Subgroups — C₈₉×#34474 #36412322

Order 22784.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2379	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2377	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2368	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2357	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2337	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2333	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2332	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2318	C₂	1	2	yes	maximal, complemented
20	C₈₉×#2310	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	#548×C₈₉	C₄	1	16	yes	complemented
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₈₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
44	#391×C₈₉	C₂²	1	1	yes	characteristic
45	#391×C₈₉	C₂²	1	1	yes	characteristic
46	#391×C₈₉	C₂²	1	1	yes	characteristic
47	#391×C₈₉	C₂²	1	2	yes	—
48	#391×C₈₉	C₂²	1	1	yes	characteristic
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	1	yes	characteristic
52	#391×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
54	#390×C₈₉	C₂²	1	1	yes	characteristic
55	#390×C₈₉	C₂²	1	1	yes	characteristic
56	#390×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	2	yes	—
58	#390×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#388×C₈₉	C₂²	1	1	yes	characteristic
62	#388×C₈₉	C₂²	1	2	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#388×C₈₉	C₂²	1	2	yes	—
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	1	yes	characteristic
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	1	yes	characteristic
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	1	yes	characteristic
81	#386×C₈₉	C₂²	1	2	yes	—
82	#386×C₈₉	C₂²	1	2	yes	—
83	#386×C₈₉	C₂²	1	2	yes	—
84	#386×C₈₉	C₂²	1	2	yes	—
85	#386×C₈₉	C₂²	1	1	yes	characteristic
86	#386×C₈₉	C₂²	1	2	yes	—
87	#386×C₈₉	C₂²	1	2	yes	—
88	#386×C₈₉	C₂²	1	1	yes	characteristic
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	2	yes	—
92	#385×C₈₉	C₂²	1	2	yes	—
93	#385×C₈₉	C₂²	1	2	yes	—
94	#385×C₈₉	C₂²	1	1	yes	characteristic
95	#385×C₈₉	C₂²	1	1	yes	characteristic
96	#384×C₈₉	C₂²	1	1	yes	characteristic
97	#383×C₈₉	C₂²	1	2	yes	—
98	#382×C₈₉	C₂²	1	2	yes	—
99	#382×C₈₉	C₂²	1	2	yes	—
100	#381×C₈₉	C₂²	1	2	yes	—
101	#381×C₈₉	C₂²	1	2	yes	—
102	#381×C₈₉	C₂²	1	2	yes	—
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	#380×C₈₉	C₂²	1	2	yes	—
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
122	#376×C₈₉	C₂²	1	1	yes	characteristic
123	C₂×#95×C₈₉	C₂²	1	2	yes	—
124	C₂×#41×C₈₉	—	4	2	no	—
125	C₂×#41×C₈₉	—	4	2	no	—
126	C₂×#41×C₈₉	C₂×C₄	1	8	yes	—
127	C₂²×Q₈×C₈₉	—	4	2	no	—
128	C₂²×Q₈×C₈₉	—	4	2	no	—
129	C₂²×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
135	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
145	#124×C₈₉	C₂×C₄	1	8	yes	complemented
146	#124×C₈₉	C₂×C₄	1	16	yes	complemented
147	C₂²⋊Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
148	C₂²⋊Q₈×C₈₉	C₂×C₄	1	16	yes	complemented
149	#121×C₈₉	C₂×C₄	1	8	yes	complemented
150	#121×C₈₉	C₂×C₄	1	16	yes	complemented
151	C₄×Q₈×C₈₉	—	4	2	no	—
152	C₄×Q₈×C₈₉	—	4	2	no	—
153	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
