Subgroups — C₈₉×#60526 #36438374

Order 22784.

2166 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3489	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3098	C₂	1	6	yes	maximal, complemented
4	C₈₉×#3097	C₂	1	6	yes	maximal, complemented
5	C₈₉×#3095	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3092	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3091	C₂	1	3	yes	maximal, complemented
8	C₂×#484×C₈₉	C₂	1	3	yes	maximal, complemented
9	C₈₉×#2913	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2898	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₈₉	C₂²	1	2	yes	—
15	D₄×Q₈×C₈₉	—	2	1	no	—
16	#548×C₈₉	—	2	1	no	—
17	#547×C₈₉	—	2	3	no	—
18	#546×C₈₉	—	2	3	no	—
19	#537×C₈₉	C₂²	1	3	yes	—
20	#536×C₈₉	C₂²	1	3	yes	—
21	#525×C₈₉	C₂²	1	3	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	—
23	#520×C₈₉	—	2	3	no	—
24	#520×C₈₉	—	2	1	no	—
25	#520×C₈₉	C₂²	1	6	yes	—
26	#520×C₈₉	C₂²	1	2	yes	—
27	#520×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
29	C₂×C₄×D₄×C₈₉	—	2	3	no	—
30	C₂×#117×C₈₉	C₂²	1	3	yes	—
31	C₂²×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
32	#485×C₈₉	C₂²	1	6	yes	complemented
33	#485×C₈₉	C₂²	1	12	yes	complemented
34	#484×C₈₉	C₂²	1	3	yes	—
35	#484×C₈₉	C₂²	1	6	yes	—
36	#484×C₈₉	C₂²	1	12	yes	complemented
37	#483×C₈₉	C₂²	1	3	yes	—
38	#483×C₈₉	C₂²	1	6	yes	complemented
39	#482×C₈₉	C₂²	1	6	yes	complemented
40	#481×C₈₉	C₂²	1	3	yes	—
41	#480×C₈₉	C₂²	1	1	yes	characteristic
42	#480×C₈₉	C₂²	1	6	yes	complemented
43	#428×C₈₉	C₂²	1	6	yes	complemented
44	#428×C₈₉	C₂²	1	6	yes	complemented
45	#427×C₈₉	C₂²	1	6	yes	complemented
46	C₂×#107×C₈₉	C₂²	1	6	yes	complemented
47	#419×C₈₉	C₂²	1	6	yes	complemented
48	#417×C₈₉	C₂²	1	6	yes	complemented
49	#416×C₈₉	C₂²	1	6	yes	complemented
50	C₂×#103×C₈₉	C₂²	1	6	yes	complemented
51	#408×C₈₉	C₂²	1	6	yes	—
52	#407×C₈₉	C₂²	1	3	yes	—
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	3	yes	—
54	2₋¹⁺⁴×C₈₉	—	2	8	no	—
55	C₂×#41×C₈₉	—	2	8	no	—
56	C₂×#41×C₈₉	—	2	3	no	—
57	C₂×#41×C₈₉	D₄	1	3	yes	—
58	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
59	C₂×#41×C₈₉	C₂³	1	3	yes	—
60	C₂×#41×C₈₉	C₂³	1	3	yes	—
61	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₈₉	—	2	1	no	—
63	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
65	C₂²×D₄×C₈₉	D₄	1	3	yes	—
66	C₂³×C₄×C₈₉	—	2	3	no	—
67	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
68	#131×C₈₉	—	2	8	no	—
69	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
70	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
71	C₄⋊Q₈×C₈₉	—	2	3	no	—
72	#124×C₈₉	—	2	3	no	—
73	#123×C₈₉	—	2	6	no	—
74	#123×C₈₉	—	2	3	no	—
75	C₂²⋊Q₈×C₈₉	—	2	3	no	—
76	C₂²⋊Q₈×C₈₉	—	2	3	no	—
77	C₂²⋊Q₈×C₈₉	—	2	3	no	—
78	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
79	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
80	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
81	#121×C₈₉	—	2	6	no	—
82	#121×C₈₉	—	2	3	no	—
83	#121×C₈₉	C₂³	1	1	yes	characteristic
84	#121×C₈₉	C₂³	1	3	yes	—
