Subgroups — C₈₉×#60710 #36438558

Order 22784.

1966 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3494	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3184	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3183	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3179	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3176	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3173	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3171	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3136	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2946	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	#555×C₈₉	—	2	2	no	—
24	#553×C₈₉	—	2	2	no	—
25	#553×C₈₉	—	2	2	no	—
26	#551×C₈₉	—	2	4	no	—
27	#547×C₈₉	—	2	2	no	—
28	#546×C₈₉	—	2	4	no	—
29	#544×C₈₉	C₂²	1	2	yes	—
30	#542×C₈₉	C₂²	1	4	yes	complemented
31	#540×C₈₉	C₂²	1	4	yes	complemented
32	#535×C₈₉	C₂²	1	2	yes	—
33	#532×C₈₉	C₂²	1	4	yes	complemented
34	#529×C₈₉	C₂²	1	4	yes	complemented
35	#525×C₈₉	C₂²	1	2	yes	—
36	C₂×#121×C₈₉	C₂²	1	2	yes	—
37	#520×C₈₉	C₂²	1	2	yes	—
38	#518×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
40	#501×C₈₉	C₂²	1	4	yes	complemented
41	#499×C₈₉	C₂²	1	2	yes	complemented
42	#498×C₈₉	C₂²	1	2	yes	complemented
43	#496×C₈₉	C₂²	1	4	yes	complemented
44	#495×C₈₉	C₂²	1	2	yes	complemented
45	#493×C₈₉	C₂²	1	2	yes	complemented
46	#490×C₈₉	C₂²	1	4	yes	complemented
47	#489×C₈₉	C₂²	1	4	yes	complemented
48	#488×C₈₉	C₂²	1	4	yes	complemented
49	#486×C₈₉	C₂²	1	4	yes	complemented
50	#470×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#470×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#469×C₈₉	C₂²	1	2	yes	—
53	#469×C₈₉	C₂²	1	2	yes	—
54	#469×C₈₉	C₂²	1	2	yes	—
55	#469×C₈₉	C₂²	1	2	yes	—
56	#469×C₈₉	C₂²	1	4	yes	complemented
57	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#468×C₈₉	C₂²	1	2	yes	complemented
60	#468×C₈₉	C₂²	1	4	yes	complemented
61	#468×C₈₉	C₂²	1	2	yes	complemented
62	#466×C₈₉	C₂²	1	4	yes	complemented
63	#465×C₈₉	C₂²	1	4	yes	complemented
64	#442×C₈₉	C₂²	1	2	yes	complemented
65	#442×C₈₉	C₂²	1	2	yes	complemented
66	#442×C₈₉	C₂²	1	2	yes	complemented
67	#442×C₈₉	C₂²	1	4	yes	complemented
68	#441×C₈₉	C₂²	1	2	yes	complemented
69	#440×C₈₉	C₂²	1	4	yes	complemented
70	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
71	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
72	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
73	C₄×D₈×C₈₉	C₂²	1	4	yes	complemented
74	#428×C₈₉	C₂²	1	2	yes	—
75	#427×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
77	#418×C₈₉	C₂²	1	2	yes	—
78	#417×C₈₉	C₂²	1	2	yes	—
79	#416×C₈₉	C₂²	1	2	yes	—
80	C₂×#102×C₈₉	C₂²	1	2	yes	—
81	#405×C₈₉	C₂²	1	1	yes	characteristic
82	#405×C₈₉	C₂²	1	1	yes	characteristic
83	#405×C₈₉	C₂²	1	1	yes	characteristic
84	#405×C₈₉	C₂²	1	1	yes	characteristic
85	#405×C₈₉	C₂²	1	2	yes	complemented
86	#405×C₈₉	C₂²	1	2	yes	complemented
87	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
88	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
89	C₂×#41×C₈₉	—	2	4	no	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₉	—	2	2	no	—
92	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
