes	—
138	#123×C₈₉	—	2	1	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	1	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	2	no	—
146	C₂²⋊Q₈×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	4	no	—
148	C₂²⋊Q₈×C₈₉	—	2	4	no	—
149	C₂²⋊Q₈×C₈₉	—	2	4	no	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
154	#121×C₈₉	—	2	2	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	—	2	2	no	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#121×C₈₉	C₂³	1	1	yes	characteristic
161	#120×C₈₉	—	2	2	no	—
162	#120×C₈₉	—	2	2	no	—
163	C₄×Q₈×C₈₉	—	2	2	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	—	2	2	no	—
166	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₈₉	—	2	1	no	—
173	C₄×D₄×C₈₉	—	2	2	no	—
174	C₄×D₄×C₈₉	—	2	4	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	1	no	—
181	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
182	C₄×D₄×C₈₉	D₄	1	2	yes	—
183	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂³	1	2	yes	—
185	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₈₉	C₂³	1	2	yes	—
187	#117×C₈₉	—	2	2	no	—
188	#117×C₈₉	—	2	1	no	—
189	#117×C₈₉	—	2	1	no	—
190	#117×C₈₉	—	2	1	no	—
191	#117×C₈₉	—	2	2	no	—
192	#117×C₈₉	D₄	1	2	yes	—
193	#117×C₈₉	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
195	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	#107×C₈₉	C₂³	1	2	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#106×C₈₉	C₂³	1	2	yes	—
206	#106×C₈₉	C₂³	1	4	yes	—
207	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
209	#103×C₈₉	C₂³	1	2	yes	—
210	#103×C₈₉	C₂³	1	4	yes	—
211	#103×C₈₉	C₂³	1	4	yes	—
212	#103×C₈₉	C₂³	1	4	yes	—
213	#103×C₈₉	C₂³	1	4	yes	—
214	#103×C₈₉	C₂³	1	2	yes	—
215	#103×C₈₉	C₂³	1	2	yes	—
216	#102×C₈₉	C₂³	1	2	yes	—
217	#102×C₈₉	C₂³	1	4	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
223	#97×C₈₉	C₂³	1	1	yes	characteristic
224	#97×C₈₉	C₂³	1	2	yes	—
225	#97×C₈₉	C₂³	1	4	yes	—
226	#97×C₈₉	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₈₉	C₂³	1	2	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	#41×C₈₉	—	2	4	no	—
230	#41×C₈₉	—	4	4	no	—
231	C₂×Q₈×C₈₉	—	2	1	no	—
232	C₂×Q₈×C₈₉	—	2	2	no	—
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	4	no	—
235	C₂×Q₈×C₈₉	—	2	2	no	—
236	C₂×Q₈×C₈₉	—	4	4	no	—
237	C₂×Q₈×C₈₉	—	8	4	no	—
238	C₂×Q₈×C₈₉	—	8	2	no	—
239	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	1	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	1	no	—
247	C₂×D₄×C₈₉	—	2	1	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	4	4	no	—
250	C₂×D₄×C₈₉	—	4	4	no	—
251	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	4	no	—
258	C₂²×C₄×C₈₉	—	2	1	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₈₉	—	4	4	no	—
268	Q₁₆×C₈₉	—	4	2	no	—
269	SD₁₆×C₈₉	—	4	4	no	—
270	SD₁₆×C₈₉	—	4	2	no	—
271	M₁₆×C₈₉	—	4	2	no	—
272	C₂×C₈×C₈₉	—	4	4	no	—
273	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
274	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
276	C₄⋊C₄×C₈₉	—	2	1	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	4	no	—
