Subgroups — C₈₉×#60870 #36438718

Order 22784.

1690 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3244	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3243	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3165	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3140	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3095	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3094	C₂	1	2	yes	maximal
9	C₈₉×#3078	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3077	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	#544×C₈₉	—	2	1	no	—
13	#544×C₈₉	—	2	1	no	—
14	#544×C₈₉	C₂²	1	4	yes	complemented
15	#544×C₈₉	C₂²	1	4	yes	complemented
16	#543×C₈₉	—	2	1	no	—
17	#543×C₈₉	—	2	1	no	—
18	#542×C₈₉	—	2	4	no	—
19	#542×C₈₉	C₂²	1	8	yes	—
20	#533×C₈₉	—	2	4	no	—
21	#533×C₈₉	C₂²	1	2	yes	—
22	#533×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#126×C₈₉	—	2	1	no	—
25	C₂×#124×C₈₉	—	2	1	no	—
26	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#123×C₈₉	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	C₂²	1	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	#501×C₈₉	C₂²	1	8	yes	complemented
36	#500×C₈₉	C₂²	1	4	yes	complemented
37	#498×C₈₉	C₂²	1	4	yes	complemented
38	#489×C₈₉	C₂²	1	4	yes	complemented
39	#489×C₈₉	C₂²	1	4	yes	complemented
40	#488×C₈₉	C₂²	1	8	yes	complemented
41	#485×C₈₉	C₂²	1	8	yes	complemented
42	#484×C₈₉	C₂²	1	4	yes	complemented
43	#483×C₈₉	C₂²	1	4	yes	complemented
44	#482×C₈₉	C₂²	1	8	yes	—
45	#481×C₈₉	C₂²	1	4	yes	—
46	#480×C₈₉	C₂²	1	4	yes	—
47	#479×C₈₉	C₂²	1	8	yes	complemented
48	#478×C₈₉	C₂²	1	8	yes	complemented
49	#477×C₈₉	C₂²	1	4	yes	complemented
50	#476×C₈₉	C₂²	1	4	yes	complemented
51	#475×C₈₉	C₂²	1	4	yes	complemented
52	#474×C₈₉	C₂²	1	4	yes	complemented
53	#433×C₈₉	C₂²	1	8	yes	complemented
54	#428×C₈₉	C₂²	1	4	yes	—
55	#428×C₈₉	C₂²	1	4	yes	—
56	#423×C₈₉	C₂²	1	2	yes	—
57	#419×C₈₉	C₂²	1	4	yes	—
58	#418×C₈₉	C₂²	1	4	yes	—
59	#407×C₈₉	C₂²	1	2	yes	—
60	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
61	C₂²×Q₈×C₈₉	—	2	1	no	—
62	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
68	C₄⋊Q₈×C₈₉	—	2	4	no	—
69	C₄⋊Q₈×C₈₉	—	2	4	no	—
70	C₄⋊Q₈×C₈₉	—	2	2	no	—
71	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
72	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
74	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
76	#126×C₈₉	—	2	8	no	—
77	#125×C₈₉	—	2	4	no	—
78	#125×C₈₉	—	2	4	no	—
79	#125×C₈₉	C₂³	1	4	yes	—
80	#125×C₈₉	C₂³	1	4	yes	—
81	#124×C₈₉	—	2	8	no	—
82	#124×C₈₉	—	2	2	no	—
83	#124×C₈₉	C₂³	1	4	yes	—
84	#123×C₈₉	—	2	8	no	—
85	C₂²⋊Q₈×C₈₉	—	2	2	no	—
86	C₂²⋊Q₈×C₈₉	—	2	2	no	—
87	C₂²⋊Q₈×C₈₉	—	2	2	no	—
88	C₂²⋊Q₈×C₈₉	—	2	2	no	—
89	C₂²⋊Q₈×C₈₉	—	2	2	no	—
90	C₂²⋊Q₈×C₈₉	—	2	8	no	—
91	C₂²⋊Q₈×C₈₉	—	2	4	no	—
92	C₂²⋊Q₈×C₈₉	—	2	4	no	—
93	C₂²⋊Q₈×C₈₉	—	2	4	no	—
94	C₂²⋊Q₈×C₈₉	—	2	4	no	—
95	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
96	#121×C₈₉	—	2	2	no	—
97	#121×C₈₉	C₂³	1	4	yes	—
98	C₄×Q₈×C₈₉	—	2	2	no	—
99	C₄×Q₈×C₈₉	—	2	2	no	—
