Subgroups — C₈₉×#22626 #36400474

Order 22784.

744 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1917	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1916	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1798	C₂	1	2	yes	maximal
7	C₈₉×#1797	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1750	C₂	1	2	yes	maximal
11	C₄×C₂²⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#117×C₈₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#97×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
25	#384×C₈₉	C₄	1	1	yes	characteristic
26	#384×C₈₉	C₄	1	1	yes	characteristic
27	#382×C₈₉	C₄	1	2	yes	—
28	#380×C₈₉	C₄	1	1	yes	characteristic
29	#380×C₈₉	C₄	1	1	yes	characteristic
30	#380×C₈₉	C₄	1	2	yes	—
31	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#336×C₈₉	C₂²	1	2	yes	—
35	#336×C₈₉	C₂²	1	2	yes	—
36	#336×C₈₉	C₂²	1	2	yes	—
37	#336×C₈₉	C₂²	1	1	yes	characteristic
38	#336×C₈₉	C₂²	1	2	yes	—
39	#336×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	2	yes	—
41	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	#117×C₈₉	—	4	2	no	—
51	#117×C₈₉	—	4	2	no	—
52	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₈₉	—	2	2	no	—
63	C₂×C₄²×C₈₉	—	2	2	no	—
64	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₈₉	—	2	2	no	—
71	C₄⋊C₈×C₈₉	—	2	2	no	—
72	C₄⋊C₈×C₈₉	—	4	2	no	—
73	C₄⋊C₈×C₈₉	—	4	2	no	—
74	C₂²⋊C₈×C₈₉	—	2	4	no	—
75	C₂²⋊C₈×C₈₉	—	2	2	no	—
76	C₂²⋊C₈×C₈₉	Q₈	1	4	yes	—
77	#97×C₈₉	—	4	2	no	—
78	C₄×C₈×C₈₉	—	2	2	no	—
79	C₄×C₈×C₈₉	—	2	2	no	—
80	C₄×C₈×C₈₉	—	4	2	no	—
81	#95×C₈₉	C₂×C₄	1	2	yes	—
82	#95×C₈₉	C₂×C₄	1	2	yes	—
83	#95×C₈₉	C₂×C₄	1	2	yes	—
84	#95×C₈₉	C₂×C₄	1	2	yes	—
85	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	—	2	1	no	—
87	C₂²×C₄×C₈₉	—	2	1	no	—
88	C₂²×C₄×C₈₉	—	2	1	no	—
89	C₂²×C₄×C₈₉	—	2	1	no	—
90	C₂²×C₄×C₈₉	—	2	2	no	—
91	C₂²×C₄×C₈₉	—	2	2	no	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
93	C₂²×C₄×C₈₉	—	2	2	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	4	1	no	—
96	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₈₉	#41	1	2	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₈₉	—	2	1	no	—
109	C₂×C₈×C₈₉	—	2	1	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	—	2	1	no	—
115	C₂×C₈×C₈₉	—	2	1	no	—
116	C₂×C₈×C₈₉	—	2	2	no	—
117	C₂×C₈×C₈₉	—	2	2	no	—
118	C₂×C₈×C₈₉	—	2	2	no	—
119	C₂×C₈×C₈₉	—	2	2	no	—
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
125	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	4	2	no	—
132	C₄⋊C₄×C₈₉	—	4	2	no	—
133	C₄⋊C₄×C₈₉	—	4	2	no	—
134	C₂²⋊C₄×C₈₉	—	4	2	no	—
135	C₂²⋊C₄×C₈₉	—	4	2	no	—
136	C₄²×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	—	2	1	no	—
139	C₄²×C₈₉	—	2	1	no	—
140	C₄²×C₈₉	—	2	2	no	—
141	C₄²×C₈₉	—	2	2	no	—
142	C₄²×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	#41	1	2	yes	—
145	C₄²×C₈₉	#41	1	2	yes	—
146	C₂³×C₈₉	—	2	1	no	—
147	C₂³×C₈₉	—	2	1	no	—
148	C₂³×C₈₉	—	2	1	no	—
149	C₂³×C₈₉	—	2	1	no	—
150	C₂³×C₈₉	—	2	1	no	—
151	C₂³×C₈₉	—	2	1	no	—
152	C₂³×C₈₉	C₄×Q₈	1	2	yes	—
