Subgroups — C₈₉×#61447 #36439295

Order 22784.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3349	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3315	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3313	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3269	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3172	C₂	1	2	yes	maximal, complemented
16	C₈₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#3104	C₂	1	2	yes	maximal, complemented
20	C₈₉×#3102	C₂	1	2	yes	maximal, complemented
21	C₈₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137×C₈₉	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₈₉	C₂²	1	2	yes	—
25	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
26	#557×C₈₉	C₂²	1	1	yes	characteristic
27	#557×C₈₉	C₂²	1	1	yes	characteristic
28	#556×C₈₉	—	2	1	no	—
29	#556×C₈₉	C₂²	1	1	yes	characteristic
30	#556×C₈₉	C₂²	1	1	yes	characteristic
31	#556×C₈₉	C₂²	1	2	yes	—
32	#552×C₈₉	—	2	2	no	—
33	#552×C₈₉	—	2	2	no	—
34	#552×C₈₉	—	2	1	no	—
35	#552×C₈₉	C₂²	1	2	yes	—
36	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	#548×C₈₉	—	2	1	no	—
39	#548×C₈₉	C₂²	1	2	yes	—
40	#547×C₈₉	—	2	1	no	—
41	#547×C₈₉	C₂²	1	1	yes	characteristic
42	#547×C₈₉	C₂²	1	2	yes	—
43	#547×C₈₉	C₂²	1	1	yes	characteristic
44	#533×C₈₉	—	2	1	no	—
45	#533×C₈₉	C₂²	1	2	yes	—
46	#533×C₈₉	C₂²	1	1	yes	characteristic
47	#533×C₈₉	C₂²	1	1	yes	characteristic
48	#529×C₈₉	—	2	2	no	—
49	#529×C₈₉	—	2	1	no	—
50	#529×C₈₉	—	2	2	no	—
51	#529×C₈₉	C₂²	1	2	yes	—
52	C₄×#41×C₈₉	—	2	1	no	—
53	C₄×#41×C₈₉	C₂²	1	2	yes	—
54	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
58	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
59	#501×C₈₉	C₂²	1	2	yes	—
60	#500×C₈₉	C₂²	1	1	yes	characteristic
61	#497×C₈₉	C₂²	1	2	yes	—
62	#494×C₈₉	C₂²	1	1	yes	characteristic
63	#491×C₈₉	C₂²	1	2	yes	—
64	#489×C₈₉	C₂²	1	2	yes	—
65	#487×C₈₉	C₂²	1	1	yes	characteristic
66	#487×C₈₉	C₂²	1	1	yes	characteristic
67	#485×C₈₉	C₂²	1	2	yes	—
68	#485×C₈₉	C₂²	1	2	yes	—
69	#485×C₈₉	C₂²	1	2	yes	—
70	#484×C₈₉	C₂²	1	2	yes	—
71	#484×C₈₉	C₂²	1	2	yes	—
72	#482×C₈₉	C₂²	1	2	yes	—
73	#479×C₈₉	C₂²	1	2	yes	—
74	#478×C₈₉	C₂²	1	2	yes	—
75	#477×C₈₉	C₂²	1	2	yes	—
76	#477×C₈₉	C₂²	1	2	yes	—
77	#475×C₈₉	C₂²	1	1	yes	characteristic
78	#475×C₈₉	C₂²	1	1	yes	characteristic
79	#474×C₈₉	C₂²	1	1	yes	characteristic
80	#474×C₈₉	C₂²	1	1	yes	characteristic
81	#470×C₈₉	C₂²	1	2	yes	—
82	#470×C₈₉	C₂²	1	2	yes	—
83	#468×C₈₉	C₂²	1	2	yes	—
84	#468×C₈₉	C₂²	1	2	yes	—
85	#467×C₈₉	C₂²	1	2	yes	—
86	#467×C₈₉	C₂²	1	2	yes	—
87	#464×C₈₉	C₂²	1	2	yes	—
88	#463×C₈₉	C₂²	1	2	yes	—
89	#462×C₈₉	C₂²	1	1	yes	characteristic
90	#462×C₈₉	C₂²	1	2	yes	—
91	#462×C₈₉	C₂²	1	2	yes	—
92	#462×C₈₉	C₂²	1	1	yes	characteristic
93	#461×C₈₉	C₂²	1	1	yes	characteristic
94	#461×C₈₉	C₂²	1	1	yes	characteristic
95	#452×C₈₉	C₂²	1	2	yes	—
96	#452×C₈₉	C₂²	1	2	yes	—
97	#452×C₈₉	C₂²	1	2	yes	—
98	#451×C₈₉	C₂²	1	2	yes	—
99	#451×C₈₉	C₂²	1	2	yes	—
100	#449×C₈₉	C₂²	1	2	yes	—
101	#446×C₈₉	C₂²	1	1	yes	characteristic
102	#446×C₈₉	C₂²	1	1	yes	characteristic
103	#441×C₈₉	C₂²	1	2	yes	—
104	#441×C₈₉	C₂²	1	2	yes	—
105	#440×C₈₉	C₂²	1	2	yes	—
106	#440×C₈₉	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
108	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