100	C₄×Q₈×C₈₉	—	2	2	no	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	2	2	no	—
103	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	C₄×D₄×C₈₉	C₂³	1	4	yes	—
106	#117×C₈₉	—	2	2	no	—
107	#117×C₈₉	—	2	2	no	—
108	#117×C₈₉	D₄	1	4	yes	—
109	#117×C₈₉	C₂³	1	4	yes	—
110	#117×C₈₉	C₂³	1	4	yes	—
111	#117×C₈₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	—	2	2	no	—
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	#107×C₈₉	C₂³	1	8	yes	—
134	#107×C₈₉	C₂³	1	8	yes	—
135	#106×C₈₉	C₂³	1	8	yes	—
136	#106×C₈₉	C₂³	1	8	yes	—
137	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
138	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
139	#103×C₈₉	C₂³	1	8	yes	—
140	#103×C₈₉	C₂³	1	8	yes	—
141	#102×C₈₉	C₂³	1	8	yes	—
142	#102×C₈₉	C₂³	1	8	yes	—
143	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
144	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
145	#97×C₈₉	C₂³	1	4	yes	—
146	C₄×C₈×C₈₉	C₂³	1	4	yes	—
147	C₂⁴×C₈₉	—	2	1	no	—
148	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₈₉	—	2	1	no	—
150	C₂×Q₈×C₈₉	—	2	2	no	—
151	C₂×Q₈×C₈₉	—	2	2	no	—
152	C₂×Q₈×C₈₉	—	2	2	no	—
153	C₂×Q₈×C₈₉	—	2	2	no	—
154	C₂×Q₈×C₈₉	—	2	4	no	—
155	C₂×Q₈×C₈₉	—	2	4	no	—
156	C₂×Q₈×C₈₉	—	8	2	no	—
157	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
158	C₂×D₄×C₈₉	—	2	4	no	—
159	C₂×D₄×C₈₉	—	2	1	no	—
160	C₂×D₄×C₈₉	—	2	4	no	—
161	C₂×D₄×C₈₉	—	8	2	no	—
162	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₈₉	—	2	4	no	—
164	C₂²×C₄×C₈₉	—	2	1	no	—
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	2	no	—
168	C₂²×C₄×C₈₉	—	2	2	no	—
169	C₂²×C₄×C₈₉	—	2	4	no	—
170	C₂²×C₄×C₈₉	—	8	2	no	—
171	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	M₁₆×C₈₉	—	2	8	no	—
180	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
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	2	no	—
185	C₄⋊C₄×C₈₉	—	2	2	no	—
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	2	no	—
189	C₄⋊C₄×C₈₉	—	2	2	no	—
190	C₄⋊C₄×C₈₉	—	2	2	no	—
191	C₄⋊C₄×C₈₉	—	2	2	no	—
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
197	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
198	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
199	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
200	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
201	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
202	C₂²⋊C₄×C₈₉	—	2	4	no	—
203	C₂²⋊C₄×C₈₉	—	2	4	no	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	2	4	no	—
207	C₂²⋊C₄×C₈₉	—	2	4	no	—
208	C₂²⋊C₄×C₈₉	—	2	4	no	—
209	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
210	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
211	C₄²×C₈₉	—	2	4	no	—
212	C₄²×C₈₉	—	2	4	no	—
213	C₄²×C₈₉	—	2	4	no	—
214	C₄²×C₈₉	C₂×D₄	1	2	yes	—
215	C₄²×C₈₉	C₂×D₄	1	2	yes	—
216	C₄²×C₈₉	C₂⁴	1	2	yes	—
217	C₄²×C₈₉	C₂⁴	1	2	yes	—
218	C₂³×C₈₉	—	2	2	no	—
219	C₂³×C₈₉	—	2	2	no	—
220	C₂³×C₈₉	—	4	1	no	—
221	C₂³×C₈₉	—	4	1	no	—
222	C₂³×C₈₉	—	4	2	no	—
223	C₂³×C₈₉	—	4	2	no	—
224	C₂³×C₈₉	—	4	2	no	—
225	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
