Subgroups — C₈₉×#62143 #36439991

Order 22784.

1830 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3380	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3361	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3357	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3355	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3322	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3251	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3233	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3100	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3077	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₈₉	C₂²	1	1	yes	characteristic
19	#556×C₈₉	—	2	1	no	—
20	#555×C₈₉	C₂²	1	2	yes	—
21	#554×C₈₉	C₂²	1	1	yes	characteristic
22	#554×C₈₉	C₂²	1	1	yes	characteristic
23	#554×C₈₉	C₂²	1	2	yes	complemented
24	#553×C₈₉	—	2	1	no	—
25	#553×C₈₉	C₂²	1	2	yes	—
26	#553×C₈₉	C₂²	1	4	yes	complemented
27	#551×C₈₉	—	2	2	no	—
28	#548×C₈₉	—	2	2	no	—
29	#547×C₈₉	—	2	1	no	—
30	#546×C₈₉	—	2	1	no	—
31	#546×C₈₉	C₂²	1	2	yes	—
32	D₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#542×C₈₉	—	2	2	no	—
34	#537×C₈₉	—	2	1	no	—
35	#533×C₈₉	C₂²	1	2	yes	complemented
36	#532×C₈₉	C₂²	1	1	yes	characteristic
37	#532×C₈₉	C₂²	1	2	yes	complemented
38	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#529×C₈₉	—	2	1	no	—
41	#529×C₈₉	C₂²	1	2	yes	—
42	#525×C₈₉	—	2	2	no	—
43	#520×C₈₉	—	2	1	no	—
44	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	—	2	1	no	—
47	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
48	#500×C₈₉	C₂²	1	2	yes	complemented
49	#499×C₈₉	C₂²	1	4	yes	complemented
50	#488×C₈₉	C₂²	1	4	yes	complemented
51	#486×C₈₉	C₂²	1	2	yes	—
52	#485×C₈₉	C₂²	1	4	yes	complemented
53	#482×C₈₉	C₂²	1	4	yes	—
54	#482×C₈₉	C₂²	1	2	yes	complemented
55	#480×C₈₉	C₂²	1	4	yes	complemented
56	#480×C₈₉	C₂²	1	4	yes	complemented
57	#478×C₈₉	C₂²	1	4	yes	—
58	#478×C₈₉	C₂²	1	4	yes	complemented
59	#478×C₈₉	C₂²	1	4	yes	complemented
60	#477×C₈₉	C₂²	1	2	yes	complemented
61	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#476×C₈₉	C₂²	1	2	yes	—
63	#476×C₈₉	C₂²	1	1	yes	characteristic
64	#476×C₈₉	C₂²	1	2	yes	complemented
65	#476×C₈₉	C₂²	1	2	yes	complemented
66	#475×C₈₉	C₂²	1	2	yes	complemented
67	#474×C₈₉	C₂²	1	2	yes	—
68	#474×C₈₉	C₂²	1	2	yes	complemented
69	#474×C₈₉	C₂²	1	2	yes	complemented
70	#469×C₈₉	C₂²	1	4	yes	—
71	#469×C₈₉	C₂²	1	4	yes	complemented
72	#468×C₈₉	C₂²	1	4	yes	complemented
73	#463×C₈₉	C₂²	1	4	yes	complemented
74	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#459×C₈₉	C₂²	1	2	yes	—
76	#459×C₈₉	C₂²	1	1	yes	characteristic
77	#459×C₈₉	C₂²	1	2	yes	complemented
78	#449×C₈₉	C₂²	1	2	yes	—
79	#447×C₈₉	C₂²	1	4	yes	—
80	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
82	C₄×D₈×C₈₉	C₂²	1	4	yes	—
83	C₄×D₈×C₈₉	C₂²	1	2	yes	—
84	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
