Subgroups — C₈₉×#61018 #36438866

Order 22784.

1672 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3258	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3240	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3237	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3218	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3215	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3202	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3200	C₂	1	2	yes	maximal
10	C₈₉×#3181	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3172	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3127	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3123	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3121	C₂	1	4	yes	maximal, complemented
15	C₈₉×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	#559×C₈₉	—	2	2	no	—
17	#557×C₈₉	—	2	2	no	—
18	#556×C₈₉	—	2	2	no	—
19	#556×C₈₉	—	2	2	no	—
20	#552×C₈₉	—	2	2	no	—
21	#552×C₈₉	—	2	2	no	—
22	#551×C₈₉	—	2	2	no	—
23	#551×C₈₉	—	2	2	no	—
24	#542×C₈₉	C₂²	1	2	yes	—
25	#542×C₈₉	C₂²	1	2	yes	—
26	#541×C₈₉	C₂²	1	2	yes	—
27	#541×C₈₉	C₂²	1	2	yes	complemented
28	#536×C₈₉	C₂²	1	2	yes	—
29	#536×C₈₉	C₂²	1	1	yes	characteristic
30	#535×C₈₉	C₂²	1	1	yes	characteristic
31	#533×C₈₉	C₂²	1	2	yes	—
32	#533×C₈₉	C₂²	1	1	yes	characteristic
33	#533×C₈₉	C₂²	1	2	yes	complemented
34	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#529×C₈₉	C₂²	1	2	yes	—
37	#529×C₈₉	C₂²	1	2	yes	—
38	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
39	#519×C₈₉	C₂²	1	1	yes	characteristic
40	#519×C₈₉	C₂²	1	2	yes	complemented
41	#518×C₈₉	C₂²	1	1	yes	characteristic
42	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
43	#501×C₈₉	C₂²	1	2	yes	complemented
44	#501×C₈₉	C₂²	1	2	yes	complemented
45	#497×C₈₉	C₂²	1	2	yes	—
46	#497×C₈₉	C₂²	1	2	yes	—
47	#491×C₈₉	C₂²	1	2	yes	complemented
48	#491×C₈₉	C₂²	1	2	yes	complemented
49	#489×C₈₉	C₂²	1	2	yes	—
50	#489×C₈₉	C₂²	1	2	yes	—
51	#485×C₈₉	C₂²	1	4	yes	—
52	#485×C₈₉	C₂²	1	4	yes	—
53	#485×C₈₉	C₂²	1	4	yes	complemented
54	#482×C₈₉	C₂²	1	4	yes	—
55	#479×C₈₉	C₂²	1	4	yes	complemented
56	#478×C₈₉	C₂²	1	4	yes	—
57	#477×C₈₉	C₂²	1	4	yes	complemented
58	#475×C₈₉	C₂²	1	4	yes	complemented
59	#470×C₈₉	C₂²	1	4	yes	complemented
60	#468×C₈₉	C₂²	1	4	yes	—
61	#467×C₈₉	C₂²	1	4	yes	complemented
62	#465×C₈₉	C₂²	1	4	yes	—
63	#464×C₈₉	C₂²	1	4	yes	—
64	#464×C₈₉	C₂²	1	4	yes	—
65	#462×C₈₉	C₂²	1	4	yes	complemented
66	#461×C₈₉	C₂²	1	4	yes	—
67	#451×C₈₉	C₂²	1	4	yes	—
68	#451×C₈₉	C₂²	1	4	yes	complemented
69	#450×C₈₉	C₂²	1	4	yes	—
70	#448×C₈₉	C₂²	1	4	yes	—
71	#441×C₈₉	C₂²	1	4	yes	complemented
72	#440×C₈₉	C₂²	1	4	yes	—
73	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
75	#433×C₈₉	C₂²	1	2	yes	—
76	#433×C₈₉	C₂²	1	2	yes	complemented
77	#432×C₈₉	C₂²	1	2	yes	—
78	#432×C₈₉	C₂²	1	2	yes	complemented
