Subgroups — C₈₉×#25408 #36403256

Order 22784.

926 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3153	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#472×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#471×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#100×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
26	#532×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	#497×C₈₉	—	2	1	no	—
30	#496×C₈₉	—	2	1	no	—
31	#495×C₈₉	—	2	1	no	—
32	#495×C₈₉	—	2	1	no	—
33	#472×C₈₉	—	2	4	no	—
34	#471×C₈₉	—	2	4	no	—
35	#463×C₈₉	—	2	1	no	—
36	#463×C₈₉	—	2	1	no	—
37	#463×C₈₉	—	2	1	no	—
38	#463×C₈₉	—	2	1	no	—
39	#463×C₈₉	—	2	1	no	—
40	#463×C₈₉	—	2	1	no	—
41	#461×C₈₉	—	2	1	no	—
42	#459×C₈₉	—	2	1	no	—
43	#436×C₈₉	—	2	1	no	—
44	#435×C₈₉	—	2	1	no	—
45	#435×C₈₉	—	2	1	no	—
46	C₈×D₄×C₈₉	—	2	1	no	—
47	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
49	#423×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
51	#417×C₈₉	C₂²	1	1	yes	characteristic
52	#417×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#100×C₈₉	C₂²	1	1	yes	characteristic
61	#408×C₈₉	C₂²	1	1	yes	characteristic
62	#408×C₈₉	C₂²	1	1	yes	characteristic
63	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
64	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
65	#343×C₈₉	C₂²	1	1	yes	characteristic
66	#343×C₈₉	C₂²	1	1	yes	characteristic
67	#341×C₈₉	C₂²	1	1	yes	characteristic
68	#341×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	#137×C₈₉	—	2	2	no	—
76	#137×C₈₉	—	2	2	no	—
77	#137×C₈₉	—	4	1	no	—
78	#137×C₈₉	—	4	1	no	—
79	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
80	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
81	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
82	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
83	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
84	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
85	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
86	AGL(1,ℤ/8)×C₈₉	—	4	1	no	—
87	C₂×Q₁₆×C₈₉	—	2	1	no	—
88	C₂×Q₁₆×C₈₉	—	2	1	no	—
89	C₂×SD₁₆×C₈₉	—	2	1	no	—
90	C₂×SD₁₆×C₈₉	—	2	1	no	—
91	C₂×SD₁₆×C₈₉	—	2	1	no	—
92	C₂×SD₁₆×C₈₉	—	2	1	no	—
93	C₂×SD₁₆×C₈₉	—	2	2	no	—
94	C₂×SD₁₆×C₈₉	—	2	1	no	—
95	C₂×SD₁₆×C₈₉	—	2	1	no	—
96	C₂×SD₁₆×C₈₉	—	2	1	no	—
97	C₂×SD₁₆×C₈₉	—	2	1	no	—
98	C₂×SD₁₆×C₈₉	—	4	1	no	—
99	C₂×D₈×C₈₉	—	2	1	no	—
100	C₂×D₈×C₈₉	—	2	1	no	—
101	C₂×D₈×C₈₉	—	2	2	no	—
102	C₂×D₈×C₈₉	—	2	1	no	—
103	C₂×D₈×C₈₉	—	2	1	no	—
104	C₂×D₈×C₈₉	—	2	1	no	—
105	C₂×D₈×C₈₉	—	2	1	no	—
106	C₂×D₈×C₈₉	—	4	1	no	—
107	#131×C₈₉	—	2	2	no	—
108	#131×C₈₉	—	2	2	no	—
109	#131×C₈₉	—	4	1	no	—
110	#131×C₈₉	—	4	1	no	—
111	C₂×M₁₆×C₈₉	—	2	1	no	—
112	C₂×M₁₆×C₈₉	—	2	1	no	—
