Subgroups — C₈₉×#33432 #36411280

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#504×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2929	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2168	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₆×C₈₉	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	#525×C₈₉	C₄	1	1	yes	characteristic
13	#504×C₈₉	—	2	4	no	—
14	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₈₉	C₂²	1	2	yes	complemented
17	C₂²×C₁₆×C₈₉	—	2	4	no	—
18	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
20	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	complemented
23	#435×C₈₉	C₄	1	4	yes	—
24	C₈×D₄×C₈₉	C₂²	1	4	yes	—
25	#424×C₈₉	C₄	1	1	yes	characteristic
26	#408×C₈₉	C₄	1	1	yes	characteristic
27	#407×C₈₉	C₄	1	1	yes	characteristic
28	#405×C₈₉	C₂²	1	1	yes	characteristic
29	C₄⋊C₁₆×C₈₉	C₂²	1	4	yes	complemented
30	C₂²⋊C₁₆×C₈₉	C₂²	1	4	yes	—
31	C₂²⋊C₁₆×C₈₉	C₂²	1	4	yes	complemented
32	#346×C₈₉	C₂²	1	2	yes	complemented
33	C₄×C₁₆×C₈₉	C₂²	1	2	yes	complemented
34	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
36	#131×C₈₉	—	2	2	no	—
37	#131×C₈₉	—	2	2	no	—
38	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₈₉	—	2	2	no	—
42	C₂²×C₈×C₈₉	—	2	2	no	—
43	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
48	#123×C₈₉	C₈	1	2	yes	—
49	C₂²⋊Q₈×C₈₉	C₈	1	2	yes	—
50	#121×C₈₉	C₈	1	2	yes	—
51	#120×C₈₉	C₈	1	2	yes	—
52	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
53	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
54	M₃₂×C₈₉	—	2	2	no	—
55	M₃₂×C₈₉	—	2	2	no	—
56	M₃₂×C₈₉	—	2	4	no	—
57	C₂×C₁₆×C₈₉	—	2	2	no	—
58	C₂×C₁₆×C₈₉	—	2	4	no	—
59	C₂×C₁₆×C₈₉	—	2	4	no	—
60	C₂×C₁₆×C₈₉	—	2	4	no	—
61	C₂×C₁₆×C₈₉	D₄	1	4	yes	complemented
62	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
63	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
64	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
65	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
68	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
69	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
70	#97×C₈₉	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₈₉	C₂³	1	2	yes	—
72	C₂⁴×C₈₉	C₂×C₈	1	1	yes	characteristic
73	#41×C₈₉	—	2	2	no	—
74	#41×C₈₉	—	2	2	no	—
75	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
76	C₂×D₄×C₈₉	C₂×C₈	1	4	yes	—
77	C₂×D₄×C₈₉	C₂×C₈	1	2	yes	—
78	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	—	2	2	no	—
80	C₂²×C₄×C₈₉	—	2	2	no	—
81	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
86	M₁₆×C₈₉	—	2	2	no	—
87	M₁₆×C₈₉	—	2	2	no	—
88	M₁₆×C₈₉	—	2	4	no	—
89	C₂×C₈×C₈₉	—	2	2	no	—
90	C₂×C₈×C₈₉	—	2	4	no	—
91	C₂×C₈×C₈₉	—	2	2	no	—
92	C₂×C₈×C₈₉	—	2	2	no	—
93	C₂×C₈×C₈₉	—	2	2	no	—
94	C₂×C₈×C₈₉	—	2	2	no	—
95	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₈₉	#41	1	2	yes	—
101	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
