Subgroups — C₈₉×#29555 #36407403

Order 22784.

856 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2041	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2014	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1968	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1934	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1926	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1880	C₂	1	2	yes	maximal, complemented
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×#127×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#124×C₈₉	—	2	1	no	—
16	C₂×#124×C₈₉	—	2	1	no	—
17	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#106×C₈₉	C₂²	1	2	yes	—
19	C₂×#103×C₈₉	C₂²	1	2	yes	—
20	C₂×#102×C₈₉	C₂²	1	2	yes	—
21	C₂×#102×C₈₉	C₂²	1	2	yes	—
22	C₂×#102×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
24	#391×C₈₉	C₂²	1	1	yes	characteristic
25	#391×C₈₉	C₂²	1	1	yes	characteristic
26	#390×C₈₉	—	2	1	no	—
27	#390×C₈₉	—	2	1	no	—
28	#390×C₈₉	C₂²	1	2	yes	—
29	#390×C₈₉	C₂²	1	2	yes	—
30	#389×C₈₉	C₂²	1	1	yes	characteristic
31	#389×C₈₉	C₂²	1	1	yes	characteristic
32	#387×C₈₉	—	2	1	no	—
33	#387×C₈₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	#376×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	1	yes	characteristic
45	C₂²×D₄×C₈₉	—	2	1	no	—
46	C₂²×D₄×C₈₉	—	2	1	no	—
47	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₈₉	—	2	4	no	—
49	C₂×SD₁₆×C₈₉	—	2	4	no	—
50	C₂×SD₁₆×C₈₉	—	4	2	no	—
51	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₈₉	—	4	2	no	—
54	#127×C₈₉	—	4	2	no	—
55	#124×C₈₉	—	4	4	no	—
56	#124×C₈₉	—	4	4	no	—
57	C₄×Q₈×C₈₉	—	2	2	no	—
58	C₄×Q₈×C₈₉	—	2	2	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	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₄²×C₈₉	—	2	1	no	—
72	C₂×C₄²×C₈₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	#106×C₈₉	—	4	2	no	—
81	#103×C₈₉	—	4	2	no	—
82	#102×C₈₉	—	2	4	no	—
83	#102×C₈₉	—	2	4	no	—
84	#102×C₈₉	—	4	2	no	—
85	C₄×C₈×C₈₉	—	2	4	no	—
86	#95×C₈₉	—	2	1	no	—
87	#95×C₈₉	—	2	1	no	—
88	#95×C₈₉	—	2	1	no	—
89	#95×C₈₉	—	2	1	no	—
90	#95×C₈₉	—	2	1	no	—
91	#95×C₈₉	—	2	1	no	—
92	#95×C₈₉	—	2	1	no	—
93	C₂⁴×C₈₉	—	2	2	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	4	2	no	—
98	C₂×Q₈×C₈₉	—	4	2	no	—
99	C₂×Q₈×C₈₉	—	4	2	no	—
100	C₂×Q₈×C₈₉	#41	1	2	yes	—
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	2	2	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	2	no	—
107	C₂×D₄×C₈₉	—	4	2	no	—
108	C₂×D₄×C₈₉	—	4	2	no	—
109	C₂×D₄×C₈₉	—	4	2	no	—
110	C₂×D₄×C₈₉	—	4	2	no	—
111	C₂×D₄×C₈₉	—	4	2	no	—
112	C₂×D₄×C₈₉	—	4	2	no	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
125	SD₁₆×C₈₉	—	4	8	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	#41	1	4	yes	—
132	C₄⋊C₄×C₈₉	—	2	4	no	—
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	4	2	no	—
139	C₄⋊C₄×C₈₉	—	4	2	no	—
140	C₄⋊C₄×C₈₉	—	4	2	no	—
141	C₄⋊C₄×C₈₉	#41	1	2	yes	—
142	C₂²⋊C₄×C₈₉	—	4	4	no	—
143	C₂²⋊C₄×C₈₉	—	4	4	no	—
144	C₂²⋊C₄×C₈₉	—	4	4	no	—
145	C₂²⋊C₄×C₈₉	—	4	4	no	—
146	C₄²×C₈₉	—	2	4	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	—	4	1	no	—
154	C₄²×C₈₉	—	4	2	no	—
155	C₄²×C₈₉	SD₁₆	1	4	yes	complemented
156	C₂³×C₈₉	—	4	2	no	—
157	C₂³×C₈₉	—	4	2	no	—
158	C₂³×C₈₉	—	4	2	no	—
159	C₂³×C₈₉	—	4	2	no	—