95	#135×C₈₉	—	2	4	no	—
96	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
99	C₂×D₈×C₈₉	—	2	4	no	—
100	C₂×D₈×C₈₉	C₂³	1	2	yes	—
101	C₂×D₈×C₈₉	C₂³	1	4	yes	—
102	C₂×D₈×C₈₉	C₂³	1	2	yes	—
103	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₈₉	—	2	4	no	—
105	C₂×M₁₆×C₈₉	—	2	4	no	—
106	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
115	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₉	—	2	2	no	—
117	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
118	#127×C₈₉	C₂³	1	4	yes	—
119	#126×C₈₉	—	2	4	no	—
120	#126×C₈₉	—	2	4	no	—
121	#125×C₈₉	—	2	2	no	—
122	#125×C₈₉	C₂³	1	4	yes	—
123	#124×C₈₉	—	2	4	no	—
124	#124×C₈₉	—	2	4	no	—
125	#124×C₈₉	C₂³	1	4	yes	—
126	#123×C₈₉	—	2	2	no	—
127	#123×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	4	no	—
130	#123×C₈₉	—	2	4	no	—
131	C₂²⋊Q₈×C₈₉	—	2	4	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
135	#121×C₈₉	—	2	2	no	—
136	#121×C₈₉	—	2	2	no	—
137	#121×C₈₉	—	2	4	no	—
138	#121×C₈₉	—	2	2	no	—
139	#121×C₈₉	—	2	2	no	—
140	#121×C₈₉	—	2	4	no	—
141	#121×C₈₉	—	2	4	no	—
142	#121×C₈₉	C₂³	1	4	yes	—
143	#121×C₈₉	C₂³	1	2	yes	—
144	#121×C₈₉	C₂³	1	4	yes	—
145	#121×C₈₉	C₂³	1	2	yes	—
146	#120×C₈₉	—	2	2	no	—
147	#120×C₈₉	—	2	4	no	—
148	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	4	no	—
152	C₄×D₄×C₈₉	—	2	2	no	—
153	C₄×D₄×C₈₉	—	2	2	no	—
154	C₄×D₄×C₈₉	—	2	4	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	C₂³	1	4	yes	—
157	C₄×D₄×C₈₉	C₂³	1	4	yes	—
158	C₄×D₄×C₈₉	C₂³	1	4	yes	—
159	#117×C₈₉	—	2	2	no	—
160	#117×C₈₉	—	2	4	no	—
161	#117×C₈₉	D₄	1	2	yes	—
162	#117×C₈₉	D₄	1	2	yes	—
163	#117×C₈₉	C₂³	1	2	yes	—
164	#117×C₈₉	C₂³	1	1	yes	characteristic
165	#117×C₈₉	C₂³	1	1	yes	characteristic
166	#117×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
168	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
171	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
172	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
173	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
174	#107×C₈₉	C₂³	1	2	yes	—
175	#107×C₈₉	C₂³	1	4	yes	—
176	#106×C₈₉	C₂³	1	2	yes	—
177	#106×C₈₉	C₂³	1	2	yes	—
178	#106×C₈₉	C₂³	1	1	yes	characteristic
179	#106×C₈₉	C₂³	1	1	yes	characteristic
180	#106×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	2	yes	—
182	#103×C₈₉	C₂³	1	2	yes	—
183	#103×C₈₉	C₂³	1	4	yes	—
184	#102×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	#102×C₈₉	C₂³	1	2	yes	—
187	#102×C₈₉	C₂³	1	2	yes	—
188	#102×C₈₉	C₂³	1	4	yes	—
189	#102×C₈₉	C₂³	1	4	yes	—
190	#102×C₈₉	C₂³	1	4	yes	—
191	#97×C₈₉	C₂³	1	2	yes	—
192	#97×C₈₉	C₂³	1	2	yes	—
193	#97×C₈₉	C₂³	1	2	yes	—
194	#97×C₈₉	C₂³	1	2	yes	—
195	C₄×C₈×C₈₉	C₂³	1	2	yes	—
196	C₄×C₈×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	C₄×C₈×C₈₉	C₂³	1	2	yes	—
199	C₂⁴×C₈₉	—	2	2	no	—
200	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
201	#41×C₈₉	—	2	4	no	—
202	#41×C₈₉	—	2	4	no	—
203	#41×C₈₉	—	8	8	no	—
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
206	C₂×D₄×C₈₉	—	2	2	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	2	4	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	4	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	4	no	—
216	C₂×D₄×C₈₉	—	8	4	no	—
