Subgroups — C₈₉×#25334 #36403182

Order 22784.

928 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
22	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	#489×C₈₉	—	2	4	no	—
26	#463×C₈₉	—	2	4	no	—
27	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
39	#399×C₈₉	—	2	1	no	—
40	#399×C₈₉	—	2	1	no	—
41	#391×C₈₉	C₂²	1	1	yes	characteristic
42	#390×C₈₉	C₂²	1	1	yes	characteristic
43	#390×C₈₉	C₂²	1	1	yes	characteristic
44	#390×C₈₉	C₂²	1	1	yes	characteristic
45	#388×C₈₉	—	2	1	no	—
46	#388×C₈₉	—	2	1	no	—
47	#385×C₈₉	—	2	1	no	—
48	#384×C₈₉	C₂²	1	1	yes	characteristic
49	#384×C₈₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₈₉	—	2	1	no	—
62	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	—	2	1	no	—
67	C₂×SD₁₆×C₈₉	—	2	2	no	—
68	C₂×SD₁₆×C₈₉	—	2	2	no	—
69	C₂×SD₁₆×C₈₉	—	4	1	no	—
70	C₂×D₈×C₈₉	—	2	2	no	—
71	C₂×D₈×C₈₉	—	2	2	no	—
72	C₂×D₈×C₈₉	—	4	1	no	—
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₈₉	—	2	2	no	—
78	C₄⋊Q₈×C₈₉	—	2	2	no	—
79	#124×C₈₉	—	2	2	no	—
80	#124×C₈₉	D₄	1	4	yes	—
81	C₂²⋊Q₈×C₈₉	—	4	4	no	—
82	C₂²⋊Q₈×C₈₉	—	4	4	no	—
83	C₄×Q₈×C₈₉	—	2	2	no	—
84	C₄×Q₈×C₈₉	—	4	1	no	—
85	C₄×D₄×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	—	2	2	no	—
87	C₄×D₄×C₈₉	—	2	2	no	—
88	C₄×D₄×C₈₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	D₄	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×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄²×C₈₉	—	2	1	no	—
113	C₂×C₄²×C₈₉	—	2	1	no	—
114	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₈₉	—	2	2	no	—
118	C₄⋊C₈×C₈₉	—	4	1	no	—
119	C₄⋊C₈×C₈₉	—	4	1	no	—
120	#103×C₈₉	—	2	2	no	—
121	#103×C₈₉	—	2	2	no	—
122	#103×C₈₉	—	2	2	no	—
123	#102×C₈₉	—	2	2	no	—
124	#102×C₈₉	—	2	2	no	—
125	#102×C₈₉	—	2	2	no	—
126	#102×C₈₉	—	2	2	no	—
127	#102×C₈₉	—	2	2	no	—
128	#97×C₈₉	—	2	2	no	—
129	#95×C₈₉	—	2	1	no	—
130	#95×C₈₉	—	2	1	no	—
131	#95×C₈₉	—	2	1	no	—
132	#95×C₈₉	D₄	1	1	yes	characteristic
133	#95×C₈₉	D₄	1	1	yes	characteristic
134	C₂⁴×C₈₉	—	2	1	no	—
135	C₂⁴×C₈₉	—	2	1	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×Q₈×C₈₉	—	2	1	no	—
141	C₂×Q₈×C₈₉	—	4	2	no	—
142	C₂×Q₈×C₈₉	—	4	2	no	—
143	C₂×Q₈×C₈₉	—	4	2	no	—
144	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	—	2	1	no	—
147	C₂×D₄×C₈₉	—	2	1	no	—
148	C₂×D₄×C₈₉	—	2	1	no	—
149	C₂×D₄×C₈₉	—	2	1	no	—
150	C₂×D₄×C₈₉	—	2	1	no	—
151	C₂×D₄×C₈₉	—	2	1	no	—
152	C₂×D₄×C₈₉	—	2	1	no	—
153	C₂×D₄×C₈₉	—	2	1	no	—
154	C₂×D₄×C₈₉	—	2	1	no	—
155	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₈₉	#41	1	2	yes	—
157	C₂²×C₄×C₈₉	—	2	1	no	—
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	4	2	no	—
164	C₂²×C₄×C₈₉	—	4	2	no	—
165	C₂²×C₄×C₈₉	—	4	2	no	—
166	C₂²×C₄×C₈₉	—	4	2	no	—
167	C₂²×C₄×C₈₉	—	4	2	no	—
168	C₂²×C₄×C₈₉	—	8	1	no	—