85	#436×C₈₉	C₂²	1	2	yes	—
86	#436×C₈₉	C₂²	1	4	yes	complemented
87	#431×C₈₉	C₂²	1	2	yes	complemented
88	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	#428×C₈₉	C₂²	1	4	yes	complemented
90	#428×C₈₉	C₂²	1	2	yes	complemented
91	#423×C₈₉	C₂²	1	2	yes	complemented
92	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#418×C₈₉	C₂²	1	4	yes	—
94	#417×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	1	no	—
97	C₂×#41×C₈₉	—	2	2	no	—
98	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
99	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	—	2	2	no	—
104	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
105	C₂×D₈×C₈₉	C₂³	1	2	yes	—
106	C₂×D₈×C₈₉	C₂³	1	4	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₈₉	—	2	1	no	—
110	C₄⋊Q₈×C₈₉	—	2	1	no	—
111	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
115	#127×C₈₉	C₂³	1	1	yes	characteristic
116	#127×C₈₉	C₂³	1	1	yes	characteristic
117	#126×C₈₉	—	2	2	no	—
118	#126×C₈₉	—	2	4	no	—
119	#126×C₈₉	—	2	2	no	—
120	#125×C₈₉	—	2	1	no	—
121	#125×C₈₉	C₂³	1	4	yes	—
122	#125×C₈₉	C₂³	1	2	yes	—
123	#124×C₈₉	—	2	1	no	—
124	#124×C₈₉	—	2	4	no	—
125	#124×C₈₉	—	2	1	no	—
126	#124×C₈₉	—	2	1	no	—
127	#124×C₈₉	—	2	2	no	—
128	#124×C₈₉	C₂³	1	2	yes	—
129	#123×C₈₉	—	2	2	no	—
130	#123×C₈₉	—	2	2	no	—
131	#123×C₈₉	—	2	2	no	—
132	#123×C₈₉	—	2	2	no	—
133	#123×C₈₉	—	2	4	no	—
134	C₂²⋊Q₈×C₈₉	—	2	1	no	—
135	C₂²⋊Q₈×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	2	no	—
137	C₂²⋊Q₈×C₈₉	—	2	2	no	—
138	C₂²⋊Q₈×C₈₉	—	2	2	no	—
139	C₂²⋊Q₈×C₈₉	—	2	4	no	—
140	C₂²⋊Q₈×C₈₉	—	2	2	no	—
141	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
142	#121×C₈₉	—	2	2	no	—
143	#121×C₈₉	—	2	2	no	—
144	#121×C₈₉	—	2	4	no	—
145	#121×C₈₉	—	2	1	no	—
146	#121×C₈₉	—	2	2	no	—
147	#121×C₈₉	—	2	1	no	—
148	#121×C₈₉	—	2	1	no	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	C₂³	1	4	yes	—
151	#121×C₈₉	C₂³	1	2	yes	—
152	#121×C₈₉	C₂³	1	2	yes	—
153	#121×C₈₉	C₂³	1	2	yes	—
154	#120×C₈₉	—	2	2	no	—
155	#120×C₈₉	—	2	2	no	—
156	C₄×Q₈×C₈₉	—	2	2	no	—
157	C₄×Q₈×C₈₉	—	2	2	no	—
158	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₈₉	—	2	1	no	—
163	C₄×D₄×C₈₉	—	2	2	no	—
164	C₄×D₄×C₈₉	—	2	1	no	—
165	C₄×D₄×C₈₉	—	2	1	no	—
166	C₄×D₄×C₈₉	—	2	1	no	—
167	C₄×D₄×C₈₉	—	2	2	no	—
168	C₄×D₄×C₈₉	—	2	4	no	—
169	C₄×D₄×C₈₉	—	2	1	no	—
170	C₄×D₄×C₈₉	—	2	2	no	—
171	C₄×D₄×C₈₉	—	2	2	no	—
172	C₄×D₄×C₈₉	—	2	2	no	—
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
175	C₄×D₄×C₈₉	D₄	1	2	yes	—
176	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₈₉	C₂³	1	2	yes	—
178	C₄×D₄×C₈₉	C₂³	1	4	yes	—
179	C₄×D₄×C₈₉	C₂³	1	2	yes	—
180	C₄×D₄×C₈₉	C₂³	1	2	yes	—
181	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₈₉	C₂³	1	2	yes	—
183	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂³	1	2	yes	—
185	#117×C₈₉	—	2	2	no	—
186	#117×C₈₉	—	2	1	no	—
187	#117×C₈₉	—	2	2	no	—
188	#117×C₈₉	D₄	1	1	yes	characteristic