103	C₄⋊C₄×C₈₉	C₂×C₈	1	4	yes	—
104	C₂²⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
105	C₂²⋊C₄×C₈₉	C₂×C₈	1	4	yes	—
106	C₂²⋊C₄×C₈₉	C₂×C₈	1	4	yes	—
107	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
108	C₁₆×C₈₉	—	2	2	no	—
109	C₁₆×C₈₉	—	2	2	no	—
110	C₁₆×C₈₉	—	2	2	no	—
111	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
112	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
113	C₂³×C₈₉	—	2	2	no	—
114	C₂³×C₈₉	—	2	4	no	—
115	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
116	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
117	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
118	Q₈×C₈₉	—	2	2	no	—
119	D₄×C₈₉	—	2	4	no	—
120	D₄×C₈₉	—	2	8	no	—
121	D₄×C₈₉	—	2	2	no	—
122	C₂×C₄×C₈₉	—	2	2	no	—
123	C₂×C₄×C₈₉	—	2	2	no	—
124	C₂×C₄×C₈₉	—	2	2	no	—
125	C₂×C₄×C₈₉	—	2	2	no	—
126	C₂×C₄×C₈₉	—	2	2	no	—
127	C₂×C₄×C₈₉	—	2	4	no	—
128	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
130	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₄×C₈₉	#131	1	2	yes	—
134	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
135	C₈×C₈₉	—	2	2	no	—
136	C₈×C₈₉	—	2	2	no	—
137	C₈×C₈₉	—	2	2	no	—
138	C₈×C₈₉	C₄×D₄	1	2	yes	—
139	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
140	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
141	C₂²×C₈₉	—	2	8	no	—
142	C₂²×C₈₉	—	2	2	no	—
143	C₂²×C₈₉	—	2	2	no	—
144	C₂²×C₈₉	—	2	2	no	—
145	C₂²×C₈₉	—	2	4	no	—
146	C₂²×C₈₉	—	2	2	no	—
147	C₂²×C₈₉	C₈×D₄	1	2	yes	—
148	C₂²×C₈₉	#504	1	4	yes	complemented
149	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
150	C₄×C₈₉	—	2	4	no	—
151	C₄×C₈₉	—	2	2	no	—
152	C₄×C₈₉	—	2	2	no	—
153	C₄×C₈₉	C₈×D₄	1	2	yes	—
154	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
155	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
156	#33432	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂×C₈₉	—	2	2	no	—
158	C₂×C₈₉	—	2	4	no	—
159	C₂×C₈₉	—	4	2	no	—
160	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
161	C₂×C₈₉	C₂×#504	1	2	yes	—
162	C₂×#504	C₂×C₈₉	1	1	yes	characteristic, complemented
163	C₂³×C₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
164	#2929	C₂×C₈₉	1	1	yes	characteristic
165	#2168	C₂×C₈₉	1	4	yes	complemented
166	D₄×C₁₆	C₂×C₈₉	1	4	yes	complemented
167	#2151	C₂×C₈₉	1	1	yes	characteristic, complemented
168	#2113	C₂×C₈₉	1	1	yes	characteristic, complemented
169	#2112	C₂×C₈₉	1	1	yes	characteristic, complemented
170	#2108	C₂×C₈₉	1	1	yes	characteristic, complemented
171	C₈₉	#33432	1	1	yes	characteristic, direct product factor, Sylow
172	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
174	#525	C₄×C₈₉	1	1	yes	characteristic
175	#504	—	2	4	no	—
176	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
177	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
178	C₂×M₃₂	C₂²×C₈₉	1	2	yes	complemented
179	C₂²×C₁₆	—	2	4	no	—
