Subgroups — C₈₉×#19462 #36397310

Order 22784.

680 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3109	C₂	1	1	yes	maximal, characteristic
3	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1701	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1681	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₈₉	—	2	1	no	—
13	#532×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	#498×C₈₉	C₂²	1	2	yes	complemented
17	#486×C₈₉	C₂²	1	2	yes	complemented
18	#481×C₈₉	—	2	1	no	—
19	#481×C₈₉	—	2	1	no	—
20	#481×C₈₉	—	2	1	no	—
21	#476×C₈₉	—	2	2	no	—
22	#476×C₈₉	C₂²	1	1	yes	characteristic
23	#476×C₈₉	C₂²	1	1	yes	characteristic
24	#461×C₈₉	—	2	1	no	—
25	#461×C₈₉	—	2	1	no	—
26	#461×C₈₉	C₂²	1	2	yes	—
27	#461×C₈₉	C₂²	1	2	yes	—
28	#459×C₈₉	C₂²	1	1	yes	characteristic
29	#459×C₈₉	C₂²	1	1	yes	characteristic
30	#447×C₈₉	—	2	1	no	—
31	#442×C₈₉	—	2	1	no	—
32	#442×C₈₉	—	2	1	no	—
33	#436×C₈₉	C₂²	1	2	yes	—
34	#435×C₈₉	—	2	2	no	—
35	C₈×D₄×C₈₉	C₂²	1	2	yes	—
36	#432×C₈₉	C₂²	1	1	yes	characteristic
37	#432×C₈₉	C₂²	1	1	yes	characteristic
38	#431×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₈₉	—	2	1	no	—
41	#407×C₈₉	—	2	1	no	—
42	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
43	#335×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×Q₈×C₈₉	—	2	1	no	—
51	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	—	2	1	no	—
53	C₂×SD₁₆×C₈₉	—	2	2	no	—
54	C₂×SD₁₆×C₈₉	—	2	2	no	—
55	C₂×SD₁₆×C₈₉	—	4	4	no	—
56	C₂×D₈×C₈₉	—	2	1	no	—
57	C₂×D₈×C₈₉	—	2	1	no	—
58	C₂×M₁₆×C₈₉	—	2	2	no	—
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	2	no	—
61	C₄⋊Q₈×C₈₉	—	2	1	no	—
62	C₄⋊Q₈×C₈₉	—	2	1	no	—
63	C₄⋊Q₈×C₈₉	—	2	1	no	—
64	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
66	#127×C₈₉	C₂³	1	1	yes	characteristic
67	#124×C₈₉	—	2	1	no	—
68	#121×C₈₉	—	2	1	no	—
69	#121×C₈₉	—	2	1	no	—
70	C₄×D₄×C₈₉	—	2	1	no	—
71	C₄×D₄×C₈₉	—	2	1	no	—
72	C₄×D₄×C₈₉	—	2	1	no	—
73	C₄×D₄×C₈₉	—	2	1	no	—
74	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	#106×C₈₉	—	2	2	no	—
84	#106×C₈₉	—	2	2	no	—
85	#106×C₈₉	—	2	1	no	—
86	#106×C₈₉	—	2	1	no	—
87	C₄⋊C₈×C₈₉	—	2	1	no	—
88	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	#103×C₈₉	—	2	2	no	—
94	#103×C₈₉	—	2	2	no	—
95	#102×C₈₉	—	2	1	no	—
96	#102×C₈₉	—	2	1	no	—
97	#102×C₈₉	—	2	2	no	—
98	#102×C₈₉	—	2	2	no	—
99	#102×C₈₉	—	2	1	no	—
100	#102×C₈₉	—	2	1	no	—
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₂²⋊C₈×C₈₉	—	2	1	no	—
103	C₂²⋊C₈×C₈₉	—	2	2	no	—
104	C₂²⋊C₈×C₈₉	—	2	2	no	—
105	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
107	#97×C₈₉	—	2	1	no	—
108	#97×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	C₂⁴×C₈₉	—	2	1	no	—
111	#41×C₈₉	—	8	2	no	—
112	C₂×Q₈×C₈₉	—	2	2	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	4	2	no	—
115	C₂×Q₈×C₈₉	—	4	2	no	—
116	C₂×Q₈×C₈₉	—	4	1	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	1	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	—	4	1	no	—
124	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	—	4	1	no	—
132	C₂²×C₄×C₈₉	—	4	1	no	—
133	C₂²×C₄×C₈₉	—	8	2	no	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	SD₁₆×C₈₉	—	4	4	no	—
138	SD₁₆×C₈₉	—	4	4	no	—
139	D₈×C₈₉	—	4	2	no	—
140	D₈×C₈₉	—	4	2	no	—
141	M₁₆×C₈₉	—	8	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	4	2	no	—
147	C₂×C₈×C₈₉	—	8	2	no	—
148	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	—	4	1	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₈₉	—	2	1	no	—
160	C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₂²⋊C₄×C₈₉	—	2	1	no	—
162	C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₂²⋊C₄×C₈₉	—	4	1	no	—
164	C₂²⋊C₄×C₈₉	—	4	1	no	—
165	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	#41	1	1	yes	characteristic
168	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂³×C₈₉	—	2	1	no	—
170	C₂³×C₈₉	—	2	1	no	—
