Subgroups — C₈₉×#22865 #36400713

Order 22784.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#419×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2363	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	#448×C₈₉	C₄	1	8	yes	complemented
26	#440×C₈₉	—	2	4	no	—
27	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
29	#419×C₈₉	—	2	4	no	—
30	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	#391×C₈₉	—	2	1	no	—
42	#391×C₈₉	—	2	1	no	—
43	#391×C₈₉	C₂²	1	1	yes	characteristic
44	#391×C₈₉	C₂²	1	1	yes	characteristic
45	#390×C₈₉	—	2	1	no	—
46	#390×C₈₉	C₂²	1	1	yes	characteristic
47	#389×C₈₉	C₂²	1	1	yes	characteristic
48	#388×C₈₉	—	2	1	no	—
49	#386×C₈₉	—	2	1	no	—
50	#380×C₈₉	—	2	1	no	—
51	#380×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₈₉	—	2	1	no	—
63	C₂²×Q₈×C₈₉	—	2	2	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	2	no	—
66	C₂²×Q₈×C₈₉	—	4	1	no	—
67	C₂²×Q₈×C₈₉	—	4	1	no	—
68	C₂²×Q₈×C₈₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	—	2	1	no	—
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×SD₁₆×C₈₉	—	2	2	no	—
77	C₂×SD₁₆×C₈₉	—	2	2	no	—
78	C₂×SD₁₆×C₈₉	—	4	1	no	—
79	C₂×SD₁₆×C₈₉	—	4	1	no	—
80	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	—
81	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	—
82	C₂×M₁₆×C₈₉	—	2	2	no	—
83	C₂×M₁₆×C₈₉	—	2	2	no	—
84	C₂×M₁₆×C₈₉	—	4	1	no	—
85	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	#121×C₈₉	—	2	2	no	—
90	#121×C₈₉	C₂×C₄	1	4	yes	—
91	C₄×Q₈×C₈₉	—	2	2	no	—
92	C₄×Q₈×C₈₉	—	2	2	no	—
93	C₄×Q₈×C₈₉	—	4	1	no	—
94	C₄×Q₈×C₈₉	—	4	1	no	—
95	C₄×D₄×C₈₉	—	2	2	no	—
96	C₄×D₄×C₈₉	—	4	1	no	—
97	#117×C₈₉	—	2	2	no	—
98	#117×C₈₉	—	4	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	—	2	1	no	—
116	C₂×C₄²×C₈₉	—	2	1	no	—
117	C₂×C₄²×C₈₉	—	2	1	no	—
118	C₂×C₄²×C₈₉	—	2	1	no	—
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	#107×C₈₉	—	2	2	no	—
122	#106×C₈₉	—	4	1	no	—
123	#103×C₈₉	—	2	2	no	—
124	#103×C₈₉	—	2	2	no	—
125	#103×C₈₉	—	2	2	no	—
126	#103×C₈₉	C₂×C₄	1	4	yes	complemented
127	#103×C₈₉	C₂×C₄	1	4	yes	complemented
128	#103×C₈₉	D₄	1	4	yes	complemented
129	#102×C₈₉	—	2	2	no	—
130	#102×C₈₉	—	4	1	no	—
131	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
132	#97×C₈₉	—	2	2	no	—
133	C₄×C₈×C₈₉	—	4	1	no	—
134	#95×C₈₉	—	2	1	no	—
135	#95×C₈₉	—	2	1	no	—
136	#95×C₈₉	—	2	1	no	—
137	#95×C₈₉	—	2	1	no	—
138	#95×C₈₉	—	2	1	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	D₄	1	1	yes	characteristic
142	#95×C₈₉	D₄	1	1	yes	characteristic
143	C₂⁴×C₈₉	—	2	1	no	—
144	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₈₉	—	2	4	no	—
146	C₂×Q₈×C₈₉	—	2	1	no	—
147	C₂×Q₈×C₈₉	—	2	1	no	—
148	C₂×Q₈×C₈₉	—	2	1	no	—
149	C₂×Q₈×C₈₉	—	2	1	no	—
150	C₂×Q₈×C₈₉	—	2	8	no	—
151	C₂×Q₈×C₈₉	—	2	1	no	—
152	C₂×Q₈×C₈₉	—	2	1	no	—
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	4	2	no	—
156	C₂×Q₈×C₈₉	—	4	2	no	—
157	C₂×Q₈×C₈₉	—	4	4	no	—
158	C₂×Q₈×C₈₉	—	4	4	no	—
159	C₂×Q₈×C₈₉	—	4	4	no	—
160	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
161	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
162	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
163	C₂×Q₈×C₈₉	#41	1	2	yes	—
164	C₂×D₄×C₈₉	—	2	4	no	—
