Subgroups — C₈₉×#36535 #36414383

Order 22784.

1590 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2864	C₂	1	2	yes	maximal
2	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2590	C₂	1	4	yes	maximal
4	C₈₉×#2588	C₂	1	4	yes	maximal
5	C₈₉×#2581	C₂	1	2	yes	maximal
6	C₈₉×#2571	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2570	C₂	1	2	yes	maximal
8	C₈₉×#2565	C₂	1	2	yes	maximal
9	C₈₉×#2552	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2550	C₂	1	2	yes	maximal
11	C₈₉×#2370	C₂	1	2	yes	maximal
12	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2355	C₂	1	2	yes	maximal
15	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₄×#125×C₈₉	C₂	1	2	yes	maximal
17	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#125×C₈₉	C₂²	1	2	yes	—
20	C₂×#125×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	#400×C₈₉	C₂²	1	4	yes	—
26	#400×C₈₉	C₂²	1	4	yes	—
27	#398×C₈₉	C₂²	1	4	yes	—
28	#398×C₈₉	C₂²	1	4	yes	—
29	#398×C₈₉	C₂²	1	4	yes	—
30	#395×C₈₉	C₂²	1	4	yes	—
31	#391×C₈₉	C₂²	1	4	yes	—
32	#391×C₈₉	C₂²	1	2	yes	—
33	#391×C₈₉	C₂²	1	2	yes	—
34	#391×C₈₉	C₂²	1	2	yes	—
35	#389×C₈₉	C₂²	1	2	yes	—
36	#389×C₈₉	C₂²	1	2	yes	—
37	#389×C₈₉	C₂²	1	4	yes	—
38	#389×C₈₉	C₂²	1	2	yes	—
39	#389×C₈₉	C₂²	1	2	yes	—
40	#389×C₈₉	C₂²	1	1	yes	characteristic
41	#389×C₈₉	C₂²	1	2	yes	—
42	#389×C₈₉	C₂²	1	2	yes	—
43	#389×C₈₉	C₂²	1	1	yes	characteristic
44	#389×C₈₉	C₂²	1	2	yes	—
45	#389×C₈₉	C₂²	1	2	yes	—
46	#389×C₈₉	C₂²	1	2	yes	—
47	#387×C₈₉	C₂²	1	4	yes	—
48	#387×C₈₉	C₂²	1	4	yes	—
49	#387×C₈₉	C₂²	1	4	yes	—
50	#387×C₈₉	C₂²	1	4	yes	—
51	#387×C₈₉	C₂²	1	4	yes	—
52	#387×C₈₉	C₂²	1	4	yes	—
53	#387×C₈₉	C₂²	1	4	yes	—
54	#387×C₈₉	C₂²	1	4	yes	—
55	#387×C₈₉	C₂²	1	4	yes	—
56	#387×C₈₉	C₂²	1	4	yes	—
57	#384×C₈₉	C₂²	1	2	yes	—
58	#384×C₈₉	C₂²	1	1	yes	characteristic
59	#384×C₈₉	C₂²	1	1	yes	characteristic
60	#384×C₈₉	C₂²	1	1	yes	characteristic
61	#382×C₈₉	C₂²	1	2	yes	—
62	#382×C₈₉	C₂²	1	2	yes	—
63	#382×C₈₉	C₂²	1	2	yes	—
64	#382×C₈₉	C₂²	1	2	yes	—
65	#382×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
72	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄³×C₈₉	C₂²	1	2	yes	—
82	C₄³×C₈₉	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
84	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	—	2	4	no	—
86	#125×C₈₉	—	2	8	no	—
87	#125×C₈₉	—	2	8	no	—
88	C₄×Q₈×C₈₉	—	2	4	no	—
89	C₄×Q₈×C₈₉	—	2	8	no	—
90	C₄×Q₈×C₈₉	—	2	4	no	—
91	C₄×Q₈×C₈₉	Q₈	1	8	yes	complemented
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	#95×C₈₉	C₂³	1	2	yes	—
137	#95×C₈₉	C₂³	1	2	yes	—
138	#95×C₈₉	C₂³	1	2	yes	—
139	#95×C₈₉	C₂³	1	2	yes	—
140	#95×C₈₉	C₂³	1	4	yes	—
141	#95×C₈₉	C₂³	1	4	yes	—
142	#95×C₈₉	C₂³	1	4	yes	—
143	#95×C₈₉	C₂³	1	4	yes	—
144	#95×C₈₉	C₂³	1	4	yes	—
145	#95×C₈₉	C₂³	1	2	yes	—
146	#95×C₈₉	C₂³	1	4	yes	—
147	#95×C₈₉	C₂³	1	4	yes	—
148	#95×C₈₉	C₂³	1	2	yes	—
149	#95×C₈₉	C₂³	1	2	yes	—
150	#95×C₈₉	C₂³	1	4	yes	—
151	#95×C₈₉	C₂³	1	4	yes	—
152	#95×C₈₉	C₂³	1	4	yes	—
153	#95×C₈₉	C₂³	1	4	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	C₂×Q₈×C₈₉	—	2	2	no	—
156	C₂×Q₈×C₈₉	—	2	2	no	—
157	C₂×Q₈×C₈₉	—	2	4	no	—
158	C₂×Q₈×C₈₉	—	2	4	no	—
159	C₂×Q₈×C₈₉	—	4	2	no	—
160	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₈₉	—	2	4	no	—
179	C₄⋊C₄×C₈₉	—	2	4	no	—
180	C₄⋊C₄×C₈₉	—	2	4	no	—
181	C₄⋊C₄×C₈₉	—	2	4	no	—
182	C₄⋊C₄×C₈₉	—	2	2	no	—
183	C₄⋊C₄×C₈₉	—	2	2	no	—
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	8	no	—
186	C₄⋊C₄×C₈₉	—	2	8	no	—
187	C₄⋊C₄×C₈₉	—	2	8	no	—
188	C₄⋊C₄×C₈₉	—	2	8	no	—