160	C₂³×C₈₉	—	4	2	no	—
161	C₂³×C₈₉	—	4	2	no	—
162	C₂³×C₈₉	—	4	2	no	—
163	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	4	no	—
165	Q₈×C₈₉	—	4	2	no	—
166	Q₈×C₈₉	—	8	4	no	—
167	D₄×C₈₉	—	4	2	no	—
168	D₄×C₈₉	—	4	2	no	—
169	D₄×C₈₉	—	4	2	no	—
170	D₄×C₈₉	—	4	2	no	—
171	D₄×C₈₉	—	8	4	no	—
172	D₄×C₈₉	—	8	4	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	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	2	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	1	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
204	C₂×C₄×C₈₉	#135	1	2	yes	—
205	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
208	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
210	C₈×C₈₉	—	2	4	no	—
211	C₈×C₈₉	—	4	2	no	—
212	C₂²×C₈₉	—	8	2	no	—
213	C₂²×C₈₉	—	8	2	no	—
214	C₂²×C₈₉	—	8	2	no	—
215	C₂²×C₈₉	—	8	2	no	—
216	C₂²×C₈₉	—	8	2	no	—
217	C₂²×C₈₉	—	8	2	no	—
218	C₂²×C₈₉	—	8	2	no	—
219	C₂²×C₈₉	#525	1	1	yes	characteristic
220	C₂²×C₈₉	#532	1	1	yes	characteristic
221	C₂²×C₈₉	#535	1	1	yes	characteristic
222	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
223	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
224	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₂²×C₈₉	#575	1	1	yes	characteristic
226	C₄×C₈₉	—	2	2	no	—
227	C₄×C₈₉	—	2	2	no	—
228	C₄×C₈₉	—	2	2	no	—
229	C₄×C₈₉	—	2	2	no	—
230	C₄×C₈₉	—	2	2	no	—
231	C₄×C₈₉	—	4	1	no	—
232	C₄×C₈₉	—	4	2	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	—	8	2	no	—
236	C₄×C₈₉	—	8	1	no	—
237	C₄×C₈₉	#551	1	2	yes	—
238	C₄×C₈₉	#555	1	2	yes	—
239	#29555	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₈₉	—	16	2	no	—
241	C₂×C₈₉	#2610	1	1	yes	characteristic
242	C₂×C₈₉	#3103	1	1	yes	characteristic
243	C₂×C₈₉	#3106	1	1	yes	characteristic
244	C₂×C₈₉	#3167	1	1	yes	characteristic
245	C₂×C₈₉	#3180	1	1	yes	characteristic
246	C₂×C₈₉	#3208	1	1	yes	characteristic
247	C₂×C₈₉	#3211	1	1	yes	characteristic
248	#2858	C₂×C₈₉	1	1	yes	characteristic
249	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#2058	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#2041	C₂×C₈₉	1	1	yes	characteristic
252	#2024	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#2014	C₂×C₈₉	1	1	yes	characteristic
254	#1968	C₂×C₈₉	1	2	yes	complemented
255	#1934	C₂×C₈₉	1	2	yes	complemented
256	#1926	C₂×C₈₉	1	2	yes	complemented
257	#1880	C₂×C₈₉	1	2	yes	complemented
258	#1744	C₂×C₈₉	1	1	yes	characteristic, complemented
259	C₈₉	#29555	1	1	yes	characteristic, direct product factor, Sylow
260	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
262	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
263	C₂×#124	—	2	1	no	—
264	C₂×#124	—	2	1	no	—
265	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#106	C₂²×C₈₉	1	2	yes	—
267	C₂×#103	C₂²×C₈₉	1	2	yes	—
268	C₂×#102	C₂²×C₈₉	1	2	yes	—
269	C₂×#102	C₂²×C₈₉	1	2	yes	—
270	C₂×#102	C₂²×C₈₉	1	2	yes	—
271	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
272	#391	C₂²×C₈₉	1	1	yes	characteristic
273	#391	C₂²×C₈₉	1	1	yes	characteristic
274	#390	—	2	1	no	—
275	#390	—	2	1	no	—
276	#390	C₂²×C₈₉	1	2	yes	—
277	#390	C₂²×C₈₉	1	2	yes	—
278	#389	C₂²×C₈₉	1	1	yes	characteristic
279	#389	C₂²×C₈₉	1	1	yes	characteristic
280	#387	—	2	1	no	—
281	#387	—	2	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
