Subgroups — C₈₉×#19167 #36397015

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3101	C₂	1	1	yes	maximal, characteristic
3	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic
4	D₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1699	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1679	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₈₉	—	2	1	no	—
13	#533×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	#491×C₈₉	—	2	2	no	—
17	#487×C₈₉	C₂²	1	2	yes	complemented
18	#487×C₈₉	C₂²	1	2	yes	complemented
19	#483×C₈₉	—	2	1	no	—
20	#476×C₈₉	C₂²	1	1	yes	characteristic
21	#476×C₈₉	C₂²	1	1	yes	characteristic
22	#474×C₈₉	—	2	1	no	—
23	#474×C₈₉	—	2	1	no	—
24	#474×C₈₉	C₂²	1	2	yes	—
25	#474×C₈₉	C₂²	1	2	yes	—
26	#461×C₈₉	C₂²	1	1	yes	characteristic
27	#461×C₈₉	C₂²	1	1	yes	characteristic
28	#450×C₈₉	—	2	1	no	—
29	C₄×SD₁₆×C₈₉	—	2	1	no	—
30	C₄×SD₁₆×C₈₉	—	2	1	no	—
31	#436×C₈₉	C₂²	1	2	yes	—
32	#435×C₈₉	—	2	2	no	—
33	C₈×D₄×C₈₉	C₂²	1	2	yes	—
34	#431×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#107×C₈₉	—	2	1	no	—
36	#423×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	#419×C₈₉	—	2	1	no	—
39	#419×C₈₉	—	2	1	no	—
40	C₂×#102×C₈₉	—	2	1	no	—
41	#407×C₈₉	—	2	1	no	—
42	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
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	#332×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×Q₈×C₈₉	—	2	1	no	—
50	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	C₂×SD₁₆×C₈₉	—	2	1	no	—
53	C₂×SD₁₆×C₈₉	—	2	1	no	—
54	C₂×M₁₆×C₈₉	—	2	1	no	—
55	C₂×M₁₆×C₈₉	—	2	2	no	—
56	C₂×M₁₆×C₈₉	—	4	4	no	—
57	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
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	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
67	#125×C₈₉	—	2	1	no	—
68	C₂²⋊Q₈×C₈₉	—	2	1	no	—
69	C₂²⋊Q₈×C₈₉	—	2	1	no	—
70	C₄×Q₈×C₈₉	—	2	1	no	—
71	C₄×Q₈×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	#117×C₈₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	#107×C₈₉	—	2	2	no	—
85	#107×C₈₉	—	2	2	no	—
86	#106×C₈₉	—	2	1	no	—
87	#106×C₈₉	—	2	1	no	—
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
91	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#103×C₈₉	—	2	2	no	—
95	#103×C₈₉	—	2	2	no	—
96	#103×C₈₉	—	2	2	no	—
97	#103×C₈₉	—	2	2	no	—
98	#103×C₈₉	—	2	1	no	—
99	#103×C₈₉	—	2	1	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	C₂²⋊C₈×C₈₉	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	2	no	—
106	C₂²⋊C₈×C₈₉	—	2	2	no	—
107	#97×C₈₉	D₄	1	2	yes	—
108	C₄×C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	C₂⁴×C₈₉	—	2	1	no	—
111	C₂×Q₈×C₈₉	—	2	2	no	—
112	C₂×Q₈×C₈₉	—	2	1	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	4	1	no	—
115	C₂×Q₈×C₈₉	—	4	2	no	—
116	C₂×Q₈×C₈₉	—	4	2	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	1	no	—
119	C₂×D₄×C₈₉	—	4	1	no	—
120	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	4	2	no	—
128	C₂²×C₄×C₈₉	—	4	2	no	—
129	C₂²×C₄×C₈₉	—	4	1	no	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	SD₁₆×C₈₉	—	4	2	no	—
134	SD₁₆×C₈₉	—	4	2	no	—
135	M₁₆×C₈₉	—	2	2	no	—
136	M₁₆×C₈₉	—	2	2	no	—
137	M₁₆×C₈₉	—	4	4	no	—
138	M₁₆×C₈₉	—	4	2	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	4	4	no	—
144	C₂×C₈×C₈₉	—	4	2	no	—
145	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	2	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	4	1	no	—
155	C₄⋊C₄×C₈₉	—	4	1	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₄⋊C₄×C₈₉	—	4	1	no	—
158	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
164	C₂²⋊C₄×C₈₉	—	4	1	no	—
165	C₄²×C₈₉	—	4	1	no	—
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	#41	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	—	2	1	no	—
