Subgroups — C₈₉×#22493 #36400341

Order 22784.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1825	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#340×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	#553×C₈₉	—	2	4	no	—
19	#553×C₈₉	C₄	1	8	yes	complemented
20	C₂×#126×C₈₉	—	2	1	no	—
21	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₈₉	—	2	1	no	—
23	C₂×#121×C₈₉	—	2	1	no	—
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₈₉	—	2	1	no	—
27	C₂×C₄×D₄×C₈₉	—	2	1	no	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#435×C₈₉	—	2	4	no	—
35	C₂×C₄⋊C₈×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×#102×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
43	#389×C₈₉	—	2	1	no	—
44	#385×C₈₉	—	2	1	no	—
45	#385×C₈₉	—	2	1	no	—
46	#384×C₈₉	C₂²	1	1	yes	characteristic
47	#380×C₈₉	C₂²	1	1	yes	characteristic
48	#380×C₈₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
50	#340×C₈₉	C₂²	1	1	yes	characteristic
51	#340×C₈₉	C₂²	1	1	yes	characteristic
52	#340×C₈₉	C₂²	1	1	yes	characteristic
53	#340×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#340×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	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#340×C₈₉	C₂²	1	1	yes	characteristic
62	C₂²×D₄×C₈₉	—	2	1	no	—
63	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₈₉	—	2	1	no	—
67	C₂³×C₄×C₈₉	—	2	1	no	—
68	C₂³×C₄×C₈₉	—	2	1	no	—
69	C₂³×C₄×C₈₉	—	2	1	no	—
70	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₈₉	—	2	2	no	—
73	C₂×M₁₆×C₈₉	—	2	2	no	—
74	C₂×M₁₆×C₈₉	—	4	1	no	—
75	C₂²×C₈×C₈₉	—	2	2	no	—
76	C₂²×C₈×C₈₉	—	2	2	no	—
77	C₂²×C₈×C₈₉	—	4	1	no	—
78	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	#126×C₈₉	—	2	8	no	—
83	#125×C₈₉	—	2	2	no	—
84	#125×C₈₉	C₂×C₄	1	4	yes	complemented
85	#123×C₈₉	—	2	8	no	—
86	#121×C₈₉	—	2	8	no	—
87	#121×C₈₉	—	2	2	no	—
88	#121×C₈₉	—	2	2	no	—
89	#121×C₈₉	C₂×C₄	1	4	yes	complemented
90	#121×C₈₉	C₂×C₄	1	4	yes	complemented
91	C₄×D₄×C₈₉	—	2	8	no	—
92	C₄×D₄×C₈₉	—	2	2	no	—
93	C₄×D₄×C₈₉	—	4	4	no	—
94	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
95	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	complemented
96	C₄×D₄×C₈₉	D₄	1	4	yes	—
97	#117×C₈₉	—	2	2	no	—
98	#117×C₈₉	C₂×C₄	1	4	yes	complemented
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
110	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
111	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	complemented
112	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	—	2	1	no	—
129	C₂×C₄²×C₈₉	—	2	1	no	—
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₈₉	—	2	2	no	—
132	#102×C₈₉	—	2	2	no	—
133	#102×C₈₉	—	2	2	no	—
134	#102×C₈₉	—	4	1	no	—
135	#102×C₈₉	—	4	1	no	—
136	C₂²⋊C₈×C₈₉	—	2	2	no	—
137	C₂²⋊C₈×C₈₉	—	2	2	no	—
138	#97×C₈₉	—	2	2	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	—	2	1	no	—
142	C₂⁴×C₈₉	—	2	1	no	—
143	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₈₉	—	2	2	no	—
146	C₂×D₄×C₈₉	—	2	2	no	—
147	C₂×D₄×C₈₉	—	2	4	no	—
148	C₂×D₄×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	1	no	—
150	C₂×D₄×C₈₉	—	2	1	no	—
151	C₂×D₄×C₈₉	—	2	1	no	—
152	C₂×D₄×C₈₉	—	2	1	no	—
153	C₂×D₄×C₈₉	—	2	1	no	—
154	C₂×D₄×C₈₉	—	4	2	no	—
155	C₂×D₄×C₈₉	—	4	2	no	—
156	C₂×D₄×C₈₉	—	8	1	no	—
157	C₂×D₄×C₈₉	—	8	1	no	—
158	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
159	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	2	1	no	—
