Subgroups — C₈₉×#61157 #36439005

Order 22784.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3329	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3328	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3320	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3312	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3299	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3298	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3095	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3004	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#419×C₈₉	C₂	1	2	yes	maximal, complemented
18	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#137×C₈₉	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
22	#556×C₈₉	C₂²	1	1	yes	characteristic
23	#555×C₈₉	C₂²	1	1	yes	characteristic
24	#554×C₈₉	C₂²	1	1	yes	characteristic
25	#553×C₈₉	C₂²	1	2	yes	—
26	#552×C₈₉	—	2	1	no	—
27	#552×C₈₉	C₂²	1	2	yes	—
28	#551×C₈₉	—	2	2	no	—
29	D₄×Q₈×C₈₉	—	2	1	no	—
30	D₄×Q₈×C₈₉	—	2	2	no	—
31	D₄×Q₈×C₈₉	—	2	1	no	—
32	D₄×Q₈×C₈₉	C₂²	1	4	yes	—
33	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
34	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
35	#547×C₈₉	C₂²	1	1	yes	characteristic
36	#546×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	#529×C₈₉	—	2	2	no	—
41	#529×C₈₉	—	2	1	no	—
42	#525×C₈₉	C₂²	1	2	yes	—
43	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
44	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
45	C₄×#41×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	—	2	1	no	—
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	C₂²	1	2	yes	—
51	#491×C₈₉	C₂²	1	4	yes	complemented
52	#487×C₈₉	C₂²	1	2	yes	complemented
53	#487×C₈₉	C₂²	1	2	yes	complemented
54	#485×C₈₉	C₂²	1	4	yes	complemented
55	#485×C₈₉	C₂²	1	4	yes	complemented
56	#484×C₈₉	C₂²	1	4	yes	complemented
57	#483×C₈₉	C₂²	1	4	yes	complemented
58	#479×C₈₉	C₂²	1	4	yes	complemented
59	#477×C₈₉	C₂²	1	2	yes	complemented
60	#475×C₈₉	C₂²	1	2	yes	complemented
61	#470×C₈₉	C₂²	1	4	yes	complemented
62	#468×C₈₉	C₂²	1	4	yes	complemented
63	#467×C₈₉	C₂²	1	4	yes	complemented
64	#465×C₈₉	C₂²	1	4	yes	complemented
65	#462×C₈₉	C₂²	1	2	yes	complemented
66	#462×C₈₉	C₂²	1	2	yes	complemented
67	#461×C₈₉	C₂²	1	2	yes	complemented
68	#461×C₈₉	C₂²	1	2	yes	complemented
69	#451×C₈₉	C₂²	1	4	yes	complemented
70	#451×C₈₉	C₂²	1	4	yes	complemented
71	#448×C₈₉	C₂²	1	4	yes	complemented
72	#448×C₈₉	C₂²	1	4	yes	complemented
73	#441×C₈₉	C₂²	1	2	yes	complemented
74	#440×C₈₉	C₂²	1	2	yes	complemented
75	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
77	#436×C₈₉	C₂²	1	2	yes	—
78	#435×C₈₉	C₂²	1	4	yes	—
79	C₈×D₄×C₈₉	C₂²	1	2	yes	—
80	#428×C₈₉	C₂²	1	2	yes	—
81	#428×C₈₉	C₂²	1	1	yes	characteristic
82	#423×C₈₉	C₂²	1	1	yes	characteristic
83	#419×C₈₉	C₂²	1	2	yes	—
84	#419×C₈₉	C₂²	1	2	yes	—
85	#419×C₈₉	C₂²	1	2	yes	—
86	#419×C₈₉	C₂²	1	2	yes	—
87	#419×C₈₉	C₂²	1	1	yes	characteristic
88	#419×C₈₉	C₂²	1	4	yes	complemented
89	#419×C₈₉	C₂²	1	4	yes	complemented
90	#417×C₈₉	C₂²	1	1	yes	characteristic
91	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
92	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