154	C₄×D₄×C₈₉	—	4	2	no	—
155	C₄×D₄×C₈₉	—	4	2	no	—
156	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₈₉	C₂×C₄	1	16	yes	complemented
158	#117×C₈₉	—	4	2	no	—
159	#117×C₈₉	—	4	2	no	—
160	#117×C₈₉	—	4	2	no	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₈₉	—	4	2	no	—
202	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
212	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
217	#95×C₈₉	C₂³	1	1	yes	characteristic
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	1	yes	characteristic
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	1	yes	characteristic
224	#95×C₈₉	C₂³	1	1	yes	characteristic
225	#95×C₈₉	C₂³	1	1	yes	characteristic
226	#95×C₈₉	C₂³	1	1	yes	characteristic
227	#95×C₈₉	C₂³	1	2	yes	—
228	#95×C₈₉	C₂³	1	1	yes	characteristic
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	#95×C₈₉	C₂³	1	2	yes	—
233	#95×C₈₉	C₂³	1	2	yes	—
234	#95×C₈₉	C₂³	1	2	yes	—
235	#95×C₈₉	C₂³	1	2	yes	—
236	#95×C₈₉	C₂³	1	2	yes	—
237	#95×C₈₉	C₂³	1	1	yes	characteristic
238	#95×C₈₉	C₂³	1	2	yes	—
239	#95×C₈₉	C₂³	1	2	yes	—
240	#95×C₈₉	C₂³	1	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	2	yes	—
243	#95×C₈₉	C₂³	1	2	yes	—
244	#95×C₈₉	C₂³	1	2	yes	—
245	#95×C₈₉	C₂³	1	1	yes	characteristic
246	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
249	#41×C₈₉	—	4	16	no	—
250	C₂×Q₈×C₈₉	—	2	2	no	—
251	C₂×Q₈×C₈₉	—	2	2	no	—
252	C₂×Q₈×C₈₉	—	2	2	no	—
253	C₂×Q₈×C₈₉	—	2	2	no	—
254	C₂×Q₈×C₈₉	—	4	2	no	—
255	C₂×Q₈×C₈₉	—	4	2	no	—
256	C₂×Q₈×C₈₉	—	4	16	no	—
257	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
258	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
259	C₂×Q₈×C₈₉	C₂²×C₄	1	8	yes	—
260	C₂×D₄×C₈₉	—	2	2	no	—
261	C₂×D₄×C₈₉	—	2	2	no	—
262	C₂×D₄×C₈₉	—	4	1	no	—
263	C₂×D₄×C₈₉	—	4	2	no	—
264	C₂×D₄×C₈₉	—	4	2	no	—
265	C₂×D₄×C₈₉	—	4	1	no	—
266	C₂×D₄×C₈₉	—	4	2	no	—
267	C₂×D₄×C₈₉	—	4	2	no	—
268	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
269	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
270	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
271	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
272	C₂²×C₄×C₈₉	—	2	2	no	—
273	C₂²×C₄×C₈₉	—	2	2	no	—
274	C₂²×C₄×C₈₉	—	2	2	no	—
275	C₂²×C₄×C₈₉	—	2	2	no	—
276	C₂²×C₄×C₈₉	—	2	2	no	—
277	C₂²×C₄×C₈₉	—	4	1	no	—
278	C₂²×C₄×C₈₉	—	4	1	no	—
279	C₂²×C₄×C₈₉	—	4	1	no	—
280	C₂²×C₄×C₈₉	—	4	1	no	—
281	C₂²×C₄×C₈₉	—	4	1	no	—
282	C₂²×C₄×C₈₉	—	4	2	no	—
283	C₂²×C₄×C₈₉	—	4	2	no	—
284	C₂²×C₄×C₈₉	—	4	2	no	—
285	C₂²×C₄×C₈₉	—	4	2	no	—
286	C₂²×C₄×C₈₉	—	4	2	no	—
287	C₂²×C₄×C₈₉	—	4	2	no	—
288	C₂²×C₄×C₈₉	—	4	2	no	—
289	C₂²×C₄×C₈₉	—	4	2	no	—
290	C₂²×C₄×C₈₉	—	4	2	no	—
291	C₂²×C₄×C₈₉	—	4	2	no	—
292	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
293	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
294	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
295	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
296	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₈₉	—	2	2	no	—
317	C₄⋊C₄×C₈₉	—	2	2	no	—
318	C₄⋊C₄×C₈₉	—	2	2	no	—
319	C₄⋊C₄×C₈₉	—	2	2	no	—
320	C₄⋊C₄×C₈₉	—	2	2	no	—
321	C₄⋊C₄×C₈₉	—	4	2	no	—
322	C₄⋊C₄×C₈₉	—	4	1	no	—
323	C₄⋊C₄×C₈₉	—	4	2	no	—
