Subgroups — C₈₉×#33471 #36411319

Order 22784.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#509×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×AGL(1,ℤ/16)	C₂	1	8	yes	maximal, complemented
5	C₈₉×#2155	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#361×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2145	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2110	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
11	#568×C₈₉	—	2	1	no	—
12	#518×C₈₉	—	2	1	no	—
13	#509×C₈₉	C₄	1	4	yes	complemented
14	#509×C₈₉	C₂²	1	4	yes	—
15	C₂×SD₃₂×C₈₉	C₄	1	2	yes	complemented
16	C₂×D₁₆×C₈₉	C₄	1	2	yes	complemented
17	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
19	#444×C₈₉	C₂²	1	4	yes	complemented
20	#443×C₈₉	—	2	2	no	—
21	#442×C₈₉	C₂²	1	4	yes	complemented
22	C₄×D₈×C₈₉	—	2	2	no	—
23	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
24	#427×C₈₉	C₂²	1	1	yes	characteristic
25	#421×C₈₉	—	2	1	no	—
26	#418×C₈₉	—	2	1	no	—
27	#405×C₈₉	C₂²	1	1	yes	characteristic
28	#365×C₈₉	C₂²	1	4	yes	complemented
29	#361×C₈₉	C₂²	1	4	yes	complemented
30	#360×C₈₉	C₂²	1	4	yes	complemented
31	#347×C₈₉	C₂²	1	4	yes	complemented
32	C₂×#41×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	—	2	1	no	—
34	#135×C₈₉	—	2	1	no	—
35	#135×C₈₉	—	2	1	no	—
36	#135×C₈₉	C₂×C₄	1	2	yes	complemented
37	#135×C₈₉	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂×SD₁₆×C₈₉	—	2	1	no	—
40	C₂×D₈×C₈₉	—	2	1	no	—
41	C₂×D₈×C₈₉	—	2	1	no	—
42	C₂×D₈×C₈₉	—	2	1	no	—
43	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
44	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×D₈×C₈₉	C₂³	1	2	yes	—
47	#131×C₈₉	—	2	4	no	—
48	#131×C₈₉	—	4	2	no	—
49	C₂×M₁₆×C₈₉	—	2	1	no	—
50	C₂×M₁₆×C₈₉	—	4	2	no	—
51	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₈₉	—	2	4	no	—
54	C₄×D₄×C₈₉	—	4	2	no	—
55	#117×C₈₉	—	2	1	no	—
56	#117×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
58	SD₃₂×C₈₉	C₂×C₄	1	8	yes	complemented
59	D₁₆×C₈₉	C₂×C₄	1	8	yes	complemented
60	M₃₂×C₈₉	—	2	1	no	—
61	M₃₂×C₈₉	C₂×C₄	1	2	yes	complemented
62	M₃₂×C₈₉	C₂³	1	2	yes	—
63	M₃₂×C₈₉	C₂³	1	2	yes	—
64	C₂×C₁₆×C₈₉	—	2	1	no	—
65	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
66	#108×C₈₉	—	2	1	no	—
67	#108×C₈₉	C₂³	1	2	yes	—
68	#107×C₈₉	—	2	1	no	—
69	#106×C₈₉	C₂³	1	2	yes	—
70	#104×C₈₉	—	2	4	no	—
71	#102×C₈₉	—	2	4	no	—
72	#97×C₈₉	C₂³	1	2	yes	—
73	C₄×C₈×C₈₉	D₄	1	2	yes	—
74	C₂⁴×C₈₉	—	4	1	no	—
75	#41×C₈₉	—	2	2	no	—
76	#41×C₈₉	—	2	2	no	—
77	#41×C₈₉	—	4	1	no	—
78	#41×C₈₉	—	4	1	no	—
79	C₂×Q₈×C₈₉	—	2	1	no	—
80	C₂×D₄×C₈₉	—	2	2	no	—
81	C₂×D₄×C₈₉	—	2	2	no	—
82	C₂×D₄×C₈₉	—	2	1	no	—
83	C₂×D₄×C₈₉	—	2	2	no	—
84	C₂×D₄×C₈₉	—	4	1	no	—
85	C₂×D₄×C₈₉	—	4	1	no	—
86	C₂×D₄×C₈₉	—	4	1	no	—
87	C₂×D₄×C₈₉	—	4	1	no	—
88	C₂²×C₄×C₈₉	—	4	4	no	—
89	C₂²×C₄×C₈₉	—	4	1	no	—
90	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	Q₁₆×C₈₉	—	2	1	no	—
92	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	—
