Subgroups — C₈₉×#60773 #36438621

Order 22784.

2118 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3489	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3204	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3202	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3201	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3197	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3196	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3195	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3099	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3097	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3056	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3013	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3011	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#137×C₈₉	C₂²	1	2	yes	complemented
19	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₈₉	—	2	2	no	—
24	#548×C₈₉	—	2	2	no	—
25	#547×C₈₉	—	2	4	no	—
26	#547×C₈₉	—	2	2	no	—
27	#546×C₈₉	—	2	4	no	—
28	#546×C₈₉	—	2	2	no	—
29	#537×C₈₉	C₂²	1	2	yes	—
30	#537×C₈₉	C₂²	1	4	yes	—
31	#536×C₈₉	C₂²	1	2	yes	—
32	#536×C₈₉	C₂²	1	4	yes	—
33	#525×C₈₉	C₂²	1	4	yes	—
34	#525×C₈₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
36	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
37	#520×C₈₉	C₂²	1	2	yes	—
38	#485×C₈₉	C₂²	1	4	yes	complemented
39	#485×C₈₉	C₂²	1	4	yes	complemented
40	#485×C₈₉	C₂²	1	4	yes	complemented
41	#484×C₈₉	C₂²	1	4	yes	complemented
42	#483×C₈₉	C₂²	1	4	yes	complemented
43	#483×C₈₉	C₂²	1	4	yes	complemented
44	#482×C₈₉	C₂²	1	4	yes	complemented
45	#481×C₈₉	C₂²	1	4	yes	complemented
46	#470×C₈₉	C₂²	1	1	yes	characteristic
47	#470×C₈₉	C₂²	1	4	yes	—
48	#470×C₈₉	C₂²	1	2	yes	—
49	#470×C₈₉	C₂²	1	2	yes	—
50	#470×C₈₉	C₂²	1	2	yes	complemented
51	#470×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#470×C₈₉	C₂²	1	2	yes	complemented
53	#469×C₈₉	C₂²	1	1	yes	characteristic
54	#469×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#468×C₈₉	C₂²	1	2	yes	—
56	#468×C₈₉	C₂²	1	4	yes	—
57	#468×C₈₉	C₂²	1	2	yes	complemented
58	#467×C₈₉	C₂²	1	4	yes	complemented
59	#465×C₈₉	C₂²	1	4	yes	complemented
60	#452×C₈₉	C₂²	1	4	yes	complemented
61	#452×C₈₉	C₂²	1	4	yes	complemented
62	#452×C₈₉	C₂²	1	4	yes	complemented
63	#451×C₈₉	C₂²	1	4	yes	complemented
64	#451×C₈₉	C₂²	1	4	yes	complemented
65	#451×C₈₉	C₂²	1	4	yes	complemented
66	#449×C₈₉	C₂²	1	4	yes	complemented
67	#448×C₈₉	C₂²	1	4	yes	complemented
68	#428×C₈₉	C₂²	1	2	yes	complemented
69	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	#419×C₈₉	C₂²	1	2	yes	complemented
72	#417×C₈₉	C₂²	1	2	yes	complemented
73	#416×C₈₉	C₂²	1	2	yes	complemented
74	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
75	#408×C₈₉	C₂²	1	2	yes	—
76	#408×C₈₉	C₂²	1	2	yes	—
77	#408×C₈₉	C₂²	1	2	yes	—