85	#120×C₈₉	—	2	3	no	—
86	C₄×Q₈×C₈₉	—	2	6	no	—
87	C₄×Q₈×C₈₉	—	2	2	no	—
88	C₄×Q₈×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	—	2	12	no	—
90	C₄×D₄×C₈₉	—	2	6	no	—
91	C₄×D₄×C₈₉	—	2	6	no	—
92	C₄×D₄×C₈₉	—	2	3	no	—
93	C₄×D₄×C₈₉	—	2	3	no	—
94	C₄×D₄×C₈₉	—	2	3	no	—
95	#117×C₈₉	—	2	3	no	—
96	#117×C₈₉	—	2	3	no	—
97	#117×C₈₉	C₂³	1	6	yes	—
98	#117×C₈₉	C₂³	1	3	yes	—
99	#117×C₈₉	C₂³	1	6	yes	—
100	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
111	C₂×C₄²×C₈₉	—	2	3	no	—
112	#107×C₈₉	C₂³	1	6	yes	—
113	#107×C₈₉	C₂³	1	12	yes	—
114	#107×C₈₉	C₂³	1	2	yes	—
115	#106×C₈₉	C₂³	1	6	yes	—
116	#106×C₈₉	C₂³	1	6	yes	—
117	#103×C₈₉	C₂³	1	6	yes	—
118	#103×C₈₉	C₂³	1	12	yes	—
119	#103×C₈₉	C₂³	1	6	yes	—
120	#102×C₈₉	C₂³	1	2	yes	—
121	#102×C₈₉	C₂³	1	6	yes	—
122	C₂²⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
124	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
125	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
126	C₂⁴×C₈₉	C₂×D₄	1	3	yes	—
127	#41×C₈₉	—	2	4	no	—
128	#41×C₈₉	—	2	12	no	—
129	#41×C₈₉	—	2	12	no	—
130	#41×C₈₉	—	2	12	no	—
131	#41×C₈₉	—	4	12	no	—
132	#41×C₈₉	#41	1	8	yes	—
133	C₂×Q₈×C₈₉	—	2	4	no	—
134	C₂×Q₈×C₈₉	—	2	3	no	—
135	C₂×Q₈×C₈₉	—	2	12	no	—
136	C₂×Q₈×C₈₉	—	4	4	no	—
137	C₂×Q₈×C₈₉	C₂×D₄	1	3	yes	—
138	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
140	C₂×D₄×C₈₉	—	2	12	no	—
141	C₂×D₄×C₈₉	—	2	1	no	—
142	C₂×D₄×C₈₉	—	2	3	no	—
143	C₂×D₄×C₈₉	—	2	3	no	—
144	C₂×D₄×C₈₉	C₂×D₄	1	6	yes	—
145	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
146	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
147	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	—	2	12	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	3	no	—
151	C₂²×C₄×C₈₉	—	2	3	no	—
152	C₂²×C₄×C₈₉	—	2	3	no	—
153	C₂²×C₄×C₈₉	—	2	6	no	—
154	C₂²×C₄×C₈₉	—	2	6	no	—
155	C₂²×C₄×C₈₉	—	2	3	no	—
156	C₂²×C₄×C₈₉	—	8	6	no	—
157	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
160	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
163	M₁₆×C₈₉	—	2	12	no	—
164	C₂×C₈×C₈₉	—	2	12	no	—
165	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
166	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₈₉	—	2	3	no	—
168	C₄⋊C₄×C₈₉	—	2	6	no	—
169	C₄⋊C₄×C₈₉	—	2	6	no	—
170	C₄⋊C₄×C₈₉	—	2	3	no	—
171	C₄⋊C₄×C₈₉	—	2	6	no	—
172	C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₄⋊C₄×C₈₉	—	2	3	no	—
174	C₄⋊C₄×C₈₉	—	2	3	no	—
175	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
176	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
177	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
179	C₂²⋊C₄×C₈₉	—	2	3	no	—
180	C₂²⋊C₄×C₈₉	—	2	6	no	—
181	C₂²⋊C₄×C₈₉	—	2	6	no	—
182	C₂²⋊C₄×C₈₉	—	2	6	no	—
183	C₂²⋊C₄×C₈₉	—	2	3	no	—
184	C₂²⋊C₄×C₈₉	—	2	3	no	—
185	C₂²⋊C₄×C₈₉	—	2	1	no	—
186	C₂²⋊C₄×C₈₉	—	2	3	no	—
187	C₄²×C₈₉	—	2	6	no	—
188	C₄²×C₈₉	—	2	6	no	—
189	C₄²×C₈₉	—	2	3	no	—
190	C₂³×C₈₉	—	2	6	no	—
191	C₂³×C₈₉	—	2	6	no	—
192	C₂³×C₈₉	—	2	1	no	—
193	C₂³×C₈₉	—	4	3	no	—
194	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