153	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	4	4	no	—
180	C₂×C₄×C₈₉	—	4	4	no	—
181	C₂×C₄×C₈₉	#117	1	2	yes	—
182	C₂×C₄×C₈₉	#117	1	2	yes	—
183	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
184	C₂×C₄×C₈₉	#131	1	2	yes	—
185	C₂×C₄×C₈₉	#131	1	2	yes	—
186	C₂×C₄×C₈₉	#131	1	2	yes	—
187	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	2	2	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	—	4	1	no	—
197	C₈×C₈₉	—	4	2	no	—
198	C₈×C₈₉	—	4	2	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	2	2	no	—
201	C₂²×C₈₉	—	2	2	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	—	4	1	no	—
204	C₂²×C₈₉	—	4	1	no	—
205	C₂²×C₈₉	—	4	1	no	—
206	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
207	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₂²×C₈₉	#518	1	1	yes	characteristic
209	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
210	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
211	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
212	C₂²×C₈₉	#568	1	1	yes	characteristic
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	2	2	no	—
216	C₄×C₈₉	—	4	1	no	—
217	C₄×C₈₉	—	4	2	no	—
218	C₄×C₈₉	—	4	2	no	—
219	C₄×C₈₉	—	4	2	no	—
220	C₄×C₈₉	—	4	2	no	—
221	C₄×C₈₉	#433	1	4	yes	—
222	C₄×C₈₉	#553	1	1	yes	characteristic
223	C₄×C₈₉	#553	1	1	yes	characteristic
224	C₄×C₈₉	#554	1	1	yes	characteristic
225	C₄×C₈₉	#554	1	1	yes	characteristic
226	#22626	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₈₉	—	4	2	no	—
228	C₂×C₈₉	#2345	1	1	yes	characteristic
229	C₂×C₈₉	C₂×#433	1	1	yes	characteristic
230	C₂×C₈₉	#2924	1	1	yes	characteristic
231	C₂×C₈₉	#2960	1	1	yes	characteristic
232	C₂×C₈₉	#2962	1	1	yes	characteristic
233	C₂×C₈₉	#2979	1	1	yes	characteristic
234	C₂×C₈₉	#2981	1	1	yes	characteristic
235	#2285	C₂×C₈₉	1	1	yes	characteristic
236	#1939	C₂×C₈₉	1	1	yes	characteristic, complemented
237	#1939	C₂×C₈₉	1	1	yes	characteristic, complemented
238	#1917	C₂×C₈₉	1	2	yes	complemented
239	#1916	C₂×C₈₉	1	2	yes	complemented
240	#1798	C₂×C₈₉	1	2	yes	—
241	#1797	C₂×C₈₉	1	1	yes	characteristic
242	#1770	C₂×C₈₉	1	1	yes	characteristic, complemented
243	C₈×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
244	#1750	C₂×C₈₉	1	2	yes	—
245	C₄×C₂²⋊C₈	C₂×C₈₉	1	1	yes	characteristic
246	C₈₉	#22626	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×#117	C₂²×C₈₉	1	2	yes	—
248	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
253	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
256	C₂×#97	C₂²×C₈₉	1	2	yes	—
257	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
260	#384	C₄×C₈₉	1	1	yes	characteristic
261	#384	C₄×C₈₉	1	1	yes	characteristic
262	#382	C₄×C₈₉	1	2	yes	—
263	#380	C₄×C₈₉	1	1	yes	characteristic
264	#380	C₄×C₈₉	1	1	yes	characteristic
265	#380	C₄×C₈₉	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
267	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
269	#336	C₂²×C₈₉	1	2	yes	—
270	#336	C₂²×C₈₉	1	2	yes	—
271	#336	C₂²×C₈₉	1	2	yes	—
272	#336	C₂²×C₈₉	1	1	yes	characteristic
