Subgroups — C₈₉×#8893 #36386741

Order 22784.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2354	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
9	C₂×#117×C₈₉	—	2	1	no	—
10	C₂×#106×C₈₉	—	2	1	no	—
11	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#102×C₈₉	—	2	1	no	—
14	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	#390×C₈₉	—	2	1	no	—
16	#388×C₈₉	—	2	2	no	—
17	#384×C₈₉	C₂²	1	1	yes	characteristic
18	#384×C₈₉	C₂²	1	1	yes	characteristic
19	#380×C₈₉	—	2	1	no	—
20	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	#340×C₈₉	—	2	1	no	—
23	#340×C₈₉	—	2	2	no	—
24	#340×C₈₉	—	2	1	no	—
25	D₄⋊C₈×C₈₉	C₄	1	4	yes	complemented
26	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₈₉	—	2	1	no	—
28	C₂²×C₈×C₈₉	—	2	1	no	—
29	C₂²×C₈×C₈₉	—	2	1	no	—
30	C₂²×C₈×C₈₉	—	2	1	no	—
31	C₄×D₄×C₈₉	—	2	1	no	—
32	C₄×D₄×C₈₉	—	2	1	no	—
33	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
34	C₄×D₄×C₈₉	Q₈	1	2	yes	—
35	#117×C₈₉	—	4	2	no	—
36	#117×C₈₉	—	4	2	no	—
37	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
49	C₂×C₄²×C₈₉	—	2	2	no	—
50	C₂×C₄²×C₈₉	—	2	1	no	—
51	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
52	#106×C₈₉	—	4	2	no	—
53	C₄⋊C₈×C₈₉	—	2	1	no	—
54	C₄⋊C₈×C₈₉	—	2	1	no	—
55	C₄⋊C₈×C₈₉	—	2	1	no	—
56	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
57	#102×C₈₉	—	4	2	no	—
58	C₄×C₈×C₈₉	—	2	1	no	—
59	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
60	#95×C₈₉	—	2	2	no	—
61	#95×C₈₉	—	2	1	no	—
62	C₂⁴×C₈₉	—	2	1	no	—
63	C₂×D₄×C₈₉	—	2	1	no	—
64	C₂×D₄×C₈₉	—	2	1	no	—
65	C₂×D₄×C₈₉	—	2	1	no	—
66	C₂×D₄×C₈₉	—	2	1	no	—
67	C₂×D₄×C₈₉	—	2	1	no	—
68	C₂×D₄×C₈₉	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₈₉	—	2	1	no	—
70	C₂²×C₄×C₈₉	—	2	1	no	—
71	C₂²×C₄×C₈₉	—	2	2	no	—
72	C₂²×C₄×C₈₉	—	2	2	no	—
73	C₂²×C₄×C₈₉	—	2	1	no	—
74	C₂²×C₄×C₈₉	—	2	2	no	—
75	C₂²×C₄×C₈₉	—	4	1	no	—
76	C₂²×C₄×C₈₉	—	4	1	no	—
77	C₂²×C₄×C₈₉	—	4	1	no	—
78	C₂²×C₄×C₈₉	—	4	1	no	—
79	C₂²×C₄×C₈₉	—	4	1	no	—
80	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₈₉	—	2	2	no	—
84	C₂×C₈×C₈₉	—	2	2	no	—
85	C₂×C₈×C₈₉	—	4	1	no	—
86	C₂×C₈×C₈₉	—	4	1	no	—
87	C₂×C₈×C₈₉	—	4	1	no	—
88	C₂×C₈×C₈₉	—	4	1	no	—
89	C₂×C₈×C₈₉	—	4	1	no	—
90	C₂×C₈×C₈₉	—	4	1	no	—
91	C₂×C₈×C₈₉	—	4	1	no	—
92	C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₄⋊C₄×C₈₉	—	4	2	no	—
97	C₄⋊C₄×C₈₉	—	4	2	no	—
98	C₄⋊C₄×C₈₉	—	4	1	no	—
99	C₄⋊C₄×C₈₉	—	4	1	no	—
100	C₄⋊C₄×C₈₉	—	4	1	no	—
101	C₄⋊C₄×C₈₉	—	4	1	no	—
102	C₄⋊C₄×C₈₉	—	4	1	no	—
103	C₄⋊C₄×C₈₉	—	4	1	no	—
104	C₄⋊C₄×C₈₉	—	4	1	no	—
105	C₄⋊C₄×C₈₉	—	4	1	no	—
106	C₄⋊C₄×C₈₉	C₄⋊C₄	1	2	yes	—
107	C₄⋊C₄×C₈₉	SD₁₆	1	2	yes	—
108	C₂²⋊C₄×C₈₉	—	2	2	no	—
109	C₂²⋊C₄×C₈₉	—	2	2	no	—
110	C₂²⋊C₄×C₈₉	—	4	4	no	—
111	C₂²⋊C₄×C₈₉	—	8	2	no	—
112	C₄²×C₈₉	—	4	4	no	—
113	C₄²×C₈₉	—	4	1	no	—
114	C₄²×C₈₉	—	4	1	no	—
115	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₈₉	#41	1	1	yes	characteristic
118	C₄²×C₈₉	#41	1	1	yes	characteristic
119	C₂³×C₈₉	—	2	2	no	—
120	C₂³×C₈₉	—	4	1	no	—
121	C₂³×C₈₉	—	4	1	no	—
122	C₂³×C₈₉	—	4	1	no	—
123	C₂³×C₈₉	—	4	1	no	—
124	C₂³×C₈₉	—	4	1	no	—
125	C₂³×C₈₉	—	4	1	no	—
126	C₂³×C₈₉	#120	1	1	yes	characteristic
127	D₄×C₈₉	—	2	2	no	—
128	D₄×C₈₉	—	2	2	no	—
129	D₄×C₈₉	—	4	1	no	—