171	C₂³×C₈₉	—	4	2	no	—
172	C₂³×C₈₉	—	4	2	no	—
173	C₂³×C₈₉	—	4	1	no	—
174	C₂³×C₈₉	—	8	1	no	—
175	C₂³×C₈₉	#121	1	1	yes	characteristic
176	Q₈×C₈₉	—	4	2	no	—
177	Q₈×C₈₉	—	4	2	no	—
178	Q₈×C₈₉	—	8	1	no	—
179	Q₈×C₈₉	—	8	2	no	—
180	D₄×C₈₉	—	2	1	no	—
181	D₄×C₈₉	—	2	1	no	—
182	D₄×C₈₉	—	2	1	no	—
183	D₄×C₈₉	—	4	2	no	—
184	D₄×C₈₉	—	4	1	no	—
185	D₄×C₈₉	—	4	1	no	—
186	D₄×C₈₉	—	4	2	no	—
187	D₄×C₈₉	—	8	1	no	—
188	D₄×C₈₉	—	8	2	no	—
189	D₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	—	4	2	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	8	1	no	—
201	C₂×C₄×C₈₉	—	8	1	no	—
202	C₂×C₄×C₈₉	—	8	2	no	—
203	C₂×C₄×C₈₉	—	8	1	no	—
204	C₂×C₄×C₈₉	—	8	2	no	—
205	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
211	C₈×C₈₉	—	2	2	no	—
212	C₈×C₈₉	—	2	2	no	—
213	C₈×C₈₉	—	4	2	no	—
214	C₈×C₈₉	—	4	1	no	—
215	C₈×C₈₉	—	4	1	no	—
216	C₈×C₈₉	—	4	2	no	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	2	2	no	—
220	C₂²×C₈₉	—	4	1	no	—
221	C₂²×C₈₉	—	4	1	no	—
222	C₂²×C₈₉	—	4	1	no	—
223	C₂²×C₈₉	—	4	1	no	—
224	C₂²×C₈₉	—	4	1	no	—
225	C₂²×C₈₉	—	8	4	no	—
226	C₂²×C₈₉	—	8	1	no	—
227	C₂²×C₈₉	—	8	1	no	—
228	C₂²×C₈₉	—	8	1	no	—
229	C₂²×C₈₉	#471	1	2	yes	—
230	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	2	1	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	4	1	no	—
236	C₄×C₈₉	—	4	1	no	—
237	C₄×C₈₉	—	8	2	no	—
238	C₄×C₈₉	—	8	1	no	—
239	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₄×C₈₉	#575	1	1	yes	characteristic
241	C₄×C₈₉	#577	1	2	yes	—
242	#19462	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₈₉	—	2	2	no	—
244	C₂×C₈₉	—	4	2	no	—
245	C₂×C₈₉	—	8	1	no	—
246	C₂×C₈₉	—	16	1	no	—
247	C₂×C₈₉	#3042	1	1	yes	characteristic
248	C₂×C₈₉	#3055	1	1	yes	characteristic
249	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
250	#3227	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#3109	C₂×C₈₉	1	1	yes	characteristic
252	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#2974	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#1701	C₂×C₈₉	1	2	yes	complemented
255	#1691	C₂×C₈₉	1	2	yes	complemented
256	#1681	C₂×C₈₉	1	2	yes	complemented
257	#1671	C₂×C₈₉	1	2	yes	complemented
258	#1573	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#1556	C₂×C₈₉	1	1	yes	characteristic, complemented
260	#1551	C₂×C₈₉	1	1	yes	characteristic, complemented
261	C₈₉	#19462	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×SD₁₆	—	2	1	no	—
263	#532	C₂²×C₈₉	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
266	#498	C₂²×C₈₉	1	2	yes	complemented
267	#486	C₂²×C₈₉	1	2	yes	complemented
268	#481	—	2	1	no	—
269	#481	—	2	1	no	—
270	#481	—	2	1	no	—
271	#476	—	2	2	no	—
272	#476	C₂²×C₈₉	1	1	yes	characteristic
273	#476	C₂²×C₈₉	1	1	yes	characteristic
274	#461	—	2	1	no	—
275	#461	—	2	1	no	—
276	#461	C₂²×C₈₉	1	2	yes	—
277	#461	C₂²×C₈₉	1	2	yes	—
278	#459	C₂²×C₈₉	1	1	yes	characteristic
279	#459	C₂²×C₈₉	1	1	yes	characteristic
280	#447	—	2	1	no	—
281	#442	—	2	1	no	—
282	#442	—	2	1	no	—
283	#436	C₂²×C₈₉	1	2	yes	—
284	#435	—	2	2	no	—
285	C₈×D₄	C₂²×C₈₉	1	2	yes	—
286	#432	C₂²×C₈₉	1	1	yes	characteristic
287	#432	C₂²×C₈₉	1	1	yes	characteristic
288	#431	C₂²×C₈₉	1	1	yes	characteristic
289	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
290	C₂×#103	—	2	1	no	—
291	#407	—	2	1	no	—
292	C₂×C₂²⋊C₈	—	2	1	no	—
293	#335	C₂²×C₈₉	1	2	yes	complemented
294	#334	C₂²×C₈₉	1	2	yes	complemented
295	#333	C₂²×C₈₉	1	2	yes	complemented
296	#332	C₂²×C₈₉	1	2	yes	complemented
297	#332	C₂²×C₈₉	1	2	yes	complemented
298	#331	C₂²×C₈₉	1	2	yes	complemented
299	C₂×#41	—	2	1	no	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
302	C₂³×C₄	—	2	1	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	4	4	no	—
306	C₂×D₈	—	2	1	no	—
307	C₂×D₈	—	2	1	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
316	#127	C₂³×C₈₉	1	1	yes	characteristic
