Subgroups — C₈₉×#29554 #36407402

Order 22784.

808 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2023	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2013	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1968	C₂	1	2	yes	maximal
8	C₈₉×#1933	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1927	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1877	C₂	1	2	yes	maximal
11	C₈₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₈₉	—	2	1	no	—
17	C₂×#106×C₈₉	C₂²	1	2	yes	—
18	C₂×#103×C₈₉	C₂²	1	2	yes	—
19	C₂×#103×C₈₉	C₂²	1	2	yes	—
20	C₂×#103×C₈₉	C₂²	1	2	yes	—
21	C₂×#102×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
23	#391×C₈₉	—	2	1	no	—
24	#391×C₈₉	—	2	1	no	—
25	#391×C₈₉	C₂²	1	2	yes	—
26	#391×C₈₉	C₂²	1	2	yes	—
27	#390×C₈₉	C₂²	1	1	yes	characteristic
28	#390×C₈₉	C₂²	1	1	yes	characteristic
29	#389×C₈₉	C₂²	1	1	yes	characteristic
30	#389×C₈₉	C₂²	1	1	yes	characteristic
31	#388×C₈₉	—	2	1	no	—
32	#388×C₈₉	—	2	1	no	—
33	#382×C₈₉	—	2	1	no	—
34	#382×C₈₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
37	C₄³×C₈₉	C₂²	1	1	yes	characteristic
38	#340×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	2	yes	—
40	#336×C₈₉	C₂²	1	1	yes	characteristic
41	#336×C₈₉	C₂²	1	1	yes	characteristic
42	#336×C₈₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₈₉	—	2	1	no	—
44	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
45	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₈₉	—	2	1	no	—
47	C₂×SD₁₆×C₈₉	—	2	4	no	—
48	C₂×SD₁₆×C₈₉	—	2	4	no	—
49	C₂×SD₁₆×C₈₉	—	4	2	no	—
50	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₈₉	—	4	2	no	—
53	C₄⋊Q₈×C₈₉	—	4	2	no	—
54	C₄×D₄×C₈₉	—	2	2	no	—
55	C₄×D₄×C₈₉	—	2	2	no	—
56	#117×C₈₉	—	4	4	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄²×C₈₉	—	2	1	no	—
72	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	#106×C₈₉	—	4	2	no	—
80	#103×C₈₉	—	2	4	no	—
81	#103×C₈₉	—	2	4	no	—
82	#103×C₈₉	—	4	2	no	—
83	#102×C₈₉	—	4	2	no	—
84	C₄×C₈×C₈₉	—	2	4	no	—
85	#95×C₈₉	—	2	1	no	—
86	#95×C₈₉	—	2	1	no	—
87	#95×C₈₉	—	2	1	no	—
88	#95×C₈₉	—	2	2	no	—
89	#95×C₈₉	—	2	2	no	—
90	#95×C₈₉	—	2	2	no	—
91	#95×C₈₉	—	2	2	no	—
92	C₂⁴×C₈₉	—	2	1	no	—
93	C₂×Q₈×C₈₉	—	2	2	no	—
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	2	no	—
98	C₂×Q₈×C₈₉	—	2	2	no	—
99	C₂×Q₈×C₈₉	—	4	2	no	—
100	C₂×Q₈×C₈₉	—	4	2	no	—
101	C₂×Q₈×C₈₉	—	4	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	#41	1	2	yes	—
106	C₂²×C₄×C₈₉	—	2	4	no	—
107	C₂²×C₄×C₈₉	—	2	1	no	—
108	C₂²×C₄×C₈₉	—	2	2	no	—
109	C₂²×C₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	C₂²×C₄×C₈₉	—	2	1	no	—
112	C₂²×C₄×C₈₉	—	4	2	no	—
113	C₂²×C₄×C₈₉	—	4	2	no	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₈₉	—	4	8	no	—
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₂×C₈×C₈₉	—	2	2	no	—
125	C₂×C₈×C₈₉	—	2	2	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	#41	1	4	yes	—
128	C₄⋊C₄×C₈₉	—	2	1	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	2	2	no	—
132	C₄⋊C₄×C₈₉	—	2	2	no	—
133	C₄⋊C₄×C₈₉	—	4	2	no	—
134	C₄⋊C₄×C₈₉	—	4	2	no	—
135	C₄⋊C₄×C₈₉	—	4	2	no	—
136	C₄⋊C₄×C₈₉	—	4	2	no	—
137	C₄⋊C₄×C₈₉	—	4	2	no	—
138	C₄⋊C₄×C₈₉	#41	1	2	yes	—
139	C₂²⋊C₄×C₈₉	—	2	4	no	—
140	C₂²⋊C₄×C₈₉	—	4	2	no	—
141	C₂²⋊C₄×C₈₉	—	4	2	no	—
142	C₂²⋊C₄×C₈₉	—	4	2	no	—
143	C₂²⋊C₄×C₈₉	—	4	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	4	1	no	—