279	C₄⋊C₄×C₈₉	—	2	2	no	—
280	C₄⋊C₄×C₈₉	—	2	2	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	1	no	—
283	C₄⋊C₄×C₈₉	—	2	1	no	—
284	C₄⋊C₄×C₈₉	—	2	1	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	2	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	4	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	4	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	1	no	—
296	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₈₉	—	2	2	no	—
305	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	—	2	4	no	—
307	C₂²⋊C₄×C₈₉	—	2	1	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	1	no	—
310	C₂²⋊C₄×C₈₉	—	2	1	no	—
311	C₂²⋊C₄×C₈₉	—	2	1	no	—
312	C₂²⋊C₄×C₈₉	—	2	2	no	—
313	C₂²⋊C₄×C₈₉	—	2	2	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	1	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
323	C₄²×C₈₉	—	2	2	no	—
324	C₄²×C₈₉	—	2	1	no	—
325	C₄²×C₈₉	—	2	4	no	—
326	C₄²×C₈₉	—	2	2	no	—
327	C₄²×C₈₉	C₂×D₄	1	2	yes	—
328	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₈₉	C₂×D₄	1	2	yes	—
331	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₄²×C₈₉	C₂⁴	1	2	yes	—
334	C₂³×C₈₉	—	2	1	no	—
335	C₂³×C₈₉	—	2	2	no	—
336	C₂³×C₈₉	—	4	4	no	—
337	C₂³×C₈₉	—	8	2	no	—
338	C₂³×C₈₉	—	8	2	no	—
339	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
341	Q₈×C₈₉	—	2	2	no	—
342	Q₈×C₈₉	—	2	2	no	—
343	Q₈×C₈₉	—	2	2	no	—
344	Q₈×C₈₉	—	2	2	no	—
345	Q₈×C₈₉	—	2	4	no	—
346	Q₈×C₈₉	—	4	2	no	—
347	Q₈×C₈₉	—	4	4	no	—
348	Q₈×C₈₉	—	8	2	no	—
349	Q₈×C₈₉	—	8	4	no	—
350	Q₈×C₈₉	—	8	2	no	—
351	D₄×C₈₉	—	2	4	no	—
352	D₄×C₈₉	—	2	2	no	—
353	D₄×C₈₉	—	2	4	no	—
354	D₄×C₈₉	—	4	4	no	—
355	D₄×C₈₉	—	4	2	no	—
356	D₄×C₈₉	—	8	1	no	—
357	D₄×C₈₉	—	8	2	no	—
358	D₄×C₈₉	—	8	1	no	—
359	D₄×C₈₉	—	8	2	no	—
360	D₄×C₈₉	#137	1	4	yes	—
361	C₂×C₄×C₈₉	—	2	4	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	4	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	4	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	4	2	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	2	no	—
375	C₂×C₄×C₈₉	—	8	2	no	—
376	C₂×C₄×C₈₉	—	8	2	no	—
377	C₂×C₄×C₈₉	—	8	2	no	—
378	C₂×C₄×C₈₉	—	8	4	no	—
379	C₂×C₄×C₈₉	—	8	2	no	—
380	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
389	C₈×C₈₉	—	2	2	no	—
390	C₈×C₈₉	—	2	4	no	—
391	C₈×C₈₉	—	2	2	no	—
392	C₂²×C₈₉	—	2	2	no	—
393	C₂²×C₈₉	—	2	2	no	—
394	C₂²×C₈₉	—	2	1	no	—
395	C₂²×C₈₉	—	2	1	no	—
396	C₂²×C₈₉	—	2	1	no	—
397	C₂²×C₈₉	—	4	2	no	—
398	C₂²×C₈₉	—	4	1	no	—
399	C₂²×C₈₉	—	4	2	no	—
400	C₂²×C₈₉	—	4	1	no	—
401	C₂²×C₈₉	—	4	1	no	—
402	C₂²×C₈₉	—	4	2	no	—
403	C₂²×C₈₉	—	16	4	no	—
404	C₂²×C₈₉	C₂×#137	1	4	yes	—
405	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
406	C₄×C₈₉	—	2	1	no	—
407	C₄×C₈₉	—	2	2	no	—
408	C₄×C₈₉	—	2	1	no	—
409	C₄×C₈₉	—	2	1	no	—
410	C₄×C₈₉	—	2	2	no	—
411	C₄×C₈₉	—	2	1	no	—
412	C₄×C₈₉	—	2	2	no	—
413	C₄×C₈₉	—	4	1	no	—
414	C₄×C₈₉	—	4	2	no	—
415	C₄×C₈₉	—	4	4	no	—
416	C₄×C₈₉	—	4	2	no	—
417	C₄×C₈₉	—	4	1	no	—
418	C₄×C₈₉	—	4	2	no	—
419	C₄×C₈₉	—	4	1	no	—
