Subgroups — C₈₉×#60302 #36438150

Order 22784.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2995	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2992	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2981	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2980	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2968	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2967	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2925	C₂	1	2	yes	maximal, complemented
21	C₈₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2923	C₂	1	2	yes	maximal, complemented
23	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₈₉	C₄	1	1	yes	characteristic
25	#559×C₈₉	C₄	1	2	yes	—
26	#557×C₈₉	C₄	1	1	yes	characteristic
27	#556×C₈₉	C₄	1	1	yes	characteristic
28	#556×C₈₉	C₄	1	2	yes	—
29	#553×C₈₉	C₄	1	1	yes	characteristic
30	#553×C₈₉	C₄	1	1	yes	characteristic
31	#553×C₈₉	C₄	1	2	yes	—
32	#553×C₈₉	C₄	1	2	yes	—
33	#550×C₈₉	C₄	1	1	yes	characteristic
34	#548×C₈₉	C₄	1	1	yes	characteristic
35	#548×C₈₉	C₄	1	1	yes	characteristic
36	#532×C₈₉	C₂²	1	1	yes	characteristic
37	#532×C₈₉	C₂²	1	2	yes	—
38	#529×C₈₉	C₂²	1	1	yes	characteristic
39	#529×C₈₉	C₂²	1	2	yes	—
40	#529×C₈₉	C₂²	1	2	yes	—
41	#529×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
47	#446×C₈₉	C₂²	1	1	yes	characteristic
48	#446×C₈₉	C₂²	1	1	yes	characteristic
49	#446×C₈₉	C₂²	1	1	yes	characteristic
50	#446×C₈₉	C₂²	1	2	yes	—
51	#446×C₈₉	C₂²	1	2	yes	—
52	#446×C₈₉	C₂²	1	2	yes	—
53	#446×C₈₉	C₂²	1	2	yes	—
54	#446×C₈₉	C₂²	1	1	yes	characteristic
55	#446×C₈₉	C₂²	1	1	yes	characteristic
56	#446×C₈₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
59	#436×C₈₉	C₂²	1	1	yes	characteristic
60	#436×C₈₉	C₂²	1	1	yes	characteristic
61	#436×C₈₉	C₂²	1	1	yes	characteristic
62	#436×C₈₉	C₂²	1	2	yes	—
63	#436×C₈₉	C₂²	1	2	yes	—
64	#436×C₈₉	C₂²	1	1	yes	characteristic
65	#436×C₈₉	C₂²	1	2	yes	—
66	#435×C₈₉	C₂²	1	2	yes	—
67	#435×C₈₉	C₂²	1	2	yes	—
68	#435×C₈₉	C₂²	1	2	yes	—
69	#435×C₈₉	C₂²	1	2	yes	—
70	#435×C₈₉	C₂²	1	2	yes	—
71	#435×C₈₉	C₂²	1	2	yes	—
72	#435×C₈₉	C₂²	1	2	yes	—
73	#435×C₈₉	C₂²	1	2	yes	—
74	#435×C₈₉	C₂²	1	2	yes	—
75	#435×C₈₉	C₂²	1	2	yes	—
76	#435×C₈₉	C₂²	1	2	yes	—
77	#435×C₈₉	C₂²	1	2	yes	—
78	#435×C₈₉	C₂²	1	2	yes	—
79	#435×C₈₉	C₂²	1	2	yes	—
80	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₈₉	C₂²	1	2	yes	—
82	C₈×D₄×C₈₉	C₂²	1	2	yes	—
83	C₈×D₄×C₈₉	C₂²	1	2	yes	—
84	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
85	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
86	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
87	#433×C₈₉	C₂²	1	1	yes	characteristic
88	#433×C₈₉	C₂²	1	1	yes	characteristic
89	#433×C₈₉	C₂²	1	1	yes	characteristic
90	#433×C₈₉	C₂²	1	1	yes	characteristic
91	#433×C₈₉	C₂²	1	2	yes	—
92	#433×C₈₉	C₂²	1	2	yes	—
93	#433×C₈₉	C₂²	1	2	yes	—
94	#433×C₈₉	C₂²	1	2	yes	—
95	#433×C₈₉	C₂²	1	2	yes	—
96	#433×C₈₉	C₂²	1	2	yes	—
97	#432×C₈₉	C₂²	1	2	yes	—
98	#432×C₈₉	C₂²	1	2	yes	—
99	#432×C₈₉	C₂²	1	2	yes	—
100	#432×C₈₉	C₂²	1	2	yes	—
101	#432×C₈₉	C₂²	1	1	yes	characteristic
102	#432×C₈₉	C₂²	1	2	yes	—
103	#432×C₈₉	C₂²	1	2	yes	—
104	#432×C₈₉	C₂²	1	1	yes	characteristic
105	#431×C₈₉	C₂²	1	1	yes	characteristic
106	#431×C₈₉	C₂²	1	1	yes	characteristic
107	#431×C₈₉	C₂²	1	1	yes	characteristic
108	#431×C₈₉	C₂²	1	1	yes	characteristic
109	#431×C₈₉	C₂²	1	2	yes	—
110	#431×C₈₉	C₂²	1	1	yes	characteristic
111	#431×C₈₉	C₂²	1	1	yes	characteristic
112	#431×C₈₉	C₂²	1	2	yes	—
113	#424×C₈₉	C₂²	1	1	yes	characteristic
114	#424×C₈₉	C₂²	1	1	yes	characteristic
115	#424×C₈₉	C₂²	1	2	yes	—
116	#424×C₈₉	C₂²	1	2	yes	—
117	#423×C₈₉	C₂²	1	2	yes	—
118	#423×C₈₉	C₂²	1	1	yes	characteristic
119	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
121	#408×C₈₉	C₂²	1	1	yes	characteristic
122	#408×C₈₉	C₂²	1	1	yes	characteristic
123	#408×C₈₉	C₂²	1	2	yes	—
124	#408×C₈₉	C₂²	1	2	yes	—
125	#408×C₈₉	C₂²	1	2	yes	—
126	#408×C₈₉	C₂²	1	2	yes	—
127	#408×C₈₉	C₂²	1	2	yes	—
128	#405×C₈₉	C₂²	1	2	yes	—
129	#405×C₈₉	C₂²	1	2	yes	—
130	#405×C₈₉	C₂²	1	2	yes	—
131	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
133	C₂×#97×C₈₉	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×#41×C₈₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
140	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
143	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
144	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
