Subgroups — C₈₉×#26264 #36404112

Order 22784.

1038 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2445	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2054	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2041	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1879	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₈₉	C₂²	1	2	yes	—
16	C₂×#123×C₈₉	—	2	2	no	—
17	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
18	#493×C₈₉	—	2	4	no	—
19	#442×C₈₉	—	2	4	no	—
20	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₈₉	C₂²	1	2	yes	—
24	C₂×#102×C₈₉	C₂²	1	2	yes	—
25	C₂×#102×C₈₉	C₂²	1	2	yes	—
26	C₂×#102×C₈₉	C₂²	1	2	yes	—
27	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
30	#394×C₈₉	—	2	2	no	—
31	#394×C₈₉	—	2	2	no	—
32	#390×C₈₉	C₂²	1	2	yes	—
33	#390×C₈₉	C₂²	1	2	yes	—
34	#390×C₈₉	C₂²	1	2	yes	—
35	#389×C₈₉	C₂²	1	2	yes	—
36	#386×C₈₉	—	2	2	no	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	#340×C₈₉	C₂²	1	2	yes	—
39	#336×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₈₉	—	2	2	no	—
42	C₂²×D₄×C₈₉	—	2	2	no	—
43	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₈₉	—	2	2	no	—
46	C₂×D₈×C₈₉	—	2	4	no	—
47	C₂×D₈×C₈₉	—	2	2	no	—
48	C₂×D₈×C₈₉	—	2	2	no	—
49	C₂×D₈×C₈₉	—	2	2	no	—
50	C₂×D₈×C₈₉	—	2	4	no	—
51	C₂×D₈×C₈₉	—	2	2	no	—
52	C₂×D₈×C₈₉	—	2	2	no	—
53	C₂×D₈×C₈₉	—	4	2	no	—
54	C₂×D₈×C₈₉	D₄	1	4	yes	—
55	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
59	#127×C₈₉	—	2	4	no	—
60	#127×C₈₉	—	4	2	no	—
61	#123×C₈₉	—	4	8	no	—
62	C₄×D₄×C₈₉	—	2	4	no	—
63	C₄×D₄×C₈₉	—	4	2	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₈₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
75	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#106×C₈₉	—	2	2	no	—
79	#106×C₈₉	—	2	2	no	—
80	C₄⋊C₈×C₈₉	—	2	2	no	—
81	#102×C₈₉	—	2	4	no	—
82	#102×C₈₉	—	4	2	no	—
83	#102×C₈₉	—	4	2	no	—
84	#102×C₈₉	—	4	2	no	—
85	#97×C₈₉	—	2	2	no	—
86	#97×C₈₉	—	2	2	no	—
87	C₄×C₈×C₈₉	—	2	2	no	—
88	#95×C₈₉	—	2	2	no	—
89	#95×C₈₉	D₄	1	2	yes	—
90	C₂⁴×C₈₉	—	2	2	no	—
91	C₂⁴×C₈₉	—	2	2	no	—
92	C₂×D₄×C₈₉	—	2	2	no	—
93	C₂×D₄×C₈₉	—	2	2	no	—
94	C₂×D₄×C₈₉	—	2	2	no	—
95	C₂×D₄×C₈₉	—	2	2	no	—
96	C₂×D₄×C₈₉	—	2	2	no	—
97	C₂×D₄×C₈₉	—	2	2	no	—
98	C₂×D₄×C₈₉	—	2	2	no	—
99	C₂×D₄×C₈₉	—	2	2	no	—
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	4	4	no	—
104	C₂×D₄×C₈₉	—	4	4	no	—
105	C₂×D₄×C₈₉	—	4	4	no	—
106	C₂×D₄×C₈₉	—	4	4	no	—
107	C₂×D₄×C₈₉	—	8	2	no	—
108	C₂×D₄×C₈₉	—	8	2	no	—
109	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	4	4	no	—
113	C₂²×C₄×C₈₉	—	4	4	no	—
114	C₂²×C₄×C₈₉	—	8	2	no	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	D₈×C₈₉	—	2	8	no	—
121	D₈×C₈₉	—	4	8	no	—
122	D₈×C₈₉	—	4	4	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₈₉	#41	1	2	yes	—
133	C₂×C₈×C₈₉	#41	1	2	yes	—
134	C₂×C₈×C₈₉	#41	1	2	yes	—
135	C₄⋊C₄×C₈₉	—	2	4	no	—
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	2	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	4	4	no	—
141	C₂²⋊C₄×C₈₉	—	4	4	no	—
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	—	8	2	no	—
146	C₂²⋊C₄×C₈₉	—	8	2	no	—
147	C₂²⋊C₄×C₈₉	—	8	2	no	—
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₂³×C₈₉	—	2	4	no	—
155	C₂³×C₈₉	—	4	2	no	—
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	—	4	2	no	—
164	C₂³×C₈₉	—	4	2	no	—