121	#436×C₈₉	C₂²	1	1	yes	characteristic
122	#436×C₈₉	C₂²	1	1	yes	characteristic
123	#435×C₈₉	C₂²	1	2	yes	—
124	#435×C₈₉	C₂²	1	2	yes	—
125	#431×C₈₉	C₂²	1	2	yes	—
126	#431×C₈₉	C₂²	1	1	yes	characteristic
127	#428×C₈₉	C₂²	1	2	yes	—
128	#427×C₈₉	C₂²	1	1	yes	characteristic
129	#419×C₈₉	C₂²	1	2	yes	—
130	#417×C₈₉	C₂²	1	2	yes	—
131	#416×C₈₉	C₂²	1	1	yes	characteristic
132	#416×C₈₉	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	—	2	1	no	—
136	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×#41×C₈₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₈₉	—	2	1	no	—
141	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
142	#137×C₈₉	—	2	8	no	—
143	#135×C₈₉	—	2	4	no	—
144	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
155	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
156	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₈₉	—	2	1	no	—
159	C₄⋊Q₈×C₈₉	—	2	1	no	—
160	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
166	#126×C₈₉	—	2	2	no	—
167	#126×C₈₉	—	2	2	no	—
168	#126×C₈₉	—	2	2	no	—
169	#126×C₈₉	—	2	2	no	—
170	#126×C₈₉	—	2	2	no	—
171	#126×C₈₉	—	2	2	no	—
172	#125×C₈₉	—	2	1	no	—
173	#125×C₈₉	—	2	2	no	—
174	#125×C₈₉	—	2	2	no	—
175	#125×C₈₉	—	2	2	no	—
176	#125×C₈₉	—	2	1	no	—
177	#125×C₈₉	—	2	1	no	—
178	#125×C₈₉	—	2	2	no	—
179	#125×C₈₉	C₂³	1	2	yes	—
180	#124×C₈₉	—	2	1	no	—
181	#124×C₈₉	—	2	2	no	—
182	#124×C₈₉	—	2	2	no	—
183	#124×C₈₉	C₂³	1	2	yes	—
184	#123×C₈₉	—	2	2	no	—
185	#123×C₈₉	—	2	2	no	—
186	#123×C₈₉	—	2	2	no	—
187	#123×C₈₉	—	2	2	no	—
188	#123×C₈₉	—	2	2	no	—
189	#123×C₈₉	—	2	2	no	—
190	C₂²⋊Q₈×C₈₉	—	2	1	no	—
191	C₂²⋊Q₈×C₈₉	—	2	1	no	—
192	C₂²⋊Q₈×C₈₉	—	2	1	no	—
193	C₂²⋊Q₈×C₈₉	—	2	2	no	—
194	C₂²⋊Q₈×C₈₉	—	2	1	no	—
195	C₂²⋊Q₈×C₈₉	—	2	2	no	—
196	C₂²⋊Q₈×C₈₉	—	2	1	no	—
197	C₂²⋊Q₈×C₈₉	—	2	2	no	—
198	C₂²⋊Q₈×C₈₉	—	2	2	no	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
204	#121×C₈₉	—	2	2	no	—
205	#121×C₈₉	—	2	1	no	—
206	#121×C₈₉	—	2	2	no	—
207	#121×C₈₉	C₂³	1	2	yes	—
208	C₄×Q₈×C₈₉	—	2	1	no	—
209	C₄×Q₈×C₈₉	—	2	2	no	—
210	C₄×Q₈×C₈₉	—	2	1	no	—
211	C₄×Q₈×C₈₉	—	2	1	no	—
212	C₄×Q₈×C₈₉	—	2	1	no	—
213	C₄×Q₈×C₈₉	—	2	2	no	—
214	C₄×Q₈×C₈₉	—	2	2	no	—
215	C₄×Q₈×C₈₉	—	2	2	no	—
216	C₄×Q₈×C₈₉	—	2	1	no	—
217	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
221	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
225	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
226	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
227	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₈₉	—	2	1	no	—
229	C₄×D₄×C₈₉	—	2	2	no	—
230	C₄×D₄×C₈₉	—	2	1	no	—
231	C₄×D₄×C₈₉	—	2	2	no	—
232	C₄×D₄×C₈₉	—	2	1	no	—
233	C₄×D₄×C₈₉	—	2	1	no	—
234	C₄×D₄×C₈₉	—	2	1	no	—
235	C₄×D₄×C₈₉	—	2	2	no	—
236	C₄×D₄×C₈₉	—	2	2	no	—
237	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
238	C₄×D₄×C₈₉	D₄	1	2	yes	—
239	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₈₉	C₂³	1	2	yes	—
244	C₄×D₄×C₈₉	C₂³	1	2	yes	—
245	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
246	#117×C₈₉	—	2	2	no	—
247	#117×C₈₉	—	2	1	no	—
248	#117×C₈₉	—	2	1	no	—
249	#117×C₈₉	—	2	1	no	—
250	#117×C₈₉	—	2	2	no	—
251	#117×C₈₉	—	2	1	no	—
252	#117×C₈₉	—	2	1	no	—
253	#117×C₈₉	—	2	2	no	—
254	#117×C₈₉	—	2	2	no	—
255	#117×C₈₉	D₄	1	2	yes	—
256	#117×C₈₉	D₄	1	1	yes	characteristic
