Subgroups — C₈₉×#60967 #36438815

Order 22784.

1824 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3254	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3233	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3212	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3197	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3183	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3116	C₂	1	4	yes	maximal, complemented
10	C₈₉×#3115	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₈₉	C₂²	1	2	yes	—
13	#533×C₈₉	C₂²	1	2	yes	—
14	#533×C₈₉	C₂²	1	2	yes	—
15	#532×C₈₉	C₂²	1	2	yes	—
16	#532×C₈₉	C₂²	1	2	yes	—
17	#532×C₈₉	C₂²	1	2	yes	—
18	#529×C₈₉	—	2	2	no	—
19	#529×C₈₉	—	2	2	no	—
20	#529×C₈₉	—	2	2	no	—
21	#529×C₈₉	—	2	2	no	—
22	#529×C₈₉	C₂²	1	4	yes	—
23	#529×C₈₉	C₂²	1	4	yes	—
24	#525×C₈₉	—	2	2	no	—
25	#525×C₈₉	—	2	2	no	—
26	#525×C₈₉	C₂²	1	4	yes	—
27	C₄×#41×C₈₉	—	2	2	no	—
28	C₄×#41×C₈₉	—	2	2	no	—
29	C₄×#41×C₈₉	C₂²	1	4	yes	—
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#499×C₈₉	C₂²	1	4	yes	complemented
32	#495×C₈₉	C₂²	1	4	yes	complemented
33	#488×C₈₉	C₂²	1	8	yes	complemented
34	#485×C₈₉	C₂²	1	8	yes	—
35	#482×C₈₉	C₂²	1	8	yes	—
36	#477×C₈₉	C₂²	1	4	yes	complemented
37	#476×C₈₉	C₂²	1	4	yes	complemented
38	#475×C₈₉	C₂²	1	4	yes	complemented
39	#474×C₈₉	C₂²	1	4	yes	complemented
40	#470×C₈₉	C₂²	1	4	yes	—
41	#469×C₈₉	C₂²	1	4	yes	—
42	#468×C₈₉	C₂²	1	8	yes	—
43	#462×C₈₉	C₂²	1	4	yes	complemented
44	#461×C₈₉	C₂²	1	4	yes	complemented
45	#460×C₈₉	C₂²	1	4	yes	complemented
46	#459×C₈₉	C₂²	1	4	yes	complemented
47	#452×C₈₉	C₂²	1	8	yes	—
48	#449×C₈₉	C₂²	1	8	yes	—
49	#442×C₈₉	C₂²	1	4	yes	complemented
50	#441×C₈₉	C₂²	1	4	yes	complemented
51	#440×C₈₉	C₂²	1	8	yes	complemented
52	#432×C₈₉	C₂²	1	4	yes	—
53	#431×C₈₉	C₂²	1	4	yes	—
54	#423×C₈₉	C₂²	1	1	yes	characteristic
55	#423×C₈₉	C₂²	1	1	yes	characteristic
56	#407×C₈₉	C₂²	1	2	yes	—
57	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
58	C₂×#41×C₈₉	—	2	2	no	—
59	C₂×#41×C₈₉	—	2	2	no	—
60	C₂×#41×C₈₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₈₉	D₄	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
64	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
65	C₂×D₈×C₈₉	C₂³	1	4	yes	—
66	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
71	#127×C₈₉	C₂³	1	2	yes	—
72	#126×C₈₉	—	2	4	no	—
73	#126×C₈₉	—	2	4	no	—
74	#125×C₈₉	—	2	2	no	—
75	#125×C₈₉	—	2	2	no	—
76	#125×C₈₉	C₂³	1	4	yes	—
77	#124×C₈₉	—	2	2	no	—
78	#124×C₈₉	—	2	2	no	—
79	#124×C₈₉	C₂³	1	4	yes	—
80	#123×C₈₉	—	2	4	no	—
81	#123×C₈₉	—	2	4	no	—
82	#123×C₈₉	—	2	4	no	—
83	C₂²⋊Q₈×C₈₉	—	2	2	no	—
84	C₂²⋊Q₈×C₈₉	—	2	2	no	—
85	C₂²⋊Q₈×C₈₉	—	2	2	no	—
86	C₂²⋊Q₈×C₈₉	—	2	2	no	—
87	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
88	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
89	#121×C₈₉	—	2	2	no	—
90	#121×C₈₉	—	2	2	no	—
91	#121×C₈₉	—	2	2	no	—
92	#121×C₈₉	—	2	2	no	—
93	#121×C₈₉	C₂³	1	4	yes	—
94	#121×C₈₉	C₂³	1	4	yes	—
95	#120×C₈₉	—	2	4	no	—
96	C₄×Q₈×C₈₉	—	2	2	no	—
97	C₄×Q₈×C₈₉	—	2	2	no	—
98	C₄×Q₈×C₈₉	—	2	2	no	—