145	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
146	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
147	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
151	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
152	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
153	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
156	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
157	#127×C₈₉	C₂×C₄	1	2	yes	—
158	#126×C₈₉	C₂×C₄	1	2	yes	—
159	#126×C₈₉	C₂×C₄	1	2	yes	—
160	#126×C₈₉	C₂×C₄	1	2	yes	—
161	#126×C₈₉	C₂×C₄	1	2	yes	—
162	#126×C₈₉	C₂×C₄	1	2	yes	—
163	#126×C₈₉	C₂×C₄	1	2	yes	—
164	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
165	#125×C₈₉	C₂×C₄	1	2	yes	—
166	#125×C₈₉	C₂×C₄	1	2	yes	—
167	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
168	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
169	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
170	#124×C₈₉	C₂×C₄	1	2	yes	—
171	#124×C₈₉	C₂×C₄	1	2	yes	—
172	#124×C₈₉	C₂×C₄	1	2	yes	—
173	#124×C₈₉	C₂×C₄	1	2	yes	—
174	#124×C₈₉	C₂×C₄	1	2	yes	—
175	#123×C₈₉	C₂×C₄	1	2	yes	—
176	#123×C₈₉	C₂×C₄	1	2	yes	—
177	#123×C₈₉	C₂×C₄	1	2	yes	—
178	#123×C₈₉	C₂×C₄	1	2	yes	—
179	#123×C₈₉	C₂×C₄	1	2	yes	—
180	#123×C₈₉	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
183	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
185	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
186	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
187	#121×C₈₉	C₂×C₄	1	2	yes	—
188	#121×C₈₉	C₂×C₄	1	2	yes	—
189	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
190	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
191	#121×C₈₉	C₂×C₄	1	2	yes	—
192	#121×C₈₉	C₂×C₄	1	2	yes	—
193	#121×C₈₉	C₂×C₄	1	2	yes	—
194	#121×C₈₉	C₂×C₄	1	2	yes	—
195	#121×C₈₉	C₂×C₄	1	2	yes	—
196	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
199	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
201	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
202	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
203	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
204	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
205	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
208	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
211	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
212	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
214	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
215	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
217	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
221	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
224	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₈₉	C₂³	1	2	yes	—
227	C₄×D₄×C₈₉	C₂³	1	2	yes	—
228	C₄×D₄×C₈₉	C₂³	1	2	yes	—
229	C₄×D₄×C₈₉	C₂³	1	2	yes	—
230	C₄×D₄×C₈₉	C₂³	1	2	yes	—
231	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
232	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
233	#117×C₈₉	C₂×C₄	1	2	yes	—
234	#117×C₈₉	C₂×C₄	1	2	yes	—
235	#117×C₈₉	C₂³	1	2	yes	—
236	#117×C₈₉	C₂³	1	1	yes	characteristic
237	#117×C₈₉	C₂³	1	1	yes	characteristic
238	#117×C₈₉	C₂³	1	2	yes	—
239	#117×C₈₉	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
242	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
244	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
246	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
248	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
249	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
250	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
251	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
252	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
253	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
254	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
255	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
256	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
257	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
258	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
259	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
260	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
265	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
267	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
268	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