151	C₄²×C₈₉	—	4	2	no	—
152	C₄²×C₈₉	SD₁₆	1	4	yes	complemented
153	C₂³×C₈₉	—	2	2	no	—
154	C₂³×C₈₉	—	4	1	no	—
155	C₂³×C₈₉	—	4	1	no	—
156	C₂³×C₈₉	—	4	1	no	—
157	C₂³×C₈₉	—	4	1	no	—
158	C₂³×C₈₉	—	4	1	no	—
159	C₂³×C₈₉	—	4	1	no	—
160	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₈₉	—	4	2	no	—
162	Q₈×C₈₉	—	4	2	no	—
163	Q₈×C₈₉	—	4	2	no	—
164	Q₈×C₈₉	—	4	2	no	—
165	Q₈×C₈₉	—	8	4	no	—
166	D₄×C₈₉	—	2	4	no	—
167	D₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	4	8	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	4	1	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	1	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	—	4	2	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	4	2	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
198	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
199	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₈₉	#135	1	2	yes	—
201	C₂×C₄×C₈₉	#137	1	2	yes	—
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₈₉	—	2	4	no	—
207	C₈×C₈₉	—	4	2	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	—	8	1	no	—
212	C₂²×C₈₉	—	8	1	no	—
213	C₂²×C₈₉	—	8	1	no	—
214	C₂²×C₈₉	—	8	1	no	—
215	C₂²×C₈₉	#525	1	1	yes	characteristic
216	C₂²×C₈₉	#532	1	1	yes	characteristic
217	C₂²×C₈₉	#535	1	1	yes	characteristic
218	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
220	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
221	C₂²×C₈₉	#575	1	1	yes	characteristic
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	—	2	2	no	—
225	C₄×C₈₉	—	2	2	no	—
226	C₄×C₈₉	—	2	2	no	—
227	C₄×C₈₉	—	4	2	no	—
228	C₄×C₈₉	—	4	1	no	—
229	C₄×C₈₉	—	8	2	no	—
230	C₄×C₈₉	—	8	1	no	—
231	C₄×C₈₉	—	8	1	no	—
232	C₄×C₈₉	—	8	2	no	—
233	C₄×C₈₉	#551	1	2	yes	—
234	C₄×C₈₉	#555	1	2	yes	—
235	#29554	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂×C₈₉	—	8	2	no	—
237	C₂×C₈₉	#2610	1	1	yes	characteristic
238	C₂×C₈₉	#3101	1	1	yes	characteristic
239	C₂×C₈₉	#3107	1	1	yes	characteristic
240	C₂×C₈₉	#3167	1	1	yes	characteristic
241	C₂×C₈₉	#3181	1	1	yes	characteristic
242	C₂×C₈₉	#3206	1	1	yes	characteristic
243	C₂×C₈₉	#3211	1	1	yes	characteristic
244	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
245	#2293	C₂×C₈₉	1	1	yes	characteristic
246	#2058	C₂×C₈₉	1	1	yes	characteristic, complemented
247	#2043	C₂×C₈₉	1	1	yes	characteristic, complemented
248	#2023	C₂×C₈₉	1	1	yes	characteristic
249	#2013	C₂×C₈₉	1	1	yes	characteristic
250	#1968	C₂×C₈₉	1	2	yes	—
251	#1933	C₂×C₈₉	1	2	yes	complemented
252	#1927	C₂×C₈₉	1	2	yes	complemented
253	#1877	C₂×C₈₉	1	2	yes	—
254	#1744	C₂×C₈₉	1	1	yes	characteristic, complemented
255	C₈₉	#29554	1	1	yes	characteristic, direct product factor, Sylow
256	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
260	C₂×#117	—	2	1	no	—
261	C₂×#106	C₂²×C₈₉	1	2	yes	—
262	C₂×#103	C₂²×C₈₉	1	2	yes	—
263	C₂×#103	C₂²×C₈₉	1	2	yes	—
264	C₂×#103	C₂²×C₈₉	1	2	yes	—
265	C₂×#102	C₂²×C₈₉	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
267	#391	—	2	1	no	—
268	#391	—	2	1	no	—
269	#391	C₂²×C₈₉	1	2	yes	—
270	#391	C₂²×C₈₉	1	2	yes	—
271	#390	C₂²×C₈₉	1	1	yes	characteristic
272	#390	C₂²×C₈₉	1	1	yes	characteristic
273	#389	C₂²×C₈₉	1	1	yes	characteristic
274	#389	C₂²×C₈₉	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#388	—	2	1	no	—
