Subgroups — C₈₉×#60558 #36438406

Order 22784.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3114	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3110	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3109	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3105	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3101	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3100	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3092	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3077	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3036	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3003	C₂	1	2	yes	maximal, complemented
13	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	4	yes	maximal, complemented
14	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₈₉	—	2	1	no	—
17	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	—
18	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#532×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#529×C₈₉	—	2	1	no	—
25	#529×C₈₉	—	2	1	no	—
26	#529×C₈₉	—	2	1	no	—
27	#529×C₈₉	—	2	1	no	—
28	#529×C₈₉	C₂²	1	2	yes	complemented
29	#529×C₈₉	C₂²	1	2	yes	complemented
30	#525×C₈₉	—	2	1	no	—
31	#525×C₈₉	—	2	1	no	—
32	#525×C₈₉	C₂²	1	2	yes	—
33	C₄×#41×C₈₉	—	2	1	no	—
34	C₄×#41×C₈₉	—	2	1	no	—
35	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₈₉	—	2	1	no	—
37	C₂×C₄×D₄×C₈₉	—	2	1	no	—
38	C₂×C₄×D₄×C₈₉	—	2	1	no	—
39	C₂×C₄×D₄×C₈₉	—	2	1	no	—
40	C₂×C₄×D₄×C₈₉	—	2	1	no	—
41	C₂×C₄×D₄×C₈₉	—	2	1	no	—
42	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
48	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
50	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
51	#484×C₈₉	C₂²	1	4	yes	complemented
52	#483×C₈₉	C₂²	1	4	yes	complemented
53	#481×C₈₉	C₂²	1	4	yes	complemented
54	#480×C₈₉	C₂²	1	4	yes	complemented
55	#478×C₈₉	C₂²	1	8	yes	complemented
56	#476×C₈₉	C₂²	1	4	yes	complemented
57	#474×C₈₉	C₂²	1	4	yes	complemented
58	#463×C₈₉	C₂²	1	8	yes	complemented
59	#461×C₈₉	C₂²	1	4	yes	complemented
60	#459×C₈₉	C₂²	1	4	yes	complemented
61	#450×C₈₉	C₂²	1	4	yes	—
62	#450×C₈₉	C₂²	1	4	yes	—
63	#447×C₈₉	C₂²	1	4	yes	—
64	#447×C₈₉	C₂²	1	4	yes	—
65	#442×C₈₉	C₂²	1	8	yes	complemented
66	#440×C₈₉	C₂²	1	8	yes	complemented
67	C₄×SD₁₆×C₈₉	C₂²	1	8	yes	complemented
68	C₄×D₈×C₈₉	C₂²	1	8	yes	complemented
69	#432×C₈₉	C₂²	1	2	yes	complemented
70	#432×C₈₉	C₂²	1	2	yes	complemented
71	#431×C₈₉	C₂²	1	2	yes	complemented
72	#431×C₈₉	C₂²	1	2	yes	complemented
73	#428×C₈₉	C₂²	1	4	yes	complemented
74	#423×C₈₉	C₂²	1	2	yes	complemented
75	#418×C₈₉	C₂²	1	4	yes	—
76	#417×C₈₉	C₂²	1	4	yes	complemented
77	#407×C₈₉	C₂²	1	2	yes	—
78	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
79	C₂⁵×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	C₂×#41×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	—	2	8	no	—
84	C₂²×D₄×C₈₉	—	2	1	no	—
85	C₂²×D₄×C₈₉	—	2	1	no	—
86	C₂²×D₄×C₈₉	—	2	1	no	—
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₈₉	—	2	1	no	—
91	C₂³×C₄×C₈₉	—	2	2	no	—
92	C₂³×C₄×C₈₉	—	2	2	no	—