317	#124	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
325	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
326	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
327	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
333	#106	—	2	2	no	—
334	#106	—	2	2	no	—
335	#106	—	2	1	no	—
336	#106	—	2	1	no	—
337	C₄⋊C₈	—	2	1	no	—
338	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
339	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
340	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
342	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
343	#103	—	2	2	no	—
344	#103	—	2	2	no	—
345	#102	—	2	1	no	—
346	#102	—	2	1	no	—
347	#102	—	2	2	no	—
348	#102	—	2	2	no	—
349	#102	—	2	1	no	—
350	#102	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
356	C₂²⋊C₈	D₄×C₈₉	1	1	yes	characteristic
357	#97	—	2	1	no	—
358	#97	—	2	1	no	—
359	C₄×C₈	C₂³×C₈₉	1	2	yes	—
360	C₂⁴	—	2	1	no	—
361	#41	—	8	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	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	—	2	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
375	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	8	2	no	—
384	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
386	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
387	SD₁₆	—	4	4	no	—
388	SD₁₆	—	4	4	no	—
389	D₈	—	4	2	no	—
390	D₈	—	4	2	no	—
391	M₁₆	—	8	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	8	2	no	—
398	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
417	C₄²	#41×C₈₉	1	1	yes	characteristic
418	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	8	1	no	—
425	C₂³	#121×C₈₉	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	8	1	no	—
429	Q₈	—	8	2	no	—
430	D₄	—	2	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	1	no	—
438	D₄	—	8	2	no	—
439	D₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
456	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
457	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
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	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	#471×C₈₉	1	2	yes	—
480	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
490	C₄	#575×C₈₉	1	1	yes	characteristic
491	C₄	#577×C₈₉	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	16	1	no	—
496	C₂	C₈₉×#3042	1	1	yes	characteristic
497	C₂	C₈₉×#3055	1	1	yes	characteristic
498	C₂	C₂×#471×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3109	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×#3227	C₂	semidirect
3. C₂×#461×C₈₉	C₂	semidirect
4. C₈₉×#2974	C₂	semidirect
5. C₈₉×#1701	C₂	semidirect
6. C₈₉×#1691	C₂	semidirect
7. C₈₉×#1681	C₂	semidirect
8. C₈₉×#1671	C₂	semidirect
9. C₈₉×#1573	C₂	semidirect
10. C₈₉×#1556	C₂	semidirect
11. C₈₉×#1551	C₂	semidirect
16. #498×C₈₉	C₂²	semidirect
17. #486×C₈₉	C₂²	semidirect
43. #335×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
242. #19462	C₈₉	direct (N × H)
250. #3227	C₂×C₈₉	semidirect
252. C₂×#461	C₂×C₈₉	semidirect
253. #2974	C₂×C₈₉	semidirect
254. #1701	C₂×C₈₉	semidirect
255. #1691	C₂×C₈₉	semidirect
256. #1681	C₂×C₈₉	semidirect
257. #1671	C₂×C₈₉	semidirect
258. #1573	C₂×C₈₉	semidirect
259. #1556	C₂×C₈₉	semidirect
260. #1551	C₂×C₈₉	semidirect
261. C₈₉	#19462	direct (N × H)
266. #498	C₂²×C₈₉	semidirect
267. #486	C₂²×C₈₉	semidirect
293. #335	C₂²×C₈₉	semidirect
294. #334	C₂²×C₈₉	semidirect
295. #333	C₂²×C₈₉	semidirect
296. #332	C₂²×C₈₉	semidirect
297. #332	C₂²×C₈₉	semidirect
298. #331	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3227	2
C₈₉×#3109	2
C₂×#461×C₈₉	2
C₈₉×#2974	2
C₈₉×#1701	2
C₈₉×#1691	2
C₈₉×#1681	2
C₈₉×#1671	2
C₈₉×#1573	2
C₈₉×#1556	2
C₈₉×#1551	2
#19462	89

Subgroups — C89×#19462 #36397310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19462 #36397310