Subgroups — C₈₉×#23678 #36401526

Order 22784.

1016 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2065	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2055	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2014	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₈₉	C₂	1	2	yes	maximal, complemented
12	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₈₉	—	2	1	no	—
16	C₂×C₄×D₄×C₈₉	—	2	1	no	—
17	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
18	C₄×SD₁₆×C₈₉	—	2	8	no	—
19	C₂×#106×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
21	C₂×#103×C₈₉	C₂²	1	2	yes	—
22	C₂×#102×C₈₉	C₂²	1	2	yes	—
23	C₂×#102×C₈₉	C₂²	1	2	yes	—
24	C₂×#102×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
26	#391×C₈₉	C₂²	1	1	yes	characteristic
27	#391×C₈₉	C₂²	1	1	yes	characteristic
28	#390×C₈₉	—	2	1	no	—
29	#390×C₈₉	—	2	1	no	—
30	#390×C₈₉	C₂²	1	2	yes	—
31	#389×C₈₉	C₂²	1	1	yes	characteristic
32	#389×C₈₉	C₂²	1	1	yes	characteristic
33	#387×C₈₉	—	2	1	no	—
34	#387×C₈₉	—	2	1	no	—
35	#384×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	#376×C₈₉	—	2	1	no	—
39	C₄³×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	2	yes	—
41	#340×C₈₉	C₂²	1	2	yes	—
42	#336×C₈₉	C₂²	1	1	yes	characteristic
43	#336×C₈₉	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₈₉	—	2	1	no	—
46	C₂²×D₄×C₈₉	—	2	1	no	—
47	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₈₉	—	2	2	no	—
49	C₂×SD₁₆×C₈₉	—	2	4	no	—
50	C₂×SD₁₆×C₈₉	—	2	4	no	—
51	C₂×SD₁₆×C₈₉	—	2	4	no	—
52	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
54	#127×C₈₉	—	2	4	no	—
55	C₄×Q₈×C₈₉	—	2	2	no	—
56	C₄×Q₈×C₈₉	D₄	1	4	yes	complemented
57	C₄×D₄×C₈₉	—	2	4	no	—
58	C₄×D₄×C₈₉	—	2	4	no	—
59	C₄×D₄×C₈₉	—	4	4	no	—
60	C₄×D₄×C₈₉	—	4	4	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	1	no	—
75	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	#106×C₈₉	—	2	4	no	—
83	C₄⋊C₈×C₈₉	—	2	4	no	—
84	#103×C₈₉	—	2	4	no	—
85	#102×C₈₉	—	2	4	no	—
86	#102×C₈₉	—	2	4	no	—
87	#102×C₈₉	—	2	4	no	—
88	C₄×C₈×C₈₉	—	2	4	no	—
89	#95×C₈₉	—	2	1	no	—
90	#95×C₈₉	—	2	1	no	—
91	#95×C₈₉	—	2	1	no	—
92	#95×C₈₉	—	2	1	no	—
93	#95×C₈₉	—	2	1	no	—
94	#95×C₈₉	—	2	1	no	—
95	#95×C₈₉	—	2	1	no	—
96	C₂⁴×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	1	no	—
98	C₂×Q₈×C₈₉	—	2	2	no	—
99	C₂×Q₈×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₈₉	—	2	4	no	—
102	C₂×D₄×C₈₉	—	2	4	no	—
103	C₂×D₄×C₈₉	—	2	2	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	2	no	—
107	C₂×D₄×C₈₉	—	2	2	no	—
108	C₂×D₄×C₈₉	—	4	2	no	—
109	C₂×D₄×C₈₉	—	4	2	no	—
110	C₂×D₄×C₈₉	—	4	2	no	—
111	C₂×D₄×C₈₉	—	4	2	no	—
112	C₂×D₄×C₈₉	#41	1	4	yes	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	4	4	no	—
119	C₂²×C₄×C₈₉	—	4	4	no	—
120	C₂²×C₄×C₈₉	—	4	4	no	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
128	SD₁₆×C₈₉	—	2	16	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	#41	1	4	yes	—
135	C₄⋊C₄×C₈₉	—	2	4	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	2	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	4	2	no	—
142	C₄⋊C₄×C₈₉	—	4	2	no	—
143	C₄⋊C₄×C₈₉	—	4	2	no	—
144	C₄⋊C₄×C₈₉	—	4	2	no	—
145	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₈₉	—	4	4	no	—
147	C₂²⋊C₄×C₈₉	—	4	4	no	—
148	C₂²⋊C₄×C₈₉	—	4	4	no	—
149	C₄²×C₈₉	—	2	4	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	—	2	2	no	—
154	C₄²×C₈₉	—	4	1	no	—
155	C₄²×C₈₉	—	4	2	no	—
156	C₄²×C₈₉	SD₁₆	1	4	yes	complemented
157	C₄²×C₈₉	C₂×D₄	1	2	yes	—
158	C₄²×C₈₉	#41	1	2	yes	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	4	2	no	—
