Subgroups — C₈₉×#29397 #36407245

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2073	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2025	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1926	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1925	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1864	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1839	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₈₉	—	2	1	no	—
19	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
27	#390×C₈₉	C₂²	1	1	yes	characteristic
28	#390×C₈₉	C₂²	1	1	yes	characteristic
29	#389×C₈₉	C₂²	1	1	yes	characteristic
30	#389×C₈₉	C₂²	1	1	yes	characteristic
31	#389×C₈₉	C₂²	1	1	yes	characteristic
32	#389×C₈₉	C₂²	1	1	yes	characteristic
33	#388×C₈₉	—	2	1	no	—
34	#388×C₈₉	—	2	1	no	—
35	#387×C₈₉	—	2	1	no	—
36	#387×C₈₉	—	2	1	no	—
37	#382×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
44	C₄³×C₈₉	C₂²	1	1	yes	characteristic
45	#340×C₈₉	C₂²	1	1	yes	characteristic
46	#340×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	#336×C₈₉	C₂²	1	1	yes	characteristic
54	#336×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	#336×C₈₉	C₂²	1	1	yes	characteristic
58	#336×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	—	2	1	no	—
61	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	#125×C₈₉	—	2	2	no	—
66	#125×C₈₉	—	2	2	no	—
67	C₄×D₄×C₈₉	—	2	2	no	—
68	C₄×D₄×C₈₉	—	2	2	no	—
69	#117×C₈₉	—	4	4	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄²×C₈₉	—	2	1	no	—
89	C₂×C₄²×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	#107×C₈₉	—	2	2	no	—
99	#107×C₈₉	—	2	2	no	—
100	#106×C₈₉	—	2	2	no	—
101	#106×C₈₉	—	2	2	no	—
102	#102×C₈₉	—	2	2	no	—
103	#102×C₈₉	—	2	2	no	—
104	#102×C₈₉	—	2	2	no	—
105	#102×C₈₉	—	2	2	no	—
106	#95×C₈₉	—	2	1	no	—
107	#95×C₈₉	—	2	1	no	—
108	#95×C₈₉	—	2	1	no	—
109	#95×C₈₉	—	2	1	no	—
110	#95×C₈₉	—	2	1	no	—
111	#95×C₈₉	—	2	1	no	—
112	#95×C₈₉	—	2	1	no	—
113	#95×C₈₉	—	2	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	C₂⁴×C₈₉	—	2	1	no	—
116	C₂×D₄×C₈₉	—	2	1	no	—
117	C₂×D₄×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	—	2	1	no	—
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	#41	1	2	yes	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	4	2	no	—
131	C₂²×C₄×C₈₉	—	4	2	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	2	1	no	—
149	C₂×C₈×C₈₉	—	2	1	no	—
150	C₂×C₈×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	4	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	4	2	no	—
165	C₄⋊C₄×C₈₉	—	4	2	no	—
166	C₄⋊C₄×C₈₉	—	4	2	no	—
167	C₄⋊C₄×C₈₉	—	4	2	no	—
168	C₄⋊C₄×C₈₉	#41	1	2	yes	—
169	C₄⋊C₄×C₈₉	#41	1	2	yes	—
170	C₄⋊C₄×C₈₉	#41	1	2	yes	—
171	C₂²⋊C₄×C₈₉	—	2	4	no	—
172	C₂²⋊C₄×C₈₉	—	4	2	no	—
173	C₂²⋊C₄×C₈₉	—	4	2	no	—
174	C₂²⋊C₄×C₈₉	—	4	2	no	—
175	C₂²⋊C₄×C₈₉	—	4	2	no	—
176	C₄²×C₈₉	—	2	2	no	—
177	C₄²×C₈₉	—	2	2	no	—
178	C₄²×C₈₉	—	2	1	no	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₄²×C₈₉	—	2	1	no	—
181	C₄²×C₈₉	—	2	1	no	—
182	C₄²×C₈₉	—	2	1	no	—
183	C₄²×C₈₉	—	2	1	no	—
184	C₄²×C₈₉	—	4	1	no	—
185	C₄²×C₈₉	—	4	1	no	—
186	C₄²×C₈₉	—	4	2	no	—
187	C₄²×C₈₉	—	4	2	no	—
188	C₄²×C₈₉	—	4	2	no	—
189	C₂³×C₈₉	—	2	2	no	—
190	C₂³×C₈₉	—	4	1	no	—
191	C₂³×C₈₉	—	4	1	no	—
192	C₂³×C₈₉	—	4	1	no	—
193	C₂³×C₈₉	—	4	1	no	—
194	C₂³×C₈₉	—	4	1	no	—
195	C₂³×C₈₉	—	4	1	no	—
196	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	D₄×C₈₉	—	2	2	no	—
198	D₄×C₈₉	—	2	2	no	—
199	D₄×C₈₉	—	4	1	no	—
200	D₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	2	1	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	2	2	no	—