257	#117×C₈₉	C₂³	1	1	yes	characteristic
258	#117×C₈₉	C₂³	1	1	yes	characteristic
259	#117×C₈₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
261	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
262	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
264	C₂×C₄²×C₈₉	—	2	2	no	—
265	C₂×C₄²×C₈₉	—	2	1	no	—
266	C₂×C₄²×C₈₉	—	2	2	no	—
267	C₂×C₄²×C₈₉	—	2	1	no	—
268	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
270	#107×C₈₉	C₂³	1	1	yes	characteristic
271	#107×C₈₉	C₂³	1	1	yes	characteristic
272	#107×C₈₉	C₂³	1	2	yes	—
273	#107×C₈₉	C₂³	1	2	yes	—
274	#107×C₈₉	C₂³	1	2	yes	—
275	#107×C₈₉	C₂³	1	2	yes	—
276	#106×C₈₉	C₂³	1	1	yes	characteristic
277	#106×C₈₉	C₂³	1	1	yes	characteristic
278	#106×C₈₉	C₂³	1	2	yes	—
279	#106×C₈₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
284	#103×C₈₉	C₂³	1	1	yes	characteristic
285	#103×C₈₉	C₂³	1	1	yes	characteristic
286	#103×C₈₉	C₂³	1	1	yes	characteristic
287	#103×C₈₉	C₂³	1	1	yes	characteristic
288	#103×C₈₉	C₂³	1	2	yes	—
289	#103×C₈₉	C₂³	1	2	yes	—
290	#103×C₈₉	C₂³	1	2	yes	—
291	#103×C₈₉	C₂³	1	2	yes	—
292	#103×C₈₉	C₂³	1	2	yes	—
293	#103×C₈₉	C₂³	1	2	yes	—
294	#103×C₈₉	C₂³	1	2	yes	—
295	#103×C₈₉	C₂³	1	2	yes	—
296	#103×C₈₉	C₂³	1	2	yes	—
297	#103×C₈₉	C₂³	1	2	yes	—
298	#102×C₈₉	C₂³	1	1	yes	characteristic
299	#102×C₈₉	C₂³	1	1	yes	characteristic
300	#102×C₈₉	C₂³	1	1	yes	characteristic
301	#102×C₈₉	C₂³	1	1	yes	characteristic
302	#102×C₈₉	C₂³	1	2	yes	—
303	#102×C₈₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
307	#97×C₈₉	C₂³	1	2	yes	—
308	#97×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₈₉	C₂³	1	2	yes	—
314	#41×C₈₉	—	2	2	no	—
315	#41×C₈₉	—	2	2	no	—
316	#41×C₈₉	—	2	4	no	—
317	#41×C₈₉	—	4	2	no	—
318	#41×C₈₉	—	4	1	no	—
319	#41×C₈₉	—	4	1	no	—
320	#41×C₈₉	—	4	2	no	—
321	#41×C₈₉	—	4	4	no	—
322	C₂×Q₈×C₈₉	—	2	2	no	—
323	C₂×Q₈×C₈₉	—	2	2	no	—
324	C₂×Q₈×C₈₉	—	2	1	no	—
325	C₂×Q₈×C₈₉	—	2	1	no	—
326	C₂×Q₈×C₈₉	—	2	4	no	—
327	C₂×Q₈×C₈₉	—	4	2	no	—
328	C₂×Q₈×C₈₉	—	4	4	no	—
329	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₈₉	—	2	1	no	—
335	C₂×D₄×C₈₉	—	2	2	no	—
336	C₂×D₄×C₈₉	—	2	1	no	—
337	C₂×D₄×C₈₉	—	2	2	no	—
338	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₈₉	—	2	2	no	—
343	C₂²×C₄×C₈₉	—	2	2	no	—
344	C₂²×C₄×C₈₉	—	2	1	no	—
345	C₂²×C₄×C₈₉	—	2	2	no	—
346	C₂²×C₄×C₈₉	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₈₉	—	2	2	no	—
359	Q₁₆×C₈₉	—	2	4	no	—
360	Q₁₆×C₈₉	—	2	4	no	—
361	Q₁₆×C₈₉	—	4	2	no	—
362	Q₁₆×C₈₉	—	4	2	no	—
363	SD₁₆×C₈₉	—	2	4	no	—
364	SD₁₆×C₈₉	—	2	2	no	—
365	SD₁₆×C₈₉	—	4	2	no	—
366	SD₁₆×C₈₉	#41	1	4	yes	complemented
367	D₈×C₈₉	—	2	2	no	—
368	M₁₆×C₈₉	—	2	4	no	—
369	M₁₆×C₈₉	—	4	2	no	—
370	C₂×C₈×C₈₉	—	2	2	no	—
371	C₂×C₈×C₈₉	—	4	1	no	—
372	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
376	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
377	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₈₉	—	2	1	no	—
379	C₄⋊C₄×C₈₉	—	2	2	no	—
380	C₄⋊C₄×C₈₉	—	2	1	no	—
381	C₄⋊C₄×C₈₉	—	2	2	no	—
382	C₄⋊C₄×C₈₉	—	2	2	no	—
383	C₄⋊C₄×C₈₉	—	2	2	no	—
384	C₄⋊C₄×C₈₉	—	2	2	no	—
385	C₄⋊C₄×C₈₉	—	2	2	no	—
386	C₄⋊C₄×C₈₉	—	2	2	no	—
387	C₄⋊C₄×C₈₉	—	2	2	no	—
388	C₄⋊C₄×C₈₉	—	2	1	no	—
389	C₄⋊C₄×C₈₉	—	2	2	no	—
390	C₄⋊C₄×C₈₉	—	2	2	no	—
391	C₄⋊C₄×C₈₉	—	2	1	no	—
