Subgroups — C₈₉×#60430 #36438278

Order 22784.

2762 conjugacy classes of subgroups.

The subgroup lattice has 742 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	C₂×#576×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×H(5,𝔽₂)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3046	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3045	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3042	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3041	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3040	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3036	C₂	1	3	yes	maximal, complemented
11	C₈₉×#3035	C₂	1	3	yes	maximal, complemented
12	C₂×#463×C₈₉	C₂	1	3	yes	maximal, complemented
13	C₈₉×#2906	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	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic
19	#577×C₈₉	—	2	8	no	—
20	#576×C₈₉	—	2	8	no	—
21	C₂×#137×C₈₉	C₂²	1	3	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	—
23	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	—
24	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	complemented
25	C₂×#135×C₈₉	C₂²	1	3	yes	—
26	C₂×#135×C₈₉	C₂²	1	3	yes	complemented
27	C₂²×SD₁₆×C₈₉	C₂²	1	3	yes	complemented
28	C₂²×D₈×C₈₉	C₂²	1	3	yes	—
29	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
31	#548×C₈₉	—	2	1	no	—
32	#548×C₈₉	—	2	1	no	—
33	#546×C₈₉	—	2	3	no	—
34	#546×C₈₉	—	2	3	no	—
35	#536×C₈₉	C₂²	1	3	yes	complemented
36	#535×C₈₉	C₂²	1	3	yes	complemented
37	#532×C₈₉	C₂²	1	3	yes	complemented
38	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
39	#520×C₈₉	—	2	1	no	—
40	#520×C₈₉	C₂²	1	1	yes	characteristic
41	#520×C₈₉	C₂²	1	3	yes	complemented
42	#518×C₈₉	—	2	3	no	—
43	#518×C₈₉	C₂²	1	3	yes	complemented
44	C₄×#41×C₈₉	—	2	1	no	—
45	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×#41×C₈₉	C₂²	1	3	yes	complemented
47	C₂×C₄×D₄×C₈₉	—	2	3	no	—
48	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	complemented
49	#464×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#464×C₈₉	C₂²	1	3	yes	complemented
51	#464×C₈₉	C₂²	1	6	yes	complemented
52	#463×C₈₉	C₂²	1	3	yes	complemented
53	#463×C₈₉	C₂²	1	6	yes	complemented
54	#463×C₈₉	C₂²	1	6	yes	complemented
55	#463×C₈₉	C₂²	1	6	yes	complemented
56	#463×C₈₉	C₂²	1	3	yes	complemented
57	#463×C₈₉	C₂²	1	6	yes	complemented
58	#462×C₈₉	C₂²	1	3	yes	complemented
59	#461×C₈₉	C₂²	1	3	yes	complemented
60	#461×C₈₉	C₂²	1	6	yes	complemented
61	#460×C₈₉	C₂²	1	3	yes	complemented
62	#459×C₈₉	C₂²	1	3	yes	complemented
63	#459×C₈₉	C₂²	1	6	yes	complemented
64	#424×C₈₉	C₂²	1	3	yes	complemented
65	#424×C₈₉	C₂²	1	3	yes	complemented
66	#423×C₈₉	C₂²	1	3	yes	complemented
67	C₂×C₄⋊C₈×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	H(5,𝔽₂)×C₈₉	—	2	4	no	—
81	H(5,𝔽₂)×C₈₉	D₄	1	8	yes	complemented
82	C₂×#41×C₈₉	—	2	1	no	—
83	C₂×#41×C₈₉	—	2	1	no	—
84	C₂×#41×C₈₉	—	2	3	no	—
85	C₂×#41×C₈₉	C₂³	1	3	yes	—
86	C₂×#41×C₈₉	C₂³	1	3	yes	—
87	C₂×#41×C₈₉	C₂³	1	3	yes	—
88	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₈₉	—	2	1	no	—
90	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
91	C₂²×D₄×C₈₉	—	2	3	no	—
92	C₂²×D₄×C₈₉	—	2	3	no	—
93	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
94	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
95	C₂³×C₄×C₈₉	—	2	3	no	—
