Subgroups — C₂×C₈₉×#3240 #36438701

Order 22784.

1790 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3240	C₂	1	16	yes	maximal, direct product factor
4	C₂×#501×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#501×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#485×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂×#482×C₈₉	C₂	1	2	yes	maximal
10	C₂×#479×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
12	C₂×#432×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#533×C₈₉	—	2	4	no	—
14	#533×C₈₉	C₂²	1	8	yes	complemented
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	#529×C₈₉	—	2	4	no	—
18	#529×C₈₉	C₂²	1	8	yes	—
19	C₂×#126×C₈₉	—	2	1	no	—
20	C₂×#125×C₈₉	C₂²	1	2	yes	—
21	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₈₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
29	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	—	2	1	no	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	—	2	1	no	—
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#501×C₈₉	C₂²	1	8	yes	complemented
37	#501×C₈₉	C₂²	1	8	yes	complemented
38	#489×C₈₉	C₂²	1	8	yes	complemented
39	#489×C₈₉	C₂²	1	8	yes	complemented
40	#485×C₈₉	C₂²	1	16	yes	complemented
41	#482×C₈₉	C₂²	1	16	yes	—
42	#479×C₈₉	C₂²	1	16	yes	complemented
43	#478×C₈₉	C₂²	1	16	yes	complemented
44	#432×C₈₉	C₂²	1	8	yes	complemented
45	C₂×#107×C₈₉	C₂²	1	2	yes	—
46	C₂×#107×C₈₉	C₂²	1	2	yes	—
47	C₂×#106×C₈₉	C₂²	1	2	yes	—
48	C₂×#106×C₈₉	C₂²	1	2	yes	—
49	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
50	C₂×#103×C₈₉	C₂²	1	2	yes	—
51	C₂×#103×C₈₉	C₂²	1	2	yes	—
52	C₂×#102×C₈₉	C₂²	1	2	yes	—
53	C₂×#102×C₈₉	C₂²	1	2	yes	—
54	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
55	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×Q₈×C₈₉	—	2	1	no	—
58	C₂²×Q₈×C₈₉	—	2	1	no	—
59	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₈₉	—	2	1	no	—
61	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	—	2	1	no	—
63	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
67	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₈₉	—	2	2	no	—
69	C₄⋊Q₈×C₈₉	—	2	2	no	—
70	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
71	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
72	#126×C₈₉	—	2	8	no	—
73	#125×C₈₉	—	2	2	no	—
74	#125×C₈₉	—	2	4	no	—
75	#125×C₈₉	C₂³	1	8	yes	—
76	#125×C₈₉	C₂³	1	4	yes	—
77	#124×C₈₉	—	2	2	no	—
78	#124×C₈₉	C₂³	1	4	yes	—
79	#123×C₈₉	—	2	8	no	—
80	C₂²⋊Q₈×C₈₉	—	2	8	no	—
81	C₂²⋊Q₈×C₈₉	—	2	8	no	—
82	C₂²⋊Q₈×C₈₉	—	2	2	no	—
83	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
84	#121×C₈₉	—	2	2	no	—
85	#121×C₈₉	C₂³	1	4	yes	—
86	C₄×Q₈×C₈₉	—	2	8	no	—
87	C₄×Q₈×C₈₉	—	2	8	no	—
88	C₄×Q₈×C₈₉	—	2	2	no	—
89	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
90	C₄×D₄×C₈₉	—	2	8	no	—
91	C₄×D₄×C₈₉	—	2	2	no	—
92	C₄×D₄×C₈₉	C₂³	1	4	yes	—
93	#117×C₈₉	—	2	4	no	—
94	#117×C₈₉	—	2	8	no	—
95	#117×C₈₉	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₄²×C₈₉	—	2	1	no	—
115	C₂×C₄²×C₈₉	—	2	2	no	—
116	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	D₄	1	4	yes	—
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
122	#107×C₈₉	C₂³	1	8	yes	—
123	#107×C₈₉	C₂³	1	8	yes	—
124	#106×C₈₉	C₂³	1	8	yes	—
125	#106×C₈₉	C₂³	1	8	yes	—
126	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
127	#103×C₈₉	C₂³	1	8	yes	—
128	#103×C₈₉	C₂³	1	8	yes	—
129	#102×C₈₉	C₂³	1	8	yes	—
130	#102×C₈₉	C₂³	1	8	yes	—
131	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