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	SD₁₆×C₈₉	—	4	4	no	—
177	D₈×C₈₉	—	4	4	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	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	—	2	1	no	—
188	C₂×C₈×C₈₉	—	2	1	no	—
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	2	no	—
191	C₄⋊C₄×C₈₉	—	2	2	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	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄⋊C₄×C₈₉	—	2	1	no	—
199	C₄⋊C₄×C₈₉	—	2	1	no	—
200	C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₄⋊C₄×C₈₉	—	4	2	no	—
202	C₄⋊C₄×C₈₉	—	4	2	no	—
203	C₄⋊C₄×C₈₉	—	4	2	no	—
204	C₄⋊C₄×C₈₉	—	4	2	no	—
205	C₄⋊C₄×C₈₉	—	4	2	no	—
206	C₄⋊C₄×C₈₉	—	4	2	no	—
207	C₄⋊C₄×C₈₉	#41	1	2	yes	—
208	C₂²⋊C₄×C₈₉	—	2	4	no	—
209	C₂²⋊C₄×C₈₉	—	2	4	no	—
210	C₂²⋊C₄×C₈₉	—	4	2	no	—
211	C₂²⋊C₄×C₈₉	—	4	2	no	—
212	C₂²⋊C₄×C₈₉	—	4	2	no	—
213	C₂²⋊C₄×C₈₉	—	4	2	no	—
214	C₂²⋊C₄×C₈₉	—	4	2	no	—
215	C₂²⋊C₄×C₈₉	—	4	2	no	—
216	C₂²⋊C₄×C₈₉	—	4	2	no	—
217	C₂²⋊C₄×C₈₉	—	8	1	no	—
218	C₄²×C₈₉	—	2	1	no	—
219	C₄²×C₈₉	—	2	1	no	—
220	C₄²×C₈₉	—	2	1	no	—
221	C₄²×C₈₉	—	2	1	no	—
222	C₄²×C₈₉	—	4	2	no	—
223	C₄²×C₈₉	—	8	1	no	—
224	C₄²×C₈₉	C₂×D₄	1	2	yes	—
225	C₄²×C₈₉	#41	1	2	yes	—
226	C₂³×C₈₉	—	2	2	no	—
227	C₂³×C₈₉	—	2	2	no	—
228	C₂³×C₈₉	—	4	1	no	—
229	C₂³×C₈₉	—	4	1	no	—
230	C₂³×C₈₉	—	4	1	no	—
231	C₂³×C₈₉	—	4	1	no	—
232	C₂³×C₈₉	—	4	1	no	—
233	C₂³×C₈₉	—	4	1	no	—
234	C₂³×C₈₉	—	4	1	no	—
235	C₂³×C₈₉	—	4	1	no	—
236	C₂³×C₈₉	—	4	1	no	—
237	C₂³×C₈₉	—	4	1	no	—
238	C₂³×C₈₉	—	4	1	no	—
239	C₂³×C₈₉	—	4	1	no	—
240	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₈₉	—	2	2	no	—
242	Q₈×C₈₉	—	2	2	no	—
243	Q₈×C₈₉	—	4	1	no	—
244	Q₈×C₈₉	—	4	1	no	—
245	Q₈×C₈₉	—	8	4	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	2	2	no	—
248	D₄×C₈₉	—	2	2	no	—
249	D₄×C₈₉	—	2	2	no	—
250	D₄×C₈₉	—	4	1	no	—
251	D₄×C₈₉	—	4	1	no	—
252	D₄×C₈₉	—	4	1	no	—
253	D₄×C₈₉	—	4	1	no	—
254	C₂×C₄×C₈₉	—	2	1	no	—
255	C₂×C₄×C₈₉	—	2	1	no	—
256	C₂×C₄×C₈₉	—	2	1	no	—
257	C₂×C₄×C₈₉	—	2	1	no	—
258	C₂×C₄×C₈₉	—	2	1	no	—
259	C₂×C₄×C₈₉	—	2	1	no	—
260	C₂×C₄×C₈₉	—	2	1	no	—
261	C₂×C₄×C₈₉	—	2	1	no	—
262	C₂×C₄×C₈₉	—	2	2	no	—
263	C₂×C₄×C₈₉	—	2	1	no	—
264	C₂×C₄×C₈₉	—	2	1	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	1	no	—
267	C₂×C₄×C₈₉	—	2	1	no	—
268	C₂×C₄×C₈₉	—	2	1	no	—
269	C₂×C₄×C₈₉	—	2	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	—	4	1	no	—
279	C₂×C₄×C₈₉	—	4	1	no	—
280	C₂×C₄×C₈₉	—	4	1	no	—
281	C₂×C₄×C₈₉	—	4	1	no	—
282	C₂×C₄×C₈₉	—	4	1	no	—
283	C₂×C₄×C₈₉	—	4	1	no	—
284	C₂×C₄×C₈₉	—	4	1	no	—
285	C₂×C₄×C₈₉	—	4	1	no	—
286	C₂×C₄×C₈₉	—	8	4	no	—
287	C₂×C₄×C₈₉	—	8	4	no	—
288	C₂×C₄×C₈₉	#121	1	2	yes	—
289	C₂×C₄×C₈₉	#121	1	2	yes	—
290	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
291	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