226	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₈₉	—	2	4	no	—
228	Q₈×C₈₉	—	4	2	no	—
229	Q₈×C₈₉	—	8	2	no	—
230	Q₈×C₈₉	—	8	2	no	—
231	Q₈×C₈₉	—	8	2	no	—
232	Q₈×C₈₉	—	8	2	no	—
233	Q₈×C₈₉	—	8	4	no	—
234	D₄×C₈₉	—	2	4	no	—
235	D₄×C₈₉	—	4	2	no	—
236	D₄×C₈₉	—	8	4	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	4	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	4	no	—
242	C₂×C₄×C₈₉	—	2	4	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	4	1	no	—
246	C₂×C₄×C₈₉	—	4	1	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	1	no	—
249	C₂×C₄×C₈₉	—	4	2	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	—	4	2	no	—
252	C₂×C₄×C₈₉	—	8	4	no	—
253	C₂×C₄×C₈₉	—	8	2	no	—
254	C₂×C₄×C₈₉	—	8	2	no	—
255	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
262	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
263	C₈×C₈₉	—	2	8	no	—
264	C₂²×C₈₉	—	2	1	no	—
265	C₂²×C₈₉	—	2	1	no	—
266	C₂²×C₈₉	—	2	2	no	—
267	C₂²×C₈₉	—	2	2	no	—
268	C₂²×C₈₉	—	2	2	no	—
269	C₂²×C₈₉	—	4	2	no	—
270	C₂²×C₈₉	—	4	2	no	—
271	C₂²×C₈₉	—	4	2	no	—
272	C₂²×C₈₉	—	8	2	no	—
273	C₂²×C₈₉	—	8	4	no	—
274	C₂²×C₈₉	#536	1	2	yes	—
275	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	2	2	no	—
278	C₄×C₈₉	—	2	2	no	—
279	C₄×C₈₉	—	2	2	no	—
280	C₄×C₈₉	—	2	2	no	—
281	C₄×C₈₉	—	4	2	no	—
282	C₄×C₈₉	—	4	2	no	—
283	C₄×C₈₉	—	4	4	no	—
284	C₄×C₈₉	—	4	4	no	—
285	C₄×C₈₉	—	4	2	no	—
286	C₄×C₈₉	#536	1	2	yes	—
287	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
288	#60870	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂×C₈₉	—	2	2	no	—
290	C₂×C₈₉	—	4	2	no	—
291	C₂×C₈₉	—	8	2	no	—
292	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
293	C₂×C₈₉	#3585	1	1	yes	characteristic
294	C₂×C₈₉	#3586	1	1	yes	characteristic
295	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
296	C₂×#542	C₂×C₈₉	1	1	yes	characteristic
297	#3244	C₂×C₈₉	1	8	yes	complemented
298	#3243	C₂×C₈₉	1	8	yes	complemented
299	#3165	C₂×C₈₉	1	2	yes	complemented
300	#3140	C₂×C₈₉	1	2	yes	complemented
301	#3095	C₂×C₈₉	1	2	yes	complemented
302	#3094	C₂×C₈₉	1	2	yes	—
303	#3078	C₂×C₈₉	1	2	yes	complemented
304	#3077	C₂×C₈₉	1	2	yes	complemented
305	#2921	C₂×C₈₉	1	1	yes	characteristic, complemented
306	C₈₉	#60870	1	1	yes	characteristic, direct product factor, Sylow
307	#544	—	2	1	no	—
308	#544	—	2	1	no	—
309	#544	C₂²×C₈₉	1	4	yes	complemented
310	#544	C₂²×C₈₉	1	4	yes	complemented
311	#543	—	2	1	no	—
312	#543	—	2	1	no	—
313	#542	—	2	4	no	—
314	#542	C₂²×C₈₉	1	8	yes	—
315	#533	—	2	4	no	—
316	#533	C₂²×C₈₉	1	2	yes	—
317	#533	C₂²×C₈₉	1	2	yes	—
318	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
319	C₂×#126	—	2	1	no	—
320	C₂×#124	—	2	1	no	—
321	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
322	C₂×#123	—	2	1	no	—
323	C₂×C₂²⋊Q₈	—	2	1	no	—
324	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
325	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×#117	C₂²×C₈₉	1	2	yes	—
329	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
330	#501	C₂²×C₈₉	1	8	yes	complemented
331	#500	C₂²×C₈₉	1	4	yes	complemented
