Subgroups — C₈₉×#19254 #36397102

Order 22784.

744 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1679	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1677	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1671	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
13	C₂³×C₈×C₈₉	—	2	1	no	—
14	#533×C₈₉	C₂²	1	1	yes	characteristic
15	#532×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	#478×C₈₉	—	2	2	no	—
22	#476×C₈₉	C₂²	1	2	yes	—
23	#474×C₈₉	C₂²	1	2	yes	—
24	#465×C₈₉	—	2	1	no	—
25	#465×C₈₉	—	2	1	no	—
26	#463×C₈₉	—	2	2	no	—
27	#461×C₈₉	C₂²	1	2	yes	—
28	#459×C₈₉	C₂²	1	2	yes	—
29	C₄×SD₁₆×C₈₉	—	2	1	no	—
30	C₄×SD₁₆×C₈₉	—	2	1	no	—
31	C₈×D₄×C₈₉	—	2	1	no	—
32	C₈×D₄×C₈₉	—	2	1	no	—
33	C₈×D₄×C₈₉	C₂²	1	2	yes	—
34	C₈×D₄×C₈₉	C₂²	1	2	yes	—
35	#428×C₈₉	—	2	1	no	—
36	#423×C₈₉	C₂²	1	1	yes	characteristic
37	#423×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	#418×C₈₉	—	2	1	no	—
40	#417×C₈₉	—	2	1	no	—
41	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#334×C₈₉	C₂²	1	2	yes	complemented
44	#334×C₈₉	C₂²	1	2	yes	complemented
45	#333×C₈₉	C₂²	1	2	yes	complemented
46	#332×C₈₉	C₂²	1	2	yes	complemented
47	#332×C₈₉	C₂²	1	2	yes	complemented
48	#331×C₈₉	C₂²	1	2	yes	complemented
49	C₂×#41×C₈₉	—	2	1	no	—
50	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
53	C₂×SD₁₆×C₈₉	—	2	2	no	—
54	C₂×SD₁₆×C₈₉	—	2	1	no	—
55	C₂×SD₁₆×C₈₉	—	2	1	no	—
56	C₂×D₈×C₈₉	—	2	2	no	—
57	C₂×M₁₆×C₈₉	—	2	1	no	—
58	C₂×M₁₆×C₈₉	—	2	1	no	—
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	2	no	—
61	C₂²×C₈×C₈₉	—	2	2	no	—
62	C₂²×C₈×C₈₉	—	4	4	no	—
63	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
68	#127×C₈₉	C₂³	1	1	yes	characteristic
69	#125×C₈₉	—	2	1	no	—
70	#124×C₈₉	—	2	1	no	—
71	C₂²⋊Q₈×C₈₉	—	2	1	no	—
72	C₂²⋊Q₈×C₈₉	—	2	1	no	—
73	#121×C₈₉	—	2	1	no	—
74	#121×C₈₉	—	2	1	no	—
75	C₄×Q₈×C₈₉	—	2	1	no	—
76	C₄×Q₈×C₈₉	—	2	1	no	—
77	C₄×D₄×C₈₉	—	2	1	no	—
78	C₄×D₄×C₈₉	—	2	1	no	—
79	C₄×D₄×C₈₉	—	2	1	no	—
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	D₄	1	2	yes	—
82	C₄×D₄×C₈₉	C₂³	1	2	yes	—
83	#117×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
87	#107×C₈₉	—	2	2	no	—
88	#106×C₈₉	—	2	1	no	—
89	#106×C₈₉	—	2	1	no	—
90	#106×C₈₉	—	2	2	no	—
91	C₄⋊C₈×C₈₉	—	2	1	no	—
92	C₄⋊C₈×C₈₉	—	2	1	no	—
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
95	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
97	#103×C₈₉	—	2	1	no	—
98	#103×C₈₉	—	2	1	no	—
99	#103×C₈₉	—	2	2	no	—
100	#102×C₈₉	—	2	2	no	—
101	#102×C₈₉	—	2	2	no	—
102	#102×C₈₉	—	2	1	no	—
103	#102×C₈₉	—	2	1	no	—
104	#102×C₈₉	—	2	2	no	—
105	C₂²⋊C₈×C₈₉	—	2	2	no	—
106	C₂²⋊C₈×C₈₉	—	2	2	no	—
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂⁴×C₈₉	—	2	1	no	—
112	#41×C₈₉	—	4	2	no	—
113	#41×C₈₉	—	4	2	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	—	2	1	no	—
117	C₂×D₄×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	—	2	1	no	—
122	C₂×D₄×C₈₉	—	4	1	no	—
123	C₂×D₄×C₈₉	SD₁₆	1	4	yes	complemented
124	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	2	no	—
128	C₂²×C₄×C₈₉	—	4	2	no	—
129	C₂²×C₄×C₈₉	—	4	2	no	—