269	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
277	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
288	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
289	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
290	#97×C₈₉	C₂³	1	1	yes	characteristic
291	#97×C₈₉	C₂³	1	2	yes	—
292	#97×C₈₉	C₂³	1	2	yes	—
293	#97×C₈₉	C₂³	1	2	yes	—
294	#97×C₈₉	C₂³	1	1	yes	characteristic
295	#97×C₈₉	C₂³	1	2	yes	—
296	#97×C₈₉	C₂³	1	2	yes	—
297	#97×C₈₉	C₂³	1	2	yes	—
298	#97×C₈₉	C₂³	1	2	yes	—
299	#97×C₈₉	C₂³	1	2	yes	—
300	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
302	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
304	C₄×C₈×C₈₉	C₂³	1	2	yes	—
305	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₈₉	C₂³	1	2	yes	—
308	C₄×C₈×C₈₉	C₂³	1	2	yes	—
309	C₄×C₈×C₈₉	C₂³	1	2	yes	—
310	#41×C₈₉	—	4	1	no	—
311	#41×C₈₉	—	4	2	no	—
312	#41×C₈₉	—	4	1	no	—
313	#41×C₈₉	—	4	2	no	—
314	#41×C₈₉	—	4	2	no	—
315	#41×C₈₉	—	4	2	no	—
316	C₂×Q₈×C₈₉	—	4	2	no	—
317	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
319	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
321	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
327	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
328	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
330	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
332	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
333	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
338	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
339	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
341	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
342	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
345	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
352	M₁₆×C₈₉	—	4	1	no	—
353	M₁₆×C₈₉	—	4	2	no	—
354	M₁₆×C₈₉	—	4	2	no	—
355	M₁₆×C₈₉	—	4	1	no	—
356	M₁₆×C₈₉	—	4	2	no	—
357	M₁₆×C₈₉	—	4	2	no	—
358	M₁₆×C₈₉	—	4	2	no	—
359	C₂×C₈×C₈₉	—	4	2	no	—
360	C₂×C₈×C₈₉	—	4	1	no	—
361	C₂×C₈×C₈₉	—	4	2	no	—
362	C₂×C₈×C₈₉	—	4	2	no	—
363	C₂×C₈×C₈₉	—	4	2	no	—
364	C₂×C₈×C₈₉	—	4	2	no	—
365	C₂×C₈×C₈₉	—	4	1	no	—
366	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
372	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
373	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
377	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
390	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
399	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
403	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
404	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
406	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
424	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
426	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
427	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
428	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
429	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
430	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
432	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
433	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
434	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
435	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
436	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
437	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
438	C₄²×C₈₉	C₂⁴	1	2	yes	—
439	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
440	C₄²×C₈₉	C₂⁴	1	2	yes	—
441	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
442	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
443	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
444	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
445	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
446	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
447	Q₈×C₈₉	—	2	2	no	—
448	Q₈×C₈₉	—	2	2	no	—
449	Q₈×C₈₉	—	4	2	no	—
450	Q₈×C₈₉	—	4	1	no	—
451	Q₈×C₈₉	—	4	2	no	—
452	D₄×C₈₉	—	2	2	no	—
453	D₄×C₈₉	—	2	2	no	—
454	D₄×C₈₉	—	4	2	no	—
455	D₄×C₈₉	—	4	2	no	—
456	D₄×C₈₉	—	4	2	no	—
457	D₄×C₈₉	—	4	1	no	—
458	D₄×C₈₉	—	4	2	no	—
459	D₄×C₈₉	—	4	1	no	—
460	D₄×C₈₉	—	4	2	no	—
461	D₄×C₈₉	—	4	1	no	—
462	D₄×C₈₉	—	4	2	no	—
463	D₄×C₈₉	—	4	2	no	—
464	D₄×C₈₉	—	4	2	no	—
465	C₂×C₄×C₈₉	—	2	2	no	—
466	C₂×C₄×C₈₉	—	2	2	no	—
467	C₂×C₄×C₈₉	—	2	2	no	—
468	C₂×C₄×C₈₉	—	2	2	no	—
469	C₂×C₄×C₈₉	—	2	1	no	—
