Subgroups — C₈₉×#60713 #36438561

Order 22784.

1878 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3183	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3175	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3173	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3168	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#495×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3140	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3058	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#3057	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2949	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
21	#559×C₈₉	—	2	4	no	—
22	#556×C₈₉	—	2	4	no	—
23	#551×C₈₉	—	2	8	no	—
24	#542×C₈₉	C₂²	1	8	yes	complemented
25	#536×C₈₉	C₂²	1	2	yes	—
26	#535×C₈₉	C₂²	1	2	yes	—
27	#533×C₈₉	C₂²	1	2	yes	—
28	#529×C₈₉	C₂²	1	8	yes	complemented
29	C₂×#124×C₈₉	C₂²	1	2	yes	—
30	#519×C₈₉	C₂²	1	2	yes	—
31	#518×C₈₉	C₂²	1	2	yes	—
32	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
33	#500×C₈₉	C₂²	1	2	yes	complemented
34	#499×C₈₉	C₂²	1	2	yes	complemented
35	#499×C₈₉	C₂²	1	2	yes	complemented
36	#498×C₈₉	C₂²	1	2	yes	complemented
37	#495×C₈₉	C₂²	1	2	yes	—
38	#495×C₈₉	C₂²	1	2	yes	—
39	#495×C₈₉	C₂²	1	2	yes	—
40	#495×C₈₉	C₂²	1	2	yes	—
41	#489×C₈₉	C₂²	1	8	yes	complemented
42	#488×C₈₉	C₂²	1	8	yes	complemented
43	#470×C₈₉	C₂²	1	4	yes	complemented
44	#469×C₈₉	C₂²	1	4	yes	—
45	#468×C₈₉	C₂²	1	8	yes	complemented
46	#467×C₈₉	C₂²	1	4	yes	complemented
47	#466×C₈₉	C₂²	1	4	yes	—
48	#465×C₈₉	C₂²	1	8	yes	complemented
49	#442×C₈₉	C₂²	1	4	yes	—
50	#441×C₈₉	C₂²	1	4	yes	complemented
51	#440×C₈₉	C₂²	1	8	yes	complemented
52	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
53	C₄×SD₁₆×C₈₉	C₂²	1	8	yes	complemented
54	C₄×D₈×C₈₉	C₂²	1	4	yes	—
55	#427×C₈₉	C₂²	1	1	yes	characteristic
56	#427×C₈₉	C₂²	1	2	yes	—
57	#427×C₈₉	C₂²	1	1	yes	characteristic
58	#419×C₈₉	C₂²	1	2	yes	—
59	#419×C₈₉	C₂²	1	2	yes	—
60	#418×C₈₉	C₂²	1	2	yes	—
61	#418×C₈₉	C₂²	1	2	yes	—
62	#405×C₈₉	C₂²	1	1	yes	characteristic
63	#405×C₈₉	C₂²	1	1	yes	characteristic
64	#405×C₈₉	C₂²	1	2	yes	complemented
65	#405×C₈₉	C₂²	1	2	yes	complemented
66	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
67	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
68	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	complemented
70	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
73	C₂×Q₁₆×C₈₉	—	2	4	no	—
74	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
75	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
76	C₂×SD₁₆×C₈₉	—	2	8	no	—
77	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
78	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
79	C₂×D₈×C₈₉	—	2	4	no	—
80	C₂×D₈×C₈₉	C₂³	1	2	yes	—
81	C₂×D₈×C₈₉	C₂³	1	2	yes	—
82	#131×C₈₉	—	2	4	no	—
83	#131×C₈₉	—	2	4	no	—
84	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
87	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
89	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊Q₈×C₈₉	—	2	2	no	—