93	#407×C₈₉	C₂²	1	2	yes	—
94	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	—	2	2	no	—
98	C₂²×Q₈×C₈₉	—	2	2	no	—
99	C₂²×Q₈×C₈₉	—	2	2	no	—
100	C₂²×Q₈×C₈₉	—	2	8	no	—
101	C₂²×Q₈×C₈₉	—	4	4	no	—
102	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
103	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
104	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
105	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	—	2	2	no	—
108	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
109	#137×C₈₉	—	2	4	no	—
110	#137×C₈₉	—	4	4	no	—
111	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×M₁₆×C₈₉	—	4	4	no	—
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
119	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
120	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
121	C₄⋊Q₈×C₈₉	—	2	2	no	—
122	C₄⋊Q₈×C₈₉	—	2	2	no	—
123	C₄⋊Q₈×C₈₉	—	2	4	no	—
124	C₄⋊Q₈×C₈₉	—	2	1	no	—
125	C₄⋊Q₈×C₈₉	—	2	1	no	—
126	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
129	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
130	#126×C₈₉	—	2	2	no	—
131	#126×C₈₉	—	2	2	no	—
132	#126×C₈₉	—	2	2	no	—
133	#125×C₈₉	—	2	2	no	—
134	#125×C₈₉	—	2	1	no	—
135	#125×C₈₉	C₂³	1	2	yes	—
136	#124×C₈₉	—	2	1	no	—
137	#124×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	2	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	no	—
146	C₂²⋊Q₈×C₈₉	—	2	1	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	—	2	4	no	—
151	C₂²⋊Q₈×C₈₉	—	2	2	no	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	1	no	—
158	#121×C₈₉	C₂³	1	2	yes	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	#120×C₈₉	—	2	2	no	—
161	C₄×Q₈×C₈₉	—	2	1	no	—
162	C₄×Q₈×C₈₉	—	2	1	no	—
163	C₄×Q₈×C₈₉	—	2	1	no	—
164	C₄×Q₈×C₈₉	—	2	1	no	—
165	C₄×Q₈×C₈₉	—	2	1	no	—
166	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
167	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₈₉	—	2	4	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	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
180	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
181	C₄×D₄×C₈₉	D₄	1	2	yes	—
182	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₈₉	C₂³	1	2	yes	—
186	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	#117×C₈₉	—	2	2	no	—
188	#117×C₈₉	—	2	2	no	—
189	#117×C₈₉	—	2	1	no	—
190	#117×C₈₉	—	2	2	no	—
191	#117×C₈₉	—	2	1	no	—
192	#117×C₈₉	C₂³	1	1	yes	characteristic
193	#117×C₈₉	C₂³	1	2	yes	—
194	#117×C₈₉	C₂³	1	2	yes	—
195	#117×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
200	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
207	C₂×C₄²×C₈₉	—	2	2	no	—
208	C₂×C₄²×C₈₉	—	2	1	no	—
209	C₂×C₄²×C₈₉	—	2	1	no	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	#107×C₈₉	C₂³	1	2	yes	—
212	#107×C₈₉	C₂³	1	4	yes	—
213	#106×C₈₉	C₂³	1	2	yes	—
214	#106×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	2	yes	—
219	#103×C₈₉	C₂³	1	4	yes	—
220	#103×C₈₉	C₂³	1	4	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#103×C₈₉	C₂³	1	4	yes	—
223	#103×C₈₉	C₂³	1	4	yes	—
224	#103×C₈₉	C₂³	1	4	yes	—
225	#103×C₈₉	C₂³	1	2	yes	—
226	#103×C₈₉	C₂³	1	4	yes	—
227	#103×C₈₉	C₂³	1	4	yes	—
228	#102×C₈₉	C₂³	1	2	yes	—
