Subgroups — C₈₉×#60457 #36438305

Order 22784.

2756 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3063	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3062	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3060	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3057	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3056	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3055	C₂	1	3	yes	maximal, complemented
11	C₈₉×#3050	C₂	1	3	yes	maximal, complemented
12	C₂×#465×C₈₉	C₂	1	3	yes	maximal, complemented
13	C₈₉×#2912	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	#577×C₈₉	—	2	8	no	—
20	C₂×#137×C₈₉	C₂²	1	3	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	complemented
22	C₂×#135×C₈₉	C₂²	1	3	yes	complemented
23	C₂²×SD₁₆×C₈₉	C₂²	1	3	yes	complemented
24	C₂×#131×C₈₉	—	2	8	no	—
25	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
28	C₂×#131×C₈₉	C₂²	1	3	yes	complemented
29	C₂²×M₁₆×C₈₉	C₂²	1	3	yes	complemented
30	C₂³×C₈×C₈₉	C₂²	1	3	yes	complemented
31	#550×C₈₉	—	2	1	no	—
32	D₄×Q₈×C₈₉	—	2	1	no	—
33	#548×C₈₉	—	2	1	no	—
34	#548×C₈₉	—	2	1	no	—
35	#547×C₈₉	—	2	3	no	—
36	#546×C₈₉	—	2	3	no	—
37	#546×C₈₉	—	2	3	no	—
38	D₄²×C₈₉	—	2	3	no	—
39	#537×C₈₉	C₂²	1	3	yes	—
40	#537×C₈₉	C₂²	1	3	yes	complemented
41	#536×C₈₉	C₂²	1	3	yes	complemented
42	#535×C₈₉	C₂²	1	3	yes	—
43	#525×C₈₉	C₂²	1	3	yes	—
44	#525×C₈₉	C₂²	1	3	yes	complemented
45	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
46	C₂×#121×C₈₉	C₂²	1	3	yes	—
47	#520×C₈₉	C₂²	1	1	yes	characteristic
48	#520×C₈₉	C₂²	1	1	yes	characteristic
49	#470×C₈₉	C₂²	1	6	yes	complemented
50	#469×C₈₉	C₂²	1	6	yes	complemented
51	#468×C₈₉	C₂²	1	6	yes	complemented
52	#468×C₈₉	C₂²	1	6	yes	complemented
53	#467×C₈₉	C₂²	1	3	yes	complemented
54	#467×C₈₉	C₂²	1	3	yes	complemented
55	#466×C₈₉	C₂²	1	3	yes	complemented
56	#466×C₈₉	C₂²	1	3	yes	complemented
57	#465×C₈₉	C₂²	1	6	yes	complemented
58	#465×C₈₉	C₂²	1	3	yes	complemented
59	#465×C₈₉	C₂²	1	6	yes	complemented
60	#465×C₈₉	C₂²	1	6	yes	complemented
61	#465×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#465×C₈₉	C₂²	1	3	yes	complemented
63	#465×C₈₉	C₂²	1	3	yes	complemented
64	#428×C₈₉	C₂²	1	3	yes	complemented
65	#428×C₈₉	C₂²	1	3	yes	complemented
66	#427×C₈₉	C₂²	1	3	yes	complemented
67	C₂×#106×C₈₉	C₂²	1	3	yes	complemented
68	#419×C₈₉	C₂²	1	3	yes	complemented
69	#418×C₈₉	C₂²	1	3	yes	complemented
70	#417×C₈₉	C₂²	1	3	yes	complemented
71	#417×C₈₉	C₂²	1	3	yes	complemented
72	#416×C₈₉	C₂²	1	3	yes	complemented
73	#416×C₈₉	C₂²	1	3	yes	complemented
74	C₂×#103×C₈₉	C₂²	1	3	yes	complemented
75	C₂×#102×C₈₉	C₂²	1	3	yes	complemented
76	2₋¹⁺⁴×C₈₉	—	2	4	no	—
77	2₋¹⁺⁴×C₈₉	—	2	4	no	—
78	H(5,𝔽₂)×C₈₉	—	2	4	no	—
79	H(5,𝔽₂)×C₈₉	—	2	4	no	—
80	C₂×#41×C₈₉	—	2	4	no	—
81	C₂×#41×C₈₉	—	2	4	no	—
82	C₂×#41×C₈₉	—	2	1	no	—
83	C₂×#41×C₈₉	—	2	3	no	—
84	C₂×#41×C₈₉	D₄	1	3	yes	—
85	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
86	C₂×#41×C₈₉	C₂³	1	3	yes	—
87	C₂×#41×C₈₉	C₂³	1	3	yes	—
88	C₂×#41×C₈₉	C₂³	1	3	yes	—
89	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₈₉	—	2	1	no	—
91	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
93	C₂²×D₄×C₈₉	—	2	3	no	—
94	C₂²×D₄×C₈₉	—	2	3	no	—
95	C₂²×D₄×C₈₉	D₄	1	3	yes	—
96	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
98	#137×C₈₉	—	2	12	no	—
99	AGL(1,ℤ/8)×C₈₉	—	2	12	no	—
100	#135×C₈₉	—	2	12	no	—