195	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
196	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₈₉	—	2	6	no	—
198	Q₈×C₈₉	—	2	6	no	—
199	Q₈×C₈₉	—	4	6	no	—
200	Q₈×C₈₉	#123	1	4	yes	—
201	D₄×C₈₉	—	2	12	no	—
202	D₄×C₈₉	—	2	6	no	—
203	D₄×C₈₉	—	2	2	no	—
204	D₄×C₈₉	—	4	6	no	—
205	D₄×C₈₉	—	4	2	no	—
206	D₄×C₈₉	—	8	3	no	—
207	D₄×C₈₉	#123	1	12	yes	—
208	C₂×C₄×C₈₉	—	2	6	no	—
209	C₂×C₄×C₈₉	—	2	6	no	—
210	C₂×C₄×C₈₉	—	2	6	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	6	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	6	no	—
216	C₂×C₄×C₈₉	—	2	3	no	—
217	C₂×C₄×C₈₉	—	2	3	no	—
218	C₂×C₄×C₈₉	—	4	6	no	—
219	C₂×C₄×C₈₉	—	4	6	no	—
220	C₂×C₄×C₈₉	—	4	2	no	—
221	C₂×C₄×C₈₉	—	4	6	no	—
222	C₂×C₄×C₈₉	—	8	3	no	—
223	C₂×C₄×C₈₉	—	8	6	no	—
224	C₂×C₄×C₈₉	—	8	6	no	—
225	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
226	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
228	C₂×C₄×C₈₉	C₂×#41	1	12	yes	—
229	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
230	C₈×C₈₉	—	2	2	no	—
231	C₈×C₈₉	—	2	6	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	3	no	—
234	C₂²×C₈₉	—	2	1	no	—
235	C₂²×C₈₉	—	2	3	no	—
236	C₂²×C₈₉	—	2	3	no	—
237	C₂²×C₈₉	—	2	3	no	—
238	C₂²×C₈₉	—	2	3	no	—
239	C₂²×C₈₉	—	4	12	no	—
240	C₂²×C₈₉	—	4	1	no	—
241	C₂²×C₈₉	—	4	1	no	—
242	C₂²×C₈₉	—	4	1	no	—
243	C₂²×C₈₉	C₂×#123	1	6	yes	—
244	C₂²×C₈₉	#578	1	2	yes	—
245	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	2	3	no	—
248	C₄×C₈₉	—	4	6	no	—
249	C₄×C₈₉	—	4	3	no	—
250	C₄×C₈₉	—	4	3	no	—
251	C₄×C₈₉	—	4	2	no	—
252	C₄×C₈₉	—	4	1	no	—
253	C₄×C₈₉	C₂×#123	1	6	yes	—
254	C₄×C₈₉	C₂²×#41	1	2	yes	—
255	#60526	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂×C₈₉	—	2	2	no	—
257	C₂×C₈₉	—	2	6	no	—
258	C₂×C₈₉	—	4	3	no	—
259	C₂×C₈₉	—	8	1	no	—
260	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
261	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
262	C₂×C₈₉	#3585	1	1	yes	characteristic
263	#3489	C₂×C₈₉	1	1	yes	characteristic
264	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
265	#3098	C₂×C₈₉	1	6	yes	complemented
266	#3097	C₂×C₈₉	1	6	yes	complemented
267	#3095	C₂×C₈₉	1	3	yes	complemented
268	#3092	C₂×C₈₉	1	3	yes	complemented
269	#3091	C₂×C₈₉	1	3	yes	complemented
270	C₂×#484	C₂×C₈₉	1	3	yes	complemented
271	#2913	C₂×C₈₉	1	2	yes	complemented
272	#2898	C₂×C₈₉	1	2	yes	complemented
273	#2880	C₂×C₈₉	1	1	yes	characteristic, complemented
274	C₈₉	#60526	1	1	yes	characteristic, direct product factor, Sylow
275	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
276	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
277	C₂×#131	C₂²×C₈₉	1	2	yes	—
278	D₄×Q₈	—	2	1	no	—
279	#548	—	2	1	no	—
280	#547	—	2	3	no	—
281	#546	—	2	3	no	—
282	#537	C₂²×C₈₉	1	3	yes	—
283	#536	C₂²×C₈₉	1	3	yes	—
284	#525	C₂²×C₈₉	1	3	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	—
286	#520	—	2	3	no	—
287	#520	—	2	1	no	—
288	#520	C₂²×C₈₉	1	6	yes	—
289	#520	C₂²×C₈₉	1	2	yes	—
290	#520	C₂²×C₈₉	1	1	yes	characteristic