165	C₂³×C₈₉	—	4	2	no	—
166	C₂³×C₈₉	—	4	2	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₈₉	—	2	4	no	—
170	D₄×C₈₉	—	2	4	no	—
171	D₄×C₈₉	—	4	2	no	—
172	D₄×C₈₉	—	4	2	no	—
173	D₄×C₈₉	—	4	2	no	—
174	D₄×C₈₉	—	4	2	no	—
175	D₄×C₈₉	—	4	2	no	—
176	D₄×C₈₉	—	4	2	no	—
177	D₄×C₈₉	—	8	8	no	—
178	D₄×C₈₉	—	8	8	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	4	2	no	—
189	C₂×C₄×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	—	4	2	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	8	8	no	—
195	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
202	C₈×C₈₉	—	2	2	no	—
203	C₈×C₈₉	—	4	1	no	—
204	C₈×C₈₉	—	4	1	no	—
205	C₈×C₈₉	#123	1	4	yes	complemented
206	C₂²×C₈₉	—	4	4	no	—
207	C₂²×C₈₉	—	4	4	no	—
208	C₂²×C₈₉	—	4	4	no	—
209	C₂²×C₈₉	—	8	2	no	—
210	C₂²×C₈₉	—	8	2	no	—
211	C₂²×C₈₉	—	8	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	—	8	2	no	—
220	C₂²×C₈₉	#532	1	1	yes	characteristic
221	C₂²×C₈₉	D₄²	1	1	yes	characteristic
222	C₂²×C₈₉	#550	1	1	yes	characteristic
223	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
224	C₂²×C₈₉	#576	1	2	yes	—
225	C₄×C₈₉	—	2	4	no	—
226	C₄×C₈₉	—	4	1	no	—
227	C₄×C₈₉	—	4	1	no	—
228	C₄×C₈₉	—	4	2	no	—
229	C₄×C₈₉	—	8	2	no	—
230	C₄×C₈₉	—	8	2	no	—
231	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
232	C₄×C₈₉	#540	1	1	yes	characteristic
233	C₄×C₈₉	#546	1	1	yes	characteristic
234	C₄×C₈₉	#559	1	1	yes	characteristic
235	#26264	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂×C₈₉	—	8	4	no	—
237	C₂×C₈₉	—	16	2	no	—
238	C₂×C₈₉	#2445	1	1	yes	characteristic
239	C₂×C₈₉	#3176	1	1	yes	characteristic
240	C₂×C₈₉	#3184	1	1	yes	characteristic
241	C₂×C₈₉	#3264	1	2	yes	—
242	C₂×C₈₉	#3399	1	2	yes	—
243	C₂×#493	C₂×C₈₉	1	1	yes	characteristic
244	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
245	#2445	C₂×C₈₉	1	2	yes	complemented
246	#2054	C₂×C₈₉	1	2	yes	complemented
247	#2041	C₂×C₈₉	1	2	yes	complemented
248	#1972	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#1972	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#1972	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#1941	C₂×C₈₉	1	1	yes	characteristic, complemented
252	#1879	C₂×C₈₉	1	2	yes	complemented
253	#1771	C₂×C₈₉	1	1	yes	characteristic, complemented
254	C₈₉	#26264	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
256	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
257	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×#127	C₂²×C₈₉	1	2	yes	—
259	C₂×#123	—	2	2	no	—
260	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
261	#493	—	2	4	no	—
262	#442	—	2	4	no	—
263	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
264	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#102	C₂²×C₈₉	1	2	yes	—
267	C₂×#102	C₂²×C₈₉	1	2	yes	—
268	C₂×#102	C₂²×C₈₉	1	2	yes	—
269	C₂×#102	C₂²×C₈₉	1	2	yes	—
270	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
271	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
273	#394	—	2	2	no	—
274	#394	—	2	2	no	—
275	#390	C₂²×C₈₉	1	2	yes	—
276	#390	C₂²×C₈₉	1	2	yes	—
277	#390	C₂²×C₈₉	1	2	yes	—
278	#389	C₂²×C₈₉	1	2	yes	—
279	#386	—	2	2	no	—
280	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
281	#340	C₂²×C₈₉	1	2	yes	—
282	#336	C₂²×C₈₉	1	1	yes	characteristic
283	#336	C₂²×C₈₉	1	1	yes	characteristic
