Subgroups — C₈₉×#35312 #36413160

Order 22784.

2262 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2862	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2861	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2642	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2640	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2492	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2489	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2488	C₂	1	8	yes	maximal, complemented
10	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2310	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic
13	C₂×#391×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	#544×C₈₉	—	2	8	no	—
18	#536×C₈₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	C₂×#125×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	2	yes	—
25	C₂×#123×C₈₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	#400×C₈₉	C₂²	1	8	yes	—
35	#400×C₈₉	C₂²	1	8	yes	—
36	#397×C₈₉	C₂²	1	8	yes	—
37	#393×C₈₉	C₂²	1	8	yes	—
38	#391×C₈₉	C₂²	1	2	yes	—
39	#391×C₈₉	C₂²	1	2	yes	—
40	#391×C₈₉	C₂²	1	4	yes	—
41	#391×C₈₉	C₂²	1	1	yes	characteristic
42	#391×C₈₉	C₂²	1	1	yes	characteristic
43	#391×C₈₉	C₂²	1	2	yes	—
44	#391×C₈₉	C₂²	1	2	yes	—
45	#391×C₈₉	C₂²	1	4	yes	—
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	8	yes	—
48	#390×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	2	yes	—
51	#388×C₈₉	C₂²	1	8	yes	—
52	#388×C₈₉	C₂²	1	8	yes	—
53	#386×C₈₉	C₂²	1	4	yes	—
54	#386×C₈₉	C₂²	1	4	yes	—
55	#382×C₈₉	C₂²	1	8	yes	—
56	#381×C₈₉	C₂²	1	4	yes	—
57	#380×C₈₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
62	#376×C₈₉	C₂²	1	2	yes	—
63	C₂×#95×C₈₉	C₂²	1	4	yes	—
64	C₄³×C₈₉	C₂²	1	2	yes	—
65	C₂×#41×C₈₉	—	2	4	no	—
66	C₂×#41×C₈₉	—	2	4	no	—
67	C₂×#41×C₈₉	—	2	4	no	—
68	C₂²×Q₈×C₈₉	—	2	4	no	—
69	C₂²×Q₈×C₈₉	—	2	4	no	—
70	C₂²×Q₈×C₈₉	—	2	4	no	—
71	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
72	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	—	2	8	no	—
83	C₄⋊Q₈×C₈₉	—	2	8	no	—
84	C₄⋊Q₈×C₈₉	—	2	8	no	—
85	#125×C₈₉	—	2	8	no	—
86	#125×C₈₉	—	2	8	no	—
87	#124×C₈₉	—	2	8	no	—
88	#123×C₈₉	—	2	16	no	—
89	C₂²⋊Q₈×C₈₉	—	2	8	no	—
90	C₂²⋊Q₈×C₈₉	—	2	8	no	—
91	C₂²⋊Q₈×C₈₉	—	2	16	no	—
92	#117×C₈₉	—	2	4	no	—
93	#117×C₈₉	—	2	4	no	—
94	#117×C₈₉	D₄	1	8	yes	—
95	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₈₉	—	2	4	no	—
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
125	#95×C₈₉	C₂³	1	8	yes	—
126	#95×C₈₉	C₂³	1	8	yes	—
127	#95×C₈₉	C₂³	1	4	yes	—
128	#95×C₈₉	C₂³	1	4	yes	—
129	#95×C₈₉	C₂³	1	4	yes	—
130	#95×C₈₉	C₂³	1	4	yes	—
131	#95×C₈₉	C₂³	1	8	yes	—
132	#95×C₈₉	C₂³	1	8	yes	—
133	#95×C₈₉	C₂³	1	8	yes	—
134	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
135	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
136	#41×C₈₉	—	4	16	no	—
137	C₂×Q₈×C₈₉	—	2	4	no	—
138	C₂×Q₈×C₈₉	—	2	4	no	—
139	C₂×Q₈×C₈₉	—	2	2	no	—
140	C₂×Q₈×C₈₉	—	2	8	no	—
141	C₂×Q₈×C₈₉	—	2	4	no	—
142	C₂×Q₈×C₈₉	—	2	4	no	—
143	C₂×Q₈×C₈₉	—	2	4	no	—
144	C₂×Q₈×C₈₉	—	2	4	no	—
145	C₂×Q₈×C₈₉	—	2	2	no	—
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	—	4	8	no	—
148	C₂×Q₈×C₈₉	—	4	16	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	4	no	—
151	C₂×D₄×C₈₉	—	2	4	no	—
152	C₂×D₄×C₈₉	—	2	2	no	—
153	C₂×D₄×C₈₉	—	2	2	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂²×C₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	2	4	no	—
157	C₂²×C₄×C₈₉	—	2	4	no	—
158	C₂²×C₄×C₈₉	—	2	4	no	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	2	4	no	—