101	C₂×Q₁₆×C₈₉	C₂³	1	3	yes	—
102	C₂×SD₁₆×C₈₉	—	2	12	no	—
103	C₂×SD₁₆×C₈₉	C₂³	1	3	yes	—
104	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
106	C₂×D₈×C₈₉	C₂³	1	3	yes	—
107	#131×C₈₉	—	2	4	no	—
108	#131×C₈₉	—	2	12	no	—
109	#131×C₈₉	—	2	12	no	—
110	#131×C₈₉	D₄	1	8	yes	complemented
111	C₂×M₁₆×C₈₉	—	2	12	no	—
112	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
113	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
114	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
115	C₂²×C₈×C₈₉	—	2	12	no	—
116	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
117	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
119	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
120	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
122	C₄⋊Q₈×C₈₉	—	2	3	no	—
123	#127×C₈₉	—	2	3	no	—
124	#124×C₈₉	—	2	3	no	—
125	#124×C₈₉	—	2	3	no	—
126	#123×C₈₉	—	2	6	no	—
127	#123×C₈₉	—	2	3	no	—
128	#123×C₈₉	—	2	3	no	—
129	C₂²⋊Q₈×C₈₉	—	2	3	no	—
130	C₂²⋊Q₈×C₈₉	—	2	3	no	—
131	C₂²⋊Q₈×C₈₉	—	2	3	no	—
132	C₂²⋊Q₈×C₈₉	—	2	3	no	—
133	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
134	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
135	C₂²⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
137	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
138	#121×C₈₉	—	2	6	no	—
139	#121×C₈₉	—	2	3	no	—
140	#121×C₈₉	—	2	6	no	—
141	#121×C₈₉	—	2	3	no	—
142	#121×C₈₉	—	2	3	no	—
143	#121×C₈₉	—	2	3	no	—
144	#121×C₈₉	C₂³	1	3	yes	—
145	#121×C₈₉	C₂³	1	6	yes	—
146	#121×C₈₉	C₂³	1	1	yes	characteristic
147	#121×C₈₉	C₂³	1	3	yes	—
148	#121×C₈₉	C₂³	1	3	yes	—
149	#120×C₈₉	—	2	3	no	—
150	#120×C₈₉	—	2	3	no	—
151	#120×C₈₉	—	2	6	no	—
152	C₄×Q₈×C₈₉	—	2	1	no	—
153	C₄×Q₈×C₈₉	—	2	1	no	—
154	C₄×D₄×C₈₉	—	2	3	no	—
155	C₄×D₄×C₈₉	—	2	3	no	—
156	C₄×D₄×C₈₉	—	2	3	no	—
157	C₄×D₄×C₈₉	—	2	3	no	—
158	C₄×D₄×C₈₉	—	2	3	no	—
159	C₄×D₄×C₈₉	—	2	3	no	—
160	#117×C₈₉	C₂³	1	3	yes	—
161	#117×C₈₉	C₂³	1	3	yes	—
162	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
165	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
166	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
167	#107×C₈₉	C₂³	1	3	yes	—
168	#107×C₈₉	C₂³	1	3	yes	—
169	#106×C₈₉	C₂³	1	3	yes	—
170	#106×C₈₉	C₂³	1	6	yes	—
171	#106×C₈₉	C₂³	1	1	yes	characteristic
172	#103×C₈₉	C₂³	1	3	yes	—
173	#103×C₈₉	C₂³	1	6	yes	—
174	#103×C₈₉	C₂³	1	1	yes	characteristic
175	#103×C₈₉	C₂³	1	3	yes	—
176	#103×C₈₉	C₂³	1	3	yes	—
177	#102×C₈₉	C₂³	1	3	yes	—
178	#102×C₈₉	C₂³	1	6	yes	—
179	#102×C₈₉	C₂³	1	1	yes	characteristic
180	#102×C₈₉	C₂³	1	3	yes	—
181	#102×C₈₉	C₂³	1	3	yes	—
182	C₂⁴×C₈₉	—	2	3	no	—
183	C₂⁴×C₈₉	C₂×D₄	1	3	yes	—
184	#41×C₈₉	—	2	4	no	—
185	#41×C₈₉	—	2	12	no	—
186	#41×C₈₉	—	2	6	no	—
187	#41×C₈₉	—	2	6	no	—
188	#41×C₈₉	—	2	6	no	—
189	#41×C₈₉	—	2	6	no	—
190	#41×C₈₉	—	2	6	no	—
191	#41×C₈₉	—	2	6	no	—
192	#41×C₈₉	—	4	4	no	—
193	#41×C₈₉	—	4	12	no	—
194	#41×C₈₉	C₂×D₄	1	4	yes	—
195	#41×C₈₉	#41	1	4	yes	—
196	C₂×Q₈×C₈₉	—	2	4	no	—
197	C₂×Q₈×C₈₉	—	2	3	no	—
198	C₂×Q₈×C₈₉	—	2	6	no	—
199	C₂×Q₈×C₈₉	—	2	6	no	—
200	C₂×Q₈×C₈₉	—	4	4	no	—
201	C₂×Q₈×C₈₉	C₂×D₄	1	3	yes	—
202	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
204	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂×D₄×C₈₉	—	2	12	no	—
206	C₂×D₄×C₈₉	—	2	1	no	—
207	C₂×D₄×C₈₉	—	2	3	no	—
208	C₂×D₄×C₈₉	—	2	3	no	—
209	C₂×D₄×C₈₉	—	2	3	no	—
210	C₂×D₄×C₈₉	—	2	3	no	—
211	C₂×D₄×C₈₉	—	2	3	no	—