292	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₈₉	—	4	1	no	—
299	C₈×C₈₉	—	4	1	no	—
300	C₈×C₈₉	—	4	1	no	—
301	C₈×C₈₉	—	4	1	no	—
302	C₂²×C₈₉	—	4	2	no	—
303	C₂²×C₈₉	—	4	2	no	—
304	C₂²×C₈₉	—	4	2	no	—
305	C₂²×C₈₉	—	4	2	no	—
306	C₂²×C₈₉	—	4	2	no	—
307	C₂²×C₈₉	—	4	2	no	—
308	C₂²×C₈₉	—	8	1	no	—
309	C₂²×C₈₉	—	8	1	no	—
310	C₂²×C₈₉	—	8	1	no	—
311	C₂²×C₈₉	—	8	1	no	—
312	C₂²×C₈₉	—	8	1	no	—
313	C₂²×C₈₉	—	8	1	no	—
314	C₂²×C₈₉	—	8	1	no	—
315	C₂²×C₈₉	—	8	1	no	—
316	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
317	C₂²×C₈₉	#546	1	1	yes	characteristic
318	C₂²×C₈₉	#548	1	1	yes	characteristic
319	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₂²×C₈₉	#577	1	1	yes	characteristic
322	C₂²×C₈₉	#578	1	1	yes	characteristic
323	C₄×C₈₉	—	2	2	no	—
324	C₄×C₈₉	—	2	2	no	—
325	C₄×C₈₉	—	2	2	no	—
326	C₄×C₈₉	—	2	2	no	—
327	C₄×C₈₉	—	4	2	no	—
328	C₄×C₈₉	—	4	1	no	—
329	C₄×C₈₉	—	4	2	no	—
330	C₄×C₈₉	—	4	1	no	—
331	C₄×C₈₉	—	8	1	no	—
332	C₄×C₈₉	—	8	1	no	—
333	C₄×C₈₉	—	8	1	no	—
334	C₄×C₈₉	—	8	1	no	—
335	C₄×C₈₉	#529	1	1	yes	characteristic
336	C₄×C₈₉	#542	1	1	yes	characteristic
337	C₄×C₈₉	#546	1	1	yes	characteristic
338	C₄×C₈₉	#547	1	1	yes	characteristic
339	#25334	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂×C₈₉	—	8	2	no	—
341	C₂×C₈₉	—	8	2	no	—
342	C₂×C₈₉	#2427	1	1	yes	characteristic
343	C₂×C₈₉	#3038	1	1	yes	characteristic
344	C₂×C₈₉	#3046	1	1	yes	characteristic
345	C₂×C₈₉	#3306	1	1	yes	characteristic
346	C₂×C₈₉	#3308	1	1	yes	characteristic
347	C₂×C₈₉	#3367	1	1	yes	characteristic
348	C₂×C₈₉	#3373	1	1	yes	characteristic
349	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
350	C₂×#463	C₂×C₈₉	1	1	yes	characteristic
351	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
352	#2367	C₂×C₈₉	1	1	yes	characteristic, complemented
353	#2072	C₂×C₈₉	1	1	yes	characteristic, complemented
354	#2071	C₂×C₈₉	1	1	yes	characteristic, complemented
355	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
356	#2054	C₂×C₈₉	1	1	yes	characteristic
357	#1987	C₂×C₈₉	1	1	yes	characteristic, complemented
358	#1940	C₂×C₈₉	1	1	yes	characteristic, complemented
359	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
360	#1879	C₂×C₈₉	1	1	yes	characteristic
361	#1803	C₂×C₈₉	1	1	yes	characteristic, complemented
362	#1802	C₂×C₈₉	1	1	yes	characteristic, complemented
363	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
364	C₈₉	#25334	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
366	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
367	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
368	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	—	2	1	no	—
370	C₂×C₂²⋊Q₈	—	2	1	no	—
371	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