79	#424×C₈₉	C₂²	1	2	yes	complemented
80	#408×C₈₉	C₂²	1	2	yes	—
81	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
91	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
92	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₈₉	—	2	1	no	—
94	C₄⋊Q₈×C₈₉	—	2	2	no	—
95	C₄⋊Q₈×C₈₉	—	2	2	no	—
96	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
100	#127×C₈₉	—	2	1	no	—
101	#126×C₈₉	—	2	2	no	—
102	#126×C₈₉	—	2	2	no	—
103	#126×C₈₉	—	2	4	no	—
104	#126×C₈₉	—	2	4	no	—
105	#126×C₈₉	—	2	2	no	—
106	#126×C₈₉	—	2	2	no	—
107	#125×C₈₉	—	2	4	no	—
108	#125×C₈₉	—	2	4	no	—
109	#125×C₈₉	—	2	2	no	—
110	#125×C₈₉	—	2	2	no	—
111	#125×C₈₉	C₂³	1	2	yes	—
112	#125×C₈₉	C₂³	1	2	yes	—
113	#124×C₈₉	—	2	1	no	—
114	#124×C₈₉	—	2	2	no	—
115	#124×C₈₉	—	2	1	no	—
116	#124×C₈₉	—	2	2	no	—
117	#124×C₈₉	—	2	2	no	—
118	#124×C₈₉	—	2	2	no	—
119	#124×C₈₉	C₂³	1	2	yes	—
120	#124×C₈₉	C₂³	1	2	yes	—
121	#123×C₈₉	—	2	1	no	—
122	#123×C₈₉	—	2	1	no	—
123	#123×C₈₉	—	2	2	no	—
124	#123×C₈₉	—	2	2	no	—
125	#123×C₈₉	—	2	2	no	—
126	#123×C₈₉	—	2	2	no	—
127	#123×C₈₉	—	2	2	no	—
128	#123×C₈₉	—	2	2	no	—
129	C₂²⋊Q₈×C₈₉	—	2	2	no	—
130	C₂²⋊Q₈×C₈₉	—	2	2	no	—
131	C₂²⋊Q₈×C₈₉	—	2	2	no	—
132	C₂²⋊Q₈×C₈₉	—	2	2	no	—
133	C₂²⋊Q₈×C₈₉	—	2	2	no	—
134	C₂²⋊Q₈×C₈₉	—	2	2	no	—
135	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
137	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	#121×C₈₉	C₂³	1	2	yes	—
140	#121×C₈₉	C₂³	1	2	yes	—
141	#120×C₈₉	—	2	1	no	—
142	#120×C₈₉	—	2	1	no	—
143	C₄×Q₈×C₈₉	—	2	2	no	—
144	C₄×Q₈×C₈₉	—	2	4	no	—
145	C₄×Q₈×C₈₉	—	2	2	no	—
146	C₄×Q₈×C₈₉	—	2	2	no	—
147	C₄×Q₈×C₈₉	—	2	2	no	—
148	C₄×Q₈×C₈₉	—	2	2	no	—
149	C₄×Q₈×C₈₉	D₄	1	2	yes	—
150	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
151	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
152	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
153	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
154	C₄×D₄×C₈₉	—	2	2	no	—
155	C₄×D₄×C₈₉	—	2	2	no	—
156	C₄×D₄×C₈₉	—	2	2	no	—
157	C₄×D₄×C₈₉	D₄	1	2	yes	—
158	C₄×D₄×C₈₉	D₄	1	2	yes	—
159	C₄×D₄×C₈₉	D₄	1	2	yes	—
160	C₄×D₄×C₈₉	C₂³	1	2	yes	—
161	C₄×D₄×C₈₉	C₂³	1	2	yes	—
162	#117×C₈₉	—	2	2	no	—
163	#117×C₈₉	—	2	2	no	—
164	#117×C₈₉	—	2	2	no	—
165	#117×C₈₉	—	2	4	no	—
166	#117×C₈₉	—	2	2	no	—
167	#117×C₈₉	—	2	2	no	—
168	#117×C₈₉	C₂³	1	2	yes	—
169	#117×C₈₉	C₂³	1	1	yes	characteristic
170	#117×C₈₉	C₂³	1	1	yes	characteristic
171	#117×C₈₉	C₂³	1	1	yes	characteristic
172	#117×C₈₉	C₂³	1	1	yes	characteristic
173	#117×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
176	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
177	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
180	#107×C₈₉	C₂³	1	4	yes	—
181	#107×C₈₉	C₂³	1	4	yes	—
182	#106×C₈₉	C₂³	1	4	yes	—
183	#106×C₈₉	C₂³	1	4	yes	—
184	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