130	C₂²×C₄×C₈₉	—	4	1	no	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	SD₁₆×C₈₉	—	4	2	no	—
135	SD₁₆×C₈₉	—	4	4	no	—
136	SD₁₆×C₈₉	—	4	2	no	—
137	D₈×C₈₉	—	4	4	no	—
138	M₁₆×C₈₉	—	4	2	no	—
139	M₁₆×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₂×C₈×C₈₉	—	4	1	no	—
145	C₂×C₈×C₈₉	—	4	4	no	—
146	C₂×C₈×C₈₉	—	4	2	no	—
147	C₂×C₈×C₈₉	—	4	4	no	—
148	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	4	1	no	—
160	C₄⋊C₄×C₈₉	—	4	1	no	—
161	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₈₉	—	2	2	no	—
163	C₂²⋊C₄×C₈₉	—	2	2	no	—
164	C₂²⋊C₄×C₈₉	—	4	1	no	—
165	C₂²⋊C₄×C₈₉	—	4	1	no	—
166	C₂²⋊C₄×C₈₉	—	4	1	no	—
167	C₄²×C₈₉	—	4	1	no	—
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	#41	1	1	yes	characteristic
171	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₈₉	—	2	2	no	—
173	C₂³×C₈₉	—	2	4	no	—
174	C₂³×C₈₉	—	4	2	no	—
175	C₂³×C₈₉	—	4	2	no	—
176	C₂³×C₈₉	—	4	1	no	—
177	C₂³×C₈₉	#121	1	1	yes	characteristic
178	Q₈×C₈₉	—	4	1	no	—
179	Q₈×C₈₉	—	4	1	no	—
180	Q₈×C₈₉	—	4	1	no	—
181	Q₈×C₈₉	—	4	1	no	—
182	Q₈×C₈₉	—	8	1	no	—
183	D₄×C₈₉	—	2	2	no	—
184	D₄×C₈₉	—	2	4	no	—
185	D₄×C₈₉	—	4	1	no	—
186	D₄×C₈₉	—	4	1	no	—
187	D₄×C₈₉	—	4	1	no	—
188	D₄×C₈₉	—	4	1	no	—
189	D₄×C₈₉	—	8	1	no	—
190	D₄×C₈₉	—	8	2	no	—
191	D₄×C₈₉	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	4	no	—
197	C₂×C₄×C₈₉	—	4	2	no	—
198	C₂×C₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	8	2	no	—
204	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₈₉	#135	1	2	yes	—
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
212	C₈×C₈₉	—	2	1	no	—
213	C₈×C₈₉	—	2	1	no	—
214	C₈×C₈₉	—	2	1	no	—
215	C₈×C₈₉	—	4	2	no	—
216	C₈×C₈₉	—	4	2	no	—
217	C₈×C₈₉	—	4	2	no	—
218	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	4	no	—
222	C₂²×C₈₉	—	4	8	no	—
223	C₂²×C₈₉	—	4	2	no	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	8	1	no	—
226	C₂²×C₈₉	—	8	1	no	—
227	C₂²×C₈₉	—	8	1	no	—
228	C₂²×C₈₉	#465	1	2	yes	—
229	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	—	8	1	no	—
236	C₄×C₈₉	—	8	1	no	—
237	C₄×C₈₉	#465	1	2	yes	—
238	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
239	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
240	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₈₉	#575	1	1	yes	characteristic
242	#19254	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₈₉	—	2	2	no	—
244	C₂×C₈₉	—	4	4	no	—
245	C₂×C₈₉	—	16	1	no	—
246	C₂×C₈₉	#3036	1	1	yes	characteristic
247	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
248	C₂×C₈₉	#3067	1	1	yes	characteristic
249	#3167	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#3077	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#3036	C₂×C₈₉	1	1	yes	characteristic
252	C₂×C₈×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#1679	C₂×C₈₉	1	2	yes	complemented
254	#1677	C₂×C₈₉	1	2	yes	complemented
255	#1671	C₂×C₈₉	1	2	yes	complemented
256	#1665	C₂×C₈₉	1	2	yes	complemented
257	#1566	C₂×C₈₉	1	1	yes	characteristic, complemented
258	#1550	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#1547	C₂×C₈₉	1	1	yes	characteristic, complemented