217	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
218	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	2	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	2	4	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₈₉	—	2	2	no	—
234	SD₁₆×C₈₉	—	2	4	no	—
235	SD₁₆×C₈₉	—	2	8	no	—
236	D₈×C₈₉	—	2	4	no	—
237	D₈×C₈₉	—	2	4	no	—
238	D₈×C₈₉	—	2	2	no	—
239	D₈×C₈₉	—	2	8	no	—
240	M₁₆×C₈₉	—	2	2	no	—
241	M₁₆×C₈₉	—	2	4	no	—
242	M₁₆×C₈₉	—	2	2	no	—
243	M₁₆×C₈₉	—	2	2	no	—
244	M₁₆×C₈₉	—	2	2	no	—
245	M₁₆×C₈₉	—	2	2	no	—
246	M₁₆×C₈₉	#41	1	4	yes	complemented
247	C₂×C₈×C₈₉	—	2	2	no	—
248	C₂×C₈×C₈₉	—	2	4	no	—
249	C₂×C₈×C₈₉	#41	1	4	yes	complemented
250	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
252	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
255	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	—	2	4	no	—
260	C₄⋊C₄×C₈₉	—	2	4	no	—
261	C₄⋊C₄×C₈₉	—	2	4	no	—
262	C₄⋊C₄×C₈₉	—	2	2	no	—
263	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
266	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₈₉	—	2	2	no	—
270	C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₂²⋊C₄×C₈₉	—	2	4	no	—
277	C₂²⋊C₄×C₈₉	—	2	4	no	—
278	C₂²⋊C₄×C₈₉	—	2	2	no	—
279	C₂²⋊C₄×C₈₉	—	2	4	no	—
280	C₂²⋊C₄×C₈₉	—	2	2	no	—
281	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
284	C₄²×C₈₉	—	2	4	no	—
285	C₄²×C₈₉	—	2	2	no	—
286	C₄²×C₈₉	C₂×D₄	1	4	yes	—
287	C₄²×C₈₉	C₂⁴	1	2	yes	—
288	C₄²×C₈₉	C₂⁴	1	2	yes	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	4	no	—
291	C₂³×C₈₉	—	2	2	no	—
292	C₂³×C₈₉	—	4	2	no	—
293	C₂³×C₈₉	—	4	4	no	—
294	C₂³×C₈₉	—	8	2	no	—
295	C₂³×C₈₉	—	8	2	no	—
296	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₈₉	—	2	2	no	—
300	Q₈×C₈₉	—	2	2	no	—
301	Q₈×C₈₉	—	8	4	no	—
302	D₄×C₈₉	—	2	4	no	—
303	D₄×C₈₉	—	2	2	no	—
304	D₄×C₈₉	—	2	4	no	—
305	D₄×C₈₉	—	2	2	no	—
306	D₄×C₈₉	—	4	8	no	—
307	D₄×C₈₉	—	4	4	no	—
308	D₄×C₈₉	—	4	4	no	—
309	D₄×C₈₉	—	4	4	no	—
310	D₄×C₈₉	—	8	4	no	—
311	D₄×C₈₉	—	8	4	no	—
312	D₄×C₈₉	—	8	2	no	—
313	D₄×C₈₉	—	8	4	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	4	no	—
325	C₂×C₄×C₈₉	—	4	4	no	—
326	C₂×C₄×C₈₉	—	4	4	no	—
327	C₂×C₄×C₈₉	—	8	4	no	—
328	C₂×C₄×C₈₉	—	8	4	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	2	no	—
331	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
339	C₈×C₈₉	—	2	1	no	—
340	C₈×C₈₉	—	2	1	no	—
341	C₈×C₈₉	—	2	2	no	—
342	C₈×C₈₉	C₂×#41	1	4	yes	—
343	C₈×C₈₉	C₂×#41	1	2	yes	—
344	C₈×C₈₉	C₂×#41	1	2	yes	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	1	no	—
349	C₂²×C₈₉	—	2	1	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	4	no	—
352	C₂²×C₈₉	—	4	4	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	—	4	2	no	—
355	C₂²×C₈₉	—	4	4	no	—
356	C₂²×C₈₉	—	8	2	no	—
357	C₂²×C₈₉	—	16	4	no	—
358	C₂²×C₈₉	#532	1	2	yes	—
359	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₈₉	—	2	4	no	—
361	C₄×C₈₉	—	2	4	no	—
362	C₄×C₈₉	—	2	1	no	—
363	C₄×C₈₉	—	2	1	no	—
364	C₄×C₈₉	—	4	4	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	2	no	—
368	C₄×C₈₉	#532	1	2	yes	—
369	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
370	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
371	#60710	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
