Subgroups — C₈₉×#60937 #36438785

Order 22784.

1878 conjugacy classes of subgroups.

The subgroup lattice has 726 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×#3263	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3259	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3257	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3256	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3253	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3251	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3084	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3081	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3055	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#469×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3045	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3041	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
17	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	#555×C₈₉	—	2	2	no	—
22	#553×C₈₉	—	2	2	no	—
23	#553×C₈₉	—	2	2	no	—
24	#551×C₈₉	—	2	4	no	—
25	#547×C₈₉	—	2	2	no	—
26	#546×C₈₉	—	2	4	no	—
27	#544×C₈₉	C₂²	1	2	yes	—
28	#542×C₈₉	C₂²	1	4	yes	complemented
29	#540×C₈₉	C₂²	1	4	yes	complemented
30	#535×C₈₉	C₂²	1	2	yes	—
31	#532×C₈₉	C₂²	1	4	yes	complemented
32	#529×C₈₉	C₂²	1	4	yes	complemented
33	#525×C₈₉	C₂²	1	2	yes	—
34	C₂×#121×C₈₉	C₂²	1	2	yes	—
35	#520×C₈₉	C₂²	1	2	yes	—
36	#518×C₈₉	C₂²	1	2	yes	—
37	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
38	#479×C₈₉	C₂²	1	4	yes	complemented
39	#478×C₈₉	C₂²	1	4	yes	complemented
40	#478×C₈₉	C₂²	1	4	yes	complemented
41	#478×C₈₉	C₂²	1	4	yes	complemented
42	#476×C₈₉	C₂²	1	4	yes	complemented
43	#476×C₈₉	C₂²	1	4	yes	complemented
44	#475×C₈₉	C₂²	1	4	yes	complemented
45	#474×C₈₉	C₂²	1	4	yes	complemented
46	#470×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#470×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	#469×C₈₉	C₂²	1	2	yes	—
49	#469×C₈₉	C₂²	1	2	yes	—
50	#469×C₈₉	C₂²	1	2	yes	—
51	#469×C₈₉	C₂²	1	2	yes	—
52	#469×C₈₉	C₂²	1	4	yes	complemented
53	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#468×C₈₉	C₂²	1	2	yes	complemented
56	#468×C₈₉	C₂²	1	4	yes	complemented
57	#468×C₈₉	C₂²	1	2	yes	complemented
58	#466×C₈₉	C₂²	1	4	yes	complemented
59	#465×C₈₉	C₂²	1	4	yes	complemented
60	#464×C₈₉	C₂²	1	4	yes	complemented
61	#463×C₈₉	C₂²	1	4	yes	complemented
62	#463×C₈₉	C₂²	1	4	yes	complemented
63	#463×C₈₉	C₂²	1	4	yes	complemented
64	#460×C₈₉	C₂²	1	4	yes	complemented
65	#459×C₈₉	C₂²	1	4	yes	complemented
66	#459×C₈₉	C₂²	1	4	yes	complemented
67	#459×C₈₉	C₂²	1	4	yes	complemented
68	#428×C₈₉	C₂²	1	2	yes	—
69	#427×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
71	#424×C₈₉	C₂²	1	2	yes	—
72	#424×C₈₉	C₂²	1	2	yes	—
73	#424×C₈₉	C₂²	1	2	yes	complemented
74	#424×C₈₉	C₂²	1	2	yes	complemented
75	#423×C₈₉	C₂²	1	2	yes	complemented
76	#423×C₈₉	C₂²	1	2	yes	complemented
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	C₂×#41×C₈₉	—	2	4	no	—
82	C₂×#41×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	—	2	2	no	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