78	#408×C₈₉	C₂²	1	2	yes	—
79	#407×C₈₉	C₂²	1	2	yes	—
80	#407×C₈₉	C₂²	1	2	yes	—
81	2₋¹⁺⁴×C₈₉	—	4	4	no	—
82	2₋¹⁺⁴×C₈₉	—	4	4	no	—
83	C₂×#41×C₈₉	—	2	4	no	—
84	C₂×#41×C₈₉	—	2	2	no	—
85	C₂×#41×C₈₉	—	4	2	no	—
86	C₂×#41×C₈₉	—	4	2	no	—
87	C₂×#41×C₈₉	D₄	1	2	yes	—
88	C₂×#41×C₈₉	D₄	1	2	yes	—
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂×#41×C₈₉	C₂³	1	4	yes	—
91	C₂×#41×C₈₉	C₂³	1	2	yes	—
92	C₂×#41×C₈₉	C₂³	1	2	yes	—
93	C₂²×Q₈×C₈₉	—	2	2	no	—
94	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
96	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₈₉	D₄	1	2	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
101	#137×C₈₉	—	4	4	no	—
102	#135×C₈₉	—	4	2	no	—
103	C₂×Q₁₆×C₈₉	—	4	2	no	—
104	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₈₉	—	4	2	no	—
112	C₂×M₁₆×C₈₉	—	4	2	no	—
113	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
116	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	—	2	2	no	—
123	C₄⋊Q₈×C₈₉	—	2	4	no	—
124	#124×C₈₉	—	2	2	no	—
125	#124×C₈₉	—	2	4	no	—
126	#123×C₈₉	—	2	4	no	—
127	#123×C₈₉	—	2	4	no	—
128	#123×C₈₉	—	2	4	no	—
129	#123×C₈₉	—	2	2	no	—
130	#123×C₈₉	—	2	4	no	—
131	C₂²⋊Q₈×C₈₉	—	2	2	no	—
132	C₂²⋊Q₈×C₈₉	—	2	4	no	—
133	C₂²⋊Q₈×C₈₉	—	2	2	no	—
134	C₂²⋊Q₈×C₈₉	—	2	4	no	—
135	C₂²⋊Q₈×C₈₉	—	2	2	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
139	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
141	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
142	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
144	#121×C₈₉	—	2	4	no	—
145	#121×C₈₉	—	2	4	no	—
146	#121×C₈₉	—	2	4	no	—
147	#121×C₈₉	—	2	2	no	—
148	#121×C₈₉	—	2	4	no	—
149	#121×C₈₉	C₂³	1	4	yes	—
150	#121×C₈₉	C₂³	1	2	yes	—
151	#121×C₈₉	C₂³	1	2	yes	—
152	#120×C₈₉	—	2	2	no	—
153	#120×C₈₉	—	2	4	no	—
154	C₄×Q₈×C₈₉	—	2	2	no	—
155	C₄×D₄×C₈₉	—	2	4	no	—
156	C₄×D₄×C₈₉	—	2	2	no	—
157	C₄×D₄×C₈₉	—	2	2	no	—
158	C₄×D₄×C₈₉	—	2	4	no	—
159	C₄×D₄×C₈₉	—	2	2	no	—
160	C₄×D₄×C₈₉	—	2	4	no	—
161	#117×C₈₉	C₂³	1	2	yes	—
162	#117×C₈₉	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
168	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
169	#107×C₈₉	C₂³	1	2	yes	—
170	#107×C₈₉	C₂³	1	4	yes	—
171	#106×C₈₉	C₂³	1	2	yes	—
172	#106×C₈₉	C₂³	1	2	yes	—
173	#106×C₈₉	C₂³	1	1	yes	characteristic
174	#106×C₈₉	C₂³	1	1	yes	characteristic
175	#106×C₈₉	C₂³	1	4	yes	—
176	#103×C₈₉	C₂³	1	4	yes	—
177	#103×C₈₉	C₂³	1	4	yes	—
178	#103×C₈₉	C₂³	1	2	yes	—
179	#103×C₈₉	C₂³	1	2	yes	—
180	#103×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	4	yes	—
182	#103×C₈₉	C₂³	1	4	yes	—
183	#102×C₈₉	C₂³	1	2	yes	—
184	#102×C₈₉	C₂³	1	2	yes	—
185	#102×C₈₉	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
189	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
190	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
192	#41×C₈₉	—	2	4	no	—