189	#117×C₈₉	D₄	1	2	yes	—
190	#117×C₈₉	C₂³	1	4	yes	—
191	#117×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
199	C₂×C₄²×C₈₉	—	2	1	no	—
200	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
202	#107×C₈₉	C₂³	1	4	yes	—
203	#107×C₈₉	C₂³	1	4	yes	—
204	#107×C₈₉	C₂³	1	4	yes	—
205	#107×C₈₉	C₂³	1	2	yes	—
206	#106×C₈₉	C₂³	1	2	yes	—
207	#106×C₈₉	C₂³	1	4	yes	—
208	#106×C₈₉	C₂³	1	4	yes	—
209	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
214	#103×C₈₉	C₂³	1	4	yes	—
215	#103×C₈₉	C₂³	1	2	yes	—
216	#102×C₈₉	C₂³	1	4	yes	—
217	#102×C₈₉	C₂³	1	2	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	#102×C₈₉	C₂³	1	2	yes	—
222	#102×C₈₉	C₂³	1	2	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
226	C₄×C₈×C₈₉	C₂³	1	2	yes	—
227	C₄×C₈×C₈₉	C₂³	1	4	yes	—
228	C₂⁴×C₈₉	—	2	2	no	—
229	#41×C₈₉	—	2	2	no	—
230	#41×C₈₉	—	4	2	no	—
231	#41×C₈₉	—	4	1	no	—
232	#41×C₈₉	—	4	4	no	—
233	#41×C₈₉	—	8	2	no	—
234	#41×C₈₉	—	8	4	no	—
235	C₂×Q₈×C₈₉	—	2	1	no	—
236	C₂×Q₈×C₈₉	—	2	2	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	2	no	—
239	C₂×Q₈×C₈₉	—	8	2	no	—
240	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₈₉	—	2	4	no	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	2	no	—
247	C₂×D₄×C₈₉	—	2	4	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	1	no	—
250	C₂×D₄×C₈₉	—	2	1	no	—
251	C₂×D₄×C₈₉	—	2	1	no	—
252	C₂×D₄×C₈₉	—	2	1	no	—
253	C₂×D₄×C₈₉	—	4	2	no	—
254	C₂×D₄×C₈₉	—	4	4	no	—
255	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	2	no	—
267	C₂²×C₄×C₈₉	—	2	2	no	—
268	C₂²×C₄×C₈₉	—	2	4	no	—
269	C₂²×C₄×C₈₉	—	2	2	no	—
270	C₂²×C₄×C₈₉	—	8	4	no	—
271	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
277	SD₁₆×C₈₉	—	4	2	no	—
278	D₈×C₈₉	—	2	4	no	—
279	D₈×C₈₉	—	4	4	no	—
280	M₁₆×C₈₉	—	4	2	no	—
281	M₁₆×C₈₉	—	4	4	no	—
282	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
283	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
284	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₈₉	—	2	2	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	2	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	1	no	—
293	C₄⋊C₄×C₈₉	—	2	1	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	2	no	—
296	C₄⋊C₄×C₈₉	—	2	1	no	—
297	C₄⋊C₄×C₈₉	—	2	4	no	—
298	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₈₉	—	2	2	no	—
308	C₂²⋊C₄×C₈₉	—	2	1	no	—
309	C₂²⋊C₄×C₈₉	—	2	4	no	—
310	C₂²⋊C₄×C₈₉	—	2	1	no	—
311	C₂²⋊C₄×C₈₉	—	2	2	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	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	1	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	2	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
326	C₄²×C₈₉	—	2	1	no	—
327	C₄²×C₈₉	—	2	1	no	—
328	C₄²×C₈₉	—	2	1	no	—
329	C₄²×C₈₉	—	2	4	no	—
330	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₈₉	C₂×D₄	1	2	yes	—
333	C₄²×C₈₉	C₂×D₄	1	2	yes	—
334	C₄²×C₈₉	C₂⁴	1	2	yes	—
