Subgroups — C₈₉×#60927 #36438775

Order 22784.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3263	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3262	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3258	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3258	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3250	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3248	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3062	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#3042	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
30	#559×C₈₉	—	2	1	no	—
31	#559×C₈₉	—	2	1	no	—
32	#556×C₈₉	—	2	1	no	—
33	#556×C₈₉	—	2	1	no	—
34	#551×C₈₉	—	2	2	no	—
35	#551×C₈₉	—	2	2	no	—
36	#544×C₈₉	C₂²	1	1	yes	characteristic
37	#542×C₈₉	—	2	1	no	—
38	#542×C₈₉	C₂²	1	2	yes	—
39	#542×C₈₉	C₂²	1	2	yes	—
40	#542×C₈₉	C₂²	1	2	yes	complemented
41	#541×C₈₉	—	2	1	no	—
42	#541×C₈₉	C₂²	1	2	yes	complemented
43	#539×C₈₉	—	2	2	no	—
44	#537×C₈₉	C₂²	1	1	yes	characteristic
45	#536×C₈₉	C₂²	1	1	yes	characteristic
46	#536×C₈₉	C₂²	1	1	yes	characteristic
47	#536×C₈₉	C₂²	1	1	yes	characteristic
48	#535×C₈₉	C₂²	1	1	yes	characteristic
49	#533×C₈₉	—	2	1	no	—
50	#533×C₈₉	C₂²	1	1	yes	characteristic
51	#533×C₈₉	C₂²	1	2	yes	complemented
52	#529×C₈₉	—	2	2	no	—
53	#529×C₈₉	—	2	1	no	—
54	#529×C₈₉	C₂²	1	2	yes	—
55	#529×C₈₉	C₂²	1	2	yes	—
56	#529×C₈₉	C₂²	1	2	yes	complemented
57	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
58	#519×C₈₉	C₂²	1	1	yes	characteristic
59	#518×C₈₉	C₂²	1	1	yes	characteristic
60	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
63	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#479×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	#479×C₈₉	C₂²	1	2	yes	complemented
66	#479×C₈₉	C₂²	1	2	yes	complemented
67	#479×C₈₉	C₂²	1	2	yes	complemented
68	#479×C₈₉	C₂²	1	2	yes	complemented
69	#478×C₈₉	C₂²	1	2	yes	—
70	#478×C₈₉	C₂²	1	2	yes	—
71	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#478×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#477×C₈₉	C₂²	1	2	yes	complemented
75	#477×C₈₉	C₂²	1	2	yes	complemented
76	#476×C₈₉	C₂²	1	2	yes	—
77	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#475×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#475×C₈₉	C₂²	1	2	yes	complemented
80	#475×C₈₉	C₂²	1	2	yes	complemented
81	#474×C₈₉	C₂²	1	2	yes	—
82	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#470×C₈₉	C₂²	1	2	yes	complemented
84	#470×C₈₉	C₂²	1	2	yes	complemented
85	#470×C₈₉	C₂²	1	2	yes	complemented
86	#469×C₈₉	C₂²	1	2	yes	—
87	#468×C₈₉	C₂²	1	2	yes	—
88	#468×C₈₉	C₂²	1	2	yes	—
89	#468×C₈₉	C₂²	1	2	yes	—
90	#468×C₈₉	C₂²	1	2	yes	complemented
91	#467×C₈₉	C₂²	1	2	yes	complemented
92	#467×C₈₉	C₂²	1	2	yes	complemented
93	#467×C₈₉	C₂²	1	2	yes	complemented
94	#466×C₈₉	C₂²	1	2	yes	—
95	#465×C₈₉	C₂²	1	2	yes	—
96	#465×C₈₉	C₂²	1	2	yes	—
97	#465×C₈₉	C₂²	1	2	yes	—
98	#465×C₈₉	C₂²	1	2	yes	complemented
99	#464×C₈₉	C₂²	1	2	yes	—
100	#464×C₈₉	C₂²	1	2	yes	—
101	#464×C₈₉	C₂²	1	2	yes	—
102	#464×C₈₉	C₂²	1	2	yes	—
103	#464×C₈₉	C₂²	1	2	yes	—
104	#464×C₈₉	C₂²	1	2	yes	—
105	#464×C₈₉	C₂²	1	2	yes	complemented
106	#464×C₈₉	C₂²	1	2	yes	complemented
107	#463×C₈₉	C₂²	1	2	yes	—
108	#463×C₈₉	C₂²	1	2	yes	—
109	#463×C₈₉	C₂²	1	2	yes	—
110	#463×C₈₉	C₂²	1	2	yes	—
111	#462×C₈₉	C₂²	1	2	yes	complemented
112	#462×C₈₉	C₂²	1	2	yes	complemented
113	#461×C₈₉	C₂²	1	2	yes	—
114	#461×C₈₉	C₂²	1	2	yes	—
115	#428×C₈₉	C₂²	1	1	yes	characteristic
116	#428×C₈₉	C₂²	1	1	yes	characteristic
117	#427×C₈₉	C₂²	1	1	yes	characteristic
118	#427×C₈₉	C₂²	1	1	yes	characteristic
119	#424×C₈₉	C₂²	1	1	yes	characteristic