113	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
120	C₂²×C₈×C₈₉	—	2	1	no	—
121	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
124	#127×C₈₉	D₄	1	1	yes	characteristic
125	#124×C₈₉	—	2	1	no	—
126	#124×C₈₉	—	2	1	no	—
127	#124×C₈₉	—	2	1	no	—
128	#124×C₈₉	—	2	1	no	—
129	#124×C₈₉	D₄	1	1	yes	characteristic
130	#124×C₈₉	D₄	1	1	yes	characteristic
131	#121×C₈₉	—	2	1	no	—
132	#121×C₈₉	—	2	1	no	—
133	C₄×D₄×C₈₉	—	2	1	no	—
134	C₄×D₄×C₈₉	—	2	1	no	—
135	C₄×D₄×C₈₉	—	2	1	no	—
136	C₄×D₄×C₈₉	—	2	1	no	—
137	C₄×D₄×C₈₉	—	2	1	no	—
138	C₄×D₄×C₈₉	—	2	1	no	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
143	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
144	#108×C₈₉	—	2	2	no	—
145	#108×C₈₉	—	2	2	no	—
146	C₄⋊C₈×C₈₉	—	2	1	no	—
147	C₄⋊C₈×C₈₉	—	2	1	no	—
148	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
149	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
150	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
151	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
152	#103×C₈₉	—	2	1	no	—
153	#103×C₈₉	—	2	1	no	—
154	#103×C₈₉	—	2	1	no	—
155	#103×C₈₉	—	2	1	no	—
156	#102×C₈₉	—	2	1	no	—
157	#102×C₈₉	—	2	1	no	—
158	#102×C₈₉	—	2	1	no	—
159	#102×C₈₉	—	2	1	no	—
160	#101×C₈₉	—	2	2	no	—
161	#101×C₈₉	—	4	1	no	—
162	#100×C₈₉	—	2	2	no	—
163	#100×C₈₉	—	2	2	no	—
164	#100×C₈₉	—	4	1	no	—
165	#100×C₈₉	D₄	1	4	yes	complemented
166	C₂²⋊C₈×C₈₉	—	2	1	no	—
167	C₂²⋊C₈×C₈₉	—	2	1	no	—
168	C₂²⋊C₈×C₈₉	—	2	1	no	—
169	C₂²⋊C₈×C₈₉	—	2	1	no	—
170	#97×C₈₉	—	2	1	no	—
171	#97×C₈₉	—	2	1	no	—
172	C₄×C₈×C₈₉	—	2	1	no	—
173	C₄×C₈×C₈₉	—	2	1	no	—
174	C₂⁴×C₈₉	—	2	1	no	—
175	C₂⁴×C₈₉	—	2	1	no	—
176	#41×C₈₉	—	2	1	no	—
177	#41×C₈₉	—	2	1	no	—
178	#41×C₈₉	—	2	1	no	—
179	#41×C₈₉	—	2	1	no	—
180	#41×C₈₉	—	2	1	no	—
181	#41×C₈₉	—	2	1	no	—
182	#41×C₈₉	—	2	1	no	—
183	#41×C₈₉	—	2	1	no	—
184	C₂×Q₈×C₈₉	—	2	1	no	—
185	C₂×Q₈×C₈₉	—	2	1	no	—
186	C₂×Q₈×C₈₉	—	2	1	no	—
187	C₂×Q₈×C₈₉	—	2	1	no	—
188	C₂×Q₈×C₈₉	—	2	1	no	—
189	C₂×Q₈×C₈₉	—	2	1	no	—
190	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	2	1	no	—
205	C₂×D₄×C₈₉	—	2	1	no	—
206	C₂×D₄×C₈₉	—	2	1	no	—
207	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	—	2	1	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	4	1	no	—
215	C₂²×C₄×C₈₉	—	4	1	no	—
216	C₂²×C₄×C₈₉	—	8	2	no	—
217	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₈₉	—	4	2	no	—
221	Q₁₆×C₈₉	—	4	2	no	—
222	SD₁₆×C₈₉	—	4	2	no	—
223	SD₁₆×C₈₉	—	4	2	no	—
224	SD₁₆×C₈₉	—	4	2	no	—
225	SD₁₆×C₈₉	—	4	2	no	—
226	SD₁₆×C₈₉	—	4	2	no	—
227	SD₁₆×C₈₉	—	4	2	no	—
228	SD₁₆×C₈₉	—	4	2	no	—
229	SD₁₆×C₈₉	—	4	2	no	—
230	D₈×C₈₉	—	4	2	no	—
231	D₈×C₈₉	—	4	2	no	—
232	D₈×C₈₉	—	4	2	no	—
233	D₈×C₈₉	—	4	2	no	—