185	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
186	#103×C₈₉	C₂³	1	4	yes	—
187	#103×C₈₉	C₂³	1	4	yes	—
188	#103×C₈₉	C₂³	1	4	yes	—
189	#103×C₈₉	C₂³	1	4	yes	—
190	#103×C₈₉	C₂³	1	4	yes	—
191	#103×C₈₉	C₂³	1	4	yes	—
192	#102×C₈₉	C₂³	1	4	yes	—
193	#102×C₈₉	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
196	#97×C₈₉	C₂³	1	2	yes	—
197	#97×C₈₉	C₂³	1	2	yes	—
198	#97×C₈₉	C₂³	1	2	yes	—
199	C₄×C₈×C₈₉	C₂³	1	2	yes	—
200	C₂⁴×C₈₉	—	2	1	no	—
201	#41×C₈₉	—	4	2	no	—
202	C₂×Q₈×C₈₉	—	2	2	no	—
203	C₂×Q₈×C₈₉	—	2	1	no	—
204	C₂×Q₈×C₈₉	—	2	2	no	—
205	C₂×Q₈×C₈₉	—	2	2	no	—
206	C₂×Q₈×C₈₉	—	4	2	no	—
207	C₂×Q₈×C₈₉	—	4	2	no	—
208	C₂×Q₈×C₈₉	—	4	2	no	—
209	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	2	2	no	—
214	C₂×D₄×C₈₉	—	2	1	no	—
215	C₂×D₄×C₈₉	—	4	2	no	—
216	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	—	2	1	no	—
221	C₂²×C₄×C₈₉	—	2	2	no	—
222	C₂²×C₄×C₈₉	—	2	2	no	—
223	C₂²×C₄×C₈₉	—	2	2	no	—
224	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₈₉	—	4	4	no	—
231	Q₁₆×C₈₉	—	4	4	no	—
232	SD₁₆×C₈₉	—	4	4	no	—
233	SD₁₆×C₈₉	—	4	4	no	—
234	M₁₆×C₈₉	—	4	2	no	—
235	C₂×C₈×C₈₉	—	4	2	no	—
236	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
237	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	2	no	—
244	C₄⋊C₄×C₈₉	—	2	2	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	—	2	2	no	—
249	C₄⋊C₄×C₈₉	—	2	2	no	—
250	C₄⋊C₄×C₈₉	—	2	2	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
258	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₈₉	—	2	1	no	—
261	C₂²⋊C₄×C₈₉	—	2	1	no	—
262	C₂²⋊C₄×C₈₉	—	2	2	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂²⋊C₄×C₈₉	—	2	2	no	—
267	C₂²⋊C₄×C₈₉	—	2	2	no	—
268	C₂²⋊C₄×C₈₉	—	2	2	no	—
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	2	no	—
273	C₂²⋊C₄×C₈₉	—	2	2	no	—
274	C₂²⋊C₄×C₈₉	—	2	2	no	—
275	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
278	C₄²×C₈₉	—	2	2	no	—
279	C₄²×C₈₉	—	2	2	no	—
280	C₄²×C₈₉	—	2	4	no	—
281	C₄²×C₈₉	—	2	4	no	—
282	C₄²×C₈₉	—	2	1	no	—
283	C₄²×C₈₉	—	2	1	no	—
284	C₄²×C₈₉	—	2	2	no	—
285	C₄²×C₈₉	C₂×D₄	1	2	yes	—
286	C₄²×C₈₉	C₂×D₄	1	2	yes	—
287	C₄²×C₈₉	C₂×D₄	1	2	yes	—
288	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
290	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂³×C₈₉	—	2	2	no	—
293	C₂³×C₈₉	—	4	2	no	—
294	C₂³×C₈₉	—	8	2	no	—
295	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₈₉	—	2	4	no	—
299	Q₈×C₈₉	—	2	4	no	—
300	Q₈×C₈₉	—	2	4	no	—
301	Q₈×C₈₉	—	4	1	no	—
302	Q₈×C₈₉	—	4	4	no	—
303	Q₈×C₈₉	—	4	2	no	—
304	Q₈×C₈₉	—	4	4	no	—
305	Q₈×C₈₉	—	8	2	no	—
306	D₄×C₈₉	—	2	4	no	—
307	D₄×C₈₉	—	4	1	no	—
308	D₄×C₈₉	—	4	1	no	—
309	D₄×C₈₉	—	4	1	no	—
310	D₄×C₈₉	—	4	2	no	—
311	D₄×C₈₉	—	8	2	no	—
312	D₄×C₈₉	—	8	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	4	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	4	2	no	—
322	C₂×C₄×C₈₉	—	4	2	no	—