210	C₂×C₄×C₈₉	—	2	2	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	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	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	4	8	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	4	1	no	—
232	C₂×C₄×C₈₉	—	4	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	—	4	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	#135	1	2	yes	—
240	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
241	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
246	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	C₈×C₈₉	—	4	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₂²×C₈₉	—	4	2	no	—
252	C₂²×C₈₉	—	4	2	no	—
253	C₂²×C₈₉	—	4	2	no	—
254	C₂²×C₈₉	—	8	1	no	—
255	C₂²×C₈₉	—	8	1	no	—
256	C₂²×C₈₉	—	8	1	no	—
257	C₂²×C₈₉	—	8	1	no	—
258	C₂²×C₈₉	#525	1	1	yes	characteristic
259	C₂²×C₈₉	#525	1	1	yes	characteristic
260	C₂²×C₈₉	#536	1	1	yes	characteristic
261	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
262	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₈₉	#575	1	1	yes	characteristic
264	C₂²×C₈₉	#575	1	1	yes	characteristic
265	C₄×C₈₉	—	2	2	no	—
266	C₄×C₈₉	—	2	2	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	—	4	2	no	—
270	C₄×C₈₉	—	4	1	no	—
271	C₄×C₈₉	—	4	2	no	—
272	C₄×C₈₉	—	4	2	no	—
273	C₄×C₈₉	—	4	1	no	—
274	C₄×C₈₉	—	8	1	no	—
275	C₄×C₈₉	—	8	1	no	—
276	C₄×C₈₉	—	8	1	no	—
277	C₄×C₈₉	—	8	1	no	—
278	C₄×C₈₉	#552	1	1	yes	characteristic
279	C₄×C₈₉	#552	1	1	yes	characteristic
280	C₄×C₈₉	#556	1	1	yes	characteristic
281	C₄×C₈₉	#556	1	1	yes	characteristic
282	#29397	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂×C₈₉	—	8	2	no	—
284	C₂×C₈₉	#2599	1	1	yes	characteristic
285	C₂×C₈₉	#3102	1	1	yes	characteristic
286	C₂×C₈₉	#3106	1	1	yes	characteristic
287	C₂×C₈₉	#3111	1	1	yes	characteristic
288	C₂×C₈₉	#3114	1	1	yes	characteristic
289	C₂×C₈₉	#3232	1	1	yes	characteristic
290	C₂×C₈₉	#3235	1	1	yes	characteristic
291	C₄×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
292	#2293	C₂×C₈₉	1	1	yes	characteristic
293	#2085	C₂×C₈₉	1	1	yes	characteristic, complemented
294	#2073	C₂×C₈₉	1	1	yes	characteristic
295	#2059	C₂×C₈₉	1	1	yes	characteristic, complemented
296	#2025	C₂×C₈₉	1	1	yes	characteristic
297	#1926	C₂×C₈₉	1	1	yes	characteristic
298	#1925	C₂×C₈₉	1	1	yes	characteristic
299	#1921	C₂×C₈₉	1	1	yes	characteristic, complemented
300	#1920	C₂×C₈₉	1	1	yes	characteristic, complemented
301	#1920	C₂×C₈₉	1	1	yes	characteristic, complemented
302	#1918	C₂×C₈₉	1	1	yes	characteristic, complemented
303	#1864	C₂×C₈₉	1	1	yes	characteristic
304	#1862	C₂×C₈₉	1	1	yes	characteristic
305	#1839	C₂×C₈₉	1	1	yes	characteristic, complemented
306	C₈₉	#29397	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
309	C₂×#117	—	2	1	no	—
310	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
311	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
312	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
313	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
315	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
316	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
317	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
318	#390	C₂²×C₈₉	1	1	yes	characteristic
319	#390	C₂²×C₈₉	1	1	yes	characteristic
320	#389	C₂²×C₈₉	1	1	yes	characteristic
321	#389	C₂²×C₈₉	1	1	yes	characteristic
322	#389	C₂²×C₈₉	1	1	yes	characteristic
323	#389	C₂²×C₈₉	1	1	yes	characteristic
324	#388	—	2	1	no	—
325	#388	—	2	1	no	—
326	#387	—	2	1	no	—
327	#387	—	2	1	no	—
328	#382	C₂²×C₈₉	1	1	yes	characteristic
329	C₄×C₄⋊C₄	—	2	1	no	—
330	C₄×C₄⋊C₄	—	2	1	no	—
