Subgroups — C₈₉×#22927 #36400775

Order 22784.

818 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	C₂×#483×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2362	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2345	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1894	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	#483×C₈₉	C₄	1	8	yes	complemented
22	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
33	#391×C₈₉	C₂²	1	1	yes	characteristic
34	#389×C₈₉	C₂²	1	1	yes	characteristic
35	#389×C₈₉	C₂²	1	1	yes	characteristic
36	#389×C₈₉	C₂²	1	1	yes	characteristic
37	#388×C₈₉	—	2	1	no	—
38	#388×C₈₉	—	2	1	no	—
39	#387×C₈₉	—	2	1	no	—
40	#387×C₈₉	—	2	1	no	—
41	#387×C₈₉	—	2	1	no	—
42	#380×C₈₉	—	2	1	no	—
43	#380×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
45	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
49	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
50	#340×C₈₉	C₂²	1	1	yes	characteristic
51	#340×C₈₉	C₂²	1	1	yes	characteristic
52	#340×C₈₉	C₂²	1	1	yes	characteristic
53	#340×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#340×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	#336×C₈₉	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	—	2	1	no	—
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₈₉	—	2	2	no	—
64	C₂×M₁₆×C₈₉	—	2	2	no	—
65	C₂×M₁₆×C₈₉	—	4	1	no	—
66	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²⋊Q₈×C₈₉	—	2	2	no	—
71	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₈₉	—	2	2	no	—
73	C₄×Q₈×C₈₉	—	4	1	no	—
74	#117×C₈₉	—	2	2	no	—
75	#117×C₈₉	—	4	1	no	—
76	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	—	2	1	no	—
98	C₂×C₄²×C₈₉	—	2	1	no	—
99	C₂×C₄²×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	#107×C₈₉	—	2	2	no	—
104	#106×C₈₉	—	4	1	no	—
105	#106×C₈₉	C₂×C₄	1	4	yes	—
106	#106×C₈₉	C₂×C₄	1	4	yes	—
107	#103×C₈₉	—	2	2	no	—
108	#103×C₈₉	—	4	1	no	—
109	#103×C₈₉	C₂×C₄	1	4	yes	—
110	#103×C₈₉	C₂×C₄	1	4	yes	—
111	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
112	#97×C₈₉	—	2	2	no	—
113	C₄×C₈×C₈₉	—	4	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	#95×C₈₉	—	2	1	no	—
116	#95×C₈₉	—	2	1	no	—
117	#95×C₈₉	—	2	1	no	—
118	#95×C₈₉	—	2	1	no	—
119	#95×C₈₉	—	2	1	no	—
120	#95×C₈₉	—	2	1	no	—
121	#95×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	1	no	—
123	#95×C₈₉	D₄	1	1	yes	characteristic
124	#95×C₈₉	D₄	1	1	yes	characteristic
125	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	1	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	—	2	1	no	—
139	C₂²×C₄×C₈₉	—	2	1	no	—
140	C₂²×C₄×C₈₉	—	2	1	no	—
141	C₂²×C₄×C₈₉	—	2	4	no	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	8	1	no	—
146	C₂²×C₄×C₈₉	—	8	1	no	—
147	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	#41	1	2	yes	—
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₈₉	—	4	4	no	—
156	C₂×C₈×C₈₉	—	2	1	no	—
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	1	no	—
159	C₂×C₈×C₈₉	—	2	1	no	—
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₈₉	#41	1	2	yes	—
168	C₄⋊C₄×C₈₉	—	2	4	no	—
169	C₄⋊C₄×C₈₉	—	2	4	no	—
170	C₄⋊C₄×C₈₉	—	2	1	no	—