165	C₂×D₄×C₈₉	—	2	1	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	8	1	no	—
171	C₂×D₄×C₈₉	—	8	1	no	—
172	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₈₉	—	2	1	no	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	1	no	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	4	no	—
179	C₂²×C₄×C₈₉	—	2	1	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	1	no	—
184	C₂²×C₄×C₈₉	—	2	1	no	—
185	C₂²×C₄×C₈₉	—	4	2	no	—
186	C₂²×C₄×C₈₉	—	4	2	no	—
187	C₂²×C₄×C₈₉	—	4	2	no	—
188	C₂²×C₄×C₈₉	—	4	2	no	—
189	C₂²×C₄×C₈₉	—	8	1	no	—
190	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	#41	1	2	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
198	SD₁₆×C₈₉	—	2	8	no	—
199	SD₁₆×C₈₉	—	4	4	no	—
200	M₁₆×C₈₉	—	4	4	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	2	1	no	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	2	1	no	—
210	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
211	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
213	C₄⋊C₄×C₈₉	—	2	1	no	—
214	C₄⋊C₄×C₈₉	—	2	1	no	—
215	C₄⋊C₄×C₈₉	—	2	1	no	—
216	C₄⋊C₄×C₈₉	—	2	1	no	—
217	C₄⋊C₄×C₈₉	—	2	1	no	—
218	C₄⋊C₄×C₈₉	—	2	1	no	—
219	C₄⋊C₄×C₈₉	—	2	1	no	—
220	C₄⋊C₄×C₈₉	—	2	1	no	—
221	C₄⋊C₄×C₈₉	—	4	2	no	—
222	C₄⋊C₄×C₈₉	—	4	2	no	—
223	C₄⋊C₄×C₈₉	—	8	1	no	—
224	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
225	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₈₉	—	2	4	no	—
227	C₂²⋊C₄×C₈₉	—	2	2	no	—
228	C₂²⋊C₄×C₈₉	—	4	1	no	—
229	C₂²⋊C₄×C₈₉	—	4	2	no	—
230	C₂²⋊C₄×C₈₉	—	4	2	no	—
231	C₂²⋊C₄×C₈₉	—	4	2	no	—
232	C₂²⋊C₄×C₈₉	—	4	2	no	—
233	C₂²⋊C₄×C₈₉	—	8	1	no	—
234	C₄²×C₈₉	—	2	1	no	—
235	C₄²×C₈₉	—	2	1	no	—
236	C₄²×C₈₉	—	2	1	no	—
237	C₄²×C₈₉	—	2	1	no	—
238	C₄²×C₈₉	—	4	2	no	—
239	C₄²×C₈₉	—	4	2	no	—
240	C₄²×C₈₉	—	4	2	no	—
241	C₄²×C₈₉	—	8	1	no	—
242	C₂³×C₈₉	—	2	1	no	—
243	C₂³×C₈₉	—	2	1	no	—
244	C₂³×C₈₉	—	2	1	no	—
245	C₂³×C₈₉	—	2	1	no	—
246	C₂³×C₈₉	—	2	1	no	—
247	C₂³×C₈₉	—	2	1	no	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	4	1	no	—
250	C₂³×C₈₉	—	4	1	no	—
251	C₂³×C₈₉	—	4	1	no	—
252	C₂³×C₈₉	—	4	1	no	—
253	C₂³×C₈₉	—	4	1	no	—
254	C₂³×C₈₉	—	4	1	no	—
255	C₂³×C₈₉	C₄×D₄	1	2	yes	—
256	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
257	Q₈×C₈₉	—	2	2	no	—
258	Q₈×C₈₉	—	2	2	no	—
259	Q₈×C₈₉	—	2	2	no	—
260	Q₈×C₈₉	—	2	2	no	—
261	Q₈×C₈₉	—	2	2	no	—
262	Q₈×C₈₉	—	4	8	no	—
263	Q₈×C₈₉	—	4	1	no	—
264	Q₈×C₈₉	—	4	1	no	—
265	Q₈×C₈₉	C₄×D₄	1	4	yes	—
266	D₄×C₈₉	—	2	2	no	—
267	D₄×C₈₉	—	2	2	no	—
268	D₄×C₈₉	—	4	1	no	—
269	D₄×C₈₉	—	4	1	no	—
270	D₄×C₈₉	—	8	4	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	2	1	no	—
273	C₂×C₄×C₈₉	—	2	2	no	—
274	C₂×C₄×C₈₉	—	2	1	no	—
275	C₂×C₄×C₈₉	—	2	2	no	—
276	C₂×C₄×C₈₉	—	2	1	no	—
277	C₂×C₄×C₈₉	—	2	1	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	1	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	4	8	no	—
295	C₂×C₄×C₈₉	—	4	1	no	—
296	C₂×C₄×C₈₉	—	4	1	no	—
297	C₂×C₄×C₈₉	—	4	1	no	—
298	C₂×C₄×C₈₉	—	4	1	no	—
299	C₂×C₄×C₈₉	—	4	1	no	—
300	C₂×C₄×C₈₉	—	4	1	no	—
301	C₂×C₄×C₈₉	—	4	1	no	—
302	C₂×C₄×C₈₉	—	4	1	no	—
303	C₂×C₄×C₈₉	—	4	1	no	—
304	C₂×C₄×C₈₉	—	4	1	no	—
305	C₂×C₄×C₈₉	—	4	1	no	—
306	C₂×C₄×C₈₉	—	4	1	no	—
307	C₂×C₄×C₈₉	—	4	1	no	—
308	C₂×C₄×C₈₉	—	4	1	no	—