130	D₄×C₈₉	—	4	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	—	2	2	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	4	1	no	—
136	C₂×C₄×C₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	1	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	8	1	no	—
150	C₂×C₄×C₈₉	—	8	1	no	—
151	C₂×C₄×C₈₉	—	8	1	no	—
152	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
166	C₈×C₈₉	—	4	2	no	—
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	—	8	1	no	—
169	C₂²×C₈₉	—	4	2	no	—
170	C₂²×C₈₉	—	4	2	no	—
171	C₂²×C₈₉	—	4	2	no	—
172	C₂²×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	—	8	1	no	—
174	C₂²×C₈₉	—	8	1	no	—
175	C₂²×C₈₉	—	8	1	no	—
176	C₂²×C₈₉	#385	1	1	yes	characteristic
177	C₂²×C₈₉	#449	1	1	yes	characteristic
178	C₂²×C₈₉	#449	1	1	yes	characteristic
179	C₂²×C₈₉	#450	1	1	yes	characteristic
180	C₂²×C₈₉	#452	1	1	yes	characteristic
181	C₂²×C₈₉	#454	1	1	yes	characteristic
182	C₂²×C₈₉	#455	1	1	yes	characteristic
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	4	2	no	—
186	C₄×C₈₉	—	4	2	no	—
187	C₄×C₈₉	—	8	2	no	—
188	C₄×C₈₉	—	8	1	no	—
189	C₄×C₈₉	—	16	1	no	—
190	C₄×C₈₉	#427	1	1	yes	characteristic
191	C₄×C₈₉	#428	1	1	yes	characteristic
192	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
193	C₄×C₈₉	#442	1	1	yes	characteristic
194	C₄×C₈₉	#476	1	1	yes	characteristic
195	C₄×C₈₉	#478	1	1	yes	characteristic
196	C₄×C₈₉	#482	1	1	yes	characteristic
197	C₄×C₈₉	#485	1	1	yes	characteristic
198	#8893	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₈₉	—	8	2	no	—
200	C₂×C₈₉	#1628	1	1	yes	characteristic
201	C₂×C₈₉	#1635	1	1	yes	characteristic
202	C₂×C₈₉	#1642	1	1	yes	characteristic
203	C₂×C₈₉	#1646	1	1	yes	characteristic
204	C₂×C₈₉	#1854	1	1	yes	characteristic
205	C₂×C₈₉	#1860	1	1	yes	characteristic
206	C₂×C₈₉	#1864	1	1	yes	characteristic
207	#2354	C₂×C₈₉	1	1	yes	characteristic
208	#1948	C₂×C₈₉	1	1	yes	characteristic, complemented
209	#1834	C₂×C₈₉	1	1	yes	characteristic, complemented
210	#1802	C₂×C₈₉	1	1	yes	characteristic
211	C₂×D₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic
212	#1296	C₂×C₈₉	1	1	yes	characteristic, complemented
213	#1279	C₂×C₈₉	1	1	yes	characteristic, complemented
214	C₈₉	#8893	1	1	yes	characteristic, direct product factor, Sylow
215	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
216	C₂×#117	—	2	1	no	—
217	C₂×#106	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
220	C₂×#102	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
222	#390	—	2	1	no	—
223	#388	—	2	2	no	—
224	#384	C₂²×C₈₉	1	1	yes	characteristic
225	#384	C₂²×C₈₉	1	1	yes	characteristic
226	#380	—	2	1	no	—
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
229	#340	—	2	1	no	—
230	#340	—	2	2	no	—
231	#340	—	2	1	no	—
232	D₄⋊C₈	C₄×C₈₉	1	4	yes	complemented
233	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	C₂×C₄×C₈₉	1	2	yes	—
241	C₄×D₄	Q₈×C₈₉	1	2	yes	—
242	#117	—	4	2	no	—
243	#117	—	4	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
252	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
259	#106	—	4	2	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	C₂×C₄×C₈₉	1	2	yes	—
264	#102	—	4	2	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	C₂×C₄×C₈₉	1	2	yes	—