171	C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₄⋊C₄×C₈₉	—	2	1	no	—
174	C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	4	2	no	—
181	C₄⋊C₄×C₈₉	—	4	2	no	—
182	C₄⋊C₄×C₈₉	—	8	1	no	—
183	C₄⋊C₄×C₈₉	—	8	1	no	—
184	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
185	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
186	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₈₉	#41	1	2	yes	—
188	C₂²⋊C₄×C₈₉	—	2	4	no	—
189	C₂²⋊C₄×C₈₉	—	2	2	no	—
190	C₂²⋊C₄×C₈₉	—	4	1	no	—
191	C₂²⋊C₄×C₈₉	—	4	2	no	—
192	C₂²⋊C₄×C₈₉	—	4	2	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	—	2	1	no	—
195	C₄²×C₈₉	—	2	1	no	—
196	C₄²×C₈₉	—	2	1	no	—
197	C₄²×C₈₉	—	4	2	no	—
198	C₄²×C₈₉	—	4	2	no	—
199	C₄²×C₈₉	—	4	2	no	—
200	C₄²×C₈₉	—	8	1	no	—
201	C₄²×C₈₉	—	8	1	no	—
202	C₂³×C₈₉	—	2	1	no	—
203	C₂³×C₈₉	—	2	1	no	—
204	C₂³×C₈₉	—	2	1	no	—
205	C₂³×C₈₉	—	2	1	no	—
206	C₂³×C₈₉	—	2	1	no	—
207	C₂³×C₈₉	—	2	1	no	—
208	C₂³×C₈₉	C₄×D₄	1	2	yes	—
209	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₈₉	—	2	2	no	—
211	Q₈×C₈₉	—	2	2	no	—
212	Q₈×C₈₉	—	4	1	no	—
213	Q₈×C₈₉	—	4	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	2	2	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	2	no	—
224	C₂×C₄×C₈₉	—	2	2	no	—
225	C₂×C₄×C₈₉	—	2	2	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	1	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	1	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	4	1	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	—	4	1	no	—
240	C₂×C₄×C₈₉	—	4	1	no	—
241	C₂×C₄×C₈₉	—	4	1	no	—
242	C₂×C₄×C₈₉	—	4	1	no	—
243	C₂×C₄×C₈₉	—	4	1	no	—
244	C₂×C₄×C₈₉	—	4	1	no	—
245	C₂×C₄×C₈₉	—	4	1	no	—
246	C₂×C₄×C₈₉	—	4	1	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	—	4	1	no	—
250	C₂×C₄×C₈₉	—	4	1	no	—
251	C₂×C₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	—	4	1	no	—
253	C₂×C₄×C₈₉	—	4	1	no	—
254	C₂×C₄×C₈₉	—	4	1	no	—
255	C₂×C₄×C₈₉	—	8	4	no	—
256	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₈₉	#137	1	2	yes	—
258	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
264	C₈×C₈₉	—	2	2	no	—
265	C₈×C₈₉	—	2	2	no	—
266	C₈×C₈₉	—	2	2	no	—
267	C₈×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	—	2	2	no	—
269	C₂²×C₈₉	—	2	2	no	—
270	C₂²×C₈₉	—	2	2	no	—
271	C₂²×C₈₉	—	4	1	no	—
272	C₂²×C₈₉	—	4	1	no	—
273	C₂²×C₈₉	—	4	1	no	—
274	C₂²×C₈₉	—	4	1	no	—
275	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₈₉	#546	1	1	yes	characteristic
277	C₂²×C₈₉	#547	1	1	yes	characteristic
278	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
279	C₂²×C₈₉	#575	1	1	yes	characteristic
280	C₂²×C₈₉	#577	1	1	yes	characteristic
281	C₂²×C₈₉	#577	1	1	yes	characteristic
282	C₄×C₈₉	—	2	2	no	—
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	4	1	no	—
285	C₄×C₈₉	—	4	1	no	—
286	C₄×C₈₉	—	4	2	no	—
287	C₄×C₈₉	—	4	2	no	—
288	C₄×C₈₉	—	4	2	no	—
289	C₄×C₈₉	—	4	2	no	—
290	C₄×C₈₉	—	4	1	no	—
291	C₄×C₈₉	—	4	2	no	—
292	C₄×C₈₉	—	8	1	no	—
293	C₄×C₈₉	—	8	1	no	—
294	C₄×C₈₉	—	8	1	no	—
295	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
296	C₄×C₈₉	#520	1	1	yes	characteristic
297	C₄×C₈₉	#551	1	1	yes	characteristic
298	C₄×C₈₉	#552	1	1	yes	characteristic