309	C₂×C₄×C₈₉	—	4	1	no	—
310	C₂×C₄×C₈₉	—	8	4	no	—
311	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
312	C₂×C₄×C₈₉	#137	1	2	yes	—
313	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
319	C₈×C₈₉	—	2	2	no	—
320	C₈×C₈₉	—	2	2	no	—
321	C₈×C₈₉	—	2	2	no	—
322	C₈×C₈₉	—	4	1	no	—
323	C₂²×C₈₉	—	2	2	no	—
324	C₂²×C₈₉	—	2	2	no	—
325	C₂²×C₈₉	—	2	2	no	—
326	C₂²×C₈₉	—	4	1	no	—
327	C₂²×C₈₉	—	4	1	no	—
328	C₂²×C₈₉	—	4	1	no	—
329	C₂²×C₈₉	—	4	1	no	—
330	C₂²×C₈₉	—	4	2	no	—
331	C₂²×C₈₉	—	4	2	no	—
332	C₂²×C₈₉	—	4	2	no	—
333	C₂²×C₈₉	—	8	1	no	—
334	C₂²×C₈₉	—	8	1	no	—
335	C₂²×C₈₉	—	8	1	no	—
336	C₂²×C₈₉	—	8	1	no	—
337	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
338	C₂²×C₈₉	D₄²	1	1	yes	characteristic
339	C₂²×C₈₉	#546	1	1	yes	characteristic
340	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
341	C₂²×C₈₉	#575	1	1	yes	characteristic
342	C₂²×C₈₉	#577	1	1	yes	characteristic
343	C₂²×C₈₉	#577	1	1	yes	characteristic
344	C₄×C₈₉	—	2	2	no	—
345	C₄×C₈₉	—	2	4	no	—
346	C₄×C₈₉	—	2	2	no	—
347	C₄×C₈₉	—	4	2	no	—
348	C₄×C₈₉	—	4	2	no	—
349	C₄×C₈₉	—	4	1	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	1	no	—
352	C₄×C₈₉	—	4	1	no	—
353	C₄×C₈₉	—	8	1	no	—
354	C₄×C₈₉	—	8	1	no	—
355	C₄×C₈₉	—	8	1	no	—
356	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
357	C₄×C₈₉	#518	1	1	yes	characteristic
358	C₄×C₈₉	#546	1	1	yes	characteristic
359	C₄×C₈₉	#551	1	1	yes	characteristic
360	#22865	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₈₉	—	4	2	no	—
362	C₂×C₈₉	—	8	2	no	—
363	C₂×C₈₉	#2358	1	1	yes	characteristic
364	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
365	C₂×C₈₉	#2949	1	1	yes	characteristic
366	C₂×C₈₉	#3275	1	1	yes	characteristic
367	C₂×C₈₉	#3278	1	1	yes	characteristic
368	C₂×C₈₉	#3320	1	1	yes	characteristic
369	C₂×C₈₉	#3321	1	1	yes	characteristic
370	C₂×#448	C₂×C₈₉	1	1	yes	characteristic
371	C₂×#440	C₂×C₈₉	1	1	yes	characteristic, complemented
372	C₂×#419	C₂×C₈₉	1	1	yes	characteristic, complemented
373	#2363	C₂×C₈₉	1	1	yes	characteristic
374	Q₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
375	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
376	#1935	C₂×C₈₉	1	1	yes	characteristic, complemented
377	#1928	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#1895	C₂×C₈₉	1	1	yes	characteristic
379	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
382	#1854	C₂×C₈₉	1	1	yes	characteristic, complemented
383	C₄×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
384	#1753	C₂×C₈₉	1	1	yes	characteristic, complemented
385	C₈₉	#22865	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
388	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
389	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
390	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
395	#448	C₄×C₈₉	1	8	yes	complemented
396	#440	—	2	4	no	—
397	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
398	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
399	#419	—	2	4	no	—
400	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
401	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
402	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
411	#391	—	2	1	no	—