234	D₈×C₈₉	—	4	2	no	—
235	D₈×C₈₉	—	4	2	no	—
236	M₁₆×C₈₉	—	2	1	no	—
237	M₁₆×C₈₉	—	2	1	no	—
238	M₁₆×C₈₉	—	2	1	no	—
239	M₁₆×C₈₉	—	2	1	no	—
240	M₁₆×C₈₉	—	2	1	no	—
241	M₁₆×C₈₉	—	2	1	no	—
242	M₁₆×C₈₉	—	2	1	no	—
243	M₁₆×C₈₉	—	2	1	no	—
244	M₁₆×C₈₉	—	2	1	no	—
245	M₁₆×C₈₉	—	4	2	no	—
246	M₁₆×C₈₉	—	4	2	no	—
247	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
248	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
249	M₁₆×C₈₉	#41	1	2	yes	—
250	C₂×C₈×C₈₉	—	2	1	no	—
251	C₂×C₈×C₈₉	—	2	1	no	—
252	C₂×C₈×C₈₉	—	2	1	no	—
253	C₂×C₈×C₈₉	—	2	1	no	—
254	C₂×C₈×C₈₉	—	2	1	no	—
255	C₂×C₈×C₈₉	—	2	1	no	—
256	C₂×C₈×C₈₉	—	2	1	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	—	4	2	no	—
261	C₂×C₈×C₈₉	—	4	2	no	—
262	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₄⋊C₄×C₈₉	—	2	1	no	—
269	C₄⋊C₄×C₈₉	—	2	1	no	—
270	C₂²⋊C₄×C₈₉	—	2	1	no	—
271	C₂²⋊C₄×C₈₉	—	2	1	no	—
272	C₂²⋊C₄×C₈₉	—	2	1	no	—
273	C₂²⋊C₄×C₈₉	—	2	1	no	—
274	C₂²⋊C₄×C₈₉	—	4	1	no	—
275	C₂²⋊C₄×C₈₉	—	4	1	no	—
276	C₂²⋊C₄×C₈₉	—	4	1	no	—
277	C₂²⋊C₄×C₈₉	—	4	1	no	—
278	C₂²⋊C₄×C₈₉	—	4	1	no	—
279	C₂²⋊C₄×C₈₉	—	4	1	no	—
280	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
284	C₂³×C₈₉	—	2	1	no	—
285	C₂³×C₈₉	—	2	1	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	4	1	no	—
288	C₂³×C₈₉	—	4	1	no	—
289	C₂³×C₈₉	—	4	1	no	—
290	C₂³×C₈₉	—	4	1	no	—
291	C₂³×C₈₉	—	4	1	no	—
292	C₂³×C₈₉	—	8	1	no	—
293	C₂³×C₈₉	—	8	1	no	—
294	C₂³×C₈₉	—	8	1	no	—
295	C₂³×C₈₉	—	8	1	no	—
296	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
297	Q₈×C₈₉	—	2	1	no	—
298	Q₈×C₈₉	—	2	1	no	—
299	Q₈×C₈₉	—	2	1	no	—
300	Q₈×C₈₉	—	2	1	no	—
301	Q₈×C₈₉	—	4	1	no	—
302	Q₈×C₈₉	—	4	1	no	—
303	Q₈×C₈₉	—	4	1	no	—
304	Q₈×C₈₉	—	4	1	no	—
305	D₄×C₈₉	—	2	1	no	—
306	D₄×C₈₉	—	2	2	no	—
307	D₄×C₈₉	—	2	2	no	—
308	D₄×C₈₉	—	2	1	no	—
309	D₄×C₈₉	—	2	1	no	—
310	D₄×C₈₉	—	2	1	no	—
311	D₄×C₈₉	—	4	2	no	—
312	D₄×C₈₉	—	4	1	no	—
313	D₄×C₈₉	—	4	1	no	—
314	D₄×C₈₉	—	4	1	no	—
315	D₄×C₈₉	—	4	1	no	—
316	D₄×C₈₉	—	4	1	no	—
317	D₄×C₈₉	—	4	1	no	—
318	D₄×C₈₉	—	4	1	no	—
319	D₄×C₈₉	—	4	1	no	—
320	D₄×C₈₉	—	4	1	no	—
321	D₄×C₈₉	—	4	1	no	—
322	D₄×C₈₉	—	8	1	no	—
323	C₂×C₄×C₈₉	—	2	1	no	—
324	C₂×C₄×C₈₉	—	2	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	4	1	no	—
330	C₂×C₄×C₈₉	—	4	1	no	—
331	C₂×C₄×C₈₉	—	4	1	no	—
332	C₂×C₄×C₈₉	—	4	1	no	—
333	C₂×C₄×C₈₉	—	4	1	no	—
334	C₂×C₄×C₈₉	—	4	1	no	—
335	C₂×C₄×C₈₉	—	8	2	no	—
336	C₂×C₄×C₈₉	—	8	2	no	—
337	C₂×C₄×C₈₉	—	8	1	no	—
338	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
339	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
340	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
341	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
342	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