193	#41×C₈₉	—	2	4	no	—
194	#41×C₈₉	—	2	4	no	—
195	#41×C₈₉	—	2	4	no	—
196	#41×C₈₉	—	4	2	no	—
197	#41×C₈₉	—	4	2	no	—
198	#41×C₈₉	—	4	4	no	—
199	#41×C₈₉	—	4	4	no	—
200	#41×C₈₉	—	4	4	no	—
201	#41×C₈₉	—	4	4	no	—
202	#41×C₈₉	—	4	16	no	—
203	#41×C₈₉	—	4	8	no	—
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	—	2	2	no	—
206	C₂×Q₈×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	—	2	4	no	—
208	C₂×Q₈×C₈₉	—	4	2	no	—
209	C₂×Q₈×C₈₉	—	4	4	no	—
210	C₂×Q₈×C₈₉	—	4	4	no	—
211	C₂×Q₈×C₈₉	—	4	8	no	—
212	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
215	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
216	C₂×D₄×C₈₉	—	2	2	no	—
217	C₂×D₄×C₈₉	—	2	4	no	—
218	C₂×D₄×C₈₉	—	2	2	no	—
219	C₂×D₄×C₈₉	—	2	2	no	—
220	C₂×D₄×C₈₉	—	2	4	no	—
221	C₂×D₄×C₈₉	—	4	2	no	—
222	C₂×D₄×C₈₉	—	4	4	no	—
223	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	—	2	2	no	—
229	C₂²×C₄×C₈₉	—	2	2	no	—
230	C₂²×C₄×C₈₉	—	2	4	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	2	4	no	—
233	C₂²×C₄×C₈₉	—	2	2	no	—
234	C₂²×C₄×C₈₉	—	2	4	no	—
235	C₂²×C₄×C₈₉	—	2	2	no	—
236	C₂²×C₄×C₈₉	—	4	2	no	—
237	C₂²×C₄×C₈₉	—	4	2	no	—
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	Q₁₆×C₈₉	—	4	2	no	—
248	Q₁₆×C₈₉	—	4	2	no	—
249	Q₁₆×C₈₉	—	4	1	no	—
250	Q₁₆×C₈₉	—	4	4	no	—
251	SD₁₆×C₈₉	—	4	2	no	—
252	SD₁₆×C₈₉	—	4	4	no	—
253	D₈×C₈₉	—	4	1	no	—
254	M₁₆×C₈₉	—	2	4	no	—
255	M₁₆×C₈₉	—	4	1	no	—
256	M₁₆×C₈₉	—	4	1	no	—
257	M₁₆×C₈₉	—	4	1	no	—
258	M₁₆×C₈₉	—	4	1	no	—
259	M₁₆×C₈₉	—	4	2	no	—
260	C₂×C₈×C₈₉	—	2	2	no	—
261	C₂×C₈×C₈₉	—	2	2	no	—
262	C₂×C₈×C₈₉	—	4	2	no	—
263	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
266	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
267	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₈₉	—	2	4	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	4	no	—
271	C₄⋊C₄×C₈₉	—	2	4	no	—
272	C₄⋊C₄×C₈₉	—	2	4	no	—
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	4	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²⋊C₄×C₈₉	—	2	4	no	—
281	C₂²⋊C₄×C₈₉	—	2	2	no	—
282	C₂²⋊C₄×C₈₉	—	2	4	no	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	2	no	—
287	C₂²⋊C₄×C₈₉	—	2	2	no	—
288	C₂²⋊C₄×C₈₉	—	2	4	no	—
289	C₂²⋊C₄×C₈₉	—	2	2	no	—
290	C₂²⋊C₄×C₈₉	—	2	4	no	—
291	C₂²⋊C₄×C₈₉	—	2	2	no	—
292	C₄²×C₈₉	—	2	4	no	—
293	C₄²×C₈₉	—	2	2	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	4	2	no	—
297	C₂³×C₈₉	—	4	2	no	—
298	C₂³×C₈₉	—	4	4	no	—
299	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
300	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
302	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₈₉	—	2	4	no	—
304	Q₈×C₈₉	—	2	4	no	—
305	Q₈×C₈₉	—	2	2	no	—
306	Q₈×C₈₉	—	2	4	no	—
307	Q₈×C₈₉	—	2	2	no	—
308	Q₈×C₈₉	—	4	2	no	—
309	Q₈×C₈₉	—	4	8	no	—
310	Q₈×C₈₉	—	4	4	no	—
311	D₄×C₈₉	—	2	8	no	—
312	D₄×C₈₉	—	2	4	no	—
313	D₄×C₈₉	—	2	2	no	—