93	C₂³×C₄×C₈₉	—	2	2	no	—
94	C₂³×C₄×C₈₉	—	2	2	no	—
95	C₂³×C₄×C₈₉	—	2	2	no	—
96	C₂³×C₄×C₈₉	—	2	2	no	—
97	C₂³×C₄×C₈₉	—	4	8	no	—
98	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
101	AGL(1,ℤ/8)×C₈₉	—	2	16	no	—
102	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
103	C₂×D₈×C₈₉	C₂³	1	8	yes	—
104	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
106	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
107	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
108	#127×C₈₉	C₂³	1	1	yes	characteristic, complemented
109	#126×C₈₉	—	2	2	no	—
110	#126×C₈₉	—	2	2	no	—
111	#125×C₈₉	—	2	1	no	—
112	#125×C₈₉	—	2	1	no	—
113	#125×C₈₉	C₂³	1	2	yes	complemented
114	#124×C₈₉	—	2	1	no	—
115	#124×C₈₉	—	2	1	no	—
116	#124×C₈₉	C₂³	1	2	yes	complemented
117	#123×C₈₉	—	2	2	no	—
118	#123×C₈₉	—	2	2	no	—
119	#123×C₈₉	—	2	2	no	—
120	C₂²⋊Q₈×C₈₉	—	2	1	no	—
121	C₂²⋊Q₈×C₈₉	—	2	1	no	—
122	C₂²⋊Q₈×C₈₉	—	2	1	no	—
123	C₂²⋊Q₈×C₈₉	—	2	1	no	—
124	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
126	#121×C₈₉	—	2	1	no	—
127	#121×C₈₉	—	2	1	no	—
128	#121×C₈₉	—	2	1	no	—
129	#121×C₈₉	—	2	1	no	—
130	#121×C₈₉	C₂³	1	2	yes	—
131	#121×C₈₉	C₂³	1	2	yes	—
132	#120×C₈₉	—	2	2	no	—
133	C₄×Q₈×C₈₉	—	2	1	no	—
134	C₄×Q₈×C₈₉	—	2	1	no	—
135	C₄×Q₈×C₈₉	—	2	1	no	—
136	C₄×Q₈×C₈₉	—	2	1	no	—
137	C₄×Q₈×C₈₉	C₂³	1	2	yes	complemented
138	C₄×Q₈×C₈₉	C₂³	1	2	yes	complemented
139	C₄×D₄×C₈₉	—	2	2	no	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	—	2	2	no	—
142	C₄×D₄×C₈₉	—	2	2	no	—
143	C₄×D₄×C₈₉	—	2	2	no	—
144	C₄×D₄×C₈₉	—	2	2	no	—
145	C₄×D₄×C₈₉	—	2	2	no	—
146	C₄×D₄×C₈₉	—	2	2	no	—
147	C₄×D₄×C₈₉	—	2	2	no	—
148	C₄×D₄×C₈₉	—	2	2	no	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	2	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	2	no	—
155	C₄×D₄×C₈₉	—	2	2	no	—
156	C₄×D₄×C₈₉	—	2	2	no	—
157	C₄×D₄×C₈₉	—	2	1	no	—
158	C₄×D₄×C₈₉	—	2	1	no	—
159	C₄×D₄×C₈₉	—	2	1	no	—
160	C₄×D₄×C₈₉	—	2	1	no	—
161	C₄×D₄×C₈₉	C₂³	1	4	yes	—
162	C₄×D₄×C₈₉	C₂³	1	4	yes	—
163	C₄×D₄×C₈₉	C₂³	1	4	yes	—
164	C₄×D₄×C₈₉	C₂³	1	4	yes	—
165	C₄×D₄×C₈₉	C₂³	1	2	yes	complemented
166	C₄×D₄×C₈₉	C₂³	1	2	yes	complemented
167	#117×C₈₉	—	2	1	no	—
168	#117×C₈₉	—	2	1	no	—
169	#117×C₈₉	—	2	2	no	—
170	#117×C₈₉	—	2	2	no	—
171	#117×C₈₉	—	2	2	no	—
172	#117×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
174	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
180	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
181	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
182	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
183	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
184	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
185	C₂×C₄²×C₈₉	—	2	2	no	—
186	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	#107×C₈₉	C₂³	1	8	yes	complemented
199	#106×C₈₉	C₂³	1	8	yes	complemented
200	C₄⋊C₈×C₈₉	C₂³	1	4	yes	complemented
201	C₄⋊C₈×C₈₉	C₂³	1	4	yes	complemented
202	#103×C₈₉	C₂³	1	8	yes	complemented
203	#102×C₈₉	C₂³	1	8	yes	—
204	#102×C₈₉	C₂³	1	8	yes	—
205	#102×C₈₉	C₂³	1	8	yes	complemented
206	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
