Subgroups — C₈₉×#26216 #36404064

Order 22784.

840 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2415	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1928	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, complemented
10	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1870	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₈₉	—	2	1	no	—
20	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#107×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×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
33	#397×C₈₉	—	2	1	no	—
34	#394×C₈₉	—	2	1	no	—
35	#391×C₈₉	C₂²	1	1	yes	characteristic
36	#389×C₈₉	—	2	1	no	—
37	#389×C₈₉	—	2	1	no	—
38	#389×C₈₉	C₂²	1	1	yes	characteristic
39	#388×C₈₉	—	2	1	no	—
40	#385×C₈₉	—	2	1	no	—
41	#385×C₈₉	—	2	1	no	—
42	#384×C₈₉	C₂²	1	1	yes	characteristic
43	#380×C₈₉	C₂²	1	1	yes	characteristic
44	#380×C₈₉	C₂²	1	1	yes	characteristic
45	#380×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
47	#340×C₈₉	C₂²	1	1	yes	characteristic
48	#340×C₈₉	C₂²	1	1	yes	characteristic
49	#340×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	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	—	2	1	no	—
62	C₂³×C₄×C₈₉	—	2	1	no	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₈₉	—	2	2	no	—
66	C₂×M₁₆×C₈₉	—	4	1	no	—
67	C₂×M₁₆×C₈₉	—	4	1	no	—
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²⋊Q₈×C₈₉	—	2	2	no	—
73	C₂²⋊Q₈×C₈₉	—	2	2	no	—
74	C₂²⋊Q₈×C₈₉	—	2	2	no	—
75	C₂²⋊Q₈×C₈₉	—	4	1	no	—
76	C₄×D₄×C₈₉	—	2	2	no	—
77	C₄×D₄×C₈₉	—	2	2	no	—
78	C₄×D₄×C₈₉	—	4	4	no	—
79	#117×C₈₉	—	2	2	no	—
80	#117×C₈₉	—	4	1	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
91	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
92	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	—	2	1	no	—
109	C₂×C₄²×C₈₉	—	2	1	no	—
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	#107×C₈₉	—	4	1	no	—
112	#106×C₈₉	—	2	2	no	—
113	#103×C₈₉	—	2	2	no	—
114	#103×C₈₉	—	4	1	no	—
115	#103×C₈₉	—	4	1	no	—
116	#103×C₈₉	—	4	1	no	—
117	C₂²⋊C₈×C₈₉	—	2	2	no	—
118	C₂²⋊C₈×C₈₉	—	4	1	no	—
119	C₂²⋊C₈×C₈₉	—	4	1	no	—
120	#95×C₈₉	—	2	1	no	—
121	#95×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	1	no	—
123	#95×C₈₉	—	2	1	no	—
124	#95×C₈₉	—	2	1	no	—
125	#95×C₈₉	—	2	1	no	—
126	#95×C₈₉	—	2	1	no	—
127	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	—	2	2	no	—
137	C₂×D₄×C₈₉	—	2	2	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	1	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	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	—	4	2	no	—
157	C₂²×C₄×C₈₉	—	4	2	no	—
158	C₂²×C₄×C₈₉	—	4	2	no	—
159	C₂²×C₄×C₈₉	—	4	2	no	—
160	C₂²×C₄×C₈₉	—	8	1	no	—
161	C₂²×C₄×C₈₉	—	8	1	no	—
162	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	#41	1	2	yes	—
167	C₂²×C₄×C₈₉	#41	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	M₁₆×C₈₉	—	4	4	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	—	2	1	no	—
172	C₂×C₈×C₈₉	—	2	1	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	2	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	—	2	1	no	—
185	C₄⋊C₄×C₈₉	—	2	1	no	—
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	4	2	no	—