120	#424×C₈₉	C₂²	1	1	yes	characteristic
121	#424×C₈₉	C₂²	1	2	yes	complemented
122	#424×C₈₉	C₂²	1	2	yes	complemented
123	#423×C₈₉	C₂²	1	1	yes	characteristic
124	#423×C₈₉	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
127	#419×C₈₉	C₂²	1	1	yes	characteristic
128	#419×C₈₉	C₂²	1	1	yes	characteristic
129	#419×C₈₉	C₂²	1	1	yes	characteristic
130	#418×C₈₉	C₂²	1	1	yes	characteristic
131	#416×C₈₉	C₂²	1	1	yes	characteristic
132	#416×C₈₉	C₂²	1	1	yes	characteristic
133	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
134	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
140	#137×C₈₉	—	4	2	no	—
141	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
142	C₂×Q₁₆×C₈₉	—	4	2	no	—
143	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₈₉	—	4	2	no	—
147	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×D₈×C₈₉	C₂³	1	2	yes	—
152	#131×C₈₉	—	4	2	no	—
153	#131×C₈₉	—	4	2	no	—
154	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
157	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
158	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
169	#127×C₈₉	—	2	1	no	—
170	#126×C₈₉	—	2	2	no	—
171	#126×C₈₉	—	2	2	no	—
172	#126×C₈₉	—	2	2	no	—
173	#126×C₈₉	—	2	2	no	—
174	#126×C₈₉	—	2	2	no	—
175	#126×C₈₉	—	2	2	no	—
176	#126×C₈₉	—	2	2	no	—
177	#126×C₈₉	—	2	2	no	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	—	2	1	no	—
180	#125×C₈₉	—	2	2	no	—
181	#125×C₈₉	—	2	2	no	—
182	#125×C₈₉	C₂³	1	2	yes	—
183	#125×C₈₉	C₂³	1	1	yes	characteristic
184	#125×C₈₉	C₂³	1	1	yes	characteristic
185	#124×C₈₉	—	2	1	no	—
186	#124×C₈₉	—	2	1	no	—
187	#124×C₈₉	—	2	1	no	—
188	#124×C₈₉	—	2	2	no	—
189	#124×C₈₉	—	2	2	no	—
190	#124×C₈₉	—	2	2	no	—
191	#124×C₈₉	—	2	1	no	—
192	#124×C₈₉	—	2	1	no	—
193	#124×C₈₉	C₂³	1	2	yes	—
194	#124×C₈₉	C₂³	1	2	yes	—
195	#124×C₈₉	C₂³	1	2	yes	—
196	#123×C₈₉	—	2	2	no	—
197	#123×C₈₉	—	2	2	no	—
198	#123×C₈₉	—	2	2	no	—
199	#123×C₈₉	—	2	2	no	—
200	#123×C₈₉	—	2	2	no	—
201	#123×C₈₉	—	2	2	no	—
202	#123×C₈₉	—	2	2	no	—
203	#123×C₈₉	—	2	2	no	—
204	#123×C₈₉	—	2	2	no	—
205	C₂²⋊Q₈×C₈₉	—	2	1	no	—
206	C₂²⋊Q₈×C₈₉	—	2	1	no	—
207	C₂²⋊Q₈×C₈₉	—	2	1	no	—
208	C₂²⋊Q₈×C₈₉	—	2	2	no	—
209	C₂²⋊Q₈×C₈₉	—	2	1	no	—
210	C₂²⋊Q₈×C₈₉	—	2	1	no	—
211	C₂²⋊Q₈×C₈₉	—	2	2	no	—
212	C₂²⋊Q₈×C₈₉	—	2	2	no	—
213	C₂²⋊Q₈×C₈₉	—	2	2	no	—
214	C₂²⋊Q₈×C₈₉	—	2	2	no	—
215	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
220	#121×C₈₉	—	2	2	no	—
221	#121×C₈₉	—	2	1	no	—
222	#121×C₈₉	C₂³	1	2	yes	—
223	#121×C₈₉	C₂³	1	2	yes	—
224	#121×C₈₉	C₂³	1	2	yes	—
225	#120×C₈₉	—	2	2	no	—
226	C₄×Q₈×C₈₉	—	2	1	no	—
227	C₄×Q₈×C₈₉	—	2	1	no	—
228	C₄×Q₈×C₈₉	—	2	1	no	—
229	C₄×Q₈×C₈₉	—	2	1	no	—
230	C₄×Q₈×C₈₉	—	2	2	no	—
231	C₄×Q₈×C₈₉	—	2	1	no	—
232	C₄×Q₈×C₈₉	—	2	1	no	—
233	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	—	2	1	no	—
242	C₄×D₄×C₈₉	—	2	1	no	—
243	C₄×D₄×C₈₉	—	2	2	no	—
244	C₄×D₄×C₈₉	—	2	2	no	—
245	C₄×D₄×C₈₉	—	2	2	no	—
246	C₄×D₄×C₈₉	—	2	1	no	—
247	C₄×D₄×C₈₉	—	2	1	no	—
248	C₄×D₄×C₈₉	D₄	1	2	yes	—
249	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
250	C₄×D₄×C₈₉	D₄	1	2	yes	—
251	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
252	C₄×D₄×C₈₉	C₂³	1	2	yes	—
253	C₄×D₄×C₈₉	C₂³	1	2	yes	—
254	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
256	#117×C₈₉	—	2	2	no	—
257	#117×C₈₉	—	2	2	no	—
258	#117×C₈₉	—	2	1	no	—
259	#117×C₈₉	—	2	2	no	—
260	#117×C₈₉	—	2	2	no	—
261	#117×C₈₉	—	2	2	no	—
262	#117×C₈₉	C₂³	1	1	yes	characteristic
263	#117×C₈₉	C₂³	1	1	yes	characteristic
264	#117×C₈₉	C₂³	1	1	yes	characteristic
265	#117×C₈₉	C₂³	1	1	yes	characteristic
266	#117×C₈₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂×C₄²×C₈₉	—	2	1	no	—