207	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
208	#97×C₈₉	C₂³	1	4	yes	complemented
209	C₄×C₈×C₈₉	C₂³	1	4	yes	complemented
210	C₂⁴×C₈₉	—	2	8	no	—
211	C₂⁴×C₈₉	—	2	2	no	—
212	C₂⁴×C₈₉	—	2	2	no	—
213	C₂⁴×C₈₉	—	2	2	no	—
214	C₂⁴×C₈₉	—	4	4	no	—
215	C₂⁴×C₈₉	—	4	4	no	—
216	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
217	#41×C₈₉	—	2	8	no	—
218	#41×C₈₉	—	4	4	no	—
219	#41×C₈₉	—	4	4	no	—
220	C₂×Q₈×C₈₉	—	2	1	no	—
221	C₂×Q₈×C₈₉	—	2	1	no	—
222	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
223	C₂×D₄×C₈₉	—	2	8	no	—
224	C₂×D₄×C₈₉	—	2	8	no	—
225	C₂×D₄×C₈₉	—	2	8	no	—
226	C₂×D₄×C₈₉	—	2	8	no	—
227	C₂×D₄×C₈₉	—	2	8	no	—
228	C₂×D₄×C₈₉	—	2	2	no	—
229	C₂×D₄×C₈₉	—	2	2	no	—
230	C₂×D₄×C₈₉	—	2	2	no	—
231	C₂×D₄×C₈₉	—	2	2	no	—
232	C₂×D₄×C₈₉	—	2	2	no	—
233	C₂×D₄×C₈₉	—	2	2	no	—
234	C₂×D₄×C₈₉	—	2	1	no	—
235	C₂×D₄×C₈₉	—	2	1	no	—
236	C₂×D₄×C₈₉	—	2	4	no	—
237	C₂×D₄×C₈₉	#41	1	8	yes	complemented
238	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₈₉	—	2	4	no	—
241	C₂²×C₄×C₈₉	—	2	4	no	—
242	C₂²×C₄×C₈₉	—	2	2	no	—
243	C₂²×C₄×C₈₉	—	2	2	no	—
244	C₂²×C₄×C₈₉	—	2	2	no	—
245	C₂²×C₄×C₈₉	—	2	2	no	—
246	C₂²×C₄×C₈₉	—	2	2	no	—
247	C₂²×C₄×C₈₉	—	2	4	no	—
248	C₂²×C₄×C₈₉	—	2	4	no	—
249	C₂²×C₄×C₈₉	—	2	4	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	2	4	no	—
252	C₂²×C₄×C₈₉	—	4	2	no	—
253	C₂²×C₄×C₈₉	—	4	8	no	—
254	C₂²×C₄×C₈₉	—	4	8	no	—
255	C₂²×C₄×C₈₉	—	4	8	no	—
256	C₂²×C₄×C₈₉	—	4	8	no	—
257	C₂²×C₄×C₈₉	—	4	8	no	—
258	C₂²×C₄×C₈₉	—	4	4	no	—
259	C₂²×C₄×C₈₉	—	4	8	no	—
260	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
278	SD₁₆×C₈₉	—	2	16	no	—
279	D₈×C₈₉	—	2	16	no	—
280	M₁₆×C₈₉	—	2	8	no	—
281	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
282	C₄⋊C₄×C₈₉	—	2	2	no	—
283	C₄⋊C₄×C₈₉	—	2	2	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	1	no	—
287	C₄⋊C₄×C₈₉	—	2	1	no	—
288	C₄⋊C₄×C₈₉	—	2	1	no	—
289	C₄⋊C₄×C₈₉	—	2	2	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
298	C₂²⋊C₄×C₈₉	—	2	2	no	—
299	C₂²⋊C₄×C₈₉	—	2	2	no	—
300	C₂²⋊C₄×C₈₉	—	2	2	no	—
301	C₂²⋊C₄×C₈₉	—	2	4	no	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	4	no	—
304	C₂²⋊C₄×C₈₉	—	2	4	no	—
305	C₂²⋊C₄×C₈₉	—	2	2	no	—
306	C₂²⋊C₄×C₈₉	—	2	2	no	—
307	C₂²⋊C₄×C₈₉	—	2	2	no	—
308	C₂²⋊C₄×C₈₉	—	2	2	no	—
309	C₂²⋊C₄×C₈₉	—	2	2	no	—
310	C₂²⋊C₄×C₈₉	—	2	2	no	—
311	C₄²×C₈₉	—	2	2	no	—
312	C₄²×C₈₉	—	2	2	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
327	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
328	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
329	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
330	C₂³×C₈₉	—	2	2	no	—
331	C₂³×C₈₉	—	2	2	no	—
332	C₂³×C₈₉	—	2	2	no	—
333	C₂³×C₈₉	—	2	8	no	—
334	C₂³×C₈₉	—	2	8	no	—
335	C₂³×C₈₉	—	2	8	no	—
336	C₂³×C₈₉	—	2	4	no	—
337	C₂³×C₈₉	—	2	2	no	—
338	C₂³×C₈₉	—	4	4	no	—
339	C₂³×C₈₉	—	4	4	no	—
340	C₂³×C₈₉	—	4	32	no	—
341	C₂³×C₈₉	—	4	4	no	—
342	C₂³×C₈₉	—	4	4	no	—
343	C₂³×C₈₉	—	4	4	no	—
344	C₂³×C₈₉	—	4	4	no	—
345	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
346	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₈₉	—	2	4	no	—