171	C₂³×C₈₉	—	2	1	no	—
172	C₂³×C₈₉	—	4	2	no	—
173	C₂³×C₈₉	—	4	2	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	—	4	1	no	—
179	Q₈×C₈₉	—	4	1	no	—
180	Q₈×C₈₉	—	8	1	no	—
181	Q₈×C₈₉	—	8	2	no	—
182	D₄×C₈₉	—	2	1	no	—
183	D₄×C₈₉	—	2	1	no	—
184	D₄×C₈₉	—	2	1	no	—
185	D₄×C₈₉	—	4	2	no	—
186	D₄×C₈₉	#137	1	2	yes	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	2	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	2	no	—
198	C₂×C₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	—	4	1	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	4	2	no	—
202	C₂×C₄×C₈₉	—	8	2	no	—
203	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₈₉	#135	1	2	yes	—
207	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
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	2	no	—
216	C₈×C₈₉	—	4	1	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	#463	1	2	yes	—
227	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	4	1	no	—
232	C₄×C₈₉	—	4	1	no	—
233	C₄×C₈₉	—	8	2	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	—	8	1	no	—
236	C₄×C₈₉	#463	1	2	yes	—
237	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
238	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
240	C₄×C₈₉	#575	1	1	yes	characteristic
241	#19167	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₈₉	—	2	2	no	—
243	C₂×C₈₉	—	4	2	no	—
244	C₂×C₈₉	—	8	1	no	—
245	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
246	C₂×C₈₉	#3056	1	1	yes	characteristic
247	C₂×C₈₉	#3069	1	1	yes	characteristic
248	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#3101	C₂×C₈₉	1	1	yes	characteristic
250	C₂×#474	C₂×C₈₉	1	1	yes	characteristic
251	D₄×M₁₆	C₂×C₈₉	1	1	yes	characteristic
252	#1703	C₂×C₈₉	1	2	yes	complemented
253	#1699	C₂×C₈₉	1	2	yes	complemented
254	#1683	C₂×C₈₉	1	2	yes	complemented
255	#1679	C₂×C₈₉	1	2	yes	complemented
256	#1565	C₂×C₈₉	1	1	yes	characteristic, complemented
257	#1550	C₂×C₈₉	1	1	yes	characteristic, complemented
258	#1546	C₂×C₈₉	1	1	yes	characteristic, complemented
259	C₈₉	#19167	1	1	yes	characteristic, direct product factor, Sylow
260	C₂²×M₁₆	—	2	1	no	—
261	#533	C₂²×C₈₉	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
264	#491	—	2	2	no	—
265	#487	C₂²×C₈₉	1	2	yes	complemented
266	#487	C₂²×C₈₉	1	2	yes	complemented
267	#483	—	2	1	no	—
268	#476	C₂²×C₈₉	1	1	yes	characteristic
269	#476	C₂²×C₈₉	1	1	yes	characteristic
270	#474	—	2	1	no	—
271	#474	—	2	1	no	—
272	#474	C₂²×C₈₉	1	2	yes	—
273	#474	C₂²×C₈₉	1	2	yes	—
274	#461	C₂²×C₈₉	1	1	yes	characteristic
275	#461	C₂²×C₈₉	1	1	yes	characteristic
276	#450	—	2	1	no	—
277	C₄×SD₁₆	—	2	1	no	—
278	C₄×SD₁₆	—	2	1	no	—
279	#436	C₂²×C₈₉	1	2	yes	—
280	#435	—	2	2	no	—
281	C₈×D₄	C₂²×C₈₉	1	2	yes	—
282	#431	C₂²×C₈₉	1	1	yes	characteristic
283	C₂×#107	—	2	1	no	—
284	#423	C₂²×C₈₉	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
286	#419	—	2	1	no	—
287	#419	—	2	1	no	—
288	C₂×#102	—	2	1	no	—
289	#407	—	2	1	no	—
290	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
291	#335	C₂²×C₈₉	1	2	yes	complemented
292	#334	C₂²×C₈₉	1	2	yes	complemented
293	#333	C₂²×C₈₉	1	2	yes	complemented
294	#332	C₂²×C₈₉	1	2	yes	complemented
295	#332	C₂²×C₈₉	1	2	yes	complemented
296	#332	C₂²×C₈₉	1	2	yes	complemented
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂×SD₁₆	—	2	1	no	—
301	C₂×SD₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	4	4	no	—
305	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
306	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
313	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
315	#125	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
323	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
324	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