161	C₂³×C₈₉	—	4	2	no	—
162	C₂³×C₈₉	—	4	2	no	—
163	C₂³×C₈₉	—	4	2	no	—
164	C₂³×C₈₉	—	4	2	no	—
165	C₂³×C₈₉	—	4	2	no	—
166	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₈₉	—	2	4	no	—
168	Q₈×C₈₉	—	4	2	no	—
169	D₄×C₈₉	—	2	4	no	—
170	D₄×C₈₉	—	2	4	no	—
171	D₄×C₈₉	—	4	8	no	—
172	D₄×C₈₉	—	4	8	no	—
173	D₄×C₈₉	—	4	2	no	—
174	D₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	2	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	8	8	no	—
202	C₂×C₄×C₈₉	#121	1	2	yes	—
203	C₂×C₄×C₈₉	#121	1	2	yes	—
204	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
207	C₂×C₄×C₈₉	#135	1	2	yes	—
208	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
211	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
213	C₈×C₈₉	—	2	4	no	—
214	C₈×C₈₉	—	4	2	no	—
215	C₂²×C₈₉	—	4	4	no	—
216	C₂²×C₈₉	—	4	4	no	—
217	C₂²×C₈₉	—	4	4	no	—
218	C₂²×C₈₉	—	8	2	no	—
219	C₂²×C₈₉	—	8	2	no	—
220	C₂²×C₈₉	—	8	2	no	—
221	C₂²×C₈₉	—	8	2	no	—
222	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
223	C₂²×C₈₉	#525	1	1	yes	characteristic
224	C₂²×C₈₉	#532	1	1	yes	characteristic
225	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
226	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
227	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂²×C₈₉	#575	1	1	yes	characteristic
229	C₄×C₈₉	—	2	2	no	—
230	C₄×C₈₉	—	2	2	no	—
231	C₄×C₈₉	—	2	2	no	—
232	C₄×C₈₉	—	2	2	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	4	1	no	—
235	C₄×C₈₉	—	4	2	no	—
236	C₄×C₈₉	—	8	1	no	—
237	C₄×C₈₉	—	8	1	no	—
238	C₄×C₈₉	—	8	2	no	—
239	C₄×C₈₉	#460	1	4	yes	—
240	C₄×C₈₉	#525	1	2	yes	—
241	C₄×C₈₉	#529	1	2	yes	—
242	#23678	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₈₉	—	8	4	no	—
244	C₂×C₈₉	#2392	1	1	yes	characteristic
245	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
246	C₂×C₈₉	#3035	1	1	yes	characteristic
247	C₂×C₈₉	#3101	1	1	yes	characteristic
248	C₂×C₈₉	#3105	1	1	yes	characteristic
249	C₂×C₈₉	#3167	1	1	yes	characteristic
250	C₂×C₈₉	#3171	1	1	yes	characteristic
251	C₂×C₄×SD₁₆	C₂×C₈₉	1	2	yes	complemented
252	C₄×#127	C₂×C₈₉	1	1	yes	characteristic
253	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#2084	C₂×C₈₉	1	1	yes	characteristic, complemented
255	#2072	C₂×C₈₉	1	1	yes	characteristic, complemented
256	#2065	C₂×C₈₉	1	2	yes	complemented
257	#2055	C₂×C₈₉	1	2	yes	complemented
258	#2041	C₂×C₈₉	1	1	yes	characteristic
259	#2014	C₂×C₈₉	1	1	yes	characteristic
260	C₄×C₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
261	C₄×#102	C₂×C₈₉	1	2	yes	complemented
262	C₈₉	#23678	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
264	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
269	C₄×SD₁₆	—	2	8	no	—
270	C₂×#106	C₂²×C₈₉	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
272	C₂×#103	C₂²×C₈₉	1	2	yes	—
273	C₂×#102	C₂²×C₈₉	1	2	yes	—
274	C₂×#102	C₂²×C₈₉	1	2	yes	—
275	C₂×#102	C₂²×C₈₉	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
277	#391	C₂²×C₈₉	1	1	yes	characteristic
278	#391	C₂²×C₈₉	1	1	yes	characteristic
279	#390	—	2	1	no	—
280	#390	—	2	1	no	—
281	#390	C₂²×C₈₉	1	2	yes	—
282	#389	C₂²×C₈₉	1	1	yes	characteristic
283	#389	C₂²×C₈₉	1	1	yes	characteristic
284	#387	—	2	1	no	—
285	#387	—	2	1	no	—
286	#384	C₂²×C₈₉	1	1	yes	characteristic
287	C₄×C₄⋊C₄	—	2	1	no	—
288	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
289	#376	—	2	1	no	—
290	C₄³	C₂²×C₈₉	1	1	yes	characteristic
291	#340	C₂²×C₈₉	1	2	yes	—
292	#340	C₂²×C₈₉	1	2	yes	—