189	C₄⋊C₄×C₈₉	—	2	4	no	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	2	no	—
194	C₄⋊C₄×C₈₉	—	2	2	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₄⋊C₄×C₈₉	—	4	2	no	—
198	C₄⋊C₄×C₈₉	—	4	2	no	—
199	C₄⋊C₄×C₈₉	—	4	2	no	—
200	C₄⋊C₄×C₈₉	—	4	4	no	—
201	C₄⋊C₄×C₈₉	—	4	4	no	—
202	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
203	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
204	C₄⋊C₄×C₈₉	#41	1	4	yes	—
205	C₄²×C₈₉	—	2	4	no	—
206	C₄²×C₈₉	—	2	4	no	—
207	C₄²×C₈₉	—	2	4	no	—
208	C₄²×C₈₉	—	2	4	no	—
209	C₄²×C₈₉	—	2	4	no	—
210	C₄²×C₈₉	—	2	2	no	—
211	C₄²×C₈₉	—	2	2	no	—
212	C₄²×C₈₉	—	4	2	no	—
213	C₄²×C₈₉	—	4	2	no	—
214	C₄²×C₈₉	—	4	4	no	—
215	C₄²×C₈₉	—	4	1	no	—
216	C₄²×C₈₉	—	4	1	no	—
217	C₄²×C₈₉	—	4	4	no	—
218	C₄²×C₈₉	C₂×Q₈	1	8	yes	—
219	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
220	C₄²×C₈₉	#41	1	4	yes	—
221	C₄²×C₈₉	#41	1	4	yes	—
222	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
223	Q₈×C₈₉	—	2	8	no	—
224	Q₈×C₈₉	—	4	8	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	2	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	1	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	4	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	2	4	no	—
251	C₂×C₄×C₈₉	—	2	2	no	—
252	C₂×C₄×C₈₉	—	2	2	no	—
253	C₂×C₄×C₈₉	—	2	2	no	—
254	C₂×C₄×C₈₉	—	2	4	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	2	2	no	—
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	4	no	—
259	C₂×C₄×C₈₉	—	2	4	no	—
260	C₂×C₄×C₈₉	—	2	2	no	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
263	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
264	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
265	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
266	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
267	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
268	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
269	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
270	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
271	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
272	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
273	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
274	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
275	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
276	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
277	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
278	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
280	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
281	C₂²×C₈₉	#585	1	1	yes	characteristic
282	C₂²×C₈₉	#585	1	1	yes	characteristic
283	C₄×C₈₉	—	2	4	no	—
284	C₄×C₈₉	—	2	4	no	—
285	C₄×C₈₉	—	2	2	no	—
286	C₄×C₈₉	—	2	2	no	—
287	C₄×C₈₉	—	2	4	no	—
288	C₄×C₈₉	—	2	2	no	—
289	C₄×C₈₉	—	2	2	no	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	4	2	no	—
292	C₄×C₈₉	—	4	2	no	—
293	C₄×C₈₉	—	4	2	no	—
294	C₄×C₈₉	—	4	4	no	—
295	C₄×C₈₉	—	4	2	no	—
296	C₄×C₈₉	—	4	2	no	—
297	C₄×C₈₉	—	4	4	no	—
298	C₄×C₈₉	#533	1	4	yes	—
299	C₄×C₈₉	#557	1	4	yes	—
300	#36535	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
302	C₂×C₈₉	#3475	1	1	yes	characteristic
303	C₂×C₈₉	C₂×#557	1	1	yes	characteristic
304	C₂×C₈₉	#3480	1	1	yes	characteristic
305	C₂×C₈₉	#3504	1	1	yes	characteristic
306	C₂×C₈₉	#3507	1	1	yes	characteristic
307	C₂×C₈₉	#3507	1	1	yes	characteristic
308	#2864	C₂×C₈₉	1	2	yes	—
309	#2859	C₂×C₈₉	1	1	yes	characteristic