325	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
326	#117	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
332	#107	—	2	2	no	—
333	#107	—	2	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	—	2	1	no	—
338	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
339	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
340	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
341	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
342	#103	—	2	2	no	—
343	#103	—	2	2	no	—
344	#103	—	2	2	no	—
345	#103	—	2	2	no	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#102	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	1	no	—
351	#102	—	2	1	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	#97	D₄×C₈₉	1	2	yes	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	C₂³×C₈₉	1	2	yes	—
358	C₂⁴	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	4	1	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
369	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
380	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
381	SD₁₆	—	4	2	no	—
382	SD₁₆	—	4	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	4	4	no	—
386	M₁₆	—	4	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₄²	—	4	1	no	—
414	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
416	C₄²	#41×C₈₉	1	1	yes	characteristic
417	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	8	1	no	—
423	C₂³	#121×C₈₉	1	1	yes	characteristic
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	4	1	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	#137×C₈₉	1	2	yes	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
452	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
453	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
454	C₂×C₄	#135×C₈₉	1	2	yes	—
455	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	2	2	no	—
461	C₈	—	4	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	8	4	no	—
474	C₂²	#463×C₈₉	1	2	yes	—
475	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	1	no	—
484	C₄	#463×C₈₉	1	2	yes	—
485	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
486	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
487	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
488	C₄	#575×C₈₉	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	4	2	no	—
491	C₂	—	8	1	no	—
492	C₂	C₂×#463×C₈₉	1	1	yes	characteristic
493	C₂	C₈₉×#3056	1	1	yes	characteristic
494	C₂	C₈₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	D₄
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×#3139	C₂	semidirect
5. C₈₉×#1703	C₂	semidirect
6. C₈₉×#1699	C₂	semidirect
7. C₈₉×#1683	C₂	semidirect
8. C₈₉×#1679	C₂	semidirect
9. C₈₉×#1565	C₂	semidirect
10. C₈₉×#1550	C₂	semidirect
11. C₈₉×#1546	C₂	semidirect
17. #487×C₈₉	C₂²	semidirect
18. #487×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. #332×C₈₉	C₂²	semidirect
241. #19167	C₈₉	direct (N × H)
248. #3139	C₂×C₈₉	semidirect
252. #1703	C₂×C₈₉	semidirect
253. #1699	C₂×C₈₉	semidirect
254. #1683	C₂×C₈₉	semidirect
255. #1679	C₂×C₈₉	semidirect
256. #1565	C₂×C₈₉	semidirect
257. #1550	C₂×C₈₉	semidirect
258. #1546	C₂×C₈₉	semidirect
259. C₈₉	#19167	direct (N × H)
265. #487	C₂²×C₈₉	semidirect
266. #487	C₂²×C₈₉	semidirect
291. #335	C₂²×C₈₉	semidirect
292. #334	C₂²×C₈₉	semidirect
293. #333	C₂²×C₈₉	semidirect
294. #332	C₂²×C₈₉	semidirect
295. #332	C₂²×C₈₉	semidirect
296. #332	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×#3139	2
C₈₉×#3101	2
C₂×#474×C₈₉	2
D₄×M₁₆×C₈₉	2
C₈₉×#1703	2
C₈₉×#1699	2
C₈₉×#1683	2
C₈₉×#1679	2
C₈₉×#1565	2
C₈₉×#1550	2
C₈₉×#1546	2
#19167	89

Subgroups — C89×#19167 #36397015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19167 #36397015