323	C₂×C₄×C₈₉	—	4	2	no	—
324	C₂×C₄×C₈₉	—	4	4	no	—
325	C₂×C₄×C₈₉	—	4	2	no	—
326	C₂×C₄×C₈₉	—	8	2	no	—
327	C₂×C₄×C₈₉	—	8	2	no	—
328	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
336	C₈×C₈₉	—	2	4	no	—
337	C₈×C₈₉	—	2	4	no	—
338	C₂²×C₈₉	—	2	2	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	2	2	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	1	no	—
344	C₂²×C₈₉	—	4	2	no	—
345	C₂²×C₈₉	—	4	2	no	—
346	C₂²×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	—	16	2	no	—
348	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	2	2	no	—
351	C₄×C₈₉	—	2	2	no	—
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	1	no	—
355	C₄×C₈₉	—	2	1	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	—	4	2	no	—
358	C₄×C₈₉	—	4	4	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	#585	1	2	yes	—
362	#61018	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
363	C₂×C₈₉	—	4	1	no	—
364	C₂×C₈₉	—	4	1	no	—
365	C₂×C₈₉	—	4	1	no	—
366	C₂×C₈₉	—	8	2	no	—
367	C₂×C₈₉	#3449	1	1	yes	characteristic
368	C₂×C₈₉	#3586	1	2	yes	—
369	#3510	C₂×C₈₉	1	1	yes	characteristic
370	#3509	C₂×C₈₉	1	1	yes	characteristic, complemented
371	#3258	C₂×C₈₉	1	4	yes	complemented
372	#3240	C₂×C₈₉	1	2	yes	complemented
373	#3237	C₂×C₈₉	1	2	yes	complemented
374	#3218	C₂×C₈₉	1	2	yes	complemented
375	#3215	C₂×C₈₉	1	2	yes	complemented
376	#3202	C₂×C₈₉	1	2	yes	complemented
377	#3200	C₂×C₈₉	1	2	yes	—
378	#3181	C₂×C₈₉	1	2	yes	complemented
379	#3172	C₂×C₈₉	1	2	yes	complemented
380	#3127	C₂×C₈₉	1	2	yes	complemented
381	#3123	C₂×C₈₉	1	2	yes	complemented
382	#3121	C₂×C₈₉	1	4	yes	complemented
383	#2923	C₂×C₈₉	1	1	yes	characteristic, complemented
384	C₈₉	#61018	1	1	yes	characteristic, direct product factor, Sylow
385	#559	—	2	2	no	—
386	#557	—	2	2	no	—
387	#556	—	2	2	no	—
388	#556	—	2	2	no	—
389	#552	—	2	2	no	—
390	#552	—	2	2	no	—
391	#551	—	2	2	no	—
392	#551	—	2	2	no	—
393	#542	C₂²×C₈₉	1	2	yes	—
394	#542	C₂²×C₈₉	1	2	yes	—
395	#541	C₂²×C₈₉	1	2	yes	—
396	#541	C₂²×C₈₉	1	2	yes	complemented
397	#536	C₂²×C₈₉	1	2	yes	—
398	#536	C₂²×C₈₉	1	1	yes	characteristic
399	#535	C₂²×C₈₉	1	1	yes	characteristic
400	#533	C₂²×C₈₉	1	2	yes	—
401	#533	C₂²×C₈₉	1	1	yes	characteristic
402	#533	C₂²×C₈₉	1	2	yes	complemented
403	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
404	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
405	#529	C₂²×C₈₉	1	2	yes	—
406	#529	C₂²×C₈₉	1	2	yes	—
407	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
408	#519	C₂²×C₈₉	1	1	yes	characteristic
409	#519	C₂²×C₈₉	1	2	yes	complemented
410	#518	C₂²×C₈₉	1	1	yes	characteristic
411	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
412	#501	C₂²×C₈₉	1	2	yes	complemented
413	#501	C₂²×C₈₉	1	2	yes	complemented
414	#497	C₂²×C₈₉	1	2	yes	—
415	#497	C₂²×C₈₉	1	2	yes	—
416	#491	C₂²×C₈₉	1	2	yes	complemented
