Subgroups — C₈₉×#60883 #36438731

Order 22784.

1742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3241	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3235	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3234	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#490×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3096	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3081	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2923	C₂	1	1	yes	maximal, characteristic, complemented
13	#559×C₈₉	—	2	2	no	—
14	#557×C₈₉	—	2	2	no	—
15	#554×C₈₉	—	2	4	no	—
16	#554×C₈₉	—	2	2	no	—
17	#550×C₈₉	—	2	2	no	—
18	#546×C₈₉	—	2	4	no	—
19	#544×C₈₉	C₂²	1	2	yes	—
20	#544×C₈₉	C₂²	1	4	yes	complemented
21	#540×C₈₉	C₂²	1	4	yes	—
22	#535×C₈₉	C₂²	1	2	yes	—
23	#533×C₈₉	C₂²	1	1	yes	characteristic
24	#533×C₈₉	C₂²	1	1	yes	characteristic
25	#533×C₈₉	C₂²	1	2	yes	complemented
26	#532×C₈₉	C₂²	1	4	yes	—
27	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
30	#520×C₈₉	C₂²	1	2	yes	—
31	#518×C₈₉	C₂²	1	2	yes	—
32	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
33	#501×C₈₉	C₂²	1	2	yes	complemented
34	#501×C₈₉	C₂²	1	2	yes	complemented
35	#501×C₈₉	C₂²	1	4	yes	complemented
36	#501×C₈₉	C₂²	1	4	yes	complemented
37	#499×C₈₉	C₂²	1	4	yes	complemented
38	#490×C₈₉	C₂²	1	4	yes	—
39	#490×C₈₉	C₂²	1	4	yes	—
40	#490×C₈₉	C₂²	1	2	yes	—
41	#490×C₈₉	C₂²	1	2	yes	—
42	#486×C₈₉	C₂²	1	4	yes	—
43	#482×C₈₉	C₂²	1	8	yes	complemented
44	#482×C₈₉	C₂²	1	8	yes	complemented
45	#481×C₈₉	C₂²	1	8	yes	complemented
46	#480×C₈₉	C₂²	1	8	yes	complemented
47	#478×C₈₉	C₂²	1	8	yes	complemented
48	#478×C₈₉	C₂²	1	8	yes	complemented
49	#476×C₈₉	C₂²	1	8	yes	complemented
50	#474×C₈₉	C₂²	1	8	yes	complemented
51	#433×C₈₉	C₂²	1	4	yes	complemented
52	#432×C₈₉	C₂²	1	4	yes	complemented
53	#428×C₈₉	C₂²	1	4	yes	—
54	#427×C₈₉	C₂²	1	4	yes	—
55	#424×C₈₉	C₂²	1	2	yes	—
56	#418×C₈₉	C₂²	1	4	yes	—
57	C₂×#102×C₈₉	C₂²	1	4	yes	—
58	#408×C₈₉	C₂²	1	2	yes	—
59	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#41×C₈₉	—	2	4	no	—
62	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₈₉	—	2	2	no	—
64	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
65	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₈₉	—	2	2	no	—
68	C₄⋊Q₈×C₈₉	—	2	4	no	—
69	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
70	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
72	#127×C₈₉	—	2	2	no	—
73	#127×C₈₉	—	2	2	no	—
74	#127×C₈₉	C₂³	1	2	yes	—
75	#127×C₈₉	C₂³	1	2	yes	—
76	#125×C₈₉	—	2	2	no	—
77	#125×C₈₉	—	2	4	no	—
78	#125×C₈₉	—	2	2	no	—
79	#125×C₈₉	—	2	4	no	—
80	#125×C₈₉	C₂³	1	4	yes	—
81	#125×C₈₉	C₂³	1	2	yes	—
82	#125×C₈₉	C₂³	1	2	yes	—
83	#125×C₈₉	C₂³	1	1	yes	characteristic
84	#125×C₈₉	C₂³	1	1	yes	characteristic
85	#125×C₈₉	C₂³	1	2	yes	—
86	#124×C₈₉	—	2	2	no	—
87	#124×C₈₉	—	2	4	no	—
88	#123×C₈₉	—	2	8	no	—
89	C₂²⋊Q₈×C₈₉	—	2	2	no	—
90	C₂²⋊Q₈×C₈₉	—	2	2	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	#121×C₈₉	—	2	4	no	—
96	#121×C₈₉	—	2	8	no	—
97	#121×C₈₉	C₂³	1	8	yes	—
98	#120×C₈₉	—	2	4	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	4	no	—