273	C₂×C₄²×C₈₉	—	2	1	no	—
274	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
276	#107×C₈₉	C₂³	1	1	yes	characteristic
277	#107×C₈₉	C₂³	1	1	yes	characteristic
278	#107×C₈₉	C₂³	1	1	yes	characteristic
279	#107×C₈₉	C₂³	1	1	yes	characteristic
280	#107×C₈₉	C₂³	1	2	yes	—
281	#107×C₈₉	C₂³	1	2	yes	—
282	#106×C₈₉	C₂³	1	1	yes	characteristic
283	#106×C₈₉	C₂³	1	1	yes	characteristic
284	#106×C₈₉	C₂³	1	1	yes	characteristic
285	#106×C₈₉	C₂³	1	1	yes	characteristic
286	#106×C₈₉	C₂³	1	2	yes	—
287	#106×C₈₉	C₂³	1	2	yes	—
288	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
293	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
294	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
295	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
296	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
297	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
298	#103×C₈₉	C₂³	1	2	yes	—
299	#103×C₈₉	C₂³	1	2	yes	—
300	#103×C₈₉	C₂³	1	1	yes	characteristic
301	#103×C₈₉	C₂³	1	1	yes	characteristic
302	#103×C₈₉	C₂³	1	1	yes	characteristic
303	#103×C₈₉	C₂³	1	1	yes	characteristic
304	#103×C₈₉	C₂³	1	2	yes	—
305	#103×C₈₉	C₂³	1	2	yes	—
306	#103×C₈₉	C₂³	1	2	yes	—
307	#103×C₈₉	C₂³	1	2	yes	—
308	#103×C₈₉	C₂³	1	2	yes	—
309	#103×C₈₉	C₂³	1	2	yes	—
310	#102×C₈₉	C₂³	1	2	yes	—
311	#102×C₈₉	C₂³	1	2	yes	—
312	#102×C₈₉	C₂³	1	1	yes	characteristic
313	#102×C₈₉	C₂³	1	1	yes	characteristic
314	#102×C₈₉	C₂³	1	1	yes	characteristic
315	#102×C₈₉	C₂³	1	1	yes	characteristic
316	#102×C₈₉	C₂³	1	2	yes	—
317	#102×C₈₉	C₂³	1	2	yes	—
318	C₂⁴×C₈₉	—	2	1	no	—
319	#41×C₈₉	—	2	2	no	—
320	#41×C₈₉	—	2	2	no	—
321	#41×C₈₉	—	2	2	no	—
322	#41×C₈₉	—	2	2	no	—
323	C₂×Q₈×C₈₉	—	2	1	no	—
324	C₂×Q₈×C₈₉	—	2	1	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	2	1	no	—
327	C₂×Q₈×C₈₉	—	2	2	no	—
328	C₂×Q₈×C₈₉	—	2	2	no	—
329	C₂×Q₈×C₈₉	—	2	2	no	—
330	C₂×Q₈×C₈₉	—	2	2	no	—
331	C₂×Q₈×C₈₉	—	2	2	no	—
332	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	—	2	2	no	—
339	C₂×D₄×C₈₉	—	2	2	no	—
340	C₂×D₄×C₈₉	—	2	1	no	—
341	C₂×D₄×C₈₉	—	2	2	no	—
342	C₂×D₄×C₈₉	—	2	2	no	—
343	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₈₉	—	2	1	no	—
348	C₂²×C₄×C₈₉	—	2	1	no	—
349	C₂²×C₄×C₈₉	—	2	1	no	—
350	C₂²×C₄×C₈₉	—	2	1	no	—
351	C₂²×C₄×C₈₉	—	2	1	no	—
352	C₂²×C₄×C₈₉	—	2	1	no	—
353	C₂²×C₄×C₈₉	—	2	2	no	—
354	C₂²×C₄×C₈₉	—	2	2	no	—
355	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₈₉	—	4	2	no	—
362	Q₁₆×C₈₉	—	4	2	no	—
363	Q₁₆×C₈₉	—	4	2	no	—
364	SD₁₆×C₈₉	—	4	2	no	—
365	SD₁₆×C₈₉	—	4	2	no	—
366	SD₁₆×C₈₉	—	4	2	no	—
367	SD₁₆×C₈₉	—	4	2	no	—
368	D₈×C₈₉	—	4	2	no	—
369	M₁₆×C₈₉	—	2	2	no	—
370	M₁₆×C₈₉	—	2	2	no	—
371	M₁₆×C₈₉	—	4	2	no	—
372	M₁₆×C₈₉	—	4	2	no	—
373	C₂×C₈×C₈₉	—	2	2	no	—
374	C₂×C₈×C₈₉	—	2	2	no	—
375	C₂×C₈×C₈₉	—	4	2	no	—
376	C₂×C₈×C₈₉	—	4	2	no	—
377	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
380	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₈₉	—	2	2	no	—
384	C₄⋊C₄×C₈₉	—	2	2	no	—
385	C₄⋊C₄×C₈₉	—	2	1	no	—
386	C₄⋊C₄×C₈₉	—	2	1	no	—
387	C₄⋊C₄×C₈₉	—	2	1	no	—
388	C₄⋊C₄×C₈₉	—	2	1	no	—
389	C₄⋊C₄×C₈₉	—	2	1	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	2	no	—
392	C₄⋊C₄×C₈₉	—	2	2	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	2	no	—
396	C₄⋊C₄×C₈₉	—	2	2	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	1	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	2	no	—
402	C₄⋊C₄×C₈₉	—	2	2	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	—	2	1	no	—
405	C₄⋊C₄×C₈₉	—	2	1	no	—
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₈₉	—	2	1	no	—
418	C₂²⋊C₄×C₈₉	—	2	1	no	—
419	C₂²⋊C₄×C₈₉	—	2	2	no	—