420	C₄×C₈₉	C₂×#137	1	2	yes	—
421	C₄×C₈₉	#585	1	2	yes	—
422	#62582	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
423	C₂×C₈₉	—	2	4	no	—
424	C₂×C₈₉	—	4	1	no	—
425	C₂×C₈₉	—	8	2	no	—
426	C₂×C₈₉	—	8	1	no	—
427	C₂×C₈₉	#3500	1	1	yes	characteristic
428	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
429	C₂×C₈₉	#3585	1	1	yes	characteristic
430	#3514	C₂×C₈₉	1	1	yes	characteristic
431	#3503	C₂×C₈₉	1	1	yes	characteristic, complemented
432	#3375	C₂×C₈₉	1	2	yes	complemented
433	#3369	C₂×C₈₉	1	2	yes	complemented
434	#3316	C₂×C₈₉	1	4	yes	complemented
435	#3314	C₂×C₈₉	1	4	yes	complemented
436	#3299	C₂×C₈₉	1	2	yes	complemented
437	#3295	C₂×C₈₉	1	2	yes	complemented
438	#3239	C₂×C₈₉	1	2	yes	complemented
439	#3238	C₂×C₈₉	1	1	yes	characteristic, complemented
440	#3216	C₂×C₈₉	1	1	yes	characteristic, complemented
441	#3215	C₂×C₈₉	1	2	yes	complemented
442	#3181	C₂×C₈₉	1	2	yes	complemented
443	#3172	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
445	C₂×#489	C₂×C₈₉	1	2	yes	complemented
446	#2970	C₂×C₈₉	1	1	yes	characteristic, complemented
447	C₈₉	#62582	1	1	yes	characteristic, direct product factor, Sylow
448	#559	C₂²×C₈₉	1	1	yes	characteristic
449	Q₈²	C₂²×C₈₉	1	2	yes	complemented
450	#557	—	2	1	no	—
451	#556	C₂²×C₈₉	1	1	yes	characteristic
452	#555	—	2	1	no	—
453	#554	C₂²×C₈₉	1	2	yes	—
454	#554	C₂²×C₈₉	1	4	yes	complemented
455	#551	—	2	2	no	—
456	D₄×Q₈	—	2	1	no	—
457	D₄×Q₈	—	2	2	no	—
458	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
459	#548	C₂²×C₈₉	1	2	yes	—
460	#546	—	2	1	no	—
461	#546	C₂²×C₈₉	1	2	yes	—
462	D₄²	C₂²×C₈₉	1	1	yes	characteristic
463	#544	—	2	2	no	—
464	#544	—	2	1	no	—
465	#542	—	2	1	no	—
466	#538	—	2	2	no	—
467	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
468	#533	C₂²×C₈₉	1	2	yes	complemented
469	#532	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
471	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
472	#529	C₂²×C₈₉	1	1	yes	characteristic
473	#529	C₂²×C₈₉	1	2	yes	—
474	C₂×#124	C₂²×C₈₉	1	2	yes	—
475	#520	—	2	1	no	—
476	#518	—	2	1	no	—
477	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
478	#501	C₂²×C₈₉	1	1	yes	characteristic, complemented
479	#501	C₂²×C₈₉	1	2	yes	complemented
480	#497	C₂²×C₈₉	1	1	yes	characteristic
481	#497	C₂²×C₈₉	1	2	yes	complemented
482	#491	C₂²×C₈₉	1	1	yes	characteristic, complemented
483	#489	C₂²×C₈₉	1	4	yes	—
484	#489	C₂²×C₈₉	1	1	yes	characteristic
485	#489	C₂²×C₈₉	1	2	yes	—
486	#489	C₂²×C₈₉	1	4	yes	complemented
487	#489	C₂²×C₈₉	1	2	yes	complemented
488	#489	C₂²×C₈₉	1	2	yes	complemented
489	#489	C₂²×C₈₉	1	2	yes	complemented
490	#487	C₂²×C₈₉	1	2	yes	complemented
491	#486	C₂²×C₈₉	1	2	yes	—
492	#484	C₂²×C₈₉	1	4	yes	complemented
493	#483	C₂²×C₈₉	1	2	yes	complemented
494	#481	C₂²×C₈₉	1	4	yes	—
495	#480	C₂²×C₈₉	1	2	yes	—
496	#477	C₂²×C₈₉	1	2	yes	complemented
497	#476	C₂²×C₈₉	1	2	yes	—
498	#475	C₂²×C₈₉	1	4	yes	complemented
499	#474	C₂²×C₈₉	1	4	yes	complemented
500	#470	C₂²×C₈₉	1	2	yes	complemented