103	C₄×Q₈×C₈₉	D₄	1	2	yes	—
104	C₄×D₄×C₈₉	—	2	4	no	—
105	C₄×D₄×C₈₉	—	2	2	no	—
106	C₄×D₄×C₈₉	—	2	4	no	—
107	C₄×D₄×C₈₉	—	2	4	no	—
108	C₄×D₄×C₈₉	D₄	1	4	yes	—
109	C₄×D₄×C₈₉	D₄	1	2	yes	—
110	C₄×D₄×C₈₉	C₂³	1	8	yes	—
111	#117×C₈₉	C₂³	1	2	yes	—
112	#117×C₈₉	C₂³	1	2	yes	—
113	#117×C₈₉	C₂³	1	4	yes	—
114	#117×C₈₉	C₂³	1	1	yes	characteristic
115	#117×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
123	#107×C₈₉	C₂³	1	4	yes	—
124	#107×C₈₉	C₂³	1	4	yes	—
125	#107×C₈₉	C₂³	1	8	yes	—
126	#106×C₈₉	C₂³	1	4	yes	—
127	#106×C₈₉	C₂³	1	4	yes	—
128	#106×C₈₉	C₂³	1	8	yes	—
129	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
130	#102×C₈₉	C₂³	1	8	yes	—
131	#102×C₈₉	C₂³	1	8	yes	—
132	#102×C₈₉	C₂³	1	8	yes	—
133	#102×C₈₉	C₂³	1	8	yes	—
134	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
135	#97×C₈₉	C₂³	1	2	yes	—
136	#97×C₈₉	C₂³	1	2	yes	—
137	#97×C₈₉	C₂³	1	2	yes	—
138	C₄×C₈×C₈₉	C₂³	1	2	yes	—
139	C₂⁴×C₈₉	—	2	2	no	—
140	#41×C₈₉	—	2	4	no	—
141	#41×C₈₉	—	8	8	no	—
142	C₂×Q₈×C₈₉	—	2	2	no	—
143	C₂×Q₈×C₈₉	—	2	4	no	—
144	C₂×Q₈×C₈₉	—	2	2	no	—
145	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₈₉	—	2	8	no	—
147	C₂×D₄×C₈₉	—	2	2	no	—
148	C₂×D₄×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	8	no	—
151	C₂×D₄×C₈₉	—	8	4	no	—
152	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	2	2	no	—
157	C₂²×C₄×C₈₉	—	2	8	no	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₈₉	—	2	4	no	—
163	C₂×C₈×C₈₉	—	2	4	no	—
164	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
165	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₈₉	—	2	4	no	—
167	C₄⋊C₄×C₈₉	—	2	2	no	—
168	C₄⋊C₄×C₈₉	—	2	4	no	—
169	C₄⋊C₄×C₈₉	—	2	4	no	—
170	C₄⋊C₄×C₈₉	—	2	4	no	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	2	no	—
173	C₄⋊C₄×C₈₉	—	2	2	no	—
174	C₄⋊C₄×C₈₉	—	2	2	no	—
175	C₄⋊C₄×C₈₉	—	2	4	no	—
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
180	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
181	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
182	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
183	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
184	C₂²⋊C₄×C₈₉	—	2	2	no	—
185	C₂²⋊C₄×C₈₉	—	2	4	no	—
186	C₂²⋊C₄×C₈₉	—	2	2	no	—
187	C₂²⋊C₄×C₈₉	—	2	8	no	—
188	C₂²⋊C₄×C₈₉	—	2	8	no	—
189	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
190	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
191	C₄²×C₈₉	—	2	2	no	—
192	C₄²×C₈₉	—	2	4	no	—
193	C₄²×C₈₉	—	2	2	no	—
194	C₄²×C₈₉	C₂×D₄	1	4	yes	—
195	C₄²×C₈₉	C₂×D₄	1	2	yes	—
196	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
198	C₄²×C₈₉	C₂⁴	1	2	yes	—
199	C₂³×C₈₉	—	2	4	no	—
200	C₂³×C₈₉	—	4	4	no	—
201	C₂³×C₈₉	—	8	4	no	—
202	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₈₉	—	2	2	no	—
205	Q₈×C₈₉	—	4	4	no	—
206	Q₈×C₈₉	—	8	4	no	—
207	Q₈×C₈₉	—	8	2	no	—
208	D₄×C₈₉	—	2	4	no	—
209	D₄×C₈₉	—	2	2	no	—
210	D₄×C₈₉	—	2	8	no	—
211	D₄×C₈₉	—	4	8	no	—
212	D₄×C₈₉	—	4	4	no	—
213	D₄×C₈₉	—	8	4	no	—
214	D₄×C₈₉	—	8	8	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	2	no	—
217	C₂×C₄×C₈₉	—	2	4	no	—
218	C₂×C₄×C₈₉	—	2	4	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	4	2	no	—