164	C₂²×C₄×C₈₉	—	2	1	no	—
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	1	no	—
168	C₂²×C₄×C₈₉	—	2	1	no	—
169	C₂²×C₄×C₈₉	—	2	1	no	—
170	C₂²×C₄×C₈₉	—	2	1	no	—
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	—	2	4	no	—
173	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	no	—
178	C₂²×C₄×C₈₉	—	4	2	no	—
179	C₂²×C₄×C₈₉	—	4	2	no	—
180	C₂²×C₄×C₈₉	—	4	2	no	—
181	C₂²×C₄×C₈₉	—	8	1	no	—
182	C₂²×C₄×C₈₉	—	8	1	no	—
183	C₂²×C₄×C₈₉	—	8	1	no	—
184	C₂²×C₄×C₈₉	—	8	1	no	—
185	C₂²×C₄×C₈₉	—	8	1	no	—
186	C₂²×C₄×C₈₉	—	8	1	no	—
187	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
188	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
194	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
196	M₁₆×C₈₉	—	4	4	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
209	C₂×C₈×C₈₉	#41	1	2	yes	—
210	C₄⋊C₄×C₈₉	—	2	4	no	—
211	C₄⋊C₄×C₈₉	—	2	4	no	—
212	C₄⋊C₄×C₈₉	—	2	4	no	—
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	—	2	1	no	—
222	C₄⋊C₄×C₈₉	—	2	1	no	—
223	C₄⋊C₄×C₈₉	—	4	2	no	—
224	C₄⋊C₄×C₈₉	—	4	2	no	—
225	C₄⋊C₄×C₈₉	—	4	2	no	—
226	C₄⋊C₄×C₈₉	—	8	1	no	—
227	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
228	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
229	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₈₉	#41	1	2	yes	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	4	no	—
236	C₂²⋊C₄×C₈₉	—	4	2	no	—
237	C₂²⋊C₄×C₈₉	—	4	2	no	—
238	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
239	C₂²⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
240	C₄²×C₈₉	—	2	4	no	—
241	C₄²×C₈₉	—	4	2	no	—
242	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
243	C₄²×C₈₉	C₂×D₄	1	2	yes	—
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	1	no	—
249	C₂³×C₈₉	—	2	1	no	—
250	C₂³×C₈₉	—	2	1	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	2	no	—
255	C₂³×C₈₉	—	4	1	no	—
256	C₂³×C₈₉	—	4	1	no	—
257	C₂³×C₈₉	—	4	1	no	—
258	C₂³×C₈₉	—	4	1	no	—
259	C₂³×C₈₉	—	4	1	no	—
260	C₂³×C₈₉	—	4	1	no	—
261	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂³×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂³×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
264	C₂³×C₈₉	#137	1	2	yes	—
265	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
266	D₄×C₈₉	—	2	8	no	—
267	D₄×C₈₉	—	2	2	no	—
268	D₄×C₈₉	—	2	2	no	—
269	D₄×C₈₉	—	4	8	no	—
270	D₄×C₈₉	—	4	1	no	—
271	D₄×C₈₉	—	4	1	no	—
272	D₄×C₈₉	—	8	4	no	—
273	C₂×C₄×C₈₉	—	2	1	no	—
274	C₂×C₄×C₈₉	—	2	1	no	—
275	C₂×C₄×C₈₉	—	2	1	no	—
276	C₂×C₄×C₈₉	—	2	1	no	—
277	C₂×C₄×C₈₉	—	2	1	no	—
278	C₂×C₄×C₈₉	—	2	1	no	—
279	C₂×C₄×C₈₉	—	2	1	no	—
280	C₂×C₄×C₈₉	—	2	1	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	2	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	4	1	no	—
294	C₂×C₄×C₈₉	—	4	1	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	—	8	4	no	—
312	C₂×C₄×C₈₉	—	8	4	no	—
313	C₂×C₄×C₈₉	—	8	4	no	—
314	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
315	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
324	C₈×C₈₉	—	2	2	no	—
325	C₈×C₈₉	—	4	1	no	—
326	C₈×C₈₉	—	4	1	no	—
327	C₈×C₈₉	—	4	1	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	2	no	—
330	C₂²×C₈₉	—	2	2	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	2	no	—
333	C₂²×C₈₉	—	2	2	no	—
334	C₂²×C₈₉	—	2	2	no	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	4	1	no	—
338	C₂²×C₈₉	—	4	1	no	—