196	C₄⋊C₄×C₈₉	—	4	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	2	no	—
201	C₄⋊C₄×C₈₉	—	8	1	no	—
202	C₄⋊C₄×C₈₉	#41	1	2	yes	—
203	C₄⋊C₄×C₈₉	#41	1	2	yes	—
204	C₂²⋊C₄×C₈₉	—	2	2	no	—
205	C₂²⋊C₄×C₈₉	—	2	2	no	—
206	C₂²⋊C₄×C₈₉	—	4	2	no	—
207	C₂²⋊C₄×C₈₉	—	4	2	no	—
208	C₂²⋊C₄×C₈₉	—	4	2	no	—
209	C₂²⋊C₄×C₈₉	—	4	2	no	—
210	C₂²⋊C₄×C₈₉	—	4	2	no	—
211	C₂²⋊C₄×C₈₉	—	4	2	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	—	2	1	no	—
214	C₄²×C₈₉	—	4	2	no	—
215	C₄²×C₈₉	—	4	2	no	—
216	C₂³×C₈₉	—	2	1	no	—
217	C₂³×C₈₉	—	2	1	no	—
218	C₂³×C₈₉	—	2	1	no	—
219	C₂³×C₈₉	—	2	1	no	—
220	C₂³×C₈₉	—	2	1	no	—
221	C₂³×C₈₉	—	2	1	no	—
222	C₂³×C₈₉	—	2	1	no	—
223	C₂³×C₈₉	—	2	1	no	—
224	C₂³×C₈₉	—	2	1	no	—
225	C₂³×C₈₉	—	2	1	no	—
226	C₂³×C₈₉	—	2	1	no	—
227	C₂³×C₈₉	—	2	1	no	—
228	C₂³×C₈₉	#123	1	2	yes	—
229	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
230	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₈₉	—	4	1	no	—
232	Q₈×C₈₉	—	4	1	no	—
233	Q₈×C₈₉	—	4	1	no	—
234	Q₈×C₈₉	—	4	1	no	—
235	D₄×C₈₉	—	2	8	no	—
236	C₂×C₄×C₈₉	—	2	1	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	2	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	1	no	—
245	C₂×C₄×C₈₉	—	2	1	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	1	no	—
249	C₂×C₄×C₈₉	—	2	1	no	—
250	C₂×C₄×C₈₉	—	2	1	no	—
251	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	1	no	—
258	C₂×C₄×C₈₉	—	4	1	no	—
259	C₂×C₄×C₈₉	—	4	1	no	—
260	C₂×C₄×C₈₉	—	4	1	no	—
261	C₂×C₄×C₈₉	—	4	1	no	—
262	C₂×C₄×C₈₉	—	4	1	no	—
263	C₂×C₄×C₈₉	—	4	1	no	—
264	C₂×C₄×C₈₉	—	4	1	no	—
265	C₂×C₄×C₈₉	—	4	1	no	—
266	C₂×C₄×C₈₉	—	4	1	no	—
267	C₂×C₄×C₈₉	—	4	1	no	—
268	C₂×C₄×C₈₉	—	4	1	no	—
269	C₂×C₄×C₈₉	—	4	1	no	—
270	C₂×C₄×C₈₉	—	4	1	no	—
271	C₂×C₄×C₈₉	—	4	1	no	—
272	C₂×C₄×C₈₉	—	4	1	no	—
273	C₂×C₄×C₈₉	—	4	1	no	—
274	C₂×C₄×C₈₉	—	4	1	no	—
275	C₂×C₄×C₈₉	—	4	1	no	—
276	C₂×C₄×C₈₉	—	4	1	no	—
277	C₂×C₄×C₈₉	—	4	1	no	—
278	C₂×C₄×C₈₉	—	8	4	no	—
279	C₂×C₄×C₈₉	—	8	4	no	—
280	C₂×C₄×C₈₉	#123	1	2	yes	—
281	C₂×C₄×C₈₉	#137	1	2	yes	—
282	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
288	C₈×C₈₉	—	4	1	no	—
289	C₈×C₈₉	—	4	1	no	—
290	C₈×C₈₉	—	4	1	no	—
291	C₈×C₈₉	—	4	1	no	—
292	C₂²×C₈₉	—	2	2	no	—
293	C₂²×C₈₉	—	2	2	no	—
294	C₂²×C₈₉	—	2	2	no	—
295	C₂²×C₈₉	—	2	2	no	—
296	C₂²×C₈₉	—	2	2	no	—
297	C₂²×C₈₉	—	2	2	no	—
298	C₂²×C₈₉	—	4	1	no	—
299	C₂²×C₈₉	—	4	1	no	—
300	C₂²×C₈₉	—	4	1	no	—
301	C₂²×C₈₉	—	4	1	no	—
302	C₂²×C₈₉	—	4	1	no	—
303	C₂²×C₈₉	—	4	1	no	—
304	C₂²×C₈₉	—	4	1	no	—
305	C₂²×C₈₉	—	4	1	no	—
306	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
307	C₂²×C₈₉	#546	1	1	yes	characteristic
308	C₂²×C₈₉	#546	1	1	yes	characteristic
309	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
311	C₂²×C₈₉	#577	1	1	yes	characteristic
312	C₂²×C₈₉	#578	1	1	yes	characteristic
313	C₄×C₈₉	—	2	2	no	—
314	C₄×C₈₉	—	2	2	no	—
315	C₄×C₈₉	—	4	2	no	—
316	C₄×C₈₉	—	4	1	no	—
317	C₄×C₈₉	—	4	1	no	—
318	C₄×C₈₉	—	4	2	no	—
319	C₄×C₈₉	—	8	1	no	—
320	C₄×C₈₉	—	8	1	no	—
321	C₄×C₈₉	—	8	1	no	—
322	C₄×C₈₉	—	8	1	no	—
323	C₄×C₈₉	—	8	1	no	—
324	C₄×C₈₉	—	8	1	no	—
325	C₄×C₈₉	#529	1	1	yes	characteristic
326	C₄×C₈₉	#538	1	1	yes	characteristic
327	C₄×C₈₉	#553	1	1	yes	characteristic