372	C₂×C₈₉	—	2	2	no	—
373	C₂×C₈₉	—	4	1	no	—
374	C₂×C₈₉	—	4	1	no	—
375	C₂×C₈₉	—	8	2	no	—
376	C₂×C₈₉	—	8	4	no	—
377	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
378	C₂×C₈₉	#3585	1	2	yes	—
379	#3494	C₂×C₈₉	1	2	yes	complemented
380	#3184	C₂×C₈₉	1	2	yes	complemented
381	#3183	C₂×C₈₉	1	2	yes	complemented
382	#3179	C₂×C₈₉	1	4	yes	complemented
383	#3176	C₂×C₈₉	1	2	yes	complemented
384	#3173	C₂×C₈₉	1	2	yes	complemented
385	#3171	C₂×C₈₉	1	4	yes	complemented
386	#3163	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#3155	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#3136	C₂×C₈₉	1	2	yes	complemented
389	#3055	C₂×C₈₉	1	2	yes	complemented
390	#3054	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#2952	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#2948	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2946	C₂×C₈₉	1	2	yes	complemented
395	#2873	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₈₉	#60710	1	1	yes	characteristic, direct product factor, Sylow
397	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
398	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
399	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
400	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
401	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
402	#555	—	2	2	no	—
403	#553	—	2	2	no	—
404	#553	—	2	2	no	—
405	#551	—	2	4	no	—
406	#547	—	2	2	no	—
407	#546	—	2	4	no	—
408	#544	C₂²×C₈₉	1	2	yes	—
409	#542	C₂²×C₈₉	1	4	yes	complemented
410	#540	C₂²×C₈₉	1	4	yes	complemented
411	#535	C₂²×C₈₉	1	2	yes	—
412	#532	C₂²×C₈₉	1	4	yes	complemented
413	#529	C₂²×C₈₉	1	4	yes	complemented
414	#525	C₂²×C₈₉	1	2	yes	—
415	C₂×#121	C₂²×C₈₉	1	2	yes	—
416	#520	C₂²×C₈₉	1	2	yes	—
417	#518	C₂²×C₈₉	1	2	yes	—
418	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
419	#501	C₂²×C₈₉	1	4	yes	complemented
420	#499	C₂²×C₈₉	1	2	yes	complemented
421	#498	C₂²×C₈₉	1	2	yes	complemented
422	#496	C₂²×C₈₉	1	4	yes	complemented
423	#495	C₂²×C₈₉	1	2	yes	complemented
424	#493	C₂²×C₈₉	1	2	yes	complemented
425	#490	C₂²×C₈₉	1	4	yes	complemented
426	#489	C₂²×C₈₉	1	4	yes	complemented
427	#488	C₂²×C₈₉	1	4	yes	complemented
428	#486	C₂²×C₈₉	1	4	yes	complemented
429	#470	C₂²×C₈₉	1	1	yes	characteristic, complemented
430	#470	C₂²×C₈₉	1	1	yes	characteristic, complemented
431	#469	C₂²×C₈₉	1	2	yes	—
432	#469	C₂²×C₈₉	1	2	yes	—
433	#469	C₂²×C₈₉	1	2	yes	—
434	#469	C₂²×C₈₉	1	2	yes	—
435	#469	C₂²×C₈₉	1	4	yes	complemented
436	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
437	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
438	#468	C₂²×C₈₉	1	2	yes	complemented
439	#468	C₂²×C₈₉	1	4	yes	complemented
440	#468	C₂²×C₈₉	1	2	yes	complemented
441	#466	C₂²×C₈₉	1	4	yes	complemented
442	#465	C₂²×C₈₉	1	4	yes	complemented
443	#442	C₂²×C₈₉	1	2	yes	complemented
444	#442	C₂²×C₈₉	1	2	yes	complemented
445	#442	C₂²×C₈₉	1	2	yes	complemented
446	#442	C₂²×C₈₉	1	4	yes	complemented
447	#441	C₂²×C₈₉	1	2	yes	complemented
448	#440	C₂²×C₈₉	1	4	yes	complemented
449	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
450	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