99	C₄×Q₈×C₈₉	—	2	2	no	—
100	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
101	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
102	C₄×D₄×C₈₉	—	2	4	no	—
103	C₄×D₄×C₈₉	—	2	4	no	—
104	C₄×D₄×C₈₉	—	2	4	no	—
105	C₄×D₄×C₈₉	—	2	4	no	—
106	C₄×D₄×C₈₉	—	2	4	no	—
107	C₄×D₄×C₈₉	—	2	4	no	—
108	C₄×D₄×C₈₉	—	2	2	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₄×D₄×C₈₉	—	2	2	no	—
111	C₄×D₄×C₈₉	—	2	2	no	—
112	C₄×D₄×C₈₉	C₂³	1	4	yes	—
113	C₄×D₄×C₈₉	C₂³	1	4	yes	—
114	#117×C₈₉	—	2	2	no	—
115	#117×C₈₉	—	2	2	no	—
116	#117×C₈₉	—	2	4	no	—
117	#117×C₈₉	—	2	4	no	—
118	#117×C₈₉	—	2	4	no	—
119	#117×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₈₉	—	2	4	no	—
121	C₂×C₄²×C₈₉	D₄	1	2	yes	—
122	C₂×C₄²×C₈₉	D₄	1	2	yes	—
123	C₂×C₄²×C₈₉	D₄	1	2	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
128	#107×C₈₉	C₂³	1	8	yes	—
129	#106×C₈₉	C₂³	1	4	yes	—
130	#106×C₈₉	C₂³	1	4	yes	—
131	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
132	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
133	#103×C₈₉	C₂³	1	8	yes	—
134	#103×C₈₉	C₂³	1	8	yes	—
135	#102×C₈₉	C₂³	1	8	yes	—
136	#102×C₈₉	C₂³	1	8	yes	—
137	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
138	#97×C₈₉	C₂³	1	4	yes	—
139	C₄×C₈×C₈₉	C₂³	1	4	yes	—
140	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
141	#41×C₈₉	—	4	4	no	—
142	#41×C₈₉	—	4	4	no	—
143	#41×C₈₉	—	4	8	no	—
144	#41×C₈₉	—	4	8	no	—
145	C₂×Q₈×C₈₉	—	2	2	no	—
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
148	C₂×D₄×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	4	no	—
151	C₂×D₄×C₈₉	—	2	2	no	—
152	C₂×D₄×C₈₉	—	2	2	no	—
153	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₈₉	—	2	4	no	—
155	C₂²×C₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	2	4	no	—
157	C₂²×C₄×C₈₉	—	4	4	no	—
158	C₂²×C₄×C₈₉	—	4	1	no	—
159	C₂²×C₄×C₈₉	—	4	1	no	—
160	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₈₉	—	4	4	no	—
171	SD₁₆×C₈₉	—	4	8	no	—
172	D₈×C₈₉	—	4	4	no	—
173	M₁₆×C₈₉	—	4	2	no	—
174	M₁₆×C₈₉	—	4	2	no	—
175	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
176	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	—	2	2	no	—
179	C₄⋊C₄×C₈₉	—	2	2	no	—
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	—	2	4	no	—
182	C₄⋊C₄×C₈₉	—	2	4	no	—
183	C₄⋊C₄×C₈₉	—	2	4	no	—
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	4	no	—
186	C₄⋊C₄×C₈₉	—	2	4	no	—
187	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
188	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
189	C₂²⋊C₄×C₈₉	—	2	4	no	—
190	C₂²⋊C₄×C₈₉	—	2	4	no	—
191	C₂²⋊C₄×C₈₉	—	2	4	no	—
192	C₂²⋊C₄×C₈₉	—	2	4	no	—
193	C₂²⋊C₄×C₈₉	—	2	4	no	—
194	C₂²⋊C₄×C₈₉	—	2	4	no	—
195	C₂²⋊C₄×C₈₉	—	2	4	no	—
196	C₂²⋊C₄×C₈₉	—	2	4	no	—
197	C₂²⋊C₄×C₈₉	—	2	4	no	—
198	C₄²×C₈₉	—	2	4	no	—
199	C₄²×C₈₉	—	2	4	no	—
200	C₄²×C₈₉	—	2	4	no	—
201	C₄²×C₈₉	C₂×D₄	1	2	yes	—
202	C₄²×C₈₉	C₂×D₄	1	2	yes	—
203	C₄²×C₈₉	C₂×D₄	1	2	yes	—
204	C₄²×C₈₉	C₂×D₄	1	2	yes	—
205	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₈₉	C₂×D₄	1	2	yes	—
207	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₄²×C₈₉	C₂⁴	1	2	yes	—