96	#137×C₈₉	—	2	12	no	—
97	AGL(1,ℤ/8)×C₈₉	—	2	12	no	—
98	AGL(1,ℤ/8)×C₈₉	—	2	12	no	—
99	AGL(1,ℤ/8)×C₈₉	—	2	12	no	—
100	#135×C₈₉	—	2	12	no	—
101	#135×C₈₉	—	2	12	no	—
102	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×Q₁₆×C₈₉	C₂³	1	3	yes	—
104	C₂×SD₁₆×C₈₉	—	2	12	no	—
105	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×SD₁₆×C₈₉	C₂³	1	3	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	3	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	3	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
110	C₂×D₈×C₈₉	—	2	12	no	—
111	C₂×D₈×C₈₉	C₂³	1	3	yes	—
112	C₂×D₈×C₈₉	C₂³	1	3	yes	—
113	C₂×D₈×C₈₉	C₂³	1	6	yes	—
114	#131×C₈₉	—	2	4	no	—
115	#131×C₈₉	—	2	4	no	—
116	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
117	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
118	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
119	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
121	#127×C₈₉	C₂³	1	3	yes	—
122	#124×C₈₉	—	2	3	no	—
123	#124×C₈₉	—	2	3	no	—
124	#124×C₈₉	C₂³	1	3	yes	—
125	#124×C₈₉	C₂³	1	6	yes	—
126	#124×C₈₉	C₂³	1	1	yes	characteristic
127	#123×C₈₉	—	2	6	no	—
128	C₂²⋊Q₈×C₈₉	—	2	3	no	—
129	C₂²⋊Q₈×C₈₉	—	2	3	no	—
130	#121×C₈₉	—	2	3	no	—
131	#121×C₈₉	—	2	3	no	—
132	#121×C₈₉	—	2	3	no	—
133	#121×C₈₉	—	2	3	no	—
134	#120×C₈₉	—	2	6	no	—
135	C₄×Q₈×C₈₉	—	2	1	no	—
136	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
138	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
139	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₈₉	—	2	3	no	—
141	C₄×D₄×C₈₉	—	2	3	no	—
142	C₄×D₄×C₈₉	—	2	3	no	—
143	C₄×D₄×C₈₉	—	2	3	no	—
144	C₄×D₄×C₈₉	—	2	3	no	—
145	C₄×D₄×C₈₉	—	2	6	no	—
146	C₄×D₄×C₈₉	—	2	3	no	—
147	C₄×D₄×C₈₉	—	2	3	no	—
148	C₄×D₄×C₈₉	—	2	3	no	—
149	C₄×D₄×C₈₉	—	2	3	no	—
150	C₄×D₄×C₈₉	D₄	1	3	yes	—
151	C₄×D₄×C₈₉	D₄	1	3	yes	—
152	C₄×D₄×C₈₉	C₂³	1	6	yes	—
153	C₄×D₄×C₈₉	C₂³	1	3	yes	—
154	C₄×D₄×C₈₉	C₂³	1	3	yes	—
155	#117×C₈₉	—	2	3	no	—
156	#117×C₈₉	—	2	3	no	—
157	#117×C₈₉	C₂³	1	3	yes	—
158	#117×C₈₉	C₂³	1	3	yes	—
159	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
161	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
162	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
163	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
164	C₂×C₂²⋊C₄×C₈₉	—	2	6	no	—
165	C₂×C₄²×C₈₉	—	2	3	no	—
166	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
167	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
169	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
170	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
171	C₄⋊C₈×C₈₉	C₂³	1	6	yes	—
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	—	2	3	no	—
184	#41×C₈₉	—	2	8	no	—
185	#41×C₈₉	—	2	6	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	—	4	4	no	—
191	#41×C₈₉	—	4	12	no	—
192	#41×C₈₉	C₂×D₄	1	12	yes	—
193	#41×C₈₉	C₂×D₄	1	4	yes	—
194	#41×C₈₉	#41	1	4	yes	—
195	C₂×Q₈×C₈₉	—	2	3	no	—
196	C₂×Q₈×C₈₉	—	2	6	no	—
197	C₂×Q₈×C₈₉	—	2	6	no	—
198	C₂×Q₈×C₈₉	—	4	4	no	—
199	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
201	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₈₉	—	2	3	no	—
204	C₂×D₄×C₈₉	—	2	24	no	—
205	C₂×D₄×C₈₉	—	2	3	no	—
206	C₂×D₄×C₈₉	—	2	3	no	—
207	C₂×D₄×C₈₉	—	2	3	no	—
208	C₂×D₄×C₈₉	—	2	6	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	—	4	12	no	—