221	C₂×C₄×C₈₉	—	4	4	no	—
222	C₂×C₄×C₈₉	—	8	8	no	—
223	C₂×C₄×C₈₉	—	8	2	no	—
224	C₂×C₄×C₈₉	—	8	4	no	—
225	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
231	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
232	C₈×C₈₉	—	2	4	no	—
233	C₈×C₈₉	—	2	4	no	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	2	4	no	—
236	C₂²×C₈₉	—	2	2	no	—
237	C₂²×C₈₉	—	4	8	no	—
238	C₂²×C₈₉	—	4	4	no	—
239	C₂²×C₈₉	—	16	4	no	—
240	C₂²×C₈₉	#536	1	2	yes	—
241	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
242	C₄×C₈₉	—	2	2	no	—
243	C₄×C₈₉	—	2	4	no	—
244	C₄×C₈₉	—	2	2	no	—
245	C₄×C₈₉	—	2	2	no	—
246	C₄×C₈₉	—	4	4	no	—
247	C₄×C₈₉	—	4	4	no	—
248	C₄×C₈₉	—	4	2	no	—
249	C₄×C₈₉	—	4	2	no	—
250	C₄×C₈₉	#536	1	2	yes	—
251	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
252	#60883	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂×C₈₉	—	2	2	no	—
254	C₂×C₈₉	—	4	2	no	—
255	C₂×C₈₉	—	8	4	no	—
256	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
257	C₂×C₈₉	#3585	1	2	yes	—
258	#3508	C₂×C₈₉	1	1	yes	characteristic
259	#3504	C₂×C₈₉	1	1	yes	characteristic, complemented
260	#3241	C₂×C₈₉	1	8	yes	complemented
261	#3235	C₂×C₈₉	1	4	yes	complemented
262	#3234	C₂×C₈₉	1	4	yes	complemented
263	#3166	C₂×C₈₉	1	1	yes	characteristic, complemented
264	#3162	C₂×C₈₉	1	1	yes	characteristic, complemented
265	#3138	C₂×C₈₉	1	1	yes	characteristic, complemented
266	C₂×#490	C₂×C₈₉	1	1	yes	characteristic, complemented
267	#3096	C₂×C₈₉	1	4	yes	complemented
268	#3081	C₂×C₈₉	1	4	yes	complemented
269	#2923	C₂×C₈₉	1	1	yes	characteristic, complemented
270	C₈₉	#60883	1	1	yes	characteristic, direct product factor, Sylow
271	#559	—	2	2	no	—
272	#557	—	2	2	no	—
273	#554	—	2	4	no	—
274	#554	—	2	2	no	—
275	#550	—	2	2	no	—
276	#546	—	2	4	no	—
277	#544	C₂²×C₈₉	1	2	yes	—
278	#544	C₂²×C₈₉	1	4	yes	complemented
279	#540	C₂²×C₈₉	1	4	yes	—
280	#535	C₂²×C₈₉	1	2	yes	—
281	#533	C₂²×C₈₉	1	1	yes	characteristic
282	#533	C₂²×C₈₉	1	1	yes	characteristic
283	#533	C₂²×C₈₉	1	2	yes	complemented
284	#532	C₂²×C₈₉	1	4	yes	—
285	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
286	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
287	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
288	#520	C₂²×C₈₉	1	2	yes	—
289	#518	C₂²×C₈₉	1	2	yes	—
290	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
291	#501	C₂²×C₈₉	1	2	yes	complemented
292	#501	C₂²×C₈₉	1	2	yes	complemented
293	#501	C₂²×C₈₉	1	4	yes	complemented
294	#501	C₂²×C₈₉	1	4	yes	complemented
295	#499	C₂²×C₈₉	1	4	yes	complemented
296	#490	C₂²×C₈₉	1	4	yes	—
297	#490	C₂²×C₈₉	1	4	yes	—
298	#490	C₂²×C₈₉	1	2	yes	—
299	#490	C₂²×C₈₉	1	2	yes	—
300	#486	C₂²×C₈₉	1	4	yes	—
301	#482	C₂²×C₈₉	1	8	yes	complemented
302	#482	C₂²×C₈₉	1	8	yes	complemented
303	#481	C₂²×C₈₉	1	8	yes	complemented
304	#480	C₂²×C₈₉	1	8	yes	complemented
305	#478	C₂²×C₈₉	1	8	yes	complemented
306	#478	C₂²×C₈₉	1	8	yes	complemented
307	#476	C₂²×C₈₉	1	8	yes	complemented
308	#474	C₂²×C₈₉	1	8	yes	complemented
309	#433	C₂²×C₈₉	1	4	yes	complemented
310	#432	C₂²×C₈₉	1	4	yes	complemented
311	#428	C₂²×C₈₉	1	4	yes	—