335	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₂³×C₈₉	—	2	1	no	—
338	C₂³×C₈₉	—	2	2	no	—
339	C₂³×C₈₉	—	2	2	no	—
340	C₂³×C₈₉	—	4	4	no	—
341	C₂³×C₈₉	—	4	4	no	—
342	C₂³×C₈₉	—	8	2	no	—
343	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₈₉	—	2	2	no	—
346	Q₈×C₈₉	—	2	1	no	—
347	Q₈×C₈₉	—	2	1	no	—
348	Q₈×C₈₉	—	4	2	no	—
349	Q₈×C₈₉	—	4	4	no	—
350	Q₈×C₈₉	—	8	2	no	—
351	Q₈×C₈₉	—	8	1	no	—
352	D₄×C₈₉	—	2	2	no	—
353	D₄×C₈₉	—	2	2	no	—
354	D₄×C₈₉	—	2	2	no	—
355	D₄×C₈₉	—	2	1	no	—
356	D₄×C₈₉	—	2	2	no	—
357	D₄×C₈₉	—	2	2	no	—
358	D₄×C₈₉	—	4	2	no	—
359	D₄×C₈₉	—	4	4	no	—
360	D₄×C₈₉	—	4	2	no	—
361	D₄×C₈₉	—	4	2	no	—
362	D₄×C₈₉	—	4	4	no	—
363	D₄×C₈₉	—	4	4	no	—
364	D₄×C₈₉	—	4	2	no	—
365	D₄×C₈₉	—	4	2	no	—
366	D₄×C₈₉	—	8	1	no	—
367	D₄×C₈₉	—	8	2	no	—
368	D₄×C₈₉	—	8	4	no	—
369	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	4	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	1	no	—
381	C₂×C₄×C₈₉	—	2	4	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	4	2	no	—
384	C₂×C₄×C₈₉	—	4	2	no	—
385	C₂×C₄×C₈₉	—	4	2	no	—
386	C₂×C₄×C₈₉	—	4	4	no	—
387	C₂×C₄×C₈₉	—	4	2	no	—
388	C₂×C₄×C₈₉	—	4	4	no	—
389	C₂×C₄×C₈₉	—	8	2	no	—
390	C₂×C₄×C₈₉	—	8	2	no	—
391	C₂×C₄×C₈₉	—	8	4	no	—
392	C₂×C₄×C₈₉	—	8	2	no	—
393	C₂×C₄×C₈₉	—	8	2	no	—
394	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
403	C₈×C₈₉	—	2	2	no	—
404	C₈×C₈₉	—	2	4	no	—
405	C₈×C₈₉	—	2	2	no	—
406	C₂²×C₈₉	—	2	1	no	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	2	no	—
409	C₂²×C₈₉	—	2	1	no	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	1	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	4	1	no	—
414	C₂²×C₈₉	—	4	1	no	—
415	C₂²×C₈₉	—	4	2	no	—
416	C₂²×C₈₉	—	4	2	no	—
417	C₂²×C₈₉	—	4	2	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	—	4	2	no	—
420	C₂²×C₈₉	—	4	2	no	—
421	C₂²×C₈₉	—	8	8	no	—
422	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₈₉	—	2	1	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	2	1	no	—
426	C₄×C₈₉	—	2	2	no	—
427	C₄×C₈₉	—	2	2	no	—
428	C₄×C₈₉	—	2	1	no	—
429	C₄×C₈₉	—	4	1	no	—
430	C₄×C₈₉	—	4	1	no	—
431	C₄×C₈₉	—	4	2	no	—
432	C₄×C₈₉	—	4	1	no	—
433	C₄×C₈₉	—	4	2	no	—
434	C₄×C₈₉	—	4	4	no	—
435	C₄×C₈₉	#575	1	2	yes	—
436	C₄×C₈₉	#576	1	2	yes	—
437	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₄×C₈₉	#585	1	1	yes	characteristic
439	#62143	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂×C₈₉	—	4	1	no	—
441	C₂×C₈₉	—	4	2	no	—
442	C₂×C₈₉	—	4	2	no	—
443	C₂×C₈₉	—	8	2	no	—
444	C₂×C₈₉	—	8	2	no	—
445	C₂×C₈₉	#3489	1	1	yes	characteristic
446	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
447	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
448	#3511	C₂×C₈₉	1	1	yes	characteristic, complemented
449	#3481	C₂×C₈₉	1	1	yes	characteristic, complemented
450	#3380	C₂×C₈₉	1	2	yes	complemented
451	#3361	C₂×C₈₉	1	2	yes	complemented
452	#3357	C₂×C₈₉	1	2	yes	complemented
453	#3355	C₂×C₈₉	1	4	yes	complemented
454	#3325	C₂×C₈₉	1	2	yes	complemented