291	C₂×C₄×Q₈	—	2	1	no	—
292	C₂×C₄×D₄	—	2	3	no	—
293	C₂×#117	C₂²×C₈₉	1	3	yes	—
294	C₂²×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
295	#485	C₂²×C₈₉	1	6	yes	complemented
296	#485	C₂²×C₈₉	1	12	yes	complemented
297	#484	C₂²×C₈₉	1	3	yes	—
298	#484	C₂²×C₈₉	1	6	yes	—
299	#484	C₂²×C₈₉	1	12	yes	complemented
300	#483	C₂²×C₈₉	1	3	yes	—
301	#483	C₂²×C₈₉	1	6	yes	complemented
302	#482	C₂²×C₈₉	1	6	yes	complemented
303	#481	C₂²×C₈₉	1	3	yes	—
304	#480	C₂²×C₈₉	1	1	yes	characteristic
305	#480	C₂²×C₈₉	1	6	yes	complemented
306	#428	C₂²×C₈₉	1	6	yes	complemented
307	#428	C₂²×C₈₉	1	6	yes	complemented
308	#427	C₂²×C₈₉	1	6	yes	complemented
309	C₂×#107	C₂²×C₈₉	1	6	yes	complemented
310	#419	C₂²×C₈₉	1	6	yes	complemented
311	#417	C₂²×C₈₉	1	6	yes	complemented
312	#416	C₂²×C₈₉	1	6	yes	complemented
313	C₂×#103	C₂²×C₈₉	1	6	yes	complemented
314	#408	C₂²×C₈₉	1	6	yes	—
315	#407	C₂²×C₈₉	1	3	yes	—
316	C₂×C₂²⋊C₈	C₂²×C₈₉	1	3	yes	—
317	2₋¹⁺⁴	—	2	8	no	—
318	C₂×#41	—	2	8	no	—
319	C₂×#41	—	2	3	no	—
320	C₂×#41	D₄×C₈₉	1	3	yes	—
321	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
322	C₂×#41	C₂³×C₈₉	1	3	yes	—
323	C₂×#41	C₂³×C₈₉	1	3	yes	—
324	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
328	C₂²×D₄	D₄×C₈₉	1	3	yes	—
329	C₂³×C₄	—	2	3	no	—
330	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
331	#131	—	2	8	no	—
332	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
333	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
334	C₄⋊Q₈	—	2	3	no	—
335	#124	—	2	3	no	—
336	#123	—	2	6	no	—
337	#123	—	2	3	no	—
338	C₂²⋊Q₈	—	2	3	no	—
339	C₂²⋊Q₈	—	2	3	no	—
340	C₂²⋊Q₈	—	2	3	no	—
341	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
342	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
343	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
344	#121	—	2	6	no	—
345	#121	—	2	3	no	—
346	#121	C₂³×C₈₉	1	1	yes	characteristic
347	#121	C₂³×C₈₉	1	3	yes	—
348	#120	—	2	3	no	—
349	C₄×Q₈	—	2	6	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×D₄	—	2	12	no	—
353	C₄×D₄	—	2	6	no	—
354	C₄×D₄	—	2	6	no	—
355	C₄×D₄	—	2	3	no	—
356	C₄×D₄	—	2	3	no	—
357	C₄×D₄	—	2	3	no	—
358	#117	—	2	3	no	—
359	#117	—	2	3	no	—
360	#117	C₂³×C₈₉	1	6	yes	—
361	#117	C₂³×C₈₉	1	6	yes	—
362	#117	C₂³×C₈₉	1	3	yes	—
363	C₂×C₄⋊C₄	—	2	3	no	—
364	C₂×C₄⋊C₄	—	2	3	no	—
365	C₂×C₄⋊C₄	—	2	3	no	—
366	C₂×C₄⋊C₄	—	2	3	no	—
367	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
368	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
369	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
370	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
372	C₂×C₂²⋊C₄	—	2	3	no	—
373	C₂×C₂²⋊C₄	—	2	3	no	—
374	C₂×C₄²	—	2	3	no	—
375	#107	C₂³×C₈₉	1	6	yes	—
376	#107	C₂³×C₈₉	1	12	yes	—
377	#107	C₂³×C₈₉	1	2	yes	—
378	#106	C₂³×C₈₉	1	6	yes	—
379	#106	C₂³×C₈₉	1	6	yes	—
380	#103	C₂³×C₈₉	1	6	yes	—
381	#103	C₂³×C₈₉	1	12	yes	—
382	#103	C₂³×C₈₉	1	6	yes	—
383	#102	C₂³×C₈₉	1	2	yes	—
384	#102	C₂³×C₈₉	1	6	yes	—
385	C₂²⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