349	Q₈×C₈₉	—	4	2	no	—
350	Q₈×C₈₉	—	4	2	no	—
351	D₄×C₈₉	—	2	8	no	—
352	D₄×C₈₉	—	2	8	no	—
353	D₄×C₈₉	—	2	8	no	—
354	D₄×C₈₉	—	2	4	no	—
355	D₄×C₈₉	—	2	4	no	—
356	D₄×C₈₉	—	4	2	no	—
357	D₄×C₈₉	—	4	4	no	—
358	D₄×C₈₉	—	4	4	no	—
359	D₄×C₈₉	—	4	4	no	—
360	D₄×C₈₉	—	4	2	no	—
361	D₄×C₈₉	C₂×#41	1	8	yes	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	2	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	4	no	—
378	C₂×C₄×C₈₉	—	4	1	no	—
379	C₂×C₄×C₈₉	—	4	1	no	—
380	C₂×C₄×C₈₉	—	4	1	no	—
381	C₂×C₄×C₈₉	—	4	1	no	—
382	C₂×C₄×C₈₉	—	4	8	no	—
383	C₂×C₄×C₈₉	—	4	8	no	—
384	C₂×C₄×C₈₉	—	4	4	no	—
385	C₂×C₄×C₈₉	—	4	4	no	—
386	C₂×C₄×C₈₉	—	4	4	no	—
387	C₂×C₄×C₈₉	—	4	4	no	—
388	C₂×C₄×C₈₉	—	4	4	no	—
389	C₂×C₄×C₈₉	—	4	8	no	—
390	C₂×C₄×C₈₉	—	4	8	no	—
391	C₂×C₄×C₈₉	—	4	4	no	—
392	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
393	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
405	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
406	C₈×C₈₉	—	2	8	no	—
407	C₂²×C₈₉	—	2	8	no	—
408	C₂²×C₈₉	—	2	1	no	—
409	C₂²×C₈₉	—	2	1	no	—
410	C₂²×C₈₉	—	2	1	no	—
411	C₂²×C₈₉	—	2	1	no	—
412	C₂²×C₈₉	—	2	1	no	—
413	C₂²×C₈₉	—	2	1	no	—
414	C₂²×C₈₉	—	2	8	no	—
415	C₂²×C₈₉	—	4	16	no	—
416	C₂²×C₈₉	—	4	16	no	—
417	C₂²×C₈₉	—	4	16	no	—
418	C₂²×C₈₉	—	4	4	no	—
419	C₂²×C₈₉	—	4	4	no	—
420	C₂²×C₈₉	—	4	2	no	—
421	C₂²×C₈₉	—	4	2	no	—
422	C₂²×C₈₉	—	4	2	no	—
423	C₂²×C₈₉	#525	1	2	yes	—
424	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
425	C₂²×C₈₉	#575	1	2	yes	—
426	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₈₉	—	2	1	no	—
428	C₄×C₈₉	—	2	1	no	—
429	C₄×C₈₉	—	2	1	no	—
430	C₄×C₈₉	—	2	1	no	—
431	C₄×C₈₉	—	2	1	no	—
432	C₄×C₈₉	—	2	1	no	—
433	C₄×C₈₉	—	2	1	no	—
434	C₄×C₈₉	—	2	1	no	—
435	C₄×C₈₉	—	4	2	no	—
436	C₄×C₈₉	—	4	4	no	—
437	C₄×C₈₉	—	4	2	no	—
438	C₄×C₈₉	—	4	2	no	—
439	C₄×C₈₉	#525	1	2	yes	—
440	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
441	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
442	C₄×C₈₉	C₂²×#41	1	2	yes	—
443	#60558	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂×C₈₉	—	2	2	no	—
445	C₂×C₈₉	—	2	2	no	—
446	C₂×C₈₉	—	2	2	no	—
447	C₂×C₈₉	—	4	8	no	—
448	C₂×C₈₉	—	8	2	no	—
449	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
450	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
452	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
453	C₂²×C₄×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#3114	C₂×C₈₉	1	4	yes	complemented
455	#3110	C₂×C₈₉	1	2	yes	complemented
456	#3109	C₂×C₈₉	1	2	yes	complemented
457	#3105	C₂×C₈₉	1	4	yes	complemented
458	#3101	C₂×C₈₉	1	2	yes	complemented
459	#3100	C₂×C₈₉	1	2	yes	complemented
460	#3092	C₂×C₈₉	1	2	yes	complemented
461	#3077	C₂×C₈₉	1	2	yes	complemented
462	#3036	C₂×C₈₉	1	2	yes	complemented
463	#3003	C₂×C₈₉	1	2	yes	complemented
464	C₄×AGL(1,ℤ/8)	C₂×C₈₉	1	4	yes	complemented
465	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
466	C₈₉	#60558	1	1	yes	characteristic, direct product factor, Sylow
467	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
468	C₂⁴×C₄	—	2	1	no	—