455	#3322	C₂×C₈₉	1	4	yes	complemented
456	#3253	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#3251	C₂×C₈₉	1	2	yes	complemented
458	#3233	C₂×C₈₉	1	2	yes	complemented
459	#3226	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
461	#3100	C₂×C₈₉	1	2	yes	complemented
462	#3079	C₂×C₈₉	1	1	yes	characteristic, complemented
463	#3077	C₂×C₈₉	1	2	yes	complemented
464	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₈₉	#62143	1	1	yes	characteristic, direct product factor, Sylow
466	#559	C₂²×C₈₉	1	1	yes	characteristic
467	#556	—	2	1	no	—
468	#555	C₂²×C₈₉	1	2	yes	—
469	#554	C₂²×C₈₉	1	1	yes	characteristic
470	#554	C₂²×C₈₉	1	1	yes	characteristic
471	#554	C₂²×C₈₉	1	2	yes	complemented
472	#553	—	2	1	no	—
473	#553	C₂²×C₈₉	1	2	yes	—
474	#553	C₂²×C₈₉	1	4	yes	complemented
475	#551	—	2	2	no	—
476	#548	—	2	2	no	—
477	#547	—	2	1	no	—
478	#546	—	2	1	no	—
479	#546	C₂²×C₈₉	1	2	yes	—
480	D₄²	C₂²×C₈₉	1	1	yes	characteristic
481	#542	—	2	2	no	—
482	#537	—	2	1	no	—
483	#533	C₂²×C₈₉	1	2	yes	complemented
484	#532	C₂²×C₈₉	1	1	yes	characteristic
485	#532	C₂²×C₈₉	1	2	yes	complemented
486	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
487	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
488	#529	—	2	1	no	—
489	#529	C₂²×C₈₉	1	2	yes	—
490	#525	—	2	2	no	—
491	#520	—	2	1	no	—
492	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
493	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×C₄×D₄	—	2	1	no	—
495	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
496	#500	C₂²×C₈₉	1	2	yes	complemented
497	#499	C₂²×C₈₉	1	4	yes	complemented
498	#488	C₂²×C₈₉	1	4	yes	complemented
499	#486	C₂²×C₈₉	1	2	yes	—
500	#485	C₂²×C₈₉	1	4	yes	complemented
501	#482	C₂²×C₈₉	1	4	yes	—
502	#482	C₂²×C₈₉	1	2	yes	complemented
503	#480	C₂²×C₈₉	1	4	yes	complemented
504	#480	C₂²×C₈₉	1	4	yes	complemented
505	#478	C₂²×C₈₉	1	4	yes	—
506	#478	C₂²×C₈₉	1	4	yes	complemented
507	#478	C₂²×C₈₉	1	4	yes	complemented
508	#477	C₂²×C₈₉	1	2	yes	complemented
509	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
510	#476	C₂²×C₈₉	1	1	yes	characteristic
511	#476	C₂²×C₈₉	1	2	yes	—
512	#476	C₂²×C₈₉	1	2	yes	complemented
513	#476	C₂²×C₈₉	1	2	yes	complemented
514	#475	C₂²×C₈₉	1	2	yes	complemented
515	#474	C₂²×C₈₉	1	2	yes	—
516	#474	C₂²×C₈₉	1	2	yes	complemented
517	#474	C₂²×C₈₉	1	2	yes	complemented
518	#469	C₂²×C₈₉	1	4	yes	—
519	#469	C₂²×C₈₉	1	4	yes	complemented
520	#468	C₂²×C₈₉	1	4	yes	complemented
521	#463	C₂²×C₈₉	1	4	yes	complemented
522	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
523	#459	C₂²×C₈₉	1	1	yes	characteristic
524	#459	C₂²×C₈₉	1	2	yes	—
525	#459	C₂²×C₈₉	1	2	yes	complemented
526	#449	C₂²×C₈₉	1	2	yes	—
527	#447	C₂²×C₈₉	1	4	yes	—
528	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
529	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
530	C₄×D₈	C₂²×C₈₉	1	4	yes	—
