Subgroups — C₈₉×#35507 #36413355

Order 22784.

1558 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2611	C₂	1	2	yes	maximal
2	C₈₉×#2607	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2605	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2599	C₂	1	2	yes	maximal
5	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2583	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2575	C₂	1	2	yes	maximal
9	C₈₉×#2565	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2528	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2528	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2527	C₂	1	2	yes	maximal
13	C₈₉×#2499	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2484	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2336	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2332	C₂	1	1	yes	maximal, characteristic
17	C₈₉×#2298	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2295	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₈₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	#401×C₈₉	C₂²	1	2	yes	—
27	#400×C₈₉	C₂²	1	2	yes	—
28	#400×C₈₉	C₂²	1	2	yes	—
29	#400×C₈₉	C₂²	1	2	yes	—
30	#400×C₈₉	C₂²	1	2	yes	—
31	#400×C₈₉	C₂²	1	2	yes	—
32	#399×C₈₉	C₂²	1	2	yes	—
33	#398×C₈₉	C₂²	1	2	yes	—
34	#398×C₈₉	C₂²	1	2	yes	—
35	#398×C₈₉	C₂²	1	2	yes	—
36	#398×C₈₉	C₂²	1	2	yes	—
37	#397×C₈₉	C₂²	1	2	yes	—
38	#397×C₈₉	C₂²	1	2	yes	—
39	#395×C₈₉	C₂²	1	2	yes	—
40	#395×C₈₉	C₂²	1	2	yes	—
41	#393×C₈₉	C₂²	1	2	yes	—
42	#391×C₈₉	C₂²	1	2	yes	—
43	#391×C₈₉	C₂²	1	2	yes	—
44	#391×C₈₉	C₂²	1	2	yes	—
45	#391×C₈₉	C₂²	1	2	yes	—
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	1	yes	characteristic
48	#391×C₈₉	C₂²	1	1	yes	characteristic
49	#389×C₈₉	C₂²	1	2	yes	—
50	#389×C₈₉	C₂²	1	2	yes	—
51	#389×C₈₉	C₂²	1	2	yes	—
52	#389×C₈₉	C₂²	1	2	yes	—
53	#388×C₈₉	C₂²	1	2	yes	—
54	#388×C₈₉	C₂²	1	2	yes	—
55	#388×C₈₉	C₂²	1	2	yes	—
56	#388×C₈₉	C₂²	1	2	yes	—
57	#387×C₈₉	C₂²	1	2	yes	—
58	#387×C₈₉	C₂²	1	2	yes	—
59	#387×C₈₉	C₂²	1	2	yes	—
60	#387×C₈₉	C₂²	1	2	yes	—
61	#387×C₈₉	C₂²	1	2	yes	—
62	#387×C₈₉	C₂²	1	2	yes	—
63	#387×C₈₉	C₂²	1	2	yes	—
64	#387×C₈₉	C₂²	1	2	yes	—
65	#387×C₈₉	C₂²	1	2	yes	—
66	#387×C₈₉	C₂²	1	2	yes	—
67	#387×C₈₉	C₂²	1	2	yes	—
68	#387×C₈₉	C₂²	1	2	yes	—
69	#387×C₈₉	C₂²	1	2	yes	—
70	#387×C₈₉	C₂²	1	2	yes	—
71	#387×C₈₉	C₂²	1	2	yes	—
72	#387×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#385×C₈₉	C₂²	1	2	yes	—
81	#385×C₈₉	C₂²	1	2	yes	—
82	#385×C₈₉	C₂²	1	1	yes	characteristic
83	#385×C₈₉	C₂²	1	1	yes	characteristic
84	#384×C₈₉	C₂²	1	1	yes	characteristic
85	#383×C₈₉	C₂²	1	2	yes	—
86	#382×C₈₉	C₂²	1	2	yes	—
87	#382×C₈₉	C₂²	1	1	yes	characteristic