420	C₂²⋊C₄×C₈₉	—	2	2	no	—
421	C₂²⋊C₄×C₈₉	—	2	1	no	—
422	C₂²⋊C₄×C₈₉	—	2	2	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	2	no	—
426	C₂²⋊C₄×C₈₉	—	2	2	no	—
427	C₂²⋊C₄×C₈₉	—	2	2	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	—	2	2	no	—
431	C₂²⋊C₄×C₈₉	—	2	1	no	—
432	C₂²⋊C₄×C₈₉	—	2	1	no	—
433	C₂²⋊C₄×C₈₉	—	2	2	no	—
434	C₂²⋊C₄×C₈₉	—	2	2	no	—
435	C₂²⋊C₄×C₈₉	—	2	2	no	—
436	C₂²⋊C₄×C₈₉	—	2	2	no	—
437	C₂²⋊C₄×C₈₉	—	2	2	no	—
438	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
441	C₄²×C₈₉	—	2	2	no	—
442	C₄²×C₈₉	—	2	1	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	1	no	—
445	C₄²×C₈₉	—	2	2	no	—
446	C₄²×C₈₉	—	2	2	no	—
447	C₄²×C₈₉	—	2	2	no	—
448	C₄²×C₈₉	—	2	1	no	—
449	C₄²×C₈₉	—	2	1	no	—
450	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₈₉	C₂×D₄	1	2	yes	—
452	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₈₉	C₂×D₄	1	2	yes	—
454	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
455	C₄²×C₈₉	C₂⁴	1	2	yes	—
456	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
457	C₂³×C₈₉	—	2	1	no	—
458	C₂³×C₈₉	—	2	2	no	—
459	C₂³×C₈₉	—	4	2	no	—
460	C₂³×C₈₉	—	8	1	no	—
461	C₂³×C₈₉	—	8	1	no	—
462	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
463	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₈₉	—	2	2	no	—
465	Q₈×C₈₉	—	2	2	no	—
466	Q₈×C₈₉	—	2	1	no	—
467	Q₈×C₈₉	—	2	2	no	—
468	Q₈×C₈₉	—	2	2	no	—
469	Q₈×C₈₉	—	2	2	no	—
470	Q₈×C₈₉	—	2	1	no	—
471	Q₈×C₈₉	—	4	2	no	—
472	Q₈×C₈₉	—	4	2	no	—
473	Q₈×C₈₉	—	8	1	no	—
474	Q₈×C₈₉	—	8	2	no	—
475	Q₈×C₈₉	—	8	1	no	—
476	D₄×C₈₉	—	2	4	no	—
477	D₄×C₈₉	—	2	2	no	—
478	D₄×C₈₉	—	2	1	no	—
479	D₄×C₈₉	—	2	2	no	—
480	D₄×C₈₉	—	2	2	no	—
481	D₄×C₈₉	—	2	1	no	—
482	D₄×C₈₉	—	4	2	no	—
483	D₄×C₈₉	—	4	2	no	—
484	D₄×C₈₉	—	8	2	no	—
485	D₄×C₈₉	—	8	2	no	—
486	D₄×C₈₉	—	8	2	no	—
487	C₂×C₄×C₈₉	—	2	2	no	—
488	C₂×C₄×C₈₉	—	2	2	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	1	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	2	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	1	no	—
496	C₂×C₄×C₈₉	—	2	2	no	—
497	C₂×C₄×C₈₉	—	2	1	no	—
498	C₂×C₄×C₈₉	—	2	1	no	—
499	C₂×C₄×C₈₉	—	4	1	no	—
500	C₂×C₄×C₈₉	—	4	2	no	—
501	C₂×C₄×C₈₉	—	4	2	no	—
502	C₂×C₄×C₈₉	—	4	1	no	—
503	C₂×C₄×C₈₉	—	4	2	no	—
504	C₂×C₄×C₈₉	—	4	2	no	—
505	C₂×C₄×C₈₉	—	4	2	no	—
506	C₂×C₄×C₈₉	—	4	2	no	—
507	C₂×C₄×C₈₉	—	8	2	no	—
508	C₂×C₄×C₈₉	—	8	1	no	—
509	C₂×C₄×C₈₉	—	8	2	no	—
510	C₂×C₄×C₈₉	—	8	1	no	—
511	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
521	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
522	C₈×C₈₉	—	2	1	no	—
523	C₈×C₈₉	—	2	1	no	—
524	C₈×C₈₉	—	2	1	no	—
525	C₈×C₈₉	—	2	1	no	—
526	C₈×C₈₉	—	2	2	no	—
527	C₈×C₈₉	—	2	2	no	—
528	C₂²×C₈₉	—	2	1	no	—
529	C₂²×C₈₉	—	2	1	no	—
530	C₂²×C₈₉	—	2	2	no	—
531	C₂²×C₈₉	—	2	2	no	—
532	C₂²×C₈₉	—	2	2	no	—
533	C₂²×C₈₉	—	4	1	no	—
534	C₂²×C₈₉	—	4	2	no	—
535	C₂²×C₈₉	—	4	1	no	—
536	C₂²×C₈₉	—	4	2	no	—
537	C₂²×C₈₉	—	4	1	no	—
538	C₂²×C₈₉	—	4	2	no	—
539	C₂²×C₈₉	—	16	2	no	—
540	C₂²×C₈₉	#537	1	2	yes	—
541	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₈₉	—	2	1	no	—
543	C₄×C₈₉	—	2	1	no	—
544	C₄×C₈₉	—	2	2	no	—
545	C₄×C₈₉	—	2	1	no	—
546	C₄×C₈₉	—	2	2	no	—
547	C₄×C₈₉	—	2	1	no	—
548	C₄×C₈₉	—	2	2	no	—
549	C₄×C₈₉	—	4	1	no	—
550	C₄×C₈₉	—	4	2	no	—
551	C₄×C₈₉	—	4	1	no	—
552	C₄×C₈₉	—	4	1	no	—
553	C₄×C₈₉	—	4	1	no	—
554	C₄×C₈₉	—	4	1	no	—
555	C₄×C₈₉	—	4	1	no	—
556	C₄×C₈₉	—	4	1	no	—
557	C₄×C₈₉	—	4	2	no	—
558	C₄×C₈₉	—	4	2	no	—
559	C₄×C₈₉	#537	1	2	yes	—
560	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	#60927	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
563	C₂×C₈₉	—	2	2	no	—
564	C₂×C₈₉	—	4	2	no	—
565	C₂×C₈₉	—	8	1	no	—
566	C₂×C₈₉	—	8	2	no	—