332	#498	C₂²×C₈₉	1	4	yes	complemented
333	#489	C₂²×C₈₉	1	4	yes	complemented
334	#489	C₂²×C₈₉	1	4	yes	complemented
335	#488	C₂²×C₈₉	1	8	yes	complemented
336	#485	C₂²×C₈₉	1	8	yes	complemented
337	#484	C₂²×C₈₉	1	4	yes	complemented
338	#483	C₂²×C₈₉	1	4	yes	complemented
339	#482	C₂²×C₈₉	1	8	yes	—
340	#481	C₂²×C₈₉	1	4	yes	—
341	#480	C₂²×C₈₉	1	4	yes	—
342	#479	C₂²×C₈₉	1	8	yes	complemented
343	#478	C₂²×C₈₉	1	8	yes	complemented
344	#477	C₂²×C₈₉	1	4	yes	complemented
345	#476	C₂²×C₈₉	1	4	yes	complemented
346	#475	C₂²×C₈₉	1	4	yes	complemented
347	#474	C₂²×C₈₉	1	4	yes	complemented
348	#433	C₂²×C₈₉	1	8	yes	complemented
349	#428	C₂²×C₈₉	1	4	yes	—
350	#428	C₂²×C₈₉	1	4	yes	—
351	#423	C₂²×C₈₉	1	2	yes	—
352	#419	C₂²×C₈₉	1	4	yes	—
353	#418	C₂²×C₈₉	1	4	yes	—
354	#407	C₂²×C₈₉	1	2	yes	—
355	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
356	C₂²×Q₈	—	2	1	no	—
357	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
358	C₂²×D₄	—	2	1	no	—
359	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
362	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
363	C₄⋊Q₈	—	2	4	no	—
364	C₄⋊Q₈	—	2	4	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
367	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
368	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
369	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
371	#126	—	2	8	no	—
372	#125	—	2	4	no	—
373	#125	—	2	4	no	—
374	#125	C₂³×C₈₉	1	4	yes	—
375	#125	C₂³×C₈₉	1	4	yes	—
376	#124	—	2	8	no	—
377	#124	—	2	2	no	—
378	#124	C₂³×C₈₉	1	4	yes	—
379	#123	—	2	8	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	2	8	no	—
386	C₂²⋊Q₈	—	2	4	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
391	#121	—	2	2	no	—
392	#121	C₂³×C₈₉	1	4	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	C₂³×C₈₉	1	4	yes	—
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	#117	D₄×C₈₉	1	4	yes	—
404	#117	C₂³×C₈₉	1	4	yes	—
405	#117	C₂³×C₈₉	1	4	yes	—
406	#117	C₂³×C₈₉	1	4	yes	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
428	#107	C₂³×C₈₉	1	8	yes	—
429	#107	C₂³×C₈₉	1	8	yes	—
430	#106	C₂³×C₈₉	1	8	yes	—
431	#106	C₂³×C₈₉	1	8	yes	—
432	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
433	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
434	#103	C₂³×C₈₉	1	8	yes	—
435	#103	C₂³×C₈₉	1	8	yes	—
436	#102	C₂³×C₈₉	1	8	yes	—
437	#102	C₂³×C₈₉	1	8	yes	—
438	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
439	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
440	#97	C₂³×C₈₉	1	4	yes	—
441	C₄×C₈	C₂³×C₈₉	1	4	yes	—
442	C₂⁴	—	2	1	no	—
443	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	8	2	no	—
452	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	8	2	no	—
457	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	8	2	no	—
466	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
474	M₁₆	—	2	8	no	—
475	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
492	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
493	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