215	C₂×D₄×C₈₉	C₂×D₄	1	12	yes	—
216	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
217	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
218	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
220	C₂²×C₄×C₈₉	—	2	3	no	—
221	C₂²×C₄×C₈₉	—	2	3	no	—
222	C₂²×C₄×C₈₉	—	2	3	no	—
223	C₂²×C₄×C₈₉	—	2	3	no	—
224	C₂²×C₄×C₈₉	—	2	3	no	—
225	C₂²×C₄×C₈₉	—	2	3	no	—
226	C₂²×C₄×C₈₉	—	2	3	no	—
227	C₂²×C₄×C₈₉	—	2	6	no	—
228	C₂²×C₄×C₈₉	—	8	6	no	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
232	Q₁₆×C₈₉	—	2	2	no	—
233	Q₁₆×C₈₉	—	2	6	no	—
234	SD₁₆×C₈₉	—	2	2	no	—
235	SD₁₆×C₈₉	—	2	6	no	—
236	SD₁₆×C₈₉	—	2	6	no	—
237	SD₁₆×C₈₉	—	2	12	no	—
238	SD₁₆×C₈₉	—	2	6	no	—
239	D₈×C₈₉	—	2	6	no	—
240	D₈×C₈₉	—	2	12	no	—
241	D₈×C₈₉	—	2	6	no	—
242	M₁₆×C₈₉	—	2	6	no	—
243	M₁₆×C₈₉	—	2	6	no	—
244	C₂×C₈×C₈₉	—	2	6	no	—
245	C₂×C₈×C₈₉	—	2	6	no	—
246	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
248	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
250	C₄⋊C₄×C₈₉	—	2	3	no	—
251	C₄⋊C₄×C₈₉	—	2	3	no	—
252	C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₄⋊C₄×C₈₉	—	2	3	no	—
254	C₄⋊C₄×C₈₉	—	2	3	no	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
256	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
257	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
258	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂²⋊C₄×C₈₉	—	2	3	no	—
260	C₂²⋊C₄×C₈₉	—	2	3	no	—
261	C₂²⋊C₄×C₈₉	—	2	6	no	—
262	C₂²⋊C₄×C₈₉	—	2	3	no	—
263	C₂²⋊C₄×C₈₉	—	2	3	no	—
264	C₂²⋊C₄×C₈₉	—	2	3	no	—
265	C₂²⋊C₄×C₈₉	—	2	6	no	—
266	C₂²⋊C₄×C₈₉	—	2	6	no	—
267	C₂²⋊C₄×C₈₉	—	2	1	no	—
268	C₂²⋊C₄×C₈₉	—	2	1	no	—
269	C₂²⋊C₄×C₈₉	C₂×D₄	1	6	yes	—
270	C₄²×C₈₉	—	2	1	no	—
271	C₄²×C₈₉	—	2	3	no	—
272	C₄²×C₈₉	—	2	3	no	—
273	C₄²×C₈₉	C₂×D₄	1	3	yes	—
274	C₄²×C₈₉	C₂×D₄	1	3	yes	—
275	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₄²×C₈₉	C₂⁴	1	3	yes	—
277	C₂³×C₈₉	—	2	3	no	—
278	C₂³×C₈₉	—	2	12	no	—
279	C₂³×C₈₉	—	2	3	no	—
280	C₂³×C₈₉	—	2	1	no	—
281	C₂³×C₈₉	—	4	6	no	—
282	C₂³×C₈₉	—	8	3	no	—
283	C₂³×C₈₉	—	8	3	no	—
284	C₂³×C₈₉	—	8	3	no	—
285	C₂³×C₈₉	—	8	3	no	—
286	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
287	Q₈×C₈₉	—	2	1	no	—
288	Q₈×C₈₉	—	2	3	no	—
289	Q₈×C₈₉	—	2	1	no	—
290	Q₈×C₈₉	—	2	3	no	—
291	Q₈×C₈₉	—	2	1	no	—
292	Q₈×C₈₉	—	4	6	no	—
293	Q₈×C₈₉	#121	1	4	yes	—
294	Q₈×C₈₉	C₂²×D₄	1	2	yes	—
295	D₄×C₈₉	—	2	12	no	—
296	D₄×C₈₉	—	2	12	no	—
297	D₄×C₈₉	—	2	3	no	—
298	D₄×C₈₉	—	2	1	no	—
299	D₄×C₈₉	—	2	3	no	—
300	D₄×C₈₉	—	2	3	no	—
301	D₄×C₈₉	—	2	1	no	—
302	D₄×C₈₉	—	4	6	no	—
303	D₄×C₈₉	—	4	6	no	—
304	D₄×C₈₉	—	4	6	no	—
305	D₄×C₈₉	—	8	3	no	—
306	D₄×C₈₉	—	8	3	no	—
307	D₄×C₈₉	#121	1	12	yes	—
308	D₄×C₈₉	C₂²×D₄	1	6	yes	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	12	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	3	no	—
313	C₂×C₄×C₈₉	—	2	3	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	4	3	no	—
316	C₂×C₄×C₈₉	—	4	3	no	—
317	C₂×C₄×C₈₉	—	4	6	no	—
318	C₂×C₄×C₈₉	—	4	6	no	—
319	C₂×C₄×C₈₉	—	4	6	no	—
320	C₂×C₄×C₈₉	—	4	6	no	—
321	C₂×C₄×C₈₉	—	8	3	no	—
322	C₂×C₄×C₈₉	—	8	6	no	—
323	C₂×C₄×C₈₉	—	8	3	no	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
328	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
329	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
330	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