229	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
230	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
231	#97×C₈₉	C₂³	1	2	yes	—
232	C₄×C₈×C₈₉	C₂³	1	2	yes	—
233	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	2	2	no	—
236	#41×C₈₉	—	4	4	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	4	no	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	2	2	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	2	2	no	—
244	C₂×Q₈×C₈₉	—	2	8	no	—
245	C₂×Q₈×C₈₉	—	2	8	no	—
246	C₂×Q₈×C₈₉	—	2	4	no	—
247	C₂×Q₈×C₈₉	—	2	4	no	—
248	C₂×Q₈×C₈₉	—	4	8	no	—
249	C₂×Q₈×C₈₉	—	4	4	no	—
250	C₂×Q₈×C₈₉	—	4	4	no	—
251	C₂×Q₈×C₈₉	—	4	8	no	—
252	C₂×Q₈×C₈₉	—	4	8	no	—
253	C₂×Q₈×C₈₉	#41	1	4	yes	complemented
254	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
255	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
257	C₂×D₄×C₈₉	—	2	4	no	—
258	C₂×D₄×C₈₉	—	2	1	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	2	2	no	—
261	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	—	2	1	no	—
266	C₂²×C₄×C₈₉	—	2	4	no	—
267	C₂²×C₄×C₈₉	—	2	4	no	—
268	C₂²×C₄×C₈₉	—	2	1	no	—
269	C₂²×C₄×C₈₉	—	2	2	no	—
270	C₂²×C₄×C₈₉	—	2	2	no	—
271	C₂²×C₄×C₈₉	—	2	4	no	—
272	C₂²×C₄×C₈₉	—	2	4	no	—
273	C₂²×C₄×C₈₉	—	2	2	no	—
274	C₂²×C₄×C₈₉	—	2	1	no	—
275	C₂²×C₄×C₈₉	—	2	1	no	—
276	C₂²×C₄×C₈₉	—	2	1	no	—
277	C₂²×C₄×C₈₉	—	4	8	no	—
278	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
286	Q₁₆×C₈₉	—	2	4	no	—
287	Q₁₆×C₈₉	—	4	4	no	—
288	SD₁₆×C₈₉	—	2	4	no	—
289	SD₁₆×C₈₉	—	4	4	no	—
290	M₁₆×C₈₉	—	2	2	no	—
291	M₁₆×C₈₉	—	2	2	no	—
292	M₁₆×C₈₉	—	2	4	no	—
293	M₁₆×C₈₉	—	4	4	no	—
294	C₂×C₈×C₈₉	—	4	4	no	—
295	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
296	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
297	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	2	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	—	2	4	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	2	no	—
308	C₄⋊C₄×C₈₉	—	2	1	no	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	—	2	2	no	—
311	C₄⋊C₄×C₈₉	—	2	2	no	—
312	C₄⋊C₄×C₈₉	—	2	1	no	—
313	C₄⋊C₄×C₈₉	—	2	1	no	—
314	C₄⋊C₄×C₈₉	—	2	2	no	—
315	C₄⋊C₄×C₈₉	—	2	2	no	—
316	C₄⋊C₄×C₈₉	—	2	1	no	—
317	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
318	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₂²⋊C₄×C₈₉	—	2	1	no	—
326	C₂²⋊C₄×C₈₉	—	2	2	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	4	no	—
330	C₂²⋊C₄×C₈₉	—	2	4	no	—
331	C₂²⋊C₄×C₈₉	—	2	2	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	1	no	—
335	C₂²⋊C₄×C₈₉	—	2	1	no	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
341	C₄²×C₈₉	—	2	1	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	1	no	—
344	C₄²×C₈₉	—	2	2	no	—
345	C₄²×C₈₉	—	2	2	no	—
346	C₄²×C₈₉	—	2	1	no	—
347	C₄²×C₈₉	—	2	2	no	—
348	C₄²×C₈₉	—	2	2	no	—
349	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
353	C₂³×C₈₉	—	2	4	no	—
354	C₂³×C₈₉	—	2	4	no	—
355	C₂³×C₈₉	—	2	1	no	—
356	C₂³×C₈₉	—	4	2	no	—
357	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
358	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
359	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
360	Q₈×C₈₉	—	2	4	no	—
