Subgroups — C₈₉×#7589 #36385437

Order 22784.

578 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1797	C₂	1	1	yes	maximal, characteristic
3	C₂×#336×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1272	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1271	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₈₉	—	2	1	no	—
7	C₂×C₂²⋊Q₈×C₈₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₈₉	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
12	#391×C₈₉	C₂²	1	1	yes	characteristic
13	#389×C₈₉	C₂²	1	1	yes	characteristic
14	#387×C₈₉	—	2	1	no	—
15	#385×C₈₉	—	2	1	no	—
16	#380×C₈₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
18	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
19	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
20	#336×C₈₉	—	2	1	no	—
21	#336×C₈₉	C₂²	1	2	yes	—
22	#336×C₈₉	C₂²	1	2	yes	—
23	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₈₉	—	2	4	no	—
28	C₂²×C₈×C₈₉	—	2	2	no	—
29	C₂²×C₈×C₈₉	—	2	2	no	—
30	C₂²×C₈×C₈₉	—	4	2	no	—
31	C₂²×C₈×C₈₉	—	4	2	no	—
32	C₂²⋊Q₈×C₈₉	—	2	2	no	—
33	C₂²⋊Q₈×C₈₉	C₈	1	4	yes	complemented
34	C₄×Q₈×C₈₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
43	C₂×C₄²×C₈₉	—	2	1	no	—
44	C₂×C₄²×C₈₉	—	2	1	no	—
45	C₂×C₄²×C₈₉	—	4	2	no	—
46	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
50	C₄⋊C₈×C₈₉	—	4	2	no	—
51	C₂²⋊C₈×C₈₉	—	4	2	no	—
52	#95×C₈₉	—	2	1	no	—
53	#95×C₈₉	—	2	1	no	—
54	#95×C₈₉	—	2	1	no	—
55	#95×C₈₉	—	2	1	no	—
56	#95×C₈₉	—	2	1	no	—
57	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×Q₈×C₈₉	—	2	1	no	—
59	C₂×Q₈×C₈₉	—	4	1	no	—
60	C₂×Q₈×C₈₉	—	4	1	no	—
61	C₂×Q₈×C₈₉	C₂×C₈	1	2	yes	complemented
62	C₂²×C₄×C₈₉	—	2	2	no	—
63	C₂²×C₄×C₈₉	—	2	2	no	—
64	C₂²×C₄×C₈₉	—	2	1	no	—
65	C₂²×C₄×C₈₉	—	2	1	no	—
66	C₂²×C₄×C₈₉	—	2	1	no	—
67	C₂²×C₄×C₈₉	—	2	1	no	—
68	C₂²×C₄×C₈₉	—	2	1	no	—
69	C₂²×C₄×C₈₉	—	2	1	no	—
70	C₂²×C₄×C₈₉	—	4	1	no	—
71	C₂²×C₄×C₈₉	—	4	1	no	—
72	C₂²×C₄×C₈₉	—	4	1	no	—
73	C₂²×C₄×C₈₉	—	4	1	no	—
74	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₈₉	M₁₆	1	2	yes	—
79	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₈₉	—	2	4	no	—
85	C₂×C₈×C₈₉	—	4	8	no	—
86	C₂×C₈×C₈₉	—	4	2	no	—
87	C₂×C₈×C₈₉	—	4	2	no	—
88	C₂×C₈×C₈₉	—	4	2	no	—
89	C₂×C₈×C₈₉	—	4	2	no	—
90	C₂×C₈×C₈₉	—	4	2	no	—
91	C₄⋊C₄×C₈₉	—	2	4	no	—
92	C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₄⋊C₄×C₈₉	—	4	1	no	—
94	C₄⋊C₄×C₈₉	—	4	1	no	—
95	C₄⋊C₄×C₈₉	—	4	2	no	—
96	C₄⋊C₄×C₈₉	—	4	1	no	—
97	C₄⋊C₄×C₈₉	—	4	1	no	—
98	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	complemented
99	C₂²⋊C₄×C₈₉	—	2	4	no	—
100	C₂²⋊C₄×C₈₉	—	4	2	no	—
101	C₄²×C₈₉	—	2	2	no	—
102	C₄²×C₈₉	—	2	2	no	—
103	C₄²×C₈₉	—	4	1	no	—
104	C₄²×C₈₉	—	4	1	no	—
105	C₄²×C₈₉	—	4	2	no	—
106	C₄²×C₈₉	—	4	2	no	—
107	C₂³×C₈₉	—	2	1	no	—
108	C₂³×C₈₉	—	2	1	no	—
109	C₂³×C₈₉	—	2	1	no	—
110	C₂³×C₈₉	—	2	1	no	—
111	C₂³×C₈₉	C₂²⋊C₈	1	2	yes	—
112	C₂³×C₈₉	#103	1	2	yes	—
