Subgroups — C₈₉×#25342 #36403190

Order 22784.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#478×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2535	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	#478×C₈₉	—	2	4	no	—
24	C₈×D₄×C₈₉	—	2	4	no	—
25	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	#400×C₈₉	—	2	1	no	—
38	#397×C₈₉	—	2	1	no	—
39	#394×C₈₉	—	2	1	no	—
40	#392×C₈₉	—	2	1	no	—
41	#388×C₈₉	—	2	1	no	—
42	#388×C₈₉	—	2	1	no	—
43	#386×C₈₉	—	2	1	no	—
44	#386×C₈₉	—	2	1	no	—
45	#382×C₈₉	C₂²	1	1	yes	characteristic
46	#380×C₈₉	C₂²	1	1	yes	characteristic
47	#380×C₈₉	C₂²	1	1	yes	characteristic
48	#380×C₈₉	C₂²	1	1	yes	characteristic
49	#380×C₈₉	C₂²	1	1	yes	characteristic
50	#380×C₈₉	C₂²	1	1	yes	characteristic
51	#380×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×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	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₈₉	—	2	1	no	—
62	C₂²×D₄×C₈₉	—	2	1	no	—
63	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	—	2	2	no	—
69	C₂²×C₈×C₈₉	—	2	2	no	—
70	C₂²×C₈×C₈₉	—	2	2	no	—
71	C₂²×C₈×C₈₉	—	2	2	no	—
72	C₂²×C₈×C₈₉	—	4	1	no	—
73	C₂²×C₈×C₈₉	—	4	1	no	—
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	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
78	#125×C₈₉	—	2	2	no	—
79	#125×C₈₉	—	2	2	no	—
80	#121×C₈₉	—	2	2	no	—
81	#121×C₈₉	—	2	2	no	—
82	#121×C₈₉	—	4	1	no	—
83	#121×C₈₉	—	4	1	no	—
84	C₄×D₄×C₈₉	—	2	2	no	—
85	C₄×D₄×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	—	2	2	no	—
87	C₄×D₄×C₈₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	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×C₂²⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	—	2	1	no	—
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	#107×C₈₉	—	2	2	no	—
112	#107×C₈₉	—	4	1	no	—
113	#106×C₈₉	—	2	2	no	—
114	#106×C₈₉	—	4	1	no	—
115	C₄⋊C₈×C₈₉	D₄	1	4	yes	complemented
116	#102×C₈₉	—	2	2	no	—
117	#102×C₈₉	—	2	2	no	—
118	#102×C₈₉	—	2	2	no	—
119	#102×C₈₉	—	2	2	no	—
120	C₂²⋊C₈×C₈₉	—	2	2	no	—
121	C₂²⋊C₈×C₈₉	—	2	2	no	—
122	C₄×C₈×C₈₉	—	2	2	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	#95×C₈₉	—	2	1	no	—
128	#95×C₈₉	—	2	1	no	—
129	#95×C₈₉	—	2	1	no	—
130	#95×C₈₉	—	2	1	no	—
131	#95×C₈₉	—	2	1	no	—
132	C₂⁴×C₈₉	—	2	1	no	—
133	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	—	2	2	no	—
137	C₂×D₄×C₈₉	—	2	2	no	—
138	C₂×D₄×C₈₉	—	2	1	no	—
139	C₂×D₄×C₈₉	—	2	1	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	1	no	—
142	C₂×D₄×C₈₉	—	2	1	no	—
143	C₂×D₄×C₈₉	—	4	2	no	—
144	C₂×D₄×C₈₉	—	4	2	no	—
145	C₂×D₄×C₈₉	—	4	2	no	—
146	C₂×D₄×C₈₉	—	4	2	no	—
147	C₂×D₄×C₈₉	—	8	1	no	—
148	C₂×D₄×C₈₉	—	8	1	no	—
149	C₂×D₄×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
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	—	2	1	no	—
164	C₂²×C₄×C₈₉	—	2	1	no	—
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	1	no	—
168	C₂²×C₄×C₈₉	—	2	1	no	—
169	C₂²×C₄×C₈₉	—	4	2	no	—
170	C₂²×C₄×C₈₉	—	8	1	no	—
171	C₂²×C₄×C₈₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	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	—	4	4	no	—
187	C₂×C₈×C₈₉	—	4	4	no	—
188	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
202	C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₄⋊C₄×C₈₉	—	2	1	no	—
204	C₄⋊C₄×C₈₉	—	2	1	no	—
205	C₄⋊C₄×C₈₉	—	2	1	no	—
206	C₄⋊C₄×C₈₉	—	4	2	no	—
207	C₄⋊C₄×C₈₉	—	4	2	no	—
208	C₂²⋊C₄×C₈₉	—	2	2	no	—