93	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
94	#127×C₈₉	—	2	2	no	—
95	#126×C₈₉	—	2	8	no	—
96	#126×C₈₉	—	2	8	no	—
97	#125×C₈₉	C₂³	1	4	yes	—
98	#124×C₈₉	—	2	2	no	—
99	#124×C₈₉	—	2	2	no	—
100	#124×C₈₉	—	2	8	no	—
101	#124×C₈₉	—	2	4	no	—
102	#124×C₈₉	C₂³	1	4	yes	—
103	#124×C₈₉	C₂³	1	4	yes	—
104	#123×C₈₉	—	2	4	no	—
105	#123×C₈₉	—	2	8	no	—
106	#123×C₈₉	—	2	8	no	—
107	C₂²⋊Q₈×C₈₉	—	2	4	no	—
108	C₂²⋊Q₈×C₈₉	—	2	8	no	—
109	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
110	#121×C₈₉	C₂³	1	8	yes	—
111	#120×C₈₉	—	2	4	no	—
112	C₄×Q₈×C₈₉	—	2	4	no	—
113	C₄×Q₈×C₈₉	—	2	4	no	—
114	C₄×Q₈×C₈₉	D₄	1	2	yes	—
115	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
116	C₄×D₄×C₈₉	—	2	8	no	—
117	C₄×D₄×C₈₉	—	2	4	no	—
118	C₄×D₄×C₈₉	D₄	1	4	yes	—
119	C₄×D₄×C₈₉	D₄	1	2	yes	—
120	C₄×D₄×C₈₉	C₂³	1	8	yes	—
121	#117×C₈₉	—	2	4	no	—
122	#117×C₈₉	—	2	8	no	—
123	#117×C₈₉	C₂³	1	2	yes	—
124	#117×C₈₉	C₂³	1	2	yes	—
125	#117×C₈₉	C₂³	1	1	yes	characteristic
126	#117×C₈₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
131	#107×C₈₉	C₂³	1	2	yes	—
132	#107×C₈₉	C₂³	1	2	yes	—
133	#107×C₈₉	C₂³	1	4	yes	—
134	#106×C₈₉	C₂³	1	4	yes	—
135	#106×C₈₉	C₂³	1	2	yes	—
136	#106×C₈₉	C₂³	1	2	yes	—
137	#103×C₈₉	C₂³	1	8	yes	—
138	#103×C₈₉	C₂³	1	8	yes	—
139	#102×C₈₉	C₂³	1	8	yes	—
140	#102×C₈₉	C₂³	1	8	yes	—
141	#97×C₈₉	C₂³	1	2	yes	—
142	#97×C₈₉	C₂³	1	2	yes	—
143	#97×C₈₉	C₂³	1	2	yes	—
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₈₉	C₂³	1	2	yes	—
149	C₄×C₈×C₈₉	C₂³	1	2	yes	—
150	C₄×C₈×C₈₉	C₂³	1	2	yes	—
151	C₂⁴×C₈₉	—	2	2	no	—
152	#41×C₈₉	—	2	2	no	—
153	#41×C₈₉	—	2	2	no	—
154	C₂×Q₈×C₈₉	—	2	2	no	—
155	C₂×Q₈×C₈₉	—	2	4	no	—
156	C₂×Q₈×C₈₉	—	2	4	no	—
157	C₂×Q₈×C₈₉	—	2	4	no	—
158	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
160	C₂×D₄×C₈₉	—	2	8	no	—
161	C₂×D₄×C₈₉	—	2	2	no	—
162	C₂×D₄×C₈₉	—	2	4	no	—
163	C₂×D₄×C₈₉	—	2	4	no	—
164	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₈₉	—	2	2	no	—
168	C₂²×C₄×C₈₉	—	2	8	no	—
169	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	Q₁₆×C₈₉	—	2	4	no	—
174	Q₁₆×C₈₉	—	2	4	no	—
175	SD₁₆×C₈₉	—	2	8	no	—
176	SD₁₆×C₈₉	—	2	8	no	—
177	D₈×C₈₉	—	2	4	no	—
178	D₈×C₈₉	—	2	4	no	—
179	M₁₆×C₈₉	—	2	2	no	—
180	M₁₆×C₈₉	—	2	2	no	—
181	M₁₆×C₈₉	—	2	4	no	—
182	M₁₆×C₈₉	—	2	4	no	—
183	C₂×C₈×C₈₉	—	2	4	no	—
184	C₂×C₈×C₈₉	—	2	4	no	—
185	C₂×C₈×C₈₉	#41	1	4	yes	—
186	C₂×C₈×C₈₉	#41	1	4	yes	—
187	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
188	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
189	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	8	no	—
195	C₄⋊C₄×C₈₉	—	2	8	no	—
196	C₄⋊C₄×C₈₉	—	2	4	no	—
197	C₄⋊C₄×C₈₉	—	2	4	no	—
198	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
200	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
201	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
202	C₂²⋊C₄×C₈₉	—	2	2	no	—
203	C₂²⋊C₄×C₈₉	—	2	2	no	—
204	C₂²⋊C₄×C₈₉	—	2	8	no	—
205	C₂²⋊C₄×C₈₉	—	2	8	no	—
206	C₂²⋊C₄×C₈₉	—	2	8	no	—
207	C₂²⋊C₄×C₈₉	—	2	8	no	—
208	C₂²⋊C₄×C₈₉	—	2	8	no	—
209	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