310	#2590	C₂×C₈₉	1	4	yes	—
311	#2588	C₂×C₈₉	1	4	yes	—
312	#2581	C₂×C₈₉	1	2	yes	—
313	#2571	C₂×C₈₉	1	1	yes	characteristic
314	#2570	C₂×C₈₉	1	2	yes	—
315	#2565	C₂×C₈₉	1	2	yes	—
316	#2552	C₂×C₈₉	1	1	yes	characteristic
317	#2550	C₂×C₈₉	1	2	yes	—
318	#2370	C₂×C₈₉	1	2	yes	—
319	#2355	C₂×C₈₉	1	2	yes	—
320	#2355	C₂×C₈₉	1	1	yes	characteristic
321	#2355	C₂×C₈₉	1	1	yes	characteristic
322	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
323	C₄×#125	C₂×C₈₉	1	2	yes	—
324	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic
325	C₈₉	#36535	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#125	C₂²×C₈₉	1	2	yes	—
328	C₂×#125	C₂²×C₈₉	1	2	yes	—
329	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
330	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
333	#400	C₂²×C₈₉	1	4	yes	—
334	#400	C₂²×C₈₉	1	4	yes	—
335	#398	C₂²×C₈₉	1	4	yes	—
336	#398	C₂²×C₈₉	1	4	yes	—
337	#398	C₂²×C₈₉	1	4	yes	—
338	#395	C₂²×C₈₉	1	4	yes	—
339	#391	C₂²×C₈₉	1	2	yes	—
340	#391	C₂²×C₈₉	1	2	yes	—
341	#391	C₂²×C₈₉	1	2	yes	—
342	#391	C₂²×C₈₉	1	4	yes	—
343	#389	C₂²×C₈₉	1	1	yes	characteristic
344	#389	C₂²×C₈₉	1	2	yes	—
345	#389	C₂²×C₈₉	1	2	yes	—
346	#389	C₂²×C₈₉	1	1	yes	characteristic
347	#389	C₂²×C₈₉	1	2	yes	—
348	#389	C₂²×C₈₉	1	2	yes	—
349	#389	C₂²×C₈₉	1	2	yes	—
350	#389	C₂²×C₈₉	1	2	yes	—
351	#389	C₂²×C₈₉	1	2	yes	—
352	#389	C₂²×C₈₉	1	2	yes	—
353	#389	C₂²×C₈₉	1	2	yes	—
354	#389	C₂²×C₈₉	1	4	yes	—
355	#387	C₂²×C₈₉	1	4	yes	—
356	#387	C₂²×C₈₉	1	4	yes	—
357	#387	C₂²×C₈₉	1	4	yes	—
358	#387	C₂²×C₈₉	1	4	yes	—
359	#387	C₂²×C₈₉	1	4	yes	—
360	#387	C₂²×C₈₉	1	4	yes	—
361	#387	C₂²×C₈₉	1	4	yes	—
362	#387	C₂²×C₈₉	1	4	yes	—
363	#387	C₂²×C₈₉	1	4	yes	—
364	#387	C₂²×C₈₉	1	4	yes	—
365	#384	C₂²×C₈₉	1	1	yes	characteristic
366	#384	C₂²×C₈₉	1	2	yes	—
367	#384	C₂²×C₈₉	1	1	yes	characteristic
368	#384	C₂²×C₈₉	1	1	yes	characteristic
369	#382	C₂²×C₈₉	1	2	yes	—
370	#382	C₂²×C₈₉	1	2	yes	—
371	#382	C₂²×C₈₉	1	2	yes	—
372	#382	C₂²×C₈₉	1	2	yes	—
373	#382	C₂²×C₈₉	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
376	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
377	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
382	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
384	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
385	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
386	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
387	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
388	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
389	C₄³	C₂²×C₈₉	1	2	yes	—
390	C₄³	C₂²×C₈₉	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
392	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
393	C₄⋊Q₈	—	2	4	no	—
394	#125	—	2	8	no	—
395	#125	—	2	8	no	—
396	C₄×Q₈	—	2	4	no	—
397	C₄×Q₈	—	2	8	no	—
398	C₄×Q₈	—	2	4	no	—
399	C₄×Q₈	Q₈×C₈₉	1	8	yes	complemented
400	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
428	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
429	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
430	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
431	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
432	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
435	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
439	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
440	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
441	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
444	#95	C₂³×C₈₉	1	2	yes	—