361	Q₈×C₈₉	—	2	2	no	—
362	Q₈×C₈₉	—	2	1	no	—
363	Q₈×C₈₉	—	2	4	no	—
364	Q₈×C₈₉	—	2	4	no	—
365	Q₈×C₈₉	—	2	1	no	—
366	Q₈×C₈₉	—	4	8	no	—
367	Q₈×C₈₉	—	4	8	no	—
368	Q₈×C₈₉	—	4	4	no	—
369	Q₈×C₈₉	—	4	2	no	—
370	Q₈×C₈₉	—	8	1	no	—
371	Q₈×C₈₉	C₂×#41	1	4	yes	—
372	D₄×C₈₉	—	2	4	no	—
373	D₄×C₈₉	—	2	2	no	—
374	D₄×C₈₉	—	2	1	no	—
375	D₄×C₈₉	—	2	1	no	—
376	D₄×C₈₉	—	4	2	no	—
377	D₄×C₈₉	—	4	4	no	—
378	D₄×C₈₉	—	8	2	no	—
379	D₄×C₈₉	#137	1	4	yes	complemented
380	C₂×C₄×C₈₉	—	2	4	no	—
381	C₂×C₄×C₈₉	—	2	4	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	2	4	no	—
384	C₂×C₄×C₈₉	—	2	4	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	2	no	—
393	C₂×C₄×C₈₉	—	2	1	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	4	no	—
397	C₂×C₄×C₈₉	—	4	1	no	—
398	C₂×C₄×C₈₉	—	4	8	no	—
399	C₂×C₄×C₈₉	—	4	8	no	—
400	C₂×C₄×C₈₉	—	4	2	no	—
401	C₂×C₄×C₈₉	—	4	4	no	—
402	C₂×C₄×C₈₉	—	4	4	no	—
403	C₂×C₄×C₈₉	—	4	2	no	—
404	C₂×C₄×C₈₉	—	4	2	no	—
405	C₂×C₄×C₈₉	—	8	1	no	—
406	C₂×C₄×C₈₉	—	8	2	no	—
407	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
415	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
417	C₈×C₈₉	—	2	2	no	—
418	C₈×C₈₉	—	2	2	no	—
419	C₈×C₈₉	—	2	4	no	—
420	C₂²×C₈₉	—	2	1	no	—
421	C₂²×C₈₉	—	2	2	no	—
422	C₂²×C₈₉	—	2	2	no	—
423	C₂²×C₈₉	—	2	1	no	—
424	C₂²×C₈₉	—	2	2	no	—
425	C₂²×C₈₉	—	2	2	no	—
426	C₂²×C₈₉	—	2	2	no	—
427	C₂²×C₈₉	—	4	8	no	—
428	C₂²×C₈₉	—	4	1	no	—
429	C₂²×C₈₉	—	4	1	no	—
430	C₂²×C₈₉	—	4	1	no	—
431	C₂²×C₈₉	#546	1	2	yes	—
432	C₂²×C₈₉	C₂×#137	1	4	yes	—
433	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₈₉	—	2	1	no	—
435	C₄×C₈₉	—	2	1	no	—
436	C₄×C₈₉	—	2	2	no	—
437	C₄×C₈₉	—	2	2	no	—
438	C₄×C₈₉	—	2	4	no	—
439	C₄×C₈₉	—	2	1	no	—
440	C₄×C₈₉	—	4	2	no	—
441	C₄×C₈₉	—	4	1	no	—
442	C₄×C₈₉	—	4	2	no	—
443	C₄×C₈₉	—	4	4	no	—
444	C₄×C₈₉	—	4	1	no	—
445	C₄×C₈₉	—	4	1	no	—
446	C₄×C₈₉	—	4	2	no	—
447	C₄×C₈₉	#546	1	2	yes	—
448	C₄×C₈₉	C₂×#137	1	2	yes	—
449	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
450	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	#61157	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂×C₈₉	—	2	2	no	—
453	C₂×C₈₉	—	2	4	no	—
454	C₂×C₈₉	—	4	2	no	—
455	C₂×C₈₉	—	8	1	no	—
456	C₂×C₈₉	C₂×#546	1	1	yes	characteristic
457	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
458	C₂×C₈₉	#3586	1	1	yes	characteristic
459	#3475	C₂×C₈₉	1	1	yes	characteristic
460	C₂×D₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
461	#3329	C₂×C₈₉	1	2	yes	complemented
462	#3328	C₂×C₈₉	1	2	yes	complemented
463	#3320	C₂×C₈₉	1	4	yes	complemented
464	#3312	C₂×C₈₉	1	4	yes	complemented
465	#3299	C₂×C₈₉	1	2	yes	complemented
466	#3298	C₂×C₈₉	1	2	yes	complemented
467	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
468	#3095	C₂×C₈₉	1	2	yes	complemented
469	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#3056	C₂×C₈₉	1	2	yes	complemented
471	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
472	#3004	C₂×C₈₉	1	2	yes	complemented
473	C₄×#137	C₂×C₈₉	1	1	yes	characteristic, complemented
474	D₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
475	C₂×#419	C₂×C₈₉	1	2	yes	complemented
476	C₈₉	#61157	1	1	yes	characteristic, direct product factor, Sylow