164	C₂²×C₄×C₈₉	—	4	2	no	—
165	C₂²×C₄×C₈₉	—	4	4	no	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₈₉	#41	1	4	yes	—
168	C₂²×C₄×C₈₉	#41	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₈₉	—	2	4	no	—
182	C₄⋊C₄×C₈₉	—	2	4	no	—
183	C₄⋊C₄×C₈₉	—	2	2	no	—
184	C₄⋊C₄×C₈₉	—	2	2	no	—
185	C₄⋊C₄×C₈₉	—	2	8	no	—
186	C₄⋊C₄×C₈₉	—	2	8	no	—
187	C₄⋊C₄×C₈₉	—	2	8	no	—
188	C₄⋊C₄×C₈₉	—	2	8	no	—
189	C₄⋊C₄×C₈₉	—	2	8	no	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
193	C₂²⋊C₄×C₈₉	—	2	4	no	—
194	C₂²⋊C₄×C₈₉	—	2	4	no	—
195	C₂²⋊C₄×C₈₉	—	2	8	no	—
196	C₂²⋊C₄×C₈₉	—	2	8	no	—
197	C₂²⋊C₄×C₈₉	—	2	8	no	—
198	C₂²⋊C₄×C₈₉	—	4	8	no	—
199	C₂²⋊C₄×C₈₉	—	4	4	no	—
200	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
201	C₄²×C₈₉	—	2	4	no	—
202	C₄²×C₈₉	—	2	2	no	—
203	C₄²×C₈₉	—	2	4	no	—
204	C₄²×C₈₉	—	2	2	no	—
205	C₄²×C₈₉	—	2	4	no	—
206	C₄²×C₈₉	—	2	8	no	—
207	C₄²×C₈₉	—	4	4	no	—
208	C₄²×C₈₉	C₂×D₄	1	8	yes	—
209	C₂³×C₈₉	—	2	2	no	—
210	C₂³×C₈₉	—	2	2	no	—
211	C₂³×C₈₉	—	2	2	no	—
212	C₂³×C₈₉	—	2	2	no	—
213	C₂³×C₈₉	—	2	2	no	—
214	C₂³×C₈₉	—	2	4	no	—
215	C₂³×C₈₉	—	2	4	no	—
216	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
217	C₂³×C₈₉	C₂×#41	1	2	yes	—
218	C₂³×C₈₉	C₂×#41	1	2	yes	—
219	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
220	Q₈×C₈₉	—	4	8	no	—
221	Q₈×C₈₉	—	4	8	no	—
222	Q₈×C₈₉	—	4	4	no	—
223	Q₈×C₈₉	—	8	8	no	—
224	D₄×C₈₉	—	4	8	no	—
225	D₄×C₈₉	—	4	4	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	4	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	4	no	—
230	C₂×C₄×C₈₉	—	2	2	no	—
231	C₂×C₄×C₈₉	—	2	2	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	4	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	4	no	—
240	C₂×C₄×C₈₉	—	2	4	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	4	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	8	no	—
247	C₂×C₄×C₈₉	—	2	4	no	—
248	C₂×C₄×C₈₉	—	4	8	no	—
249	C₂×C₄×C₈₉	—	4	8	no	—
250	C₂×C₄×C₈₉	—	4	8	no	—
251	C₂×C₄×C₈₉	—	8	4	no	—
252	C₂×C₄×C₈₉	#124	1	16	yes	—
253	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
258	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
259	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
260	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
261	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
262	C₂²×C₈₉	—	2	4	no	—
263	C₂²×C₈₉	—	2	4	no	—
264	C₂²×C₈₉	—	2	2	no	—
265	C₂²×C₈₉	—	2	2	no	—
266	C₂²×C₈₉	—	4	2	no	—
267	C₂²×C₈₉	—	4	4	no	—
268	C₂²×C₈₉	—	4	4	no	—
269	C₂²×C₈₉	—	4	2	no	—
270	C₂²×C₈₉	—	4	2	no	—
271	C₂²×C₈₉	C₂×#124	1	4	yes	—
272	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
273	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
274	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
275	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
276	C₂²×C₈₉	#585	1	2	yes	—
277	C₄×C₈₉	—	2	4	no	—
278	C₄×C₈₉	—	2	4	no	—
279	C₄×C₈₉	—	2	4	no	—
280	C₄×C₈₉	—	4	2	no	—
281	C₄×C₈₉	—	4	4	no	—
282	C₄×C₈₉	—	4	4	no	—
283	C₄×C₈₉	—	4	2	no	—
284	C₄×C₈₉	—	4	2	no	—
285	C₄×C₈₉	—	4	4	no	—
286	C₄×C₈₉	—	4	2	no	—
287	C₄×C₈₉	C₂×#124	1	4	yes	—
288	C₄×C₈₉	C₂×#124	1	4	yes	—
289	#35312	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂×C₈₉	—	2	4	no	—
291	C₂×C₈₉	—	8	2	no	—
292	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
293	C₂×C₈₉	#3461	1	2	yes	—
294	C₂×C₈₉	#3495	1	2	yes	—
295	C₂×C₈₉	#3499	1	1	yes	characteristic
296	C₂×C₈₉	#3500	1	1	yes	characteristic
297	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
298	C₂×#536	C₂×C₈₉	1	1	yes	characteristic
299	#2862	C₂×C₈₉	1	2	yes	complemented