324	C₄⋊C₄×C₈₉	—	4	2	no	—
325	C₄⋊C₄×C₈₉	—	4	2	no	—
326	C₄⋊C₄×C₈₉	—	4	1	no	—
327	C₄⋊C₄×C₈₉	—	4	1	no	—
328	C₄⋊C₄×C₈₉	—	4	2	no	—
329	C₄⋊C₄×C₈₉	—	4	2	no	—
330	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
331	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
332	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
333	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	2	no	—
336	C₂²⋊C₄×C₈₉	—	4	1	no	—
337	C₂²⋊C₄×C₈₉	—	4	2	no	—
338	C₂²⋊C₄×C₈₉	—	4	2	no	—
339	C₂²⋊C₄×C₈₉	—	4	2	no	—
340	C₂²⋊C₄×C₈₉	—	4	2	no	—
341	C₂²⋊C₄×C₈₉	—	4	2	no	—
342	C₂²⋊C₄×C₈₉	—	4	1	no	—
343	C₂²⋊C₄×C₈₉	—	4	1	no	—
344	C₂²⋊C₄×C₈₉	—	4	1	no	—
345	C₂²⋊C₄×C₈₉	—	4	1	no	—
346	C₂²⋊C₄×C₈₉	—	4	2	no	—
347	C₂²⋊C₄×C₈₉	—	4	2	no	—
348	C₂²⋊C₄×C₈₉	—	4	2	no	—
349	C₂²⋊C₄×C₈₉	—	4	2	no	—
350	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
352	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
356	C₄²×C₈₉	—	2	2	no	—
357	C₄²×C₈₉	—	2	2	no	—
358	C₄²×C₈₉	—	2	2	no	—
359	C₄²×C₈₉	—	2	2	no	—
360	C₄²×C₈₉	—	4	1	no	—
361	C₄²×C₈₉	—	4	1	no	—
362	C₄²×C₈₉	—	4	2	no	—
363	C₄²×C₈₉	—	4	2	no	—
364	C₄²×C₈₉	—	4	2	no	—
365	C₄²×C₈₉	—	4	2	no	—
366	C₄²×C₈₉	—	4	2	no	—
367	C₄²×C₈₉	—	4	2	no	—
368	C₄²×C₈₉	—	4	2	no	—
369	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
370	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
371	C₂³×C₈₉	—	2	1	no	—
372	C₂³×C₈₉	—	2	1	no	—
373	C₂³×C₈₉	—	2	1	no	—
374	C₂³×C₈₉	—	2	2	no	—
375	C₂³×C₈₉	—	2	2	no	—
376	C₂³×C₈₉	—	2	1	no	—
377	C₂³×C₈₉	—	2	1	no	—
378	C₂³×C₈₉	—	2	2	no	—
379	C₂³×C₈₉	—	2	1	no	—
380	C₂³×C₈₉	—	2	1	no	—
381	C₂³×C₈₉	—	2	1	no	—
382	C₂³×C₈₉	—	2	2	no	—
383	C₂³×C₈₉	—	2	1	no	—
384	C₂³×C₈₉	—	2	2	no	—
385	C₂³×C₈₉	—	2	1	no	—
386	C₂³×C₈₉	—	2	2	no	—
387	C₂³×C₈₉	—	2	1	no	—
388	C₂³×C₈₉	—	2	1	no	—
389	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
390	C₂³×C₈₉	C₂³×C₄	1	4	yes	—
391	C₂³×C₈₉	C₂³×C₄	1	2	yes	—
392	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
393	Q₈×C₈₉	—	2	8	no	—
394	Q₈×C₈₉	—	2	8	no	—
395	Q₈×C₈₉	—	4	8	no	—
396	D₄×C₈₉	—	2	8	no	—
397	D₄×C₈₉	—	4	4	no	—
398	D₄×C₈₉	—	4	8	no	—
399	D₄×C₈₉	—	4	8	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	2	no	—
408	C₂×C₄×C₈₉	—	2	2	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	2	no	—
413	C₂×C₄×C₈₉	—	2	1	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	1	no	—
416	C₂×C₄×C₈₉	—	2	8	no	—
417	C₂×C₄×C₈₉	—	2	8	no	—
418	C₂×C₄×C₈₉	—	2	1	no	—
419	C₂×C₄×C₈₉	—	2	1	no	—
420	C₂×C₄×C₈₉	—	2	1	no	—
421	C₂×C₄×C₈₉	—	2	1	no	—
422	C₂×C₄×C₈₉	—	2	1	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	2	no	—
426	C₂×C₄×C₈₉	—	2	2	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	1	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	1	no	—
432	C₂×C₄×C₈₉	—	2	1	no	—
433	C₂×C₄×C₈₉	—	2	1	no	—
434	C₂×C₄×C₈₉	—	2	2	no	—
435	C₂×C₄×C₈₉	—	2	2	no	—
436	C₂×C₄×C₈₉	—	2	2	no	—
437	C₂×C₄×C₈₉	—	2	2	no	—
438	C₂×C₄×C₈₉	—	2	2	no	—
439	C₂×C₄×C₈₉	—	2	1	no	—
440	C₂×C₄×C₈₉	—	2	1	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	1	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	2	2	no	—
446	C₂×C₄×C₈₉	—	2	1	no	—
447	C₂×C₄×C₈₉	—	2	1	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	1	no	—