477	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
478	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×#137	C₂²×C₈₉	1	2	yes	—
480	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
481	#556	C₂²×C₈₉	1	1	yes	characteristic
482	#555	C₂²×C₈₉	1	1	yes	characteristic
483	#554	C₂²×C₈₉	1	1	yes	characteristic
484	#553	C₂²×C₈₉	1	2	yes	—
485	#552	—	2	1	no	—
486	#552	C₂²×C₈₉	1	2	yes	—
487	#551	—	2	2	no	—
488	D₄×Q₈	—	2	1	no	—
489	D₄×Q₈	—	2	2	no	—
490	D₄×Q₈	—	2	1	no	—
491	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
492	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
493	D₄×Q₈	C₂²×C₈₉	1	4	yes	—
494	#547	C₂²×C₈₉	1	1	yes	characteristic
495	#546	—	2	1	no	—
496	#533	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×C₄⋊Q₈	—	2	1	no	—
498	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
499	#529	—	2	2	no	—
500	#529	—	2	1	no	—
501	#525	C₂²×C₈₉	1	2	yes	—
502	C₂×C₂²⋊Q₈	—	2	2	no	—
503	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
504	C₄×#41	—	2	1	no	—
505	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
507	C₂×C₄×D₄	—	2	1	no	—
508	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×#117	C₂²×C₈₉	1	2	yes	—
510	#491	C₂²×C₈₉	1	4	yes	complemented
511	#487	C₂²×C₈₉	1	2	yes	complemented
512	#487	C₂²×C₈₉	1	2	yes	complemented
513	#485	C₂²×C₈₉	1	4	yes	complemented
514	#485	C₂²×C₈₉	1	4	yes	complemented
515	#484	C₂²×C₈₉	1	4	yes	complemented
516	#483	C₂²×C₈₉	1	4	yes	complemented
517	#479	C₂²×C₈₉	1	4	yes	complemented
518	#477	C₂²×C₈₉	1	2	yes	complemented
519	#475	C₂²×C₈₉	1	2	yes	complemented
520	#470	C₂²×C₈₉	1	4	yes	complemented
521	#468	C₂²×C₈₉	1	4	yes	complemented
522	#467	C₂²×C₈₉	1	4	yes	complemented
523	#465	C₂²×C₈₉	1	4	yes	complemented
524	#462	C₂²×C₈₉	1	2	yes	complemented
525	#462	C₂²×C₈₉	1	2	yes	complemented
526	#461	C₂²×C₈₉	1	2	yes	complemented
527	#461	C₂²×C₈₉	1	2	yes	complemented
528	#451	C₂²×C₈₉	1	4	yes	complemented
529	#451	C₂²×C₈₉	1	4	yes	complemented
530	#448	C₂²×C₈₉	1	4	yes	complemented
531	#448	C₂²×C₈₉	1	4	yes	complemented
532	#441	C₂²×C₈₉	1	2	yes	complemented
533	#440	C₂²×C₈₉	1	2	yes	complemented
534	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
535	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
536	#436	C₂²×C₈₉	1	2	yes	—
537	#435	C₂²×C₈₉	1	4	yes	—
538	C₈×D₄	C₂²×C₈₉	1	2	yes	—
539	#428	C₂²×C₈₉	1	2	yes	—
540	#428	C₂²×C₈₉	1	1	yes	characteristic
541	#423	C₂²×C₈₉	1	1	yes	characteristic
542	#419	C₂²×C₈₉	1	2	yes	—
543	#419	C₂²×C₈₉	1	2	yes	—
544	#419	C₂²×C₈₉	1	2	yes	—
545	#419	C₂²×C₈₉	1	2	yes	—
546	#419	C₂²×C₈₉	1	1	yes	characteristic
547	#419	C₂²×C₈₉	1	4	yes	complemented
548	#419	C₂²×C₈₉	1	4	yes	complemented
549	#417	C₂²×C₈₉	1	1	yes	characteristic
550	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
551	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
552	#407	C₂²×C₈₉	1	2	yes	—
553	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
554	C₂×#41	—	2	1	no	—
555	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
556	C₂²×Q₈	—	2	2	no	—
557	C₂²×Q₈	—	2	2	no	—
558	C₂²×Q₈	—	2	2	no	—
559	C₂²×Q₈	—	2	8	no	—
560	C₂²×Q₈	—	4	4	no	—
561	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