417	#491	C₂²×C₈₉	1	2	yes	complemented
418	#489	C₂²×C₈₉	1	2	yes	—
419	#489	C₂²×C₈₉	1	2	yes	—
420	#485	C₂²×C₈₉	1	4	yes	—
421	#485	C₂²×C₈₉	1	4	yes	—
422	#485	C₂²×C₈₉	1	4	yes	complemented
423	#482	C₂²×C₈₉	1	4	yes	—
424	#479	C₂²×C₈₉	1	4	yes	complemented
425	#478	C₂²×C₈₉	1	4	yes	—
426	#477	C₂²×C₈₉	1	4	yes	complemented
427	#475	C₂²×C₈₉	1	4	yes	complemented
428	#470	C₂²×C₈₉	1	4	yes	complemented
429	#468	C₂²×C₈₉	1	4	yes	—
430	#467	C₂²×C₈₉	1	4	yes	complemented
431	#465	C₂²×C₈₉	1	4	yes	—
432	#464	C₂²×C₈₉	1	4	yes	—
433	#464	C₂²×C₈₉	1	4	yes	—
434	#462	C₂²×C₈₉	1	4	yes	complemented
435	#461	C₂²×C₈₉	1	4	yes	—
436	#451	C₂²×C₈₉	1	4	yes	—
437	#451	C₂²×C₈₉	1	4	yes	complemented
438	#450	C₂²×C₈₉	1	4	yes	—
439	#448	C₂²×C₈₉	1	4	yes	—
440	#441	C₂²×C₈₉	1	4	yes	complemented
441	#440	C₂²×C₈₉	1	4	yes	—
442	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
443	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
444	#433	C₂²×C₈₉	1	2	yes	—
445	#433	C₂²×C₈₉	1	2	yes	complemented
446	#432	C₂²×C₈₉	1	2	yes	—
447	#432	C₂²×C₈₉	1	2	yes	complemented
448	#424	C₂²×C₈₉	1	2	yes	complemented
449	#408	C₂²×C₈₉	1	2	yes	—
450	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
451	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
452	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
455	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
456	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
457	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
459	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
460	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
461	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
462	C₄⋊Q₈	—	2	1	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
469	#127	—	2	1	no	—
470	#126	—	2	2	no	—
471	#126	—	2	2	no	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	2	no	—
475	#126	—	2	2	no	—
476	#125	—	2	4	no	—
477	#125	—	2	4	no	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	C₂³×C₈₉	1	2	yes	—
481	#125	C₂³×C₈₉	1	2	yes	—
482	#124	—	2	1	no	—
483	#124	—	2	2	no	—
484	#124	—	2	1	no	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	—	2	2	no	—
488	#124	C₂³×C₈₉	1	2	yes	—
489	#124	C₂³×C₈₉	1	2	yes	—
490	#123	—	2	1	no	—
491	#123	—	2	1	no	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	#123	—	2	2	no	—
495	#123	—	2	2	no	—
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
506	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
507	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
508	#121	C₂³×C₈₉	1	2	yes	—
509	#121	C₂³×C₈₉	1	2	yes	—
510	#120	—	2	1	no	—
511	#120	—	2	1	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	4	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	D₄×C₈₉	1	2	yes	—
519	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
520	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