445	#95	C₂³×C₈₉	1	2	yes	—
446	#95	C₂³×C₈₉	1	2	yes	—
447	#95	C₂³×C₈₉	1	2	yes	—
448	#95	C₂³×C₈₉	1	4	yes	—
449	#95	C₂³×C₈₉	1	4	yes	—
450	#95	C₂³×C₈₉	1	4	yes	—
451	#95	C₂³×C₈₉	1	4	yes	—
452	#95	C₂³×C₈₉	1	4	yes	—
453	#95	C₂³×C₈₉	1	2	yes	—
454	#95	C₂³×C₈₉	1	4	yes	—
455	#95	C₂³×C₈₉	1	4	yes	—
456	#95	C₂³×C₈₉	1	2	yes	—
457	#95	C₂³×C₈₉	1	2	yes	—
458	#95	C₂³×C₈₉	1	4	yes	—
459	#95	C₂³×C₈₉	1	4	yes	—
460	#95	C₂³×C₈₉	1	4	yes	—
461	#95	C₂³×C₈₉	1	4	yes	—
462	#95	C₂³×C₈₉	1	4	yes	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	4	2	no	—
468	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	2	8	no	—
495	C₄⋊C₄	—	2	8	no	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	4	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
511	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
512	C₄⋊C₄	#41×C₈₉	1	4	yes	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	4	2	no	—
522	C₄²	—	4	4	no	—
523	C₄²	—	4	1	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	4	no	—
526	C₄²	C₂×Q₈×C₈₉	1	8	yes	—
527	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
528	C₄²	#41×C₈₉	1	4	yes	—
529	C₄²	#41×C₈₉	1	4	yes	—
530	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
531	Q₈	—	2	8	no	—
532	Q₈	—	4	8	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
571	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
572	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
573	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
574	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
575	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
576	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
577	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
578	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
579	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
580	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
581	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
582	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
583	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
584	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
585	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
586	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
587	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
588	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
589	C₂²	#585×C₈₉	1	1	yes	characteristic
590	C₂²	#585×C₈₉	1	1	yes	characteristic
591	C₄	—	2	4	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	4	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	4	no	—
606	C₄	#533×C₈₉	1	4	yes	—
607	C₄	#557×C₈₉	1	4	yes	—
608	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
609	C₂	C₈₉×#3475	1	1	yes	characteristic
610	C₂	C₂×#557×C₈₉	1	1	yes	characteristic
611	C₂	C₈₉×#3480	1	1	yes	characteristic
612	C₂	C₈₉×#3504	1	1	yes	characteristic
613	C₂	C₈₉×#3507	1	1	yes	characteristic
614	C₂	C₈₉×#3507	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
91. C₄×Q₈×C₈₉	Q₈	semidirect
300. #36535	C₈₉	direct (N × H)
325. C₈₉	#36535	direct (N × H)
399. C₄×Q₈	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2864	2
C₈₉×#2859	2
C₈₉×#2590	2
C₈₉×#2588	2
C₈₉×#2581	2
C₈₉×#2571	2
C₈₉×#2570	2
C₈₉×#2565	2
C₈₉×#2552	2
C₈₉×#2550	2
C₈₉×#2370	2
C₈₉×#2355	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#125×C₈₉	2
C₄²×Q₈×C₈₉	2
#36535	89

Subgroups — C89×#36535 #36414383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36535 #36414383