212	C₂×D₄×C₈₉	—	2	6	no	—
213	C₂×D₄×C₈₉	—	2	6	no	—
214	C₂×D₄×C₈₉	—	2	3	no	—
215	C₂×D₄×C₈₉	—	2	6	no	—
216	C₂×D₄×C₈₉	—	4	12	no	—
217	C₂×D₄×C₈₉	—	8	6	no	—
218	C₂×D₄×C₈₉	C₂×D₄	1	6	yes	—
219	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
220	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
221	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
223	C₂²×C₄×C₈₉	—	2	6	no	—
224	C₂²×C₄×C₈₉	—	2	6	no	—
225	C₂²×C₄×C₈₉	—	2	3	no	—
226	C₂²×C₄×C₈₉	—	2	3	no	—
227	C₂²×C₄×C₈₉	—	2	3	no	—
228	C₂²×C₄×C₈₉	—	2	3	no	—
229	C₂²×C₄×C₈₉	—	2	3	no	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
232	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
236	Q₁₆×C₈₉	—	2	6	no	—
237	SD₁₆×C₈₉	—	2	6	no	—
238	SD₁₆×C₈₉	—	2	12	no	—
239	SD₁₆×C₈₉	—	2	2	no	—
240	D₈×C₈₉	—	2	6	no	—
241	M₁₆×C₈₉	—	2	6	no	—
242	M₁₆×C₈₉	—	2	12	no	—
243	M₁₆×C₈₉	C₂×D₄	1	12	yes	complemented
244	C₂×C₈×C₈₉	—	2	6	no	—
245	C₂×C₈×C₈₉	—	2	2	no	—
246	C₂×C₈×C₈₉	—	2	6	no	—
247	C₂×C₈×C₈₉	—	2	6	no	—
248	C₂×C₈×C₈₉	—	2	6	no	—
249	C₂×C₈×C₈₉	C₂×D₄	1	12	yes	complemented
250	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
252	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
254	C₄⋊C₄×C₈₉	—	2	3	no	—
255	C₄⋊C₄×C₈₉	—	2	6	no	—
256	C₄⋊C₄×C₈₉	—	2	3	no	—
257	C₄⋊C₄×C₈₉	—	2	3	no	—
258	C₄⋊C₄×C₈₉	—	2	1	no	—
259	C₄⋊C₄×C₈₉	—	2	3	no	—
260	C₄⋊C₄×C₈₉	—	2	3	no	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
262	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
264	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²⋊C₄×C₈₉	—	2	3	no	—
266	C₂²⋊C₄×C₈₉	—	2	6	no	—
267	C₂²⋊C₄×C₈₉	—	2	3	no	—
268	C₂²⋊C₄×C₈₉	—	2	3	no	—
269	C₂²⋊C₄×C₈₉	—	2	1	no	—
270	C₂²⋊C₄×C₈₉	—	2	3	no	—
271	C₂²⋊C₄×C₈₉	—	2	3	no	—
272	C₂²⋊C₄×C₈₉	—	2	3	no	—
273	C₂²⋊C₄×C₈₉	—	2	6	no	—
274	C₂²⋊C₄×C₈₉	—	2	1	no	—
275	C₂²⋊C₄×C₈₉	—	2	3	no	—
276	C₂²⋊C₄×C₈₉	—	2	3	no	—
277	C₄²×C₈₉	—	2	3	no	—
278	C₄²×C₈₉	—	2	3	no	—
279	C₂³×C₈₉	—	2	6	no	—
280	C₂³×C₈₉	—	2	6	no	—
281	C₂³×C₈₉	—	2	1	no	—
282	C₂³×C₈₉	—	2	3	no	—
283	C₂³×C₈₉	—	4	3	no	—
284	C₂³×C₈₉	—	4	6	no	—
285	C₂³×C₈₉	—	8	3	no	—
286	C₂³×C₈₉	—	8	3	no	—
287	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
288	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
289	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₈₉	—	2	6	no	—
291	Q₈×C₈₉	—	2	3	no	—
292	Q₈×C₈₉	—	2	1	no	—
293	Q₈×C₈₉	—	2	3	no	—
294	Q₈×C₈₉	—	2	1	no	—
295	Q₈×C₈₉	—	4	6	no	—
296	Q₈×C₈₉	#121	1	4	yes	—
297	D₄×C₈₉	—	2	12	no	—
298	D₄×C₈₉	—	2	6	no	—
299	D₄×C₈₉	—	2	1	no	—
300	D₄×C₈₉	—	2	3	no	—
301	D₄×C₈₉	—	2	3	no	—
302	D₄×C₈₉	—	2	1	no	—
303	D₄×C₈₉	—	4	6	no	—
304	D₄×C₈₉	—	4	6	no	—
305	D₄×C₈₉	—	4	2	no	—
306	D₄×C₈₉	—	4	6	no	—
307	D₄×C₈₉	—	4	6	no	—
308	D₄×C₈₉	—	8	3	no	—
309	D₄×C₈₉	—	8	3	no	—
310	D₄×C₈₉	—	8	6	no	—
311	D₄×C₈₉	#121	1	12	yes	—
312	C₂×C₄×C₈₉	—	2	6	no	—
313	C₂×C₄×C₈₉	—	2	6	no	—
314	C₂×C₄×C₈₉	—	2	6	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	3	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	3	no	—
319	C₂×C₄×C₈₉	—	2	1	no	—
320	C₂×C₄×C₈₉	—	2	1	no	—
321	C₂×C₄×C₈₉	—	2	3	no	—
322	C₂×C₄×C₈₉	—	2	3	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	3	no	—
325	C₂×C₄×C₈₉	—	4	6	no	—
326	C₂×C₄×C₈₉	—	4	6	no	—
327	C₂×C₄×C₈₉	—	4	6	no	—
328	C₂×C₄×C₈₉	—	8	3	no	—
329	C₂×C₄×C₈₉	—	8	3	no	—
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
334	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