331	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
332	C₈×C₈₉	—	2	1	no	—
333	C₈×C₈₉	—	2	1	no	—
334	C₈×C₈₉	—	2	3	no	—
335	C₈×C₈₉	—	2	3	no	—
336	C₂²×C₈₉	—	2	3	no	—
337	C₂²×C₈₉	—	2	3	no	—
338	C₂²×C₈₉	—	2	6	no	—
339	C₂²×C₈₉	—	4	3	no	—
340	C₂²×C₈₉	—	4	3	no	—
341	C₂²×C₈₉	—	4	1	no	—
342	C₂²×C₈₉	—	4	3	no	—
343	C₂²×C₈₉	—	4	1	no	—
344	C₂²×C₈₉	—	4	3	no	—
345	C₂²×C₈₉	—	4	1	no	—
346	C₂²×C₈₉	—	4	3	no	—
347	C₂²×C₈₉	—	8	12	no	—
348	C₂²×C₈₉	—	16	6	no	—
349	C₂²×C₈₉	C₂×#121	1	6	yes	—
350	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₈₉	—	2	1	no	—
352	C₄×C₈₉	—	2	3	no	—
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	3	no	—
355	C₄×C₈₉	—	2	2	no	—
356	C₄×C₈₉	—	4	1	no	—
357	C₄×C₈₉	—	4	3	no	—
358	C₄×C₈₉	—	4	1	no	—
359	C₄×C₈₉	—	4	3	no	—
360	C₄×C₈₉	C₂×#121	1	6	yes	—
361	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
363	#60430	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂×C₈₉	—	2	6	no	—
365	C₂×C₈₉	—	4	6	no	—
366	C₂×C₈₉	—	8	1	no	—
367	C₂×C₈₉	—	8	3	no	—
368	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
369	C₂×C₈₉	#3584	1	1	yes	characteristic
370	C₂×C₈₉	#3585	1	1	yes	characteristic
371	C₂×#577	C₂×C₈₉	1	1	yes	characteristic, complemented
372	C₂×#576	C₂×C₈₉	1	1	yes	characteristic, complemented
373	#3500	C₂×C₈₉	1	1	yes	characteristic, complemented
374	C₄×H(5,𝔽₂)	C₂×C₈₉	1	1	yes	characteristic, complemented
375	#3046	C₂×C₈₉	1	3	yes	complemented
376	#3045	C₂×C₈₉	1	3	yes	complemented
377	#3042	C₂×C₈₉	1	3	yes	complemented
378	#3041	C₂×C₈₉	1	3	yes	complemented
379	#3040	C₂×C₈₉	1	3	yes	complemented
380	#3036	C₂×C₈₉	1	3	yes	complemented
381	#3035	C₂×C₈₉	1	3	yes	complemented
382	C₂×#463	C₂×C₈₉	1	3	yes	complemented
383	#2906	C₂×C₈₉	1	1	yes	characteristic, complemented
384	#2898	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#2897	C₂×C₈₉	1	1	yes	characteristic, complemented
386	C₈₉	#60430	1	1	yes	characteristic, direct product factor, Sylow
387	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	1	yes	characteristic
388	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
389	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	1	yes	characteristic
390	#577	—	2	8	no	—
391	#576	—	2	8	no	—
392	C₂×#137	C₂²×C₈₉	1	3	yes	complemented
393	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	3	yes	—
394	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	3	yes	—
395	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	3	yes	complemented
396	C₂×#135	C₂²×C₈₉	1	3	yes	—
397	C₂×#135	C₂²×C₈₉	1	3	yes	complemented
398	C₂²×SD₁₆	C₂²×C₈₉	1	3	yes	complemented
399	C₂²×D₈	C₂²×C₈₉	1	3	yes	—
400	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
401	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
402	#548	—	2	1	no	—
403	#548	—	2	1	no	—
404	#546	—	2	3	no	—
405	#546	—	2	3	no	—
406	#536	C₂²×C₈₉	1	3	yes	complemented
407	#535	C₂²×C₈₉	1	3	yes	complemented
408	#532	C₂²×C₈₉	1	3	yes	complemented
409	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
410	#520	—	2	1	no	—
411	#520	C₂²×C₈₉	1	1	yes	characteristic
412	#520	C₂²×C₈₉	1	3	yes	complemented
413	#518	—	2	3	no	—
414	#518	C₂²×C₈₉	1	3	yes	complemented
415	C₄×#41	—	2	1	no	—
416	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
417	C₄×#41	C₂²×C₈₉	1	3	yes	complemented
418	C₂×C₄×D₄	—	2	3	no	—