260	C₈₉	#19254	1	1	yes	characteristic, direct product factor, Sylow
261	C₂×AGL(1,ℤ/8)	—	2	1	no	—
262	C₂³×C₈	—	2	1	no	—
263	#533	C₂²×C₈₉	1	1	yes	characteristic
264	#532	C₂²×C₈₉	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
266	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
267	#492	C₂²×C₈₉	1	1	yes	characteristic, complemented
268	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
269	#486	C₂²×C₈₉	1	1	yes	characteristic, complemented
270	#478	—	2	2	no	—
271	#476	C₂²×C₈₉	1	2	yes	—
272	#474	C₂²×C₈₉	1	2	yes	—
273	#465	—	2	1	no	—
274	#465	—	2	1	no	—
275	#463	—	2	2	no	—
276	#461	C₂²×C₈₉	1	2	yes	—
277	#459	C₂²×C₈₉	1	2	yes	—
278	C₄×SD₁₆	—	2	1	no	—
279	C₄×SD₁₆	—	2	1	no	—
280	C₈×D₄	—	2	1	no	—
281	C₈×D₄	—	2	1	no	—
282	C₈×D₄	C₂²×C₈₉	1	2	yes	—
283	C₈×D₄	C₂²×C₈₉	1	2	yes	—
284	#428	—	2	1	no	—
285	#423	C₂²×C₈₉	1	1	yes	characteristic
286	#423	C₂²×C₈₉	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
288	#418	—	2	1	no	—
289	#417	—	2	1	no	—
290	C₂×C₂²⋊C₈	—	2	1	no	—
291	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
292	#334	C₂²×C₈₉	1	2	yes	complemented
293	#334	C₂²×C₈₉	1	2	yes	complemented
294	#333	C₂²×C₈₉	1	2	yes	complemented
295	#332	C₂²×C₈₉	1	2	yes	complemented
296	#332	C₂²×C₈₉	1	2	yes	complemented
297	#331	C₂²×C₈₉	1	2	yes	complemented
298	C₂×#41	—	2	1	no	—
299	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	AGL(1,ℤ/8)	—	4	4	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	1	no	—
304	C₂×SD₁₆	—	2	1	no	—
305	C₂×D₈	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	4	4	no	—
312	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
313	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
315	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
317	#127	C₂³×C₈₉	1	1	yes	characteristic
318	#125	—	2	1	no	—
319	#124	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	D₄×C₈₉	1	2	yes	—
331	C₄×D₄	C₂³×C₈₉	1	2	yes	—
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	#106	—	2	1	no	—
338	#106	—	2	1	no	—
339	#106	—	2	2	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
344	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
345	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#103	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	2	no	—
351	#102	—	2	1	no	—
352	#102	—	2	1	no	—
353	#102	—	2	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
357	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
358	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
359	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
360	C₂⁴	—	2	1	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	SD₁₆×C₈₉	1	4	yes	complemented
373	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
382	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
383	SD₁₆	—	4	2	no	—
384	SD₁₆	—	4	4	no	—
385	SD₁₆	—	4	2	no	—
386	D₈	—	4	4	no	—
387	M₁₆	—	4	2	no	—
388	M₁₆	—	4	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	1	no	—
394	C₂×C₈	—	4	4	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	4	4	no	—
397	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