392	C₄⋊C₄×C₈₉	—	2	1	no	—
393	C₄⋊C₄×C₈₉	—	2	2	no	—
394	C₄⋊C₄×C₈₉	—	2	2	no	—
395	C₄⋊C₄×C₈₉	—	2	1	no	—
396	C₄⋊C₄×C₈₉	—	2	1	no	—
397	C₄⋊C₄×C₈₉	—	2	2	no	—
398	C₄⋊C₄×C₈₉	—	2	1	no	—
399	C₄⋊C₄×C₈₉	—	2	2	no	—
400	C₄⋊C₄×C₈₉	—	2	2	no	—
401	C₄⋊C₄×C₈₉	—	2	1	no	—
402	C₄⋊C₄×C₈₉	—	2	1	no	—
403	C₄⋊C₄×C₈₉	—	2	2	no	—
404	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₈₉	—	2	2	no	—
415	C₂²⋊C₄×C₈₉	—	2	2	no	—
416	C₂²⋊C₄×C₈₉	—	2	2	no	—
417	C₂²⋊C₄×C₈₉	—	2	2	no	—
418	C₂²⋊C₄×C₈₉	—	2	2	no	—
419	C₂²⋊C₄×C₈₉	—	2	1	no	—
420	C₂²⋊C₄×C₈₉	—	2	1	no	—
421	C₂²⋊C₄×C₈₉	—	2	2	no	—
422	C₂²⋊C₄×C₈₉	—	2	1	no	—
423	C₂²⋊C₄×C₈₉	—	2	2	no	—
424	C₂²⋊C₄×C₈₉	—	2	2	no	—
425	C₂²⋊C₄×C₈₉	—	2	1	no	—
426	C₂²⋊C₄×C₈₉	—	2	1	no	—
427	C₂²⋊C₄×C₈₉	—	2	1	no	—
428	C₂²⋊C₄×C₈₉	—	2	2	no	—
429	C₂²⋊C₄×C₈₉	—	2	2	no	—
430	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
433	C₄²×C₈₉	—	2	1	no	—
434	C₄²×C₈₉	—	2	2	no	—
435	C₄²×C₈₉	—	2	1	no	—
436	C₄²×C₈₉	—	2	2	no	—
437	C₄²×C₈₉	—	2	1	no	—
438	C₄²×C₈₉	—	2	2	no	—
439	C₄²×C₈₉	—	2	2	no	—
440	C₄²×C₈₉	—	2	1	no	—
441	C₄²×C₈₉	—	2	1	no	—
442	C₄²×C₈₉	—	2	2	no	—
443	C₄²×C₈₉	—	2	1	no	—
444	C₄²×C₈₉	—	2	2	no	—
445	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₈₉	C₂×D₄	1	2	yes	—
447	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₈₉	C₂×D₄	1	2	yes	—
449	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₈₉	C₂⁴	1	2	yes	—
451	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
452	C₂³×C₈₉	—	2	1	no	—
453	C₂³×C₈₉	—	2	1	no	—
454	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
455	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
456	Q₈×C₈₉	—	2	2	no	—
457	Q₈×C₈₉	—	2	1	no	—
458	Q₈×C₈₉	—	2	2	no	—
459	Q₈×C₈₉	—	2	1	no	—
460	Q₈×C₈₉	—	2	2	no	—
461	Q₈×C₈₉	—	2	2	no	—
462	Q₈×C₈₉	—	2	2	no	—
463	Q₈×C₈₉	—	2	1	no	—
464	Q₈×C₈₉	—	4	4	no	—
465	Q₈×C₈₉	—	4	4	no	—
466	Q₈×C₈₉	—	4	2	no	—
467	Q₈×C₈₉	—	4	2	no	—
468	Q₈×C₈₉	C₂×#41	1	2	yes	—
469	D₄×C₈₉	—	2	2	no	—
470	D₄×C₈₉	—	2	1	no	—
471	D₄×C₈₉	—	2	1	no	—
472	D₄×C₈₉	—	2	1	no	—
473	D₄×C₈₉	—	4	2	no	—
474	D₄×C₈₉	—	4	2	no	—
475	D₄×C₈₉	—	4	4	no	—
476	D₄×C₈₉	—	4	2	no	—
477	D₄×C₈₉	—	4	4	no	—
478	D₄×C₈₉	C₂×#41	1	2	yes	—
479	C₂×C₄×C₈₉	—	2	1	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	4	no	—
482	C₂×C₄×C₈₉	—	2	2	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	2	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	2	no	—
487	C₂×C₄×C₈₉	—	2	1	no	—
488	C₂×C₄×C₈₉	—	2	1	no	—
489	C₂×C₄×C₈₉	—	2	1	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	2	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	4	2	no	—
497	C₂×C₄×C₈₉	—	4	2	no	—
498	C₂×C₄×C₈₉	—	4	4	no	—
499	C₂×C₄×C₈₉	—	4	2	no	—
500	C₂×C₄×C₈₉	—	4	4	no	—
501	C₂×C₄×C₈₉	—	4	4	no	—
502	C₂×C₄×C₈₉	—	4	4	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	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
514	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
516	C₈×C₈₉	—	2	1	no	—
517	C₈×C₈₉	—	2	2	no	—
518	C₈×C₈₉	—	2	1	no	—
519	C₈×C₈₉	—	2	1	no	—
520	C₈×C₈₉	—	2	2	no	—
521	C₈×C₈₉	C₂×#41	1	2	yes	—
522	C₂²×C₈₉	—	2	2	no	—
523	C₂²×C₈₉	—	2	1	no	—
524	C₂²×C₈₉	—	2	2	no	—
525	C₂²×C₈₉	—	2	1	no	—
526	C₂²×C₈₉	—	2	2	no	—
527	C₂²×C₈₉	—	2	1	no	—
528	C₂²×C₈₉	—	2	2	no	—
529	C₂²×C₈₉	—	4	1	no	—
530	C₂²×C₈₉	—	4	1	no	—
531	C₂²×C₈₉	—	4	1	no	—
532	C₂²×C₈₉	—	4	1	no	—