470	C₂×C₄×C₈₉	—	2	1	no	—
471	C₂×C₄×C₈₉	—	2	2	no	—
472	C₂×C₄×C₈₉	—	2	2	no	—
473	C₂×C₄×C₈₉	—	2	1	no	—
474	C₂×C₄×C₈₉	—	2	1	no	—
475	C₂×C₄×C₈₉	—	2	2	no	—
476	C₂×C₄×C₈₉	—	2	1	no	—
477	C₂×C₄×C₈₉	—	2	1	no	—
478	C₂×C₄×C₈₉	—	4	1	no	—
479	C₂×C₄×C₈₉	—	4	2	no	—
480	C₂×C₄×C₈₉	—	4	1	no	—
481	C₂×C₄×C₈₉	—	4	2	no	—
482	C₂×C₄×C₈₉	—	4	1	no	—
483	C₂×C₄×C₈₉	—	4	2	no	—
484	C₂×C₄×C₈₉	—	4	2	no	—
485	C₂×C₄×C₈₉	—	4	2	no	—
486	C₂×C₄×C₈₉	—	4	2	no	—
487	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
492	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
495	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
500	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
503	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
504	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
505	C₈×C₈₉	—	2	1	no	—
506	C₈×C₈₉	—	2	2	no	—
507	C₈×C₈₉	—	2	1	no	—
508	C₈×C₈₉	—	2	1	no	—
509	C₈×C₈₉	—	2	1	no	—
510	C₈×C₈₉	—	2	2	no	—
511	C₈×C₈₉	—	2	1	no	—
512	C₈×C₈₉	—	2	2	no	—
513	C₈×C₈₉	—	2	2	no	—
514	C₈×C₈₉	—	2	1	no	—
515	C₈×C₈₉	—	2	1	no	—
516	C₈×C₈₉	—	2	1	no	—
517	C₂²×C₈₉	—	2	1	no	—
518	C₂²×C₈₉	—	2	1	no	—
519	C₂²×C₈₉	—	2	2	no	—
520	C₂²×C₈₉	—	2	1	no	—
521	C₂²×C₈₉	—	2	2	no	—
522	C₂²×C₈₉	—	2	1	no	—
523	C₂²×C₈₉	—	2	1	no	—
524	C₂²×C₈₉	—	2	1	no	—
525	C₂²×C₈₉	—	2	2	no	—
526	C₂²×C₈₉	—	2	2	no	—
527	C₂²×C₈₉	—	2	1	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	C₂⁴×C₄	1	1	yes	characteristic
533	C₄×C₈₉	—	2	1	no	—
534	C₄×C₈₉	—	2	2	no	—
535	C₄×C₈₉	—	2	1	no	—
536	C₄×C₈₉	—	2	1	no	—
537	C₄×C₈₉	—	2	2	no	—
538	C₄×C₈₉	—	2	1	no	—
539	C₄×C₈₉	—	2	1	no	—
540	C₄×C₈₉	—	2	1	no	—
541	C₄×C₈₉	—	2	2	no	—
542	C₄×C₈₉	—	2	2	no	—
543	C₄×C₈₉	—	2	1	no	—
544	C₄×C₈₉	—	2	1	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	#568	1	2	yes	—
550	C₄×C₈₉	#585	1	1	yes	characteristic
551	C₄×C₈₉	#585	1	1	yes	characteristic
552	#60302	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
553	C₂×C₈₉	—	4	1	no	—
554	C₂×C₈₉	—	4	1	no	—
555	C₂×C₈₉	—	4	1	no	—
556	C₂×C₈₉	—	4	2	no	—
557	C₂×C₈₉	—	4	2	no	—
558	C₂×C₈₉	#3428	1	1	yes	characteristic
559	C₂×C₈₉	C₂×#568	1	1	yes	characteristic
560	C₂×C₈₉	#3573	1	1	yes	characteristic
561	#3480	C₂×C₈₉	1	1	yes	characteristic
562	#2995	C₂×C₈₉	1	2	yes	complemented
563	#2994	C₂×C₈₉	1	1	yes	characteristic, complemented
564	#2993	C₂×C₈₉	1	1	yes	characteristic, complemented
565	#2992	C₂×C₈₉	1	2	yes	complemented
566	#2990	C₂×C₈₉	1	1	yes	characteristic, complemented
567	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
568	#2984	C₂×C₈₉	1	1	yes	characteristic, complemented
569	#2983	C₂×C₈₉	1	1	yes	characteristic, complemented
570	#2981	C₂×C₈₉	1	1	yes	characteristic, complemented
571	#2981	C₂×C₈₉	1	2	yes	complemented
572	#2980	C₂×C₈₉	1	2	yes	complemented
573	#2979	C₂×C₈₉	1	1	yes	characteristic, complemented
574	#2970	C₂×C₈₉	1	1	yes	characteristic, complemented
575	#2969	C₂×C₈₉	1	1	yes	characteristic, complemented
576	#2968	C₂×C₈₉	1	2	yes	complemented
577	#2967	C₂×C₈₉	1	2	yes	complemented
578	#2966	C₂×C₈₉	1	1	yes	characteristic, complemented
579	#2965	C₂×C₈₉	1	1	yes	characteristic, complemented
580	#2925	C₂×C₈₉	1	1	yes	characteristic, complemented
581	#2925	C₂×C₈₉	1	2	yes	complemented
582	#2923	C₂×C₈₉	1	2	yes	complemented
583	#2922	C₂×C₈₉	1	1	yes	characteristic, complemented
584	C₈₉	#60302	1	1	yes	characteristic, direct product factor, Sylow
585	#559	C₄×C₈₉	1	1	yes	characteristic
586	#559	C₄×C₈₉	1	2	yes	—
587	#557	C₄×C₈₉	1	1	yes	characteristic
588	#556	C₄×C₈₉	1	1	yes	characteristic
589	#556	C₄×C₈₉	1	2	yes	—
590	#553	C₄×C₈₉	1	1	yes	characteristic
591	#553	C₄×C₈₉	1	1	yes	characteristic
592	#553	C₄×C₈₉	1	2	yes	—
593	#553	C₄×C₈₉	1	2	yes	—
594	#550	C₄×C₈₉	1	1	yes	characteristic
595	#548	C₄×C₈₉	1	1	yes	characteristic
596	#548	C₄×C₈₉	1	1	yes	characteristic
597	#532	C₂²×C₈₉	1	1	yes	characteristic
598	#532	C₂²×C₈₉	1	2	yes	—
599	#529	C₂²×C₈₉	1	1	yes	characteristic
600	#529	C₂²×C₈₉	1	2	yes	—
601	#529	C₂²×C₈₉	1	2	yes	—
602	#529	C₂²×C₈₉	1	1	yes	characteristic
603	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
604	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
605	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
606	C₄×#41	C₂²×C₈₉	1	2	yes	—
607	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
608	#446	C₂²×C₈₉	1	1	yes	characteristic
609	#446	C₂²×C₈₉	1	1	yes	characteristic
610	#446	C₂²×C₈₉	1	1	yes	characteristic