450	C₂×C₄×C₈₉	—	2	1	no	—
451	C₂×C₄×C₈₉	—	4	8	no	—
452	C₂×C₄×C₈₉	—	4	8	no	—
453	C₂×C₄×C₈₉	—	4	4	no	—
454	C₂×C₄×C₈₉	—	4	4	no	—
455	C₂×C₄×C₈₉	—	8	4	no	—
456	C₂×C₄×C₈₉	—	8	4	no	—
457	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
459	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
460	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
466	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
467	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
468	C₂²×C₈₉	—	2	2	no	—
469	C₂²×C₈₉	—	2	2	no	—
470	C₂²×C₈₉	—	2	4	no	—
471	C₂²×C₈₉	—	2	2	no	—
472	C₂²×C₈₉	—	2	2	no	—
473	C₂²×C₈₉	—	2	4	no	—
474	C₂²×C₈₉	—	2	2	no	—
475	C₂²×C₈₉	—	2	4	no	—
476	C₂²×C₈₉	—	2	2	no	—
477	C₂²×C₈₉	—	4	1	no	—
478	C₂²×C₈₉	—	4	2	no	—
479	C₂²×C₈₉	—	4	1	no	—
480	C₂²×C₈₉	—	4	1	no	—
481	C₂²×C₈₉	—	4	1	no	—
482	C₂²×C₈₉	—	4	2	no	—
483	C₂²×C₈₉	—	4	1	no	—
484	C₂²×C₈₉	—	4	1	no	—
485	C₂²×C₈₉	—	4	2	no	—
486	C₂²×C₈₉	—	4	2	no	—
487	C₂²×C₈₉	—	4	1	no	—
488	C₂²×C₈₉	—	4	1	no	—
489	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
490	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₈₉	#585	1	1	yes	characteristic
494	C₂²×C₈₉	#585	1	1	yes	characteristic
495	C₂²×C₈₉	#585	1	1	yes	characteristic
496	C₄×C₈₉	—	2	2	no	—
497	C₄×C₈₉	—	2	2	no	—
498	C₄×C₈₉	—	2	4	no	—
499	C₄×C₈₉	—	2	4	no	—
500	C₄×C₈₉	—	2	2	no	—
501	C₄×C₈₉	—	2	4	no	—
502	C₄×C₈₉	—	2	2	no	—
503	C₄×C₈₉	—	2	2	no	—
504	C₄×C₈₉	—	4	1	no	—
505	C₄×C₈₉	—	4	1	no	—
506	C₄×C₈₉	—	4	2	no	—
507	C₄×C₈₉	—	4	1	no	—
508	C₄×C₈₉	—	4	1	no	—
509	C₄×C₈₉	—	4	1	no	—
510	C₄×C₈₉	—	4	1	no	—
511	C₄×C₈₉	—	4	2	no	—
512	C₄×C₈₉	—	4	2	no	—
513	C₄×C₈₉	—	4	2	no	—
514	C₄×C₈₉	—	4	1	no	—
515	C₄×C₈₉	#518	1	4	yes	—
516	#34474	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
517	C₂×C₈₉	—	4	2	no	—
518	C₂×C₈₉	—	4	2	no	—
519	C₂×C₈₉	—	4	4	no	—
520	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
521	C₂×C₈₉	#3428	1	1	yes	characteristic
522	C₂×C₈₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂×C₈₉	#3540	1	1	yes	characteristic
524	C₂×C₈₉	#3541	1	1	yes	characteristic
525	C₂×C₈₉	#3554	1	1	yes	characteristic
526	C₂×C₈₉	#3562	1	1	yes	characteristic
527	C₂×#548	C₂×C₈₉	1	1	yes	characteristic
528	#2379	C₂×C₈₉	1	2	yes	complemented
529	#2377	C₂×C₈₉	1	2	yes	complemented
530	#2368	C₂×C₈₉	1	2	yes	complemented
531	#2367	C₂×C₈₉	1	1	yes	characteristic, complemented
532	#2363	C₂×C₈₉	1	1	yes	characteristic, complemented
533	#2362	C₂×C₈₉	1	1	yes	characteristic, complemented
534	#2357	C₂×C₈₉	1	2	yes	complemented
535	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
536	#2354	C₂×C₈₉	1	1	yes	characteristic, complemented
537	Q₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
538	#2339	C₂×C₈₉	1	1	yes	characteristic, complemented
539	#2337	C₂×C₈₉	1	2	yes	complemented
540	#2333	C₂×C₈₉	1	2	yes	complemented
541	#2332	C₂×C₈₉	1	2	yes	complemented
542	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
543	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
544	#2320	C₂×C₈₉	1	1	yes	characteristic, complemented
545	#2318	C₂×C₈₉	1	2	yes	complemented
546	#2310	C₂×C₈₉	1	1	yes	characteristic, complemented
547	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