335	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
336	C₈×C₈₉	—	2	1	no	—
337	C₈×C₈₉	—	2	3	no	—
338	C₈×C₈₉	C₂²×D₄	1	2	yes	—
339	C₈×C₈₉	C₂²×D₄	1	6	yes	—
340	C₂²×C₈₉	—	2	3	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	3	no	—
344	C₂²×C₈₉	—	2	3	no	—
345	C₂²×C₈₉	—	2	3	no	—
346	C₂²×C₈₉	—	2	3	no	—
347	C₂²×C₈₉	—	4	12	no	—
348	C₂²×C₈₉	—	4	1	no	—
349	C₂²×C₈₉	—	4	3	no	—
350	C₂²×C₈₉	—	4	1	no	—
351	C₂²×C₈₉	—	4	3	no	—
352	C₂²×C₈₉	—	4	3	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	16	6	no	—
355	C₂²×C₈₉	C₂×#121	1	6	yes	—
356	C₂²×C₈₉	#577	1	2	yes	complemented
357	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	2	3	no	—
360	C₄×C₈₉	—	4	3	no	—
361	C₄×C₈₉	—	4	1	no	—
362	C₄×C₈₉	—	4	1	no	—
363	C₄×C₈₉	—	4	3	no	—
364	C₄×C₈₉	—	4	3	no	—
365	C₄×C₈₉	—	4	1	no	—
366	C₄×C₈₉	C₂×#121	1	6	yes	—
367	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
369	#60457	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂×C₈₉	—	2	2	no	—
371	C₂×C₈₉	—	2	6	no	—
372	C₂×C₈₉	—	4	3	no	—
373	C₂×C₈₉	—	8	1	no	—
374	C₂×C₈₉	—	8	3	no	—
375	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
376	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
377	C₂×C₈₉	#3584	1	1	yes	characteristic
378	C₂×#577	C₂×C₈₉	1	1	yes	characteristic, complemented
379	C₂²×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#3489	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#3488	C₂×C₈₉	1	1	yes	characteristic, complemented
382	#3063	C₂×C₈₉	1	3	yes	complemented
383	#3062	C₂×C₈₉	1	3	yes	complemented
384	#3060	C₂×C₈₉	1	3	yes	complemented
385	#3057	C₂×C₈₉	1	3	yes	complemented
386	#3056	C₂×C₈₉	1	3	yes	complemented
387	#3055	C₂×C₈₉	1	3	yes	complemented
388	#3050	C₂×C₈₉	1	3	yes	complemented
389	C₂×#465	C₂×C₈₉	1	3	yes	complemented
390	#2912	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#2898	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#2897	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₈₉	#60457	1	1	yes	characteristic, direct product factor, Sylow
394	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
396	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
397	#577	—	2	8	no	—
398	C₂×#137	C₂²×C₈₉	1	3	yes	complemented
399	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	3	yes	complemented
400	C₂×#135	C₂²×C₈₉	1	3	yes	complemented
401	C₂²×SD₁₆	C₂²×C₈₉	1	3	yes	complemented
402	C₂×#131	—	2	8	no	—
403	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
406	C₂×#131	C₂²×C₈₉	1	3	yes	complemented
407	C₂²×M₁₆	C₂²×C₈₉	1	3	yes	complemented
408	C₂³×C₈	C₂²×C₈₉	1	3	yes	complemented
409	#550	—	2	1	no	—
410	D₄×Q₈	—	2	1	no	—
411	#548	—	2	1	no	—
412	#548	—	2	1	no	—
413	#547	—	2	3	no	—
414	#546	—	2	3	no	—
415	#546	—	2	3	no	—
416	D₄²	—	2	3	no	—
417	#537	C₂²×C₈₉	1	3	yes	—
418	#537	C₂²×C₈₉	1	3	yes	complemented
419	#536	C₂²×C₈₉	1	3	yes	complemented
420	#535	C₂²×C₈₉	1	3	yes	—
421	#525	C₂²×C₈₉	1	3	yes	—
422	#525	C₂²×C₈₉	1	3	yes	complemented
423	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
424	C₂×#121	C₂²×C₈₉	1	3	yes	—
425	#520	C₂²×C₈₉	1	1	yes	characteristic
426	#520	C₂²×C₈₉	1	1	yes	characteristic
427	#470	C₂²×C₈₉	1	6	yes	complemented
428	#469	C₂²×C₈₉	1	6	yes	complemented
429	#468	C₂²×C₈₉	1	6	yes	complemented
430	#468	C₂²×C₈₉	1	6	yes	complemented
431	#467	C₂²×C₈₉	1	3	yes	complemented
432	#467	C₂²×C₈₉	1	3	yes	complemented