267	#95	—	2	2	no	—
268	#95	—	2	1	no	—
269	C₂⁴	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₄⋊C₄×C₈₉	1	2	yes	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₄⋊C₄×C₈₉	1	2	yes	—
314	C₄⋊C₄	SD₁₆×C₈₉	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	8	2	no	—
319	C₄²	—	4	4	no	—
320	C₄²	—	4	1	no	—
321	C₄²	—	4	1	no	—
322	C₄²	C₂²×C₄×C₈₉	1	1	yes	characteristic
323	C₄²	C₂×Q₈×C₈₉	1	1	yes	characteristic
324	C₄²	#41×C₈₉	1	1	yes	characteristic
325	C₄²	#41×C₈₉	1	1	yes	characteristic
326	C₂³	—	2	2	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	#120×C₈₉	1	1	yes	characteristic
334	D₄	—	2	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	4	1	no	—
337	D₄	—	4	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	1	yes	characteristic
360	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
362	C₂×C₄	C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
363	C₂×C₄	C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
364	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
366	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
367	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
368	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
369	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
370	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
371	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
372	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	8	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	#385×C₈₉	1	1	yes	characteristic
384	C₂²	#449×C₈₉	1	1	yes	characteristic
385	C₂²	#449×C₈₉	1	1	yes	characteristic
386	C₂²	#450×C₈₉	1	1	yes	characteristic
387	C₂²	#452×C₈₉	1	1	yes	characteristic
388	C₂²	#454×C₈₉	1	1	yes	characteristic
389	C₂²	#455×C₈₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	16	1	no	—
397	C₄	#427×C₈₉	1	1	yes	characteristic
398	C₄	#428×C₈₉	1	1	yes	characteristic
399	C₄	C₄×SD₁₆×C₈₉	1	1	yes	characteristic
400	C₄	#442×C₈₉	1	1	yes	characteristic
401	C₄	#476×C₈₉	1	1	yes	characteristic
402	C₄	#478×C₈₉	1	1	yes	characteristic
403	C₄	#482×C₈₉	1	1	yes	characteristic
404	C₄	#485×C₈₉	1	1	yes	characteristic
405	C₂	—	8	2	no	—
406	C₂	C₈₉×#1628	1	1	yes	characteristic
407	C₂	C₈₉×#1635	1	1	yes	characteristic
408	C₂	C₈₉×#1642	1	1	yes	characteristic
409	C₂	C₈₉×#1646	1	1	yes	characteristic
410	C₂	C₈₉×#1854	1	1	yes	characteristic
411	C₂	C₈₉×#1860	1	1	yes	characteristic
412	C₂	C₈₉×#1864	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	#120
commutator	C₄²	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂²×D₄×C₈₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#1948	C₂	semidirect
3. C₈₉×#1834	C₂	semidirect
6. C₈₉×#1296	C₂	semidirect
7. C₈₉×#1279	C₂	semidirect
25. D₄⋊C₈×C₈₉	C₄	semidirect
198. #8893	C₈₉	direct (N × H)
208. #1948	C₂×C₈₉	semidirect
209. #1834	C₂×C₈₉	semidirect
212. #1296	C₂×C₈₉	semidirect
213. #1279	C₂×C₈₉	semidirect
214. C₈₉	#8893	direct (N × H)
232. D₄⋊C₈	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2354	2
C₈₉×#1948	2
C₈₉×#1834	2
C₈₉×#1802	2
C₂×D₄⋊C₈×C₈₉	2
C₈₉×#1296	2
C₈₉×#1279	2
#8893	89

Subgroups — C89×#8893 #36386741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#8893 #36386741