386	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
387	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
388	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
389	C₂⁴	C₂×D₄×C₈₉	1	3	yes	—
390	#41	—	2	4	no	—
391	#41	—	2	12	no	—
392	#41	—	2	12	no	—
393	#41	—	2	12	no	—
394	#41	—	4	12	no	—
395	#41	#41×C₈₉	1	8	yes	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	3	no	—
398	C₂×Q₈	—	2	12	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	C₂×D₄×C₈₉	1	3	yes	—
401	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
402	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
403	C₂×D₄	—	2	12	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	3	no	—
406	C₂×D₄	—	2	3	no	—
407	C₂×D₄	C₂×D₄×C₈₉	1	6	yes	—
408	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
409	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
410	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
411	C₂²×C₄	—	2	12	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	3	no	—
414	C₂²×C₄	—	2	3	no	—
415	C₂²×C₄	—	2	3	no	—
416	C₂²×C₄	—	2	6	no	—
417	C₂²×C₄	—	2	6	no	—
418	C₂²×C₄	—	2	3	no	—
419	C₂²×C₄	—	8	6	no	—
420	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
421	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
422	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
423	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
425	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
426	M₁₆	—	2	12	no	—
427	C₂×C₈	—	2	12	no	—
428	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
429	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
430	C₄⋊C₄	—	2	3	no	—
431	C₄⋊C₄	—	2	6	no	—
432	C₄⋊C₄	—	2	6	no	—
433	C₄⋊C₄	—	2	3	no	—
434	C₄⋊C₄	—	2	6	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	3	no	—
437	C₄⋊C₄	—	2	3	no	—
438	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
439	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
440	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
441	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
442	C₂²⋊C₄	—	2	3	no	—
443	C₂²⋊C₄	—	2	6	no	—
444	C₂²⋊C₄	—	2	6	no	—
445	C₂²⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	3	no	—
447	C₂²⋊C₄	—	2	3	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	3	no	—
450	C₄²	—	2	6	no	—
451	C₄²	—	2	6	no	—
452	C₄²	—	2	3	no	—
453	C₂³	—	2	6	no	—
454	C₂³	—	2	6	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	3	no	—
457	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
458	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
459	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
460	Q₈	—	2	6	no	—
461	Q₈	—	2	6	no	—
462	Q₈	—	4	6	no	—
463	Q₈	#123×C₈₉	1	4	yes	—
464	D₄	—	2	12	no	—
465	D₄	—	2	6	no	—
466	D₄	—	2	2	no	—
467	D₄	—	4	6	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	3	no	—
470	D₄	#123×C₈₉	1	12	yes	—
471	C₂×C₄	—	2	6	no	—
472	C₂×C₄	—	2	6	no	—
473	C₂×C₄	—	2	6	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	6	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	6	no	—