531	C₄×D₈	C₂²×C₈₉	1	2	yes	—
532	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
533	#436	C₂²×C₈₉	1	2	yes	—
534	#436	C₂²×C₈₉	1	4	yes	complemented
535	#431	C₂²×C₈₉	1	2	yes	complemented
536	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
537	#428	C₂²×C₈₉	1	4	yes	complemented
538	#428	C₂²×C₈₉	1	2	yes	complemented
539	#423	C₂²×C₈₉	1	2	yes	complemented
540	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
541	#418	C₂²×C₈₉	1	4	yes	—
542	#417	C₂²×C₈₉	1	2	yes	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	1	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
547	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
551	C₂³×C₄	—	2	2	no	—
552	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
553	C₂×D₈	C₂³×C₈₉	1	2	yes	—
554	C₂×D₈	C₂³×C₈₉	1	4	yes	—
555	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
556	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
563	#127	C₂³×C₈₉	1	1	yes	characteristic
564	#127	C₂³×C₈₉	1	1	yes	characteristic
565	#126	—	2	2	no	—
566	#126	—	2	4	no	—
567	#126	—	2	2	no	—
568	#125	—	2	1	no	—
569	#125	C₂³×C₈₉	1	2	yes	—
570	#125	C₂³×C₈₉	1	4	yes	—
571	#124	—	2	1	no	—
572	#124	—	2	4	no	—
573	#124	—	2	1	no	—
574	#124	—	2	1	no	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₈₉	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	4	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	—	2	1	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	#121	C₂³×C₈₉	1	2	yes	—
599	#121	C₂³×C₈₉	1	2	yes	—
600	#121	C₂³×C₈₉	1	2	yes	—
601	#121	C₂³×C₈₉	1	4	yes	—
602	#120	—	2	2	no	—
603	#120	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
623	C₄×D₄	D₄×C₈₉	1	2	yes	—
624	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₈₉	1	2	yes	—
626	C₄×D₄	C₂³×C₈₉	1	2	yes	—
627	C₄×D₄	C₂³×C₈₉	1	2	yes	—
628	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₈₉	1	4	yes	—
630	C₄×D₄	C₂³×C₈₉	1	2	yes	—
631	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₈₉	1	2	yes	—
633	#117	—	2	2	no	—
634	#117	—	2	1	no	—
635	#117	—	2	2	no	—
636	#117	D₄×C₈₉	1	1	yes	characteristic
637	#117	D₄×C₈₉	1	2	yes	—
638	#117	C₂³×C₈₉	1	1	yes	characteristic
639	#117	C₂³×C₈₉	1	4	yes	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	2	no	—
643	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₂²⋊C₄	—	2	2	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
649	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
650	#107	C₂³×C₈₉	1	4	yes	—
651	#107	C₂³×C₈₉	1	4	yes	—
652	#107	C₂³×C₈₉	1	4	yes	—
653	#107	C₂³×C₈₉	1	2	yes	—
654	#106	C₂³×C₈₉	1	2	yes	—
655	#106	C₂³×C₈₉	1	4	yes	—
656	#106	C₂³×C₈₉	1	4	yes	—
657	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
658	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
659	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
660	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
661	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