86	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
87	#135×C₈₉	—	4	2	no	—
88	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
91	C₂×D₈×C₈₉	—	4	2	no	—
92	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×D₈×C₈₉	C₂³	1	4	yes	—
94	C₂×D₈×C₈₉	C₂³	1	2	yes	—
95	C₂×D₈×C₈₉	C₂³	1	2	yes	—
96	C₂×M₁₆×C₈₉	—	4	2	no	—
97	C₂×M₁₆×C₈₉	—	4	2	no	—
98	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
101	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₈₉	—	2	2	no	—
108	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
109	#127×C₈₉	C₂³	1	4	yes	—
110	#126×C₈₉	—	2	4	no	—
111	#126×C₈₉	—	2	4	no	—
112	#125×C₈₉	—	2	2	no	—
113	#125×C₈₉	C₂³	1	4	yes	—
114	#124×C₈₉	—	2	4	no	—
115	#124×C₈₉	—	2	4	no	—
116	#124×C₈₉	C₂³	1	4	yes	—
117	#123×C₈₉	—	2	2	no	—
118	#123×C₈₉	—	2	4	no	—
119	#123×C₈₉	—	2	4	no	—
120	#123×C₈₉	—	2	4	no	—
121	#123×C₈₉	—	2	4	no	—
122	C₂²⋊Q₈×C₈₉	—	2	4	no	—
123	C₂²⋊Q₈×C₈₉	—	2	4	no	—
124	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
126	#121×C₈₉	—	2	2	no	—
127	#121×C₈₉	—	2	2	no	—
128	#121×C₈₉	—	2	4	no	—
129	#121×C₈₉	—	2	2	no	—
130	#121×C₈₉	—	2	2	no	—
131	#121×C₈₉	—	2	4	no	—
132	#121×C₈₉	—	2	4	no	—
133	#121×C₈₉	C₂³	1	4	yes	—
134	#121×C₈₉	C₂³	1	2	yes	—
135	#121×C₈₉	C₂³	1	4	yes	—
136	#121×C₈₉	C₂³	1	2	yes	—
137	#120×C₈₉	—	2	2	no	—
138	#120×C₈₉	—	2	4	no	—
139	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	—	2	2	no	—
142	C₄×D₄×C₈₉	—	2	4	no	—
143	C₄×D₄×C₈₉	—	2	2	no	—
144	C₄×D₄×C₈₉	—	2	2	no	—
145	C₄×D₄×C₈₉	—	2	4	no	—
146	C₄×D₄×C₈₉	—	2	4	no	—
147	C₄×D₄×C₈₉	C₂³	1	4	yes	—
148	C₄×D₄×C₈₉	C₂³	1	4	yes	—
149	C₄×D₄×C₈₉	C₂³	1	4	yes	—
150	#117×C₈₉	—	2	2	no	—
151	#117×C₈₉	—	2	4	no	—
152	#117×C₈₉	D₄	1	2	yes	—
153	#117×C₈₉	D₄	1	1	yes	characteristic
154	#117×C₈₉	D₄	1	1	yes	characteristic
155	#117×C₈₉	C₂³	1	2	yes	—
156	#117×C₈₉	C₂³	1	2	yes	—
157	#117×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
159	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	#107×C₈₉	C₂³	1	2	yes	—
166	#107×C₈₉	C₂³	1	4	yes	—
167	#106×C₈₉	C₂³	1	2	yes	—
168	#106×C₈₉	C₂³	1	2	yes	—
169	#106×C₈₉	C₂³	1	1	yes	characteristic
170	#106×C₈₉	C₂³	1	1	yes	characteristic
171	#106×C₈₉	C₂³	1	4	yes	—
172	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
173	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
174	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
175	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
176	#103×C₈₉	C₂³	1	2	yes	—
177	#103×C₈₉	C₂³	1	2	yes	—
178	#103×C₈₉	C₂³	1	4	yes	—
179	#102×C₈₉	C₂³	1	4	yes	—
180	#102×C₈₉	C₂³	1	4	yes	—
181	#102×C₈₉	C₂³	1	2	yes	—
182	#102×C₈₉	C₂³	1	2	yes	—
183	#102×C₈₉	C₂³	1	4	yes	—
184	#102×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	C₂⁴×C₈₉	—	2	2	no	—
187	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
188	#41×C₈₉	—	2	4	no	—
189	#41×C₈₉	—	2	4	no	—
190	#41×C₈₉	—	8	8	no	—
191	C₂×Q₈×C₈₉	—	2	4	no	—
192	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
193	C₂×D₄×C₈₉	—	2	2	no	—
194	C₂×D₄×C₈₉	—	2	2	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	2	no	—