469	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	—
470	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
471	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
472	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
473	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
474	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	#532	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	#529	—	2	1	no	—
477	#529	—	2	1	no	—
478	#529	—	2	1	no	—
479	#529	—	2	1	no	—
480	#529	C₂²×C₈₉	1	2	yes	complemented
481	#529	C₂²×C₈₉	1	2	yes	complemented
482	#525	—	2	1	no	—
483	#525	—	2	1	no	—
484	#525	C₂²×C₈₉	1	2	yes	—
485	C₄×#41	—	2	1	no	—
486	C₄×#41	—	2	1	no	—
487	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
488	C₂×C₄×D₄	—	2	1	no	—
489	C₂×C₄×D₄	—	2	1	no	—
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	—	2	1	no	—
492	C₂×C₄×D₄	—	2	1	no	—
493	C₂×C₄×D₄	—	2	1	no	—
494	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
496	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
500	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	—	2	1	no	—
502	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
503	#484	C₂²×C₈₉	1	4	yes	complemented
504	#483	C₂²×C₈₉	1	4	yes	complemented
505	#481	C₂²×C₈₉	1	4	yes	complemented
506	#480	C₂²×C₈₉	1	4	yes	complemented
507	#478	C₂²×C₈₉	1	8	yes	complemented
508	#476	C₂²×C₈₉	1	4	yes	complemented
509	#474	C₂²×C₈₉	1	4	yes	complemented
510	#463	C₂²×C₈₉	1	8	yes	complemented
511	#461	C₂²×C₈₉	1	4	yes	complemented
512	#459	C₂²×C₈₉	1	4	yes	complemented
513	#450	C₂²×C₈₉	1	4	yes	—
514	#450	C₂²×C₈₉	1	4	yes	—
515	#447	C₂²×C₈₉	1	4	yes	—
516	#447	C₂²×C₈₉	1	4	yes	—
517	#442	C₂²×C₈₉	1	8	yes	complemented
518	#440	C₂²×C₈₉	1	8	yes	complemented
519	C₄×SD₁₆	C₂²×C₈₉	1	8	yes	complemented
520	C₄×D₈	C₂²×C₈₉	1	8	yes	complemented
521	#432	C₂²×C₈₉	1	2	yes	complemented
522	#432	C₂²×C₈₉	1	2	yes	complemented
523	#431	C₂²×C₈₉	1	2	yes	complemented
524	#431	C₂²×C₈₉	1	2	yes	complemented
525	#428	C₂²×C₈₉	1	4	yes	complemented
526	#423	C₂²×C₈₉	1	2	yes	complemented
527	#418	C₂²×C₈₉	1	4	yes	—
528	#417	C₂²×C₈₉	1	4	yes	complemented
529	#407	C₂²×C₈₉	1	2	yes	—
530	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
531	C₂⁵	—	2	1	no	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	C₂³×C₈₉	1	2	yes	—
535	C₂²×D₄	—	2	8	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	2	1	no	—
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
540	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
541	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	2	no	—
544	C₂³×C₄	—	2	2	no	—
545	C₂³×C₄	—	2	2	no	—
546	C₂³×C₄	—	2	2	no	—
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	—	2	2	no	—
549	C₂³×C₄	—	4	8	no	—
550	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
551	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
553	AGL(1,ℤ/8)	—	2	16	no	—
554	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
555	C₂×D₈	C₂³×C₈₉	1	8	yes	—
556	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