548	#2297	C₂×C₈₉	1	1	yes	characteristic, complemented
549	#2290	C₂×C₈₉	1	1	yes	characteristic, complemented
550	C₈₉	#34474	1	1	yes	characteristic, direct product factor, Sylow
551	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
552	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
553	#548	C₄×C₈₉	1	16	yes	complemented
554	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
555	C₂×#124	C₂²×C₈₉	1	2	yes	—
556	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
557	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
558	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
559	C₂×#121	C₂²×C₈₉	1	2	yes	—
560	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
561	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
562	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
566	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
567	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
568	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
569	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
570	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
571	#391	C₂²×C₈₉	1	1	yes	characteristic
572	#391	C₂²×C₈₉	1	1	yes	characteristic
573	#391	C₂²×C₈₉	1	2	yes	—
574	#391	C₂²×C₈₉	1	1	yes	characteristic
575	#391	C₂²×C₈₉	1	1	yes	characteristic
576	#391	C₂²×C₈₉	1	2	yes	—
577	#391	C₂²×C₈₉	1	1	yes	characteristic
578	#391	C₂²×C₈₉	1	2	yes	—
579	#391	C₂²×C₈₉	1	2	yes	—
580	#391	C₂²×C₈₉	1	1	yes	characteristic
581	#390	C₂²×C₈₉	1	1	yes	characteristic
582	#390	C₂²×C₈₉	1	2	yes	—
583	#390	C₂²×C₈₉	1	2	yes	—
584	#390	C₂²×C₈₉	1	2	yes	—
585	#390	C₂²×C₈₉	1	1	yes	characteristic
586	#389	C₂²×C₈₉	1	1	yes	characteristic
587	#389	C₂²×C₈₉	1	1	yes	characteristic
588	#388	C₂²×C₈₉	1	1	yes	characteristic
589	#388	C₂²×C₈₉	1	2	yes	—
590	#388	C₂²×C₈₉	1	2	yes	—
591	#388	C₂²×C₈₉	1	2	yes	—
592	#388	C₂²×C₈₉	1	2	yes	—
593	#388	C₂²×C₈₉	1	2	yes	—
594	#388	C₂²×C₈₉	1	2	yes	—
595	#388	C₂²×C₈₉	1	2	yes	—
596	#388	C₂²×C₈₉	1	2	yes	—
597	#388	C₂²×C₈₉	1	2	yes	—
598	#388	C₂²×C₈₉	1	2	yes	—
599	#388	C₂²×C₈₉	1	1	yes	characteristic
600	#387	C₂²×C₈₉	1	2	yes	—
601	#387	C₂²×C₈₉	1	2	yes	—
602	#387	C₂²×C₈₉	1	2	yes	—
603	#387	C₂²×C₈₉	1	2	yes	—
604	#387	C₂²×C₈₉	1	1	yes	characteristic
605	#387	C₂²×C₈₉	1	2	yes	—
606	#387	C₂²×C₈₉	1	2	yes	—
607	#387	C₂²×C₈₉	1	1	yes	characteristic
608	#386	C₂²×C₈₉	1	2	yes	—
609	#386	C₂²×C₈₉	1	2	yes	—
610	#386	C₂²×C₈₉	1	1	yes	characteristic
611	#386	C₂²×C₈₉	1	2	yes	—
612	#386	C₂²×C₈₉	1	2	yes	—
613	#386	C₂²×C₈₉	1	2	yes	—
614	#386	C₂²×C₈₉	1	1	yes	characteristic
615	#386	C₂²×C₈₉	1	2	yes	—
616	#385	C₂²×C₈₉	1	2	yes	—
617	#385	C₂²×C₈₉	1	2	yes	—
618	#385	C₂²×C₈₉	1	2	yes	—
619	#385	C₂²×C₈₉	1	2	yes	—
620	#385	C₂²×C₈₉	1	1	yes	characteristic
621	#385	C₂²×C₈₉	1	2	yes	—
622	#385	C₂²×C₈₉	1	1	yes	characteristic
623	#384	C₂²×C₈₉	1	1	yes	characteristic
624	#383	C₂²×C₈₉	1	2	yes	—
625	#382	C₂²×C₈₉	1	2	yes	—
626	#382	C₂²×C₈₉	1	2	yes	—
627	#381	C₂²×C₈₉	1	2	yes	—
628	#381	C₂²×C₈₉	1	2	yes	—
629	#381	C₂²×C₈₉	1	2	yes	—
630	#380	C₂²×C₈₉	1	2	yes	—
631	#380	C₂²×C₈₉	1	1	yes	characteristic
632	#380	C₂²×C₈₉	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