314	D₄×C₈₉	—	2	2	no	—
315	D₄×C₈₉	—	4	2	no	—
316	D₄×C₈₉	—	4	4	no	—
317	D₄×C₈₉	—	4	4	no	—
318	D₄×C₈₉	—	4	8	no	—
319	D₄×C₈₉	—	4	4	no	—
320	D₄×C₈₉	—	8	2	no	—
321	D₄×C₈₉	—	8	4	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	1	no	—
326	C₂×C₄×C₈₉	—	2	1	no	—
327	C₂×C₄×C₈₉	—	2	1	no	—
328	C₂×C₄×C₈₉	—	2	1	no	—
329	C₂×C₄×C₈₉	—	2	4	no	—
330	C₂×C₄×C₈₉	—	2	4	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	4	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	4	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	4	2	no	—
337	C₂×C₄×C₈₉	—	4	4	no	—
338	C₂×C₄×C₈₉	—	4	8	no	—
339	C₂×C₄×C₈₉	—	4	8	no	—
340	C₂×C₄×C₈₉	—	4	4	no	—
341	C₂×C₄×C₈₉	—	4	4	no	—
342	C₂×C₄×C₈₉	—	8	2	no	—
343	C₂×C₄×C₈₉	—	8	4	no	—
344	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
350	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
351	C₈×C₈₉	—	2	1	no	—
352	C₈×C₈₉	—	2	1	no	—
353	C₈×C₈₉	—	2	1	no	—
354	C₈×C₈₉	—	2	1	no	—
355	C₈×C₈₉	—	2	4	no	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	4	no	—
358	C₂²×C₈₉	—	2	2	no	—
359	C₂²×C₈₉	—	2	2	no	—
360	C₂²×C₈₉	—	2	4	no	—
361	C₂²×C₈₉	—	2	1	no	—
362	C₂²×C₈₉	—	2	1	no	—
363	C₂²×C₈₉	—	2	4	no	—
364	C₂²×C₈₉	—	4	2	no	—
365	C₂²×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	4	2	no	—
367	C₂²×C₈₉	—	8	2	no	—
368	C₂²×C₈₉	—	8	4	no	—
369	C₂²×C₈₉	#534	1	2	yes	—
370	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₈₉	—	2	1	no	—
372	C₄×C₈₉	—	2	1	no	—
373	C₄×C₈₉	—	2	4	no	—
374	C₄×C₈₉	—	4	4	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	4	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	#534	1	2	yes	—
380	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	#60773	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₈₉	—	2	2	no	—
384	C₂×C₈₉	—	4	4	no	—
385	C₂×C₈₉	—	4	1	no	—
386	C₂×C₈₉	—	4	1	no	—
387	C₂×C₈₉	—	8	2	no	—
388	C₂×C₈₉	C₂×#534	1	1	yes	characteristic
389	C₂×C₈₉	#3586	1	2	yes	—
390	#3489	C₂×C₈₉	1	2	yes	complemented
391	#3204	C₂×C₈₉	1	2	yes	complemented
392	#3202	C₂×C₈₉	1	2	yes	complemented
393	#3201	C₂×C₈₉	1	4	yes	complemented
394	#3197	C₂×C₈₉	1	2	yes	complemented
395	#3196	C₂×C₈₉	1	4	yes	complemented
396	#3195	C₂×C₈₉	1	2	yes	complemented
397	#3099	C₂×C₈₉	1	2	yes	complemented
398	#3097	C₂×C₈₉	1	2	yes	complemented
399	#3056	C₂×C₈₉	1	2	yes	complemented
400	#3054	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₂×#470	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#3013	C₂×C₈₉	1	2	yes	complemented
403	#3011	C₂×C₈₉	1	2	yes	complemented
404	#2879	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₈₉	#60773	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
407	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#137	C₂²×C₈₉	1	2	yes	complemented
409	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic, complemented