374	#489	—	2	4	no	—
375	#463	—	2	4	no	—
376	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
382	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
383	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
387	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
388	#399	—	2	1	no	—
389	#399	—	2	1	no	—
390	#391	C₂²×C₈₉	1	1	yes	characteristic
391	#390	C₂²×C₈₉	1	1	yes	characteristic
392	#390	C₂²×C₈₉	1	1	yes	characteristic
393	#390	C₂²×C₈₉	1	1	yes	characteristic
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#385	—	2	1	no	—
397	#384	C₂²×C₈₉	1	1	yes	characteristic
398	#384	C₂²×C₈₉	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
400	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
401	C₄×C₂²⋊C₄	—	2	1	no	—
402	#340	C₂²×C₈₉	1	1	yes	characteristic
403	#340	C₂²×C₈₉	1	1	yes	characteristic
404	#340	C₂²×C₈₉	1	1	yes	characteristic
405	#340	C₂²×C₈₉	1	1	yes	characteristic
406	#340	C₂²×C₈₉	1	1	yes	characteristic
407	#340	C₂²×C₈₉	1	1	yes	characteristic
408	#336	C₂²×C₈₉	1	1	yes	characteristic
409	#336	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂×SD₁₆	—	2	2	no	—
417	C₂×SD₁₆	—	2	2	no	—
418	C₂×SD₁₆	—	4	1	no	—
419	C₂×D₈	—	2	2	no	—
420	C₂×D₈	—	2	2	no	—
421	C₂×D₈	—	4	1	no	—
422	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	2	no	—
428	#124	—	2	2	no	—
429	#124	D₄×C₈₉	1	4	yes	—
430	C₂²⋊Q₈	—	4	4	no	—
431	C₂²⋊Q₈	—	4	4	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	4	1	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	4	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
466	C₄⋊C₈	—	2	2	no	—
467	C₄⋊C₈	—	4	1	no	—
468	C₄⋊C₈	—	4	1	no	—
469	#103	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#102	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	—	2	2	no	—
476	#102	—	2	2	no	—
477	#97	—	2	2	no	—
478	#95	—	2	1	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	D₄×C₈₉	1	1	yes	characteristic
482	#95	D₄×C₈₉	1	1	yes	characteristic
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	2	no	—
492	C₂×Q₈	—	4	2	no	—
493	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
505	C₂×D₄	#41×C₈₉	1	2	yes	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	8	1	no	—
518	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
525	SD₁₆	—	4	4	no	—
526	D₈	—	4	4	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	#41×C₈₉	1	2	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	8	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	8	1	no	—
573	C₄²	C₂×D₄×C₈₉	1	2	yes	—
574	C₄²	#41×C₈₉	1	2	yes	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
590	Q₈	—	2	2	no	—