494	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
496	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
505	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	2	4	no	—
509	C₄²	C₂×D₄×C₈₉	1	2	yes	—
510	C₄²	C₂×D₄×C₈₉	1	2	yes	—
511	C₄²	C₂⁴×C₈₉	1	2	yes	—
512	C₄²	C₂⁴×C₈₉	1	2	yes	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
521	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	8	2	no	—
525	Q₈	—	8	2	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	Q₈	—	8	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
556	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
557	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
558	C₈	—	2	8	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	4	no	—
569	C₂²	#536×C₈₉	1	2	yes	—
570	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	2	no	—
581	C₄	#536×C₈₉	1	2	yes	—
582	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	2	no	—
586	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
587	C₂	C₈₉×#3585	1	1	yes	characteristic
588	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3458	C₂	semidirect
3. C₈₉×#3244	C₂	semidirect
4. C₈₉×#3243	C₂	semidirect
5. C₈₉×#3165	C₂	semidirect
6. C₈₉×#3140	C₂	semidirect
7. C₈₉×#3095	C₂	semidirect
9. C₈₉×#3078	C₂	semidirect
10. C₈₉×#3077	C₂	semidirect
11. C₈₉×#2921	C₂	semidirect
14. #544×C₈₉	C₂²	semidirect
15. #544×C₈₉	C₂²	semidirect
35. #501×C₈₉	C₂²	semidirect
36. #500×C₈₉	C₂²	semidirect
37. #498×C₈₉	C₂²	semidirect
38. #489×C₈₉	C₂²	semidirect
39. #489×C₈₉	C₂²	semidirect
40. #488×C₈₉	C₂²	semidirect
41. #485×C₈₉	C₂²	semidirect
42. #484×C₈₉	C₂²	semidirect
43. #483×C₈₉	C₂²	semidirect
47. #479×C₈₉	C₂²	semidirect
48. #478×C₈₉	C₂²	semidirect
49. #477×C₈₉	C₂²	semidirect
50. #476×C₈₉	C₂²	semidirect
51. #475×C₈₉	C₂²	semidirect
52. #474×C₈₉	C₂²	semidirect
53. #433×C₈₉	C₂²	semidirect
288. #60870	C₈₉	direct (N × H)
295. #3458	C₂×C₈₉	semidirect
297. #3244	C₂×C₈₉	semidirect
298. #3243	C₂×C₈₉	semidirect
299. #3165	C₂×C₈₉	semidirect
300. #3140	C₂×C₈₉	semidirect
301. #3095	C₂×C₈₉	semidirect
303. #3078	C₂×C₈₉	semidirect
304. #3077	C₂×C₈₉	semidirect
305. #2921	C₂×C₈₉	semidirect
306. C₈₉	#60870	direct (N × H)
309. #544	C₂²×C₈₉	semidirect
310. #544	C₂²×C₈₉	semidirect
330. #501	C₂²×C₈₉	semidirect
331. #500	C₂²×C₈₉	semidirect
332. #498	C₂²×C₈₉	semidirect
333. #489	C₂²×C₈₉	semidirect
334. #489	C₂²×C₈₉	semidirect
335. #488	C₂²×C₈₉	semidirect
336. #485	C₂²×C₈₉	semidirect
337. #484	C₂²×C₈₉	semidirect
338. #483	C₂²×C₈₉	semidirect
342. #479	C₂²×C₈₉	semidirect
343. #478	C₂²×C₈₉	semidirect
344. #477	C₂²×C₈₉	semidirect
345. #476	C₂²×C₈₉	semidirect
346. #475	C₂²×C₈₉	semidirect
347. #474	C₂²×C₈₉	semidirect
348. #433	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×#3458	2
C₂×#542×C₈₉	2
C₈₉×#3244	2
C₈₉×#3243	2
C₈₉×#3165	2
C₈₉×#3140	2
C₈₉×#3095	2
C₈₉×#3094	2
C₈₉×#3078	2
C₈₉×#3077	2
C₈₉×#2921	2
#60870	89

Subgroups — C89×#60870 #36438718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60870 #36438718