611	#446	C₂²×C₈₉	1	2	yes	—
612	#446	C₂²×C₈₉	1	2	yes	—
613	#446	C₂²×C₈₉	1	2	yes	—
614	#446	C₂²×C₈₉	1	2	yes	—
615	#446	C₂²×C₈₉	1	1	yes	characteristic
616	#446	C₂²×C₈₉	1	1	yes	characteristic
617	#446	C₂²×C₈₉	1	1	yes	characteristic
618	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
619	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
620	#436	C₂²×C₈₉	1	1	yes	characteristic
621	#436	C₂²×C₈₉	1	1	yes	characteristic
622	#436	C₂²×C₈₉	1	1	yes	characteristic
623	#436	C₂²×C₈₉	1	2	yes	—
624	#436	C₂²×C₈₉	1	2	yes	—
625	#436	C₂²×C₈₉	1	1	yes	characteristic
626	#436	C₂²×C₈₉	1	2	yes	—
627	#435	C₂²×C₈₉	1	2	yes	—
628	#435	C₂²×C₈₉	1	2	yes	—
629	#435	C₂²×C₈₉	1	2	yes	—
630	#435	C₂²×C₈₉	1	2	yes	—
631	#435	C₂²×C₈₉	1	2	yes	—
632	#435	C₂²×C₈₉	1	2	yes	—
633	#435	C₂²×C₈₉	1	2	yes	—
634	#435	C₂²×C₈₉	1	2	yes	—
635	#435	C₂²×C₈₉	1	2	yes	—
636	#435	C₂²×C₈₉	1	2	yes	—
637	#435	C₂²×C₈₉	1	2	yes	—
638	#435	C₂²×C₈₉	1	2	yes	—
639	#435	C₂²×C₈₉	1	2	yes	—
640	#435	C₂²×C₈₉	1	2	yes	—
641	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
642	C₈×D₄	C₂²×C₈₉	1	2	yes	—
643	C₈×D₄	C₂²×C₈₉	1	2	yes	—
644	C₈×D₄	C₂²×C₈₉	1	2	yes	—
645	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
646	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
647	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
648	#433	C₂²×C₈₉	1	1	yes	characteristic
649	#433	C₂²×C₈₉	1	1	yes	characteristic
650	#433	C₂²×C₈₉	1	1	yes	characteristic
651	#433	C₂²×C₈₉	1	1	yes	characteristic
652	#433	C₂²×C₈₉	1	2	yes	—
653	#433	C₂²×C₈₉	1	2	yes	—
654	#433	C₂²×C₈₉	1	2	yes	—
655	#433	C₂²×C₈₉	1	2	yes	—
656	#433	C₂²×C₈₉	1	2	yes	—
657	#433	C₂²×C₈₉	1	2	yes	—
658	#432	C₂²×C₈₉	1	2	yes	—
659	#432	C₂²×C₈₉	1	2	yes	—
660	#432	C₂²×C₈₉	1	2	yes	—
661	#432	C₂²×C₈₉	1	2	yes	—
662	#432	C₂²×C₈₉	1	1	yes	characteristic
663	#432	C₂²×C₈₉	1	2	yes	—
664	#432	C₂²×C₈₉	1	2	yes	—
665	#432	C₂²×C₈₉	1	1	yes	characteristic
666	#431	C₂²×C₈₉	1	1	yes	characteristic
667	#431	C₂²×C₈₉	1	1	yes	characteristic
668	#431	C₂²×C₈₉	1	1	yes	characteristic
669	#431	C₂²×C₈₉	1	1	yes	characteristic
670	#431	C₂²×C₈₉	1	2	yes	—
671	#431	C₂²×C₈₉	1	1	yes	characteristic
672	#431	C₂²×C₈₉	1	1	yes	characteristic
673	#431	C₂²×C₈₉	1	2	yes	—
674	#424	C₂²×C₈₉	1	1	yes	characteristic
675	#424	C₂²×C₈₉	1	1	yes	characteristic
676	#424	C₂²×C₈₉	1	2	yes	—
677	#424	C₂²×C₈₉	1	2	yes	—
678	#423	C₂²×C₈₉	1	2	yes	—
679	#423	C₂²×C₈₉	1	1	yes	characteristic
680	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
681	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
682	#408	C₂²×C₈₉	1	1	yes	characteristic
683	#408	C₂²×C₈₉	1	1	yes	characteristic
684	#408	C₂²×C₈₉	1	2	yes	—
685	#408	C₂²×C₈₉	1	2	yes	—
686	#408	C₂²×C₈₉	1	2	yes	—
687	#408	C₂²×C₈₉	1	2	yes	—
688	#408	C₂²×C₈₉	1	2	yes	—
689	#405	C₂²×C₈₉	1	2	yes	—
690	#405	C₂²×C₈₉	1	2	yes	—
691	#405	C₂²×C₈₉	1	2	yes	—
692	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
693	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
694	C₂×#97	C₂²×C₈₉	1	2	yes	—
695	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
696	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
697	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
698	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
699	C₂×#41	C₂³×C₈₉	1	2	yes	—
700	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
701	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
702	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
704	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
705	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
706	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
707	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
708	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
711	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
712	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
713	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
714	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
715	C₄⋊Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
716	C₄⋊Q₈	C₂×C₄×C₈₉	1	2	yes	—
717	#127	C₂×C₄×C₈₉	1	1	yes	characteristic
718	#127	C₂×C₄×C₈₉	1	2	yes	—
719	#126	C₂×C₄×C₈₉	1	2	yes	—
720	#126	C₂×C₄×C₈₉	1	2	yes	—
721	#126	C₂×C₄×C₈₉	1	2	yes	—
722	#126	C₂×C₄×C₈₉	1	2	yes	—
723	#126	C₂×C₄×C₈₉	1	2	yes	—
724	#126	C₂×C₄×C₈₉	1	2	yes	—
725	#125	C₂×C₄×C₈₉	1	1	yes	characteristic
726	#125	C₂×C₄×C₈₉	1	2	yes	—