197	C₂×D₄×C₈₉	—	2	4	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	4	no	—
201	C₂×D₄×C₈₉	—	2	4	no	—
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	8	4	no	—
204	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
205	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	—	2	2	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	4	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₈₉	—	4	1	no	—
221	SD₁₆×C₈₉	—	4	2	no	—
222	SD₁₆×C₈₉	—	4	4	no	—
223	D₈×C₈₉	—	4	2	no	—
224	D₈×C₈₉	—	4	2	no	—
225	D₈×C₈₉	—	4	1	no	—
226	D₈×C₈₉	—	4	4	no	—
227	M₁₆×C₈₉	—	2	4	no	—
228	M₁₆×C₈₉	—	4	1	no	—
229	M₁₆×C₈₉	—	4	1	no	—
230	M₁₆×C₈₉	—	4	1	no	—
231	M₁₆×C₈₉	—	4	1	no	—
232	M₁₆×C₈₉	—	4	2	no	—
233	C₂×C₈×C₈₉	—	2	2	no	—
234	C₂×C₈×C₈₉	—	2	2	no	—
235	C₂×C₈×C₈₉	—	4	2	no	—
236	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
239	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	2	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	2	no	—
248	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²⋊C₄×C₈₉	—	2	2	no	—
255	C₂²⋊C₄×C₈₉	—	2	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	2	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	2	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
267	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
269	C₄²×C₈₉	—	2	4	no	—
270	C₄²×C₈₉	—	2	2	no	—
271	C₄²×C₈₉	C₂×D₄	1	2	yes	—
272	C₄²×C₈₉	C₂×D₄	1	2	yes	—
273	C₄²×C₈₉	C₂⁴	1	4	yes	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	4	no	—
276	C₂³×C₈₉	—	2	2	no	—
277	C₂³×C₈₉	—	4	2	no	—
278	C₂³×C₈₉	—	4	4	no	—
279	C₂³×C₈₉	—	8	2	no	—
280	C₂³×C₈₉	—	8	2	no	—
281	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₈₉	—	2	2	no	—
285	Q₈×C₈₉	—	2	2	no	—
286	Q₈×C₈₉	—	8	4	no	—
287	D₄×C₈₉	—	2	4	no	—
288	D₄×C₈₉	—	2	2	no	—
289	D₄×C₈₉	—	2	4	no	—
290	D₄×C₈₉	—	2	2	no	—
291	D₄×C₈₉	—	4	8	no	—
292	D₄×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	4	4	no	—
294	D₄×C₈₉	—	4	4	no	—
295	D₄×C₈₉	—	8	4	no	—
296	D₄×C₈₉	—	8	4	no	—
297	D₄×C₈₉	—	8	2	no	—
298	D₄×C₈₉	—	8	4	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	4	no	—
310	C₂×C₄×C₈₉	—	4	4	no	—
311	C₂×C₄×C₈₉	—	4	4	no	—
312	C₂×C₄×C₈₉	—	8	4	no	—
313	C₂×C₄×C₈₉	—	8	4	no	—
314	C₂×C₄×C₈₉	—	8	4	no	—
315	C₂×C₄×C₈₉	—	8	2	no	—
316	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
322	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
323	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
324	C₈×C₈₉	—	2	1	no	—
325	C₈×C₈₉	—	2	1	no	—
326	C₈×C₈₉	—	2	1	no	—
327	C₈×C₈₉	—	2	1	no	—
328	C₈×C₈₉	—	2	4	no	—
329	C₂²×C₈₉	—	2	2	no	—
330	C₂²×C₈₉	—	2	2	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	1	no	—
333	C₂²×C₈₉	—	2	1	no	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	4	no	—
336	C₂²×C₈₉	—	4	4	no	—
337	C₂²×C₈₉	—	4	2	no	—
338	C₂²×C₈₉	—	4	2	no	—
339	C₂²×C₈₉	—	4	4	no	—
340	C₂²×C₈₉	—	8	2	no	—
341	C₂²×C₈₉	—	16	4	no	—
342	C₂²×C₈₉	#537	1	2	yes	—
343	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
344	C₄×C₈₉	—	2	4	no	—
345	C₄×C₈₉	—	2	4	no	—
346	C₄×C₈₉	—	2	1	no	—
347	C₄×C₈₉	—	2	1	no	—
348	C₄×C₈₉	—	4	4	no	—