312	#427	C₂²×C₈₉	1	4	yes	—
313	#424	C₂²×C₈₉	1	2	yes	—
314	#418	C₂²×C₈₉	1	4	yes	—
315	C₂×#102	C₂²×C₈₉	1	4	yes	—
316	#408	C₂²×C₈₉	1	2	yes	—
317	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
318	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
319	C₂×#41	—	2	4	no	—
320	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
323	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
324	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	4	no	—
327	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
330	#127	—	2	2	no	—
331	#127	—	2	2	no	—
332	#127	C₂³×C₈₉	1	2	yes	—
333	#127	C₂³×C₈₉	1	2	yes	—
334	#125	—	2	2	no	—
335	#125	—	2	4	no	—
336	#125	—	2	2	no	—
337	#125	—	2	4	no	—
338	#125	C₂³×C₈₉	1	2	yes	—
339	#125	C₂³×C₈₉	1	2	yes	—
340	#125	C₂³×C₈₉	1	1	yes	characteristic
341	#125	C₂³×C₈₉	1	4	yes	—
342	#125	C₂³×C₈₉	1	1	yes	characteristic
343	#125	C₂³×C₈₉	1	2	yes	—
344	#124	—	2	2	no	—
345	#124	—	2	4	no	—
346	#123	—	2	8	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	8	no	—
355	#121	C₂³×C₈₉	1	8	yes	—
356	#120	—	2	4	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	D₄×C₈₉	1	2	yes	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	D₄×C₈₉	1	4	yes	—
367	C₄×D₄	D₄×C₈₉	1	2	yes	—
368	C₄×D₄	C₂³×C₈₉	1	8	yes	—
369	#117	C₂³×C₈₉	1	2	yes	—
370	#117	C₂³×C₈₉	1	2	yes	—
371	#117	C₂³×C₈₉	1	4	yes	—
372	#117	C₂³×C₈₉	1	1	yes	characteristic
373	#117	C₂³×C₈₉	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	4	no	—
376	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
381	#107	C₂³×C₈₉	1	4	yes	—
382	#107	C₂³×C₈₉	1	4	yes	—
383	#107	C₂³×C₈₉	1	8	yes	—
384	#106	C₂³×C₈₉	1	4	yes	—
385	#106	C₂³×C₈₉	1	4	yes	—
386	#106	C₂³×C₈₉	1	8	yes	—
387	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
388	#102	C₂³×C₈₉	1	8	yes	—
389	#102	C₂³×C₈₉	1	8	yes	—
390	#102	C₂³×C₈₉	1	8	yes	—
391	#102	C₂³×C₈₉	1	8	yes	—
392	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
393	#97	C₂³×C₈₉	1	2	yes	—
394	#97	C₂³×C₈₉	1	2	yes	—
395	#97	C₂³×C₈₉	1	2	yes	—
396	C₄×C₈	C₂³×C₈₉	1	2	yes	—
397	C₂⁴	—	2	2	no	—
398	#41	—	2	4	no	—
399	#41	—	8	8	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	8	4	no	—
410	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
411	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
412	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
417	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
420	M₁₆	—	2	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
423	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
438	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
439	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
440	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
441	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
448	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₈₉	1	4	yes	—
453	C₄²	C₂×D₄×C₈₉	1	2	yes	—
454	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
455	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
456	C₄²	C₂⁴×C₈₉	1	2	yes	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	8	4	no	—
460	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