348	C₈×C₈₉	—	2	1	no	—
349	C₈×C₈₉	—	2	1	no	—
350	C₈×C₈₉	—	2	1	no	—
351	C₈×C₈₉	—	2	1	no	—
352	C₈×C₈₉	—	2	2	no	—
353	C₈×C₈₉	—	2	2	no	—
354	C₈×C₈₉	—	2	2	no	—
355	C₈×C₈₉	—	4	1	no	—
356	C₈×C₈₉	—	4	1	no	—
357	C₈×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	2	1	no	—
359	C₂²×C₈₉	—	2	1	no	—
360	C₂²×C₈₉	—	4	1	no	—
361	C₂²×C₈₉	—	4	1	no	—
362	C₂²×C₈₉	—	4	2	no	—
363	C₂²×C₈₉	—	4	1	no	—
364	C₂²×C₈₉	—	4	1	no	—
365	C₂²×C₈₉	—	4	1	no	—
366	C₂²×C₈₉	—	4	1	no	—
367	C₂²×C₈₉	—	8	2	no	—
368	C₂²×C₈₉	—	8	2	no	—
369	C₂²×C₈₉	—	8	1	no	—
370	C₂²×C₈₉	—	8	1	no	—
371	C₂²×C₈₉	—	8	1	no	—
372	C₂²×C₈₉	—	8	1	no	—
373	C₂²×C₈₉	—	8	1	no	—
374	C₂²×C₈₉	—	16	1	no	—
375	C₂²×C₈₉	—	16	1	no	—
376	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
377	C₂²×C₈₉	#532	1	1	yes	characteristic
378	C₂²×C₈₉	#540	1	1	yes	characteristic
379	C₄×C₈₉	—	2	1	no	—
380	C₄×C₈₉	—	2	1	no	—
381	C₄×C₈₉	—	2	1	no	—
382	C₄×C₈₉	—	2	1	no	—
383	C₄×C₈₉	—	4	1	no	—
384	C₄×C₈₉	—	4	1	no	—
385	C₄×C₈₉	—	8	1	no	—
386	C₄×C₈₉	—	8	1	no	—
387	C₄×C₈₉	D₄²	1	1	yes	characteristic
388	C₄×C₈₉	D₄²	1	1	yes	characteristic
389	C₄×C₈₉	#546	1	1	yes	characteristic
390	C₄×C₈₉	#550	1	1	yes	characteristic
391	#25408	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂×C₈₉	—	2	1	no	—
393	C₂×C₈₉	—	2	1	no	—
394	C₂×C₈₉	—	8	1	no	—
395	C₂×C₈₉	—	8	1	no	—
396	C₂×C₈₉	—	8	2	no	—
397	C₂×C₈₉	—	16	1	no	—
398	C₂×C₈₉	#2428	1	1	yes	characteristic
399	C₂×C₈₉	#3067	1	1	yes	characteristic
400	C₂×C₈₉	#3068	1	1	yes	characteristic
401	#3153	C₂×C₈₉	1	1	yes	characteristic, complemented
402	C₂×#472	C₂×C₈₉	1	1	yes	characteristic, complemented
403	C₂×#471	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#3036	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
406	#2935	C₂×C₈₉	1	1	yes	characteristic, complemented
407	#2052	C₂×C₈₉	1	1	yes	characteristic, complemented
408	#2051	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#2019	C₂×C₈₉	1	1	yes	characteristic, complemented
410	#2018	C₂×C₈₉	1	1	yes	characteristic, complemented
411	#1967	C₂×C₈₉	1	1	yes	characteristic, complemented
412	#1950	C₂×C₈₉	1	1	yes	characteristic, complemented
413	#1908	C₂×C₈₉	1	1	yes	characteristic, complemented
414	#1907	C₂×C₈₉	1	1	yes	characteristic, complemented
415	C₄×#100	C₂×C₈₉	1	1	yes	characteristic, complemented
416	C₈₉	#25408	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
423	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
424	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
427	#532	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
430	#497	—	2	1	no	—
431	#496	—	2	1	no	—
432	#495	—	2	1	no	—
433	#495	—	2	1	no	—
434	#472	—	2	4	no	—
435	#471	—	2	4	no	—