419	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	complemented
420	#464	C₂²×C₈₉	1	1	yes	characteristic, complemented
421	#464	C₂²×C₈₉	1	3	yes	complemented
422	#464	C₂²×C₈₉	1	6	yes	complemented
423	#463	C₂²×C₈₉	1	3	yes	complemented
424	#463	C₂²×C₈₉	1	6	yes	complemented
425	#463	C₂²×C₈₉	1	6	yes	complemented
426	#463	C₂²×C₈₉	1	6	yes	complemented
427	#463	C₂²×C₈₉	1	3	yes	complemented
428	#463	C₂²×C₈₉	1	6	yes	complemented
429	#462	C₂²×C₈₉	1	3	yes	complemented
430	#461	C₂²×C₈₉	1	3	yes	complemented
431	#461	C₂²×C₈₉	1	6	yes	complemented
432	#460	C₂²×C₈₉	1	3	yes	complemented
433	#459	C₂²×C₈₉	1	3	yes	complemented
434	#459	C₂²×C₈₉	1	6	yes	complemented
435	#424	C₂²×C₈₉	1	3	yes	complemented
436	#424	C₂²×C₈₉	1	3	yes	complemented
437	#423	C₂²×C₈₉	1	3	yes	complemented
438	C₂×C₄⋊C₈	C₂²×C₈₉	1	3	yes	complemented
439	#419	C₂²×C₈₉	1	3	yes	complemented
440	#418	C₂²×C₈₉	1	3	yes	complemented
441	#417	C₂²×C₈₉	1	3	yes	complemented
442	#417	C₂²×C₈₉	1	3	yes	complemented
443	#416	C₂²×C₈₉	1	3	yes	complemented
444	#416	C₂²×C₈₉	1	3	yes	complemented
445	C₂×#103	C₂²×C₈₉	1	3	yes	complemented
446	C₂×#102	C₂²×C₈₉	1	3	yes	complemented
447	2₋¹⁺⁴	—	2	4	no	—
448	2₋¹⁺⁴	—	2	4	no	—
449	H(5,𝔽₂)	—	2	4	no	—
450	H(5,𝔽₂)	—	2	4	no	—
451	H(5,𝔽₂)	—	2	4	no	—
452	H(5,𝔽₂)	D₄×C₈₉	1	8	yes	complemented
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	3	no	—
456	C₂×#41	C₂³×C₈₉	1	3	yes	—
457	C₂×#41	C₂³×C₈₉	1	3	yes	—
458	C₂×#41	C₂³×C₈₉	1	3	yes	—
459	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
460	C₂²×Q₈	—	2	1	no	—
461	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
462	C₂²×D₄	—	2	3	no	—
463	C₂²×D₄	—	2	3	no	—
464	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
465	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
466	C₂³×C₄	—	2	3	no	—
467	#137	—	2	12	no	—
468	AGL(1,ℤ/8)	—	2	12	no	—
469	AGL(1,ℤ/8)	—	2	12	no	—
470	AGL(1,ℤ/8)	—	2	12	no	—
471	#135	—	2	12	no	—
472	#135	—	2	12	no	—
473	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
474	C₂×Q₁₆	C₂³×C₈₉	1	3	yes	—
475	C₂×SD₁₆	—	2	12	no	—
476	C₂×SD₁₆	C₂³×C₈₉	1	3	yes	—
477	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
478	C₂×SD₁₆	C₂³×C₈₉	1	3	yes	—
479	C₂×SD₁₆	C₂³×C₈₉	1	3	yes	—
480	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
481	C₂×D₈	—	2	12	no	—
482	C₂×D₈	C₂³×C₈₉	1	3	yes	—
483	C₂×D₈	C₂³×C₈₉	1	6	yes	—
484	C₂×D₈	C₂³×C₈₉	1	3	yes	—
485	#131	—	2	4	no	—
486	#131	—	2	4	no	—
487	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
488	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
489	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
490	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
491	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
492	#127	C₂³×C₈₉	1	3	yes	—
493	#124	—	2	3	no	—
494	#124	—	2	3	no	—
495	#124	C₂³×C₈₉	1	3	yes	—
496	#124	C₂³×C₈₉	1	6	yes	—
497	#124	C₂³×C₈₉	1	1	yes	characteristic
498	#123	—	2	6	no	—
499	C₂²⋊Q₈	—	2	3	no	—
500	C₂²⋊Q₈	—	2	3	no	—
501	#121	—	2	3	no	—
502	#121	—	2	3	no	—
503	#121	—	2	3	no	—
504	#121	—	2	3	no	—
505	#120	—	2	6	no	—
506	C₄×Q₈	—	2	1	no	—
507	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
508	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
510	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
511	C₄×D₄	—	2	3	no	—
512	C₄×D₄	—	2	3	no	—