451	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
452	C₄×D₈	C₂²×C₈₉	1	4	yes	complemented
453	#428	C₂²×C₈₉	1	2	yes	—
454	#427	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
456	#418	C₂²×C₈₉	1	2	yes	—
457	#417	C₂²×C₈₉	1	2	yes	—
458	#416	C₂²×C₈₉	1	2	yes	—
459	C₂×#102	C₂²×C₈₉	1	2	yes	—
460	#405	C₂²×C₈₉	1	1	yes	characteristic
461	#405	C₂²×C₈₉	1	1	yes	characteristic
462	#405	C₂²×C₈₉	1	1	yes	characteristic
463	#405	C₂²×C₈₉	1	1	yes	characteristic
464	#405	C₂²×C₈₉	1	2	yes	complemented
465	#405	C₂²×C₈₉	1	2	yes	complemented
466	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
467	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
468	C₂×#41	—	2	4	no	—
469	C₂×#41	C₂³×C₈₉	1	2	yes	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
473	AGL(1,ℤ/8)	—	2	8	no	—
474	#135	—	2	4	no	—
475	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
476	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
477	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
478	C₂×D₈	—	2	4	no	—
479	C₂×D₈	C₂³×C₈₉	1	2	yes	—
480	C₂×D₈	C₂³×C₈₉	1	2	yes	—
481	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
482	C₂×D₈	C₂³×C₈₉	1	4	yes	—
483	C₂×M₁₆	—	2	4	no	—
484	C₂×M₁₆	—	2	4	no	—
485	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
487	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
491	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
494	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
497	#127	C₂³×C₈₉	1	4	yes	—
498	#126	—	2	4	no	—
499	#126	—	2	4	no	—
500	#125	—	2	2	no	—
501	#125	C₂³×C₈₉	1	4	yes	—
502	#124	—	2	4	no	—
503	#124	—	2	4	no	—
504	#124	C₂³×C₈₉	1	4	yes	—
505	#123	—	2	2	no	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
513	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	4	no	—
520	#121	—	2	4	no	—
521	#121	C₂³×C₈₉	1	4	yes	—
522	#121	C₂³×C₈₉	1	4	yes	—
523	#121	C₂³×C₈₉	1	2	yes	—
524	#121	C₂³×C₈₉	1	2	yes	—
525	#120	—	2	2	no	—
526	#120	—	2	4	no	—
527	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	C₂³×C₈₉	1	4	yes	—
536	C₄×D₄	C₂³×C₈₉	1	4	yes	—
537	C₄×D₄	C₂³×C₈₉	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	4	no	—
540	#117	D₄×C₈₉	1	2	yes	—
541	#117	D₄×C₈₉	1	2	yes	—
542	#117	C₂³×C₈₉	1	2	yes	—
543	#117	C₂³×C₈₉	1	1	yes	characteristic
544	#117	C₂³×C₈₉	1	1	yes	characteristic
545	#117	C₂³×C₈₉	1	2	yes	—
546	C₂×C₄⋊C₄	—	2	2	no	—
547	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	—	2	4	no	—
551	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
553	#107	C₂³×C₈₉	1	2	yes	—
554	#107	C₂³×C₈₉	1	4	yes	—
555	#106	C₂³×C₈₉	1	2	yes	—
556	#106	C₂³×C₈₉	1	2	yes	—
557	#106	C₂³×C₈₉	1	1	yes	characteristic
558	#106	C₂³×C₈₉	1	1	yes	characteristic
559	#106	C₂³×C₈₉	1	4	yes	—
560	#103	C₂³×C₈₉	1	2	yes	—
561	#103	C₂³×C₈₉	1	2	yes	—
562	#103	C₂³×C₈₉	1	4	yes	—
563	#102	C₂³×C₈₉	1	4	yes	—
564	#102	C₂³×C₈₉	1	4	yes	—
565	#102	C₂³×C₈₉	1	2	yes	—
566	#102	C₂³×C₈₉	1	2	yes	—
567	#102	C₂³×C₈₉	1	4	yes	—
568	#102	C₂³×C₈₉	1	4	yes	—
569	#102	C₂³×C₈₉	1	4	yes	—
570	#97	C₂³×C₈₉	1	2	yes	—
571	#97	C₂³×C₈₉	1	2	yes	—
572	#97	C₂³×C₈₉	1	2	yes	—
573	#97	C₂³×C₈₉	1	2	yes	—
574	C₄×C₈	C₂³×C₈₉	1	2	yes	—
575	C₄×C₈	C₂³×C₈₉	1	2	yes	—
576	C₄×C₈	C₂³×C₈₉	1	2	yes	—
