Subgroups — C₈₉×#35246 #36413094

Order 22784.

2294 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2853	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2637	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2599	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2579	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2565	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2545	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2504	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2436	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2327	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2326	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	#529×C₈₉	—	2	8	no	—
19	C₂×#126×C₈₉	C₂²	1	2	yes	—
20	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
39	#398×C₈₉	C₂²	1	8	yes	—
40	#398×C₈₉	C₂²	1	4	yes	—
41	#397×C₈₉	C₂²	1	4	yes	—
42	#396×C₈₉	C₂²	1	8	yes	—
43	#395×C₈₉	C₂²	1	4	yes	—
44	#393×C₈₉	C₂²	1	4	yes	—
45	#391×C₈₉	C₂²	1	2	yes	—
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	2	yes	—
48	#390×C₈₉	C₂²	1	2	yes	—
49	#388×C₈₉	C₂²	1	8	yes	—
50	#388×C₈₉	C₂²	1	8	yes	—
51	#387×C₈₉	C₂²	1	8	yes	—
52	#387×C₈₉	C₂²	1	8	yes	—
53	#387×C₈₉	C₂²	1	8	yes	—
54	#386×C₈₉	C₂²	1	4	yes	—
55	#386×C₈₉	C₂²	1	4	yes	—
56	#385×C₈₉	C₂²	1	8	yes	—
57	#385×C₈₉	C₂²	1	4	yes	—
58	#385×C₈₉	C₂²	1	4	yes	—
59	#384×C₈₉	C₂²	1	2	yes	—
60	#383×C₈₉	C₂²	1	2	yes	—
61	#382×C₈₉	C₂²	1	2	yes	—
62	#382×C₈₉	C₂²	1	2	yes	—
63	#381×C₈₉	C₂²	1	2	yes	—
64	#380×C₈₉	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
68	#376×C₈₉	C₂²	1	2	yes	—
69	C₂²×Q₈×C₈₉	—	2	8	no	—
70	C₂²×Q₈×C₈₉	—	2	4	no	—
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	—	2	8	no	—
83	#126×C₈₉	—	2	8	no	—
84	#125×C₈₉	—	2	4	no	—
85	#124×C₈₉	—	2	8	no	—
86	#124×C₈₉	—	2	4	no	—
87	#123×C₈₉	—	2	8	no	—
88	C₂²⋊Q₈×C₈₉	—	2	4	no	—
89	#121×C₈₉	—	2	4	no	—
90	C₄×Q₈×C₈₉	—	2	8	no	—
91	C₄×Q₈×C₈₉	—	2	8	no	—
92	C₄×Q₈×C₈₉	—	2	8	no	—
93	C₄×Q₈×C₈₉	—	2	8	no	—
94	C₄×Q₈×C₈₉	—	2	4	no	—
95	C₄×D₄×C₈₉	—	2	8	no	—
96	C₄×D₄×C₈₉	—	2	4	no	—
97	#117×C₈₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
122	C₂×C₄²×C₈₉	—	2	8	no	—
123	C₂×C₄²×C₈₉	D₄	1	8	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	4	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	#95×C₈₉	C₂³	1	4	yes	—
134	#95×C₈₉	C₂³	1	4	yes	—
135	#95×C₈₉	C₂³	1	2	yes	—
136	#95×C₈₉	C₂³	1	2	yes	—
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	8	yes	—
139	#95×C₈₉	C₂³	1	8	yes	—
140	#95×C₈₉	C₂³	1	8	yes	—
141	#95×C₈₉	C₂³	1	8	yes	—
142	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
143	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂×Q₈×C₈₉	—	2	32	no	—
145	C₂×Q₈×C₈₉	—	2	4	no	—
146	C₂×Q₈×C₈₉	—	2	4	no	—
147	C₂×Q₈×C₈₉	—	2	2	no	—
148	C₂×Q₈×C₈₉	—	2	8	no	—
149	C₂×Q₈×C₈₉	—	2	4	no	—
150	C₂×Q₈×C₈₉	—	2	4	no	—
151	C₂×Q₈×C₈₉	#41	1	8	yes	—
152	C₂×D₄×C₈₉	—	2	4	no	—
153	C₂×D₄×C₈₉	—	2	8	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂×D₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	2	4	no	—
157	C₂²×C₄×C₈₉	—	2	4	no	—
158	C₂²×C₄×C₈₉	—	2	8	no	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	4	2	no	—
163	C₂²×C₄×C₈₉	—	4	4	no	—
164	C₂²×C₄×C₈₉	—	4	4	no	—
165	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₈₉	—	2	8	no	—
182	C₄⋊C₄×C₈₉	—	2	8	no	—