209	C₂²⋊C₄×C₈₉	—	2	2	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	—	8	1	no	—
216	C₂²⋊C₄×C₈₉	—	8	1	no	—
217	C₂²⋊C₄×C₈₉	—	8	1	no	—
218	C₂²⋊C₄×C₈₉	—	8	1	no	—
219	C₄²×C₈₉	—	8	1	no	—
220	C₄²×C₈₉	C₂×D₄	1	2	yes	—
221	C₄²×C₈₉	#41	1	2	yes	—
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	—	2	1	no	—
229	C₂³×C₈₉	—	2	1	no	—
230	C₂³×C₈₉	—	2	1	no	—
231	C₂³×C₈₉	—	2	1	no	—
232	C₂³×C₈₉	—	2	1	no	—
233	C₂³×C₈₉	—	2	1	no	—
234	C₂³×C₈₉	—	2	2	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	—	4	1	no	—
241	C₂³×C₈₉	#135	1	2	yes	—
242	C₂³×C₈₉	#135	1	2	yes	—
243	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
244	D₄×C₈₉	—	2	8	no	—
245	D₄×C₈₉	—	2	2	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	4	1	no	—
248	D₄×C₈₉	—	4	1	no	—
249	D₄×C₈₉	—	8	4	no	—
250	D₄×C₈₉	—	8	4	no	—
251	C₂×C₄×C₈₉	—	2	1	no	—
252	C₂×C₄×C₈₉	—	2	1	no	—
253	C₂×C₄×C₈₉	—	2	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	—	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	—	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	—	4	1	no	—
287	C₂×C₄×C₈₉	—	4	1	no	—
288	C₂×C₄×C₈₉	—	4	1	no	—
289	C₂×C₄×C₈₉	—	4	1	no	—
290	C₂×C₄×C₈₉	—	8	4	no	—
291	C₂×C₄×C₈₉	#121	1	2	yes	—
292	C₂×C₄×C₈₉	#121	1	2	yes	—
293	C₂×C₄×C₈₉	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
299	C₈×C₈₉	—	2	2	no	—
300	C₈×C₈₉	—	2	2	no	—
301	C₈×C₈₉	—	2	2	no	—
302	C₈×C₈₉	—	4	1	no	—
303	C₂²×C₈₉	—	2	2	no	—
304	C₂²×C₈₉	—	2	2	no	—
305	C₂²×C₈₉	—	2	2	no	—
306	C₂²×C₈₉	—	2	2	no	—
307	C₂²×C₈₉	—	2	2	no	—
308	C₂²×C₈₉	—	2	2	no	—
309	C₂²×C₈₉	—	4	1	no	—
310	C₂²×C₈₉	—	4	1	no	—
311	C₂²×C₈₉	—	4	1	no	—
312	C₂²×C₈₉	—	4	1	no	—
313	C₂²×C₈₉	—	4	1	no	—
314	C₂²×C₈₉	—	4	1	no	—
315	C₂²×C₈₉	—	4	1	no	—
316	C₂²×C₈₉	—	4	1	no	—
317	C₂²×C₈₉	—	4	2	no	—
318	C₂²×C₈₉	—	4	2	no	—
319	C₂²×C₈₉	—	4	2	no	—
320	C₂²×C₈₉	—	8	1	no	—
321	C₂²×C₈₉	—	8	1	no	—
322	C₂²×C₈₉	—	8	1	no	—
323	C₂²×C₈₉	—	8	1	no	—
324	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
325	C₂²×C₈₉	#546	1	1	yes	characteristic
326	C₂²×C₈₉	#547	1	1	yes	characteristic
327	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
328	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
329	C₂²×C₈₉	#576	1	1	yes	characteristic
330	C₂²×C₈₉	#577	1	1	yes	characteristic
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	2	no	—
333	C₄×C₈₉	—	4	1	no	—
334	C₄×C₈₉	—	4	1	no	—
335	C₄×C₈₉	—	8	1	no	—
336	C₄×C₈₉	—	8	1	no	—
337	C₄×C₈₉	—	8	1	no	—
338	C₄×C₈₉	—	8	1	no	—
339	C₄×C₈₉	—	8	1	no	—
340	C₄×C₈₉	—	8	1	no	—
341	C₄×C₈₉	—	8	1	no	—
342	C₄×C₈₉	#529	1	1	yes	characteristic
343	C₄×C₈₉	#542	1	1	yes	characteristic
344	C₄×C₈₉	#546	1	1	yes	characteristic
345	C₄×C₈₉	#548	1	1	yes	characteristic
346	#25342	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂×C₈₉	—	4	2	no	—
348	C₂×C₈₉	—	4	2	no	—
349	C₂×C₈₉	—	8	2	no	—
350	C₂×C₈₉	#2427	1	1	yes	characteristic
351	C₂×C₈₉	#3050	1	1	yes	characteristic
352	C₂×C₈₉	#3062	1	1	yes	characteristic
353	C₂×C₈₉	#3296	1	1	yes	characteristic
354	C₂×C₈₉	#3297	1	1	yes	characteristic
355	C₂×C₈₉	#3337	1	1	yes	characteristic
356	C₂×C₈₉	#3339	1	1	yes	characteristic
357	C₂×#478	C₂×C₈₉	1	1	yes	characteristic, complemented
358	C₂×C₈×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
359	#2562	C₂×C₈₉	1	1	yes	characteristic, complemented
360	#2535	C₂×C₈₉	1	1	yes	characteristic
361	#2077	C₂×C₈₉	1	1	yes	characteristic, complemented
362	#2076	C₂×C₈₉	1	1	yes	characteristic, complemented
363	#2034	C₂×C₈₉	1	1	yes	characteristic, complemented
