Subgroups — C₈₉×#35324 #36413172

Order 22784.

1566 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	C₈₉×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2855	C₂	1	2	yes	maximal
4	C₈₉×#2645	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2628	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2621	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2588	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2575	C₂	1	4	yes	maximal
9	C₈₉×#2528	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2527	C₂	1	4	yes	maximal
11	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2323	C₂	1	2	yes	maximal
14	C₈₉×#2295	C₂	1	2	yes	maximal, complemented
15	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
23	#401×C₈₉	C₂²	1	4	yes	—
24	#400×C₈₉	C₂²	1	4	yes	—
25	#400×C₈₉	C₂²	1	4	yes	—
26	#400×C₈₉	C₂²	1	2	yes	—
27	#400×C₈₉	C₂²	1	4	yes	—
28	#399×C₈₉	C₂²	1	2	yes	—
29	#398×C₈₉	C₂²	1	2	yes	—
30	#398×C₈₉	C₂²	1	2	yes	—
31	#397×C₈₉	C₂²	1	2	yes	—
32	#397×C₈₉	C₂²	1	2	yes	—
33	#395×C₈₉	C₂²	1	2	yes	—
34	#393×C₈₉	C₂²	1	2	yes	—
35	#391×C₈₉	C₂²	1	2	yes	—
36	#391×C₈₉	C₂²	1	2	yes	—
37	#391×C₈₉	C₂²	1	2	yes	—
38	#391×C₈₉	C₂²	1	2	yes	—
39	#391×C₈₉	C₂²	1	4	yes	—
40	#391×C₈₉	C₂²	1	4	yes	—
41	#389×C₈₉	C₂²	1	2	yes	—
42	#389×C₈₉	C₂²	1	2	yes	—
43	#389×C₈₉	C₂²	1	4	yes	—
44	#389×C₈₉	C₂²	1	2	yes	—
45	#389×C₈₉	C₂²	1	2	yes	—
46	#388×C₈₉	C₂²	1	4	yes	—
47	#388×C₈₉	C₂²	1	4	yes	—
48	#387×C₈₉	C₂²	1	4	yes	—
49	#387×C₈₉	C₂²	1	4	yes	—
50	#387×C₈₉	C₂²	1	4	yes	—
51	#387×C₈₉	C₂²	1	4	yes	—
52	#387×C₈₉	C₂²	1	4	yes	—
53	#387×C₈₉	C₂²	1	4	yes	—
54	#387×C₈₉	C₂²	1	4	yes	—
55	#387×C₈₉	C₂²	1	4	yes	—
56	#387×C₈₉	C₂²	1	4	yes	—
57	#387×C₈₉	C₂²	1	4	yes	—
58	#385×C₈₉	C₂²	1	4	yes	—
59	#382×C₈₉	C₂²	1	4	yes	—
60	#382×C₈₉	C₂²	1	1	yes	characteristic
61	#382×C₈₉	C₂²	1	1	yes	characteristic
62	#381×C₈₉	C₂²	1	4	yes	—
63	#380×C₈₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
70	#376×C₈₉	C₂²	1	4	yes	—
71	#376×C₈₉	C₂²	1	1	yes	characteristic
72	#376×C₈₉	C₂²	1	1	yes	characteristic
73	C₄³×C₈₉	C₂²	1	1	yes	characteristic
74	C₄³×C₈₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
76	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₈₉	—	2	4	no	—
80	C₄⋊Q₈×C₈₉	—	2	4	no	—
81	C₂²⋊Q₈×C₈₉	—	2	8	no	—
82	C₄×Q₈×C₈₉	—	2	8	no	—
83	#117×C₈₉	—	2	4	no	—
84	#117×C₈₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₈₉	—	2	4	no	—
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
113	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
119	#95×C₈₉	C₂³	1	2	yes	—
120	#95×C₈₉	C₂³	1	2	yes	—
121	#95×C₈₉	C₂³	1	2	yes	—
122	#95×C₈₉	C₂³	1	2	yes	—
123	#95×C₈₉	C₂³	1	4	yes	—
124	#95×C₈₉	C₂³	1	4	yes	—
125	#95×C₈₉	C₂³	1	4	yes	—
126	#95×C₈₉	C₂³	1	4	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	4	yes	—
132	#95×C₈₉	C₂³	1	4	yes	—
133	#95×C₈₉	C₂³	1	2	yes	—
134	#95×C₈₉	C₂³	1	2	yes	—
135	#95×C₈₉	C₂³	1	2	yes	—
136	#95×C₈₉	C₂³	1	2	yes	—
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	4	yes	—
139	#95×C₈₉	C₂³	1	4	yes	—
140	#95×C₈₉	C₂³	1	4	yes	—
141	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
146	C₂×Q₈×C₈₉	—	4	4	no	—