180	C₂²×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
181	C₂²×C₁₆	C₂²×C₈₉	1	2	yes	—
182	C₂²×C₁₆	C₂²×C₈₉	1	2	yes	—
183	C₂²×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
184	C₂²×C₁₆	C₂²×C₈₉	1	2	yes	complemented
185	#435	C₄×C₈₉	1	4	yes	—
186	C₈×D₄	C₂²×C₈₉	1	4	yes	—
187	#424	C₄×C₈₉	1	1	yes	characteristic
188	#408	C₄×C₈₉	1	1	yes	characteristic
189	#407	C₄×C₈₉	1	1	yes	characteristic
190	#405	C₂²×C₈₉	1	1	yes	characteristic
191	C₄⋊C₁₆	C₂²×C₈₉	1	4	yes	complemented
192	C₂²⋊C₁₆	C₂²×C₈₉	1	4	yes	—
193	C₂²⋊C₁₆	C₂²×C₈₉	1	4	yes	complemented
194	#346	C₂²×C₈₉	1	2	yes	complemented
195	C₄×C₁₆	C₂²×C₈₉	1	2	yes	complemented
196	C₂×#41	C₂×C₄×C₈₉	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
198	#131	—	2	2	no	—
199	#131	—	2	2	no	—
200	C₂×M₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
201	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
202	C₂×M₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	C₂×C₄×C₈₉	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
207	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
208	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
209	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
210	#123	C₈×C₈₉	1	2	yes	—
211	C₂²⋊Q₈	C₈×C₈₉	1	2	yes	—
212	#121	C₈×C₈₉	1	2	yes	—
213	#120	C₈×C₈₉	1	2	yes	—
214	C₄×D₄	C₂×C₄×C₈₉	1	4	yes	—
215	#117	C₂×C₄×C₈₉	1	1	yes	characteristic
216	M₃₂	—	2	2	no	—
217	M₃₂	—	2	2	no	—
218	M₃₂	—	2	4	no	—
219	C₂×C₁₆	—	2	2	no	—
220	C₂×C₁₆	—	2	4	no	—
221	C₂×C₁₆	—	2	4	no	—
222	C₂×C₁₆	—	2	4	no	—
223	C₂×C₁₆	D₄×C₈₉	1	4	yes	complemented
224	C₂×C₁₆	C₂³×C₈₉	1	2	yes	—
225	C₂×C₁₆	C₂³×C₈₉	1	2	yes	—
226	C₂×C₁₆	C₂³×C₈₉	1	2	yes	—
227	C₂×C₁₆	C₂³×C₈₉	1	1	yes	characteristic
228	C₂×C₁₆	C₂³×C₈₉	1	1	yes	characteristic
229	C₄⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
230	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
231	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
232	#97	C₂×C₄×C₈₉	1	2	yes	—
233	C₄×C₈	C₂³×C₈₉	1	2	yes	—
234	C₂⁴	C₂×C₈×C₈₉	1	1	yes	characteristic
235	#41	—	2	2	no	—
236	#41	—	2	2	no	—
237	C₂×Q₈	C₂×C₈×C₈₉	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₈₉	1	4	yes	—
239	C₂×D₄	C₂×C₈×C₈₉	1	2	yes	—
240	C₂×D₄	C₂×C₈×C₈₉	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	C₂×C₈×C₈₉	1	2	yes	—
244	C₂²×C₄	C₂×C₈×C₈₉	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
248	M₁₆	—	2	2	no	—
249	M₁₆	—	2	2	no	—
250	M₁₆	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
259	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
261	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
262	C₂×C₈	#41×C₈₉	1	2	yes	—
263	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
264	C₄⋊C₄	C₂×C₈×C₈₉	1	2	yes	—
265	C₄⋊C₄	C₂×C₈×C₈₉	1	4	yes	—
266	C₂²⋊C₄	C₂×C₈×C₈₉	1	2	yes	—
267	C₂²⋊C₄	C₂×C₈×C₈₉	1	4	yes	—
268	C₂²⋊C₄	C₂×C₈×C₈₉	1	4	yes	—
269	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