210	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
211	C₄²×C₈₉	—	2	8	no	—
212	C₄²×C₈₉	—	2	2	no	—
213	C₄²×C₈₉	—	2	2	no	—
214	C₄²×C₈₉	C₂×D₄	1	4	yes	—
215	C₄²×C₈₉	C₂×D₄	1	2	yes	—
216	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₄²×C₈₉	C₂⁴	1	2	yes	—
218	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂³×C₈₉	—	2	4	no	—
220	C₂³×C₈₉	—	4	4	no	—
221	C₂³×C₈₉	—	8	4	no	—
222	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
223	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₈₉	—	2	2	no	—
225	Q₈×C₈₉	—	2	4	no	—
226	Q₈×C₈₉	—	2	4	no	—
227	Q₈×C₈₉	—	4	4	no	—
228	Q₈×C₈₉	—	8	4	no	—
229	D₄×C₈₉	—	2	4	no	—
230	D₄×C₈₉	—	2	2	no	—
231	D₄×C₈₉	—	2	4	no	—
232	D₄×C₈₉	—	2	4	no	—
233	D₄×C₈₉	—	4	4	no	—
234	D₄×C₈₉	—	8	8	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	4	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	4	no	—
240	C₂×C₄×C₈₉	—	4	4	no	—
241	C₂×C₄×C₈₉	—	4	2	no	—
242	C₂×C₄×C₈₉	—	4	4	no	—
243	C₂×C₄×C₈₉	—	8	8	no	—
244	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
251	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
252	C₈×C₈₉	—	2	2	no	—
253	C₈×C₈₉	—	2	2	no	—
254	C₈×C₈₉	C₂×#41	1	2	yes	—
255	C₈×C₈₉	C₂×#41	1	2	yes	—
256	C₈×C₈₉	C₂×#41	1	2	yes	—
257	C₈×C₈₉	C₂×#41	1	2	yes	—
258	C₂²×C₈₉	—	2	2	no	—
259	C₂²×C₈₉	—	2	4	no	—
260	C₂²×C₈₉	—	2	2	no	—
261	C₂²×C₈₉	—	4	8	no	—
262	C₂²×C₈₉	—	4	4	no	—
263	C₂²×C₈₉	—	16	4	no	—
264	C₂²×C₈₉	#532	1	2	yes	—
265	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
266	C₄×C₈₉	—	2	2	no	—
267	C₄×C₈₉	—	2	4	no	—
268	C₄×C₈₉	—	2	2	no	—
269	C₄×C₈₉	—	2	2	no	—
270	C₄×C₈₉	—	4	4	no	—
271	C₄×C₈₉	—	4	4	no	—
272	C₄×C₈₉	—	4	4	no	—
273	C₄×C₈₉	#532	1	2	yes	—
274	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
275	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
276	#60713	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₈₉	—	2	2	no	—
278	C₂×C₈₉	—	4	2	no	—
279	C₂×C₈₉	—	8	4	no	—
280	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
281	C₂×C₈₉	#3584	1	2	yes	—
282	#3510	C₂×C₈₉	1	2	yes	complemented
283	#3183	C₂×C₈₉	1	4	yes	complemented
284	#3175	C₂×C₈₉	1	4	yes	complemented
285	#3173	C₂×C₈₉	1	4	yes	complemented
286	#3168	C₂×C₈₉	1	4	yes	complemented
287	#3160	C₂×C₈₉	1	1	yes	characteristic, complemented
288	C₂×#495	C₂×C₈₉	1	1	yes	characteristic, complemented
289	#3140	C₂×C₈₉	1	2	yes	complemented
290	#3059	C₂×C₈₉	1	1	yes	characteristic, complemented
291	#3058	C₂×C₈₉	1	1	yes	characteristic
292	#3057	C₂×C₈₉	1	2	yes	complemented
293	#2950	C₂×C₈₉	1	1	yes	characteristic, complemented
294	#2949	C₂×C₈₉	1	2	yes	complemented
295	#2948	C₂×C₈₉	1	1	yes	characteristic, complemented
296	C₄×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
297	C₈₉	#60713	1	1	yes	characteristic, direct product factor, Sylow
298	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
299	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
300	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
301	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