433	#466	C₂²×C₈₉	1	3	yes	complemented
434	#466	C₂²×C₈₉	1	3	yes	complemented
435	#465	C₂²×C₈₉	1	3	yes	complemented
436	#465	C₂²×C₈₉	1	6	yes	complemented
437	#465	C₂²×C₈₉	1	6	yes	complemented
438	#465	C₂²×C₈₉	1	6	yes	complemented
439	#465	C₂²×C₈₉	1	1	yes	characteristic, complemented
440	#465	C₂²×C₈₉	1	3	yes	complemented
441	#465	C₂²×C₈₉	1	3	yes	complemented
442	#428	C₂²×C₈₉	1	3	yes	complemented
443	#428	C₂²×C₈₉	1	3	yes	complemented
444	#427	C₂²×C₈₉	1	3	yes	complemented
445	C₂×#106	C₂²×C₈₉	1	3	yes	complemented
446	#419	C₂²×C₈₉	1	3	yes	complemented
447	#418	C₂²×C₈₉	1	3	yes	complemented
448	#417	C₂²×C₈₉	1	3	yes	complemented
449	#417	C₂²×C₈₉	1	3	yes	complemented
450	#416	C₂²×C₈₉	1	3	yes	complemented
451	#416	C₂²×C₈₉	1	3	yes	complemented
452	C₂×#103	C₂²×C₈₉	1	3	yes	complemented
453	C₂×#102	C₂²×C₈₉	1	3	yes	complemented
454	2₋¹⁺⁴	—	2	4	no	—
455	2₋¹⁺⁴	—	2	4	no	—
456	H(5,𝔽₂)	—	2	4	no	—
457	H(5,𝔽₂)	—	2	4	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	3	no	—
462	C₂×#41	D₄×C₈₉	1	3	yes	—
463	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
464	C₂×#41	C₂³×C₈₉	1	3	yes	—
465	C₂×#41	C₂³×C₈₉	1	3	yes	—
466	C₂×#41	C₂³×C₈₉	1	3	yes	—
467	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
468	C₂²×Q₈	—	2	1	no	—
469	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
471	C₂²×D₄	—	2	3	no	—
472	C₂²×D₄	—	2	3	no	—
473	C₂²×D₄	D₄×C₈₉	1	3	yes	—
474	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
475	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
476	#137	—	2	12	no	—
477	AGL(1,ℤ/8)	—	2	12	no	—
478	#135	—	2	12	no	—
479	C₂×Q₁₆	C₂³×C₈₉	1	3	yes	—
480	C₂×SD₁₆	—	2	12	no	—
481	C₂×SD₁₆	C₂³×C₈₉	1	3	yes	—
482	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
483	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
484	C₂×D₈	C₂³×C₈₉	1	3	yes	—
485	#131	—	2	4	no	—
486	#131	—	2	12	no	—
487	#131	—	2	12	no	—
488	#131	D₄×C₈₉	1	8	yes	complemented
489	C₂×M₁₆	—	2	12	no	—
490	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
491	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
492	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
493	C₂²×C₈	—	2	12	no	—
494	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
496	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
497	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
498	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
499	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
500	C₄⋊Q₈	—	2	3	no	—
501	#127	—	2	3	no	—
502	#124	—	2	3	no	—
503	#124	—	2	3	no	—
504	#123	—	2	6	no	—
505	#123	—	2	3	no	—
506	#123	—	2	3	no	—
507	C₂²⋊Q₈	—	2	3	no	—
508	C₂²⋊Q₈	—	2	3	no	—
509	C₂²⋊Q₈	—	2	3	no	—
510	C₂²⋊Q₈	—	2	3	no	—
511	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
512	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
513	C₂²⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
514	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
515	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
516	#121	—	2	6	no	—
517	#121	—	2	3	no	—
518	#121	—	2	6	no	—
519	#121	—	2	3	no	—
520	#121	—	2	3	no	—
521	#121	—	2	3	no	—
522	#121	C₂³×C₈₉	1	3	yes	—
523	#121	C₂³×C₈₉	1	6	yes	—
524	#121	C₂³×C₈₉	1	3	yes	—
525	#121	C₂³×C₈₉	1	1	yes	characteristic
526	#121	C₂³×C₈₉	1	3	yes	—
527	#120	—	2	3	no	—
528	#120	—	2	3	no	—
529	#120	—	2	6	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×D₄	—	2	3	no	—