183	C₄⋊C₄×C₈₉	—	2	4	no	—
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	4	no	—
186	C₄⋊C₄×C₈₉	—	2	4	no	—
187	C₄⋊C₄×C₈₉	—	2	2	no	—
188	C₄⋊C₄×C₈₉	—	2	4	no	—
189	C₄⋊C₄×C₈₉	—	2	2	no	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	—	2	16	no	—
192	C₄⋊C₄×C₈₉	—	4	4	no	—
193	C₄⋊C₄×C₈₉	—	4	8	no	—
194	C₂²⋊C₄×C₈₉	—	2	4	no	—
195	C₂²⋊C₄×C₈₉	—	2	4	no	—
196	C₂²⋊C₄×C₈₉	—	2	4	no	—
197	C₂²⋊C₄×C₈₉	—	2	4	no	—
198	C₂²⋊C₄×C₈₉	—	2	4	no	—
199	C₂²⋊C₄×C₈₉	—	2	4	no	—
200	C₂²⋊C₄×C₈₉	—	2	4	no	—
201	C₂²⋊C₄×C₈₉	—	2	16	no	—
202	C₂²⋊C₄×C₈₉	—	4	8	no	—
203	C₄²×C₈₉	—	2	8	no	—
204	C₄²×C₈₉	—	2	8	no	—
205	C₄²×C₈₉	—	2	4	no	—
206	C₄²×C₈₉	—	2	4	no	—
207	C₄²×C₈₉	—	2	4	no	—
208	C₄²×C₈₉	C₂×D₄	1	4	yes	—
209	C₄²×C₈₉	C₂×D₄	1	4	yes	—
210	C₄²×C₈₉	C₂×D₄	1	4	yes	—
211	C₄²×C₈₉	C₂×D₄	1	4	yes	—
212	C₂³×C₈₉	—	2	2	no	—
213	C₂³×C₈₉	—	2	2	no	—
214	C₂³×C₈₉	—	2	2	no	—
215	C₂³×C₈₉	—	2	4	no	—
216	C₂³×C₈₉	—	2	4	no	—
217	C₂³×C₈₉	—	2	4	no	—
218	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
219	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
220	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
221	Q₈×C₈₉	—	2	16	no	—
222	Q₈×C₈₉	—	2	16	no	—
223	Q₈×C₈₉	—	4	4	no	—
224	D₄×C₈₉	—	4	8	no	—
225	D₄×C₈₉	—	4	4	no	—
226	C₂×C₄×C₈₉	—	2	16	no	—
227	C₂×C₄×C₈₉	—	2	8	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	2	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	2	no	—
232	C₂×C₄×C₈₉	—	2	2	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	8	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	4	no	—
241	C₂×C₄×C₈₉	—	2	4	no	—
242	C₂×C₄×C₈₉	—	2	4	no	—
243	C₂×C₄×C₈₉	—	2	4	no	—
244	C₂×C₄×C₈₉	—	2	4	no	—
245	C₂×C₄×C₈₉	—	2	4	no	—
246	C₂×C₄×C₈₉	—	2	4	no	—
247	C₂×C₄×C₈₉	—	2	8	no	—
248	C₂×C₄×C₈₉	—	2	4	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	4	4	no	—
251	C₂×C₄×C₈₉	—	4	8	no	—
252	C₂×C₄×C₈₉	—	4	8	no	—
253	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
260	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
261	C₂²×C₈₉	—	2	2	no	—
262	C₂²×C₈₉	—	2	2	no	—
263	C₂²×C₈₉	—	2	8	no	—
264	C₂²×C₈₉	—	4	2	no	—
265	C₂²×C₈₉	—	4	2	no	—
266	C₂²×C₈₉	—	4	2	no	—
267	C₂²×C₈₉	—	4	8	no	—
268	C₂²×C₈₉	#536	1	4	yes	—
269	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₈₉	C₂²×#41	1	2	yes	—
271	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
272	C₂²×C₈₉	#585	1	2	yes	—
273	C₄×C₈₉	—	2	2	no	—
274	C₄×C₈₉	—	2	8	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	2	2	no	—
278	C₄×C₈₉	—	2	2	no	—
279	C₄×C₈₉	—	4	2	no	—
280	C₄×C₈₉	—	4	2	no	—
281	C₄×C₈₉	—	4	4	no	—
282	C₄×C₈₉	—	4	2	no	—
283	C₄×C₈₉	—	4	4	no	—
284	C₄×C₈₉	—	4	4	no	—
285	C₄×C₈₉	#525	1	4	yes	—
286	#35246	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₈₉	—	2	4	no	—
288	C₂×C₈₉	—	8	2	no	—
289	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
290	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
291	C₂×C₈₉	#3449	1	1	yes	characteristic
292	C₂×C₈₉	#3516	1	4	yes	—
293	C₂×#529	C₂×C₈₉	1	1	yes	characteristic
294	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
295	#2853	C₂×C₈₉	1	4	yes	complemented
296	#2637	C₂×C₈₉	1	4	yes	complemented
297	#2599	C₂×C₈₉	1	4	yes	complemented
298	#2579	C₂×C₈₉	1	4	yes	complemented
299	#2565	C₂×C₈₉	1	2	yes	complemented
300	#2545	C₂×C₈₉	1	2	yes	complemented
301	#2504	C₂×C₈₉	1	1	yes	characteristic