302	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
303	#559	—	2	4	no	—
304	#556	—	2	4	no	—
305	#551	—	2	8	no	—
306	#542	C₂²×C₈₉	1	8	yes	complemented
307	#536	C₂²×C₈₉	1	2	yes	—
308	#535	C₂²×C₈₉	1	2	yes	—
309	#533	C₂²×C₈₉	1	2	yes	—
310	#529	C₂²×C₈₉	1	8	yes	complemented
311	C₂×#124	C₂²×C₈₉	1	2	yes	—
312	#519	C₂²×C₈₉	1	2	yes	—
313	#518	C₂²×C₈₉	1	2	yes	—
314	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
315	#500	C₂²×C₈₉	1	2	yes	complemented
316	#499	C₂²×C₈₉	1	2	yes	complemented
317	#499	C₂²×C₈₉	1	2	yes	complemented
318	#498	C₂²×C₈₉	1	2	yes	complemented
319	#495	C₂²×C₈₉	1	2	yes	—
320	#495	C₂²×C₈₉	1	2	yes	—
321	#495	C₂²×C₈₉	1	2	yes	—
322	#495	C₂²×C₈₉	1	2	yes	—
323	#489	C₂²×C₈₉	1	8	yes	complemented
324	#488	C₂²×C₈₉	1	8	yes	complemented
325	#470	C₂²×C₈₉	1	4	yes	complemented
326	#469	C₂²×C₈₉	1	4	yes	—
327	#468	C₂²×C₈₉	1	8	yes	complemented
328	#467	C₂²×C₈₉	1	4	yes	complemented
329	#466	C₂²×C₈₉	1	4	yes	—
330	#465	C₂²×C₈₉	1	8	yes	complemented
331	#442	C₂²×C₈₉	1	4	yes	—
332	#441	C₂²×C₈₉	1	4	yes	complemented
333	#440	C₂²×C₈₉	1	8	yes	complemented
334	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
335	C₄×SD₁₆	C₂²×C₈₉	1	8	yes	complemented
336	C₄×D₈	C₂²×C₈₉	1	4	yes	—
337	#427	C₂²×C₈₉	1	1	yes	characteristic
338	#427	C₂²×C₈₉	1	2	yes	—
339	#427	C₂²×C₈₉	1	1	yes	characteristic
340	#419	C₂²×C₈₉	1	2	yes	—
341	#419	C₂²×C₈₉	1	2	yes	—
342	#418	C₂²×C₈₉	1	2	yes	—
343	#418	C₂²×C₈₉	1	2	yes	—
344	#405	C₂²×C₈₉	1	1	yes	characteristic
345	#405	C₂²×C₈₉	1	1	yes	characteristic
346	#405	C₂²×C₈₉	1	2	yes	complemented
347	#405	C₂²×C₈₉	1	2	yes	complemented
348	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
349	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
350	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
351	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
352	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
354	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
355	C₂×Q₁₆	—	2	4	no	—
356	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
357	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
358	C₂×SD₁₆	—	2	8	no	—
359	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
360	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
361	C₂×D₈	—	2	4	no	—
362	C₂×D₈	C₂³×C₈₉	1	2	yes	—
363	C₂×D₈	C₂³×C₈₉	1	2	yes	—
364	#131	—	2	4	no	—
365	#131	—	2	4	no	—
366	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
367	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
368	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
369	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
370	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
371	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
372	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
376	#127	—	2	2	no	—
377	#126	—	2	8	no	—
378	#126	—	2	8	no	—
379	#125	C₂³×C₈₉	1	4	yes	—
380	#124	—	2	2	no	—
381	#124	—	2	2	no	—
382	#124	—	2	8	no	—
383	#124	—	2	4	no	—
384	#124	C₂³×C₈₉	1	4	yes	—
385	#124	C₂³×C₈₉	1	4	yes	—
386	#123	—	2	4	no	—
387	#123	—	2	8	no	—