436	#463	—	2	1	no	—
437	#463	—	2	1	no	—
438	#463	—	2	1	no	—
439	#463	—	2	1	no	—
440	#463	—	2	1	no	—
441	#463	—	2	1	no	—
442	#461	—	2	1	no	—
443	#459	—	2	1	no	—
444	#436	—	2	1	no	—
445	#435	—	2	1	no	—
446	#435	—	2	1	no	—
447	C₈×D₄	—	2	1	no	—
448	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
449	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
450	#423	C₂²×C₈₉	1	1	yes	characteristic
451	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
452	#417	C₂²×C₈₉	1	1	yes	characteristic
453	#417	C₂²×C₈₉	1	1	yes	characteristic
454	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×#101	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#100	C₂²×C₈₉	1	1	yes	characteristic
462	#408	C₂²×C₈₉	1	1	yes	characteristic
463	#408	C₂²×C₈₉	1	1	yes	characteristic
464	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
465	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
466	#343	C₂²×C₈₉	1	1	yes	characteristic
467	#343	C₂²×C₈₉	1	1	yes	characteristic
468	#341	C₂²×C₈₉	1	1	yes	characteristic
469	#341	C₂²×C₈₉	1	1	yes	characteristic
470	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
471	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	#137	—	2	2	no	—
477	#137	—	2	2	no	—
478	#137	—	4	1	no	—
479	#137	—	4	1	no	—
480	AGL(1,ℤ/8)	—	2	2	no	—
481	AGL(1,ℤ/8)	—	2	2	no	—
482	AGL(1,ℤ/8)	—	2	2	no	—
483	AGL(1,ℤ/8)	—	2	2	no	—
484	AGL(1,ℤ/8)	—	4	1	no	—
485	AGL(1,ℤ/8)	—	4	1	no	—
486	AGL(1,ℤ/8)	—	4	1	no	—
487	AGL(1,ℤ/8)	—	4	1	no	—
488	C₂×Q₁₆	—	2	1	no	—
489	C₂×Q₁₆	—	2	1	no	—
490	C₂×SD₁₆	—	2	1	no	—
491	C₂×SD₁₆	—	2	1	no	—
492	C₂×SD₁₆	—	2	1	no	—
493	C₂×SD₁₆	—	2	1	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₂×SD₁₆	—	2	1	no	—
497	C₂×SD₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	1	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×D₈	—	2	2	no	—
501	C₂×D₈	—	2	1	no	—
502	C₂×D₈	—	2	1	no	—
503	C₂×D₈	—	2	1	no	—
504	C₂×D₈	—	2	1	no	—
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	2	1	no	—
507	C₂×D₈	—	4	1	no	—
508	#131	—	2	2	no	—
509	#131	—	2	2	no	—
510	#131	—	4	1	no	—
511	#131	—	4	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
520	C₂²×C₈	—	2	1	no	—
521	C₂²×C₈	—	2	1	no	—
522	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
524	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
525	#127	D₄×C₈₉	1	1	yes	characteristic
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#124	—	2	1	no	—
530	#124	D₄×C₈₉	1	1	yes	characteristic
531	#124	D₄×C₈₉	1	1	yes	characteristic
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
545	#108	—	2	2	no	—
546	#108	—	2	2	no	—
547	C₄⋊C₈	—	2	1	no	—
548	C₄⋊C₈	—	2	1	no	—
549	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