521	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
522	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	D₄×C₈₉	1	2	yes	—
527	C₄×D₄	D₄×C₈₉	1	2	yes	—
528	C₄×D₄	D₄×C₈₉	1	2	yes	—
529	C₄×D₄	C₂³×C₈₉	1	2	yes	—
530	C₄×D₄	C₂³×C₈₉	1	2	yes	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	—	2	2	no	—
534	#117	—	2	4	no	—
535	#117	—	2	2	no	—
536	#117	—	2	2	no	—
537	#117	C₂³×C₈₉	1	1	yes	characteristic
538	#117	C₂³×C₈₉	1	1	yes	characteristic
539	#117	C₂³×C₈₉	1	2	yes	—
540	#117	C₂³×C₈₉	1	1	yes	characteristic
541	#117	C₂³×C₈₉	1	1	yes	characteristic
542	#117	C₂³×C₈₉	1	1	yes	characteristic
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₂²⋊C₄	—	2	2	no	—
545	C₂×C₂²⋊C₄	—	2	2	no	—
546	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
549	#107	C₂³×C₈₉	1	4	yes	—
550	#107	C₂³×C₈₉	1	4	yes	—
551	#106	C₂³×C₈₉	1	4	yes	—
552	#106	C₂³×C₈₉	1	4	yes	—
553	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
554	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
555	#103	C₂³×C₈₉	1	4	yes	—
556	#103	C₂³×C₈₉	1	4	yes	—
557	#103	C₂³×C₈₉	1	4	yes	—
558	#103	C₂³×C₈₉	1	4	yes	—
559	#103	C₂³×C₈₉	1	4	yes	—
560	#103	C₂³×C₈₉	1	4	yes	—
561	#102	C₂³×C₈₉	1	4	yes	—
562	#102	C₂³×C₈₉	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
565	#97	C₂³×C₈₉	1	2	yes	—
566	#97	C₂³×C₈₉	1	2	yes	—
567	#97	C₂³×C₈₉	1	2	yes	—
568	C₄×C₈	C₂³×C₈₉	1	2	yes	—
569	C₂⁴	—	2	1	no	—
570	#41	—	4	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
579	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
580	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
587	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
588	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
599	Q₁₆	—	4	4	no	—
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	SD₁₆	—	4	4	no	—
603	M₁₆	—	4	2	no	—
604	C₂×C₈	—	4	2	no	—
605	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
606	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	C₂×D₄×C₈₉	1	2	yes	—
655	C₄²	C₂×D₄×C₈₉	1	2	yes	—
656	C₄²	C₂×D₄×C₈₉	1	2	yes	—
657	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
658	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
659	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
660	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	8	2	no	—
664	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
665	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
667	Q₈	—	2	4	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
704	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
705	C₈	—	2	4	no	—
706	C₈	—	2	4	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	16	2	no	—
717	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	4	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	#585×C₈₉	1	2	yes	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	4	1	no	—