349	C₄×C₈₉	—	4	2	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	2	no	—
352	C₄×C₈₉	#537	1	2	yes	—
353	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	#60937	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂×C₈₉	—	2	2	no	—
357	C₂×C₈₉	—	4	1	no	—
358	C₂×C₈₉	—	4	1	no	—
359	C₂×C₈₉	—	8	2	no	—
360	C₂×C₈₉	—	8	4	no	—
361	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
362	C₂×C₈₉	#3585	1	2	yes	—
363	#3494	C₂×C₈₉	1	2	yes	complemented
364	#3263	C₂×C₈₉	1	2	yes	complemented
365	#3259	C₂×C₈₉	1	2	yes	complemented
366	#3257	C₂×C₈₉	1	4	yes	complemented
367	#3256	C₂×C₈₉	1	2	yes	complemented
368	#3253	C₂×C₈₉	1	2	yes	complemented
369	#3251	C₂×C₈₉	1	4	yes	complemented
370	#3084	C₂×C₈₉	1	2	yes	complemented
371	#3081	C₂×C₈₉	1	2	yes	complemented
372	#3055	C₂×C₈₉	1	2	yes	complemented
373	#3054	C₂×C₈₉	1	1	yes	characteristic, complemented
374	C₂×#469	C₂×C₈₉	1	1	yes	characteristic, complemented
375	#3045	C₂×C₈₉	1	2	yes	complemented
376	#3041	C₂×C₈₉	1	2	yes	complemented
377	#2905	C₂×C₈₉	1	1	yes	characteristic, complemented
378	C₈₉	#60937	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
380	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
381	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
382	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
383	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
384	#555	—	2	2	no	—
385	#553	—	2	2	no	—
386	#553	—	2	2	no	—
387	#551	—	2	4	no	—
388	#547	—	2	2	no	—
389	#546	—	2	4	no	—
390	#544	C₂²×C₈₉	1	2	yes	—
391	#542	C₂²×C₈₉	1	4	yes	complemented
392	#540	C₂²×C₈₉	1	4	yes	complemented
393	#535	C₂²×C₈₉	1	2	yes	—
394	#532	C₂²×C₈₉	1	4	yes	complemented
395	#529	C₂²×C₈₉	1	4	yes	complemented
396	#525	C₂²×C₈₉	1	2	yes	—
397	C₂×#121	C₂²×C₈₉	1	2	yes	—
398	#520	C₂²×C₈₉	1	2	yes	—
399	#518	C₂²×C₈₉	1	2	yes	—
400	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
401	#479	C₂²×C₈₉	1	4	yes	complemented
402	#478	C₂²×C₈₉	1	4	yes	complemented
403	#478	C₂²×C₈₉	1	4	yes	complemented
404	#478	C₂²×C₈₉	1	4	yes	complemented
405	#476	C₂²×C₈₉	1	4	yes	complemented
406	#476	C₂²×C₈₉	1	4	yes	complemented
407	#475	C₂²×C₈₉	1	4	yes	complemented
408	#474	C₂²×C₈₉	1	4	yes	complemented
409	#470	C₂²×C₈₉	1	1	yes	characteristic, complemented
410	#470	C₂²×C₈₉	1	1	yes	characteristic, complemented
411	#469	C₂²×C₈₉	1	2	yes	—
412	#469	C₂²×C₈₉	1	2	yes	—
413	#469	C₂²×C₈₉	1	2	yes	—
414	#469	C₂²×C₈₉	1	2	yes	—
415	#469	C₂²×C₈₉	1	4	yes	complemented
416	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
417	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
418	#468	C₂²×C₈₉	1	2	yes	complemented
419	#468	C₂²×C₈₉	1	4	yes	complemented
420	#468	C₂²×C₈₉	1	2	yes	complemented
421	#466	C₂²×C₈₉	1	4	yes	complemented
422	#465	C₂²×C₈₉	1	4	yes	complemented
423	#464	C₂²×C₈₉	1	4	yes	complemented
424	#463	C₂²×C₈₉	1	4	yes	complemented
425	#463	C₂²×C₈₉	1	4	yes	complemented
426	#463	C₂²×C₈₉	1	4	yes	complemented
427	#460	C₂²×C₈₉	1	4	yes	complemented
428	#459	C₂²×C₈₉	1	4	yes	complemented
429	#459	C₂²×C₈₉	1	4	yes	complemented
430	#459	C₂²×C₈₉	1	4	yes	complemented
431	#428	C₂²×C₈₉	1	2	yes	—