299	#22927	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂×C₈₉	—	4	2	no	—
301	C₂×C₈₉	#2359	1	1	yes	characteristic
302	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
303	C₂×C₈₉	#2949	1	1	yes	characteristic
304	C₂×C₈₉	#3307	1	1	yes	characteristic
305	C₂×C₈₉	#3316	1	1	yes	characteristic
306	C₂×C₈₉	#3351	1	1	yes	characteristic
307	C₂×C₈₉	#3356	1	1	yes	characteristic
308	C₂×#483	C₂×C₈₉	1	1	yes	characteristic
309	#2362	C₂×C₈₉	1	1	yes	characteristic
310	#2345	C₂×C₈₉	1	1	yes	characteristic
311	#1941	C₂×C₈₉	1	1	yes	characteristic, complemented
312	#1935	C₂×C₈₉	1	1	yes	characteristic, complemented
313	#1927	C₂×C₈₉	1	1	yes	characteristic, complemented
314	#1919	C₂×C₈₉	1	1	yes	characteristic, complemented
315	#1919	C₂×C₈₉	1	1	yes	characteristic, complemented
316	#1894	C₂×C₈₉	1	1	yes	characteristic
317	#1863	C₂×C₈₉	1	1	yes	characteristic, complemented
318	#1854	C₂×C₈₉	1	1	yes	characteristic
319	#1776	C₂×C₈₉	1	1	yes	characteristic, complemented
320	C₄×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
321	#1753	C₂×C₈₉	1	1	yes	characteristic
322	#1736	C₂×C₈₉	1	1	yes	characteristic
323	C₈₉	#22927	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
325	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
329	#483	C₄×C₈₉	1	8	yes	complemented
330	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
331	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
332	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
333	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
334	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
336	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
337	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
339	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
341	#391	C₂²×C₈₉	1	1	yes	characteristic
342	#389	C₂²×C₈₉	1	1	yes	characteristic
343	#389	C₂²×C₈₉	1	1	yes	characteristic
344	#389	C₂²×C₈₉	1	1	yes	characteristic
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#387	—	2	1	no	—
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#380	—	2	1	no	—
351	#380	C₂²×C₈₉	1	1	yes	characteristic
352	C₄×C₄⋊C₄	—	2	1	no	—
353	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
356	C₄×C₂²⋊C₄	—	2	1	no	—
357	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
358	#340	C₂²×C₈₉	1	1	yes	characteristic
359	#340	C₂²×C₈₉	1	1	yes	characteristic
360	#340	C₂²×C₈₉	1	1	yes	characteristic
361	#340	C₂²×C₈₉	1	1	yes	characteristic
362	#340	C₂²×C₈₉	1	1	yes	characteristic
363	#340	C₂²×C₈₉	1	1	yes	characteristic
364	#340	C₂²×C₈₉	1	1	yes	characteristic
365	#340	C₂²×C₈₉	1	1	yes	characteristic
366	#336	C₂²×C₈₉	1	1	yes	characteristic
367	#336	C₂²×C₈₉	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂×M₁₆	—	4	1	no	—
374	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	4	1	no	—
382	#117	—	2	2	no	—
383	#117	—	4	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#106	—	4	1	no	—
413	#106	C₂×C₄×C₈₉	1	4	yes	—
414	#106	C₂×C₄×C₈₉	1	4	yes	—
415	#103	—	2	2	no	—
416	#103	—	4	1	no	—
417	#103	C₂×C₄×C₈₉	1	4	yes	—
418	#103	C₂×C₄×C₈₉	1	4	yes	—
419	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
420	#97	—	2	2	no	—