410	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
411	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
412	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
413	D₄×Q₈	—	2	2	no	—
414	#548	—	2	2	no	—
415	#547	—	2	4	no	—
416	#547	—	2	2	no	—
417	#546	—	2	4	no	—
418	#546	—	2	2	no	—
419	#537	C₂²×C₈₉	1	2	yes	—
420	#537	C₂²×C₈₉	1	4	yes	—
421	#536	C₂²×C₈₉	1	2	yes	—
422	#536	C₂²×C₈₉	1	4	yes	—
423	#525	C₂²×C₈₉	1	4	yes	—
424	#525	C₂²×C₈₉	1	2	yes	—
425	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
427	#520	C₂²×C₈₉	1	2	yes	—
428	#485	C₂²×C₈₉	1	4	yes	complemented
429	#485	C₂²×C₈₉	1	4	yes	complemented
430	#485	C₂²×C₈₉	1	4	yes	complemented
431	#484	C₂²×C₈₉	1	4	yes	complemented
432	#483	C₂²×C₈₉	1	4	yes	complemented
433	#483	C₂²×C₈₉	1	4	yes	complemented
434	#482	C₂²×C₈₉	1	4	yes	complemented
435	#481	C₂²×C₈₉	1	4	yes	complemented
436	#470	C₂²×C₈₉	1	1	yes	characteristic
437	#470	C₂²×C₈₉	1	4	yes	—
438	#470	C₂²×C₈₉	1	2	yes	—
439	#470	C₂²×C₈₉	1	2	yes	—
440	#470	C₂²×C₈₉	1	2	yes	complemented
441	#470	C₂²×C₈₉	1	1	yes	characteristic, complemented
442	#470	C₂²×C₈₉	1	2	yes	complemented
443	#469	C₂²×C₈₉	1	1	yes	characteristic
444	#469	C₂²×C₈₉	1	1	yes	characteristic, complemented
445	#468	C₂²×C₈₉	1	2	yes	—
446	#468	C₂²×C₈₉	1	4	yes	—
447	#468	C₂²×C₈₉	1	2	yes	complemented
448	#467	C₂²×C₈₉	1	4	yes	complemented
449	#465	C₂²×C₈₉	1	4	yes	complemented
450	#452	C₂²×C₈₉	1	4	yes	complemented
451	#452	C₂²×C₈₉	1	4	yes	complemented
452	#452	C₂²×C₈₉	1	4	yes	complemented
453	#451	C₂²×C₈₉	1	4	yes	complemented
454	#451	C₂²×C₈₉	1	4	yes	complemented
455	#451	C₂²×C₈₉	1	4	yes	complemented
456	#449	C₂²×C₈₉	1	4	yes	complemented
457	#448	C₂²×C₈₉	1	4	yes	complemented
458	#428	C₂²×C₈₉	1	2	yes	complemented
459	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
460	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
461	#419	C₂²×C₈₉	1	2	yes	complemented
462	#417	C₂²×C₈₉	1	2	yes	complemented
463	#416	C₂²×C₈₉	1	2	yes	complemented
464	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
465	#408	C₂²×C₈₉	1	2	yes	—
466	#408	C₂²×C₈₉	1	2	yes	—
467	#408	C₂²×C₈₉	1	2	yes	—
468	#408	C₂²×C₈₉	1	2	yes	—
469	#407	C₂²×C₈₉	1	2	yes	—
470	#407	C₂²×C₈₉	1	2	yes	—
471	2₋¹⁺⁴	—	4	4	no	—
472	2₋¹⁺⁴	—	4	4	no	—
473	C₂×#41	—	2	4	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	4	2	no	—
476	C₂×#41	—	4	2	no	—
477	C₂×#41	D₄×C₈₉	1	2	yes	—
478	C₂×#41	D₄×C₈₉	1	2	yes	—
479	C₂×#41	C₂³×C₈₉	1	2	yes	—
480	C₂×#41	C₂³×C₈₉	1	4	yes	—
481	C₂×#41	C₂³×C₈₉	1	2	yes	—
482	C₂×#41	C₂³×C₈₉	1	2	yes	—
483	C₂²×Q₈	—	2	2	no	—
484	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
486	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
487	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
488	C₂²×D₄	D₄×C₈₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
491	#137	—	4	4	no	—