662	#103	C₂³×C₈₉	1	4	yes	—
663	#103	C₂³×C₈₉	1	2	yes	—
664	#102	C₂³×C₈₉	1	4	yes	—
665	#102	C₂³×C₈₉	1	2	yes	—
666	#102	C₂³×C₈₉	1	4	yes	—
667	#102	C₂³×C₈₉	1	4	yes	—
668	#102	C₂³×C₈₉	1	4	yes	—
669	#102	C₂³×C₈₉	1	2	yes	—
670	#102	C₂³×C₈₉	1	2	yes	—
671	#102	C₂³×C₈₉	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
674	C₄×C₈	C₂³×C₈₉	1	2	yes	—
675	C₄×C₈	C₂³×C₈₉	1	4	yes	—
676	C₂⁴	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	4	no	—
681	#41	—	8	2	no	—
682	#41	—	8	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	8	2	no	—
688	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
704	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
705	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
706	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
707	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	8	4	no	—
719	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
725	SD₁₆	—	4	2	no	—
726	D₈	—	2	4	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	4	2	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
731	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
732	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	4	no	—
778	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₈₉	1	2	yes	—
781	C₄²	C₂×D₄×C₈₉	1	2	yes	—
782	C₄²	C₂⁴×C₈₉	1	2	yes	—
783	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
792	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	8	2	no	—
799	Q₈	—	8	1	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	4	no	—
817	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
851	C₈	—	2	2	no	—
852	C₈	—	2	4	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	4	no	—
882	C₄	—	4	1	no	—
883	C₄	#575×C₈₉	1	2	yes	—
884	C₄	#576×C₈₉	1	2	yes	—
885	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
886	C₄	#585×C₈₉	1	1	yes	characteristic
887	C₂	—	4	1	no	—
888	C₂	—	4	2	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	2	no	—
891	C₂	—	8	2	no	—
892	C₂	C₈₉×#3489	1	1	yes	characteristic
893	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
894	C₂	C₂×#576×C₈₉	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×#3511	C₂	semidirect
2. C₈₉×#3481	C₂	semidirect
3. C₈₉×#3380	C₂	semidirect
4. C₈₉×#3361	C₂	semidirect
5. C₈₉×#3357	C₂	semidirect
6. C₈₉×#3355	C₂	semidirect
7. C₈₉×#3325	C₂	semidirect
8. C₈₉×#3322	C₂	semidirect
9. C₈₉×#3253	C₂	semidirect
10. C₈₉×#3251	C₂	semidirect
11. C₈₉×#3233	C₂	semidirect
12. C₈₉×#3226	C₂	semidirect
13. C₈₉×#3106	C₂	semidirect
14. C₈₉×#3100	C₂	semidirect
15. C₈₉×#3079	C₂	semidirect
16. C₈₉×#3077	C₂	semidirect
17. C₈₉×#2991	C₂	semidirect
23. #554×C₈₉	C₂²	semidirect
26. #553×C₈₉	C₂²	semidirect
35. #533×C₈₉	C₂²	semidirect
37. #532×C₈₉	C₂²	semidirect
38. #532×C₈₉	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. #500×C₈₉	C₂²	semidirect
49. #499×C₈₉	C₂²	semidirect
50. #488×C₈₉	C₂²	semidirect