93	SD₁₆×C₈₉	—	2	2	no	—
94	SD₁₆×C₈₉	—	2	2	no	—
95	D₈×C₈₉	—	2	2	no	—
96	D₈×C₈₉	—	2	2	no	—
97	D₈×C₈₉	—	2	1	no	—
98	D₈×C₈₉	—	2	2	no	—
99	D₈×C₈₉	C₂²×C₄	1	2	yes	—
100	D₈×C₈₉	C₂²×C₄	1	4	yes	—
101	M₁₆×C₈₉	—	2	1	no	—
102	M₁₆×C₈₉	—	2	1	no	—
103	M₁₆×C₈₉	—	2	2	no	—
104	M₁₆×C₈₉	—	4	4	no	—
105	M₁₆×C₈₉	—	4	1	no	—
106	C₂×C₈×C₈₉	—	4	4	no	—
107	C₂×C₈×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
113	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	4	4	no	—
119	C₂²⋊C₄×C₈₉	—	4	1	no	—
120	C₄²×C₈₉	—	4	1	no	—
121	C₄²×C₈₉	C₂×D₄	1	2	yes	—
122	C₁₆×C₈₉	—	2	2	no	—
123	C₁₆×C₈₉	C₂²×C₄	1	4	yes	—
124	C₂³×C₈₉	—	4	2	no	—
125	C₂³×C₈₉	—	4	1	no	—
126	C₂³×C₈₉	—	4	2	no	—
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	16	2	no	—
129	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
130	Q₈×C₈₉	—	2	2	no	—
131	Q₈×C₈₉	—	4	1	no	—
132	D₄×C₈₉	—	2	4	no	—
133	D₄×C₈₉	—	2	2	no	—
134	D₄×C₈₉	—	4	2	no	—
135	D₄×C₈₉	—	4	2	no	—
136	D₄×C₈₉	—	4	2	no	—
137	D₄×C₈₉	—	4	2	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	4	1	no	—
142	C₂×C₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	16	4	no	—
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₈₉	—	2	2	no	—
153	C₈×C₈₉	—	4	2	no	—
154	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
157	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
158	C₂²×C₈₉	—	4	1	no	—
159	C₂²×C₈₉	—	4	2	no	—
160	C₂²×C₈₉	—	4	4	no	—
161	C₂²×C₈₉	—	8	4	no	—
162	C₂²×C₈₉	—	16	1	no	—
163	C₂²×C₈₉	—	16	2	no	—
164	C₂²×C₈₉	—	16	2	no	—
165	C₂²×C₈₉	#442	1	1	yes	characteristic
166	C₂²×C₈₉	#442	1	1	yes	characteristic
167	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₄×C₈₉	—	4	2	no	—
169	C₄×C₈₉	—	4	2	no	—
170	C₄×C₈₉	—	8	2	no	—
171	C₄×C₈₉	#442	1	1	yes	characteristic
172	C₄×C₈₉	#442	1	1	yes	characteristic
173	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
174	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
175	#33471	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂×C₈₉	—	2	1	no	—
177	C₂×C₈₉	—	2	1	no	—
178	C₂×C₈₉	—	2	1	no	—
179	C₂×C₈₉	—	8	4	no	—
180	C₂×C₈₉	—	8	2	no	—
181	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
182	C₂×#509	C₂×C₈₉	1	1	yes	characteristic
183	#2957	C₂×C₈₉	1	1	yes	characteristic, complemented
184	#2948	C₂×C₈₉	1	1	yes	characteristic, complemented
185	AGL(1,ℤ/16)	C₂×C₈₉	1	8	yes	complemented
186	#2155	C₂×C₈₉	1	1	yes	characteristic, complemented
187	C₂×#361	C₂×C₈₉	1	1	yes	characteristic, complemented
188	#2145	C₂×C₈₉	1	1	yes	characteristic, complemented
189	#2110	C₂×C₈₉	1	1	yes	characteristic, complemented
190	C₈₉	#33471	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
192	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
193	#568	—	2	1	no	—
194	#518	—	2	1	no	—
195	#509	C₄×C₈₉	1	4	yes	complemented
196	#509	C₂²×C₈₉	1	4	yes	—
197	C₂×SD₃₂	C₄×C₈₉	1	2	yes	complemented
198	C₂×D₁₆	C₄×C₈₉	1	2	yes	complemented