300	#2861	C₂×C₈₉	1	2	yes	complemented
301	#2642	C₂×C₈₉	1	2	yes	complemented
302	#2640	C₂×C₈₉	1	2	yes	complemented
303	#2492	C₂×C₈₉	1	4	yes	complemented
304	#2489	C₂×C₈₉	1	4	yes	complemented
305	#2488	C₂×C₈₉	1	8	yes	complemented
306	#2311	C₂×C₈₉	1	1	yes	characteristic
307	#2310	C₂×C₈₉	1	1	yes	characteristic, complemented
308	#2297	C₂×C₈₉	1	1	yes	characteristic
309	C₂×#391	C₂×C₈₉	1	1	yes	characteristic, complemented
310	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
311	C₈₉	#35312	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
313	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
314	#544	—	2	8	no	—
315	#536	—	2	8	no	—
316	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
317	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
318	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
319	C₂×#125	C₂²×C₈₉	1	2	yes	—
320	C₂×#125	C₂²×C₈₉	1	2	yes	—
321	C₂×#124	C₂²×C₈₉	1	2	yes	—
322	C₂×#123	C₂²×C₈₉	1	4	yes	—
323	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
324	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
326	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
330	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
331	#400	C₂²×C₈₉	1	8	yes	—
332	#400	C₂²×C₈₉	1	8	yes	—
333	#397	C₂²×C₈₉	1	8	yes	—
334	#393	C₂²×C₈₉	1	8	yes	—
335	#391	C₂²×C₈₉	1	2	yes	—
336	#391	C₂²×C₈₉	1	2	yes	—
337	#391	C₂²×C₈₉	1	4	yes	—
338	#391	C₂²×C₈₉	1	2	yes	—
339	#391	C₂²×C₈₉	1	2	yes	—
340	#391	C₂²×C₈₉	1	1	yes	characteristic
341	#391	C₂²×C₈₉	1	8	yes	—
342	#391	C₂²×C₈₉	1	2	yes	—
343	#391	C₂²×C₈₉	1	1	yes	characteristic
344	#391	C₂²×C₈₉	1	4	yes	—
345	#390	C₂²×C₈₉	1	2	yes	—
346	#390	C₂²×C₈₉	1	1	yes	characteristic
347	#390	C₂²×C₈₉	1	1	yes	characteristic
348	#388	C₂²×C₈₉	1	8	yes	—
349	#388	C₂²×C₈₉	1	8	yes	—
350	#386	C₂²×C₈₉	1	4	yes	—
351	#386	C₂²×C₈₉	1	4	yes	—
352	#382	C₂²×C₈₉	1	8	yes	—
353	#381	C₂²×C₈₉	1	4	yes	—
354	#380	C₂²×C₈₉	1	4	yes	—
355	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
359	#376	C₂²×C₈₉	1	2	yes	—
360	C₂×#95	C₂²×C₈₉	1	4	yes	—
361	C₄³	C₂²×C₈₉	1	2	yes	—
362	C₂×#41	—	2	4	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	—	2	4	no	—
365	C₂²×Q₈	—	2	4	no	—
366	C₂²×Q₈	—	2	4	no	—
367	C₂²×Q₈	—	2	4	no	—
368	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
369	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
370	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
372	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
373	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
375	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
376	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
377	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
378	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
379	C₄⋊Q₈	—	2	8	no	—
380	C₄⋊Q₈	—	2	8	no	—
381	C₄⋊Q₈	—	2	8	no	—
382	#125	—	2	8	no	—
383	#125	—	2	8	no	—
384	#124	—	2	8	no	—
385	#123	—	2	16	no	—
386	C₂²⋊Q₈	—	2	8	no	—
387	C₂²⋊Q₈	—	2	8	no	—
388	C₂²⋊Q₈	—	2	16	no	—
389	#117	—	2	4	no	—
390	#117	—	2	4	no	—
391	#117	D₄×C₈₉	1	8	yes	—
392	C₂×C₄⋊C₄	—	2	4	no	—
393	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₄²	—	2	4	no	—
414	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
415	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
416	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
418	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
420	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
421	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