52. #485×C₈₉	C₂²	semidirect
54. #482×C₈₉	C₂²	semidirect
55. #480×C₈₉	C₂²	semidirect
56. #480×C₈₉	C₂²	semidirect
58. #478×C₈₉	C₂²	semidirect
59. #478×C₈₉	C₂²	semidirect
60. #477×C₈₉	C₂²	semidirect
61. #477×C₈₉	C₂²	semidirect
64. #476×C₈₉	C₂²	semidirect
65. #476×C₈₉	C₂²	semidirect
66. #475×C₈₉	C₂²	semidirect
68. #474×C₈₉	C₂²	semidirect
69. #474×C₈₉	C₂²	semidirect
71. #469×C₈₉	C₂²	semidirect
72. #468×C₈₉	C₂²	semidirect
73. #463×C₈₉	C₂²	semidirect
74. #460×C₈₉	C₂²	semidirect
77. #459×C₈₉	C₂²	semidirect
80. C₈×Q₈×C₈₉	C₂²	semidirect
81. C₄×SD₁₆×C₈₉	C₂²	semidirect
84. C₄×D₈×C₈₉	C₂²	semidirect
86. #436×C₈₉	C₂²	semidirect
87. #431×C₈₉	C₂²	semidirect
88. #431×C₈₉	C₂²	semidirect
89. #428×C₈₉	C₂²	semidirect
90. #428×C₈₉	C₂²	semidirect
91. #423×C₈₉	C₂²	semidirect
92. #423×C₈₉	C₂²	semidirect
439. #62143	C₈₉	direct (N × H)
448. #3511	C₂×C₈₉	semidirect
449. #3481	C₂×C₈₉	semidirect
450. #3380	C₂×C₈₉	semidirect
451. #3361	C₂×C₈₉	semidirect
452. #3357	C₂×C₈₉	semidirect
453. #3355	C₂×C₈₉	semidirect
454. #3325	C₂×C₈₉	semidirect
455. #3322	C₂×C₈₉	semidirect
456. #3253	C₂×C₈₉	semidirect
457. #3251	C₂×C₈₉	semidirect
458. #3233	C₂×C₈₉	semidirect
459. #3226	C₂×C₈₉	semidirect
460. #3106	C₂×C₈₉	semidirect
461. #3100	C₂×C₈₉	semidirect
462. #3079	C₂×C₈₉	semidirect
463. #3077	C₂×C₈₉	semidirect
464. #2991	C₂×C₈₉	semidirect
465. C₈₉	#62143	direct (N × H)
471. #554	C₂²×C₈₉	semidirect
474. #553	C₂²×C₈₉	semidirect
483. #533	C₂²×C₈₉	semidirect
485. #532	C₂²×C₈₉	semidirect
486. #532	C₂²×C₈₉	semidirect
487. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
496. #500	C₂²×C₈₉	semidirect
497. #499	C₂²×C₈₉	semidirect
498. #488	C₂²×C₈₉	semidirect
500. #485	C₂²×C₈₉	semidirect
502. #482	C₂²×C₈₉	semidirect
503. #480	C₂²×C₈₉	semidirect
504. #480	C₂²×C₈₉	semidirect
506. #478	C₂²×C₈₉	semidirect
507. #478	C₂²×C₈₉	semidirect
508. #477	C₂²×C₈₉	semidirect
509. #477	C₂²×C₈₉	semidirect
512. #476	C₂²×C₈₉	semidirect
513. #476	C₂²×C₈₉	semidirect
514. #475	C₂²×C₈₉	semidirect
516. #474	C₂²×C₈₉	semidirect
517. #474	C₂²×C₈₉	semidirect
519. #469	C₂²×C₈₉	semidirect
520. #468	C₂²×C₈₉	semidirect
521. #463	C₂²×C₈₉	semidirect
522. #460	C₂²×C₈₉	semidirect
525. #459	C₂²×C₈₉	semidirect
528. C₈×Q₈	C₂²×C₈₉	semidirect
529. C₄×SD₁₆	C₂²×C₈₉	semidirect
532. C₄×D₈	C₂²×C₈₉	semidirect
534. #436	C₂²×C₈₉	semidirect
535. #431	C₂²×C₈₉	semidirect
536. #431	C₂²×C₈₉	semidirect
537. #428	C₂²×C₈₉	semidirect
538. #428	C₂²×C₈₉	semidirect
539. #423	C₂²×C₈₉	semidirect
540. #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×#3511	2
C₈₉×#3481	2
C₈₉×#3380	2
C₈₉×#3361	2
C₈₉×#3357	2
C₈₉×#3355	2
C₈₉×#3325	2
C₈₉×#3322	2
C₈₉×#3253	2
C₈₉×#3251	2
C₈₉×#3233	2
C₈₉×#3226	2
C₈₉×#3106	2
C₈₉×#3100	2
C₈₉×#3079	2
C₈₉×#3077	2
C₈₉×#2991	2
#62143	89

Subgroups — C89×#62143 #36439991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62143 #36439991