557	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
558	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
559	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
560	#127	C₂³×C₈₉	1	1	yes	characteristic, complemented
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	—	2	1	no	—
565	#125	C₂³×C₈₉	1	2	yes	complemented
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	C₂³×C₈₉	1	2	yes	complemented
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	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	C₂³×C₈₉	1	2	yes	—
583	#121	C₂³×C₈₉	1	2	yes	—
584	#120	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂³×C₈₉	1	2	yes	complemented
590	C₄×Q₈	C₂³×C₈₉	1	2	yes	complemented
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	C₂³×C₈₉	1	4	yes	—
614	C₄×D₄	C₂³×C₈₉	1	4	yes	—
615	C₄×D₄	C₂³×C₈₉	1	4	yes	—
616	C₄×D₄	C₂³×C₈₉	1	4	yes	—
617	C₄×D₄	C₂³×C₈₉	1	2	yes	complemented
618	C₄×D₄	C₂³×C₈₉	1	2	yes	complemented
619	#117	—	2	1	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	C₂³×C₈₉	1	2	yes	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
640	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
641	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
643	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
650	#107	C₂³×C₈₉	1	8	yes	complemented
651	#106	C₂³×C₈₉	1	8	yes	complemented
652	C₄⋊C₈	C₂³×C₈₉	1	4	yes	complemented
653	C₄⋊C₈	C₂³×C₈₉	1	4	yes	complemented
654	#103	C₂³×C₈₉	1	8	yes	complemented
655	#102	C₂³×C₈₉	1	8	yes	—
656	#102	C₂³×C₈₉	1	8	yes	—
657	#102	C₂³×C₈₉	1	8	yes	complemented
658	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
660	#97	C₂³×C₈₉	1	4	yes	complemented
661	C₄×C₈	C₂³×C₈₉	1	4	yes	complemented
662	C₂⁴	—	2	8	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	4	4	no	—
667	C₂⁴	—	4	4	no	—
668	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
669	#41	—	2	8	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	8	no	—
677	C₂×D₄	—	2	8	no	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	#41×C₈₉	1	8	yes	complemented
690	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
691	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	—	4	8	no	—
707	C₂²×C₄	—	4	8	no	—
708	C₂²×C₄	—	4	8	no	—
709	C₂²×C₄	—	4	8	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	8	no	—
712	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
723	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
730	SD₁₆	—	2	16	no	—
731	D₈	—	2	16	no	—
732	M₁₆	—	2	8	no	—
733	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	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	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
775	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
776	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
777	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
778	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
779	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
780	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
781	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	8	no	—