479	C₂×C₄	—	2	3	no	—
480	C₂×C₄	—	2	3	no	—
481	C₂×C₄	—	4	6	no	—
482	C₂×C₄	—	4	6	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	6	no	—
485	C₂×C₄	—	8	3	no	—
486	C₂×C₄	—	8	6	no	—
487	C₂×C₄	—	8	6	no	—
488	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
489	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
491	C₂×C₄	C₂×#41×C₈₉	1	12	yes	—
492	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	2	6	no	—
495	C₂²	—	2	3	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	3	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	3	no	—
500	C₂²	—	2	3	no	—
501	C₂²	—	2	3	no	—
502	C₂²	—	4	12	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	C₂×#123×C₈₉	1	6	yes	—
507	C₂²	#578×C₈₉	1	2	yes	—
508	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
509	C₄	—	2	1	no	—
510	C₄	—	2	3	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	6	no	—
514	C₄	—	4	3	no	—
515	C₄	—	4	3	no	—
516	C₄	C₂×#123×C₈₉	1	6	yes	—
517	C₄	C₂²×#41×C₈₉	1	2	yes	—
518	C₂	—	2	2	no	—
519	C₂	—	2	6	no	—
520	C₂	—	4	3	no	—
521	C₂	—	8	1	no	—
522	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
523	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
524	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#3098	C₂	semidirect
4. C₈₉×#3097	C₂	semidirect
5. C₈₉×#3095	C₂	semidirect
6. C₈₉×#3092	C₂	semidirect
7. C₈₉×#3091	C₂	semidirect
8. C₂×#484×C₈₉	C₂	semidirect
9. C₈₉×#2913	C₂	semidirect
10. C₈₉×#2898	C₂	semidirect
11. C₈₉×#2880	C₂	semidirect
32. #485×C₈₉	C₂²	semidirect
33. #485×C₈₉	C₂²	semidirect
36. #484×C₈₉	C₂²	semidirect
38. #483×C₈₉	C₂²	semidirect
39. #482×C₈₉	C₂²	semidirect
42. #480×C₈₉	C₂²	semidirect
43. #428×C₈₉	C₂²	semidirect
44. #428×C₈₉	C₂²	semidirect
45. #427×C₈₉	C₂²	semidirect
46. C₂×#107×C₈₉	C₂²	semidirect
47. #419×C₈₉	C₂²	semidirect
48. #417×C₈₉	C₂²	semidirect
49. #416×C₈₉	C₂²	semidirect
50. C₂×#103×C₈₉	C₂²	semidirect
255. #60526	C₈₉	direct (N × H)
264. C₂×#520	C₂×C₈₉	semidirect
265. #3098	C₂×C₈₉	semidirect
266. #3097	C₂×C₈₉	semidirect
267. #3095	C₂×C₈₉	semidirect
268. #3092	C₂×C₈₉	semidirect
269. #3091	C₂×C₈₉	semidirect
270. C₂×#484	C₂×C₈₉	semidirect
271. #2913	C₂×C₈₉	semidirect
272. #2898	C₂×C₈₉	semidirect
273. #2880	C₂×C₈₉	semidirect
274. C₈₉	#60526	direct (N × H)
295. #485	C₂²×C₈₉	semidirect
296. #485	C₂²×C₈₉	semidirect
299. #484	C₂²×C₈₉	semidirect
301. #483	C₂²×C₈₉	semidirect
302. #482	C₂²×C₈₉	semidirect
305. #480	C₂²×C₈₉	semidirect
306. #428	C₂²×C₈₉	semidirect
307. #428	C₂²×C₈₉	semidirect
308. #427	C₂²×C₈₉	semidirect
309. C₂×#107	C₂²×C₈₉	semidirect
310. #419	C₂²×C₈₉	semidirect
311. #417	C₂²×C₈₉	semidirect
312. #416	C₂²×C₈₉	semidirect
313. C₂×#103	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×#3489	2
C₂×#520×C₈₉	2
C₈₉×#3098	2
C₈₉×#3097	2
C₈₉×#3095	2
C₈₉×#3092	2
C₈₉×#3091	2
C₂×#484×C₈₉	2
C₈₉×#2913	2
C₈₉×#2898	2
C₈₉×#2880	2
#60526	89

Subgroups — C89×#60526 #36438374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60526 #36438374