399	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
400	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
419	C₄²	#41×C₈₉	1	1	yes	characteristic
420	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	#121×C₈₉	1	1	yes	characteristic
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	8	1	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	1	no	—
439	D₄	—	8	2	no	—
440	D₄	C₂×SD₁₆×C₈₉	1	4	yes	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
454	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
455	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
457	C₂×C₄	#135×C₈₉	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	AGL(1,ℤ/8)×C₈₉	1	2	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	4	8	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	#465×C₈₉	1	2	yes	—
478	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	#465×C₈₉	1	2	yes	—
487	C₄	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
488	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
489	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
490	C₄	#575×C₈₉	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	4	4	no	—
493	C₂	—	16	1	no	—
494	C₂	C₈₉×#3036	1	1	yes	characteristic
495	C₂	C₂×#465×C₈₉	1	1	yes	characteristic
496	C₂	C₈₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3036	C₂
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
1. C₈₉×#3167	C₂	semidirect
2. C₈₉×#3077	C₂	semidirect
4. C₂×C₈×D₄×C₈₉	C₂	semidirect
5. C₈₉×#1679	C₂	semidirect
6. C₈₉×#1677	C₂	semidirect
7. C₈₉×#1671	C₂	semidirect
8. C₈₉×#1665	C₂	semidirect
9. C₈₉×#1566	C₂	semidirect
10. C₈₉×#1550	C₂	semidirect
11. C₈₉×#1547	C₂	semidirect
17. #498×C₈₉	C₂²	semidirect
18. #492×C₈₉	C₂²	semidirect
19. #487×C₈₉	C₂²	semidirect
20. #486×C₈₉	C₂²	semidirect
43. #334×C₈₉	C₂²	semidirect
44. #334×C₈₉	C₂²	semidirect
45. #333×C₈₉	C₂²	semidirect
46. #332×C₈₉	C₂²	semidirect
47. #332×C₈₉	C₂²	semidirect
48. #331×C₈₉	C₂²	semidirect
123. C₂×D₄×C₈₉	SD₁₆	semidirect
218. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
242. #19254	C₈₉	direct (N × H)
249. #3167	C₂×C₈₉	semidirect
250. #3077	C₂×C₈₉	semidirect
252. C₂×C₈×D₄	C₂×C₈₉	semidirect
253. #1679	C₂×C₈₉	semidirect
254. #1677	C₂×C₈₉	semidirect
255. #1671	C₂×C₈₉	semidirect
256. #1665	C₂×C₈₉	semidirect
257. #1566	C₂×C₈₉	semidirect
258. #1550	C₂×C₈₉	semidirect
259. #1547	C₂×C₈₉	semidirect
260. C₈₉	#19254	direct (N × H)
266. #498	C₂²×C₈₉	semidirect
267. #492	C₂²×C₈₉	semidirect
268. #487	C₂²×C₈₉	semidirect
269. #486	C₂²×C₈₉	semidirect
292. #334	C₂²×C₈₉	semidirect
293. #334	C₂²×C₈₉	semidirect
294. #333	C₂²×C₈₉	semidirect
295. #332	C₂²×C₈₉	semidirect
296. #332	C₂²×C₈₉	semidirect
297. #331	C₂²×C₈₉	semidirect
372. C₂×D₄	SD₁₆×C₈₉	semidirect
467. C₈	AGL(1,ℤ/8)×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3167	2
C₈₉×#3077	2
C₈₉×#3036	2
C₂×C₈×D₄×C₈₉	2
C₈₉×#1679	2
C₈₉×#1677	2
C₈₉×#1671	2
C₈₉×#1665	2
C₈₉×#1566	2
C₈₉×#1550	2
C₈₉×#1547	2
#19254	89

Subgroups — C89×#19254 #36397102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19254 #36397102