513	C₄×D₄	—	2	3	no	—
514	C₄×D₄	—	2	3	no	—
515	C₄×D₄	—	2	3	no	—
516	C₄×D₄	—	2	6	no	—
517	C₄×D₄	—	2	3	no	—
518	C₄×D₄	—	2	3	no	—
519	C₄×D₄	—	2	3	no	—
520	C₄×D₄	—	2	3	no	—
521	C₄×D₄	D₄×C₈₉	1	3	yes	—
522	C₄×D₄	D₄×C₈₉	1	3	yes	—
523	C₄×D₄	C₂³×C₈₉	1	3	yes	—
524	C₄×D₄	C₂³×C₈₉	1	6	yes	—
525	C₄×D₄	C₂³×C₈₉	1	3	yes	—
526	#117	—	2	3	no	—
527	#117	—	2	3	no	—
528	#117	C₂³×C₈₉	1	3	yes	—
529	#117	C₂³×C₈₉	1	3	yes	—
530	C₂×C₄⋊C₄	—	2	3	no	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
532	C₂×C₂²⋊C₄	—	2	3	no	—
533	C₂×C₂²⋊C₄	—	2	3	no	—
534	C₂×C₂²⋊C₄	—	2	3	no	—
535	C₂×C₂²⋊C₄	—	2	6	no	—
536	C₂×C₄²	—	2	3	no	—
537	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
538	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
540	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
541	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
542	C₄⋊C₈	C₂³×C₈₉	1	6	yes	—
543	#103	C₂³×C₈₉	1	3	yes	—
544	#103	C₂³×C₈₉	1	6	yes	—
545	#103	C₂³×C₈₉	1	1	yes	characteristic
546	#103	C₂³×C₈₉	1	3	yes	—
547	#103	C₂³×C₈₉	1	3	yes	—
548	#102	C₂³×C₈₉	1	3	yes	—
549	#102	C₂³×C₈₉	1	6	yes	—
550	#102	C₂³×C₈₉	1	1	yes	characteristic
551	#102	C₂³×C₈₉	1	3	yes	—
552	#102	C₂³×C₈₉	1	3	yes	—
553	C₂⁴	—	2	3	no	—
554	C₂⁴	—	2	3	no	—
555	#41	—	2	8	no	—
556	#41	—	2	6	no	—
557	#41	—	2	6	no	—
558	#41	—	2	6	no	—
559	#41	—	2	6	no	—
560	#41	—	2	6	no	—
561	#41	—	4	4	no	—
562	#41	—	4	12	no	—
563	#41	C₂×D₄×C₈₉	1	12	yes	—
564	#41	C₂×D₄×C₈₉	1	4	yes	—
565	#41	#41×C₈₉	1	4	yes	—
566	C₂×Q₈	—	2	3	no	—
567	C₂×Q₈	—	2	6	no	—
568	C₂×Q₈	—	2	6	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
571	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
572	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
574	C₂×D₄	—	2	3	no	—
575	C₂×D₄	—	2	24	no	—
576	C₂×D₄	—	2	3	no	—
577	C₂×D₄	—	2	3	no	—
578	C₂×D₄	—	2	3	no	—
579	C₂×D₄	—	2	6	no	—
580	C₂×D₄	—	2	3	no	—
581	C₂×D₄	—	2	3	no	—
582	C₂×D₄	—	2	3	no	—
583	C₂×D₄	—	2	6	no	—
584	C₂×D₄	—	2	6	no	—
585	C₂×D₄	—	4	12	no	—
586	C₂×D₄	C₂×D₄×C₈₉	1	12	yes	—
587	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
588	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
589	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
591	C₂²×C₄	—	2	3	no	—
592	C₂²×C₄	—	2	3	no	—
593	C₂²×C₄	—	2	3	no	—
594	C₂²×C₄	—	2	3	no	—
595	C₂²×C₄	—	2	3	no	—
596	C₂²×C₄	—	2	3	no	—
597	C₂²×C₄	—	2	3	no	—
598	C₂²×C₄	—	2	6	no	—
599	C₂²×C₄	—	8	6	no	—
600	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
601	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
602	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
603	Q₁₆	—	2	2	no	—
604	Q₁₆	—	2	6	no	—
605	SD₁₆	—	2	2	no	—
606	SD₁₆	—	2	6	no	—
607	SD₁₆	—	2	6	no	—
608	SD₁₆	—	2	12	no	—
609	SD₁₆	—	2	6	no	—
610	D₈	—	2	6	no	—
611	D₈	—	2	12	no	—
612	D₈	—	2	6	no	—
613	M₁₆	—	2	6	no	—
614	M₁₆	—	2	6	no	—
615	C₂×C₈	—	2	6	no	—
616	C₂×C₈	—	2	6	no	—
617	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
619	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
621	C₄⋊C₄	—	2	3	no	—
622	C₄⋊C₄	—	2	3	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	3	no	—
625	C₄⋊C₄	—	2	3	no	—
626	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
627	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
628	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
629	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