388	#123	—	2	8	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	8	no	—
391	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
392	#121	C₂³×C₈₉	1	8	yes	—
393	#120	—	2	4	no	—
394	C₄×Q₈	—	2	4	no	—
395	C₄×Q₈	—	2	4	no	—
396	C₄×Q₈	D₄×C₈₉	1	2	yes	—
397	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
398	C₄×D₄	—	2	8	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	D₄×C₈₉	1	4	yes	—
401	C₄×D₄	D₄×C₈₉	1	2	yes	—
402	C₄×D₄	C₂³×C₈₉	1	8	yes	—
403	#117	—	2	4	no	—
404	#117	—	2	8	no	—
405	#117	C₂³×C₈₉	1	2	yes	—
406	#117	C₂³×C₈₉	1	2	yes	—
407	#117	C₂³×C₈₉	1	1	yes	characteristic
408	#117	C₂³×C₈₉	1	2	yes	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
413	#107	C₂³×C₈₉	1	2	yes	—
414	#107	C₂³×C₈₉	1	2	yes	—
415	#107	C₂³×C₈₉	1	4	yes	—
416	#106	C₂³×C₈₉	1	4	yes	—
417	#106	C₂³×C₈₉	1	2	yes	—
418	#106	C₂³×C₈₉	1	2	yes	—
419	#103	C₂³×C₈₉	1	8	yes	—
420	#103	C₂³×C₈₉	1	8	yes	—
421	#102	C₂³×C₈₉	1	8	yes	—
422	#102	C₂³×C₈₉	1	8	yes	—
423	#97	C₂³×C₈₉	1	2	yes	—
424	#97	C₂³×C₈₉	1	2	yes	—
425	#97	C₂³×C₈₉	1	2	yes	—
426	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
427	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₈₉	1	2	yes	—
431	C₄×C₈	C₂³×C₈₉	1	2	yes	—
432	C₄×C₈	C₂³×C₈₉	1	2	yes	—
433	C₂⁴	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
441	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
447	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
448	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
455	Q₁₆	—	2	4	no	—
456	Q₁₆	—	2	4	no	—
457	SD₁₆	—	2	8	no	—
458	SD₁₆	—	2	8	no	—
459	D₈	—	2	4	no	—
460	D₈	—	2	4	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	4	no	—
464	M₁₆	—	2	4	no	—
465	C₂×C₈	—	2	4	no	—
466	C₂×C₈	—	2	4	no	—
467	C₂×C₈	#41×C₈₉	1	4	yes	—
468	C₂×C₈	#41×C₈₉	1	4	yes	—
469	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
470	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
471	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
473	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
474	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
482	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
483	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
492	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
493	C₄²	—	2	8	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	C₂×D₄×C₈₉	1	4	yes	—
497	C₄²	C₂×D₄×C₈₉	1	2	yes	—
498	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
499	C₄²	C₂⁴×C₈₉	1	2	yes	—
500	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
501	C₂³	—	2	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
505	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	4	4	no	—
510	Q₈	—	8	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	8	8	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	8	8	no	—
526	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
531	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
532	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
533	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	C₂×#41×C₈₉	1	2	yes	—