273	#336	C₂²×C₈₉	1	2	yes	—
274	#336	C₂²×C₈₉	1	1	yes	characteristic
275	#336	C₂²×C₈₉	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
282	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
283	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
285	#117	—	4	2	no	—
286	#117	—	4	2	no	—
287	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
302	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
303	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	4	2	no	—
308	C₄⋊C₈	—	4	2	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	Q₈×C₈₉	1	4	yes	—
312	#97	—	4	2	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	4	2	no	—
316	#95	C₂×C₄×C₈₉	1	2	yes	—
317	#95	C₂×C₄×C₈₉	1	2	yes	—
318	#95	C₂×C₄×C₈₉	1	2	yes	—
319	#95	C₂×C₄×C₈₉	1	2	yes	—
320	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
341	C₂²×C₄	#41×C₈₉	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	C₂×Q₈×C₈₉	1	2	yes	—
360	C₂×C₈	C₂×Q₈×C₈₉	1	2	yes	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	#41×C₈₉	1	2	yes	—
380	C₄²	#41×C₈₉	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	C₄×Q₈×C₈₉	1	2	yes	—
388	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	#117×C₈₉	1	2	yes	—
417	C₂×C₄	#117×C₈₉	1	2	yes	—
418	C₂×C₄	C₄×Q₈×C₈₉	1	2	yes	—
419	C₂×C₄	#131×C₈₉	1	2	yes	—
420	C₂×C₄	#131×C₈₉	1	2	yes	—
421	C₂×C₄	#131×C₈₉	1	2	yes	—
422	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×#117×C₈₉	1	1	yes	characteristic
442	C₂²	C₂×C₄×Q₈×C₈₉	1	1	yes	characteristic
443	C₂²	#518×C₈₉	1	1	yes	characteristic
444	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
445	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
446	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
447	C₂²	#568×C₈₉	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	#433×C₈₉	1	4	yes	—
457	C₄	#553×C₈₉	1	1	yes	characteristic
458	C₄	#553×C₈₉	1	1	yes	characteristic
459	C₄	#554×C₈₉	1	1	yes	characteristic
460	C₄	#554×C₈₉	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	C₈₉×#2345	1	1	yes	characteristic
463	C₂	C₂×#433×C₈₉	1	1	yes	characteristic
464	C₂	C₈₉×#2924	1	1	yes	characteristic
465	C₂	C₈₉×#2960	1	1	yes	characteristic
466	C₂	C₈₉×#2962	1	1	yes	characteristic
467	C₂	C₈₉×#2979	1	1	yes	characteristic
468	C₂	C₈₉×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₈₉×#1939	C₂	semidirect
3. C₈₉×#1939	C₂	semidirect
4. C₈₉×#1917	C₂	semidirect
5. C₈₉×#1916	C₂	semidirect
8. C₈₉×#1770	C₂	semidirect
9. C₈×C₄⋊C₄×C₈₉	C₂	semidirect
226. #22626	C₈₉	direct (N × H)
236. #1939	C₂×C₈₉	semidirect
237. #1939	C₂×C₈₉	semidirect
238. #1917	C₂×C₈₉	semidirect
239. #1916	C₂×C₈₉	semidirect
242. #1770	C₂×C₈₉	semidirect
243. C₈×C₄⋊C₄	C₂×C₈₉	semidirect
246. C₈₉	#22626	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×#2285	2
C₈₉×#1939	2
C₈₉×#1917	2
C₈₉×#1916	2
C₈₉×#1798	2
C₈₉×#1797	2
C₈₉×#1770	2
C₈×C₄⋊C₄×C₈₉	2
C₈₉×#1750	2
C₄×C₂²⋊C₈×C₈₉	2
#22626	89

Subgroups — C89×#22626 #36400474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22626 #36400474