88	#381×C₈₉	C₂²	1	1	yes	characteristic
89	#381×C₈₉	C₂²	1	1	yes	characteristic
90	#381×C₈₉	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
103	#376×C₈₉	C₂²	1	2	yes	—
104	#376×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	1	yes	characteristic
106	C₄³×C₈₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	#125×C₈₉	—	2	8	no	—
113	C₂²⋊Q₈×C₈₉	—	2	4	no	—
114	C₄×Q₈×C₈₉	—	2	8	no	—
115	#117×C₈₉	—	2	4	no	—
116	#117×C₈₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	2	yes	—
169	#95×C₈₉	C₂³	1	2	yes	—
170	#95×C₈₉	C₂³	1	2	yes	—
171	#95×C₈₉	C₂³	1	2	yes	—
172	#95×C₈₉	C₂³	1	2	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
174	#95×C₈₉	C₂³	1	2	yes	—
175	#95×C₈₉	C₂³	1	2	yes	—
176	#95×C₈₉	C₂³	1	2	yes	—
177	#95×C₈₉	C₂³	1	2	yes	—
178	#95×C₈₉	C₂³	1	2	yes	—
179	#95×C₈₉	C₂³	1	2	yes	—
180	#95×C₈₉	C₂³	1	2	yes	—
181	#95×C₈₉	C₂³	1	2	yes	—
182	#95×C₈₉	C₂³	1	2	yes	—
183	#95×C₈₉	C₂³	1	2	yes	—
184	#95×C₈₉	C₂³	1	2	yes	—
185	#95×C₈₉	C₂³	1	2	yes	—
186	#95×C₈₉	C₂³	1	2	yes	—
187	#95×C₈₉	C₂³	1	2	yes	—
188	#95×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₈₉	—	2	4	no	—
202	C₂×Q₈×C₈₉	—	2	2	no	—
203	C₂×Q₈×C₈₉	—	2	4	no	—
204	C₂×Q₈×C₈₉	—	4	2	no	—
205	C₂×Q₈×C₈₉	—	4	1	no	—
206	C₂×Q₈×C₈₉	—	4	1	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	4	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	4	1	no	—
211	C₂²×C₄×C₈₉	—	4	1	no	—
212	C₂²×C₄×C₈₉	—	4	1	no	—
213	C₂²×C₄×C₈₉	—	4	1	no	—
214	C₂²×C₄×C₈₉	#41	1	4	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	no	—
235	C₄⋊C₄×C₈₉	—	2	4	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	2	no	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	4	2	no	—
253	C₄⋊C₄×C₈₉	—	4	2	no	—
254	C₄⋊C₄×C₈₉	—	4	2	no	—
255	C₄⋊C₄×C₈₉	—	4	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	2	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	4	1	no	—
263	C₂²⋊C₄×C₈₉	—	4	1	no	—
264	C₄²×C₈₉	—	2	2	no	—
265	C₄²×C₈₉	—	2	2	no	—
266	C₄²×C₈₉	—	2	4	no	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	—	4	1	no	—
271	C₄²×C₈₉	—	4	2	no	—
272	C₄²×C₈₉	—	4	2	no	—
273	C₄²×C₈₉	—	4	1	no	—
274	C₄²×C₈₉	—	4	1	no	—
275	C₄²×C₈₉	—	4	1	no	—
276	C₄²×C₈₉	—	4	1	no	—
277	C₄²×C₈₉	—	4	2	no	—
278	C₄²×C₈₉	—	4	1	no	—
279	C₄²×C₈₉	#41	1	8	yes	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	1	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	C₂×#41	1	2	yes	—
285	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
286	Q₈×C₈₉	—	4	8	no	—
287	Q₈×C₈₉	—	8	2	no	—
288	C₂×C₄×C₈₉	—	2	8	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	1	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	4	4	no	—
334	C₂×C₄×C₈₉	—	8	2	no	—