562	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
563	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
564	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
565	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
566	C₂³×C₄	—	2	2	no	—
567	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
568	#137	—	2	4	no	—
569	#137	—	4	4	no	—
570	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
571	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
574	C₂×M₁₆	—	4	4	no	—
575	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
577	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
578	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
579	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
580	C₄⋊Q₈	—	2	2	no	—
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	—	2	4	no	—
583	C₄⋊Q₈	—	2	1	no	—
584	C₄⋊Q₈	—	2	1	no	—
585	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
586	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
587	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
588	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	1	no	—
594	#125	C₂³×C₈₉	1	2	yes	—
595	#124	—	2	1	no	—
596	#124	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	1	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	4	no	—
607	C₂²⋊Q₈	—	2	4	no	—
608	C₂²⋊Q₈	—	2	4	no	—
609	C₂²⋊Q₈	—	2	4	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
613	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
614	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
615	#121	—	2	2	no	—
616	#121	—	2	1	no	—
617	#121	C₂³×C₈₉	1	2	yes	—
618	#121	C₂³×C₈₉	1	2	yes	—
619	#120	—	2	2	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
626	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
627	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
639	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
640	C₄×D₄	D₄×C₈₉	1	2	yes	—
641	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₈₉	1	2	yes	—
645	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
646	#117	—	2	2	no	—
647	#117	—	2	2	no	—
648	#117	—	2	1	no	—
649	#117	—	2	2	no	—
650	#117	—	2	1	no	—
651	#117	C₂³×C₈₉	1	1	yes	characteristic
652	#117	C₂³×C₈₉	1	2	yes	—
653	#117	C₂³×C₈₉	1	2	yes	—
654	#117	C₂³×C₈₉	1	2	yes	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	2	no	—
659	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
666	C₂×C₄²	—	2	2	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
670	#107	C₂³×C₈₉	1	2	yes	—
671	#107	C₂³×C₈₉	1	4	yes	—
672	#106	C₂³×C₈₉	1	2	yes	—
673	#106	C₂³×C₈₉	1	4	yes	—
674	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
675	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
676	#103	C₂³×C₈₉	1	2	yes	—
677	#103	C₂³×C₈₉	1	2	yes	—
678	#103	C₂³×C₈₉	1	4	yes	—
679	#103	C₂³×C₈₉	1	4	yes	—
680	#103	C₂³×C₈₉	1	4	yes	—
681	#103	C₂³×C₈₉	1	4	yes	—
682	#103	C₂³×C₈₉	1	4	yes	—
683	#103	C₂³×C₈₉	1	4	yes	—
684	#103	C₂³×C₈₉	1	2	yes	—
685	#103	C₂³×C₈₉	1	4	yes	—
686	#103	C₂³×C₈₉	1	4	yes	—
687	#102	C₂³×C₈₉	1	2	yes	—
688	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
690	#97	C₂³×C₈₉	1	2	yes	—
691	C₄×C₈	C₂³×C₈₉	1	2	yes	—