727	#125	C₂×C₄×C₈₉	1	2	yes	—
728	#125	C₂×C₄×C₈₉	1	1	yes	characteristic
729	#124	C₂×C₄×C₈₉	1	1	yes	characteristic
730	#124	C₂×C₄×C₈₉	1	1	yes	characteristic
731	#124	C₂×C₄×C₈₉	1	2	yes	—
732	#124	C₂×C₄×C₈₉	1	2	yes	—
733	#124	C₂×C₄×C₈₉	1	2	yes	—
734	#124	C₂×C₄×C₈₉	1	2	yes	—
735	#124	C₂×C₄×C₈₉	1	2	yes	—
736	#123	C₂×C₄×C₈₉	1	2	yes	—
737	#123	C₂×C₄×C₈₉	1	2	yes	—
738	#123	C₂×C₄×C₈₉	1	2	yes	—
739	#123	C₂×C₄×C₈₉	1	2	yes	—
740	#123	C₂×C₄×C₈₉	1	2	yes	—
741	#123	C₂×C₄×C₈₉	1	2	yes	—
742	C₂²⋊Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
744	C₂²⋊Q₈	C₂×C₄×C₈₉	1	2	yes	—
745	C₂²⋊Q₈	C₂×C₄×C₈₉	1	2	yes	—
746	#121	C₂×C₄×C₈₉	1	1	yes	characteristic
747	#121	C₂×C₄×C₈₉	1	1	yes	characteristic
748	#121	C₂×C₄×C₈₉	1	2	yes	—
749	#121	C₂×C₄×C₈₉	1	2	yes	—
750	#121	C₂×C₄×C₈₉	1	1	yes	characteristic
751	#121	C₂×C₄×C₈₉	1	1	yes	characteristic
752	#121	C₂×C₄×C₈₉	1	2	yes	—
753	#121	C₂×C₄×C₈₉	1	2	yes	—
754	#121	C₂×C₄×C₈₉	1	2	yes	—
755	#121	C₂×C₄×C₈₉	1	2	yes	—
756	#121	C₂×C₄×C₈₉	1	2	yes	—
757	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
758	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
759	C₄×Q₈	C₂×C₄×C₈₉	1	2	yes	—
760	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
761	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
762	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
763	C₄×Q₈	C₂×C₄×C₈₉	1	2	yes	—
764	C₄×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
765	C₄×Q₈	C₂×C₄×C₈₉	1	2	yes	—
766	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
769	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
770	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
771	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
772	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
773	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
774	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
775	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
776	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
777	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
778	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
779	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
780	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
781	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
782	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
783	C₄×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
784	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
785	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₈₉	1	2	yes	—
788	C₄×D₄	C₂³×C₈₉	1	2	yes	—
789	C₄×D₄	C₂³×C₈₉	1	2	yes	—
790	C₄×D₄	C₂³×C₈₉	1	2	yes	—
791	C₄×D₄	C₂³×C₈₉	1	2	yes	—
792	#117	C₂×C₄×C₈₉	1	1	yes	characteristic
793	#117	C₂×C₄×C₈₉	1	1	yes	characteristic
794	#117	C₂×C₄×C₈₉	1	2	yes	—
795	#117	C₂×C₄×C₈₉	1	2	yes	—
796	#117	C₂³×C₈₉	1	1	yes	characteristic
797	#117	C₂³×C₈₉	1	1	yes	characteristic
798	#117	C₂³×C₈₉	1	2	yes	—
799	#117	C₂³×C₈₉	1	1	yes	characteristic
800	#117	C₂³×C₈₉	1	2	yes	—
801	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
803	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
804	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
805	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
807	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
809	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
811	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
812	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
813	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
816	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
820	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
821	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
828	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
829	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
830	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
834	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
835	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
851	#97	C₂³×C₈₉	1	1	yes	characteristic
852	#97	C₂³×C₈₉	1	2	yes	—
853	#97	C₂³×C₈₉	1	2	yes	—
854	#97	C₂³×C₈₉	1	2	yes	—
855	#97	C₂³×C₈₉	1	1	yes	characteristic
856	#97	C₂³×C₈₉	1	2	yes	—
857	#97	C₂³×C₈₉	1	2	yes	—
858	#97	C₂³×C₈₉	1	2	yes	—
859	#97	C₂³×C₈₉	1	2	yes	—
860	#97	C₂³×C₈₉	1	2	yes	—
861	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₈₉	1	2	yes	—