132	#97×C₈₉	C₂³	1	4	yes	—
133	#97×C₈₉	C₂³	1	4	yes	—
134	C₂⁴×C₈₉	—	2	1	no	—
135	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	4	no	—
138	C₂×Q₈×C₈₉	—	2	4	no	—
139	C₂×Q₈×C₈₉	—	2	4	no	—
140	C₂×Q₈×C₈₉	—	4	4	no	—
141	C₂×Q₈×C₈₉	—	4	4	no	—
142	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
143	C₂×D₄×C₈₉	—	2	4	no	—
144	C₂×D₄×C₈₉	—	2	1	no	—
145	C₂×D₄×C₈₉	—	2	4	no	—
146	C₂×D₄×C₈₉	—	4	4	no	—
147	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₈₉	—	2	4	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	2	no	—
152	C₂²×C₄×C₈₉	—	2	2	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	4	no	—
155	C₂²×C₄×C₈₉	—	4	2	no	—
156	C₂²×C₄×C₈₉	—	4	2	no	—
157	C₂²×C₄×C₈₉	—	4	4	no	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₈₉	—	2	4	no	—
169	C₂×C₈×C₈₉	—	2	4	no	—
170	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
171	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
172	C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₄⋊C₄×C₈₉	—	2	4	no	—
174	C₄⋊C₄×C₈₉	—	2	4	no	—
175	C₄⋊C₄×C₈₉	—	2	8	no	—
176	C₄⋊C₄×C₈₉	—	2	8	no	—
177	C₄⋊C₄×C₈₉	—	2	4	no	—
178	C₄⋊C₄×C₈₉	—	2	4	no	—
179	C₄⋊C₄×C₈₉	—	2	4	no	—
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	—	2	2	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
186	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
187	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
188	C₂²⋊C₄×C₈₉	—	2	8	no	—
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	C₄²×C₈₉	—	2	4	no	—
195	C₄²×C₈₉	—	2	8	no	—
196	C₄²×C₈₉	C₂×D₄	1	4	yes	—
197	C₄²×C₈₉	C₂×D₄	1	2	yes	—
198	C₄²×C₈₉	C₂×D₄	1	4	yes	—
199	C₄²×C₈₉	C₂×D₄	1	2	yes	—
200	C₄²×C₈₉	C₂⁴	1	2	yes	—
201	C₄²×C₈₉	C₂⁴	1	2	yes	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	2	no	—
204	C₂³×C₈₉	—	2	2	no	—
205	C₂³×C₈₉	—	2	2	no	—
206	C₂³×C₈₉	—	4	2	no	—
207	C₂³×C₈₉	—	4	2	no	—
208	C₂³×C₈₉	—	4	2	no	—
209	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
210	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₈₉	—	2	4	no	—
212	Q₈×C₈₉	—	4	8	no	—
213	Q₈×C₈₉	—	4	8	no	—
214	Q₈×C₈₉	—	4	2	no	—
215	D₄×C₈₉	—	2	4	no	—
216	D₄×C₈₉	—	4	8	no	—
217	D₄×C₈₉	—	4	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	2	2	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	4	no	—
225	C₂×C₄×C₈₉	—	2	2	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	4	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	2	no	—
230	C₂×C₄×C₈₉	—	4	4	no	—
231	C₂×C₄×C₈₉	—	4	4	no	—
232	C₂×C₄×C₈₉	—	4	8	no	—
233	C₂×C₄×C₈₉	—	4	2	no	—
234	C₂×C₄×C₈₉	—	4	2	no	—
235	C₂×C₄×C₈₉	—	4	2	no	—
236	C₂×C₄×C₈₉	—	4	4	no	—
237	C₂×C₄×C₈₉	—	4	4	no	—
238	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
245	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
246	C₈×C₈₉	—	2	4	no	—
247	C₈×C₈₉	—	2	4	no	—
248	C₂²×C₈₉	—	2	2	no	—
249	C₂²×C₈₉	—	2	2	no	—
250	C₂²×C₈₉	—	2	2	no	—
251	C₂²×C₈₉	—	4	4	no	—
252	C₂²×C₈₉	—	4	2	no	—
253	C₂²×C₈₉	—	4	2	no	—
254	C₂²×C₈₉	—	4	2	no	—
255	C₂²×C₈₉	—	8	4	no	—
256	C₂²×C₈₉	#536	1	2	yes	—
257	C₂²×C₈₉	#575	1	2	yes	—
258	C₂²×C₈₉	#575	1	2	yes	—
259	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₈₉	—	2	2	no	—
261	C₄×C₈₉	—	2	2	no	—
262	C₄×C₈₉	—	2	2	no	—
263	C₄×C₈₉	—	2	2	no	—
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	4	2	no	—
266	C₄×C₈₉	—	4	2	no	—
267	C₄×C₈₉	—	4	2	no	—
268	C₄×C₈₉	—	4	4	no	—
269	C₄×C₈₉	—	4	4	no	—
270	C₄×C₈₉	#536	1	2	yes	—
271	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