302	#2502	C₂×C₈₉	1	1	yes	characteristic, complemented
303	#2436	C₂×C₈₉	1	1	yes	characteristic
304	#2434	C₂×C₈₉	1	1	yes	characteristic, complemented
305	#2327	C₂×C₈₉	1	2	yes	complemented
306	#2326	C₂×C₈₉	1	2	yes	complemented
307	#2283	C₂×C₈₉	1	1	yes	characteristic, complemented
308	C₈₉	#35246	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
310	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
311	#529	—	2	8	no	—
312	C₂×#126	C₂²×C₈₉	1	2	yes	—
313	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×#124	C₂²×C₈₉	1	2	yes	—
315	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
316	C₂×#123	C₂²×C₈₉	1	2	yes	—
317	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
318	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
319	C₂×C₄×Q₈	—	2	8	no	—
320	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
321	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
322	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
324	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
326	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₈₉	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
330	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
331	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
332	#398	C₂²×C₈₉	1	8	yes	—
333	#398	C₂²×C₈₉	1	4	yes	—
334	#397	C₂²×C₈₉	1	4	yes	—
335	#396	C₂²×C₈₉	1	8	yes	—
336	#395	C₂²×C₈₉	1	4	yes	—
337	#393	C₂²×C₈₉	1	4	yes	—
338	#391	C₂²×C₈₉	1	2	yes	—
339	#391	C₂²×C₈₉	1	2	yes	—
340	#391	C₂²×C₈₉	1	2	yes	—
341	#390	C₂²×C₈₉	1	2	yes	—
342	#388	C₂²×C₈₉	1	8	yes	—
343	#388	C₂²×C₈₉	1	8	yes	—
344	#387	C₂²×C₈₉	1	8	yes	—
345	#387	C₂²×C₈₉	1	8	yes	—
346	#387	C₂²×C₈₉	1	8	yes	—
347	#386	C₂²×C₈₉	1	4	yes	—
348	#386	C₂²×C₈₉	1	4	yes	—
349	#385	C₂²×C₈₉	1	8	yes	—
350	#385	C₂²×C₈₉	1	4	yes	—
351	#385	C₂²×C₈₉	1	4	yes	—
352	#384	C₂²×C₈₉	1	2	yes	—
353	#383	C₂²×C₈₉	1	2	yes	—
354	#382	C₂²×C₈₉	1	2	yes	—
355	#382	C₂²×C₈₉	1	2	yes	—
356	#381	C₂²×C₈₉	1	2	yes	—
357	#380	C₂²×C₈₉	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
360	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
361	#376	C₂²×C₈₉	1	2	yes	—
362	C₂²×Q₈	—	2	8	no	—
363	C₂²×Q₈	—	2	4	no	—
364	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
365	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
367	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
368	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
370	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
373	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
375	C₄⋊Q₈	—	2	8	no	—
376	#126	—	2	8	no	—
377	#125	—	2	4	no	—
378	#124	—	2	8	no	—
379	#124	—	2	4	no	—
380	#123	—	2	8	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	#121	—	2	4	no	—
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	8	no	—
386	C₄×Q₈	—	2	8	no	—
387	C₄×Q₈	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	4	no	—
390	#117	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	8	no	—
392	C₂×C₄⋊C₄	—	2	4	no	—
393	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
415	C₂×C₄²	—	2	8	no	—
416	C₂×C₄²	D₄×C₈₉	1	8	yes	—
417	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
418	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
419	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
420	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