866	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₈₉	1	2	yes	—
869	C₄×C₈	C₂³×C₈₉	1	2	yes	—
870	C₄×C₈	C₂³×C₈₉	1	2	yes	—
871	#41	—	4	1	no	—
872	#41	—	4	2	no	—
873	#41	—	4	1	no	—
874	#41	—	4	2	no	—
875	#41	—	4	2	no	—
876	#41	—	4	2	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
879	C₂×Q₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
880	C₂×Q₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
881	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
882	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
883	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
884	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
885	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
886	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
887	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
888	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
889	C₂×D₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
890	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
891	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
892	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
893	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
894	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
895	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
896	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
897	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
898	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
899	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
900	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
901	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
902	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
903	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
904	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
905	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
906	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
907	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
913	M₁₆	—	4	1	no	—
914	M₁₆	—	4	2	no	—
915	M₁₆	—	4	2	no	—
916	M₁₆	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	M₁₆	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	1	no	—
922	C₂×C₈	—	4	2	no	—
923	C₂×C₈	—	4	2	no	—
924	C₂×C₈	—	4	2	no	—
925	C₂×C₈	—	4	2	no	—
926	C₂×C₈	—	4	1	no	—
927	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
933	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
934	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
938	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
940	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
948	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
952	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
954	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
956	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
958	C₄⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
959	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
960	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
961	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
962	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
965	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
969	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
970	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
971	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
972	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
973	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
974	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
975	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
976	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
978	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
981	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
982	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
983	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
984	C₂²⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
985	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
986	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
987	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
988	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
989	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
990	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