328	C₄×C₈₉	#553	1	1	yes	characteristic
329	#26216	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₈₉	—	4	2	no	—
331	C₂×C₈₉	—	4	2	no	—
332	C₂×C₈₉	#2444	1	1	yes	characteristic
333	C₂×C₈₉	#3092	1	1	yes	characteristic
334	C₂×C₈₉	#3097	1	1	yes	characteristic
335	C₂×C₈₉	#3308	1	1	yes	characteristic
336	C₂×C₈₉	#3310	1	1	yes	characteristic
337	C₂×C₈₉	#3328	1	1	yes	characteristic
338	C₂×C₈₉	#3331	1	1	yes	characteristic
339	#2415	C₂×C₈₉	1	1	yes	characteristic
340	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
341	#2100	C₂×C₈₉	1	1	yes	characteristic, complemented
342	#2075	C₂×C₈₉	1	1	yes	characteristic, complemented
343	#2072	C₂×C₈₉	1	1	yes	characteristic, complemented
344	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
345	#1928	C₂×C₈₉	1	1	yes	characteristic, complemented
346	#1919	C₂×C₈₉	1	1	yes	characteristic, complemented
347	#1894	C₂×C₈₉	1	1	yes	characteristic, complemented
348	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
349	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
350	#1870	C₂×C₈₉	1	1	yes	characteristic
351	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
352	#1823	C₂×C₈₉	1	1	yes	characteristic, complemented
353	#1736	C₂×C₈₉	1	1	yes	characteristic, complemented
354	C₈₉	#26216	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
356	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
360	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
361	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
362	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
363	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
364	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
370	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
372	#397	—	2	1	no	—
373	#394	—	2	1	no	—
374	#391	C₂²×C₈₉	1	1	yes	characteristic
375	#389	—	2	1	no	—
376	#389	—	2	1	no	—
377	#389	C₂²×C₈₉	1	1	yes	characteristic
378	#388	—	2	1	no	—
379	#385	—	2	1	no	—
380	#385	—	2	1	no	—
381	#384	C₂²×C₈₉	1	1	yes	characteristic
382	#380	C₂²×C₈₉	1	1	yes	characteristic
383	#380	C₂²×C₈₉	1	1	yes	characteristic
384	#380	C₂²×C₈₉	1	1	yes	characteristic
385	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
386	#340	C₂²×C₈₉	1	1	yes	characteristic
387	#340	C₂²×C₈₉	1	1	yes	characteristic
388	#340	C₂²×C₈₉	1	1	yes	characteristic
389	#340	C₂²×C₈₉	1	1	yes	characteristic
390	#340	C₂²×C₈₉	1	1	yes	characteristic
391	#340	C₂²×C₈₉	1	1	yes	characteristic
392	#340	C₂²×C₈₉	1	1	yes	characteristic
393	#340	C₂²×C₈₉	1	1	yes	characteristic
394	#340	C₂²×C₈₉	1	1	yes	characteristic
395	#340	C₂²×C₈₉	1	1	yes	characteristic
396	#336	C₂²×C₈₉	1	1	yes	characteristic
397	#336	C₂²×C₈₉	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
399	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	—	4	1	no	—
406	C₂×M₁₆	—	4	1	no	—
407	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	4	1	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	4	4	no	—
418	#117	—	2	2	no	—
419	#117	—	4	1	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	4	1	no	—
430	C₂×C₄⋊C₄	—	4	1	no	—
431	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
450	#107	—	4	1	no	—