421	C₄×C₈	—	4	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	D₄×C₈₉	1	1	yes	characteristic
432	#95	D₄×C₈₉	1	1	yes	characteristic
433	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	8	1	no	—
454	C₂²×C₄	—	8	1	no	—
455	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
461	C₂²×C₄	#41×C₈₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
463	M₁₆	—	4	4	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
474	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
475	C₂×C₈	#41×C₈₉	1	2	yes	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	8	1	no	—
491	C₄⋊C₄	—	8	1	no	—
492	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
493	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
494	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
495	C₄⋊C₄	#41×C₈₉	1	2	yes	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	8	1	no	—
509	C₄²	—	8	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	C₄×D₄×C₈₉	1	2	yes	—
517	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	8	4	no	—
564	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
565	C₂×C₄	#137×C₈₉	1	2	yes	—
566	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
568	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
570	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
571	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	2	2	no	—
574	C₈	—	2	2	no	—
575	C₈	—	4	1	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
584	C₂²	#546×C₈₉	1	1	yes	characteristic
585	C₂²	#547×C₈₉	1	1	yes	characteristic
586	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
587	C₂²	#575×C₈₉	1	1	yes	characteristic
588	C₂²	#577×C₈₉	1	1	yes	characteristic
589	C₂²	#577×C₈₉	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₄×#41×C₈₉	1	1	yes	characteristic
604	C₄	#520×C₈₉	1	1	yes	characteristic
605	C₄	#551×C₈₉	1	1	yes	characteristic
606	C₄	#552×C₈₉	1	1	yes	characteristic
607	C₂	—	4	2	no	—
608	C₂	C₈₉×#2359	1	1	yes	characteristic
609	C₂	C₄×#137×C₈₉	1	1	yes	characteristic
610	C₂	C₈₉×#2949	1	1	yes	characteristic
611	C₂	C₈₉×#3307	1	1	yes	characteristic
612	C₂	C₈₉×#3316	1	1	yes	characteristic
613	C₂	C₈₉×#3351	1	1	yes	characteristic
614	C₂	C₈₉×#3356	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₈₉×#1941	C₂	semidirect
5. C₈₉×#1935	C₂	semidirect
6. C₈₉×#1927	C₂	semidirect
7. C₈₉×#1919	C₂	semidirect
8. C₈₉×#1919	C₂	semidirect
10. C₈₉×#1863	C₂	semidirect
12. C₈₉×#1776	C₂	semidirect
13. C₄×#103×C₈₉	C₂	semidirect
21. #483×C₈₉	C₄	semidirect
299. #22927	C₈₉	direct (N × H)
311. #1941	C₂×C₈₉	semidirect
312. #1935	C₂×C₈₉	semidirect
313. #1927	C₂×C₈₉	semidirect
314. #1919	C₂×C₈₉	semidirect
315. #1919	C₂×C₈₉	semidirect
317. #1863	C₂×C₈₉	semidirect
319. #1776	C₂×C₈₉	semidirect
320. C₄×#103	C₂×C₈₉	semidirect
323. C₈₉	#22927	direct (N × H)
329. #483	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#483×C₈₉	2
C₈₉×#2362	2
C₈₉×#2345	2
C₈₉×#1941	2
C₈₉×#1935	2
C₈₉×#1927	2
C₈₉×#1919	2
C₈₉×#1894	2
C₈₉×#1863	2
C₈₉×#1854	2
C₈₉×#1776	2
C₄×#103×C₈₉	2
C₈₉×#1753	2
C₈₉×#1736	2
#22927	89

Subgroups — C89×#22927 #36400775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22927 #36400775