335	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
336	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
338	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
339	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
341	C₂²×C₈₉	—	2	2	no	—
342	C₂²×C₈₉	—	2	2	no	—
343	C₂²×C₈₉	—	2	2	no	—
344	C₂²×C₈₉	—	4	2	no	—
345	C₂²×C₈₉	—	4	2	no	—
346	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₈₉	C₂²×#41	1	2	yes	—
348	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₈₉	#585	1	1	yes	characteristic
350	C₂²×C₈₉	#585	1	1	yes	characteristic
351	C₄×C₈₉	—	2	4	no	—
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	2	2	no	—
354	C₄×C₈₉	—	2	4	no	—
355	C₄×C₈₉	—	2	4	no	—
356	C₄×C₈₉	—	2	4	no	—
357	C₄×C₈₉	—	4	1	no	—
358	C₄×C₈₉	—	4	1	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	2	no	—
361	C₄×C₈₉	—	4	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	1	no	—
368	C₄×C₈₉	—	4	1	no	—
369	#35507	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂×C₈₉	—	4	2	no	—
371	C₂×C₈₉	#3444	1	1	yes	characteristic
372	C₂×C₈₉	#3491	1	1	yes	characteristic
373	C₂×C₈₉	#3495	1	2	yes	—
374	C₂×C₈₉	#3507	1	2	yes	—
375	C₂×C₈₉	#3509	1	1	yes	characteristic
376	#2611	C₂×C₈₉	1	2	yes	—
377	#2607	C₂×C₈₉	1	1	yes	characteristic
378	#2605	C₂×C₈₉	1	2	yes	complemented
379	#2599	C₂×C₈₉	1	2	yes	—
380	#2588	C₂×C₈₉	1	2	yes	complemented
381	#2588	C₂×C₈₉	1	2	yes	complemented
382	#2583	C₂×C₈₉	1	1	yes	characteristic
383	#2575	C₂×C₈₉	1	2	yes	—
384	#2565	C₂×C₈₉	1	2	yes	complemented
385	#2528	C₂×C₈₉	1	2	yes	complemented
386	#2528	C₂×C₈₉	1	2	yes	complemented
387	#2527	C₂×C₈₉	1	2	yes	—
388	#2499	C₂×C₈₉	1	1	yes	characteristic
389	#2484	C₂×C₈₉	1	1	yes	characteristic
390	#2336	C₂×C₈₉	1	2	yes	complemented
391	#2332	C₂×C₈₉	1	1	yes	characteristic
392	#2298	C₂×C₈₉	1	1	yes	characteristic
393	#2295	C₂×C₈₉	1	2	yes	complemented
394	#2274	C₂×C₈₉	1	1	yes	characteristic
395	C₈₉	#35507	1	1	yes	characteristic, direct product factor, Sylow
396	C₂×#125	C₂²×C₈₉	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
399	C₂×#117	C₂²×C₈₉	1	2	yes	—
400	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
402	#401	C₂²×C₈₉	1	2	yes	—
403	#400	C₂²×C₈₉	1	2	yes	—
404	#400	C₂²×C₈₉	1	2	yes	—
405	#400	C₂²×C₈₉	1	2	yes	—
406	#400	C₂²×C₈₉	1	2	yes	—
407	#400	C₂²×C₈₉	1	2	yes	—
408	#399	C₂²×C₈₉	1	2	yes	—
409	#398	C₂²×C₈₉	1	2	yes	—
410	#398	C₂²×C₈₉	1	2	yes	—
411	#398	C₂²×C₈₉	1	2	yes	—
412	#398	C₂²×C₈₉	1	2	yes	—
413	#397	C₂²×C₈₉	1	2	yes	—
414	#397	C₂²×C₈₉	1	2	yes	—
415	#395	C₂²×C₈₉	1	2	yes	—
416	#395	C₂²×C₈₉	1	2	yes	—
417	#393	C₂²×C₈₉	1	2	yes	—
418	#391	C₂²×C₈₉	1	2	yes	—
419	#391	C₂²×C₈₉	1	2	yes	—
420	#391	C₂²×C₈₉	1	2	yes	—