991	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
992	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
993	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
994	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
995	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
996	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
997	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
998	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
999	C₄²	C₂⁴×C₈₉	1	2	yes	—
1000	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₈₉	1	2	yes	—
1002	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
1003	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
1004	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
1005	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
1006	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
1007	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	1	no	—
1012	Q₈	—	4	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	2	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	1	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	4	1	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1049	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1050	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1051	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1052	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1053	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1054	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1055	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1056	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1057	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1058	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1059	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1060	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1061	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1062	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
1063	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1064	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	2	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	#568×C₈₉	1	2	yes	—
1111	C₄	#585×C₈₉	1	1	yes	characteristic
1112	C₄	#585×C₈₉	1	1	yes	characteristic
1113	C₂	—	4	1	no	—
1114	C₂	—	4	1	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₈₉×#3428	1	1	yes	characteristic
1119	C₂	C₂×#568×C₈₉	1	1	yes	characteristic
1120	C₂	C₈₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂⁴×C₄
prime radical	C₈₉×#3480	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2995	C₂	semidirect
3. C₈₉×#2994	C₂	semidirect
4. C₈₉×#2993	C₂	semidirect
5. C₈₉×#2992	C₂	semidirect
6. C₈₉×#2990	C₂	semidirect
7. C₈₉×#2989	C₂	semidirect
8. C₈₉×#2984	C₂	semidirect
9. C₈₉×#2983	C₂	semidirect
10. C₈₉×#2981	C₂	semidirect
11. C₈₉×#2981	C₂	semidirect
12. C₈₉×#2980	C₂	semidirect
13. C₈₉×#2979	C₂	semidirect
14. C₈₉×#2970	C₂	semidirect
15. C₈₉×#2969	C₂	semidirect
16. C₈₉×#2968	C₂	semidirect
17. C₈₉×#2967	C₂	semidirect
18. C₈₉×#2966	C₂	semidirect
19. C₈₉×#2965	C₂	semidirect
20. C₈₉×#2925	C₂	semidirect
21. C₈₉×#2925	C₂	semidirect
22. C₈₉×#2923	C₂	semidirect
23. C₈₉×#2922	C₂	semidirect
552. #60302	C₈₉	direct (N × H)
562. #2995	C₂×C₈₉	semidirect
563. #2994	C₂×C₈₉	semidirect
564. #2993	C₂×C₈₉	semidirect
565. #2992	C₂×C₈₉	semidirect
566. #2990	C₂×C₈₉	semidirect
567. #2989	C₂×C₈₉	semidirect
568. #2984	C₂×C₈₉	semidirect
569. #2983	C₂×C₈₉	semidirect
570. #2981	C₂×C₈₉	semidirect
571. #2981	C₂×C₈₉	semidirect
572. #2980	C₂×C₈₉	semidirect
573. #2979	C₂×C₈₉	semidirect
574. #2970	C₂×C₈₉	semidirect
575. #2969	C₂×C₈₉	semidirect
576. #2968	C₂×C₈₉	semidirect
577. #2967	C₂×C₈₉	semidirect
578. #2966	C₂×C₈₉	semidirect
579. #2965	C₂×C₈₉	semidirect
580. #2925	C₂×C₈₉	semidirect
581. #2925	C₂×C₈₉	semidirect
582. #2923	C₂×C₈₉	semidirect
583. #2922	C₂×C₈₉	semidirect
584. C₈₉	#60302	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3480	2
C₈₉×#2995	2
C₈₉×#2994	2
C₈₉×#2993	2
C₈₉×#2992	2
C₈₉×#2990	2
C₈₉×#2989	2
C₈₉×#2984	2
C₈₉×#2983	2
C₈₉×#2981	2
C₈₉×#2980	2
C₈₉×#2979	2
C₈₉×#2970	2
C₈₉×#2969	2
C₈₉×#2968	2
C₈₉×#2967	2
C₈₉×#2966	2
C₈₉×#2965	2
C₈₉×#2925	2
C₈₉×#2923	2
C₈₉×#2922	2
#60302	89

Subgroups — C89×#60302 #36438150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60302 #36438150