272	C₂×#3240	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₈₉	—	4	2	no	—
274	C₂×C₈₉	—	8	2	no	—
275	C₂×C₈₉	#3240	1	4	yes	direct product factor
276	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
277	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
278	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
279	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
280	C₂×#529	C₂×C₈₉	1	1	yes	characteristic
281	#3240	C₂×C₈₉	1	16	yes	direct product factor
282	C₂×#501	C₂×C₈₉	1	1	yes	characteristic, complemented
283	C₂×#501	C₂×C₈₉	1	1	yes	characteristic, complemented
284	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
285	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
286	C₂×#485	C₂×C₈₉	1	2	yes	complemented
287	C₂×#482	C₂×C₈₉	1	2	yes	—
288	C₂×#479	C₂×C₈₉	1	2	yes	complemented
289	C₂×#478	C₂×C₈₉	1	2	yes	complemented
290	C₂×#432	C₂×C₈₉	1	1	yes	characteristic, complemented
291	C₈₉	C₂×#3240	1	1	yes	characteristic, direct product factor, Sylow
292	#533	—	2	4	no	—
293	#533	C₂²×C₈₉	1	8	yes	complemented
294	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
296	#529	—	2	4	no	—
297	#529	C₂²×C₈₉	1	8	yes	—
298	C₂×#126	—	2	1	no	—
299	C₂×#125	C₂²×C₈₉	1	2	yes	—
300	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
301	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
302	C₂×#123	—	2	1	no	—
303	C₂×C₂²⋊Q₈	—	2	1	no	—
304	C₂×C₂²⋊Q₈	—	2	1	no	—
305	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
306	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
307	C₂×C₄×Q₈	—	2	1	no	—
308	C₂×C₄×Q₈	—	2	1	no	—
309	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
310	C₂×C₄×D₄	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
312	C₂×#117	—	2	1	no	—
313	C₂×#117	C₂²×C₈₉	1	2	yes	—
314	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
315	#501	C₂²×C₈₉	1	8	yes	complemented
316	#501	C₂²×C₈₉	1	8	yes	complemented
317	#489	C₂²×C₈₉	1	8	yes	complemented
318	#489	C₂²×C₈₉	1	8	yes	complemented
319	#485	C₂²×C₈₉	1	16	yes	complemented
320	#482	C₂²×C₈₉	1	16	yes	—
321	#479	C₂²×C₈₉	1	16	yes	complemented
322	#478	C₂²×C₈₉	1	16	yes	complemented
323	#432	C₂²×C₈₉	1	8	yes	complemented
324	C₂×#107	C₂²×C₈₉	1	2	yes	—
325	C₂×#107	C₂²×C₈₉	1	2	yes	—
326	C₂×#106	C₂²×C₈₉	1	2	yes	—
327	C₂×#106	C₂²×C₈₉	1	2	yes	—
328	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
329	C₂×#103	C₂²×C₈₉	1	2	yes	—
330	C₂×#103	C₂²×C₈₉	1	2	yes	—
331	C₂×#102	C₂²×C₈₉	1	2	yes	—
332	C₂×#102	C₂²×C₈₉	1	2	yes	—
333	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
334	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
343	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
346	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
350	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
351	#126	—	2	8	no	—
352	#125	—	2	2	no	—
353	#125	—	2	4	no	—
354	#125	C₂³×C₈₉	1	4	yes	—
355	#125	C₂³×C₈₉	1	8	yes	—
356	#124	—	2	2	no	—
357	#124	C₂³×C₈₉	1	4	yes	—
358	#123	—	2	8	no	—
359	C₂²⋊Q₈	—	2	8	no	—
360	C₂²⋊Q₈	—	2	8	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
363	#121	—	2	2	no	—
364	#121	C₂³×C₈₉	1	4	yes	—
365	C₄×Q₈	—	2	8	no	—
366	C₄×Q₈	—	2	8	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
369	C₄×D₄	—	2	8	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	C₂³×C₈₉	1	4	yes	—
372	#117	—	2	4	no	—
373	#117	—	2	8	no	—
374	#117	C₂³×C₈₉	1	8	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
396	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