492	#135	—	4	2	no	—
493	C₂×Q₁₆	—	4	2	no	—
494	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
495	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
496	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
498	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
499	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
500	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×M₁₆	—	4	2	no	—
502	C₂×M₁₆	—	4	2	no	—
503	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
504	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
506	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	—	2	4	no	—
514	#124	—	2	2	no	—
515	#124	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	#123	—	2	4	no	—
519	#123	—	2	2	no	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
528	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
529	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
530	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
531	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
532	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
533	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
534	#121	—	2	4	no	—
535	#121	—	2	4	no	—
536	#121	—	2	4	no	—
537	#121	—	2	2	no	—
538	#121	—	2	4	no	—
539	#121	C₂³×C₈₉	1	2	yes	—
540	#121	C₂³×C₈₉	1	4	yes	—
541	#121	C₂³×C₈₉	1	2	yes	—
542	#120	—	2	2	no	—
543	#120	—	2	4	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	#117	C₂³×C₈₉	1	2	yes	—
552	#117	C₂³×C₈₉	1	4	yes	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	4	no	—
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	#107	C₂³×C₈₉	1	2	yes	—
560	#107	C₂³×C₈₉	1	4	yes	—
561	#106	C₂³×C₈₉	1	2	yes	—
562	#106	C₂³×C₈₉	1	2	yes	—
563	#106	C₂³×C₈₉	1	1	yes	characteristic
564	#106	C₂³×C₈₉	1	1	yes	characteristic
565	#106	C₂³×C₈₉	1	4	yes	—
566	#103	C₂³×C₈₉	1	4	yes	—
567	#103	C₂³×C₈₉	1	4	yes	—
568	#103	C₂³×C₈₉	1	2	yes	—
569	#103	C₂³×C₈₉	1	2	yes	—
570	#103	C₂³×C₈₉	1	4	yes	—
571	#103	C₂³×C₈₉	1	4	yes	—
572	#103	C₂³×C₈₉	1	4	yes	—
573	#102	C₂³×C₈₉	1	2	yes	—
574	#102	C₂³×C₈₉	1	2	yes	—
575	#102	C₂³×C₈₉	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
580	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
581	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
582	#41	—	2	4	no	—
583	#41	—	2	4	no	—
584	#41	—	2	4	no	—
585	#41	—	2	4	no	—
586	#41	—	4	2	no	—
587	#41	—	4	2	no	—
588	#41	—	4	4	no	—
589	#41	—	4	4	no	—
590	#41	—	4	4	no	—
591	#41	—	4	4	no	—
592	#41	—	4	16	no	—
593	#41	—	4	8	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	4	no	—
598	C₂×Q₈	—	4	2	no	—
599	C₂×Q₈	—	4	4	no	—
600	C₂×Q₈	—	4	4	no	—
601	C₂×Q₈	—	4	8	no	—
602	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
603	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
604	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