412	#391	—	2	1	no	—
413	#391	C₂²×C₈₉	1	1	yes	characteristic
414	#391	C₂²×C₈₉	1	1	yes	characteristic
415	#390	—	2	1	no	—
416	#390	C₂²×C₈₉	1	1	yes	characteristic
417	#389	C₂²×C₈₉	1	1	yes	characteristic
418	#388	—	2	1	no	—
419	#386	—	2	1	no	—
420	#380	—	2	1	no	—
421	#380	C₂²×C₈₉	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₄×C₂²⋊C₄	—	2	1	no	—
424	C₄×C₂²⋊C₄	—	2	1	no	—
425	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
426	#340	C₂²×C₈₉	1	1	yes	characteristic
427	#340	C₂²×C₈₉	1	1	yes	characteristic
428	#340	C₂²×C₈₉	1	1	yes	characteristic
429	#340	C₂²×C₈₉	1	1	yes	characteristic
430	#336	C₂²×C₈₉	1	1	yes	characteristic
431	#336	C₂²×C₈₉	1	1	yes	characteristic
432	C₂²×Q₈	—	2	1	no	—
433	C₂²×Q₈	—	2	2	no	—
434	C₂²×Q₈	—	2	2	no	—
435	C₂²×Q₈	—	2	2	no	—
436	C₂²×Q₈	—	4	1	no	—
437	C₂²×Q₈	—	4	1	no	—
438	C₂²×Q₈	C₂×C₄×C₈₉	1	4	yes	complemented
439	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	4	1	no	—
449	C₂×SD₁₆	—	4	1	no	—
450	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	—
451	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	—
452	C₂×M₁₆	—	2	2	no	—
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	4	1	no	—
455	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
459	#121	—	2	2	no	—
460	#121	C₂×C₄×C₈₉	1	4	yes	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	4	1	no	—
464	C₄×Q₈	—	4	1	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	4	1	no	—
467	#117	—	2	2	no	—
468	#117	—	4	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
491	#107	—	2	2	no	—
492	#106	—	4	1	no	—
493	#103	—	2	2	no	—
494	#103	—	2	2	no	—
495	#103	—	2	2	no	—
496	#103	C₂×C₄×C₈₉	1	4	yes	complemented
497	#103	C₂×C₄×C₈₉	1	4	yes	complemented
498	#103	D₄×C₈₉	1	4	yes	complemented
499	#102	—	2	2	no	—
500	#102	—	4	1	no	—
501	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	complemented
502	#97	—	2	2	no	—
503	C₄×C₈	—	4	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	D₄×C₈₉	1	1	yes	characteristic
512	#95	D₄×C₈₉	1	1	yes	characteristic
513	C₂⁴	—	2	1	no	—
514	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	8	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	—	4	4	no	—
528	C₂×Q₈	—	4	4	no	—
529	C₂×Q₈	—	4	4	no	—
530	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
531	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
532	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
533	C₂×Q₈	#41×C₈₉	1	2	yes	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	8	1	no	—
541	C₂×D₄	—	8	1	no	—
542	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	8	1	no	—
560	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
561	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
566	C₂²×C₄	#41×C₈₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
568	SD₁₆	—	2	8	no	—
569	SD₁₆	—	4	4	no	—
570	M₁₆	—	4	4	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
581	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
582	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	8	1	no	—
594	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
595	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	8	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	4	2	no	—