567	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
568	C₂×C₈₉	#3584	1	1	yes	characteristic
569	C₂×C₈₉	#3586	1	1	yes	characteristic
570	#3510	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#3461	C₂×C₈₉	1	1	yes	characteristic, complemented
572	#3263	C₂×C₈₉	1	2	yes	complemented
573	#3262	C₂×C₈₉	1	2	yes	complemented
574	#3258	C₂×C₈₉	1	2	yes	complemented
575	#3258	C₂×C₈₉	1	2	yes	complemented
576	#3256	C₂×C₈₉	1	2	yes	complemented
577	#3252	C₂×C₈₉	1	2	yes	complemented
578	#3250	C₂×C₈₉	1	2	yes	complemented
579	#3248	C₂×C₈₉	1	2	yes	complemented
580	#3082	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3081	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#3078	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#3076	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#3063	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#3062	C₂×C₈₉	1	1	yes	characteristic
586	#3059	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#3057	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#3044	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#3042	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#3040	C₂×C₈₉	1	1	yes	characteristic, complemented
591	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
592	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
593	C₈₉	#60927	1	1	yes	characteristic, direct product factor, Sylow
594	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
595	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
596	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
597	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
598	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
599	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
600	#559	—	2	1	no	—
601	#559	—	2	1	no	—
602	#556	—	2	1	no	—
603	#556	—	2	1	no	—
604	#551	—	2	2	no	—
605	#551	—	2	2	no	—
606	#544	C₂²×C₈₉	1	1	yes	characteristic
607	#542	—	2	1	no	—
608	#542	C₂²×C₈₉	1	2	yes	—
609	#542	C₂²×C₈₉	1	2	yes	—
610	#542	C₂²×C₈₉	1	2	yes	complemented
611	#541	—	2	1	no	—
612	#541	C₂²×C₈₉	1	2	yes	complemented
613	#539	—	2	2	no	—
614	#537	C₂²×C₈₉	1	1	yes	characteristic
615	#536	C₂²×C₈₉	1	1	yes	characteristic
616	#536	C₂²×C₈₉	1	1	yes	characteristic
617	#536	C₂²×C₈₉	1	1	yes	characteristic
618	#535	C₂²×C₈₉	1	1	yes	characteristic
619	#533	—	2	1	no	—
620	#533	C₂²×C₈₉	1	1	yes	characteristic
621	#533	C₂²×C₈₉	1	2	yes	complemented
622	#529	—	2	2	no	—
623	#529	—	2	1	no	—
624	#529	C₂²×C₈₉	1	2	yes	—
625	#529	C₂²×C₈₉	1	2	yes	—
626	#529	C₂²×C₈₉	1	2	yes	complemented
627	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
628	#519	C₂²×C₈₉	1	1	yes	characteristic
629	#518	C₂²×C₈₉	1	1	yes	characteristic
630	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
631	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
632	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
633	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
634	#479	C₂²×C₈₉	1	1	yes	characteristic, complemented
635	#479	C₂²×C₈₉	1	2	yes	complemented
636	#479	C₂²×C₈₉	1	2	yes	complemented
637	#479	C₂²×C₈₉	1	2	yes	complemented
638	#479	C₂²×C₈₉	1	2	yes	complemented
639	#478	C₂²×C₈₉	1	2	yes	—
640	#478	C₂²×C₈₉	1	2	yes	—
641	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
642	#478	C₂²×C₈₉	1	1	yes	characteristic, complemented
643	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
644	#477	C₂²×C₈₉	1	2	yes	complemented
645	#477	C₂²×C₈₉	1	2	yes	complemented
646	#476	C₂²×C₈₉	1	2	yes	—
647	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
648	#475	C₂²×C₈₉	1	1	yes	characteristic, complemented
