Subgroups — C₈₉×#18725 #36396573

Order 22784.

876 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3550	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1645	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1640	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1543	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
10	#563×C₈₉	—	2	2	no	—
11	#559×C₈₉	C₂²	1	2	yes	—
12	Q₈²×C₈₉	C₂²	1	2	yes	—
13	#556×C₈₉	—	2	1	no	—
14	#556×C₈₉	—	2	1	no	—
15	D₄×Q₈×C₈₉	—	2	1	no	—
16	D₄×Q₈×C₈₉	—	2	1	no	—
17	#542×C₈₉	—	2	2	no	—
18	#542×C₈₉	—	2	2	no	—
19	#536×C₈₉	—	2	2	no	—
20	#533×C₈₉	C₂²	1	1	yes	characteristic
21	#533×C₈₉	C₂²	1	1	yes	characteristic
22	#532×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	#498×C₈₉	—	2	1	no	—
25	#494×C₈₉	—	2	1	no	—
26	#489×C₈₉	—	2	2	no	—
27	#487×C₈₉	—	2	1	no	—
28	#487×C₈₉	—	2	1	no	—
29	#487×C₈₉	C₂²	1	2	yes	—
30	#486×C₈₉	C₂²	1	2	yes	—
31	#483×C₈₉	—	2	2	no	—
32	#475×C₈₉	C₂²	1	4	yes	—
33	#462×C₈₉	C₂²	1	4	yes	—
34	#451×C₈₉	—	2	2	no	—
35	#431×C₈₉	C₂²	1	1	yes	characteristic
36	#431×C₈₉	C₂²	1	1	yes	characteristic
37	#417×C₈₉	—	2	2	no	—
38	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	#333×C₈₉	C₂²	1	2	yes	—
40	#331×C₈₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₈₉	C₂²	1	4	yes	—
42	Q₈⋊C₈×C₈₉	C₂²	1	4	yes	—
43	C₂×#41×C₈₉	D₄	1	2	yes	—
44	C₂²×Q₈×C₈₉	—	2	2	no	—
45	C₂²×Q₈×C₈₉	—	2	1	no	—
46	C₂×Q₁₆×C₈₉	—	2	4	no	—
47	C₂×M₁₆×C₈₉	—	2	1	no	—
48	C₄⋊Q₈×C₈₉	—	2	4	no	—
49	C₄⋊Q₈×C₈₉	—	2	2	no	—
50	C₄⋊Q₈×C₈₉	—	2	2	no	—
51	C₄⋊Q₈×C₈₉	—	2	1	no	—
52	C₄⋊Q₈×C₈₉	—	2	1	no	—
53	C₄⋊Q₈×C₈₉	—	2	1	no	—
54	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	#127×C₈₉	C₂³	1	1	yes	characteristic
61	#126×C₈₉	—	2	4	no	—
62	#126×C₈₉	—	2	4	no	—
63	#125×C₈₉	—	2	1	no	—
64	#125×C₈₉	—	2	1	no	—
65	#124×C₈₉	—	2	4	no	—
66	#124×C₈₉	—	2	2	no	—
67	#124×C₈₉	—	2	2	no	—
68	#124×C₈₉	D₄	1	2	yes	—
69	#123×C₈₉	—	2	4	no	—
70	#123×C₈₉	—	2	4	no	—
71	C₂²⋊Q₈×C₈₉	—	2	2	no	—
72	C₂²⋊Q₈×C₈₉	—	2	2	no	—
73	C₂²⋊Q₈×C₈₉	—	2	4	no	—
74	C₂²⋊Q₈×C₈₉	—	2	4	no	—
75	C₂²⋊Q₈×C₈₉	—	2	1	no	—
76	C₂²⋊Q₈×C₈₉	—	2	1	no	—
77	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
78	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
79	#121×C₈₉	—	2	1	no	—
80	#121×C₈₉	—	2	1	no	—
81	C₄×Q₈×C₈₉	—	2	2	no	—
82	C₄×Q₈×C₈₉	—	2	2	no	—
83	C₄×Q₈×C₈₉	—	2	1	no	—
84	C₄×Q₈×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
86	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
87	C₄×D₄×C₈₉	—	2	2	no	—
88	C₄×D₄×C₈₉	—	2	2	no	—
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	—	2	1	no	—
91	#117×C₈₉	—	2	2	no	—
92	#117×C₈₉	—	2	1	no	—
93	#117×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	4	no	—
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	#103×C₈₉	—	2	4	no	—
101	#103×C₈₉	—	2	4	no	—
102	#103×C₈₉	—	2	4	no	—
103	#102×C₈₉	—	2	4	no	—
104	C₂²⋊C₈×C₈₉	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	#41×C₈₉	—	4	4	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×Q₈×C₈₉	—	2	1	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	2	2	no	—
115	C₂×Q₈×C₈₉	—	4	1	no	—
116	C₂×Q₈×C₈₉	—	8	2	no	—
117	C₂×Q₈×C₈₉	—	8	4	no	—
118	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₈₉	—	2	2	no	—