432	#427	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
434	#424	C₂²×C₈₉	1	2	yes	—
435	#424	C₂²×C₈₉	1	2	yes	—
436	#424	C₂²×C₈₉	1	2	yes	complemented
437	#424	C₂²×C₈₉	1	2	yes	complemented
438	#423	C₂²×C₈₉	1	2	yes	complemented
439	#423	C₂²×C₈₉	1	2	yes	complemented
440	#418	C₂²×C₈₉	1	2	yes	—
441	#417	C₂²×C₈₉	1	2	yes	—
442	#416	C₂²×C₈₉	1	2	yes	—
443	C₂×#102	C₂²×C₈₉	1	2	yes	—
444	C₂×#41	—	2	4	no	—
445	C₂×#41	C₂³×C₈₉	1	2	yes	—
446	C₂²×D₄	—	2	2	no	—
447	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
448	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
449	AGL(1,ℤ/8)	—	4	4	no	—
450	#135	—	4	2	no	—
451	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
452	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
453	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
454	C₂×D₈	—	4	2	no	—
455	C₂×D₈	C₂³×C₈₉	1	2	yes	—
456	C₂×D₈	C₂³×C₈₉	1	2	yes	—
457	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
458	C₂×D₈	C₂³×C₈₉	1	4	yes	—
459	C₂×M₁₆	—	4	2	no	—
460	C₂×M₁₆	—	4	2	no	—
461	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
462	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
463	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
464	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
465	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
466	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
470	C₄⋊Q₈	—	2	2	no	—
471	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
472	#127	C₂³×C₈₉	1	4	yes	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	C₂³×C₈₉	1	4	yes	—
477	#124	—	2	4	no	—
478	#124	—	2	4	no	—
479	#124	C₂³×C₈₉	1	4	yes	—
480	#123	—	2	2	no	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	#123	—	2	4	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
488	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	4	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	4	no	—
495	#121	—	2	4	no	—
496	#121	C₂³×C₈₉	1	4	yes	—
497	#121	C₂³×C₈₉	1	4	yes	—
498	#121	C₂³×C₈₉	1	2	yes	—
499	#121	C₂³×C₈₉	1	2	yes	—
500	#120	—	2	2	no	—
501	#120	—	2	4	no	—
502	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	4	no	—
510	C₄×D₄	C₂³×C₈₉	1	4	yes	—
511	C₄×D₄	C₂³×C₈₉	1	4	yes	—
512	C₄×D₄	C₂³×C₈₉	1	4	yes	—
513	#117	—	2	2	no	—
514	#117	—	2	4	no	—
515	#117	D₄×C₈₉	1	2	yes	—
516	#117	D₄×C₈₉	1	1	yes	characteristic
517	#117	D₄×C₈₉	1	1	yes	characteristic
518	#117	C₂³×C₈₉	1	2	yes	—
519	#117	C₂³×C₈₉	1	2	yes	—
520	#117	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	C₂×C₂²⋊C₄	—	2	4	no	—
526	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
528	#107	C₂³×C₈₉	1	2	yes	—
529	#107	C₂³×C₈₉	1	4	yes	—
530	#106	C₂³×C₈₉	1	2	yes	—
531	#106	C₂³×C₈₉	1	2	yes	—
532	#106	C₂³×C₈₉	1	1	yes	characteristic
533	#106	C₂³×C₈₉	1	1	yes	characteristic
534	#106	C₂³×C₈₉	1	4	yes	—
535	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
536	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
537	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
538	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
539	#103	C₂³×C₈₉	1	2	yes	—