533	C₂²×C₈₉	—	4	1	no	—
534	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₈₉	—	2	1	no	—
536	C₄×C₈₉	—	2	2	no	—
537	C₄×C₈₉	—	2	2	no	—
538	C₄×C₈₉	—	2	1	no	—
539	C₄×C₈₉	—	2	2	no	—
540	C₄×C₈₉	—	2	2	no	—
541	C₄×C₈₉	—	2	1	no	—
542	C₄×C₈₉	—	4	1	no	—
543	C₄×C₈₉	—	4	2	no	—
544	C₄×C₈₉	—	4	2	no	—
545	C₄×C₈₉	—	4	1	no	—
546	C₄×C₈₉	—	4	2	no	—
547	C₄×C₈₉	—	4	2	no	—
548	C₄×C₈₉	—	4	1	no	—
549	C₄×C₈₉	—	4	1	no	—
550	C₄×C₈₉	—	4	1	no	—
551	C₄×C₈₉	#575	1	2	yes	—
552	C₄×C₈₉	#578	1	2	yes	—
553	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
554	C₄×C₈₉	#585	1	1	yes	characteristic
555	#61447	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
556	C₂×C₈₉	—	4	2	no	—
557	C₂×C₈₉	—	4	1	no	—
558	C₂×C₈₉	—	4	2	no	—
559	C₂×C₈₉	—	8	1	no	—
560	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
561	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
562	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
563	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#3398	C₂×C₈₉	1	1	yes	characteristic, complemented
566	#3386	C₂×C₈₉	1	1	yes	characteristic, complemented
567	#3374	C₂×C₈₉	1	1	yes	characteristic, complemented
568	#3367	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#3353	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#3349	C₂×C₈₉	1	2	yes	complemented
571	#3330	C₂×C₈₉	1	1	yes	characteristic, complemented
572	#3328	C₂×C₈₉	1	1	yes	characteristic, complemented
573	#3315	C₂×C₈₉	1	2	yes	complemented
574	#3313	C₂×C₈₉	1	2	yes	complemented
575	#3276	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#3269	C₂×C₈₉	1	2	yes	complemented
577	#3172	C₂×C₈₉	1	2	yes	complemented
578	#3170	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#3107	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#3104	C₂×C₈₉	1	2	yes	complemented
582	#3102	C₂×C₈₉	1	2	yes	complemented
583	#2965	C₂×C₈₉	1	1	yes	characteristic, complemented
584	C₄×#137	C₂×C₈₉	1	2	yes	complemented
585	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
586	C₈₉	#61447	1	1	yes	characteristic, direct product factor, Sylow
587	C₂×#137	C₂²×C₈₉	1	2	yes	—
588	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
589	#557	C₂²×C₈₉	1	1	yes	characteristic
590	#557	C₂²×C₈₉	1	1	yes	characteristic
591	#556	—	2	1	no	—
592	#556	C₂²×C₈₉	1	1	yes	characteristic
593	#556	C₂²×C₈₉	1	1	yes	characteristic
594	#556	C₂²×C₈₉	1	2	yes	—
595	#552	—	2	2	no	—
596	#552	—	2	2	no	—
597	#552	—	2	1	no	—
598	#552	C₂²×C₈₉	1	2	yes	—
599	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
600	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
601	#548	—	2	1	no	—
602	#548	C₂²×C₈₉	1	2	yes	—
603	#547	—	2	1	no	—
604	#547	C₂²×C₈₉	1	1	yes	characteristic
605	#547	C₂²×C₈₉	1	2	yes	—
606	#547	C₂²×C₈₉	1	1	yes	characteristic
607	#533	—	2	1	no	—
608	#533	C₂²×C₈₉	1	2	yes	—
609	#533	C₂²×C₈₉	1	1	yes	characteristic
610	#533	C₂²×C₈₉	1	1	yes	characteristic
611	#529	—	2	2	no	—
612	#529	—	2	1	no	—
613	#529	—	2	2	no	—
614	#529	C₂²×C₈₉	1	2	yes	—
615	C₄×#41	—	2	1	no	—
616	C₄×#41	C₂²×C₈₉	1	2	yes	—
617	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
618	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
619	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
620	C₂×C₄×Q₈	—	2	1	no	—