211	C₂³×C₈₉	—	2	4	no	—
212	C₂³×C₈₉	—	4	1	no	—
213	C₂³×C₈₉	—	4	2	no	—
214	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₈₉	—	2	4	no	—
217	Q₈×C₈₉	—	2	4	no	—
218	Q₈×C₈₉	—	4	4	no	—
219	Q₈×C₈₉	—	4	4	no	—
220	D₄×C₈₉	—	2	4	no	—
221	D₄×C₈₉	—	2	4	no	—
222	D₄×C₈₉	—	4	4	no	—
223	D₄×C₈₉	—	4	8	no	—
224	D₄×C₈₉	—	4	8	no	—
225	D₄×C₈₉	—	4	8	no	—
226	D₄×C₈₉	—	4	4	no	—
227	C₂×C₄×C₈₉	—	2	4	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	4	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	2	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	4	no	—
235	C₂×C₄×C₈₉	—	2	4	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	4	1	no	—
238	C₂×C₄×C₈₉	—	4	2	no	—
239	C₂×C₄×C₈₉	—	4	2	no	—
240	C₂×C₄×C₈₉	—	4	2	no	—
241	C₂×C₄×C₈₉	—	4	2	no	—
242	C₂×C₄×C₈₉	—	4	8	no	—
243	C₂×C₄×C₈₉	—	4	8	no	—
244	C₂×C₄×C₈₉	—	4	8	no	—
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	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
252	C₈×C₈₉	—	2	4	no	—
253	C₈×C₈₉	—	2	4	no	—
254	C₂²×C₈₉	—	2	2	no	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	2	2	no	—
257	C₂²×C₈₉	—	2	2	no	—
258	C₂²×C₈₉	—	2	2	no	—
259	C₂²×C₈₉	—	4	4	no	—
260	C₂²×C₈₉	—	4	4	no	—
261	C₂²×C₈₉	—	4	4	no	—
262	C₂²×C₈₉	—	4	4	no	—
263	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	2	no	—
267	C₄×C₈₉	—	2	2	no	—
268	C₄×C₈₉	—	2	2	no	—
269	C₄×C₈₉	—	4	4	no	—
270	C₄×C₈₉	—	4	4	no	—
271	C₄×C₈₉	—	4	4	no	—
272	C₄×C₈₉	#575	1	4	yes	—
273	C₄×C₈₉	#585	1	1	yes	characteristic
274	C₄×C₈₉	#585	1	1	yes	characteristic
275	#60967	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂×C₈₉	—	4	2	no	—
277	C₂×C₈₉	—	4	1	no	—
278	C₂×C₈₉	—	8	4	no	—
279	C₂×C₈₉	#3449	1	1	yes	characteristic
280	C₂×C₈₉	C₂×#575	1	2	yes	—
281	#3444	C₂×C₈₉	1	2	yes	complemented
282	#3255	C₂×C₈₉	1	1	yes	characteristic, complemented
283	#3254	C₂×C₈₉	1	2	yes	complemented
284	#3253	C₂×C₈₉	1	1	yes	characteristic, complemented
285	#3233	C₂×C₈₉	1	4	yes	complemented
286	#3212	C₂×C₈₉	1	4	yes	complemented
287	#3197	C₂×C₈₉	1	4	yes	complemented
288	#3183	C₂×C₈₉	1	4	yes	complemented
289	#3116	C₂×C₈₉	1	4	yes	complemented
290	#3115	C₂×C₈₉	1	4	yes	complemented
291	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
292	C₈₉	#60967	1	1	yes	characteristic, direct product factor, Sylow
293	#533	C₂²×C₈₉	1	2	yes	—
294	#533	C₂²×C₈₉	1	2	yes	—
295	#533	C₂²×C₈₉	1	2	yes	—
296	#532	C₂²×C₈₉	1	2	yes	—
297	#532	C₂²×C₈₉	1	2	yes	—
298	#532	C₂²×C₈₉	1	2	yes	—
299	#529	—	2	2	no	—
300	#529	—	2	2	no	—
301	#529	—	2	2	no	—
302	#529	—	2	2	no	—
303	#529	C₂²×C₈₉	1	4	yes	—
304	#529	C₂²×C₈₉	1	4	yes	—
305	#525	—	2	2	no	—
306	#525	—	2	2	no	—
307	#525	C₂²×C₈₉	1	4	yes	—
308	C₄×#41	—	2	2	no	—
309	C₄×#41	—	2	2	no	—
310	C₄×#41	C₂²×C₈₉	1	4	yes	—
311	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
312	#499	C₂²×C₈₉	1	4	yes	complemented
313	#495	C₂²×C₈₉	1	4	yes	complemented
314	#488	C₂²×C₈₉	1	8	yes	complemented
315	#485	C₂²×C₈₉	1	8	yes	—
316	#482	C₂²×C₈₉	1	8	yes	—
317	#477	C₂²×C₈₉	1	4	yes	complemented