630	C₂²⋊C₄	—	2	3	no	—
631	C₂²⋊C₄	—	2	3	no	—
632	C₂²⋊C₄	—	2	6	no	—
633	C₂²⋊C₄	—	2	3	no	—
634	C₂²⋊C₄	—	2	3	no	—
635	C₂²⋊C₄	—	2	3	no	—
636	C₂²⋊C₄	—	2	6	no	—
637	C₂²⋊C₄	—	2	6	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	C₂×D₄×C₈₉	1	6	yes	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	3	no	—
643	C₄²	—	2	3	no	—
644	C₄²	C₂×D₄×C₈₉	1	3	yes	—
645	C₄²	C₂×D₄×C₈₉	1	3	yes	—
646	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
647	C₄²	C₂⁴×C₈₉	1	3	yes	—
648	C₂³	—	2	3	no	—
649	C₂³	—	2	12	no	—
650	C₂³	—	2	3	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	4	6	no	—
653	C₂³	—	8	3	no	—
654	C₂³	—	8	3	no	—
655	C₂³	—	8	3	no	—
656	C₂³	—	8	3	no	—
657	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
658	Q₈	—	2	1	no	—
659	Q₈	—	2	3	no	—
660	Q₈	—	2	1	no	—
661	Q₈	—	2	3	no	—
662	Q₈	—	2	1	no	—
663	Q₈	—	4	6	no	—
664	Q₈	#121×C₈₉	1	4	yes	—
665	Q₈	C₂²×D₄×C₈₉	1	2	yes	—
666	D₄	—	2	12	no	—
667	D₄	—	2	12	no	—
668	D₄	—	2	3	no	—
669	D₄	—	2	1	no	—
670	D₄	—	2	3	no	—
671	D₄	—	2	3	no	—
672	D₄	—	2	1	no	—
673	D₄	—	4	6	no	—
674	D₄	—	4	6	no	—
675	D₄	—	4	6	no	—
676	D₄	—	8	3	no	—
677	D₄	—	8	3	no	—
678	D₄	#121×C₈₉	1	12	yes	—
679	D₄	C₂²×D₄×C₈₉	1	6	yes	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	12	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	3	no	—
684	C₂×C₄	—	2	3	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	4	3	no	—
687	C₂×C₄	—	4	3	no	—
688	C₂×C₄	—	4	6	no	—
689	C₂×C₄	—	4	6	no	—
690	C₂×C₄	—	4	6	no	—
691	C₂×C₄	—	4	6	no	—
692	C₂×C₄	—	8	3	no	—
693	C₂×C₄	—	8	6	no	—
694	C₂×C₄	—	8	3	no	—
695	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
697	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
699	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
700	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
701	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
702	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	3	no	—
706	C₈	—	2	3	no	—
707	C₂²	—	2	3	no	—
708	C₂²	—	2	3	no	—
709	C₂²	—	2	6	no	—
710	C₂²	—	4	3	no	—
711	C₂²	—	4	3	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	3	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	3	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	3	no	—
718	C₂²	—	8	12	no	—
719	C₂²	—	16	6	no	—
720	C₂²	C₂×#121×C₈₉	1	6	yes	—
721	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
722	C₄	—	2	1	no	—
723	C₄	—	2	3	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	3	no	—
726	C₄	—	2	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	3	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	3	no	—
731	C₄	C₂×#121×C₈₉	1	6	yes	—
732	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
733	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
734	C₂	—	2	6	no	—
735	C₂	—	4	6	no	—
736	C₂	—	8	1	no	—
737	C₂	—	8	3	no	—
738	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
739	C₂	C₈₉×#3584	1	1	yes	characteristic
740	C₂	C₈₉×#3585	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 ◁ C₄×#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. C₂×#576×C₈₉	C₂	semidirect
3. C₈₉×#3500	C₂	semidirect
4. C₄×H(5,𝔽₂)×C₈₉	C₂	semidirect
5. C₈₉×#3046	C₂	semidirect
6. C₈₉×#3045	C₂	semidirect
7. C₈₉×#3042	C₂	semidirect
8. C₈₉×#3041	C₂	semidirect
9. C₈₉×#3040	C₂	semidirect
10. C₈₉×#3036	C₂	semidirect