621	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
622	#501	C₂²×C₈₉	1	2	yes	—
623	#500	C₂²×C₈₉	1	1	yes	characteristic
624	#497	C₂²×C₈₉	1	2	yes	—
625	#494	C₂²×C₈₉	1	1	yes	characteristic
626	#491	C₂²×C₈₉	1	2	yes	—
627	#489	C₂²×C₈₉	1	2	yes	—
628	#487	C₂²×C₈₉	1	1	yes	characteristic
629	#487	C₂²×C₈₉	1	1	yes	characteristic
630	#485	C₂²×C₈₉	1	2	yes	—
631	#485	C₂²×C₈₉	1	2	yes	—
632	#485	C₂²×C₈₉	1	2	yes	—
633	#484	C₂²×C₈₉	1	2	yes	—
634	#484	C₂²×C₈₉	1	2	yes	—
635	#482	C₂²×C₈₉	1	2	yes	—
636	#479	C₂²×C₈₉	1	2	yes	—
637	#478	C₂²×C₈₉	1	2	yes	—
638	#477	C₂²×C₈₉	1	2	yes	—
639	#477	C₂²×C₈₉	1	2	yes	—
640	#475	C₂²×C₈₉	1	1	yes	characteristic
641	#475	C₂²×C₈₉	1	1	yes	characteristic
642	#474	C₂²×C₈₉	1	1	yes	characteristic
643	#474	C₂²×C₈₉	1	1	yes	characteristic
644	#470	C₂²×C₈₉	1	2	yes	—
645	#470	C₂²×C₈₉	1	2	yes	—
646	#468	C₂²×C₈₉	1	2	yes	—
647	#468	C₂²×C₈₉	1	2	yes	—
648	#467	C₂²×C₈₉	1	2	yes	—
649	#467	C₂²×C₈₉	1	2	yes	—
650	#464	C₂²×C₈₉	1	2	yes	—
651	#463	C₂²×C₈₉	1	2	yes	—
652	#462	C₂²×C₈₉	1	1	yes	characteristic
653	#462	C₂²×C₈₉	1	2	yes	—
654	#462	C₂²×C₈₉	1	2	yes	—
655	#462	C₂²×C₈₉	1	1	yes	characteristic
656	#461	C₂²×C₈₉	1	1	yes	characteristic
657	#461	C₂²×C₈₉	1	1	yes	characteristic
658	#452	C₂²×C₈₉	1	2	yes	—
659	#452	C₂²×C₈₉	1	2	yes	—
660	#452	C₂²×C₈₉	1	2	yes	—
661	#451	C₂²×C₈₉	1	2	yes	—
662	#451	C₂²×C₈₉	1	2	yes	—
663	#449	C₂²×C₈₉	1	2	yes	—
664	#446	C₂²×C₈₉	1	1	yes	characteristic
665	#446	C₂²×C₈₉	1	1	yes	characteristic
666	#441	C₂²×C₈₉	1	2	yes	—
667	#441	C₂²×C₈₉	1	2	yes	—
668	#440	C₂²×C₈₉	1	2	yes	—
669	#440	C₂²×C₈₉	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
671	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
672	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
673	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
674	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
676	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
682	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
684	#436	C₂²×C₈₉	1	1	yes	characteristic
685	#436	C₂²×C₈₉	1	1	yes	characteristic
686	#435	C₂²×C₈₉	1	2	yes	—
687	#435	C₂²×C₈₉	1	2	yes	—
688	#431	C₂²×C₈₉	1	2	yes	—
689	#431	C₂²×C₈₉	1	1	yes	characteristic
690	#428	C₂²×C₈₉	1	2	yes	—
691	#427	C₂²×C₈₉	1	1	yes	characteristic
692	#419	C₂²×C₈₉	1	2	yes	—
693	#417	C₂²×C₈₉	1	2	yes	—
694	#416	C₂²×C₈₉	1	1	yes	characteristic
695	#416	C₂²×C₈₉	1	1	yes	characteristic
696	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
697	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
698	C₂×#41	—	2	1	no	—
699	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
700	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
701	C₂×#41	C₂³×C₈₉	1	2	yes	—
702	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
705	#137	—	2	8	no	—
706	#135	—	2	4	no	—
707	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
717	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
718	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
719	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	—	2	1	no	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	C₂³×C₈₉	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	C₂³×C₈₉	1	2	yes	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