318	#476	C₂²×C₈₉	1	4	yes	complemented
319	#475	C₂²×C₈₉	1	4	yes	complemented
320	#474	C₂²×C₈₉	1	4	yes	complemented
321	#470	C₂²×C₈₉	1	4	yes	—
322	#469	C₂²×C₈₉	1	4	yes	—
323	#468	C₂²×C₈₉	1	8	yes	—
324	#462	C₂²×C₈₉	1	4	yes	complemented
325	#461	C₂²×C₈₉	1	4	yes	complemented
326	#460	C₂²×C₈₉	1	4	yes	complemented
327	#459	C₂²×C₈₉	1	4	yes	complemented
328	#452	C₂²×C₈₉	1	8	yes	—
329	#449	C₂²×C₈₉	1	8	yes	—
330	#442	C₂²×C₈₉	1	4	yes	complemented
331	#441	C₂²×C₈₉	1	4	yes	complemented
332	#440	C₂²×C₈₉	1	8	yes	complemented
333	#432	C₂²×C₈₉	1	4	yes	—
334	#431	C₂²×C₈₉	1	4	yes	—
335	#423	C₂²×C₈₉	1	1	yes	characteristic
336	#423	C₂²×C₈₉	1	1	yes	characteristic
337	#407	C₂²×C₈₉	1	2	yes	—
338	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	C₂³×C₈₉	1	4	yes	—
342	C₂³×C₄	D₄×C₈₉	1	2	yes	—
343	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
344	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
345	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
346	C₂×D₈	C₂³×C₈₉	1	4	yes	—
347	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
348	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
349	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
350	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
352	#127	C₂³×C₈₉	1	2	yes	—
353	#126	—	2	4	no	—
354	#126	—	2	4	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	C₂³×C₈₉	1	4	yes	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	C₂³×C₈₉	1	4	yes	—
361	#123	—	2	4	no	—
362	#123	—	2	4	no	—
363	#123	—	2	4	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	2	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
369	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	C₂³×C₈₉	1	4	yes	—
375	#121	C₂³×C₈₉	1	4	yes	—
376	#120	—	2	4	no	—
377	C₄×Q₈	—	2	2	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
382	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	4	no	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	C₂³×C₈₉	1	4	yes	—
394	C₄×D₄	C₂³×C₈₉	1	4	yes	—
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	#117	—	2	4	no	—
398	#117	—	2	4	no	—
399	#117	—	2	4	no	—
400	#117	C₂³×C₈₉	1	4	yes	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	D₄×C₈₉	1	2	yes	—
403	C₂×C₄²	D₄×C₈₉	1	2	yes	—
404	C₂×C₄²	D₄×C₈₉	1	2	yes	—
405	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
406	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
408	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
409	#107	C₂³×C₈₉	1	8	yes	—
410	#106	C₂³×C₈₉	1	4	yes	—
411	#106	C₂³×C₈₉	1	4	yes	—
412	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
413	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
414	#103	C₂³×C₈₉	1	8	yes	—
415	#103	C₂³×C₈₉	1	8	yes	—
416	#102	C₂³×C₈₉	1	8	yes	—
417	#102	C₂³×C₈₉	1	8	yes	—
418	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
419	#97	C₂³×C₈₉	1	4	yes	—
420	C₄×C₈	C₂³×C₈₉	1	4	yes	—
421	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
422	#41	—	4	4	no	—
423	#41	—	4	4	no	—
424	#41	—	4	8	no	—
425	#41	—	4	8	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