787	C₂³	—	2	8	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	—	4	32	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	4	no	—
796	C₂³	—	4	4	no	—
797	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
798	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
799	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
800	Q₈	—	2	4	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	4	2	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	8	no	—
805	D₄	—	2	8	no	—
806	D₄	—	2	4	no	—
807	D₄	—	2	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	C₂×#41×C₈₉	1	8	yes	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	complemented
845	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
853	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
856	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
857	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
858	C₈	—	2	8	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	8	no	—
867	C₂²	—	4	16	no	—
868	C₂²	—	4	16	no	—
869	C₂²	—	4	16	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	4	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	#525×C₈₉	1	2	yes	—
876	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
877	C₂²	#575×C₈₉	1	2	yes	—
878	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	4	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	#525×C₈₉	1	2	yes	—
892	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
893	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
894	C₄	C₂²×#41×C₈₉	1	2	yes	—
895	C₂	—	2	2	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	2	no	—
898	C₂	—	4	8	no	—
899	C₂	—	8	2	no	—
900	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
901	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
902	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3444	C₂	semidirect
2. C₂²×C₄×D₄×C₈₉	C₂	semidirect
3. C₈₉×#3114	C₂	semidirect
4. C₈₉×#3110	C₂	semidirect
5. C₈₉×#3109	C₂	semidirect
6. C₈₉×#3105	C₂	semidirect
7. C₈₉×#3101	C₂	semidirect
8. C₈₉×#3100	C₂	semidirect
9. C₈₉×#3092	C₂	semidirect
10. C₈₉×#3077	C₂	semidirect
11. C₈₉×#3036	C₂	semidirect
12. C₈₉×#3003	C₂	semidirect
13. C₄×AGL(1,ℤ/8)×C₈₉	C₂	semidirect
14. C₈₉×#2920	C₂	semidirect
18. #533×C₈₉	C₂²	semidirect
19. #533×C₈₉	C₂²	semidirect
20. #533×C₈₉	C₂²	semidirect
21. #532×C₈₉	C₂²	semidirect
22. #532×C₈₉	C₂²	semidirect
23. #532×C₈₉	C₂²	semidirect
28. #529×C₈₉	C₂²	semidirect
29. #529×C₈₉	C₂²	semidirect
35. C₄×#41×C₈₉	C₂²	semidirect
51. #484×C₈₉	C₂²	semidirect
52. #483×C₈₉	C₂²	semidirect
53. #481×C₈₉	C₂²	semidirect
54. #480×C₈₉	C₂²	semidirect
55. #478×C₈₉	C₂²	semidirect
56. #476×C₈₉	C₂²	semidirect
57. #474×C₈₉	C₂²	semidirect
58. #463×C₈₉	C₂²	semidirect
59. #461×C₈₉	C₂²	semidirect
60. #459×C₈₉	C₂²	semidirect
65. #442×C₈₉	C₂²	semidirect
66. #440×C₈₉	C₂²	semidirect
67. C₄×SD₁₆×C₈₉	C₂²	semidirect
68. C₄×D₈×C₈₉	C₂²	semidirect
69. #432×C₈₉	C₂²	semidirect
70. #432×C₈₉	C₂²	semidirect
71. #431×C₈₉	C₂²	semidirect
72. #431×C₈₉	C₂²	semidirect
73. #428×C₈₉	C₂²	semidirect
74. #423×C₈₉	C₂²	semidirect