537	C₈	C₂×#41×C₈₉	1	2	yes	—
538	C₈	C₂×#41×C₈₉	1	2	yes	—
539	C₈	C₂×#41×C₈₉	1	2	yes	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	16	4	no	—
546	C₂²	#532×C₈₉	1	2	yes	—
547	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	4	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	#532×C₈₉	1	2	yes	—
556	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
557	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	8	4	no	—
561	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
562	C₂	C₈₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3058	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3510	C₂	semidirect
2. C₈₉×#3183	C₂	semidirect
3. C₈₉×#3175	C₂	semidirect
4. C₈₉×#3173	C₂	semidirect
5. C₈₉×#3168	C₂	semidirect
6. C₈₉×#3160	C₂	semidirect
7. C₂×#495×C₈₉	C₂	semidirect
8. C₈₉×#3140	C₂	semidirect
9. C₈₉×#3059	C₂	semidirect
11. C₈₉×#3057	C₂	semidirect
12. C₈₉×#2950	C₂	semidirect
13. C₈₉×#2949	C₂	semidirect
14. C₈₉×#2948	C₂	semidirect
15. C₄×#131×C₈₉	C₂	semidirect
24. #542×C₈₉	C₂²	semidirect
28. #529×C₈₉	C₂²	semidirect
33. #500×C₈₉	C₂²	semidirect
34. #499×C₈₉	C₂²	semidirect
35. #499×C₈₉	C₂²	semidirect
36. #498×C₈₉	C₂²	semidirect
41. #489×C₈₉	C₂²	semidirect
42. #488×C₈₉	C₂²	semidirect
43. #470×C₈₉	C₂²	semidirect
45. #468×C₈₉	C₂²	semidirect
46. #467×C₈₉	C₂²	semidirect
48. #465×C₈₉	C₂²	semidirect
50. #441×C₈₉	C₂²	semidirect
51. #440×C₈₉	C₂²	semidirect
52. C₄×Q₁₆×C₈₉	C₂²	semidirect
53. C₄×SD₁₆×C₈₉	C₂²	semidirect
64. #405×C₈₉	C₂²	semidirect
65. #405×C₈₉	C₂²	semidirect
67. C₄×M₁₆×C₈₉	C₂²	semidirect
69. C₂×C₄×C₈×C₈₉	C₂²	semidirect
276. #60713	C₈₉	direct (N × H)
282. #3510	C₂×C₈₉	semidirect
283. #3183	C₂×C₈₉	semidirect
284. #3175	C₂×C₈₉	semidirect
285. #3173	C₂×C₈₉	semidirect
286. #3168	C₂×C₈₉	semidirect
287. #3160	C₂×C₈₉	semidirect
288. C₂×#495	C₂×C₈₉	semidirect
289. #3140	C₂×C₈₉	semidirect
290. #3059	C₂×C₈₉	semidirect
292. #3057	C₂×C₈₉	semidirect
293. #2950	C₂×C₈₉	semidirect
294. #2949	C₂×C₈₉	semidirect
295. #2948	C₂×C₈₉	semidirect
296. C₄×#131	C₂×C₈₉	semidirect
297. C₈₉	#60713	direct (N × H)
306. #542	C₂²×C₈₉	semidirect
310. #529	C₂²×C₈₉	semidirect
315. #500	C₂²×C₈₉	semidirect
316. #499	C₂²×C₈₉	semidirect
317. #499	C₂²×C₈₉	semidirect
318. #498	C₂²×C₈₉	semidirect
323. #489	C₂²×C₈₉	semidirect
324. #488	C₂²×C₈₉	semidirect
325. #470	C₂²×C₈₉	semidirect
327. #468	C₂²×C₈₉	semidirect
328. #467	C₂²×C₈₉	semidirect
330. #465	C₂²×C₈₉	semidirect
332. #441	C₂²×C₈₉	semidirect
333. #440	C₂²×C₈₉	semidirect
334. C₄×Q₁₆	C₂²×C₈₉	semidirect
335. C₄×SD₁₆	C₂²×C₈₉	semidirect
346. #405	C₂²×C₈₉	semidirect
347. #405	C₂²×C₈₉	semidirect
349. C₄×M₁₆	C₂²×C₈₉	semidirect
351. C₂×C₄×C₈	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3510	2
C₈₉×#3183	2
C₈₉×#3175	2
C₈₉×#3173	2
C₈₉×#3168	2
C₈₉×#3160	2
C₂×#495×C₈₉	2
C₈₉×#3140	2
C₈₉×#3059	2
C₈₉×#3058	2
C₈₉×#3057	2
C₈₉×#2950	2
C₈₉×#2949	2
C₈₉×#2948	2
C₄×#131×C₈₉	2
#60713	89

Subgroups — C89×#60713 #36438561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60713 #36438561