270	C₁₆	—	2	2	no	—
271	C₁₆	—	2	2	no	—
272	C₁₆	—	2	2	no	—
273	C₁₆	C₂×D₄×C₈₉	1	2	yes	—
274	C₁₆	C₂×D₄×C₈₉	1	2	yes	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	4	no	—
277	C₂³	C₂²×C₈×C₈₉	1	2	yes	—
278	C₂³	C₂²×C₈×C₈₉	1	1	yes	characteristic
279	C₂³	C₂²×C₈×C₈₉	1	2	yes	—
280	Q₈	—	2	2	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	8	no	—
283	D₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₈₉	1	4	yes	—
292	C₂×C₄	C₂²×C₈×C₈₉	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₈₉	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₈₉	1	1	yes	characteristic
295	C₂×C₄	#131×C₈₉	1	2	yes	—
296	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
297	C₈	—	2	2	no	—
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	C₄×D₄×C₈₉	1	2	yes	—
301	C₈	C₂²×D₄×C₈₉	1	1	yes	characteristic
302	C₈	C₂×#41×C₈₉	1	1	yes	characteristic
303	C₂²	—	2	8	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	2	no	—
309	C₂²	C₈×D₄×C₈₉	1	2	yes	—
310	C₂²	#504×C₈₉	1	4	yes	complemented
311	C₂²	C₂³×C₈×C₈₉	1	1	yes	characteristic
312	C₄	—	2	4	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	C₈×D₄×C₈₉	1	2	yes	—
316	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
317	C₄	C₂×#131×C₈₉	1	1	yes	characteristic
318	C₂	—	2	2	no	—
319	C₂	—	2	4	no	—
320	C₂	—	4	2	no	—
321	C₂	C₂×C₈×D₄×C₈₉	1	1	yes	characteristic
322	C₂	C₂×#504×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆×C₈₉	C₂³
commutator	C₂²	C₂³×C₈×C₈₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂³×C₈
prime radical	#525×C₈₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#504×C₈₉	C₂	semidirect
2. C₂³×C₁₆×C₈₉	C₂	semidirect
4. C₈₉×#2168	C₂	semidirect
5. D₄×C₁₆×C₈₉	C₂	semidirect
6. C₈₉×#2151	C₂	semidirect
7. C₈₉×#2113	C₂	semidirect
8. C₈₉×#2112	C₂	semidirect
9. C₈₉×#2108	C₂	semidirect
16. C₂×M₃₂×C₈₉	C₂²	semidirect
22. C₂²×C₁₆×C₈₉	C₂²	semidirect
29. C₄⋊C₁₆×C₈₉	C₂²	semidirect
31. C₂²⋊C₁₆×C₈₉	C₂²	semidirect
32. #346×C₈₉	C₂²	semidirect
33. C₄×C₁₆×C₈₉	C₂²	semidirect
61. C₂×C₁₆×C₈₉	D₄	semidirect
148. C₂²×C₈₉	#504	semidirect
156. #33432	C₈₉	direct (N × H)
162. C₂×#504	C₂×C₈₉	semidirect
163. C₂³×C₁₆	C₂×C₈₉	semidirect
165. #2168	C₂×C₈₉	semidirect
166. D₄×C₁₆	C₂×C₈₉	semidirect
167. #2151	C₂×C₈₉	semidirect
168. #2113	C₂×C₈₉	semidirect
169. #2112	C₂×C₈₉	semidirect
170. #2108	C₂×C₈₉	semidirect
171. C₈₉	#33432	direct (N × H)
178. C₂×M₃₂	C₂²×C₈₉	semidirect
184. C₂²×C₁₆	C₂²×C₈₉	semidirect
191. C₄⋊C₁₆	C₂²×C₈₉	semidirect
193. C₂²⋊C₁₆	C₂²×C₈₉	semidirect
194. #346	C₂²×C₈₉	semidirect
195. C₄×C₁₆	C₂²×C₈₉	semidirect
223. C₂×C₁₆	D₄×C₈₉	semidirect
310. C₂²	#504×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#504×C₈₉	2
C₂³×C₁₆×C₈₉	2
C₈₉×#2929	2
C₈₉×#2168	2
D₄×C₁₆×C₈₉	2
C₈₉×#2151	2
C₈₉×#2113	2
C₈₉×#2112	2
C₈₉×#2108	2
#33432	89

Subgroups — C89×#33432 #36411280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#33432 #36411280