421	#391	C₂²×C₈₉	1	1	yes	characteristic
422	#391	C₂²×C₈₉	1	2	yes	—
423	#391	C₂²×C₈₉	1	1	yes	characteristic
424	#391	C₂²×C₈₉	1	2	yes	—
425	#389	C₂²×C₈₉	1	2	yes	—
426	#389	C₂²×C₈₉	1	2	yes	—
427	#389	C₂²×C₈₉	1	2	yes	—
428	#389	C₂²×C₈₉	1	2	yes	—
429	#388	C₂²×C₈₉	1	2	yes	—
430	#388	C₂²×C₈₉	1	2	yes	—
431	#388	C₂²×C₈₉	1	2	yes	—
432	#388	C₂²×C₈₉	1	2	yes	—
433	#387	C₂²×C₈₉	1	2	yes	—
434	#387	C₂²×C₈₉	1	2	yes	—
435	#387	C₂²×C₈₉	1	2	yes	—
436	#387	C₂²×C₈₉	1	2	yes	—
437	#387	C₂²×C₈₉	1	2	yes	—
438	#387	C₂²×C₈₉	1	2	yes	—
439	#387	C₂²×C₈₉	1	2	yes	—
440	#387	C₂²×C₈₉	1	2	yes	—
441	#387	C₂²×C₈₉	1	2	yes	—
442	#387	C₂²×C₈₉	1	2	yes	—
443	#387	C₂²×C₈₉	1	2	yes	—
444	#387	C₂²×C₈₉	1	2	yes	—
445	#387	C₂²×C₈₉	1	2	yes	—
446	#387	C₂²×C₈₉	1	2	yes	—
447	#387	C₂²×C₈₉	1	2	yes	—
448	#387	C₂²×C₈₉	1	2	yes	—
449	#387	C₂²×C₈₉	1	2	yes	—
450	#387	C₂²×C₈₉	1	2	yes	—
451	#387	C₂²×C₈₉	1	2	yes	—
452	#387	C₂²×C₈₉	1	2	yes	—
453	#387	C₂²×C₈₉	1	2	yes	—
454	#387	C₂²×C₈₉	1	2	yes	—
455	#387	C₂²×C₈₉	1	2	yes	—
456	#385	C₂²×C₈₉	1	2	yes	—
457	#385	C₂²×C₈₉	1	2	yes	—
458	#385	C₂²×C₈₉	1	1	yes	characteristic
459	#385	C₂²×C₈₉	1	1	yes	characteristic
460	#384	C₂²×C₈₉	1	1	yes	characteristic
461	#383	C₂²×C₈₉	1	2	yes	—
462	#382	C₂²×C₈₉	1	2	yes	—
463	#382	C₂²×C₈₉	1	1	yes	characteristic
464	#381	C₂²×C₈₉	1	1	yes	characteristic
465	#381	C₂²×C₈₉	1	1	yes	characteristic
466	#381	C₂²×C₈₉	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
479	#376	C₂²×C₈₉	1	2	yes	—
480	#376	C₂²×C₈₉	1	2	yes	—
481	#376	C₂²×C₈₉	1	1	yes	characteristic
482	C₄³	C₂²×C₈₉	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
484	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
488	#125	—	2	8	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₄×Q₈	—	2	8	no	—
491	#117	—	2	4	no	—
492	#117	—	2	8	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
537	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
539	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
541	#95	C₂³×C₈₉	1	2	yes	—
542	#95	C₂³×C₈₉	1	2	yes	—
543	#95	C₂³×C₈₉	1	2	yes	—
544	#95	C₂³×C₈₉	1	2	yes	—
545	#95	C₂³×C₈₉	1	2	yes	—
546	#95	C₂³×C₈₉	1	2	yes	—
547	#95	C₂³×C₈₉	1	2	yes	—
548	#95	C₂³×C₈₉	1	2	yes	—
549	#95	C₂³×C₈₉	1	2	yes	—
550	#95	C₂³×C₈₉	1	2	yes	—
551	#95	C₂³×C₈₉	1	2	yes	—
552	#95	C₂³×C₈₉	1	2	yes	—
553	#95	C₂³×C₈₉	1	2	yes	—
554	#95	C₂³×C₈₉	1	2	yes	—
555	#95	C₂³×C₈₉	1	2	yes	—
556	#95	C₂³×C₈₉	1	2	yes	—
557	#95	C₂³×C₈₉	1	2	yes	—
558	#95	C₂³×C₈₉	1	2	yes	—
559	#95	C₂³×C₈₉	1	2	yes	—
560	#95	C₂³×C₈₉	1	2	yes	—
561	#95	C₂³×C₈₉	1	2	yes	—
562	#95	C₂³×C₈₉	1	2	yes	—
563	#95	C₂³×C₈₉	1	2	yes	—
564	#95	C₂³×C₈₉	1	2	yes	—
565	#95	C₂³×C₈₉	1	2	yes	—
566	#95	C₂³×C₈₉	1	2	yes	—
567	#95	C₂³×C₈₉	1	2	yes	—