113	C₂³×C₈₉	#104	1	2	yes	—
114	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	Q₈×C₈₉	—	4	2	no	—
116	Q₈×C₈₉	—	4	2	no	—
117	C₂×C₄×C₈₉	—	2	4	no	—
118	C₂×C₄×C₈₉	—	2	4	no	—
119	C₂×C₄×C₈₉	—	2	1	no	—
120	C₂×C₄×C₈₉	—	2	1	no	—
121	C₂×C₄×C₈₉	—	2	1	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	1	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	4	2	no	—
134	C₂×C₄×C₈₉	—	4	2	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	1	no	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₈₉	#99	1	2	yes	—
149	C₂×C₄×C₈₉	#103	1	2	yes	—
150	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
154	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
156	C₈×C₈₉	—	4	4	no	—
157	C₈×C₈₉	—	8	2	no	—
158	C₂²×C₈₉	—	2	2	no	—
159	C₂²×C₈₉	—	2	2	no	—
160	C₂²×C₈₉	—	2	2	no	—
161	C₂²×C₈₉	—	2	2	no	—
162	C₂²×C₈₉	—	2	2	no	—
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	Q₈⋊C₈	1	4	yes	—
165	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
166	C₂²×C₈₉	C₂×#99	1	1	yes	characteristic
167	C₂²×C₈₉	#413	1	1	yes	characteristic
168	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
169	C₂²×C₈₉	#417	1	1	yes	characteristic
170	C₂²×C₈₉	C₂×#104	1	1	yes	characteristic
171	C₂²×C₈₉	#421	1	1	yes	characteristic
172	C₄×C₈₉	—	2	2	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	2	2	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	2	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	4	2	no	—
182	C₄×C₈₉	—	4	2	no	—
183	C₄×C₈₉	—	8	1	no	—
184	C₄×C₈₉	—	8	1	no	—
185	#7589	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂×C₈₉	—	2	4	no	—
187	C₂×C₈₉	#1459	1	1	yes	characteristic
188	C₂×C₈₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
189	C₂×C₈₉	#1477	1	1	yes	characteristic
190	C₂×C₈₉	#1504	1	1	yes	characteristic
191	C₂×C₈₉	#1520	1	1	yes	characteristic
192	C₂×C₈₉	#1532	1	1	yes	characteristic
193	C₂×C₈₉	#1550	1	1	yes	characteristic
194	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
195	#1797	C₂×C₈₉	1	1	yes	characteristic
196	C₂×#336	C₂×C₈₉	1	1	yes	characteristic
197	#1272	C₂×C₈₉	1	2	yes	complemented
198	#1271	C₂×C₈₉	1	2	yes	complemented
199	C₈₉	#7589	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×C₈	—	2	1	no	—
201	C₂×C₂²⋊Q₈	C₄×C₈₉	1	1	yes	characteristic
202	C₂×C₄×Q₈	C₄×C₈₉	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	2	1	no	—
205	C₂×C₂²⋊C₈	—	2	1	no	—
206	#391	C₂²×C₈₉	1	1	yes	characteristic
207	#389	C₂²×C₈₉	1	1	yes	characteristic
208	#387	—	2	1	no	—
209	#385	—	2	1	no	—
210	#380	C₄×C₈₉	1	1	yes	characteristic
211	C₄×C₄⋊C₄	—	2	1	no	—
212	C₄×C₄⋊C₄	C₄×C₈₉	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	—	2	1	no	—
214	#336	—	2	1	no	—
215	#336	C₂²×C₈₉	1	2	yes	—
216	#336	C₂²×C₈₉	1	2	yes	—
217	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	4	2	no	—
225	C₂²×C₈	—	4	2	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	C₈×C₈₉	1	4	yes	complemented