277	#382	—	2	1	no	—
278	#382	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	C₄³	C₂²×C₈₉	1	1	yes	characteristic
282	#340	C₂²×C₈₉	1	2	yes	—
283	#340	C₂²×C₈₉	1	2	yes	—
284	#336	C₂²×C₈₉	1	1	yes	characteristic
285	#336	C₂²×C₈₉	1	2	yes	—
286	#336	C₂²×C₈₉	1	1	yes	characteristic
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
289	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	4	no	—
292	C₂×SD₁₆	—	2	4	no	—
293	C₂×SD₁₆	—	4	2	no	—
294	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
295	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
296	C₄⋊Q₈	—	4	2	no	—
297	C₄⋊Q₈	—	4	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	#117	—	4	4	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
323	#106	—	4	2	no	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#103	—	4	2	no	—
327	#102	—	4	2	no	—
328	C₄×C₈	—	2	4	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	#41×C₈₉	1	2	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
365	SD₁₆	—	4	8	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	#41×C₈₉	1	4	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	#41×C₈₉	1	2	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	2	no	—
396	C₄²	SD₁₆×C₈₉	1	4	yes	complemented
397	C₂³	—	2	2	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	8	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
442	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
443	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
444	C₂×C₄	#135×C₈₉	1	2	yes	—
445	C₂×C₄	#137×C₈₉	1	2	yes	—
446	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
448	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
449	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
450	C₈	—	2	4	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	#525×C₈₉	1	1	yes	characteristic
460	C₂²	#532×C₈₉	1	1	yes	characteristic
461	C₂²	#535×C₈₉	1	1	yes	characteristic
462	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
463	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
464	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
465	C₂²	#575×C₈₉	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	2	no	—
477	C₄	#551×C₈₉	1	2	yes	—
478	C₄	#555×C₈₉	1	2	yes	—
479	C₂	—	8	2	no	—
480	C₂	C₈₉×#2610	1	1	yes	characteristic
481	C₂	C₈₉×#3101	1	1	yes	characteristic
482	C₂	C₈₉×#3107	1	1	yes	characteristic
483	C₂	C₈₉×#3167	1	1	yes	characteristic
484	C₂	C₈₉×#3181	1	1	yes	characteristic
485	C₂	C₈₉×#3206	1	1	yes	characteristic
486	C₂	C₈₉×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2862	C₂	semidirect
3. C₈₉×#2058	C₂	semidirect
4. C₈₉×#2043	C₂	semidirect
8. C₈₉×#1933	C₂	semidirect
9. C₈₉×#1927	C₂	semidirect
11. C₈₉×#1744	C₂	semidirect
152. C₄²×C₈₉	SD₁₆	semidirect
235. #29554	C₈₉	direct (N × H)
244. #2862	C₂×C₈₉	semidirect
246. #2058	C₂×C₈₉	semidirect
247. #2043	C₂×C₈₉	semidirect
251. #1933	C₂×C₈₉	semidirect
252. #1927	C₂×C₈₉	semidirect
254. #1744	C₂×C₈₉	semidirect
255. C₈₉	#29554	direct (N × H)
396. C₄²	SD₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2862	2
C₈₉×#2293	2
C₈₉×#2058	2
C₈₉×#2043	2
C₈₉×#2023	2
C₈₉×#2013	2
C₈₉×#1968	2
C₈₉×#1933	2
C₈₉×#1927	2
C₈₉×#1877	2
C₈₉×#1744	2
#29554	89

Subgroups — C89×#29554 #36407402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29554 #36407402