11. C₈₉×#3035	C₂	semidirect
12. C₂×#463×C₈₉	C₂	semidirect
13. C₈₉×#2906	C₂	semidirect
14. C₈₉×#2898	C₂	semidirect
15. C₈₉×#2897	C₂	semidirect
21. C₂×#137×C₈₉	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
26. C₂×#135×C₈₉	C₂²	semidirect
27. C₂²×SD₁₆×C₈₉	C₂²	semidirect
35. #536×C₈₉	C₂²	semidirect
36. #535×C₈₉	C₂²	semidirect
37. #532×C₈₉	C₂²	semidirect
38. C₂×#124×C₈₉	C₂²	semidirect
41. #520×C₈₉	C₂²	semidirect
43. #518×C₈₉	C₂²	semidirect
46. C₄×#41×C₈₉	C₂²	semidirect
48. C₂×C₄×D₄×C₈₉	C₂²	semidirect
49. #464×C₈₉	C₂²	semidirect
50. #464×C₈₉	C₂²	semidirect
51. #464×C₈₉	C₂²	semidirect
52. #463×C₈₉	C₂²	semidirect
53. #463×C₈₉	C₂²	semidirect
54. #463×C₈₉	C₂²	semidirect
55. #463×C₈₉	C₂²	semidirect
56. #463×C₈₉	C₂²	semidirect
57. #463×C₈₉	C₂²	semidirect
58. #462×C₈₉	C₂²	semidirect
59. #461×C₈₉	C₂²	semidirect
60. #461×C₈₉	C₂²	semidirect
61. #460×C₈₉	C₂²	semidirect
62. #459×C₈₉	C₂²	semidirect
63. #459×C₈₉	C₂²	semidirect
64. #424×C₈₉	C₂²	semidirect
65. #424×C₈₉	C₂²	semidirect
66. #423×C₈₉	C₂²	semidirect
67. C₂×C₄⋊C₈×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
81. H(5,𝔽₂)×C₈₉	D₄	semidirect
363. #60430	C₈₉	direct (N × H)
371. C₂×#577	C₂×C₈₉	semidirect
372. C₂×#576	C₂×C₈₉	semidirect
373. #3500	C₂×C₈₉	semidirect
374. C₄×H(5,𝔽₂)	C₂×C₈₉	semidirect
375. #3046	C₂×C₈₉	semidirect
376. #3045	C₂×C₈₉	semidirect
377. #3042	C₂×C₈₉	semidirect
378. #3041	C₂×C₈₉	semidirect
379. #3040	C₂×C₈₉	semidirect
380. #3036	C₂×C₈₉	semidirect
381. #3035	C₂×C₈₉	semidirect
382. C₂×#463	C₂×C₈₉	semidirect
383. #2906	C₂×C₈₉	semidirect
384. #2898	C₂×C₈₉	semidirect
385. #2897	C₂×C₈₉	semidirect
386. C₈₉	#60430	direct (N × H)
392. C₂×#137	C₂²×C₈₉	semidirect
395. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
397. C₂×#135	C₂²×C₈₉	semidirect
398. C₂²×SD₁₆	C₂²×C₈₉	semidirect
406. #536	C₂²×C₈₉	semidirect
407. #535	C₂²×C₈₉	semidirect
408. #532	C₂²×C₈₉	semidirect
409. C₂×#124	C₂²×C₈₉	semidirect
412. #520	C₂²×C₈₉	semidirect
414. #518	C₂²×C₈₉	semidirect
417. C₄×#41	C₂²×C₈₉	semidirect
419. C₂×C₄×D₄	C₂²×C₈₉	semidirect
420. #464	C₂²×C₈₉	semidirect
421. #464	C₂²×C₈₉	semidirect
422. #464	C₂²×C₈₉	semidirect
423. #463	C₂²×C₈₉	semidirect
424. #463	C₂²×C₈₉	semidirect
425. #463	C₂²×C₈₉	semidirect
426. #463	C₂²×C₈₉	semidirect
427. #463	C₂²×C₈₉	semidirect
428. #463	C₂²×C₈₉	semidirect
429. #462	C₂²×C₈₉	semidirect
430. #461	C₂²×C₈₉	semidirect
431. #461	C₂²×C₈₉	semidirect
432. #460	C₂²×C₈₉	semidirect
433. #459	C₂²×C₈₉	semidirect
434. #459	C₂²×C₈₉	semidirect
435. #424	C₂²×C₈₉	semidirect
436. #424	C₂²×C₈₉	semidirect
437. #423	C₂²×C₈₉	semidirect
438. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
439. #419	C₂²×C₈₉	semidirect
440. #418	C₂²×C₈₉	semidirect
441. #417	C₂²×C₈₉	semidirect
442. #417	C₂²×C₈₉	semidirect
443. #416	C₂²×C₈₉	semidirect
444. #416	C₂²×C₈₉	semidirect
445. C₂×#103	C₂²×C₈₉	semidirect
446. C₂×#102	C₂²×C₈₉	semidirect
452. H(5,𝔽₂)	D₄×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
C₂×#576×C₈₉	2
C₈₉×#3500	2
C₄×H(5,𝔽₂)×C₈₉	2
C₈₉×#3046	2
C₈₉×#3045	2
C₈₉×#3042	2
C₈₉×#3041	2
C₈₉×#3040	2
C₈₉×#3036	2
C₈₉×#3035	2
C₂×#463×C₈₉	2
C₈₉×#2906	2
C₈₉×#2898	2
C₈₉×#2897	2
#60430	89

Subgroups — C89×#60430 #36438278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60430 #36438278