577	C₄×C₈	C₂³×C₈₉	1	2	yes	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	#41	—	8	8	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	8	4	no	—
596	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
597	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
612	Q₁₆	—	2	2	no	—
613	SD₁₆	—	2	4	no	—
614	SD₁₆	—	2	8	no	—
615	D₈	—	2	4	no	—
616	D₈	—	2	4	no	—
617	D₈	—	2	2	no	—
618	D₈	—	2	8	no	—
619	M₁₆	—	2	2	no	—
620	M₁₆	—	2	4	no	—
621	M₁₆	—	2	2	no	—
622	M₁₆	—	2	2	no	—
623	M₁₆	—	2	2	no	—
624	M₁₆	—	2	2	no	—
625	M₁₆	#41×C₈₉	1	4	yes	complemented
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	4	no	—
628	C₂×C₈	#41×C₈₉	1	4	yes	complemented
629	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
631	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
634	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
644	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
645	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
646	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
661	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
662	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	2	no	—
665	C₄²	C₂×D₄×C₈₉	1	4	yes	—
666	C₄²	C₂⁴×C₈₉	1	2	yes	—
667	C₄²	C₂⁴×C₈₉	1	2	yes	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	8	2	no	—
675	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
676	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
677	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	8	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	8	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
711	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
713	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
716	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
717	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
718	C₈	—	2	1	no	—
719	C₈	—	2	1	no	—
720	C₈	—	2	2	no	—
721	C₈	C₂×#41×C₈₉	1	4	yes	—
722	C₈	C₂×#41×C₈₉	1	2	yes	—
723	C₈	C₂×#41×C₈₉	1	2	yes	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	16	4	no	—
737	C₂²	#532×C₈₉	1	2	yes	—
738	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
739	C₄	—	2	4	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	4	4	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	#532×C₈₉	1	2	yes	—
748	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
749	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
750	C₂	—	2	2	no	—
751	C₂	—	4	1	no	—
752	C₂	—	4	1	no	—
753	C₂	—	8	2	no	—
754	C₂	—	8	4	no	—
755	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
756	C₂	C₈₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3494	C₂	semidirect
2. C₈₉×#3184	C₂	semidirect
3. C₈₉×#3183	C₂	semidirect
4. C₈₉×#3179	C₂	semidirect
5. C₈₉×#3176	C₂	semidirect
6. C₈₉×#3173	C₂	semidirect
7. C₈₉×#3171	C₂	semidirect
8. C₈₉×#3163	C₂	semidirect
9. C₈₉×#3155	C₂	semidirect
10. C₈₉×#3136	C₂	semidirect
11. C₈₉×#3055	C₂	semidirect
12. C₈₉×#3054	C₂	semidirect
13. C₂×#469×C₈₉	C₂	semidirect
14. C₈₉×#2952	C₂	semidirect
15. C₈₉×#2948	C₂	semidirect
16. C₈₉×#2946	C₂	semidirect
17. C₈₉×#2873	C₂	semidirect
30. #542×C₈₉	C₂²	semidirect
31. #540×C₈₉	C₂²	semidirect
33. #532×C₈₉	C₂²	semidirect
34. #529×C₈₉	C₂²	semidirect