734	C₂	—	8	2	no	—
735	C₂	C₈₉×#3449	1	1	yes	characteristic
736	C₂	C₈₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	#535×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3509	C₂	semidirect
3. C₈₉×#3258	C₂	semidirect
4. C₈₉×#3240	C₂	semidirect
5. C₈₉×#3237	C₂	semidirect
6. C₈₉×#3218	C₂	semidirect
7. C₈₉×#3215	C₂	semidirect
8. C₈₉×#3202	C₂	semidirect
10. C₈₉×#3181	C₂	semidirect
11. C₈₉×#3172	C₂	semidirect
12. C₈₉×#3127	C₂	semidirect
13. C₈₉×#3123	C₂	semidirect
14. C₈₉×#3121	C₂	semidirect
15. C₈₉×#2923	C₂	semidirect
27. #541×C₈₉	C₂²	semidirect
33. #533×C₈₉	C₂²	semidirect
34. #533×C₈₉	C₂²	semidirect
35. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
40. #519×C₈₉	C₂²	semidirect
43. #501×C₈₉	C₂²	semidirect
44. #501×C₈₉	C₂²	semidirect
47. #491×C₈₉	C₂²	semidirect
48. #491×C₈₉	C₂²	semidirect
53. #485×C₈₉	C₂²	semidirect
55. #479×C₈₉	C₂²	semidirect
57. #477×C₈₉	C₂²	semidirect
58. #475×C₈₉	C₂²	semidirect
59. #470×C₈₉	C₂²	semidirect
61. #467×C₈₉	C₂²	semidirect
65. #462×C₈₉	C₂²	semidirect
68. #451×C₈₉	C₂²	semidirect
71. #441×C₈₉	C₂²	semidirect
73. C₄×Q₁₆×C₈₉	C₂²	semidirect
76. #433×C₈₉	C₂²	semidirect
78. #432×C₈₉	C₂²	semidirect
79. #424×C₈₉	C₂²	semidirect
81. C₄×M₁₆×C₈₉	C₂²	semidirect
82. C₂×#97×C₈₉	C₂²	semidirect
362. #61018	C₈₉	direct (N × H)
370. #3509	C₂×C₈₉	semidirect
371. #3258	C₂×C₈₉	semidirect
372. #3240	C₂×C₈₉	semidirect
373. #3237	C₂×C₈₉	semidirect
374. #3218	C₂×C₈₉	semidirect
375. #3215	C₂×C₈₉	semidirect
376. #3202	C₂×C₈₉	semidirect
378. #3181	C₂×C₈₉	semidirect
379. #3172	C₂×C₈₉	semidirect
380. #3127	C₂×C₈₉	semidirect
381. #3123	C₂×C₈₉	semidirect
382. #3121	C₂×C₈₉	semidirect
383. #2923	C₂×C₈₉	semidirect
384. C₈₉	#61018	direct (N × H)
396. #541	C₂²×C₈₉	semidirect
402. #533	C₂²×C₈₉	semidirect
403. #533	C₂²×C₈₉	semidirect
404. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
409. #519	C₂²×C₈₉	semidirect
412. #501	C₂²×C₈₉	semidirect
413. #501	C₂²×C₈₉	semidirect
416. #491	C₂²×C₈₉	semidirect
417. #491	C₂²×C₈₉	semidirect
422. #485	C₂²×C₈₉	semidirect
424. #479	C₂²×C₈₉	semidirect
426. #477	C₂²×C₈₉	semidirect
427. #475	C₂²×C₈₉	semidirect
428. #470	C₂²×C₈₉	semidirect
430. #467	C₂²×C₈₉	semidirect
434. #462	C₂²×C₈₉	semidirect
437. #451	C₂²×C₈₉	semidirect
440. #441	C₂²×C₈₉	semidirect
442. C₄×Q₁₆	C₂²×C₈₉	semidirect
445. #433	C₂²×C₈₉	semidirect
447. #432	C₂²×C₈₉	semidirect
448. #424	C₂²×C₈₉	semidirect
450. C₄×M₁₆	C₂²×C₈₉	semidirect
451. C₂×#97	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×#3510	2
C₈₉×#3509	2
C₈₉×#3258	2
C₈₉×#3240	2
C₈₉×#3237	2
C₈₉×#3218	2
C₈₉×#3215	2
C₈₉×#3202	2
C₈₉×#3200	2
C₈₉×#3181	2
C₈₉×#3172	2
C₈₉×#3127	2
C₈₉×#3123	2
C₈₉×#3121	2
C₈₉×#2923	2
#61018	89

Subgroups — C89×#61018 #36438866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61018 #36438866