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₈₉	—	2	4	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	4	1	no	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	Q₁₆×C₈₉	—	8	4	no	—
132	M₁₆×C₈₉	—	4	2	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	4	no	—
137	C₄⋊C₄×C₈₉	—	2	4	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	—	2	2	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	2	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	4	1	no	—
153	C₄⋊C₄×C₈₉	—	4	1	no	—
154	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₈₉	—	2	4	no	—
157	C₂²⋊C₄×C₈₉	—	2	4	no	—
158	C₂²⋊C₄×C₈₉	—	2	4	no	—
159	C₂²⋊C₄×C₈₉	—	2	2	no	—
160	C₂²⋊C₄×C₈₉	—	2	2	no	—
161	C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₂²⋊C₄×C₈₉	—	2	2	no	—
163	C₄²×C₈₉	—	2	4	no	—
164	C₄²×C₈₉	—	2	2	no	—
165	C₄²×C₈₉	—	2	2	no	—
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	#120	1	1	yes	characteristic
172	Q₈×C₈₉	—	2	4	no	—
173	Q₈×C₈₉	—	2	4	no	—
174	Q₈×C₈₉	—	4	2	no	—
175	Q₈×C₈₉	—	4	2	no	—
176	Q₈×C₈₉	—	4	2	no	—
177	Q₈×C₈₉	—	4	4	no	—
178	Q₈×C₈₉	—	8	2	no	—
179	Q₈×C₈₉	—	8	4	no	—
180	D₄×C₈₉	—	4	2	no	—
181	D₄×C₈₉	—	4	2	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	8	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	4	4	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	8	4	no	—
195	C₂×C₄×C₈₉	—	8	2	no	—
196	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
197	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₈₉	—	4	2	no	—
203	C₈×C₈₉	—	4	2	no	—
204	C₈×C₈₉	—	4	2	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	4	2	no	—
216	C₄×C₈₉	—	4	2	no	—
217	C₄×C₈₉	—	4	2	no	—
218	C₄×C₈₉	—	4	2	no	—
219	C₄×C₈₉	—	4	2	no	—
220	C₄×C₈₉	—	8	2	no	—
221	C₄×C₈₉	#455	1	2	yes	—
222	C₄×C₈₉	#577	1	2	yes	—
223	C₄×C₈₉	#578	1	2	yes	—
224	#18725	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₈₉	—	4	1	no	—
226	C₂×C₈₉	—	8	2	no	—
227	C₂×C₈₉	#3010	1	1	yes	characteristic
228	C₂×C₈₉	#3011	1	1	yes	characteristic
229	C₂×C₈₉	C₂×#455	1	1	yes	characteristic
230	#3550	C₂×C₈₉	1	1	yes	characteristic
231	#3229	C₂×C₈₉	1	1	yes	characteristic, complemented
232	#3209	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#3141	C₂×C₈₉	1	1	yes	characteristic
234	#1645	C₂×C₈₉	1	4	yes	complemented
235	#1640	C₂×C₈₉	1	4	yes	complemented
236	#1543	C₂×C₈₉	1	1	yes	characteristic
237	#1485	C₂×C₈₉	1	1	yes	characteristic, complemented
238	#1485	C₂×C₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#18725	1	1	yes	characteristic, direct product factor, Sylow
240	#563	—	2	2	no	—
241	#559	C₂²×C₈₉	1	2	yes	—
242	Q₈²	C₂²×C₈₉	1	2	yes	—
243	#556	—	2	1	no	—
244	#556	—	2	1	no	—
245	D₄×Q₈	—	2	1	no	—
246	D₄×Q₈	—	2	1	no	—
247	#542	—	2	2	no	—
248	#542	—	2	2	no	—
249	#536	—	2	2	no	—
250	#533	C₂²×C₈₉	1	1	yes	characteristic
251	#533	C₂²×C₈₉	1	1	yes	characteristic
252	#532	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
254	#498	—	2	1	no	—
255	#494	—	2	1	no	—
256	#489	—	2	2	no	—
257	#487	—	2	1	no	—
258	#487	—	2	1	no	—
259	#487	C₂²×C₈₉	1	2	yes	—
260	#486	C₂²×C₈₉	1	2	yes	—
261	#483	—	2	2	no	—
262	#475	C₂²×C₈₉	1	4	yes	—
263	#462	C₂²×C₈₉	1	4	yes	—
264	#451	—	2	2	no	—
265	#431	C₂²×C₈₉	1	1	yes	characteristic
266	#431	C₂²×C₈₉	1	1	yes	characteristic
267	#417	—	2	2	no	—
268	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
269	#333	C₂²×C₈₉	1	2	yes	—