451	Q₁₆	—	4	4	no	—
452	SD₁₆	—	4	8	no	—
453	D₈	—	4	4	no	—
454	M₁₆	—	4	2	no	—
455	M₁₆	—	4	2	no	—
456	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
457	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	2	4	no	—
482	C₄²	C₂×D₄×C₈₉	1	2	yes	—
483	C₄²	C₂×D₄×C₈₉	1	2	yes	—
484	C₄²	C₂×D₄×C₈₉	1	2	yes	—
485	C₄²	C₂×D₄×C₈₉	1	2	yes	—
486	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₈₉	1	2	yes	—
488	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
489	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
490	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₄²	C₂⁴×C₈₉	1	2	yes	—
492	C₂³	—	2	4	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
496	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	4	4	no	—
500	Q₈	—	4	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
532	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
533	C₈	—	2	4	no	—
534	C₈	—	2	4	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	#575×C₈₉	1	4	yes	—
554	C₄	#585×C₈₉	1	1	yes	characteristic
555	C₄	#585×C₈₉	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	4	2	no	—
558	C₂	—	8	4	no	—
559	C₂	C₈₉×#3449	1	1	yes	characteristic
560	C₂	C₂×#575×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3444	C₂	semidirect
2. C₈₉×#3255	C₂	semidirect
3. C₈₉×#3254	C₂	semidirect
4. C₈₉×#3253	C₂	semidirect
5. C₈₉×#3233	C₂	semidirect
6. C₈₉×#3212	C₂	semidirect
7. C₈₉×#3197	C₂	semidirect
8. C₈₉×#3183	C₂	semidirect
9. C₈₉×#3116	C₂	semidirect
10. C₈₉×#3115	C₂	semidirect
11. C₈₉×#2920	C₂	semidirect
31. #499×C₈₉	C₂²	semidirect
32. #495×C₈₉	C₂²	semidirect
33. #488×C₈₉	C₂²	semidirect
36. #477×C₈₉	C₂²	semidirect
37. #476×C₈₉	C₂²	semidirect
38. #475×C₈₉	C₂²	semidirect
39. #474×C₈₉	C₂²	semidirect
43. #462×C₈₉	C₂²	semidirect
44. #461×C₈₉	C₂²	semidirect
45. #460×C₈₉	C₂²	semidirect
46. #459×C₈₉	C₂²	semidirect
49. #442×C₈₉	C₂²	semidirect
50. #441×C₈₉	C₂²	semidirect
51. #440×C₈₉	C₂²	semidirect
275. #60967	C₈₉	direct (N × H)
281. #3444	C₂×C₈₉	semidirect
282. #3255	C₂×C₈₉	semidirect
283. #3254	C₂×C₈₉	semidirect
284. #3253	C₂×C₈₉	semidirect
285. #3233	C₂×C₈₉	semidirect
286. #3212	C₂×C₈₉	semidirect
287. #3197	C₂×C₈₉	semidirect
288. #3183	C₂×C₈₉	semidirect
289. #3116	C₂×C₈₉	semidirect
290. #3115	C₂×C₈₉	semidirect
291. #2920	C₂×C₈₉	semidirect
292. C₈₉	#60967	direct (N × H)
312. #499	C₂²×C₈₉	semidirect
313. #495	C₂²×C₈₉	semidirect
314. #488	C₂²×C₈₉	semidirect
317. #477	C₂²×C₈₉	semidirect
318. #476	C₂²×C₈₉	semidirect
319. #475	C₂²×C₈₉	semidirect
320. #474	C₂²×C₈₉	semidirect
324. #462	C₂²×C₈₉	semidirect
325. #461	C₂²×C₈₉	semidirect
326. #460	C₂²×C₈₉	semidirect
327. #459	C₂²×C₈₉	semidirect
330. #442	C₂²×C₈₉	semidirect
331. #441	C₂²×C₈₉	semidirect
332. #440	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×#3444	2
C₈₉×#3255	2
C₈₉×#3254	2
C₈₉×#3253	2
C₈₉×#3233	2
C₈₉×#3212	2
C₈₉×#3197	2
C₈₉×#3183	2
C₈₉×#3116	2
C₈₉×#3115	2
C₈₉×#2920	2
#60967	89

Subgroups — C89×#60967 #36438815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60967 #36438815