636	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
637	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
638	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
640	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
641	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
642	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
643	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
646	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
648	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
649	#376	C₂²×C₈₉	1	1	yes	characteristic
650	C₂×#95	C₂²×C₈₉	1	2	yes	—
651	C₂×#41	—	4	2	no	—
652	C₂×#41	—	4	2	no	—
653	C₂×#41	C₂×C₄×C₈₉	1	8	yes	—
654	C₂²×Q₈	—	4	2	no	—
655	C₂²×Q₈	—	4	2	no	—
656	C₂²×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
657	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
658	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
659	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
660	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
661	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
662	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
664	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
666	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
668	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
669	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
671	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
672	#124	C₂×C₄×C₈₉	1	8	yes	complemented
673	#124	C₂×C₄×C₈₉	1	16	yes	complemented
674	C₂²⋊Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
675	C₂²⋊Q₈	C₂×C₄×C₈₉	1	16	yes	complemented
676	#121	C₂×C₄×C₈₉	1	8	yes	complemented
677	#121	C₂×C₄×C₈₉	1	16	yes	complemented
678	C₄×Q₈	—	4	2	no	—
679	C₄×Q₈	—	4	2	no	—
680	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
681	C₄×D₄	—	4	2	no	—
682	C₄×D₄	—	4	2	no	—
683	C₄×D₄	C₂×C₄×C₈₉	1	8	yes	complemented
684	C₄×D₄	C₂×C₄×C₈₉	1	16	yes	complemented
685	#117	—	4	2	no	—
686	#117	—	4	2	no	—
687	#117	—	4	2	no	—
688	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
728	C₂×C₄²	—	4	2	no	—
729	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
734	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
735	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
736	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
737	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
738	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
741	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
742	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
744	#95	C₂³×C₈₉	1	1	yes	characteristic
745	#95	C₂³×C₈₉	1	2	yes	—
746	#95	C₂³×C₈₉	1	2	yes	—
747	#95	C₂³×C₈₉	1	2	yes	—
748	#95	C₂³×C₈₉	1	1	yes	characteristic
749	#95	C₂³×C₈₉	1	1	yes	characteristic
750	#95	C₂³×C₈₉	1	1	yes	characteristic
751	#95	C₂³×C₈₉	1	1	yes	characteristic
752	#95	C₂³×C₈₉	1	1	yes	characteristic
753	#95	C₂³×C₈₉	1	1	yes	characteristic
754	#95	C₂³×C₈₉	1	2	yes	—
755	#95	C₂³×C₈₉	1	1	yes	characteristic
756	#95	C₂³×C₈₉	1	2	yes	—
757	#95	C₂³×C₈₉	1	2	yes	—
758	#95	C₂³×C₈₉	1	2	yes	—
759	#95	C₂³×C₈₉	1	2	yes	—
760	#95	C₂³×C₈₉	1	2	yes	—