767	#121	—	2	2	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	C₂³×C₈₉	1	2	yes	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
783	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
784	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
785	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
790	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
801	C₄×D₄	D₄×C₈₉	1	2	yes	—
802	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₈₉	1	2	yes	—
806	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₈₉	1	2	yes	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	2	no	—
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	D₄×C₈₉	1	2	yes	—
819	#117	D₄×C₈₉	1	1	yes	characteristic
820	#117	C₂³×C₈₉	1	1	yes	characteristic
821	#117	C₂³×C₈₉	1	1	yes	characteristic
822	#117	C₂³×C₈₉	1	2	yes	—
823	C₂×C₄⋊C₄	—	2	2	no	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
827	C₂×C₄²	—	2	2	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
832	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
833	#107	C₂³×C₈₉	1	1	yes	characteristic
834	#107	C₂³×C₈₉	1	1	yes	characteristic
835	#107	C₂³×C₈₉	1	2	yes	—
836	#107	C₂³×C₈₉	1	2	yes	—
837	#107	C₂³×C₈₉	1	2	yes	—
838	#107	C₂³×C₈₉	1	2	yes	—
839	#106	C₂³×C₈₉	1	1	yes	characteristic
840	#106	C₂³×C₈₉	1	1	yes	characteristic
841	#106	C₂³×C₈₉	1	2	yes	—
842	#106	C₂³×C₈₉	1	2	yes	—
843	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
844	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
845	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
847	#103	C₂³×C₈₉	1	1	yes	characteristic
848	#103	C₂³×C₈₉	1	1	yes	characteristic
849	#103	C₂³×C₈₉	1	1	yes	characteristic
850	#103	C₂³×C₈₉	1	1	yes	characteristic
851	#103	C₂³×C₈₉	1	2	yes	—
852	#103	C₂³×C₈₉	1	2	yes	—
853	#103	C₂³×C₈₉	1	2	yes	—
854	#103	C₂³×C₈₉	1	2	yes	—
855	#103	C₂³×C₈₉	1	2	yes	—
856	#103	C₂³×C₈₉	1	2	yes	—
857	#103	C₂³×C₈₉	1	2	yes	—
858	#103	C₂³×C₈₉	1	2	yes	—
859	#103	C₂³×C₈₉	1	2	yes	—
860	#103	C₂³×C₈₉	1	2	yes	—
861	#102	C₂³×C₈₉	1	1	yes	characteristic
862	#102	C₂³×C₈₉	1	1	yes	characteristic
863	#102	C₂³×C₈₉	1	1	yes	characteristic
864	#102	C₂³×C₈₉	1	1	yes	characteristic
865	#102	C₂³×C₈₉	1	2	yes	—
866	#102	C₂³×C₈₉	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
870	#97	C₂³×C₈₉	1	2	yes	—
871	#97	C₂³×C₈₉	1	2	yes	—
872	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₈₉	1	2	yes	—
877	#41	—	2	2	no	—
878	#41	—	2	2	no	—
879	#41	—	2	4	no	—
880	#41	—	4	2	no	—
881	#41	—	4	1	no	—
882	#41	—	4	1	no	—
883	#41	—	4	2	no	—
884	#41	—	4	4	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	4	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	—	4	4	no	—
892	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
902	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
903	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
916	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
919	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
921	Q₁₆	—	2	2	no	—
922	Q₁₆	—	2	4	no	—
923	Q₁₆	—	2	4	no	—
924	Q₁₆	—	4	2	no	—
925	Q₁₆	—	4	2	no	—
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	2	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	#41×C₈₉	1	4	yes	complemented
930	D₈	—	2	2	no	—
931	M₁₆	—	2	4	no	—
932	M₁₆	—	4	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	4	1	no	—