270	#331	C₂²×C₈₉	1	2	yes	—
271	Q₈⋊C₈	C₂²×C₈₉	1	4	yes	—
272	Q₈⋊C₈	C₂²×C₈₉	1	4	yes	—
273	C₂×#41	D₄×C₈₉	1	2	yes	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂×Q₁₆	—	2	4	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
285	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
286	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
287	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
288	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
290	#127	C₂³×C₈₉	1	1	yes	characteristic
291	#126	—	2	4	no	—
292	#126	—	2	4	no	—
293	#125	—	2	1	no	—
294	#125	—	2	1	no	—
295	#124	—	2	4	no	—
296	#124	—	2	2	no	—
297	#124	—	2	2	no	—
298	#124	D₄×C₈₉	1	2	yes	—
299	#123	—	2	4	no	—
300	#123	—	2	4	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
308	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
309	#121	—	2	1	no	—
310	#121	—	2	1	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
316	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	—	2	2	no	—
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
327	#106	—	2	4	no	—
328	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
329	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
330	#103	—	2	4	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#102	—	2	4	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	#97	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	1	no	—
339	C₄×C₈	C₂³×C₈₉	1	2	yes	—
340	#41	—	4	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	8	2	no	—
347	C₂×Q₈	—	8	4	no	—
348	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
349	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
350	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
361	Q₁₆	—	8	4	no	—
362	M₁₆	—	4	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
385	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
399	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
400	C₂³	—	2	2	no	—
401	C₂³	#120×C₈₉	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	4	no	—
408	Q₈	—	8	2	no	—
409	Q₈	—	8	4	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	8	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
427	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
428	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	#455×C₈₉	1	2	yes	—
452	C₄	#577×C₈₉	1	2	yes	—
453	C₄	#578×C₈₉	1	2	yes	—
454	C₂	—	4	1	no	—
455	C₂	—	8	2	no	—
456	C₂	C₈₉×#3010	1	1	yes	characteristic
457	C₂	C₈₉×#3011	1	1	yes	characteristic
458	C₂	C₂×#455×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	#532×C₈₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3229	C₂	semidirect
3. C₈₉×#3209	C₂	semidirect
5. C₈₉×#1645	C₂	semidirect
6. C₈₉×#1640	C₂	semidirect
8. C₈₉×#1485	C₂	semidirect
9. C₈₉×#1485	C₂	semidirect
224. #18725	C₈₉	direct (N × H)
231. #3229	C₂×C₈₉	semidirect
232. #3209	C₂×C₈₉	semidirect
234. #1645	C₂×C₈₉	semidirect
235. #1640	C₂×C₈₉	semidirect
237. #1485	C₂×C₈₉	semidirect
238. #1485	C₂×C₈₉	semidirect
239. C₈₉	#18725	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×#3550	2
C₈₉×#3229	2
C₈₉×#3209	2
C₈₉×#3141	2
C₈₉×#1645	2
C₈₉×#1640	2
C₈₉×#1543	2
C₈₉×#1485	2
#18725	89

Subgroups — C89×#18725 #36396573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#18725 #36396573