761	#95	C₂³×C₈₉	1	2	yes	—
762	#95	C₂³×C₈₉	1	2	yes	—
763	#95	C₂³×C₈₉	1	2	yes	—
764	#95	C₂³×C₈₉	1	1	yes	characteristic
765	#95	C₂³×C₈₉	1	2	yes	—
766	#95	C₂³×C₈₉	1	2	yes	—
767	#95	C₂³×C₈₉	1	2	yes	—
768	#95	C₂³×C₈₉	1	2	yes	—
769	#95	C₂³×C₈₉	1	2	yes	—
770	#95	C₂³×C₈₉	1	2	yes	—
771	#95	C₂³×C₈₉	1	2	yes	—
772	#95	C₂³×C₈₉	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
775	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
776	#41	—	4	16	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	—	4	2	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	16	no	—
784	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
785	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
786	C₂×Q₈	C₂²×C₄×C₈₉	1	8	yes	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	1	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	2	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	C₂²×C₄×C₈₉	1	4	yes	—
796	C₂×D₄	C₂²×C₄×C₈₉	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
798	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
820	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
821	C₂²×C₄	C₂²×C₄×C₈₉	1	8	yes	—
822	C₂²×C₄	C₂²×C₄×C₈₉	1	8	yes	—
823	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	4	1	no	—
849	C₄⋊C₄	—	4	1	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	1	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
858	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
859	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
860	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	4	1	no	—
864	C₂²⋊C₄	—	4	1	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	1	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	1	no	—
876	C₂²⋊C₄	—	4	1	no	—
877	C₂²⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	4	1	no	—
888	C₄²	—	4	1	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
897	C₄²	C₂²×C₄×C₈₉	1	4	yes	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
917	C₂³	C₂³×C₄×C₈₉	1	4	yes	—
918	C₂³	C₂³×C₄×C₈₉	1	2	yes	—
919	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
920	Q₈	—	2	8	no	—
921	Q₈	—	2	8	no	—
922	Q₈	—	4	8	no	—
923	D₄	—	2	8	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	8	no	—
926	D₄	—	4	8	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	8	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	8	4	no	—
983	C₂×C₄	—	8	4	no	—
984	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
986	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
989	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
990	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
991	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
992	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
993	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
994	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	4	1	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
1017	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1018	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1019	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1020	C₂²	#585×C₈₉	1	1	yes	characteristic
1021	C₂²	#585×C₈₉	1	1	yes	characteristic