649	#475	C₂²×C₈₉	1	2	yes	complemented
650	#475	C₂²×C₈₉	1	2	yes	complemented
651	#474	C₂²×C₈₉	1	2	yes	—
652	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
653	#470	C₂²×C₈₉	1	2	yes	complemented
654	#470	C₂²×C₈₉	1	2	yes	complemented
655	#470	C₂²×C₈₉	1	2	yes	complemented
656	#469	C₂²×C₈₉	1	2	yes	—
657	#468	C₂²×C₈₉	1	2	yes	—
658	#468	C₂²×C₈₉	1	2	yes	—
659	#468	C₂²×C₈₉	1	2	yes	—
660	#468	C₂²×C₈₉	1	2	yes	complemented
661	#467	C₂²×C₈₉	1	2	yes	complemented
662	#467	C₂²×C₈₉	1	2	yes	complemented
663	#467	C₂²×C₈₉	1	2	yes	complemented
664	#466	C₂²×C₈₉	1	2	yes	—
665	#465	C₂²×C₈₉	1	2	yes	—
666	#465	C₂²×C₈₉	1	2	yes	—
667	#465	C₂²×C₈₉	1	2	yes	—
668	#465	C₂²×C₈₉	1	2	yes	complemented
669	#464	C₂²×C₈₉	1	2	yes	—
670	#464	C₂²×C₈₉	1	2	yes	—
671	#464	C₂²×C₈₉	1	2	yes	—
672	#464	C₂²×C₈₉	1	2	yes	—
673	#464	C₂²×C₈₉	1	2	yes	—
674	#464	C₂²×C₈₉	1	2	yes	—
675	#464	C₂²×C₈₉	1	2	yes	complemented
676	#464	C₂²×C₈₉	1	2	yes	complemented
677	#463	C₂²×C₈₉	1	2	yes	—
678	#463	C₂²×C₈₉	1	2	yes	—
679	#463	C₂²×C₈₉	1	2	yes	—
680	#463	C₂²×C₈₉	1	2	yes	—
681	#462	C₂²×C₈₉	1	2	yes	complemented
682	#462	C₂²×C₈₉	1	2	yes	complemented
683	#461	C₂²×C₈₉	1	2	yes	—
684	#461	C₂²×C₈₉	1	2	yes	—
685	#428	C₂²×C₈₉	1	1	yes	characteristic
686	#428	C₂²×C₈₉	1	1	yes	characteristic
687	#427	C₂²×C₈₉	1	1	yes	characteristic
688	#427	C₂²×C₈₉	1	1	yes	characteristic
689	#424	C₂²×C₈₉	1	1	yes	characteristic
690	#424	C₂²×C₈₉	1	1	yes	characteristic
691	#424	C₂²×C₈₉	1	2	yes	complemented
692	#424	C₂²×C₈₉	1	2	yes	complemented
693	#423	C₂²×C₈₉	1	1	yes	characteristic
694	#423	C₂²×C₈₉	1	2	yes	complemented
695	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
696	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
697	#419	C₂²×C₈₉	1	1	yes	characteristic
698	#419	C₂²×C₈₉	1	1	yes	characteristic
699	#419	C₂²×C₈₉	1	1	yes	characteristic
700	#418	C₂²×C₈₉	1	1	yes	characteristic
701	#416	C₂²×C₈₉	1	1	yes	characteristic
702	#416	C₂²×C₈₉	1	1	yes	characteristic
703	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
704	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
705	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
706	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
708	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
710	#137	—	4	2	no	—
711	AGL(1,ℤ/8)	—	4	2	no	—
712	C₂×Q₁₆	—	4	2	no	—
713	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
715	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
716	C₂×SD₁₆	—	4	2	no	—
717	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
721	C₂×D₈	C₂³×C₈₉	1	2	yes	—
722	#131	—	4	2	no	—
723	#131	—	4	2	no	—
724	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
727	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
728	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
731	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
739	#127	—	2	1	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₈₉	1	1	yes	characteristic
753	#125	C₂³×C₈₉	1	1	yes	characteristic
754	#125	C₂³×C₈₉	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	—	2	1	no	—
763	#124	C₂³×C₈₉	1	2	yes	—
764	#124	C₂³×C₈₉	1	2	yes	—
765	#124	C₂³×C₈₉	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	C₂³×C₈₉	1	2	yes	—
793	#121	C₂³×C₈₉	1	2	yes	—
794	#121	C₂³×C₈₉	1	2	yes	—
795	#120	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
804	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
806	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
807	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
810	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	D₄×C₈₉	1	2	yes	—