540	#103	C₂³×C₈₉	1	2	yes	—
541	#103	C₂³×C₈₉	1	4	yes	—
542	#102	C₂³×C₈₉	1	4	yes	—
543	#102	C₂³×C₈₉	1	4	yes	—
544	#102	C₂³×C₈₉	1	2	yes	—
545	#102	C₂³×C₈₉	1	2	yes	—
546	#102	C₂³×C₈₉	1	4	yes	—
547	#102	C₂³×C₈₉	1	4	yes	—
548	#102	C₂³×C₈₉	1	4	yes	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
551	#41	—	2	4	no	—
552	#41	—	2	4	no	—
553	#41	—	8	8	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	8	4	no	—
567	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
568	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
583	Q₁₆	—	4	1	no	—
584	SD₁₆	—	4	2	no	—
585	SD₁₆	—	4	4	no	—
586	D₈	—	4	2	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	1	no	—
589	D₈	—	4	4	no	—
590	M₁₆	—	2	4	no	—
591	M₁₆	—	4	1	no	—
592	M₁₆	—	4	1	no	—
593	M₁₆	—	4	1	no	—
594	M₁₆	—	4	1	no	—
595	M₁₆	—	4	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	4	2	no	—
599	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
600	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
601	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
602	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
603	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
613	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
615	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
630	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
631	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	C₂×D₄×C₈₉	1	2	yes	—
635	C₄²	C₂×D₄×C₈₉	1	2	yes	—
636	C₄²	C₂⁴×C₈₉	1	4	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	4	2	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	8	2	no	—
643	C₂³	—	8	2	no	—
644	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
645	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
646	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
647	Q₈	—	2	2	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	8	4	no	—
650	D₄	—	2	4	no	—
651	D₄	—	2	2	no	—
652	D₄	—	2	4	no	—
653	D₄	—	2	2	no	—
654	D₄	—	4	8	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	4	no	—
658	D₄	—	8	4	no	—
659	D₄	—	8	4	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
684	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
685	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
686	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
687	C₈	—	2	1	no	—
688	C₈	—	2	1	no	—
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	4	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	8	2	no	—
704	C₂²	—	16	4	no	—
705	C₂²	#537×C₈₉	1	2	yes	—
706	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	4	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	#537×C₈₉	1	2	yes	—
716	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
717	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	1	no	—
720	C₂	—	4	1	no	—
721	C₂	—	8	2	no	—
722	C₂	—	8	4	no	—
723	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
724	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×#3263	C₂	semidirect
3. C₈₉×#3259	C₂	semidirect
4. C₈₉×#3257	C₂	semidirect
5. C₈₉×#3256	C₂	semidirect
6. C₈₉×#3253	C₂	semidirect