76. #417×C₈₉	C₂²	semidirect
78. C₄×M₁₆×C₈₉	C₂²	semidirect
105. C₄⋊Q₈×C₈₉	C₂³	semidirect
106. C₄⋊Q₈×C₈₉	C₂³	semidirect
107. C₄⋊Q₈×C₈₉	C₂³	semidirect
108. #127×C₈₉	C₂³	semidirect
113. #125×C₈₉	C₂³	semidirect
116. #124×C₈₉	C₂³	semidirect
137. C₄×Q₈×C₈₉	C₂³	semidirect
138. C₄×Q₈×C₈₉	C₂³	semidirect
165. C₄×D₄×C₈₉	C₂³	semidirect
166. C₄×D₄×C₈₉	C₂³	semidirect
198. #107×C₈₉	C₂³	semidirect
199. #106×C₈₉	C₂³	semidirect
200. C₄⋊C₈×C₈₉	C₂³	semidirect
201. C₄⋊C₈×C₈₉	C₂³	semidirect
202. #103×C₈₉	C₂³	semidirect
205. #102×C₈₉	C₂³	semidirect
208. #97×C₈₉	C₂³	semidirect
209. C₄×C₈×C₈₉	C₂³	semidirect
237. C₂×D₄×C₈₉	#41	semidirect
392. C₂×C₄×C₈₉	AGL(1,ℤ/8)	semidirect
443. #60558	C₈₉	direct (N × H)
452. #3444	C₂×C₈₉	semidirect
453. C₂²×C₄×D₄	C₂×C₈₉	semidirect
454. #3114	C₂×C₈₉	semidirect
455. #3110	C₂×C₈₉	semidirect
456. #3109	C₂×C₈₉	semidirect
457. #3105	C₂×C₈₉	semidirect
458. #3101	C₂×C₈₉	semidirect
459. #3100	C₂×C₈₉	semidirect
460. #3092	C₂×C₈₉	semidirect
461. #3077	C₂×C₈₉	semidirect
462. #3036	C₂×C₈₉	semidirect
463. #3003	C₂×C₈₉	semidirect
464. C₄×AGL(1,ℤ/8)	C₂×C₈₉	semidirect
465. #2920	C₂×C₈₉	semidirect
466. C₈₉	#60558	direct (N × H)
470. #533	C₂²×C₈₉	semidirect
471. #533	C₂²×C₈₉	semidirect
472. #533	C₂²×C₈₉	semidirect
473. #532	C₂²×C₈₉	semidirect
474. #532	C₂²×C₈₉	semidirect
475. #532	C₂²×C₈₉	semidirect
480. #529	C₂²×C₈₉	semidirect
481. #529	C₂²×C₈₉	semidirect
487. C₄×#41	C₂²×C₈₉	semidirect
503. #484	C₂²×C₈₉	semidirect
504. #483	C₂²×C₈₉	semidirect
505. #481	C₂²×C₈₉	semidirect
506. #480	C₂²×C₈₉	semidirect
507. #478	C₂²×C₈₉	semidirect
508. #476	C₂²×C₈₉	semidirect
509. #474	C₂²×C₈₉	semidirect
510. #463	C₂²×C₈₉	semidirect
511. #461	C₂²×C₈₉	semidirect
512. #459	C₂²×C₈₉	semidirect
517. #442	C₂²×C₈₉	semidirect
518. #440	C₂²×C₈₉	semidirect
519. C₄×SD₁₆	C₂²×C₈₉	semidirect
520. C₄×D₈	C₂²×C₈₉	semidirect
521. #432	C₂²×C₈₉	semidirect
522. #432	C₂²×C₈₉	semidirect
523. #431	C₂²×C₈₉	semidirect
524. #431	C₂²×C₈₉	semidirect
525. #428	C₂²×C₈₉	semidirect
526. #423	C₂²×C₈₉	semidirect
528. #417	C₂²×C₈₉	semidirect
530. C₄×M₁₆	C₂²×C₈₉	semidirect
557. C₄⋊Q₈	C₂³×C₈₉	semidirect
558. C₄⋊Q₈	C₂³×C₈₉	semidirect
559. C₄⋊Q₈	C₂³×C₈₉	semidirect
560. #127	C₂³×C₈₉	semidirect
565. #125	C₂³×C₈₉	semidirect
568. #124	C₂³×C₈₉	semidirect
589. C₄×Q₈	C₂³×C₈₉	semidirect
590. C₄×Q₈	C₂³×C₈₉	semidirect
617. C₄×D₄	C₂³×C₈₉	semidirect
618. C₄×D₄	C₂³×C₈₉	semidirect
650. #107	C₂³×C₈₉	semidirect
651. #106	C₂³×C₈₉	semidirect
652. C₄⋊C₈	C₂³×C₈₉	semidirect
653. C₄⋊C₈	C₂³×C₈₉	semidirect
654. #103	C₂³×C₈₉	semidirect
657. #102	C₂³×C₈₉	semidirect
660. #97	C₂³×C₈₉	semidirect
661. C₄×C₈	C₂³×C₈₉	semidirect
689. C₂×D₄	#41×C₈₉	semidirect
844. C₂×C₄	AGL(1,ℤ/8)×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3444	2
C₂²×C₄×D₄×C₈₉	2
C₈₉×#3114	2
C₈₉×#3110	2
C₈₉×#3109	2
C₈₉×#3105	2
C₈₉×#3101	2
C₈₉×#3100	2
C₈₉×#3092	2
C₈₉×#3077	2
C₈₉×#3036	2
C₈₉×#3003	2
C₄×AGL(1,ℤ/8)×C₈₉	2
C₈₉×#2920	2
#60558	89

Subgroups — C89×#60558 #36438406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60558 #36438406