339	C₂²×C₈₉	—	4	1	no	—
340	C₂²×C₈₉	—	4	1	no	—
341	C₂²×C₈₉	—	4	2	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	8	1	no	—
345	C₂²×C₈₉	—	8	1	no	—
346	C₂²×C₈₉	—	8	1	no	—
347	C₂²×C₈₉	—	8	1	no	—
348	C₂²×C₈₉	#417	1	4	yes	—
349	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
350	C₂²×C₈₉	#546	1	1	yes	characteristic
351	C₂²×C₈₉	#547	1	1	yes	characteristic
352	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
354	C₂²×C₈₉	#576	1	1	yes	characteristic
355	C₂²×C₈₉	#577	1	1	yes	characteristic
356	C₄×C₈₉	—	2	2	no	—
357	C₄×C₈₉	—	2	2	no	—
358	C₄×C₈₉	—	2	2	no	—
359	C₄×C₈₉	—	2	2	no	—
360	C₄×C₈₉	—	4	2	no	—
361	C₄×C₈₉	—	4	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	8	1	no	—
365	C₄×C₈₉	—	8	1	no	—
366	C₄×C₈₉	—	8	1	no	—
367	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
368	C₄×C₈₉	#520	1	1	yes	characteristic
369	C₄×C₈₉	#546	1	1	yes	characteristic
370	C₄×C₈₉	#547	1	1	yes	characteristic
371	#22493	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₈₉	—	2	4	no	—
373	C₂×C₈₉	—	4	2	no	—
374	C₂×C₈₉	—	8	2	no	—
375	C₂×C₈₉	#2339	1	1	yes	characteristic
376	C₂×C₈₉	C₂×#417	1	1	yes	characteristic
377	C₂×C₈₉	#2897	1	1	yes	characteristic
378	C₂×C₈₉	#3318	1	1	yes	characteristic
379	C₂×C₈₉	#3320	1	1	yes	characteristic
380	C₂×C₈₉	#3345	1	1	yes	characteristic
381	C₂×C₈₉	#3346	1	1	yes	characteristic
382	C₂×#553	C₂×C₈₉	1	1	yes	characteristic
383	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
384	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#1992	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#1989	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#1874	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#1825	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#1824	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#1802	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#1736	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₂×#340	C₂×C₈₉	1	1	yes	characteristic, complemented
397	C₈₉	#22493	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
399	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
400	#553	—	2	4	no	—
401	#553	C₄×C₈₉	1	8	yes	complemented
402	C₂×#126	—	2	1	no	—
403	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#123	—	2	1	no	—
405	C₂×#121	—	2	1	no	—
406	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₄×D₄	—	2	1	no	—
409	C₂×C₄×D₄	—	2	1	no	—
410	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
416	#435	—	2	4	no	—
417	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
425	#389	—	2	1	no	—
426	#385	—	2	1	no	—
427	#385	—	2	1	no	—
428	#384	C₂²×C₈₉	1	1	yes	characteristic
429	#380	C₂²×C₈₉	1	1	yes	characteristic
430	#380	C₂²×C₈₉	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
432	#340	C₂²×C₈₉	1	1	yes	characteristic
433	#340	C₂²×C₈₉	1	1	yes	characteristic
434	#340	C₂²×C₈₉	1	1	yes	characteristic
435	#340	C₂²×C₈₉	1	1	yes	characteristic
436	#340	C₂²×C₈₉	1	1	yes	characteristic
437	#340	C₂²×C₈₉	1	1	yes	characteristic
438	#340	C₂²×C₈₉	1	1	yes	characteristic
439	#340	C₂²×C₈₉	1	1	yes	characteristic
440	#340	C₂²×C₈₉	1	1	yes	characteristic
441	#340	C₂²×C₈₉	1	1	yes	characteristic
442	#340	C₂²×C₈₉	1	1	yes	characteristic
443	#340	C₂²×C₈₉	1	1	yes	characteristic
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	—	2	2	no	—
456	C₂×M₁₆	—	4	1	no	—
457	C₂²×C₈	—	2	2	no	—
458	C₂²×C₈	—	2	2	no	—