331	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
334	C₄×C₂²⋊C₄	—	2	1	no	—
335	C₄³	C₂²×C₈₉	1	1	yes	characteristic
336	#340	C₂²×C₈₉	1	1	yes	characteristic
337	#340	C₂²×C₈₉	1	1	yes	characteristic
338	#340	C₂²×C₈₉	1	1	yes	characteristic
339	#340	C₂²×C₈₉	1	1	yes	characteristic
340	#340	C₂²×C₈₉	1	1	yes	characteristic
341	#340	C₂²×C₈₉	1	1	yes	characteristic
342	#340	C₂²×C₈₉	1	1	yes	characteristic
343	#340	C₂²×C₈₉	1	1	yes	characteristic
344	#336	C₂²×C₈₉	1	1	yes	characteristic
345	#336	C₂²×C₈₉	1	1	yes	characteristic
346	#336	C₂²×C₈₉	1	1	yes	characteristic
347	#336	C₂²×C₈₉	1	1	yes	characteristic
348	#336	C₂²×C₈₉	1	1	yes	characteristic
349	#336	C₂²×C₈₉	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
356	#125	—	2	2	no	—
357	#125	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	#117	—	4	4	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
383	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
384	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
389	#107	—	2	2	no	—
390	#107	—	2	2	no	—
391	#106	—	2	2	no	—
392	#106	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	C₂⁴	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	#41×C₈₉	1	2	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	#41×C₈₉	1	2	yes	—
460	C₄⋊C₄	#41×C₈₉	1	2	yes	—
461	C₄⋊C₄	#41×C₈₉	1	2	yes	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	—	4	2	no	—
478	C₄²	—	4	2	no	—
479	C₄²	—	4	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
488	D₄	—	2	2	no	—
489	D₄	—	2	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	#135×C₈₉	1	2	yes	—
531	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
532	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
533	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
536	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
537	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	#525×C₈₉	1	1	yes	characteristic
550	C₂²	#525×C₈₉	1	1	yes	characteristic
551	C₂²	#536×C₈₉	1	1	yes	characteristic
552	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
553	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
554	C₂²	#575×C₈₉	1	1	yes	characteristic
555	C₂²	#575×C₈₉	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	#552×C₈₉	1	1	yes	characteristic
570	C₄	#552×C₈₉	1	1	yes	characteristic
571	C₄	#556×C₈₉	1	1	yes	characteristic
572	C₄	#556×C₈₉	1	1	yes	characteristic
573	C₂	—	8	2	no	—
574	C₂	C₈₉×#2599	1	1	yes	characteristic
575	C₂	C₈₉×#3102	1	1	yes	characteristic
576	C₂	C₈₉×#3106	1	1	yes	characteristic
577	C₂	C₈₉×#3111	1	1	yes	characteristic
578	C₂	C₈₉×#3114	1	1	yes	characteristic
579	C₂	C₈₉×#3232	1	1	yes	characteristic
580	C₂	C₈₉×#3235	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×#125×C₈₉	C₂	semidirect
3. C₈₉×#2085	C₂	semidirect
5. C₈₉×#2059	C₂	semidirect
9. C₈₉×#1921	C₂	semidirect
10. C₈₉×#1920	C₂	semidirect
11. C₈₉×#1920	C₂	semidirect
12. C₈₉×#1918	C₂	semidirect
15. C₈₉×#1839	C₂	semidirect
282. #29397	C₈₉	direct (N × H)
291. C₄×#125	C₂×C₈₉	semidirect
293. #2085	C₂×C₈₉	semidirect
295. #2059	C₂×C₈₉	semidirect
299. #1921	C₂×C₈₉	semidirect
300. #1920	C₂×C₈₉	semidirect
301. #1920	C₂×C₈₉	semidirect
302. #1918	C₂×C₈₉	semidirect
305. #1839	C₂×C₈₉	semidirect
306. C₈₉	#29397	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#125×C₈₉	2
C₈₉×#2293	2
C₈₉×#2085	2
C₈₉×#2073	2
C₈₉×#2059	2
C₈₉×#2025	2
C₈₉×#1926	2
C₈₉×#1925	2
C₈₉×#1921	2
C₈₉×#1920	2
C₈₉×#1918	2
C₈₉×#1864	2
C₈₉×#1862	2
C₈₉×#1839	2
#29397	89

Subgroups — C89×#29397 #36407245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29397 #36407245