147	C₂²×C₄×C₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	2	no	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	4	no	—
151	C₂²×C₄×C₈₉	—	4	2	no	—
152	C₂²×C₄×C₈₉	#41	1	4	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₈₉	—	2	4	no	—
168	C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₄⋊C₄×C₈₉	—	2	2	no	—
170	C₄⋊C₄×C₈₉	—	2	4	no	—
171	C₄⋊C₄×C₈₉	—	2	8	no	—
172	C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₄⋊C₄×C₈₉	—	2	8	no	—
174	C₄⋊C₄×C₈₉	—	2	4	no	—
175	C₄⋊C₄×C₈₉	—	2	4	no	—
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	4	no	—
178	C₄⋊C₄×C₈₉	—	2	8	no	—
179	C₄⋊C₄×C₈₉	—	4	4	no	—
180	C₄⋊C₄×C₈₉	—	4	4	no	—
181	C₄⋊C₄×C₈₉	—	4	4	no	—
182	C₂²⋊C₄×C₈₉	—	2	8	no	—
183	C₂²⋊C₄×C₈₉	—	2	4	no	—
184	C₂²⋊C₄×C₈₉	—	2	2	no	—
185	C₂²⋊C₄×C₈₉	—	2	2	no	—
186	C₂²⋊C₄×C₈₉	—	4	4	no	—
187	C₄²×C₈₉	—	2	2	no	—
188	C₄²×C₈₉	—	2	4	no	—
189	C₄²×C₈₉	—	2	2	no	—
190	C₄²×C₈₉	—	2	2	no	—
191	C₄²×C₈₉	—	2	2	no	—
192	C₄²×C₈₉	—	2	8	no	—
193	C₄²×C₈₉	—	2	4	no	—
194	C₄²×C₈₉	—	2	4	no	—
195	C₄²×C₈₉	—	4	2	no	—
196	C₄²×C₈₉	—	4	4	no	—
197	C₄²×C₈₉	—	4	2	no	—
198	C₄²×C₈₉	#41	1	4	yes	—
199	C₄²×C₈₉	#41	1	4	yes	—
200	C₂³×C₈₉	—	2	1	no	—
201	C₂³×C₈₉	—	2	1	no	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	2	no	—
204	C₂³×C₈₉	C₂×#41	1	2	yes	—
205	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
206	Q₈×C₈₉	—	4	8	no	—
207	Q₈×C₈₉	—	8	4	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	2	no	—
215	C₂×C₄×C₈₉	—	2	2	no	—
216	C₂×C₄×C₈₉	—	2	8	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	4	no	—
222	C₂×C₄×C₈₉	—	2	4	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	4	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	4	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	4	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	2	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	4	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	4	no	—
239	C₂×C₄×C₈₉	—	4	8	no	—
240	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
241	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
242	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
243	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
246	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
247	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
248	C₂²×C₈₉	—	2	2	no	—
249	C₂²×C₈₉	—	2	4	no	—
250	C₂²×C₈₉	—	4	2	no	—
251	C₂²×C₈₉	—	4	1	no	—
252	C₂²×C₈₉	—	4	1	no	—
253	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
255	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
256	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
257	C₂²×C₈₉	#585	1	2	yes	—
258	C₄×C₈₉	—	2	2	no	—
259	C₄×C₈₉	—	2	4	no	—
260	C₄×C₈₉	—	2	4	no	—
261	C₄×C₈₉	—	2	2	no	—
262	C₄×C₈₉	—	2	2	no	—
263	C₄×C₈₉	—	4	4	no	—
264	C₄×C₈₉	—	4	2	no	—
265	C₄×C₈₉	—	4	4	no	—
266	C₄×C₈₉	—	4	4	no	—
267	C₄×C₈₉	—	4	2	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	—	4	4	no	—
271	C₄×C₈₉	#529	1	4	yes	—
272	#35324	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₈₉	—	4	2	no	—
274	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
275	C₂×C₈₉	#3461	1	2	yes	—