421	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
422	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
426	#95	C₂³×C₈₉	1	4	yes	—
427	#95	C₂³×C₈₉	1	4	yes	—
428	#95	C₂³×C₈₉	1	2	yes	—
429	#95	C₂³×C₈₉	1	2	yes	—
430	#95	C₂³×C₈₉	1	4	yes	—
431	#95	C₂³×C₈₉	1	8	yes	—
432	#95	C₂³×C₈₉	1	8	yes	—
433	#95	C₂³×C₈₉	1	8	yes	—
434	#95	C₂³×C₈₉	1	8	yes	—
435	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
436	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
437	C₂×Q₈	—	2	32	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	8	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	#41×C₈₉	1	8	yes	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	16	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	—	4	8	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	16	no	—
495	C₂²⋊C₄	—	4	8	no	—
496	C₄²	—	2	8	no	—
497	C₄²	—	2	8	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	C₂×D₄×C₈₉	1	4	yes	—
502	C₄²	C₂×D₄×C₈₉	1	4	yes	—
503	C₄²	C₂×D₄×C₈₉	1	4	yes	—
504	C₄²	C₂×D₄×C₈₉	1	4	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
512	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
513	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
514	Q₈	—	2	16	no	—
515	Q₈	—	2	16	no	—
516	Q₈	—	4	4	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	4	no	—
519	C₂×C₄	—	2	16	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
552	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
553	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	8	no	—
561	C₂²	#536×C₈₉	1	4	yes	—
562	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
563	C₂²	C₂²×#41×C₈₉	1	2	yes	—
564	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
565	C₂²	#585×C₈₉	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	8	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	4	no	—
578	C₄	#525×C₈₉	1	4	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	8	2	no	—
581	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
582	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
583	C₂	C₈₉×#3449	1	1	yes	characteristic
584	C₂	C₈₉×#3516	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
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
2. C₂²×C₄×Q₈×C₈₉	C₂	semidirect
3. C₈₉×#2853	C₂	semidirect
4. C₈₉×#2637	C₂	semidirect
5. C₈₉×#2599	C₂	semidirect
6. C₈₉×#2579	C₂	semidirect
7. C₈₉×#2565	C₂	semidirect
8. C₈₉×#2545	C₂	semidirect
10. C₈₉×#2502	C₂	semidirect
12. C₈₉×#2434	C₂	semidirect
13. C₈₉×#2327	C₂	semidirect
14. C₈₉×#2326	C₂	semidirect
15. C₈₉×#2283	C₂	semidirect
286. #35246	C₈₉	direct (N × H)
294. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
295. #2853	C₂×C₈₉	semidirect
296. #2637	C₂×C₈₉	semidirect
297. #2599	C₂×C₈₉	semidirect
298. #2579	C₂×C₈₉	semidirect
299. #2565	C₂×C₈₉	semidirect
300. #2545	C₂×C₈₉	semidirect
302. #2502	C₂×C₈₉	semidirect
304. #2434	C₂×C₈₉	semidirect
305. #2327	C₂×C₈₉	semidirect
306. #2326	C₂×C₈₉	semidirect
307. #2283	C₂×C₈₉	semidirect
308. C₈₉	#35246	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2853	2
C₈₉×#2637	2
C₈₉×#2599	2
C₈₉×#2579	2
C₈₉×#2565	2
C₈₉×#2545	2
C₈₉×#2504	2
C₈₉×#2502	2
C₈₉×#2436	2
C₈₉×#2434	2
C₈₉×#2327	2
C₈₉×#2326	2
C₈₉×#2283	2
#35246	89

Subgroups — C89×#35246 #36413094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35246 #36413094