1022	C₂²	#585×C₈₉	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	#518×C₈₉	1	4	yes	—
1043	C₂	—	4	2	no	—
1044	C₂	—	4	2	no	—
1045	C₂	—	4	4	no	—
1046	C₂	C₂×#518×C₈₉	1	1	yes	characteristic
1047	C₂	C₈₉×#3428	1	1	yes	characteristic
1048	C₂	C₄×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1049	C₂	C₈₉×#3540	1	1	yes	characteristic
1050	C₂	C₈₉×#3541	1	1	yes	characteristic
1051	C₂	C₈₉×#3554	1	1	yes	characteristic
1052	C₂	C₈₉×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#548×C₈₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2379	C₂	semidirect
3. C₈₉×#2377	C₂	semidirect
4. C₈₉×#2368	C₂	semidirect
5. C₈₉×#2367	C₂	semidirect
6. C₈₉×#2363	C₂	semidirect
7. C₈₉×#2362	C₂	semidirect
8. C₈₉×#2357	C₂	semidirect
9. C₈₉×#2355	C₂	semidirect
10. C₈₉×#2354	C₂	semidirect
11. Q₈×C₂²⋊C₄×C₈₉	C₂	semidirect
12. C₈₉×#2339	C₂	semidirect
13. C₈₉×#2337	C₂	semidirect
14. C₈₉×#2333	C₂	semidirect
15. C₈₉×#2332	C₂	semidirect
16. C₈₉×#2326	C₂	semidirect
17. C₈₉×#2324	C₂	semidirect
18. C₈₉×#2320	C₂	semidirect
19. C₈₉×#2318	C₂	semidirect
20. C₈₉×#2310	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
22. C₈₉×#2297	C₂	semidirect
23. C₈₉×#2290	C₂	semidirect
26. #548×C₈₉	C₄	semidirect
129. C₂²×Q₈×C₈₉	C₂×C₄	semidirect
145. #124×C₈₉	C₂×C₄	semidirect
146. #124×C₈₉	C₂×C₄	semidirect
147. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
148. C₂²⋊Q₈×C₈₉	C₂×C₄	semidirect
149. #121×C₈₉	C₂×C₄	semidirect
150. #121×C₈₉	C₂×C₄	semidirect
153. C₄×Q₈×C₈₉	C₂×C₄	semidirect
156. C₄×D₄×C₈₉	C₂×C₄	semidirect
157. C₄×D₄×C₈₉	C₂×C₄	semidirect
516. #34474	C₈₉	direct (N × H)
528. #2379	C₂×C₈₉	semidirect
529. #2377	C₂×C₈₉	semidirect
530. #2368	C₂×C₈₉	semidirect
531. #2367	C₂×C₈₉	semidirect
532. #2363	C₂×C₈₉	semidirect
533. #2362	C₂×C₈₉	semidirect
534. #2357	C₂×C₈₉	semidirect
535. #2355	C₂×C₈₉	semidirect
536. #2354	C₂×C₈₉	semidirect
537. Q₈×C₂²⋊C₄	C₂×C₈₉	semidirect
538. #2339	C₂×C₈₉	semidirect
539. #2337	C₂×C₈₉	semidirect
540. #2333	C₂×C₈₉	semidirect
541. #2332	C₂×C₈₉	semidirect
542. #2326	C₂×C₈₉	semidirect
543. #2324	C₂×C₈₉	semidirect
544. #2320	C₂×C₈₉	semidirect
545. #2318	C₂×C₈₉	semidirect
546. #2310	C₂×C₈₉	semidirect
547. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
548. #2297	C₂×C₈₉	semidirect
549. #2290	C₂×C₈₉	semidirect
550. C₈₉	#34474	direct (N × H)
553. #548	C₄×C₈₉	semidirect
656. C₂²×Q₈	C₂×C₄×C₈₉	semidirect
672. #124	C₂×C₄×C₈₉	semidirect
673. #124	C₂×C₄×C₈₉	semidirect
674. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
675. C₂²⋊Q₈	C₂×C₄×C₈₉	semidirect
676. #121	C₂×C₄×C₈₉	semidirect
677. #121	C₂×C₄×C₈₉	semidirect
680. C₄×Q₈	C₂×C₄×C₈₉	semidirect
683. C₄×D₄	C₂×C₄×C₈₉	semidirect
684. C₄×D₄	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₈₉	2
C₈₉×#2379	2
C₈₉×#2377	2
C₈₉×#2368	2
C₈₉×#2367	2
C₈₉×#2363	2
C₈₉×#2362	2
C₈₉×#2357	2
C₈₉×#2355	2
C₈₉×#2354	2
Q₈×C₂²⋊C₄×C₈₉	2
C₈₉×#2339	2
C₈₉×#2337	2
C₈₉×#2333	2
C₈₉×#2332	2
C₈₉×#2326	2
C₈₉×#2324	2
C₈₉×#2320	2
C₈₉×#2318	2
C₈₉×#2310	2
C₄×C₂²⋊Q₈×C₈₉	2
C₈₉×#2297	2
C₈₉×#2290	2
#34474	89

Subgroups — C89×#34474 #36412322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#34474 #36412322