550	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
551	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
552	C₄⋊C₈	D₄×C₈₉	1	1	yes	characteristic
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	—	2	1	no	—
557	#102	—	2	1	no	—
558	#102	—	2	1	no	—
559	#102	—	2	1	no	—
560	#102	—	2	1	no	—
561	#101	—	2	2	no	—
562	#101	—	4	1	no	—
563	#100	—	2	2	no	—
564	#100	—	2	2	no	—
565	#100	—	4	1	no	—
566	#100	D₄×C₈₉	1	4	yes	complemented
567	C₂²⋊C₈	—	2	1	no	—
568	C₂²⋊C₈	—	2	1	no	—
569	C₂²⋊C₈	—	2	1	no	—
570	C₂²⋊C₈	—	2	1	no	—
571	#97	—	2	1	no	—
572	#97	—	2	1	no	—
573	C₄×C₈	—	2	1	no	—
574	C₄×C₈	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	#41	—	2	1	no	—
578	#41	—	2	1	no	—
579	#41	—	2	1	no	—
580	#41	—	2	1	no	—
581	#41	—	2	1	no	—
582	#41	—	2	1	no	—
583	#41	—	2	1	no	—
584	#41	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
592	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
609	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
610	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
621	Q₁₆	—	4	2	no	—
622	Q₁₆	—	4	2	no	—
623	SD₁₆	—	4	2	no	—
624	SD₁₆	—	4	2	no	—
625	SD₁₆	—	4	2	no	—
626	SD₁₆	—	4	2	no	—
627	SD₁₆	—	4	2	no	—
628	SD₁₆	—	4	2	no	—
629	SD₁₆	—	4	2	no	—
630	SD₁₆	—	4	2	no	—
631	D₈	—	4	2	no	—
632	D₈	—	4	2	no	—
633	D₈	—	4	2	no	—
634	D₈	—	4	2	no	—
635	D₈	—	4	2	no	—
636	D₈	—	4	2	no	—
637	M₁₆	—	2	1	no	—
638	M₁₆	—	2	1	no	—
639	M₁₆	—	2	1	no	—
640	M₁₆	—	2	1	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	1	no	—
643	M₁₆	—	2	1	no	—
644	M₁₆	—	2	1	no	—
645	M₁₆	—	2	1	no	—
646	M₁₆	—	4	2	no	—
647	M₁₆	—	4	2	no	—
648	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
649	M₁₆	C₂×D₄×C₈₉	1	2	yes	—
650	M₁₆	#41×C₈₉	1	2	yes	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	4	2	no	—
662	C₂×C₈	—	4	2	no	—
663	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
664	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
665	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
666	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₂²⋊C₄	—	4	1	no	—
681	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
684	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	8	1	no	—
694	C₂³	—	8	1	no	—
695	C₂³	—	8	1	no	—
696	C₂³	—	8	1	no	—
697	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
698	Q₈	—	2	1	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	1	no	—
702	Q₈	—	4	1	no	—
703	Q₈	—	4	1	no	—
704	Q₈	—	4	1	no	—
705	Q₈	—	4	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	1	no	—
714	D₄	—	4	1	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	8	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	2	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