7. C₈₉×#3251	C₂	semidirect
8. C₈₉×#3084	C₂	semidirect
9. C₈₉×#3081	C₂	semidirect
10. C₈₉×#3055	C₂	semidirect
11. C₈₉×#3054	C₂	semidirect
12. C₂×#469×C₈₉	C₂	semidirect
13. C₈₉×#3045	C₂	semidirect
14. C₈₉×#3041	C₂	semidirect
15. C₈₉×#2905	C₂	semidirect
28. #542×C₈₉	C₂²	semidirect
29. #540×C₈₉	C₂²	semidirect
31. #532×C₈₉	C₂²	semidirect
32. #529×C₈₉	C₂²	semidirect
38. #479×C₈₉	C₂²	semidirect
39. #478×C₈₉	C₂²	semidirect
40. #478×C₈₉	C₂²	semidirect
41. #478×C₈₉	C₂²	semidirect
42. #476×C₈₉	C₂²	semidirect
43. #476×C₈₉	C₂²	semidirect
44. #475×C₈₉	C₂²	semidirect
45. #474×C₈₉	C₂²	semidirect
46. #470×C₈₉	C₂²	semidirect
47. #470×C₈₉	C₂²	semidirect
52. #469×C₈₉	C₂²	semidirect
53. #469×C₈₉	C₂²	semidirect
54. #469×C₈₉	C₂²	semidirect
55. #468×C₈₉	C₂²	semidirect
56. #468×C₈₉	C₂²	semidirect
57. #468×C₈₉	C₂²	semidirect
58. #466×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #463×C₈₉	C₂²	semidirect
62. #463×C₈₉	C₂²	semidirect
63. #463×C₈₉	C₂²	semidirect
64. #460×C₈₉	C₂²	semidirect
65. #459×C₈₉	C₂²	semidirect
66. #459×C₈₉	C₂²	semidirect
67. #459×C₈₉	C₂²	semidirect
73. #424×C₈₉	C₂²	semidirect
74. #424×C₈₉	C₂²	semidirect
75. #423×C₈₉	C₂²	semidirect
76. #423×C₈₉	C₂²	semidirect
355. #60937	C₈₉	direct (N × H)
363. #3494	C₂×C₈₉	semidirect
364. #3263	C₂×C₈₉	semidirect
365. #3259	C₂×C₈₉	semidirect
366. #3257	C₂×C₈₉	semidirect
367. #3256	C₂×C₈₉	semidirect
368. #3253	C₂×C₈₉	semidirect
369. #3251	C₂×C₈₉	semidirect
370. #3084	C₂×C₈₉	semidirect
371. #3081	C₂×C₈₉	semidirect
372. #3055	C₂×C₈₉	semidirect
373. #3054	C₂×C₈₉	semidirect
374. C₂×#469	C₂×C₈₉	semidirect
375. #3045	C₂×C₈₉	semidirect
376. #3041	C₂×C₈₉	semidirect
377. #2905	C₂×C₈₉	semidirect
378. C₈₉	#60937	direct (N × H)
391. #542	C₂²×C₈₉	semidirect
392. #540	C₂²×C₈₉	semidirect
394. #532	C₂²×C₈₉	semidirect
395. #529	C₂²×C₈₉	semidirect
401. #479	C₂²×C₈₉	semidirect
402. #478	C₂²×C₈₉	semidirect
403. #478	C₂²×C₈₉	semidirect
404. #478	C₂²×C₈₉	semidirect
405. #476	C₂²×C₈₉	semidirect
406. #476	C₂²×C₈₉	semidirect
407. #475	C₂²×C₈₉	semidirect
408. #474	C₂²×C₈₉	semidirect
409. #470	C₂²×C₈₉	semidirect
410. #470	C₂²×C₈₉	semidirect
415. #469	C₂²×C₈₉	semidirect
416. #469	C₂²×C₈₉	semidirect
417. #469	C₂²×C₈₉	semidirect
418. #468	C₂²×C₈₉	semidirect
419. #468	C₂²×C₈₉	semidirect
420. #468	C₂²×C₈₉	semidirect
421. #466	C₂²×C₈₉	semidirect
422. #465	C₂²×C₈₉	semidirect
423. #464	C₂²×C₈₉	semidirect
424. #463	C₂²×C₈₉	semidirect
425. #463	C₂²×C₈₉	semidirect
426. #463	C₂²×C₈₉	semidirect
427. #460	C₂²×C₈₉	semidirect
428. #459	C₂²×C₈₉	semidirect
429. #459	C₂²×C₈₉	semidirect
430. #459	C₂²×C₈₉	semidirect
436. #424	C₂²×C₈₉	semidirect
437. #424	C₂²×C₈₉	semidirect
438. #423	C₂²×C₈₉	semidirect
439. #423	C₂²×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×#3263	2
C₈₉×#3259	2
C₈₉×#3257	2
C₈₉×#3256	2
C₈₉×#3253	2
C₈₉×#3251	2
C₈₉×#3084	2
C₈₉×#3081	2
C₈₉×#3055	2
C₈₉×#3054	2
C₂×#469×C₈₉	2
C₈₉×#3045	2
C₈₉×#3041	2
C₈₉×#2905	2
#60937	89

Subgroups — C89×#60937 #36438785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60937 #36438785