459	C₂²×C₈	—	4	1	no	—
460	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
464	#126	—	2	8	no	—
465	#125	—	2	2	no	—
466	#125	C₂×C₄×C₈₉	1	4	yes	complemented
467	#123	—	2	8	no	—
468	#121	—	2	8	no	—
469	#121	—	2	2	no	—
470	#121	—	2	2	no	—
471	#121	C₂×C₄×C₈₉	1	4	yes	complemented
472	#121	C₂×C₄×C₈₉	1	4	yes	complemented
473	C₄×D₄	—	2	8	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	4	4	no	—
476	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	—
477	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	complemented
478	C₄×D₄	D₄×C₈₉	1	4	yes	—
479	#117	—	2	2	no	—
480	#117	C₂×C₄×C₈₉	1	4	yes	complemented
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	2	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	2	no	—
486	C₂×C₄⋊C₄	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	4	1	no	—
492	C₂×C₄⋊C₄	—	4	1	no	—
493	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	4	yes	complemented
494	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
510	C₂×C₄²	—	2	1	no	—
511	C₂×C₄²	—	2	1	no	—
512	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
513	C₄⋊C₈	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	4	1	no	—
517	#102	—	4	1	no	—
518	C₂²⋊C₈	—	2	2	no	—
519	C₂²⋊C₈	—	2	2	no	—
520	#97	—	2	2	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	C₂⁴	—	2	1	no	—
525	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
526	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	—	8	1	no	—
539	C₂×D₄	—	8	1	no	—
540	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
541	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
542	C₂²×C₄	—	2	1	no	—
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	1	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	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	8	1	no	—
564	C₂²×C₄	—	8	1	no	—
565	C₂²×C₄	—	8	1	no	—
566	C₂²×C₄	—	8	1	no	—
567	C₂²×C₄	—	8	1	no	—
568	C₂²×C₄	—	8	1	no	—
569	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
570	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
571	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
576	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
578	M₁₆	—	4	4	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	4	4	no	—
591	C₂×C₈	#41×C₈₉	1	2	yes	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	8	1	no	—
609	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
610	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
611	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
612	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
613	C₄⋊C₄	#41×C₈₉	1	2	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
621	C₂²⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
622	C₄²	—	2	4	no	—
623	C₄²	—	4	2	no	—
624	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
625	C₄²	C₂×D₄×C₈₉	1	2	yes	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
644	C₂³	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
645	C₂³	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
646	C₂³	#137×C₈₉	1	2	yes	—
647	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
648	D₄	—	2	8	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	4	8	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	8	4	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	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	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	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	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