591	Q₈	—	2	2	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	8	4	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	2	no	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	8	4	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	#121×C₈₉	1	2	yes	—
638	C₂×C₄	#121×C₈₉	1	2	yes	—
639	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
640	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
641	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
643	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
644	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
645	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
646	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
666	C₂²	#546×C₈₉	1	1	yes	characteristic
667	C₂²	#548×C₈₉	1	1	yes	characteristic
668	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
669	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
670	C₂²	#577×C₈₉	1	1	yes	characteristic
671	C₂²	#578×C₈₉	1	1	yes	characteristic
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	1	no	—
680	C₄	—	8	1	no	—
681	C₄	—	8	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	#529×C₈₉	1	1	yes	characteristic
685	C₄	#542×C₈₉	1	1	yes	characteristic
686	C₄	#546×C₈₉	1	1	yes	characteristic
687	C₄	#547×C₈₉	1	1	yes	characteristic
688	C₂	—	8	2	no	—
689	C₂	—	8	2	no	—
690	C₂	C₈₉×#2427	1	1	yes	characteristic
691	C₂	C₈₉×#3038	1	1	yes	characteristic
692	C₂	C₈₉×#3046	1	1	yes	characteristic
693	C₂	C₈₉×#3306	1	1	yes	characteristic
694	C₂	C₈₉×#3308	1	1	yes	characteristic
695	C₂	C₈₉×#3367	1	1	yes	characteristic
696	C₂	C₈₉×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₈×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₄⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#489×C₈₉	C₂	semidirect
3. C₈₉×#2542	C₂	semidirect
4. C₈₉×#2367	C₂	semidirect
5. C₈₉×#2072	C₂	semidirect
6. C₈₉×#2071	C₂	semidirect
7. C₈₉×#2055	C₂	semidirect
9. C₈₉×#1987	C₂	semidirect
10. C₈₉×#1940	C₂	semidirect
11. C₈₉×#1880	C₂	semidirect
13. C₈₉×#1803	C₂	semidirect
14. C₈₉×#1802	C₂	semidirect
15. C₈₉×#1762	C₂	semidirect
339. #25334	C₈₉	direct (N × H)
349. C₂×#489	C₂×C₈₉	semidirect
351. #2542	C₂×C₈₉	semidirect
352. #2367	C₂×C₈₉	semidirect
353. #2072	C₂×C₈₉	semidirect
354. #2071	C₂×C₈₉	semidirect
355. #2055	C₂×C₈₉	semidirect
357. #1987	C₂×C₈₉	semidirect
358. #1940	C₂×C₈₉	semidirect
359. #1880	C₂×C₈₉	semidirect
361. #1803	C₂×C₈₉	semidirect
362. #1802	C₂×C₈₉	semidirect
363. #1762	C₂×C₈₉	semidirect
364. C₈₉	#25334	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×#489×C₈₉	2
C₂×#463×C₈₉	2
C₈₉×#2542	2
C₈₉×#2367	2
C₈₉×#2072	2
C₈₉×#2071	2
C₈₉×#2055	2
C₈₉×#2054	2
C₈₉×#1987	2
C₈₉×#1940	2
C₈₉×#1880	2
C₈₉×#1879	2
C₈₉×#1803	2
C₈₉×#1802	2
C₈₉×#1762	2
#25334	89

Subgroups — C89×#25334 #36403182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25334 #36403182