605	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
614	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
615	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
617	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
637	Q₁₆	—	4	2	no	—
638	Q₁₆	—	4	2	no	—
639	Q₁₆	—	4	1	no	—
640	Q₁₆	—	4	4	no	—
641	SD₁₆	—	4	2	no	—
642	SD₁₆	—	4	4	no	—
643	D₈	—	4	1	no	—
644	M₁₆	—	2	4	no	—
645	M₁₆	—	4	1	no	—
646	M₁₆	—	4	1	no	—
647	M₁₆	—	4	1	no	—
648	M₁₆	—	4	1	no	—
649	M₁₆	—	4	2	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	4	2	no	—
653	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
654	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
655	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
656	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
657	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	4	no	—
689	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
690	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
691	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
692	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
693	Q₈	—	2	4	no	—
694	Q₈	—	2	4	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	4	8	no	—
700	Q₈	—	4	4	no	—
701	D₄	—	2	8	no	—
702	D₄	—	2	4	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	4	no	—
710	D₄	—	8	2	no	—
711	D₄	—	8	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
735	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
738	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
739	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
740	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
741	C₈	—	2	1	no	—
742	C₈	—	2	1	no	—
743	C₈	—	2	1	no	—
744	C₈	—	2	1	no	—
745	C₈	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	8	2	no	—
758	C₂²	—	8	4	no	—
759	C₂²	#534×C₈₉	1	2	yes	—
760	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	4	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	2	no	—
769	C₄	#534×C₈₉	1	2	yes	—
770	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
771	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
772	C₂	—	2	2	no	—
773	C₂	—	4	4	no	—
774	C₂	—	4	1	no	—
775	C₂	—	4	1	no	—
776	C₂	—	8	2	no	—
777	C₂	C₂×#534×C₈₉	1	1	yes	characteristic
778	C₂	C₈₉×#3586	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 ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3489	C₂	semidirect
2. C₈₉×#3204	C₂	semidirect
3. C₈₉×#3202	C₂	semidirect
4. C₈₉×#3201	C₂	semidirect
5. C₈₉×#3197	C₂	semidirect
6. C₈₉×#3196	C₂	semidirect
7. C₈₉×#3195	C₂	semidirect
8. C₈₉×#3099	C₂	semidirect
9. C₈₉×#3097	C₂	semidirect
10. C₈₉×#3056	C₂	semidirect
11. C₈₉×#3054	C₂	semidirect
12. C₂×#470×C₈₉	C₂	semidirect
13. C₈₉×#3013	C₂	semidirect
14. C₈₉×#3011	C₂	semidirect
15. C₈₉×#2879	C₂	semidirect