692	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	4	4	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	8	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	4	8	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	—	4	4	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	—	4	8	no	—
712	C₂×Q₈	#41×C₈₉	1	4	yes	complemented
713	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
714	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
715	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
721	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
722	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
723	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	4	8	no	—
737	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
745	Q₁₆	—	2	4	no	—
746	Q₁₆	—	4	4	no	—
747	SD₁₆	—	2	4	no	—
748	SD₁₆	—	4	4	no	—
749	M₁₆	—	2	2	no	—
750	M₁₆	—	2	2	no	—
751	M₁₆	—	2	4	no	—
752	M₁₆	—	4	4	no	—
753	C₂×C₈	—	4	4	no	—
754	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
755	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
756	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
778	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
779	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
780	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
783	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
797	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
799	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
810	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
811	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	4	2	no	—
816	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
817	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	4	8	no	—
826	Q₈	—	4	8	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	2	no	—
829	Q₈	—	8	1	no	—
830	Q₈	C₂×#41×C₈₉	1	4	yes	—
831	D₄	—	2	4	no	—
832	D₄	—	2	2	no	—
833	D₄	—	2	1	no	—
834	D₄	—	2	1	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	8	2	no	—
838	D₄	#137×C₈₉	1	4	yes	complemented
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
873	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
874	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
875	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
876	C₈	—	2	2	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	4	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	#546×C₈₉	1	2	yes	—
891	C₂²	C₂×#137×C₈₉	1	4	yes	—
892	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	4	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	4	no	—
905	C₄	—	4	1	no	—
906	C₄	#546×C₈₉	1	2	yes	—
907	C₄	C₂×#137×C₈₉	1	2	yes	—
908	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
909	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
910	C₂	—	2	2	no	—
911	C₂	—	2	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	8	1	no	—
914	C₂	C₂×#546×C₈₉	1	1	yes	characteristic
915	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
916	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₈₉	C₂	semidirect
3. C₈₉×#3329	C₂	semidirect
4. C₈₉×#3328	C₂	semidirect
5. C₈₉×#3320	C₂	semidirect