199	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
200	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
201	#444	C₂²×C₈₉	1	4	yes	complemented
202	#443	—	2	2	no	—
203	#442	C₂²×C₈₉	1	4	yes	complemented
204	C₄×D₈	—	2	2	no	—
205	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
206	#427	C₂²×C₈₉	1	1	yes	characteristic
207	#421	—	2	1	no	—
208	#418	—	2	1	no	—
209	#405	C₂²×C₈₉	1	1	yes	characteristic
210	#365	C₂²×C₈₉	1	4	yes	complemented
211	#361	C₂²×C₈₉	1	4	yes	complemented
212	#360	C₂²×C₈₉	1	4	yes	complemented
213	#347	C₂²×C₈₉	1	4	yes	complemented
214	C₂×#41	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	#135	—	2	1	no	—
217	#135	—	2	1	no	—
218	#135	C₂×C₄×C₈₉	1	2	yes	complemented
219	#135	C₂³×C₈₉	1	2	yes	—
220	C₂×Q₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
221	C₂×SD₁₆	—	2	1	no	—
222	C₂×D₈	—	2	1	no	—
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	—	2	1	no	—
225	C₂×D₈	C₂×C₄×C₈₉	1	2	yes	—
226	C₂×D₈	C₂×C₄×C₈₉	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
228	C₂×D₈	C₂³×C₈₉	1	2	yes	—
229	#131	—	2	4	no	—
230	#131	—	4	2	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	4	2	no	—
233	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	—	4	2	no	—
237	#117	—	2	1	no	—
238	#117	D₄×C₈₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	4	2	no	—
240	SD₃₂	C₂×C₄×C₈₉	1	8	yes	complemented
241	D₁₆	C₂×C₄×C₈₉	1	8	yes	complemented
242	M₃₂	—	2	1	no	—
243	M₃₂	C₂×C₄×C₈₉	1	2	yes	complemented
244	M₃₂	C₂³×C₈₉	1	2	yes	—
245	M₃₂	C₂³×C₈₉	1	2	yes	—
246	C₂×C₁₆	—	2	1	no	—
247	C₂×C₁₆	C₂×C₄×C₈₉	1	2	yes	complemented
248	#108	—	2	1	no	—
249	#108	C₂³×C₈₉	1	2	yes	—
250	#107	—	2	1	no	—
251	#106	C₂³×C₈₉	1	2	yes	—
252	#104	—	2	4	no	—
253	#102	—	2	4	no	—
254	#97	C₂³×C₈₉	1	2	yes	—
255	C₄×C₈	D₄×C₈₉	1	2	yes	—
256	C₂⁴	—	4	1	no	—
257	#41	—	2	2	no	—
258	#41	—	2	2	no	—
259	#41	—	4	1	no	—
260	#41	—	4	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
273	Q₁₆	—	2	1	no	—
274	Q₁₆	C₂²×C₄×C₈₉	1	2	yes	—
275	SD₁₆	—	2	2	no	—
276	SD₁₆	—	2	2	no	—
277	D₈	—	2	2	no	—
278	D₈	—	2	2	no	—
279	D₈	—	2	1	no	—
280	D₈	—	2	2	no	—
281	D₈	C₂²×C₄×C₈₉	1	2	yes	—
282	D₈	C₂²×C₄×C₈₉	1	4	yes	—
283	M₁₆	—	2	1	no	—
284	M₁₆	—	2	1	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	4	4	no	—
287	M₁₆	—	4	1	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
294	C₂×C₈	#41×C₈₉	1	1	yes	characteristic
295	C₂×C₈	#41×C₈₉	1	1	yes	characteristic
296	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₄²	—	4	1	no	—
303	C₄²	C₂×D₄×C₈₉	1	2	yes	—
304	C₁₆	—	2	2	no	—
305	C₁₆	C₂²×C₄×C₈₉	1	4	yes	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	16	2	no	—
311	C₂³	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	4	1	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	16	4	no	—
328	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
329	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
330	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