18. C₂×#137×C₈₉	C₂²	semidirect
19. C₂×#135×C₈₉	C₂²	semidirect
20. C₂²×Q₁₆×C₈₉	C₂²	semidirect
38. #485×C₈₉	C₂²	semidirect
39. #485×C₈₉	C₂²	semidirect
40. #485×C₈₉	C₂²	semidirect
41. #484×C₈₉	C₂²	semidirect
42. #483×C₈₉	C₂²	semidirect
43. #483×C₈₉	C₂²	semidirect
44. #482×C₈₉	C₂²	semidirect
45. #481×C₈₉	C₂²	semidirect
50. #470×C₈₉	C₂²	semidirect
51. #470×C₈₉	C₂²	semidirect
52. #470×C₈₉	C₂²	semidirect
54. #469×C₈₉	C₂²	semidirect
57. #468×C₈₉	C₂²	semidirect
58. #467×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #452×C₈₉	C₂²	semidirect
61. #452×C₈₉	C₂²	semidirect
62. #452×C₈₉	C₂²	semidirect
63. #451×C₈₉	C₂²	semidirect
64. #451×C₈₉	C₂²	semidirect
65. #451×C₈₉	C₂²	semidirect
66. #449×C₈₉	C₂²	semidirect
67. #448×C₈₉	C₂²	semidirect
68. #428×C₈₉	C₂²	semidirect
69. #427×C₈₉	C₂²	semidirect
70. C₂×#106×C₈₉	C₂²	semidirect
71. #419×C₈₉	C₂²	semidirect
72. #417×C₈₉	C₂²	semidirect
73. #416×C₈₉	C₂²	semidirect
74. C₂×#103×C₈₉	C₂²	semidirect
382. #60773	C₈₉	direct (N × H)
390. #3489	C₂×C₈₉	semidirect
391. #3204	C₂×C₈₉	semidirect
392. #3202	C₂×C₈₉	semidirect
393. #3201	C₂×C₈₉	semidirect
394. #3197	C₂×C₈₉	semidirect
395. #3196	C₂×C₈₉	semidirect
396. #3195	C₂×C₈₉	semidirect
397. #3099	C₂×C₈₉	semidirect
398. #3097	C₂×C₈₉	semidirect
399. #3056	C₂×C₈₉	semidirect
400. #3054	C₂×C₈₉	semidirect
401. C₂×#470	C₂×C₈₉	semidirect
402. #3013	C₂×C₈₉	semidirect
403. #3011	C₂×C₈₉	semidirect
404. #2879	C₂×C₈₉	semidirect
405. C₈₉	#60773	direct (N × H)
408. C₂×#137	C₂²×C₈₉	semidirect
409. C₂×#135	C₂²×C₈₉	semidirect
410. C₂²×Q₁₆	C₂²×C₈₉	semidirect
428. #485	C₂²×C₈₉	semidirect
429. #485	C₂²×C₈₉	semidirect
430. #485	C₂²×C₈₉	semidirect
431. #484	C₂²×C₈₉	semidirect
432. #483	C₂²×C₈₉	semidirect
433. #483	C₂²×C₈₉	semidirect
434. #482	C₂²×C₈₉	semidirect
435. #481	C₂²×C₈₉	semidirect
440. #470	C₂²×C₈₉	semidirect
441. #470	C₂²×C₈₉	semidirect
442. #470	C₂²×C₈₉	semidirect
444. #469	C₂²×C₈₉	semidirect
447. #468	C₂²×C₈₉	semidirect
448. #467	C₂²×C₈₉	semidirect
449. #465	C₂²×C₈₉	semidirect
450. #452	C₂²×C₈₉	semidirect
451. #452	C₂²×C₈₉	semidirect
452. #452	C₂²×C₈₉	semidirect
453. #451	C₂²×C₈₉	semidirect
454. #451	C₂²×C₈₉	semidirect
455. #451	C₂²×C₈₉	semidirect
456. #449	C₂²×C₈₉	semidirect
457. #448	C₂²×C₈₉	semidirect
458. #428	C₂²×C₈₉	semidirect
459. #427	C₂²×C₈₉	semidirect
460. C₂×#106	C₂²×C₈₉	semidirect
461. #419	C₂²×C₈₉	semidirect
462. #417	C₂²×C₈₉	semidirect
463. #416	C₂²×C₈₉	semidirect
464. C₂×#103	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×#3489	2
C₈₉×#3204	2
C₈₉×#3202	2
C₈₉×#3201	2
C₈₉×#3197	2
C₈₉×#3196	2
C₈₉×#3195	2
C₈₉×#3099	2
C₈₉×#3097	2
C₈₉×#3056	2
C₈₉×#3054	2
C₂×#470×C₈₉	2
C₈₉×#3013	2
C₈₉×#3011	2
C₈₉×#2879	2
#60773	89

Subgroups — C89×#60773 #36438621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60773 #36438621