819	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
820	C₄×D₄	D₄×C₈₉	1	2	yes	—
821	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₈₉	1	2	yes	—
825	C₄×D₄	C₂³×C₈₉	1	2	yes	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	2	2	no	—
831	#117	—	2	2	no	—
832	#117	C₂³×C₈₉	1	1	yes	characteristic
833	#117	C₂³×C₈₉	1	1	yes	characteristic
834	#117	C₂³×C₈₉	1	1	yes	characteristic
835	#117	C₂³×C₈₉	1	1	yes	characteristic
836	#117	C₂³×C₈₉	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
846	#107	C₂³×C₈₉	1	1	yes	characteristic
847	#107	C₂³×C₈₉	1	1	yes	characteristic
848	#107	C₂³×C₈₉	1	1	yes	characteristic
849	#107	C₂³×C₈₉	1	1	yes	characteristic
850	#107	C₂³×C₈₉	1	2	yes	—
851	#107	C₂³×C₈₉	1	2	yes	—
852	#106	C₂³×C₈₉	1	1	yes	characteristic
853	#106	C₂³×C₈₉	1	1	yes	characteristic
854	#106	C₂³×C₈₉	1	1	yes	characteristic
855	#106	C₂³×C₈₉	1	1	yes	characteristic
856	#106	C₂³×C₈₉	1	2	yes	—
857	#106	C₂³×C₈₉	1	2	yes	—
858	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
863	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
866	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
867	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
868	#103	C₂³×C₈₉	1	2	yes	—
869	#103	C₂³×C₈₉	1	2	yes	—
870	#103	C₂³×C₈₉	1	1	yes	characteristic
871	#103	C₂³×C₈₉	1	1	yes	characteristic
872	#103	C₂³×C₈₉	1	1	yes	characteristic
873	#103	C₂³×C₈₉	1	1	yes	characteristic
874	#103	C₂³×C₈₉	1	2	yes	—
875	#103	C₂³×C₈₉	1	2	yes	—
876	#103	C₂³×C₈₉	1	2	yes	—
877	#103	C₂³×C₈₉	1	2	yes	—
878	#103	C₂³×C₈₉	1	2	yes	—
879	#103	C₂³×C₈₉	1	2	yes	—
880	#102	C₂³×C₈₉	1	2	yes	—
881	#102	C₂³×C₈₉	1	2	yes	—
882	#102	C₂³×C₈₉	1	1	yes	characteristic
883	#102	C₂³×C₈₉	1	1	yes	characteristic
884	#102	C₂³×C₈₉	1	1	yes	characteristic
885	#102	C₂³×C₈₉	1	1	yes	characteristic
886	#102	C₂³×C₈₉	1	2	yes	—
887	#102	C₂³×C₈₉	1	2	yes	—
888	C₂⁴	—	2	1	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
931	Q₁₆	—	4	2	no	—
932	Q₁₆	—	4	2	no	—
933	Q₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	D₈	—	4	2	no	—
939	M₁₆	—	2	2	no	—
940	M₁₆	—	2	2	no	—
941	M₁₆	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	2	2	no	—
945	C₂×C₈	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
950	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1022	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1024	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₈₉	1	2	yes	—
1026	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1033	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1089	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
1090	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1091	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	2	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	16	2	no	—
1110	C₂²	#537×C₈₉	1	2	yes	—
1111	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	#537×C₈₉	1	2	yes	—
1130	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1131	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1132	C₂	—	2	2	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	8	1	no	—
1135	C₂	—	8	2	no	—
1136	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
1137	C₂	C₈₉×#3584	1	1	yes	characteristic
1138	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×#3062	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
1. C₈₉×#3510	C₂	semidirect
2. C₈₉×#3461	C₂	semidirect
3. C₈₉×#3263	C₂	semidirect
4. C₈₉×#3262	C₂	semidirect
5. C₈₉×#3258	C₂	semidirect
6. C₈₉×#3258	C₂	semidirect
7. C₈₉×#3256	C₂	semidirect
8. C₈₉×#3252	C₂	semidirect
9. C₈₉×#3250	C₂	semidirect
10. C₈₉×#3248	C₂	semidirect
11. C₈₉×#3082	C₂	semidirect