293	#336	C₂²×C₈₉	1	1	yes	characteristic
294	#336	C₂²×C₈₉	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
299	C₂³×C₄	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
305	#127	—	2	4	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	D₄×C₈₉	1	4	yes	complemented
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	4	4	no	—
311	C₄×D₄	—	4	4	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
327	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
333	#106	—	2	4	no	—
334	C₄⋊C₈	—	2	4	no	—
335	#103	—	2	4	no	—
336	#102	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	C₄×C₈	—	2	4	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	C₂⁴	—	2	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	#41×C₈₉	1	4	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
379	SD₁₆	—	2	16	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	#41×C₈₉	1	4	yes	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	2	no	—
407	C₄²	SD₁₆×C₈₉	1	4	yes	complemented
408	C₄²	C₂×D₄×C₈₉	1	2	yes	—
409	C₄²	#41×C₈₉	1	2	yes	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	4	2	no	—
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	8	no	—
453	C₂×C₄	#121×C₈₉	1	2	yes	—
454	C₂×C₄	#121×C₈₉	1	2	yes	—
455	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
456	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
457	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
458	C₂×C₄	#135×C₈₉	1	2	yes	—
459	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
462	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
463	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	2	no	—
472	C₂²	—	8	2	no	—
473	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
474	C₂²	#525×C₈₉	1	1	yes	characteristic
475	C₂²	#532×C₈₉	1	1	yes	characteristic
476	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
477	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
478	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
479	C₂²	#575×C₈₉	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	2	no	—
490	C₄	#460×C₈₉	1	4	yes	—
491	C₄	#525×C₈₉	1	2	yes	—
492	C₄	#529×C₈₉	1	2	yes	—
493	C₂	—	8	4	no	—
494	C₂	C₈₉×#2392	1	1	yes	characteristic
495	C₂	C₂×#460×C₈₉	1	1	yes	characteristic
496	C₂	C₈₉×#3035	1	1	yes	characteristic
497	C₂	C₈₉×#3101	1	1	yes	characteristic
498	C₂	C₈₉×#3105	1	1	yes	characteristic
499	C₂	C₈₉×#3167	1	1	yes	characteristic
500	C₂	C₈₉×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂×#127×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
3. C₈₉×#2295	C₂	semidirect
4. C₈₉×#2084	C₂	semidirect
5. C₈₉×#2072	C₂	semidirect
6. C₈₉×#2065	C₂	semidirect
7. C₈₉×#2055	C₂	semidirect
10. C₄×C₄⋊C₈×C₈₉	C₂	semidirect
11. C₄×#102×C₈₉	C₂	semidirect
56. C₄×Q₈×C₈₉	D₄	semidirect
156. C₄²×C₈₉	SD₁₆	semidirect
242. #23678	C₈₉	direct (N × H)
251. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
253. #2295	C₂×C₈₉	semidirect
254. #2084	C₂×C₈₉	semidirect
255. #2072	C₂×C₈₉	semidirect
256. #2065	C₂×C₈₉	semidirect
257. #2055	C₂×C₈₉	semidirect
260. C₄×C₄⋊C₈	C₂×C₈₉	semidirect
261. C₄×#102	C₂×C₈₉	semidirect
262. C₈₉	#23678	direct (N × H)
307. C₄×Q₈	D₄×C₈₉	semidirect
407. C₄²	SD₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×SD₁₆×C₈₉	2
C₄×#127×C₈₉	2
C₈₉×#2295	2
C₈₉×#2084	2
C₈₉×#2072	2
C₈₉×#2065	2
C₈₉×#2055	2
C₈₉×#2041	2
C₈₉×#2014	2
C₄×C₄⋊C₈×C₈₉	2
C₄×#102×C₈₉	2
#23678	89

Subgroups — C89×#23678 #36401526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23678 #36401526