276	C₂×C₈₉	#3495	1	2	yes	—
277	C₂×C₈₉	#3509	1	1	yes	characteristic
278	C₂×C₈₉	#3510	1	1	yes	characteristic
279	#2864	C₂×C₈₉	1	1	yes	characteristic, complemented
280	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
281	#2855	C₂×C₈₉	1	2	yes	—
282	#2645	C₂×C₈₉	1	2	yes	complemented
283	#2628	C₂×C₈₉	1	1	yes	characteristic
284	#2621	C₂×C₈₉	1	1	yes	characteristic
285	#2588	C₂×C₈₉	1	4	yes	complemented
286	#2575	C₂×C₈₉	1	4	yes	—
287	#2528	C₂×C₈₉	1	4	yes	complemented
288	#2527	C₂×C₈₉	1	4	yes	—
289	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
290	#2327	C₂×C₈₉	1	1	yes	characteristic, complemented
291	#2323	C₂×C₈₉	1	2	yes	—
292	#2295	C₂×C₈₉	1	2	yes	complemented
293	C₄×#117	C₂×C₈₉	1	1	yes	characteristic
294	C₈₉	#35324	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
298	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
299	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
300	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
302	#401	C₂²×C₈₉	1	4	yes	—
303	#400	C₂²×C₈₉	1	4	yes	—
304	#400	C₂²×C₈₉	1	4	yes	—
305	#400	C₂²×C₈₉	1	2	yes	—
306	#400	C₂²×C₈₉	1	4	yes	—
307	#399	C₂²×C₈₉	1	2	yes	—
308	#398	C₂²×C₈₉	1	2	yes	—
309	#398	C₂²×C₈₉	1	2	yes	—
310	#397	C₂²×C₈₉	1	2	yes	—
311	#397	C₂²×C₈₉	1	2	yes	—
312	#395	C₂²×C₈₉	1	2	yes	—
313	#393	C₂²×C₈₉	1	2	yes	—
314	#391	C₂²×C₈₉	1	2	yes	—
315	#391	C₂²×C₈₉	1	2	yes	—
316	#391	C₂²×C₈₉	1	4	yes	—
317	#391	C₂²×C₈₉	1	4	yes	—
318	#391	C₂²×C₈₉	1	2	yes	—
319	#391	C₂²×C₈₉	1	2	yes	—
320	#389	C₂²×C₈₉	1	4	yes	—
321	#389	C₂²×C₈₉	1	2	yes	—
322	#389	C₂²×C₈₉	1	2	yes	—
323	#389	C₂²×C₈₉	1	2	yes	—
324	#389	C₂²×C₈₉	1	2	yes	—
325	#388	C₂²×C₈₉	1	4	yes	—
326	#388	C₂²×C₈₉	1	4	yes	—
327	#387	C₂²×C₈₉	1	4	yes	—
328	#387	C₂²×C₈₉	1	4	yes	—
329	#387	C₂²×C₈₉	1	4	yes	—
330	#387	C₂²×C₈₉	1	4	yes	—
331	#387	C₂²×C₈₉	1	4	yes	—
332	#387	C₂²×C₈₉	1	4	yes	—
333	#387	C₂²×C₈₉	1	4	yes	—
334	#387	C₂²×C₈₉	1	4	yes	—
335	#387	C₂²×C₈₉	1	4	yes	—
336	#387	C₂²×C₈₉	1	4	yes	—
337	#385	C₂²×C₈₉	1	4	yes	—
338	#382	C₂²×C₈₉	1	4	yes	—
339	#382	C₂²×C₈₉	1	1	yes	characteristic
340	#382	C₂²×C₈₉	1	1	yes	characteristic
341	#381	C₂²×C₈₉	1	4	yes	—
342	#380	C₂²×C₈₉	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
349	#376	C₂²×C₈₉	1	1	yes	characteristic
350	#376	C₂²×C₈₉	1	1	yes	characteristic
351	#376	C₂²×C₈₉	1	4	yes	—
352	C₄³	C₂²×C₈₉	1	1	yes	characteristic
353	C₄³	C₂²×C₈₉	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
355	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
356	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
358	C₄⋊Q₈	—	2	4	no	—
359	C₄⋊Q₈	—	2	4	no	—
360	C₂²⋊Q₈	—	2	8	no	—
361	C₄×Q₈	—	2	8	no	—
362	#117	—	2	4	no	—
363	#117	—	2	4	no	—
364	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
384	C₂×C₄²	—	2	4	no	—
385	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
388	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
393	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
394	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
395	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
396	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