740	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
741	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
742	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
746	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
747	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
748	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
749	C₈	—	2	1	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	2	2	no	—
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	4	1	no	—
757	C₈	—	4	1	no	—
758	C₈	—	4	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	2	no	—
769	C₂²	—	8	2	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	16	1	no	—
776	C₂²	—	16	1	no	—
777	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
778	C₂²	#532×C₈₉	1	1	yes	characteristic
779	C₂²	#540×C₈₉	1	1	yes	characteristic
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	8	1	no	—
787	C₄	—	8	1	no	—
788	C₄	D₄²×C₈₉	1	1	yes	characteristic
789	C₄	D₄²×C₈₉	1	1	yes	characteristic
790	C₄	#546×C₈₉	1	1	yes	characteristic
791	C₄	#550×C₈₉	1	1	yes	characteristic
792	C₂	—	2	1	no	—
793	C₂	—	2	1	no	—
794	C₂	—	8	1	no	—
795	C₂	—	8	1	no	—
796	C₂	—	8	2	no	—
797	C₂	—	16	1	no	—
798	C₂	C₈₉×#2428	1	1	yes	characteristic
799	C₂	C₈₉×#3067	1	1	yes	characteristic
800	C₂	C₈₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3153	C₂	semidirect
2. C₂×#472×C₈₉	C₂	semidirect
3. C₂×#471×C₈₉	C₂	semidirect
4. C₈₉×#3036	C₂	semidirect
5. C₂×#463×C₈₉	C₂	semidirect
6. C₈₉×#2935	C₂	semidirect
7. C₈₉×#2052	C₂	semidirect
8. C₈₉×#2051	C₂	semidirect
9. C₈₉×#2019	C₂	semidirect
10. C₈₉×#2018	C₂	semidirect
11. C₈₉×#1967	C₂	semidirect
12. C₈₉×#1950	C₂	semidirect
13. C₈₉×#1908	C₂	semidirect
14. C₈₉×#1907	C₂	semidirect
15. C₄×#100×C₈₉	C₂	semidirect
165. #100×C₈₉	D₄	semidirect
391. #25408	C₈₉	direct (N × H)
401. #3153	C₂×C₈₉	semidirect
402. C₂×#472	C₂×C₈₉	semidirect
403. C₂×#471	C₂×C₈₉	semidirect
404. #3036	C₂×C₈₉	semidirect
405. C₂×#463	C₂×C₈₉	semidirect
406. #2935	C₂×C₈₉	semidirect
407. #2052	C₂×C₈₉	semidirect
408. #2051	C₂×C₈₉	semidirect
409. #2019	C₂×C₈₉	semidirect
410. #2018	C₂×C₈₉	semidirect
411. #1967	C₂×C₈₉	semidirect
412. #1950	C₂×C₈₉	semidirect
413. #1908	C₂×C₈₉	semidirect
414. #1907	C₂×C₈₉	semidirect
415. C₄×#100	C₂×C₈₉	semidirect
416. C₈₉	#25408	direct (N × H)
566. #100	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3153	2
C₂×#472×C₈₉	2
C₂×#471×C₈₉	2
C₈₉×#3036	2
C₂×#463×C₈₉	2
C₈₉×#2935	2
C₈₉×#2052	2
C₈₉×#2051	2
C₈₉×#2019	2
C₈₉×#2018	2
C₈₉×#1967	2
C₈₉×#1950	2
C₈₉×#1908	2
C₈₉×#1907	2
C₄×#100×C₈₉	2
#25408	89

Subgroups — C89×#25408 #36403256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25408 #36403256