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
287	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
288	C₂³×C₄	—	2	2	no	—
289	C₂×D₈	—	2	4	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×D₈	—	2	4	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	4	2	no	—
297	C₂×D₈	D₄×C₈₉	1	4	yes	—
298	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
302	#127	—	2	4	no	—
303	#127	—	4	2	no	—
304	#123	—	4	8	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	4	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
321	#106	—	2	2	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	#102	—	2	4	no	—
325	#102	—	4	2	no	—
326	#102	—	4	2	no	—
327	#102	—	4	2	no	—
328	#97	—	2	2	no	—
329	#97	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	D₄×C₈₉	1	2	yes	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	—	8	2	no	—
352	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
363	D₈	—	2	8	no	—
364	D₈	—	4	8	no	—
365	D₈	—	4	4	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
375	C₂×C₈	#41×C₈₉	1	2	yes	—
376	C₂×C₈	#41×C₈₉	1	2	yes	—
377	C₂×C₈	#41×C₈₉	1	2	yes	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
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	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	8	no	—
421	D₄	—	8	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	8	no	—
438	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
443	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
444	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	#123×C₈₉	1	4	yes	complemented
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	#532×C₈₉	1	1	yes	characteristic
464	C₂²	D₄²×C₈₉	1	1	yes	characteristic
465	C₂²	#550×C₈₉	1	1	yes	characteristic
466	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
467	C₂²	#576×C₈₉	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
475	C₄	#540×C₈₉	1	1	yes	characteristic
476	C₄	#546×C₈₉	1	1	yes	characteristic
477	C₄	#559×C₈₉	1	1	yes	characteristic
478	C₂	—	8	4	no	—
479	C₂	—	16	2	no	—
480	C₂	C₈₉×#2445	1	1	yes	characteristic
481	C₂	C₈₉×#3176	1	1	yes	characteristic
482	C₂	C₈₉×#3184	1	1	yes	characteristic
483	C₂	C₈₉×#3264	1	2	yes	—
484	C₂	C₈₉×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#493×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₄⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#442×C₈₉	C₂	semidirect
3. C₈₉×#2445	C₂	semidirect
4. C₈₉×#2054	C₂	semidirect
5. C₈₉×#2041	C₂	semidirect
6. C₈₉×#1972	C₂	semidirect
7. C₈₉×#1972	C₂	semidirect
8. C₈₉×#1972	C₂	semidirect
9. C₈₉×#1941	C₂	semidirect
10. C₈₉×#1879	C₂	semidirect
11. C₈₉×#1771	C₂	semidirect
205. C₈×C₈₉	#123	semidirect
235. #26264	C₈₉	direct (N × H)
244. C₂×#442	C₂×C₈₉	semidirect
245. #2445	C₂×C₈₉	semidirect
246. #2054	C₂×C₈₉	semidirect
247. #2041	C₂×C₈₉	semidirect
248. #1972	C₂×C₈₉	semidirect
249. #1972	C₂×C₈₉	semidirect
250. #1972	C₂×C₈₉	semidirect
251. #1941	C₂×C₈₉	semidirect
252. #1879	C₂×C₈₉	semidirect
253. #1771	C₂×C₈₉	semidirect
254. C₈₉	#26264	direct (N × H)
448. C₈	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×#2445	2
C₈₉×#2054	2
C₈₉×#2041	2
C₈₉×#1972	2
C₈₉×#1941	2
C₈₉×#1879	2
C₈₉×#1771	2
#26264	89

Subgroups — C89×#26264 #36404112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26264 #36404112