501	#468	C₂²×C₈₉	1	2	yes	—
502	#467	C₂²×C₈₉	1	4	yes	complemented
503	#465	C₂²×C₈₉	1	4	yes	—
504	#464	C₂²×C₈₉	1	4	yes	—
505	#464	C₂²×C₈₉	1	4	yes	complemented
506	#462	C₂²×C₈₉	1	2	yes	complemented
507	#460	C₂²×C₈₉	1	2	yes	—
508	#452	C₂²×C₈₉	1	4	yes	complemented
509	#451	C₂²×C₈₉	1	4	yes	complemented
510	#450	C₂²×C₈₉	1	4	yes	—
511	#446	C₂²×C₈₉	1	2	yes	complemented
512	#441	C₂²×C₈₉	1	4	yes	complemented
513	#440	C₂²×C₈₉	1	4	yes	complemented
514	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
515	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
516	#435	C₂²×C₈₉	1	4	yes	complemented
517	C₈×D₄	C₂²×C₈₉	1	2	yes	—
518	#432	C₂²×C₈₉	1	2	yes	complemented
519	#432	C₂²×C₈₉	1	1	yes	characteristic, complemented
520	#417	C₂²×C₈₉	1	4	yes	complemented
521	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
522	C₂×#102	C₂²×C₈₉	1	4	yes	—
523	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	C₂×#97	C₂²×C₈₉	1	2	yes	complemented
525	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
526	C₂×#41	C₂³×C₈₉	1	2	yes	—
527	C₂²×Q₈	—	2	2	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
532	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
536	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
537	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	—	2	4	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
551	#127	C₂³×C₈₉	1	1	yes	characteristic
552	#126	—	2	2	no	—
553	#126	—	2	2	no	—
554	#126	—	2	1	no	—
555	#125	—	2	2	no	—
556	#125	—	2	4	no	—
557	#125	—	2	2	no	—
558	#125	—	2	1	no	—
559	#125	C₂³×C₈₉	1	1	yes	characteristic
560	#124	—	2	1	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	C₂³×C₈₉	1	1	yes	characteristic
565	#124	C₂³×C₈₉	1	2	yes	—
566	#124	C₂³×C₈₉	1	2	yes	—
567	#124	C₂³×C₈₉	1	2	yes	—
568	#123	—	2	1	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	C₂³×C₈₉	1	2	yes	—
590	#121	C₂³×C₈₉	1	1	yes	characteristic
591	#120	—	2	2	no	—
592	#120	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
598	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
600	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
601	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	4	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
612	C₄×D₄	D₄×C₈₉	1	2	yes	—
613	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₈₉	1	2	yes	—
615	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₈₉	1	2	yes	—
617	#117	—	2	2	no	—
618	#117	—	2	1	no	—
619	#117	—	2	1	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	D₄×C₈₉	1	2	yes	—
623	#117	D₄×C₈₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
633	#107	C₂³×C₈₉	1	2	yes	—
634	#107	C₂³×C₈₉	1	4	yes	—
635	#106	C₂³×C₈₉	1	2	yes	—
636	#106	C₂³×C₈₉	1	4	yes	—
637	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
638	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
639	#103	C₂³×C₈₉	1	2	yes	—
640	#103	C₂³×C₈₉	1	4	yes	—
641	#103	C₂³×C₈₉	1	4	yes	—
642	#103	C₂³×C₈₉	1	4	yes	—
643	#103	C₂³×C₈₉	1	4	yes	—
644	#103	C₂³×C₈₉	1	2	yes	—