461	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	4	4	no	—
464	Q₈	—	8	4	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	8	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	4	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	4	no	—
483	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
486	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
488	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
489	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
490	C₈	—	2	4	no	—
491	C₈	—	2	4	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	8	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	16	4	no	—
498	C₂²	#536×C₈₉	1	2	yes	—
499	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	#536×C₈₉	1	2	yes	—
509	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	4	no	—
513	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
514	C₂	C₈₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3508	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
2. C₈₉×#3504	C₂	semidirect
3. C₈₉×#3241	C₂	semidirect
4. C₈₉×#3235	C₂	semidirect
5. C₈₉×#3234	C₂	semidirect
6. C₈₉×#3166	C₂	semidirect
7. C₈₉×#3162	C₂	semidirect
8. C₈₉×#3138	C₂	semidirect
9. C₂×#490×C₈₉	C₂	semidirect
10. C₈₉×#3096	C₂	semidirect
11. C₈₉×#3081	C₂	semidirect
12. C₈₉×#2923	C₂	semidirect
20. #544×C₈₉	C₂²	semidirect
25. #533×C₈₉	C₂²	semidirect
29. C₂×#125×C₈₉	C₂²	semidirect
33. #501×C₈₉	C₂²	semidirect
34. #501×C₈₉	C₂²	semidirect
35. #501×C₈₉	C₂²	semidirect
36. #501×C₈₉	C₂²	semidirect
37. #499×C₈₉	C₂²	semidirect
43. #482×C₈₉	C₂²	semidirect
44. #482×C₈₉	C₂²	semidirect
45. #481×C₈₉	C₂²	semidirect
46. #480×C₈₉	C₂²	semidirect
47. #478×C₈₉	C₂²	semidirect
48. #478×C₈₉	C₂²	semidirect
49. #476×C₈₉	C₂²	semidirect
50. #474×C₈₉	C₂²	semidirect
51. #433×C₈₉	C₂²	semidirect
52. #432×C₈₉	C₂²	semidirect
252. #60883	C₈₉	direct (N × H)
259. #3504	C₂×C₈₉	semidirect
260. #3241	C₂×C₈₉	semidirect
261. #3235	C₂×C₈₉	semidirect
262. #3234	C₂×C₈₉	semidirect
263. #3166	C₂×C₈₉	semidirect
264. #3162	C₂×C₈₉	semidirect
265. #3138	C₂×C₈₉	semidirect
266. C₂×#490	C₂×C₈₉	semidirect
267. #3096	C₂×C₈₉	semidirect
268. #3081	C₂×C₈₉	semidirect
269. #2923	C₂×C₈₉	semidirect
270. C₈₉	#60883	direct (N × H)
278. #544	C₂²×C₈₉	semidirect
283. #533	C₂²×C₈₉	semidirect
287. C₂×#125	C₂²×C₈₉	semidirect
291. #501	C₂²×C₈₉	semidirect
292. #501	C₂²×C₈₉	semidirect
293. #501	C₂²×C₈₉	semidirect
294. #501	C₂²×C₈₉	semidirect
295. #499	C₂²×C₈₉	semidirect
301. #482	C₂²×C₈₉	semidirect
302. #482	C₂²×C₈₉	semidirect
303. #481	C₂²×C₈₉	semidirect
304. #480	C₂²×C₈₉	semidirect
305. #478	C₂²×C₈₉	semidirect
306. #478	C₂²×C₈₉	semidirect
307. #476	C₂²×C₈₉	semidirect
308. #474	C₂²×C₈₉	semidirect
309. #433	C₂²×C₈₉	semidirect
310. #432	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×#3508	2
C₈₉×#3504	2
C₈₉×#3241	2
C₈₉×#3235	2
C₈₉×#3234	2
C₈₉×#3166	2
C₈₉×#3162	2
C₈₉×#3138	2
C₂×#490×C₈₉	2
C₈₉×#3096	2
C₈₉×#3081	2
C₈₉×#2923	2
#60883	89

Subgroups — C89×#60883 #36438731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60883 #36438731