533	C₄×D₄	—	2	3	no	—
534	C₄×D₄	—	2	3	no	—
535	C₄×D₄	—	2	3	no	—
536	C₄×D₄	—	2	3	no	—
537	C₄×D₄	—	2	3	no	—
538	#117	C₂³×C₈₉	1	3	yes	—
539	#117	C₂³×C₈₉	1	3	yes	—
540	C₂×C₄⋊C₄	—	2	3	no	—
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
543	C₂×C₂²⋊C₄	—	2	3	no	—
544	C₂×C₂²⋊C₄	—	2	3	no	—
545	#107	C₂³×C₈₉	1	3	yes	—
546	#107	C₂³×C₈₉	1	3	yes	—
547	#106	C₂³×C₈₉	1	3	yes	—
548	#106	C₂³×C₈₉	1	6	yes	—
549	#106	C₂³×C₈₉	1	1	yes	characteristic
550	#103	C₂³×C₈₉	1	3	yes	—
551	#103	C₂³×C₈₉	1	6	yes	—
552	#103	C₂³×C₈₉	1	1	yes	characteristic
553	#103	C₂³×C₈₉	1	3	yes	—
554	#103	C₂³×C₈₉	1	3	yes	—
555	#102	C₂³×C₈₉	1	3	yes	—
556	#102	C₂³×C₈₉	1	6	yes	—
557	#102	C₂³×C₈₉	1	1	yes	characteristic
558	#102	C₂³×C₈₉	1	3	yes	—
559	#102	C₂³×C₈₉	1	3	yes	—
560	C₂⁴	—	2	3	no	—
561	C₂⁴	C₂×D₄×C₈₉	1	3	yes	—
562	#41	—	2	4	no	—
563	#41	—	2	12	no	—
564	#41	—	2	6	no	—
565	#41	—	2	6	no	—
566	#41	—	2	6	no	—
567	#41	—	2	6	no	—
568	#41	—	2	6	no	—
569	#41	—	2	6	no	—
570	#41	—	4	4	no	—
571	#41	—	4	12	no	—
572	#41	C₂×D₄×C₈₉	1	4	yes	—
573	#41	#41×C₈₉	1	4	yes	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	3	no	—
576	C₂×Q₈	—	2	6	no	—
577	C₂×Q₈	—	2	6	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	C₂×D₄×C₈₉	1	3	yes	—
580	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
582	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
583	C₂×D₄	—	2	12	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	3	no	—
586	C₂×D₄	—	2	3	no	—
587	C₂×D₄	—	2	3	no	—
588	C₂×D₄	—	2	3	no	—
589	C₂×D₄	—	2	3	no	—
590	C₂×D₄	—	2	6	no	—
591	C₂×D₄	—	2	6	no	—
592	C₂×D₄	—	2	3	no	—
593	C₂×D₄	—	2	6	no	—
594	C₂×D₄	—	4	12	no	—
595	C₂×D₄	—	8	6	no	—
596	C₂×D₄	C₂×D₄×C₈₉	1	6	yes	—
597	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
598	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
599	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
600	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
601	C₂²×C₄	—	2	6	no	—
602	C₂²×C₄	—	2	6	no	—
603	C₂²×C₄	—	2	3	no	—
604	C₂²×C₄	—	2	3	no	—
605	C₂²×C₄	—	2	3	no	—
606	C₂²×C₄	—	2	3	no	—
607	C₂²×C₄	—	2	3	no	—
608	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
609	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
610	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
614	Q₁₆	—	2	6	no	—
615	SD₁₆	—	2	6	no	—
616	SD₁₆	—	2	12	no	—
617	SD₁₆	—	2	2	no	—
618	D₈	—	2	6	no	—
619	M₁₆	—	2	6	no	—
620	M₁₆	—	2	12	no	—
621	M₁₆	C₂×D₄×C₈₉	1	12	yes	complemented
622	C₂×C₈	—	2	6	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	6	no	—
625	C₂×C₈	—	2	6	no	—
626	C₂×C₈	—	2	6	no	—
627	C₂×C₈	C₂×D₄×C₈₉	1	12	yes	complemented
628	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
630	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
632	C₄⋊C₄	—	2	3	no	—
633	C₄⋊C₄	—	2	6	no	—
634	C₄⋊C₄	—	2	3	no	—
635	C₄⋊C₄	—	2	3	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	3	no	—
638	C₄⋊C₄	—	2	3	no	—
639	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
640	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
642	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
643	C₂²⋊C₄	—	2	3	no	—
644	C₂²⋊C₄	—	2	6	no	—
645	C₂²⋊C₄	—	2	3	no	—
646	C₂²⋊C₄	—	2	3	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	3	no	—
649	C₂²⋊C₄	—	2	3	no	—
650	C₂²⋊C₄	—	2	3	no	—
651	C₂²⋊C₄	—	2	6	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	3	no	—