6. C₈₉×#3312	C₂	semidirect
7. C₈₉×#3299	C₂	semidirect
8. C₈₉×#3298	C₂	semidirect
9. C₈₉×#3139	C₂	semidirect
10. C₈₉×#3095	C₂	semidirect
11. C₈₉×#3078	C₂	semidirect
12. C₈₉×#3056	C₂	semidirect
13. C₈₉×#3039	C₂	semidirect
14. C₈₉×#3004	C₂	semidirect
15. C₄×#137×C₈₉	C₂	semidirect
16. D₄×M₁₆×C₈₉	C₂	semidirect
17. C₂×#419×C₈₉	C₂	semidirect
51. #491×C₈₉	C₂²	semidirect
52. #487×C₈₉	C₂²	semidirect
53. #487×C₈₉	C₂²	semidirect
54. #485×C₈₉	C₂²	semidirect
55. #485×C₈₉	C₂²	semidirect
56. #484×C₈₉	C₂²	semidirect
57. #483×C₈₉	C₂²	semidirect
58. #479×C₈₉	C₂²	semidirect
59. #477×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #470×C₈₉	C₂²	semidirect
62. #468×C₈₉	C₂²	semidirect
63. #467×C₈₉	C₂²	semidirect
64. #465×C₈₉	C₂²	semidirect
65. #462×C₈₉	C₂²	semidirect
66. #462×C₈₉	C₂²	semidirect
67. #461×C₈₉	C₂²	semidirect
68. #461×C₈₉	C₂²	semidirect
69. #451×C₈₉	C₂²	semidirect
70. #451×C₈₉	C₂²	semidirect
71. #448×C₈₉	C₂²	semidirect
72. #448×C₈₉	C₂²	semidirect
73. #441×C₈₉	C₂²	semidirect
74. #440×C₈₉	C₂²	semidirect
75. C₄×Q₁₆×C₈₉	C₂²	semidirect
76. C₄×SD₁₆×C₈₉	C₂²	semidirect
88. #419×C₈₉	C₂²	semidirect
89. #419×C₈₉	C₂²	semidirect
91. C₂×#103×C₈₉	C₂²	semidirect
92. C₂×#103×C₈₉	C₂²	semidirect
253. C₂×Q₈×C₈₉	#41	semidirect
379. D₄×C₈₉	#137	semidirect
451. #61157	C₈₉	direct (N × H)
460. C₂×D₄×Q₈	C₂×C₈₉	semidirect
461. #3329	C₂×C₈₉	semidirect
462. #3328	C₂×C₈₉	semidirect
463. #3320	C₂×C₈₉	semidirect
464. #3312	C₂×C₈₉	semidirect
465. #3299	C₂×C₈₉	semidirect
466. #3298	C₂×C₈₉	semidirect
467. #3139	C₂×C₈₉	semidirect
468. #3095	C₂×C₈₉	semidirect
469. #3078	C₂×C₈₉	semidirect
470. #3056	C₂×C₈₉	semidirect
471. #3039	C₂×C₈₉	semidirect
472. #3004	C₂×C₈₉	semidirect
473. C₄×#137	C₂×C₈₉	semidirect
474. D₄×M₁₆	C₂×C₈₉	semidirect
475. C₂×#419	C₂×C₈₉	semidirect
476. C₈₉	#61157	direct (N × H)
510. #491	C₂²×C₈₉	semidirect
511. #487	C₂²×C₈₉	semidirect
512. #487	C₂²×C₈₉	semidirect
513. #485	C₂²×C₈₉	semidirect
514. #485	C₂²×C₈₉	semidirect
515. #484	C₂²×C₈₉	semidirect
516. #483	C₂²×C₈₉	semidirect
517. #479	C₂²×C₈₉	semidirect
518. #477	C₂²×C₈₉	semidirect
519. #475	C₂²×C₈₉	semidirect
520. #470	C₂²×C₈₉	semidirect
521. #468	C₂²×C₈₉	semidirect
522. #467	C₂²×C₈₉	semidirect
523. #465	C₂²×C₈₉	semidirect
524. #462	C₂²×C₈₉	semidirect
525. #462	C₂²×C₈₉	semidirect
526. #461	C₂²×C₈₉	semidirect
527. #461	C₂²×C₈₉	semidirect
528. #451	C₂²×C₈₉	semidirect
529. #451	C₂²×C₈₉	semidirect
530. #448	C₂²×C₈₉	semidirect
531. #448	C₂²×C₈₉	semidirect
532. #441	C₂²×C₈₉	semidirect
533. #440	C₂²×C₈₉	semidirect
534. C₄×Q₁₆	C₂²×C₈₉	semidirect
535. C₄×SD₁₆	C₂²×C₈₉	semidirect
547. #419	C₂²×C₈₉	semidirect
548. #419	C₂²×C₈₉	semidirect
550. C₂×#103	C₂²×C₈₉	semidirect
551. C₂×#103	C₂²×C₈₉	semidirect
712. C₂×Q₈	#41×C₈₉	semidirect
838. D₄	#137×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3475	2
C₂×D₄×Q₈×C₈₉	2
C₈₉×#3329	2
C₈₉×#3328	2
C₈₉×#3320	2
C₈₉×#3312	2
C₈₉×#3299	2
C₈₉×#3298	2
C₈₉×#3139	2
C₈₉×#3095	2
C₈₉×#3078	2
C₈₉×#3056	2
C₈₉×#3039	2
C₈₉×#3004	2
C₄×#137×C₈₉	2
D₄×M₁₆×C₈₉	2
C₂×#419×C₈₉	2
#61157	89

Subgroups — C89×#61157 #36439005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61157 #36439005