645	#103	C₂³×C₈₉	1	2	yes	—
646	#102	C₂³×C₈₉	1	2	yes	—
647	#102	C₂³×C₈₉	1	4	yes	—
648	#102	C₂³×C₈₉	1	4	yes	—
649	#102	C₂³×C₈₉	1	4	yes	—
650	#102	C₂³×C₈₉	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
653	#97	C₂³×C₈₉	1	1	yes	characteristic
654	#97	C₂³×C₈₉	1	2	yes	—
655	#97	C₂³×C₈₉	1	4	yes	—
656	#97	C₂³×C₈₉	1	1	yes	characteristic
657	C₄×C₈	C₂³×C₈₉	1	2	yes	—
658	C₂⁴	—	2	2	no	—
659	#41	—	2	4	no	—
660	#41	—	4	4	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	4	4	no	—
667	C₂×Q₈	—	8	4	no	—
668	C₂×Q₈	—	8	2	no	—
669	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
684	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
694	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
697	Q₁₆	—	4	4	no	—
698	Q₁₆	—	4	2	no	—
699	SD₁₆	—	4	4	no	—
700	SD₁₆	—	4	2	no	—
701	M₁₆	—	4	2	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
704	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
705	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
732	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
733	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	C₂×D₄×C₈₉	1	2	yes	—
758	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₈₉	1	2	yes	—
761	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
762	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
763	C₄²	C₂⁴×C₈₉	1	2	yes	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
770	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	8	2	no	—
779	Q₈	—	8	4	no	—
780	Q₈	—	8	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	1	no	—
787	D₄	—	8	2	no	—
788	D₄	—	8	1	no	—
789	D₄	—	8	2	no	—
790	D₄	#137×C₈₉	1	4	yes	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
818	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
819	C₈	—	2	2	no	—
820	C₈	—	2	4	no	—
821	C₈	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	16	4	no	—
834	C₂²	C₂×#137×C₈₉	1	4	yes	—
835	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	4	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	C₂×#137×C₈₉	1	2	yes	—
851	C₄	#585×C₈₉	1	2	yes	—
852	C₂	—	2	4	no	—
853	C₂	—	4	1	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	1	no	—
856	C₂	C₈₉×#3500	1	1	yes	characteristic
857	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
858	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3514	C₂
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
2. C₈₉×#3503	C₂	semidirect
3. C₈₉×#3375	C₂	semidirect
4. C₈₉×#3369	C₂	semidirect
5. C₈₉×#3316	C₂	semidirect
6. C₈₉×#3314	C₂	semidirect
7. C₈₉×#3299	C₂	semidirect
8. C₈₉×#3295	C₂	semidirect
9. C₈₉×#3239	C₂	semidirect
10. C₈₉×#3238	C₂	semidirect
11. C₈₉×#3216	C₂	semidirect
12. C₈₉×#3215	C₂	semidirect
13. C₈₉×#3181	C₂	semidirect
14. C₈₉×#3172	C₂	semidirect
15. C₈₉×#3141	C₂	semidirect
16. C₂×#489×C₈₉	C₂	semidirect
17. C₈₉×#2970	C₂	semidirect
19. Q₈²×C₈₉	C₂²	semidirect
24. #554×C₈₉	C₂²	semidirect
37. #533×C₈₉	C₂²	semidirect
38. #533×C₈₉	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. #501×C₈₉	C₂²	semidirect