364	#2033	C₂×C₈₉	1	1	yes	characteristic, complemented
365	#1991	C₂×C₈₉	1	1	yes	characteristic, complemented
366	#1949	C₂×C₈₉	1	1	yes	characteristic, complemented
367	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
368	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
369	#1808	C₂×C₈₉	1	1	yes	characteristic, complemented
370	#1807	C₂×C₈₉	1	1	yes	characteristic, complemented
371	C₄×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
372	C₈₉	#25342	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
374	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
375	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
376	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
377	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
380	#478	—	2	4	no	—
381	C₈×D₄	—	2	4	no	—
382	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
383	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
384	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
385	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
389	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
390	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
393	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
394	#400	—	2	1	no	—
395	#397	—	2	1	no	—
396	#394	—	2	1	no	—
397	#392	—	2	1	no	—
398	#388	—	2	1	no	—
399	#388	—	2	1	no	—
400	#386	—	2	1	no	—
401	#386	—	2	1	no	—
402	#382	C₂²×C₈₉	1	1	yes	characteristic
403	#380	C₂²×C₈₉	1	1	yes	characteristic
404	#380	C₂²×C₈₉	1	1	yes	characteristic
405	#380	C₂²×C₈₉	1	1	yes	characteristic
406	#380	C₂²×C₈₉	1	1	yes	characteristic
407	#380	C₂²×C₈₉	1	1	yes	characteristic
408	#380	C₂²×C₈₉	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
410	#340	C₂²×C₈₉	1	1	yes	characteristic
411	#340	C₂²×C₈₉	1	1	yes	characteristic
412	#340	C₂²×C₈₉	1	1	yes	characteristic
413	#340	C₂²×C₈₉	1	1	yes	characteristic
414	#340	C₂²×C₈₉	1	1	yes	characteristic
415	#340	C₂²×C₈₉	1	1	yes	characteristic
416	#340	C₂²×C₈₉	1	1	yes	characteristic
417	#340	C₂²×C₈₉	1	1	yes	characteristic
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	—	2	2	no	—
427	C₂²×C₈	—	2	2	no	—
428	C₂²×C₈	—	2	2	no	—
429	C₂²×C₈	—	4	1	no	—
430	C₂²×C₈	—	4	1	no	—
431	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
435	#125	—	2	2	no	—
436	#125	—	2	2	no	—
437	#121	—	2	2	no	—
438	#121	—	2	2	no	—
439	#121	—	4	1	no	—
440	#121	—	4	1	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
468	#107	—	2	2	no	—
469	#107	—	4	1	no	—
470	#106	—	2	2	no	—
471	#106	—	4	1	no	—
472	C₄⋊C₈	D₄×C₈₉	1	4	yes	complemented
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	—	2	2	no	—
476	#102	—	2	2	no	—
477	C₂²⋊C₈	—	2	2	no	—
478	C₂²⋊C₈	—	2	2	no	—
479	C₄×C₈	—	2	2	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	C₂⁴	—	2	1	no	—
490	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
491	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	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	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	8	1	no	—
505	C₂×D₄	—	8	1	no	—
506	C₂×D₄	#41×C₈₉	1	2	yes	—
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	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	8	1	no	—
528	C₂²×C₄	—	8	1	no	—
529	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	4	4	no	—
544	C₂×C₈	—	4	4	no	—
545	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
546	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