609	C₄²	—	4	2	no	—
610	C₄²	—	4	2	no	—
611	C₄²	—	8	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	C₄×D₄×C₈₉	1	2	yes	—
626	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	4	8	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	C₄×D₄×C₈₉	1	4	yes	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	8	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	4	8	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
682	C₂×C₄	#137×C₈₉	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
685	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
686	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
687	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
688	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
689	C₈	—	2	2	no	—
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	—	4	1	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
708	C₂²	D₄²×C₈₉	1	1	yes	characteristic
709	C₂²	#546×C₈₉	1	1	yes	characteristic
710	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
711	C₂²	#575×C₈₉	1	1	yes	characteristic
712	C₂²	#577×C₈₉	1	1	yes	characteristic
713	C₂²	#577×C₈₉	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
727	C₄	#518×C₈₉	1	1	yes	characteristic
728	C₄	#546×C₈₉	1	1	yes	characteristic
729	C₄	#551×C₈₉	1	1	yes	characteristic
730	C₂	—	4	2	no	—
731	C₂	—	8	2	no	—
732	C₂	C₈₉×#2358	1	1	yes	characteristic
733	C₂	C₄×#137×C₈₉	1	1	yes	characteristic
734	C₂	C₈₉×#2949	1	1	yes	characteristic
735	C₂	C₈₉×#3275	1	1	yes	characteristic
736	C₂	C₈₉×#3278	1	1	yes	characteristic
737	C₂	C₈₉×#3320	1	1	yes	characteristic
738	C₂	C₈₉×#3321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#440×C₈₉	C₂	semidirect
3. C₂×#419×C₈₉	C₂	semidirect
5. Q₈×C₂²⋊C₄×C₈₉	C₂	semidirect
6. C₈₉×#1968	C₂	semidirect
7. C₈₉×#1935	C₂	semidirect
8. C₈₉×#1928	C₂	semidirect
10. C₈₉×#1880	C₂	semidirect
11. C₈₉×#1877	C₂	semidirect
12. C₈₉×#1865	C₂	semidirect
13. C₈₉×#1854	C₂	semidirect
14. C₄×#103×C₈₉	C₂	semidirect
15. C₈₉×#1753	C₂	semidirect
25. #448×C₈₉	C₄	semidirect
68. C₂²×Q₈×C₈₉	C₂×C₄	semidirect
126. #103×C₈₉	C₂×C₄	semidirect
127. #103×C₈₉	C₂×C₄	semidirect
128. #103×C₈₉	D₄	semidirect
131. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
360. #22865	C₈₉	direct (N × H)
371. C₂×#440	C₂×C₈₉	semidirect
372. C₂×#419	C₂×C₈₉	semidirect
374. Q₈×C₂²⋊C₄	C₂×C₈₉	semidirect
375. #1968	C₂×C₈₉	semidirect
376. #1935	C₂×C₈₉	semidirect
377. #1928	C₂×C₈₉	semidirect
379. #1880	C₂×C₈₉	semidirect
380. #1877	C₂×C₈₉	semidirect
381. #1865	C₂×C₈₉	semidirect
382. #1854	C₂×C₈₉	semidirect
383. C₄×#103	C₂×C₈₉	semidirect
384. #1753	C₂×C₈₉	semidirect
385. C₈₉	#22865	direct (N × H)
395. #448	C₄×C₈₉	semidirect
438. C₂²×Q₈	C₂×C₄×C₈₉	semidirect
496. #103	C₂×C₄×C₈₉	semidirect
497. #103	C₂×C₄×C₈₉	semidirect
498. #103	D₄×C₈₉	semidirect
501. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#448×C₈₉	2
C₂×#440×C₈₉	2
C₂×#419×C₈₉	2
C₈₉×#2363	2
Q₈×C₂²⋊C₄×C₈₉	2
C₈₉×#1968	2
C₈₉×#1935	2
C₈₉×#1928	2
C₈₉×#1895	2
C₈₉×#1880	2
C₈₉×#1877	2
C₈₉×#1865	2
C₈₉×#1854	2
C₄×#103×C₈₉	2
C₈₉×#1753	2
#22865	89

Subgroups — C89×#22865 #36400713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22865 #36400713