49. #501×C₈₉	C₂²	semidirect
51. #497×C₈₉	C₂²	semidirect
52. #491×C₈₉	C₂²	semidirect
56. #489×C₈₉	C₂²	semidirect
57. #489×C₈₉	C₂²	semidirect
58. #489×C₈₉	C₂²	semidirect
59. #489×C₈₉	C₂²	semidirect
60. #487×C₈₉	C₂²	semidirect
62. #484×C₈₉	C₂²	semidirect
63. #483×C₈₉	C₂²	semidirect
66. #477×C₈₉	C₂²	semidirect
68. #475×C₈₉	C₂²	semidirect
69. #474×C₈₉	C₂²	semidirect
70. #470×C₈₉	C₂²	semidirect
72. #467×C₈₉	C₂²	semidirect
75. #464×C₈₉	C₂²	semidirect
76. #462×C₈₉	C₂²	semidirect
78. #452×C₈₉	C₂²	semidirect
79. #451×C₈₉	C₂²	semidirect
81. #446×C₈₉	C₂²	semidirect
82. #441×C₈₉	C₂²	semidirect
83. #440×C₈₉	C₂²	semidirect
84. C₄×Q₁₆×C₈₉	C₂²	semidirect
86. #435×C₈₉	C₂²	semidirect
88. #432×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
90. #417×C₈₉	C₂²	semidirect
91. C₂×#103×C₈₉	C₂²	semidirect
93. C₄×M₁₆×C₈₉	C₂²	semidirect
94. C₂×#97×C₈₉	C₂²	semidirect
422. #62582	C₈₉	direct (N × H)
431. #3503	C₂×C₈₉	semidirect
432. #3375	C₂×C₈₉	semidirect
433. #3369	C₂×C₈₉	semidirect
434. #3316	C₂×C₈₉	semidirect
435. #3314	C₂×C₈₉	semidirect
436. #3299	C₂×C₈₉	semidirect
437. #3295	C₂×C₈₉	semidirect
438. #3239	C₂×C₈₉	semidirect
439. #3238	C₂×C₈₉	semidirect
440. #3216	C₂×C₈₉	semidirect
441. #3215	C₂×C₈₉	semidirect
442. #3181	C₂×C₈₉	semidirect
443. #3172	C₂×C₈₉	semidirect
444. #3141	C₂×C₈₉	semidirect
445. C₂×#489	C₂×C₈₉	semidirect
446. #2970	C₂×C₈₉	semidirect
447. C₈₉	#62582	direct (N × H)
449. Q₈²	C₂²×C₈₉	semidirect
454. #554	C₂²×C₈₉	semidirect
467. #533	C₂²×C₈₉	semidirect
468. #533	C₂²×C₈₉	semidirect
470. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
471. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
478. #501	C₂²×C₈₉	semidirect
479. #501	C₂²×C₈₉	semidirect
481. #497	C₂²×C₈₉	semidirect
482. #491	C₂²×C₈₉	semidirect
486. #489	C₂²×C₈₉	semidirect
487. #489	C₂²×C₈₉	semidirect
488. #489	C₂²×C₈₉	semidirect
489. #489	C₂²×C₈₉	semidirect
490. #487	C₂²×C₈₉	semidirect
492. #484	C₂²×C₈₉	semidirect
493. #483	C₂²×C₈₉	semidirect
496. #477	C₂²×C₈₉	semidirect
498. #475	C₂²×C₈₉	semidirect
499. #474	C₂²×C₈₉	semidirect
500. #470	C₂²×C₈₉	semidirect
502. #467	C₂²×C₈₉	semidirect
505. #464	C₂²×C₈₉	semidirect
506. #462	C₂²×C₈₉	semidirect
508. #452	C₂²×C₈₉	semidirect
509. #451	C₂²×C₈₉	semidirect
511. #446	C₂²×C₈₉	semidirect
512. #441	C₂²×C₈₉	semidirect
513. #440	C₂²×C₈₉	semidirect
514. C₄×Q₁₆	C₂²×C₈₉	semidirect
516. #435	C₂²×C₈₉	semidirect
518. #432	C₂²×C₈₉	semidirect
519. #432	C₂²×C₈₉	semidirect
520. #417	C₂²×C₈₉	semidirect
521. C₂×#103	C₂²×C₈₉	semidirect
523. C₄×M₁₆	C₂²×C₈₉	semidirect
524. C₂×#97	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×#3514	2
C₈₉×#3503	2
C₈₉×#3375	2
C₈₉×#3369	2
C₈₉×#3316	2
C₈₉×#3314	2
C₈₉×#3299	2
C₈₉×#3295	2
C₈₉×#3239	2
C₈₉×#3238	2
C₈₉×#3216	2
C₈₉×#3215	2
C₈₉×#3181	2
C₈₉×#3172	2
C₈₉×#3141	2
C₂×#489×C₈₉	2
C₈₉×#2970	2
#62582	89

Subgroups — C89×#62582 #36440430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62582 #36440430