284	#376	—	2	1	no	—
285	C₄³	C₂²×C₈₉	1	1	yes	characteristic
286	#340	C₂²×C₈₉	1	2	yes	—
287	#340	C₂²×C₈₉	1	2	yes	—
288	#336	C₂²×C₈₉	1	1	yes	characteristic
289	#336	C₂²×C₈₉	1	2	yes	—
290	#336	C₂²×C₈₉	1	1	yes	characteristic
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
300	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
301	C₄⋊Q₈	—	4	2	no	—
302	#127	—	4	2	no	—
303	#124	—	4	4	no	—
304	#124	—	4	4	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
322	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
328	#106	—	4	2	no	—
329	#103	—	4	2	no	—
330	#102	—	2	4	no	—
331	#102	—	2	4	no	—
332	#102	—	4	2	no	—
333	C₄×C₈	—	2	4	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	C₂⁴	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	#41×C₈₉	1	2	yes	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
373	SD₁₆	—	4	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	#41×C₈₉	1	4	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	#41×C₈₉	1	2	yes	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	2	no	—
403	C₄²	SD₁₆×C₈₉	1	4	yes	complemented
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
450	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
451	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
452	C₂×C₄	#135×C₈₉	1	2	yes	—
453	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
454	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
456	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
457	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	#525×C₈₉	1	1	yes	characteristic
468	C₂²	#532×C₈₉	1	1	yes	characteristic
469	C₂²	#535×C₈₉	1	1	yes	characteristic
470	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
471	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
472	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
473	C₂²	#575×C₈₉	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	1	no	—
485	C₄	#551×C₈₉	1	2	yes	—
486	C₄	#555×C₈₉	1	2	yes	—
487	C₂	—	16	2	no	—
488	C₂	C₈₉×#2610	1	1	yes	characteristic
489	C₂	C₈₉×#3103	1	1	yes	characteristic
490	C₂	C₈₉×#3106	1	1	yes	characteristic
491	C₂	C₈₉×#3167	1	1	yes	characteristic
492	C₂	C₈₉×#3180	1	1	yes	characteristic
493	C₂	C₈₉×#3208	1	1	yes	characteristic
494	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	C₂×#127×C₈₉	C₂²
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
2. C₈₉×#2295	C₂	semidirect
3. C₈₉×#2058	C₂	semidirect
5. C₈₉×#2024	C₂	semidirect
7. C₈₉×#1968	C₂	semidirect
8. C₈₉×#1934	C₂	semidirect
9. C₈₉×#1926	C₂	semidirect
10. C₈₉×#1880	C₂	semidirect
11. C₈₉×#1744	C₂	semidirect
155. C₄²×C₈₉	SD₁₆	semidirect
239. #29555	C₈₉	direct (N × H)
249. #2295	C₂×C₈₉	semidirect
250. #2058	C₂×C₈₉	semidirect
252. #2024	C₂×C₈₉	semidirect
254. #1968	C₂×C₈₉	semidirect
255. #1934	C₂×C₈₉	semidirect
256. #1926	C₂×C₈₉	semidirect
257. #1880	C₂×C₈₉	semidirect
258. #1744	C₂×C₈₉	semidirect
259. C₈₉	#29555	direct (N × H)
403. 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×#2858	2
C₈₉×#2295	2
C₈₉×#2058	2
C₈₉×#2041	2
C₈₉×#2024	2
C₈₉×#2014	2
C₈₉×#1968	2
C₈₉×#1934	2
C₈₉×#1926	2
C₈₉×#1880	2
C₈₉×#1744	2
#29555	89

Subgroups — C89×#29555 #36407403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29555 #36407403