547	C₂×C₈	#41×C₈₉	1	2	yes	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	8	1	no	—
573	C₂²⋊C₄	—	8	1	no	—
574	C₂²⋊C₄	—	8	1	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₄²	—	8	1	no	—
577	C₄²	C₂×D₄×C₈₉	1	2	yes	—
578	C₄²	#41×C₈₉	1	2	yes	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	#135×C₈₉	1	2	yes	—
599	C₂³	#135×C₈₉	1	2	yes	—
600	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
601	D₄	—	2	8	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	8	4	no	—
607	D₄	—	8	4	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	4	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	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	8	4	no	—
648	C₂×C₄	#121×C₈₉	1	2	yes	—
649	C₂×C₄	#121×C₈₉	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
651	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
652	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
653	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
654	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
655	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	2	2	no	—
658	C₈	—	2	2	no	—
659	C₈	—	4	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
682	C₂²	#546×C₈₉	1	1	yes	characteristic
683	C₂²	#547×C₈₉	1	1	yes	characteristic
684	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
685	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
686	C₂²	#576×C₈₉	1	1	yes	characteristic
687	C₂²	#577×C₈₉	1	1	yes	characteristic
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	—	8	1	no	—
699	C₄	#529×C₈₉	1	1	yes	characteristic
700	C₄	#542×C₈₉	1	1	yes	characteristic
701	C₄	#546×C₈₉	1	1	yes	characteristic
702	C₄	#548×C₈₉	1	1	yes	characteristic
703	C₂	—	4	2	no	—
704	C₂	—	4	2	no	—
705	C₂	—	8	2	no	—
706	C₂	C₈₉×#2427	1	1	yes	characteristic
707	C₂	C₈₉×#3050	1	1	yes	characteristic
708	C₂	C₈₉×#3062	1	1	yes	characteristic
709	C₂	C₈₉×#3296	1	1	yes	characteristic
710	C₂	C₈₉×#3297	1	1	yes	characteristic
711	C₂	C₈₉×#3337	1	1	yes	characteristic
712	C₂	C₈₉×#3339	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#2535	C₂
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
1. C₂×#478×C₈₉	C₂	semidirect
2. C₂×C₈×D₄×C₈₉	C₂	semidirect
3. C₈₉×#2562	C₂	semidirect
5. C₈₉×#2077	C₂	semidirect
6. C₈₉×#2076	C₂	semidirect
7. C₈₉×#2034	C₂	semidirect
8. C₈₉×#2033	C₂	semidirect
9. C₈₉×#1991	C₂	semidirect
10. C₈₉×#1949	C₂	semidirect
11. C₈₉×#1893	C₂	semidirect
12. C₈₉×#1893	C₂	semidirect
13. C₈₉×#1808	C₂	semidirect
14. C₈₉×#1807	C₂	semidirect
15. C₄×#102×C₈₉	C₂	semidirect
115. C₄⋊C₈×C₈₉	D₄	semidirect
346. #25342	C₈₉	direct (N × H)
357. C₂×#478	C₂×C₈₉	semidirect
358. C₂×C₈×D₄	C₂×C₈₉	semidirect
359. #2562	C₂×C₈₉	semidirect
361. #2077	C₂×C₈₉	semidirect
362. #2076	C₂×C₈₉	semidirect
363. #2034	C₂×C₈₉	semidirect
364. #2033	C₂×C₈₉	semidirect
365. #1991	C₂×C₈₉	semidirect
366. #1949	C₂×C₈₉	semidirect
367. #1893	C₂×C₈₉	semidirect
368. #1893	C₂×C₈₉	semidirect
369. #1808	C₂×C₈₉	semidirect
370. #1807	C₂×C₈₉	semidirect
371. C₄×#102	C₂×C₈₉	semidirect
372. C₈₉	#25342	direct (N × H)
472. C₄⋊C₈	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#478×C₈₉	2
C₂×C₈×D₄×C₈₉	2
C₈₉×#2562	2
C₈₉×#2535	2
C₈₉×#2077	2
C₈₉×#2076	2
C₈₉×#2034	2
C₈₉×#2033	2
C₈₉×#1991	2
C₈₉×#1949	2
C₈₉×#1893	2
C₈₉×#1808	2
C₈₉×#1807	2
C₄×#102×C₈₉	2
#25342	89

Subgroups — C89×#25342 #36403190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25342 #36403190