228	C₄×Q₈	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	4	2	no	—
240	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
244	C₄⋊C₈	—	4	2	no	—
245	C₂²⋊C₈	—	4	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	C₂⁴	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	4	1	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	C₂×C₈×C₈₉	1	2	yes	complemented
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₈×C₈₉	1	2	yes	—
272	C₂²×C₄	M₁₆×C₈₉	1	2	yes	—
273	C₂²×C₄	SD₁₆×C₈₉	1	2	yes	—
274	C₂²×C₄	Q₁₆×C₈₉	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	8	no	—
280	C₂×C₈	—	4	2	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	—	4	2	no	—
284	C₂×C₈	—	4	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	C₂×C₈×C₈₉	1	2	yes	complemented
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	C₂²⋊C₈×C₈₉	1	2	yes	—
306	C₂³	#103×C₈₉	1	2	yes	—
307	C₂³	#104×C₈₉	1	2	yes	—
308	C₂³	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
309	Q₈	—	4	2	no	—
310	Q₈	—	4	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂²⋊C₈×C₈₉	1	2	yes	—
342	C₂×C₄	#99×C₈₉	1	2	yes	—
343	C₂×C₄	#103×C₈₉	1	2	yes	—
344	C₂×C₄	C₂²×C₈×C₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂×M₁₆×C₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×Q₁₆×C₈₉	1	1	yes	characteristic
348	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
349	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
350	C₈	—	4	4	no	—
351	C₈	—	8	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	Q₈⋊C₈×C₈₉	1	4	yes	—
359	C₂²	C₂×C₂²⋊C₈×C₈₉	1	1	yes	characteristic
360	C₂²	C₂×#99×C₈₉	1	1	yes	characteristic
361	C₂²	#413×C₈₉	1	1	yes	characteristic
362	C₂²	C₂×#103×C₈₉	1	1	yes	characteristic
363	C₂²	#417×C₈₉	1	1	yes	characteristic
364	C₂²	C₂×#104×C₈₉	1	1	yes	characteristic
365	C₂²	#421×C₈₉	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₂	—	2	4	no	—
380	C₂	C₈₉×#1459	1	1	yes	characteristic
381	C₂	C₂×Q₈⋊C₈×C₈₉	1	1	yes	characteristic
382	C₂	C₈₉×#1477	1	1	yes	characteristic
383	C₂	C₈₉×#1504	1	1	yes	characteristic
384	C₂	C₈₉×#1520	1	1	yes	characteristic
385	C₂	C₈₉×#1532	1	1	yes	characteristic
386	C₂	C₈₉×#1550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂⁴×C₈₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1272	C₂	semidirect
5. C₈₉×#1271	C₂	semidirect
33. C₂²⋊Q₈×C₈₉	C₈	semidirect
61. C₂×Q₈×C₈₉	C₂×C₈	semidirect
98. C₄⋊C₄×C₈₉	C₂×C₈	semidirect
185. #7589	C₈₉	direct (N × H)
197. #1272	C₂×C₈₉	semidirect
198. #1271	C₂×C₈₉	semidirect
199. C₈₉	#7589	direct (N × H)
227. C₂²⋊Q₈	C₈×C₈₉	semidirect
255. C₂×Q₈	C₂×C₈×C₈₉	semidirect
292. C₄⋊C₄	C₂×C₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊Q₈×C₈₉	2
C₈₉×#1797	2
C₂×#336×C₈₉	2
C₈₉×#1272	2
C₈₉×#1271	2
#7589	89

Subgroups — C89×#7589 #36385437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7589 #36385437