40. #501×C₈₉	C₂²	semidirect
41. #499×C₈₉	C₂²	semidirect
42. #498×C₈₉	C₂²	semidirect
43. #496×C₈₉	C₂²	semidirect
44. #495×C₈₉	C₂²	semidirect
45. #493×C₈₉	C₂²	semidirect
46. #490×C₈₉	C₂²	semidirect
47. #489×C₈₉	C₂²	semidirect
48. #488×C₈₉	C₂²	semidirect
49. #486×C₈₉	C₂²	semidirect
50. #470×C₈₉	C₂²	semidirect
51. #470×C₈₉	C₂²	semidirect
56. #469×C₈₉	C₂²	semidirect
57. #469×C₈₉	C₂²	semidirect
58. #469×C₈₉	C₂²	semidirect
59. #468×C₈₉	C₂²	semidirect
60. #468×C₈₉	C₂²	semidirect
61. #468×C₈₉	C₂²	semidirect
62. #466×C₈₉	C₂²	semidirect
63. #465×C₈₉	C₂²	semidirect
64. #442×C₈₉	C₂²	semidirect
65. #442×C₈₉	C₂²	semidirect
66. #442×C₈₉	C₂²	semidirect
67. #442×C₈₉	C₂²	semidirect
68. #441×C₈₉	C₂²	semidirect
69. #440×C₈₉	C₂²	semidirect
70. C₄×SD₁₆×C₈₉	C₂²	semidirect
71. C₄×SD₁₆×C₈₉	C₂²	semidirect
72. C₄×D₈×C₈₉	C₂²	semidirect
73. C₄×D₈×C₈₉	C₂²	semidirect
85. #405×C₈₉	C₂²	semidirect
86. #405×C₈₉	C₂²	semidirect
87. C₄×M₁₆×C₈₉	C₂²	semidirect
88. C₄×M₁₆×C₈₉	C₂²	semidirect
246. M₁₆×C₈₉	#41	semidirect
249. C₂×C₈×C₈₉	#41	semidirect
371. #60710	C₈₉	direct (N × H)
379. #3494	C₂×C₈₉	semidirect
380. #3184	C₂×C₈₉	semidirect
381. #3183	C₂×C₈₉	semidirect
382. #3179	C₂×C₈₉	semidirect
383. #3176	C₂×C₈₉	semidirect
384. #3173	C₂×C₈₉	semidirect
385. #3171	C₂×C₈₉	semidirect
386. #3163	C₂×C₈₉	semidirect
387. #3155	C₂×C₈₉	semidirect
388. #3136	C₂×C₈₉	semidirect
389. #3055	C₂×C₈₉	semidirect
390. #3054	C₂×C₈₉	semidirect
391. C₂×#469	C₂×C₈₉	semidirect
392. #2952	C₂×C₈₉	semidirect
393. #2948	C₂×C₈₉	semidirect
394. #2946	C₂×C₈₉	semidirect
395. #2873	C₂×C₈₉	semidirect
396. C₈₉	#60710	direct (N × H)
409. #542	C₂²×C₈₉	semidirect
410. #540	C₂²×C₈₉	semidirect
412. #532	C₂²×C₈₉	semidirect
413. #529	C₂²×C₈₉	semidirect
419. #501	C₂²×C₈₉	semidirect
420. #499	C₂²×C₈₉	semidirect
421. #498	C₂²×C₈₉	semidirect
422. #496	C₂²×C₈₉	semidirect
423. #495	C₂²×C₈₉	semidirect
424. #493	C₂²×C₈₉	semidirect
425. #490	C₂²×C₈₉	semidirect
426. #489	C₂²×C₈₉	semidirect
427. #488	C₂²×C₈₉	semidirect
428. #486	C₂²×C₈₉	semidirect
429. #470	C₂²×C₈₉	semidirect
430. #470	C₂²×C₈₉	semidirect
435. #469	C₂²×C₈₉	semidirect
436. #469	C₂²×C₈₉	semidirect
437. #469	C₂²×C₈₉	semidirect
438. #468	C₂²×C₈₉	semidirect
439. #468	C₂²×C₈₉	semidirect
440. #468	C₂²×C₈₉	semidirect
441. #466	C₂²×C₈₉	semidirect
442. #465	C₂²×C₈₉	semidirect
443. #442	C₂²×C₈₉	semidirect
444. #442	C₂²×C₈₉	semidirect
445. #442	C₂²×C₈₉	semidirect
446. #442	C₂²×C₈₉	semidirect
447. #441	C₂²×C₈₉	semidirect
448. #440	C₂²×C₈₉	semidirect
449. C₄×SD₁₆	C₂²×C₈₉	semidirect
450. C₄×SD₁₆	C₂²×C₈₉	semidirect
451. C₄×D₈	C₂²×C₈₉	semidirect
452. C₄×D₈	C₂²×C₈₉	semidirect
464. #405	C₂²×C₈₉	semidirect
465. #405	C₂²×C₈₉	semidirect
466. C₄×M₁₆	C₂²×C₈₉	semidirect
467. C₄×M₁₆	C₂²×C₈₉	semidirect
625. M₁₆	#41×C₈₉	semidirect
628. C₂×C₈	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3494	2
C₈₉×#3184	2
C₈₉×#3183	2
C₈₉×#3179	2
C₈₉×#3176	2
C₈₉×#3173	2
C₈₉×#3171	2
C₈₉×#3163	2
C₈₉×#3155	2
C₈₉×#3136	2
C₈₉×#3055	2
C₈₉×#3054	2
C₂×#469×C₈₉	2
C₈₉×#2952	2
C₈₉×#2948	2
C₈₉×#2946	2
C₈₉×#2873	2
#60710	89

Subgroups — C89×#60710 #36438558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60710 #36438558