451	#106	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	—	4	1	no	—
454	#103	—	4	1	no	—
455	#103	—	4	1	no	—
456	C₂²⋊C₈	—	2	2	no	—
457	C₂²⋊C₈	—	4	1	no	—
458	C₂²⋊C₈	—	4	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
467	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	8	1	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
505	C₂²×C₄	#41×C₈₉	1	2	yes	—
506	C₂²×C₄	#41×C₈₉	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
508	M₁₆	—	4	4	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	8	1	no	—
541	C₄⋊C₄	#41×C₈₉	1	2	yes	—
542	C₄⋊C₄	#41×C₈₉	1	2	yes	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	4	2	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	#123×C₈₉	1	2	yes	—
568	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
569	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	D₄	—	2	8	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	8	4	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	#123×C₈₉	1	2	yes	—
620	C₂×C₄	#137×C₈₉	1	2	yes	—
621	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
625	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
626	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
646	C₂²	#546×C₈₉	1	1	yes	characteristic
647	C₂²	#546×C₈₉	1	1	yes	characteristic
648	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
649	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
650	C₂²	#577×C₈₉	1	1	yes	characteristic
651	C₂²	#578×C₈₉	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	#529×C₈₉	1	1	yes	characteristic
665	C₄	#538×C₈₉	1	1	yes	characteristic
666	C₄	#553×C₈₉	1	1	yes	characteristic
667	C₄	#553×C₈₉	1	1	yes	characteristic
668	C₂	—	4	2	no	—
669	C₂	—	4	2	no	—
670	C₂	C₈₉×#2444	1	1	yes	characteristic
671	C₂	C₈₉×#3092	1	1	yes	characteristic
672	C₂	C₈₉×#3097	1	1	yes	characteristic
673	C₂	C₈₉×#3308	1	1	yes	characteristic
674	C₂	C₈₉×#3310	1	1	yes	characteristic
675	C₂	C₈₉×#3328	1	1	yes	characteristic
676	C₂	C₈₉×#3331	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₈₉×#2100	C₂	semidirect
4. C₈₉×#2075	C₂	semidirect
5. C₈₉×#2072	C₂	semidirect
6. C₈₉×#2035	C₂	semidirect
7. C₈₉×#1928	C₂	semidirect
8. C₈₉×#1919	C₂	semidirect
9. C₈₉×#1894	C₂	semidirect
10. C₈₉×#1872	C₂	semidirect
11. C₈₉×#1872	C₂	semidirect
13. C₈₉×#1854	C₂	semidirect
14. C₈₉×#1823	C₂	semidirect
15. C₈₉×#1736	C₂	semidirect
329. #26216	C₈₉	direct (N × H)
341. #2100	C₂×C₈₉	semidirect
342. #2075	C₂×C₈₉	semidirect
343. #2072	C₂×C₈₉	semidirect
344. #2035	C₂×C₈₉	semidirect
345. #1928	C₂×C₈₉	semidirect
346. #1919	C₂×C₈₉	semidirect
347. #1894	C₂×C₈₉	semidirect
348. #1872	C₂×C₈₉	semidirect
349. #1872	C₂×C₈₉	semidirect
351. #1854	C₂×C₈₉	semidirect
352. #1823	C₂×C₈₉	semidirect
353. #1736	C₂×C₈₉	semidirect
354. C₈₉	#26216	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2415	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#2100	2
C₈₉×#2075	2
C₈₉×#2072	2
C₈₉×#2035	2
C₈₉×#1928	2
C₈₉×#1919	2
C₈₉×#1894	2
C₈₉×#1872	2
C₈₉×#1870	2
C₈₉×#1854	2
C₈₉×#1823	2
C₈₉×#1736	2
#26216	89

Subgroups — C89×#26216 #36404064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26216 #36404064