397	C₂×C₄²	D₄×C₈₉	1	4	yes	—
398	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
401	#107	C₂³×C₈₉	1	8	yes	—
402	#107	C₂³×C₈₉	1	8	yes	—
403	#106	C₂³×C₈₉	1	8	yes	—
404	#106	C₂³×C₈₉	1	8	yes	—
405	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
406	#103	C₂³×C₈₉	1	8	yes	—
407	#103	C₂³×C₈₉	1	8	yes	—
408	#102	C₂³×C₈₉	1	8	yes	—
409	#102	C₂³×C₈₉	1	8	yes	—
410	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
411	#97	C₂³×C₈₉	1	4	yes	—
412	#97	C₂³×C₈₉	1	4	yes	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	4	4	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	—	2	4	no	—
449	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
450	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	8	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
465	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
466	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	8	no	—
475	C₄²	C₂×D₄×C₈₉	1	4	yes	—
476	C₄²	C₂×D₄×C₈₉	1	2	yes	—
477	C₄²	C₂×D₄×C₈₉	1	4	yes	—
478	C₄²	C₂×D₄×C₈₉	1	2	yes	—
479	C₄²	C₂⁴×C₈₉	1	2	yes	—
480	C₄²	C₂⁴×C₈₉	1	2	yes	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
489	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
490	Q₈	—	2	4	no	—
491	Q₈	—	4	8	no	—
492	Q₈	—	4	8	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
523	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
524	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	8	4	no	—
535	C₂²	#536×C₈₉	1	2	yes	—
536	C₂²	#575×C₈₉	1	2	yes	—
537	C₂²	#575×C₈₉	1	2	yes	—
538	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	#536×C₈₉	1	2	yes	—
550	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
551	C₂	—	4	2	no	—
552	C₂	—	8	2	no	—
553	C₂	C₈₉×#3240	1	4	yes	direct product factor
554	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
555	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
556	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3240	C₂	direct (N × H)
4. C₂×#501×C₈₉	C₂	semidirect
5. C₂×#501×C₈₉	C₂	semidirect
6. C₂×#489×C₈₉	C₂	semidirect
7. C₂×#489×C₈₉	C₂	semidirect
8. C₂×#485×C₈₉	C₂	semidirect
10. C₂×#479×C₈₉	C₂	semidirect
11. C₂×#478×C₈₉	C₂	semidirect
12. C₂×#432×C₈₉	C₂	semidirect
14. #533×C₈₉	C₂²	semidirect
36. #501×C₈₉	C₂²	semidirect
37. #501×C₈₉	C₂²	semidirect
38. #489×C₈₉	C₂²	semidirect
39. #489×C₈₉	C₂²	semidirect
40. #485×C₈₉	C₂²	semidirect
42. #479×C₈₉	C₂²	semidirect
43. #478×C₈₉	C₂²	semidirect
44. #432×C₈₉	C₂²	semidirect
272. C₂×#3240	C₈₉	direct (N × H)
275. C₂×C₈₉	#3240	direct (N × H)
279. C₂×#533	C₂×C₈₉	semidirect
281. #3240	C₂×C₈₉	direct (N × H)
282. C₂×#501	C₂×C₈₉	semidirect
283. C₂×#501	C₂×C₈₉	semidirect
284. C₂×#489	C₂×C₈₉	semidirect
285. C₂×#489	C₂×C₈₉	semidirect
286. C₂×#485	C₂×C₈₉	semidirect
288. C₂×#479	C₂×C₈₉	semidirect
289. C₂×#478	C₂×C₈₉	semidirect
290. C₂×#432	C₂×C₈₉	semidirect
291. C₈₉	C₂×#3240	direct (N × H)
293. #533	C₂²×C₈₉	semidirect
315. #501	C₂²×C₈₉	semidirect
316. #501	C₂²×C₈₉	semidirect
317. #489	C₂²×C₈₉	semidirect
318. #489	C₂²×C₈₉	semidirect
319. #485	C₂²×C₈₉	semidirect
321. #479	C₂²×C₈₉	semidirect
322. #478	C₂²×C₈₉	semidirect
323. #432	C₂²×C₈₉	semidirect
553. C₂	C₈₉×#3240	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#529×C₈₉	2
C₈₉×#3240	2
C₂×#501×C₈₉	2
C₂×#489×C₈₉	2
C₂×#485×C₈₉	2
C₂×#482×C₈₉	2
C₂×#479×C₈₉	2
C₂×#478×C₈₉	2
C₂×#432×C₈₉	2
C₂×#3240	89

Subgroups — C2×C89×#3240 #36438701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3240 #36438701