331	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
332	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	C₄×D₄×C₈₉	1	1	yes	characteristic
337	C₈	C₄×D₄×C₈₉	1	1	yes	characteristic
338	C₈	C₂³×C₄×C₈₉	1	1	yes	characteristic
339	C₈	C₂×#41×C₈₉	1	1	yes	characteristic
340	C₂²	—	4	1	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	8	4	no	—
344	C₂²	—	16	2	no	—
345	C₂²	—	16	2	no	—
346	C₂²	—	16	1	no	—
347	C₂²	#442×C₈₉	1	1	yes	characteristic
348	C₂²	#442×C₈₉	1	1	yes	characteristic
349	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	8	2	no	—
353	C₄	#442×C₈₉	1	1	yes	characteristic
354	C₄	#442×C₈₉	1	1	yes	characteristic
355	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
356	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
357	C₂	—	2	1	no	—
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	—	8	4	no	—
361	C₂	—	8	2	no	—
362	C₂	C₂×#442×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	C₂×#442
commutator	C₈	C₂³×C₄×C₈₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
prime radical	C₂×#509×C₈₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ #405×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2957	C₂	semidirect
3. C₈₉×#2948	C₂	semidirect
4. C₈₉×AGL(1,ℤ/16)	C₂	semidirect
5. C₈₉×#2155	C₂	semidirect
6. C₂×#361×C₈₉	C₂	semidirect
7. C₈₉×#2145	C₂	semidirect
8. C₈₉×#2110	C₂	semidirect
13. #509×C₈₉	C₄	semidirect
15. C₂×SD₃₂×C₈₉	C₄	semidirect
16. C₂×D₁₆×C₈₉	C₄	semidirect
19. #444×C₈₉	C₂²	semidirect
21. #442×C₈₉	C₂²	semidirect
28. #365×C₈₉	C₂²	semidirect
29. #361×C₈₉	C₂²	semidirect
30. #360×C₈₉	C₂²	semidirect
31. #347×C₈₉	C₂²	semidirect
36. #135×C₈₉	C₂×C₄	semidirect
38. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
45. C₂×D₈×C₈₉	C₂×C₄	semidirect
58. SD₃₂×C₈₉	C₂×C₄	semidirect
59. D₁₆×C₈₉	C₂×C₄	semidirect
61. M₃₂×C₈₉	C₂×C₄	semidirect
65. C₂×C₁₆×C₈₉	C₂×C₄	semidirect
175. #33471	C₈₉	direct (N × H)
183. #2957	C₂×C₈₉	semidirect
184. #2948	C₂×C₈₉	semidirect
185. AGL(1,ℤ/16)	C₂×C₈₉	semidirect
186. #2155	C₂×C₈₉	semidirect
187. C₂×#361	C₂×C₈₉	semidirect
188. #2145	C₂×C₈₉	semidirect
189. #2110	C₂×C₈₉	semidirect
190. C₈₉	#33471	direct (N × H)
195. #509	C₄×C₈₉	semidirect
197. C₂×SD₃₂	C₄×C₈₉	semidirect
198. C₂×D₁₆	C₄×C₈₉	semidirect
201. #444	C₂²×C₈₉	semidirect
203. #442	C₂²×C₈₉	semidirect
210. #365	C₂²×C₈₉	semidirect
211. #361	C₂²×C₈₉	semidirect
212. #360	C₂²×C₈₉	semidirect
213. #347	C₂²×C₈₉	semidirect
218. #135	C₂×C₄×C₈₉	semidirect
220. C₂×Q₁₆	C₂×C₄×C₈₉	semidirect
227. C₂×D₈	C₂×C₄×C₈₉	semidirect
240. SD₃₂	C₂×C₄×C₈₉	semidirect
241. D₁₆	C₂×C₄×C₈₉	semidirect
243. M₃₂	C₂×C₄×C₈₉	semidirect
247. C₂×C₁₆	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#509×C₈₉	2
C₈₉×#2957	2
C₈₉×#2948	2
C₈₉×AGL(1,ℤ/16)	2
C₈₉×#2155	2
C₂×#361×C₈₉	2
C₈₉×#2145	2
C₈₉×#2110	2
#33471	89

Subgroups — C89×#33471 #36411319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#33471 #36411319