422	#95	C₂³×C₈₉	1	8	yes	—
423	#95	C₂³×C₈₉	1	8	yes	—
424	#95	C₂³×C₈₉	1	4	yes	—
425	#95	C₂³×C₈₉	1	4	yes	—
426	#95	C₂³×C₈₉	1	4	yes	—
427	#95	C₂³×C₈₉	1	4	yes	—
428	#95	C₂³×C₈₉	1	8	yes	—
429	#95	C₂³×C₈₉	1	8	yes	—
430	#95	C₂³×C₈₉	1	8	yes	—
431	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
432	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
433	#41	—	4	16	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	4	8	no	—
445	C₂×Q₈	—	4	16	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
464	C₂²×C₄	#41×C₈₉	1	4	yes	—
465	C₂²×C₄	#41×C₈₉	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	8	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
489	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	4	8	no	—
496	C₂²⋊C₄	—	4	4	no	—
497	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	8	no	—
504	C₄²	—	4	4	no	—
505	C₄²	C₂×D₄×C₈₉	1	8	yes	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
514	C₂³	C₂×#41×C₈₉	1	2	yes	—
515	C₂³	C₂×#41×C₈₉	1	2	yes	—
516	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
517	Q₈	—	4	8	no	—
518	Q₈	—	4	8	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	8	8	no	—
521	D₄	—	4	8	no	—
522	D₄	—	4	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	—	8	4	no	—
549	C₂×C₄	#124×C₈₉	1	16	yes	—
550	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
552	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
554	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
555	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
556	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
557	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
558	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
559	C₂²	—	2	4	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	C₂×#124×C₈₉	1	4	yes	—
569	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
570	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
571	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
572	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
573	C₂²	#585×C₈₉	1	2	yes	—
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	4	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	2	no	—
584	C₄	C₂×#124×C₈₉	1	4	yes	—
585	C₄	C₂×#124×C₈₉	1	4	yes	—
586	C₂	—	2	4	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
589	C₂	C₈₉×#3461	1	2	yes	—
590	C₂	C₈₉×#3495	1	2	yes	—
591	C₂	C₈₉×#3499	1	1	yes	characteristic
592	C₂	C₈₉×#3500	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#2862	C₂	semidirect
4. C₈₉×#2861	C₂	semidirect
5. C₈₉×#2642	C₂	semidirect
6. C₈₉×#2640	C₂	semidirect
7. C₈₉×#2492	C₂	semidirect
8. C₈₉×#2489	C₂	semidirect
9. C₈₉×#2488	C₂	semidirect
11. C₈₉×#2310	C₂	semidirect
13. C₂×#391×C₈₉	C₂	semidirect
14. C₄×#117×C₈₉	C₂	semidirect
289. #35312	C₈₉	direct (N × H)
297. C₂×#544	C₂×C₈₉	semidirect
299. #2862	C₂×C₈₉	semidirect
300. #2861	C₂×C₈₉	semidirect
301. #2642	C₂×C₈₉	semidirect
302. #2640	C₂×C₈₉	semidirect
303. #2492	C₂×C₈₉	semidirect
304. #2489	C₂×C₈₉	semidirect
305. #2488	C₂×C₈₉	semidirect
307. #2310	C₂×C₈₉	semidirect
309. C₂×#391	C₂×C₈₉	semidirect
310. C₄×#117	C₂×C₈₉	semidirect
311. C₈₉	#35312	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×#544×C₈₉	2
C₂×#536×C₈₉	2
C₈₉×#2862	2
C₈₉×#2861	2
C₈₉×#2642	2
C₈₉×#2640	2
C₈₉×#2492	2
C₈₉×#2489	2
C₈₉×#2488	2
C₈₉×#2311	2
C₈₉×#2310	2
C₈₉×#2297	2
C₂×#391×C₈₉	2
C₄×#117×C₈₉	2
#35312	89

Subgroups — C89×#35312 #36413160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35312 #36413160