12. C₈₉×#3081	C₂	semidirect
13. C₈₉×#3078	C₂	semidirect
14. C₈₉×#3076	C₂	semidirect
15. C₈₉×#3063	C₂	semidirect
17. C₈₉×#3059	C₂	semidirect
18. C₈₉×#3057	C₂	semidirect
19. C₈₉×#3044	C₂	semidirect
20. C₈₉×#3042	C₂	semidirect
21. C₈₉×#3040	C₂	semidirect
22. C₂×#464×C₈₉	C₂	semidirect
23. C₈₉×#2906	C₂	semidirect
40. #542×C₈₉	C₂²	semidirect
42. #541×C₈₉	C₂²	semidirect
51. #533×C₈₉	C₂²	semidirect
56. #529×C₈₉	C₂²	semidirect
63. #479×C₈₉	C₂²	semidirect
64. #479×C₈₉	C₂²	semidirect
65. #479×C₈₉	C₂²	semidirect
66. #479×C₈₉	C₂²	semidirect
67. #479×C₈₉	C₂²	semidirect
68. #479×C₈₉	C₂²	semidirect
71. #478×C₈₉	C₂²	semidirect
72. #478×C₈₉	C₂²	semidirect
73. #477×C₈₉	C₂²	semidirect
74. #477×C₈₉	C₂²	semidirect
75. #477×C₈₉	C₂²	semidirect
77. #476×C₈₉	C₂²	semidirect
78. #475×C₈₉	C₂²	semidirect
79. #475×C₈₉	C₂²	semidirect
80. #475×C₈₉	C₂²	semidirect
82. #474×C₈₉	C₂²	semidirect
83. #470×C₈₉	C₂²	semidirect
84. #470×C₈₉	C₂²	semidirect
85. #470×C₈₉	C₂²	semidirect
90. #468×C₈₉	C₂²	semidirect
91. #467×C₈₉	C₂²	semidirect
92. #467×C₈₉	C₂²	semidirect
93. #467×C₈₉	C₂²	semidirect
98. #465×C₈₉	C₂²	semidirect
105. #464×C₈₉	C₂²	semidirect
106. #464×C₈₉	C₂²	semidirect
111. #462×C₈₉	C₂²	semidirect
112. #462×C₈₉	C₂²	semidirect
121. #424×C₈₉	C₂²	semidirect
122. #424×C₈₉	C₂²	semidirect
124. #423×C₈₉	C₂²	semidirect
126. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
562. #60927	C₈₉	direct (N × H)
570. #3510	C₂×C₈₉	semidirect
571. #3461	C₂×C₈₉	semidirect
572. #3263	C₂×C₈₉	semidirect
573. #3262	C₂×C₈₉	semidirect
574. #3258	C₂×C₈₉	semidirect
575. #3258	C₂×C₈₉	semidirect
576. #3256	C₂×C₈₉	semidirect
577. #3252	C₂×C₈₉	semidirect
578. #3250	C₂×C₈₉	semidirect
579. #3248	C₂×C₈₉	semidirect
580. #3082	C₂×C₈₉	semidirect
581. #3081	C₂×C₈₉	semidirect
582. #3078	C₂×C₈₉	semidirect
583. #3076	C₂×C₈₉	semidirect
584. #3063	C₂×C₈₉	semidirect
586. #3059	C₂×C₈₉	semidirect
587. #3057	C₂×C₈₉	semidirect
588. #3044	C₂×C₈₉	semidirect
589. #3042	C₂×C₈₉	semidirect
590. #3040	C₂×C₈₉	semidirect
591. C₂×#464	C₂×C₈₉	semidirect
592. #2906	C₂×C₈₉	semidirect
593. C₈₉	#60927	direct (N × H)
610. #542	C₂²×C₈₉	semidirect
612. #541	C₂²×C₈₉	semidirect
621. #533	C₂²×C₈₉	semidirect
626. #529	C₂²×C₈₉	semidirect
633. #479	C₂²×C₈₉	semidirect
634. #479	C₂²×C₈₉	semidirect
635. #479	C₂²×C₈₉	semidirect
636. #479	C₂²×C₈₉	semidirect
637. #479	C₂²×C₈₉	semidirect
638. #479	C₂²×C₈₉	semidirect
641. #478	C₂²×C₈₉	semidirect
642. #478	C₂²×C₈₉	semidirect
643. #477	C₂²×C₈₉	semidirect
644. #477	C₂²×C₈₉	semidirect
645. #477	C₂²×C₈₉	semidirect
647. #476	C₂²×C₈₉	semidirect
648. #475	C₂²×C₈₉	semidirect
649. #475	C₂²×C₈₉	semidirect
650. #475	C₂²×C₈₉	semidirect
652. #474	C₂²×C₈₉	semidirect
653. #470	C₂²×C₈₉	semidirect
654. #470	C₂²×C₈₉	semidirect
655. #470	C₂²×C₈₉	semidirect
660. #468	C₂²×C₈₉	semidirect
661. #467	C₂²×C₈₉	semidirect
662. #467	C₂²×C₈₉	semidirect
663. #467	C₂²×C₈₉	semidirect
668. #465	C₂²×C₈₉	semidirect
675. #464	C₂²×C₈₉	semidirect
676. #464	C₂²×C₈₉	semidirect
681. #462	C₂²×C₈₉	semidirect
682. #462	C₂²×C₈₉	semidirect
691. #424	C₂²×C₈₉	semidirect
692. #424	C₂²×C₈₉	semidirect
694. #423	C₂²×C₈₉	semidirect
696. C₂×C₄⋊C₈	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×#3510	2
C₈₉×#3461	2
C₈₉×#3263	2
C₈₉×#3262	2
C₈₉×#3258	2
C₈₉×#3256	2
C₈₉×#3252	2
C₈₉×#3250	2
C₈₉×#3248	2
C₈₉×#3082	2
C₈₉×#3081	2
C₈₉×#3078	2
C₈₉×#3076	2
C₈₉×#3063	2
C₈₉×#3062	2
C₈₉×#3059	2
C₈₉×#3057	2
C₈₉×#3044	2
C₈₉×#3042	2
C₈₉×#3040	2
C₂×#464×C₈₉	2
C₈₉×#2906	2
#60927	89

Subgroups — C89×#60927 #36438775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60927 #36438775