398	#95	C₂³×C₈₉	1	2	yes	—
399	#95	C₂³×C₈₉	1	2	yes	—
400	#95	C₂³×C₈₉	1	2	yes	—
401	#95	C₂³×C₈₉	1	2	yes	—
402	#95	C₂³×C₈₉	1	4	yes	—
403	#95	C₂³×C₈₉	1	4	yes	—
404	#95	C₂³×C₈₉	1	4	yes	—
405	#95	C₂³×C₈₉	1	4	yes	—
406	#95	C₂³×C₈₉	1	4	yes	—
407	#95	C₂³×C₈₉	1	4	yes	—
408	#95	C₂³×C₈₉	1	4	yes	—
409	#95	C₂³×C₈₉	1	4	yes	—
410	#95	C₂³×C₈₉	1	4	yes	—
411	#95	C₂³×C₈₉	1	4	yes	—
412	#95	C₂³×C₈₉	1	2	yes	—
413	#95	C₂³×C₈₉	1	2	yes	—
414	#95	C₂³×C₈₉	1	2	yes	—
415	#95	C₂³×C₈₉	1	2	yes	—
416	#95	C₂³×C₈₉	1	4	yes	—
417	#95	C₂³×C₈₉	1	4	yes	—
418	#95	C₂³×C₈₉	1	4	yes	—
419	#95	C₂³×C₈₉	1	4	yes	—
420	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	4	4	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	#41×C₈₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	4	4	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	8	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	4	2	no	—
475	C₄²	—	4	4	no	—
476	C₄²	—	4	2	no	—
477	C₄²	#41×C₈₉	1	4	yes	—
478	C₄²	#41×C₈₉	1	4	yes	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	C₂×#41×C₈₉	1	2	yes	—
484	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
485	Q₈	—	4	8	no	—
486	Q₈	—	8	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
520	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
521	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
522	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
523	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
524	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
525	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
526	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
533	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
534	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
535	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
536	C₂²	#585×C₈₉	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	1	no	—
550	C₄	#529×C₈₉	1	4	yes	—
551	C₂	—	4	2	no	—
552	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
553	C₂	C₈₉×#3461	1	2	yes	—
554	C₂	C₈₉×#3495	1	2	yes	—
555	C₂	C₈₉×#3509	1	1	yes	characteristic
556	C₂	C₈₉×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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. C₈₉×#2864	C₂	semidirect
2. C₈₉×#2862	C₂	semidirect
4. C₈₉×#2645	C₂	semidirect
7. C₈₉×#2588	C₂	semidirect
9. C₈₉×#2528	C₂	semidirect
11. C₈₉×#2331	C₂	semidirect
12. C₈₉×#2327	C₂	semidirect
14. C₈₉×#2295	C₂	semidirect
272. #35324	C₈₉	direct (N × H)
279. #2864	C₂×C₈₉	semidirect
280. #2862	C₂×C₈₉	semidirect
282. #2645	C₂×C₈₉	semidirect
285. #2588	C₂×C₈₉	semidirect
287. #2528	C₂×C₈₉	semidirect
289. #2331	C₂×C₈₉	semidirect
290. #2327	C₂×C₈₉	semidirect
292. #2295	C₂×C₈₉	semidirect
294. C₈₉	#35324	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2864	2
C₈₉×#2862	2
C₈₉×#2855	2
C₈₉×#2645	2
C₈₉×#2628	2
C₈₉×#2621	2
C₈₉×#2588	2
C₈₉×#2575	2
C₈₉×#2528	2
C₈₉×#2527	2
C₈₉×#2331	2
C₈₉×#2327	2
C₈₉×#2323	2
C₈₉×#2295	2
C₄×#117×C₈₉	2
#35324	89

Subgroups — C89×#35324 #36413172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35324 #36413172