568	#95	C₂³×C₈₉	1	2	yes	—
569	#95	C₂³×C₈₉	1	2	yes	—
570	#95	C₂³×C₈₉	1	2	yes	—
571	#95	C₂³×C₈₉	1	2	yes	—
572	#95	C₂³×C₈₉	1	2	yes	—
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	2	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	4	2	no	—
581	C₂×Q₈	—	4	1	no	—
582	C₂×Q₈	—	4	1	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	#41×C₈₉	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	4	1	no	—
639	C₂²⋊C₄	—	4	1	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	1	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	2	no	—
649	C₄²	—	4	1	no	—
650	C₄²	—	4	1	no	—
651	C₄²	—	4	1	no	—
652	C₄²	—	4	1	no	—
653	C₄²	—	4	2	no	—
654	C₄²	—	4	1	no	—
655	C₄²	#41×C₈₉	1	8	yes	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	C₂×#41×C₈₉	1	2	yes	—
661	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
662	Q₈	—	4	8	no	—
663	Q₈	—	8	2	no	—
664	C₂×C₄	—	2	8	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	8	2	no	—
711	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
712	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
713	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
714	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
715	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
716	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
723	C₂²	C₂²×#41×C₈₉	1	2	yes	—
724	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
725	C₂²	#585×C₈₉	1	1	yes	characteristic
726	C₂²	#585×C₈₉	1	1	yes	characteristic
727	C₄	—	2	4	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₈₉×#3444	1	1	yes	characteristic
747	C₂	C₈₉×#3491	1	1	yes	characteristic
748	C₂	C₈₉×#3495	1	2	yes	—
749	C₂	C₈₉×#3507	1	2	yes	—
750	C₂	C₈₉×#3509	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₈₉×#2605	C₂	semidirect
5. C₈₉×#2588	C₂	semidirect
6. C₈₉×#2588	C₂	semidirect
9. C₈₉×#2565	C₂	semidirect
10. C₈₉×#2528	C₂	semidirect
11. C₈₉×#2528	C₂	semidirect
15. C₈₉×#2336	C₂	semidirect
18. C₈₉×#2295	C₂	semidirect
369. #35507	C₈₉	direct (N × H)
378. #2605	C₂×C₈₉	semidirect
380. #2588	C₂×C₈₉	semidirect
381. #2588	C₂×C₈₉	semidirect
384. #2565	C₂×C₈₉	semidirect
385. #2528	C₂×C₈₉	semidirect
386. #2528	C₂×C₈₉	semidirect
390. #2336	C₂×C₈₉	semidirect
393. #2295	C₂×C₈₉	semidirect
395. C₈₉	#35507	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×#2611	2
C₈₉×#2607	2
C₈₉×#2605	2
C₈₉×#2599	2
C₈₉×#2588	2
C₈₉×#2583	2
C₈₉×#2575	2
C₈₉×#2565	2
C₈₉×#2528	2
C₈₉×#2527	2
C₈₉×#2499	2
C₈₉×#2484	2
C₈₉×#2336	2
C₈₉×#2332	2
C₈₉×#2298	2
C₈₉×#2295	2
C₈₉×#2274	2
#35507	89

Subgroups — C89×#35507 #36413355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35507 #36413355