697	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
698	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
699	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
700	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
702	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
704	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
705	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	#417×C₈₉	1	4	yes	—
731	C₂²	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
732	C₂²	#546×C₈₉	1	1	yes	characteristic
733	C₂²	#547×C₈₉	1	1	yes	characteristic
734	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
735	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
736	C₂²	#576×C₈₉	1	1	yes	characteristic
737	C₂²	#577×C₈₉	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	8	1	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	C₄×#41×C₈₉	1	1	yes	characteristic
750	C₄	#520×C₈₉	1	1	yes	characteristic
751	C₄	#546×C₈₉	1	1	yes	characteristic
752	C₄	#547×C₈₉	1	1	yes	characteristic
753	C₂	—	2	4	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	2	no	—
756	C₂	C₈₉×#2339	1	1	yes	characteristic
757	C₂	C₂×#417×C₈₉	1	1	yes	characteristic
758	C₂	C₈₉×#2897	1	1	yes	characteristic
759	C₂	C₈₉×#3318	1	1	yes	characteristic
760	C₂	C₈₉×#3320	1	1	yes	characteristic
761	C₂	C₈₉×#3345	1	1	yes	characteristic
762	C₂	C₈₉×#3346	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×#553×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#435×C₈₉	C₂	semidirect
3. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
4. C₈₉×#1992	C₂	semidirect
5. C₈₉×#1989	C₂	semidirect
6. C₈₉×#1895	C₂	semidirect
7. C₈₉×#1893	C₂	semidirect
8. C₈₉×#1874	C₂	semidirect
9. C₈₉×#1874	C₂	semidirect
10. C₈₉×#1825	C₂	semidirect
11. C₈₉×#1824	C₂	semidirect
12. C₈₉×#1802	C₂	semidirect
13. C₈₉×#1762	C₂	semidirect
14. C₈₉×#1736	C₂	semidirect
15. C₂×#340×C₈₉	C₂	semidirect
19. #553×C₈₉	C₄	semidirect
84. #125×C₈₉	C₂×C₄	semidirect
89. #121×C₈₉	C₂×C₄	semidirect
90. #121×C₈₉	C₂×C₄	semidirect
95. C₄×D₄×C₈₉	C₂×C₄	semidirect
98. #117×C₈₉	C₂×C₄	semidirect
111. C₂×C₄⋊C₄×C₈₉	C₂×C₄	semidirect
371. #22493	C₈₉	direct (N × H)
383. C₂×#435	C₂×C₈₉	semidirect
384. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
385. #1992	C₂×C₈₉	semidirect
386. #1989	C₂×C₈₉	semidirect
387. #1895	C₂×C₈₉	semidirect
388. #1893	C₂×C₈₉	semidirect
389. #1874	C₂×C₈₉	semidirect
390. #1874	C₂×C₈₉	semidirect
391. #1825	C₂×C₈₉	semidirect
392. #1824	C₂×C₈₉	semidirect
393. #1802	C₂×C₈₉	semidirect
394. #1762	C₂×C₈₉	semidirect
395. #1736	C₂×C₈₉	semidirect
396. C₂×#340	C₂×C₈₉	semidirect
397. C₈₉	#22493	direct (N × H)
401. #553	C₄×C₈₉	semidirect
466. #125	C₂×C₄×C₈₉	semidirect
471. #121	C₂×C₄×C₈₉	semidirect
472. #121	C₂×C₄×C₈₉	semidirect
477. C₄×D₄	C₂×C₄×C₈₉	semidirect
480. #117	C₂×C₄×C₈₉	semidirect
493. C₂×C₄⋊C₄	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×#553×C₈₉	2
C₂×#435×C₈₉	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#1992	2
C₈₉×#1989	2
C₈₉×#1895	2
C₈₉×#1893	2
C₈₉×#1874	2
C₈₉×#1825	2
C₈₉×#1824	2
C₈₉×#1802	2
C₈₉×#1762	2
C₈₉×#1736	2
C₂×#340×C₈₉	2
#22493	89

Subgroups — C89×#22493 #36400341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22493 #36400341