654	C₂²⋊C₄	—	2	3	no	—
655	C₄²	—	2	3	no	—
656	C₄²	—	2	3	no	—
657	C₂³	—	2	6	no	—
658	C₂³	—	2	6	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	3	no	—
661	C₂³	—	4	3	no	—
662	C₂³	—	4	6	no	—
663	C₂³	—	8	3	no	—
664	C₂³	—	8	3	no	—
665	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
666	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
667	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
668	Q₈	—	2	6	no	—
669	Q₈	—	2	3	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	2	3	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	4	6	no	—
674	Q₈	#121×C₈₉	1	4	yes	—
675	D₄	—	2	12	no	—
676	D₄	—	2	6	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	3	no	—
679	D₄	—	2	3	no	—
680	D₄	—	2	1	no	—
681	D₄	—	4	6	no	—
682	D₄	—	4	6	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	6	no	—
685	D₄	—	4	6	no	—
686	D₄	—	8	3	no	—
687	D₄	—	8	3	no	—
688	D₄	—	8	6	no	—
689	D₄	#121×C₈₉	1	12	yes	—
690	C₂×C₄	—	2	6	no	—
691	C₂×C₄	—	2	6	no	—
692	C₂×C₄	—	2	6	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	3	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	3	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	3	no	—
700	C₂×C₄	—	2	3	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	3	no	—
703	C₂×C₄	—	4	6	no	—
704	C₂×C₄	—	4	6	no	—
705	C₂×C₄	—	4	6	no	—
706	C₂×C₄	—	8	3	no	—
707	C₂×C₄	—	8	3	no	—
708	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
710	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
711	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
712	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
713	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	3	no	—
716	C₈	C₂²×D₄×C₈₉	1	2	yes	—
717	C₈	C₂²×D₄×C₈₉	1	6	yes	—
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	3	no	—
723	C₂²	—	2	3	no	—
724	C₂²	—	2	3	no	—
725	C₂²	—	4	12	no	—
726	C₂²	—	4	3	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	3	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	3	no	—
732	C₂²	—	16	6	no	—
733	C₂²	C₂×#121×C₈₉	1	6	yes	—
734	C₂²	#577×C₈₉	1	2	yes	complemented
735	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
736	C₄	—	2	1	no	—
737	C₄	—	2	3	no	—
738	C₄	—	4	3	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	3	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	3	no	—
744	C₄	C₂×#121×C₈₉	1	6	yes	—
745	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
746	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
747	C₂	—	2	2	no	—
748	C₂	—	2	6	no	—
749	C₂	—	4	3	no	—
750	C₂	—	8	1	no	—
751	C₂	—	8	3	no	—
752	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
753	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
754	C₂	C₈₉×#3584	1	1	yes	characteristic

	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. C₂×#577×C₈₉	C₂	semidirect
2. C₂²×#131×C₈₉	C₂	semidirect
3. C₈₉×#3489	C₂	semidirect
4. C₈₉×#3488	C₂	semidirect
5. C₈₉×#3063	C₂	semidirect
6. C₈₉×#3062	C₂	semidirect
7. C₈₉×#3060	C₂	semidirect
8. C₈₉×#3057	C₂	semidirect
9. C₈₉×#3056	C₂	semidirect
10. C₈₉×#3055	C₂	semidirect
11. C₈₉×#3050	C₂	semidirect
12. C₂×#465×C₈₉	C₂	semidirect
13. C₈₉×#2912	C₂	semidirect
14. C₈₉×#2898	C₂	semidirect
15. C₈₉×#2897	C₂	semidirect
20. C₂×#137×C₈₉	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
22. C₂×#135×C₈₉	C₂²	semidirect
23. C₂²×SD₁₆×C₈₉	C₂²	semidirect
27. C₂×#131×C₈₉	C₂²	semidirect