935	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
939	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
940	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1010	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
1011	C₄²	C₂×D₄×C₈₉	1	2	yes	—
1012	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₈₉	1	2	yes	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
1018	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	4	no	—
1028	Q₈	—	4	4	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	C₂×#41×C₈₉	1	2	yes	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	C₂×#41×C₈₉	1	2	yes	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	4	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	4	no	—
1064	C₂×C₄	—	4	4	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	C₂×#41×C₈₉	1	2	yes	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	#575×C₈₉	1	2	yes	—
1115	C₄	#578×C₈₉	1	2	yes	—
1116	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
1117	C₄	#585×C₈₉	1	1	yes	characteristic
1118	C₂	—	4	1	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	4	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
1123	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
1124	C₂	C₂×#578×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 ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3482	C₂	semidirect
2. C₈₉×#3482	C₂	semidirect
3. C₈₉×#3398	C₂	semidirect
4. C₈₉×#3386	C₂	semidirect
5. C₈₉×#3374	C₂	semidirect
6. C₈₉×#3367	C₂	semidirect
7. C₈₉×#3353	C₂	semidirect
8. C₈₉×#3349	C₂	semidirect
9. C₈₉×#3330	C₂	semidirect
10. C₈₉×#3328	C₂	semidirect
11. C₈₉×#3315	C₂	semidirect
12. C₈₉×#3313	C₂	semidirect
13. C₈₉×#3276	C₂	semidirect
14. C₈₉×#3269	C₂	semidirect
15. C₈₉×#3172	C₂	semidirect
16. C₈₉×#3170	C₂	semidirect
17. C₈₉×#3107	C₂	semidirect
18. C₈₉×#3107	C₂	semidirect
19. C₈₉×#3104	C₂	semidirect
20. C₈₉×#3102	C₂	semidirect
21. C₈₉×#2965	C₂	semidirect
22. C₄×#137×C₈₉	C₂	semidirect
23. C₄×#135×C₈₉	C₂	semidirect
366. SD₁₆×C₈₉	#41	semidirect
555. #61447	C₈₉	direct (N × H)
563. #3482	C₂×C₈₉	semidirect
564. #3482	C₂×C₈₉	semidirect
565. #3398	C₂×C₈₉	semidirect
566. #3386	C₂×C₈₉	semidirect
567. #3374	C₂×C₈₉	semidirect
568. #3367	C₂×C₈₉	semidirect
569. #3353	C₂×C₈₉	semidirect
570. #3349	C₂×C₈₉	semidirect
571. #3330	C₂×C₈₉	semidirect
572. #3328	C₂×C₈₉	semidirect
573. #3315	C₂×C₈₉	semidirect
574. #3313	C₂×C₈₉	semidirect
575. #3276	C₂×C₈₉	semidirect
576. #3269	C₂×C₈₉	semidirect
577. #3172	C₂×C₈₉	semidirect
578. #3170	C₂×C₈₉	semidirect
579. #3107	C₂×C₈₉	semidirect
580. #3107	C₂×C₈₉	semidirect
581. #3104	C₂×C₈₉	semidirect
582. #3102	C₂×C₈₉	semidirect
583. #2965	C₂×C₈₉	semidirect
584. C₄×#137	C₂×C₈₉	semidirect
585. C₄×#135	C₂×C₈₉	semidirect
586. C₈₉	#61447	direct (N × H)
929. SD₁₆	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3482	2
C₈₉×#3398	2
C₈₉×#3386	2
C₈₉×#3374	2
C₈₉×#3367	2
C₈₉×#3353	2
C₈₉×#3349	2
C₈₉×#3330	2
C₈₉×#3328	2
C₈₉×#3315	2
C₈₉×#3313	2
C₈₉×#3276	2
C₈₉×#3269	2
C₈₉×#3172	2
C₈₉×#3170	2
C₈₉×#3107	2
C₈₉×#3104	2
C₈₉×#3102	2
C₈₉×#2965	2
C₄×#137×C₈₉	2
C₄×#135×C₈₉	2
#61447	89

Subgroups — C89×#61447 #36439295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61447 #36439295