28. C₂×#131×C₈₉	C₂²	semidirect
29. C₂²×M₁₆×C₈₉	C₂²	semidirect
30. C₂³×C₈×C₈₉	C₂²	semidirect
40. #537×C₈₉	C₂²	semidirect
41. #536×C₈₉	C₂²	semidirect
44. #525×C₈₉	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
49. #470×C₈₉	C₂²	semidirect
50. #469×C₈₉	C₂²	semidirect
51. #468×C₈₉	C₂²	semidirect
52. #468×C₈₉	C₂²	semidirect
53. #467×C₈₉	C₂²	semidirect
54. #467×C₈₉	C₂²	semidirect
55. #466×C₈₉	C₂²	semidirect
56. #466×C₈₉	C₂²	semidirect
57. #465×C₈₉	C₂²	semidirect
58. #465×C₈₉	C₂²	semidirect
59. #465×C₈₉	C₂²	semidirect
60. #465×C₈₉	C₂²	semidirect
61. #465×C₈₉	C₂²	semidirect
62. #465×C₈₉	C₂²	semidirect
63. #465×C₈₉	C₂²	semidirect
64. #428×C₈₉	C₂²	semidirect
65. #428×C₈₉	C₂²	semidirect
66. #427×C₈₉	C₂²	semidirect
67. C₂×#106×C₈₉	C₂²	semidirect
68. #419×C₈₉	C₂²	semidirect
69. #418×C₈₉	C₂²	semidirect
70. #417×C₈₉	C₂²	semidirect
71. #417×C₈₉	C₂²	semidirect
72. #416×C₈₉	C₂²	semidirect
73. #416×C₈₉	C₂²	semidirect
74. C₂×#103×C₈₉	C₂²	semidirect
75. C₂×#102×C₈₉	C₂²	semidirect
110. #131×C₈₉	D₄	semidirect
243. M₁₆×C₈₉	C₂×D₄	semidirect
249. C₂×C₈×C₈₉	C₂×D₄	semidirect
356. C₂²×C₈₉	#577	semidirect
369. #60457	C₈₉	direct (N × H)
378. C₂×#577	C₂×C₈₉	semidirect
379. C₂²×#131	C₂×C₈₉	semidirect
380. #3489	C₂×C₈₉	semidirect
381. #3488	C₂×C₈₉	semidirect
382. #3063	C₂×C₈₉	semidirect
383. #3062	C₂×C₈₉	semidirect
384. #3060	C₂×C₈₉	semidirect
385. #3057	C₂×C₈₉	semidirect
386. #3056	C₂×C₈₉	semidirect
387. #3055	C₂×C₈₉	semidirect
388. #3050	C₂×C₈₉	semidirect
389. C₂×#465	C₂×C₈₉	semidirect
390. #2912	C₂×C₈₉	semidirect
391. #2898	C₂×C₈₉	semidirect
392. #2897	C₂×C₈₉	semidirect
393. C₈₉	#60457	direct (N × H)
398. C₂×#137	C₂²×C₈₉	semidirect
399. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
400. C₂×#135	C₂²×C₈₉	semidirect
401. C₂²×SD₁₆	C₂²×C₈₉	semidirect
405. C₂×#131	C₂²×C₈₉	semidirect
406. C₂×#131	C₂²×C₈₉	semidirect
407. C₂²×M₁₆	C₂²×C₈₉	semidirect
408. C₂³×C₈	C₂²×C₈₉	semidirect
418. #537	C₂²×C₈₉	semidirect
419. #536	C₂²×C₈₉	semidirect
422. #525	C₂²×C₈₉	semidirect
423. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
427. #470	C₂²×C₈₉	semidirect
428. #469	C₂²×C₈₉	semidirect
429. #468	C₂²×C₈₉	semidirect
430. #468	C₂²×C₈₉	semidirect
431. #467	C₂²×C₈₉	semidirect
432. #467	C₂²×C₈₉	semidirect
433. #466	C₂²×C₈₉	semidirect
434. #466	C₂²×C₈₉	semidirect
435. #465	C₂²×C₈₉	semidirect
436. #465	C₂²×C₈₉	semidirect
437. #465	C₂²×C₈₉	semidirect
438. #465	C₂²×C₈₉	semidirect
439. #465	C₂²×C₈₉	semidirect
440. #465	C₂²×C₈₉	semidirect
441. #465	C₂²×C₈₉	semidirect
442. #428	C₂²×C₈₉	semidirect
443. #428	C₂²×C₈₉	semidirect
444. #427	C₂²×C₈₉	semidirect
445. C₂×#106	C₂²×C₈₉	semidirect
446. #419	C₂²×C₈₉	semidirect
447. #418	C₂²×C₈₉	semidirect
448. #417	C₂²×C₈₉	semidirect
449. #417	C₂²×C₈₉	semidirect
450. #416	C₂²×C₈₉	semidirect
451. #416	C₂²×C₈₉	semidirect
452. C₂×#103	C₂²×C₈₉	semidirect
453. C₂×#102	C₂²×C₈₉	semidirect
488. #131	D₄×C₈₉	semidirect
621. M₁₆	C₂×D₄×C₈₉	semidirect
627. C₂×C₈	C₂×D₄×C₈₉	semidirect
734. C₂²	#577×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₈₉	2
C₂²×#131×C₈₉	2
C₈₉×#3489	2
C₈₉×#3488	2
C₈₉×#3063	2
C₈₉×#3062	2
C₈₉×#3060	2
C₈₉×#3057	2
C₈₉×#3056	2
C₈₉×#3055	2
C₈₉×#3050	2
C₂×#465×C₈₉	2
C₈₉×#2912	2
C₈₉×#2898	2
C₈₉×#2897	2
#60457	89

Subgroups — C89×#60457 #36438305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60457 #36438305