Subgroups — C₈₉×#20494 #36398342

Order 22784.

1234 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×#436×C₈₉	C₂	1	2	yes	maximal
2	C₂×C₄×M₁₆×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊C₄×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1753	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×#97×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×M₁₆×C₈₉	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₈₉	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
13	#436×C₈₉	C₄	1	16	yes	complemented
14	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₈₉	C₂²	1	4	yes	—
16	C₄×M₁₆×C₈₉	—	2	8	no	—
17	C₂×#97×C₈₉	C₂²	1	2	yes	—
18	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#97×C₈₉	C₂²	1	2	yes	—
20	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₈₉	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₈₉	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₈₉	C₄	1	4	yes	—
26	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
27	C₄³×C₈₉	C₂²	1	1	yes	characteristic
28	#336×C₈₉	C₂²	1	4	yes	—
29	#336×C₈₉	C₂²	1	2	yes	—
30	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₈₉	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
33	C₂×M₁₆×C₈₉	—	2	8	no	—
34	C₂×M₁₆×C₈₉	—	2	8	no	—
35	C₂×M₁₆×C₈₉	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
38	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
39	C₄×D₄×C₈₉	—	2	8	no	—
40	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₈₉	—	2	4	no	—
46	C₂×C₄²×C₈₉	—	2	4	no	—
47	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
52	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₈₉	C₂×C₄	1	8	yes	complemented
55	C₂²⋊C₈×C₈₉	C₂×C₄	1	16	yes	complemented
56	#97×C₈₉	—	2	4	no	—
57	#97×C₈₉	—	2	4	no	—
58	#97×C₈₉	—	2	2	no	—
59	#97×C₈₉	D₄	1	4	yes	complemented
60	C₄×C₈×C₈₉	—	2	8	no	—
61	C₄×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
62	#95×C₈₉	C₂×C₄	1	2	yes	—
63	#95×C₈₉	C₂×C₄	1	4	yes	—
64	C₂⁴×C₈₉	C₂²×C₄	1	2	yes	—
65	C₂×D₄×C₈₉	—	2	4	no	—
66	C₂×D₄×C₈₉	C₄²	1	4	yes	—
67	C₂²×C₄×C₈₉	—	2	2	no	—
68	C₂²×C₄×C₈₉	—	2	2	no	—
69	C₂²×C₄×C₈₉	—	2	4	no	—
70	C₂²×C₄×C₈₉	—	2	8	no	—
71	C₂²×C₄×C₈₉	—	2	8	no	—
72	C₂²×C₄×C₈₉	—	4	4	no	—
73	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
81	M₁₆×C₈₉	—	2	32	no	—
82	C₂×C₈×C₈₉	—	2	4	no	—
83	C₂×C₈×C₈₉	—	2	2	no	—
84	C₂×C₈×C₈₉	—	2	2	no	—
85	C₂×C₈×C₈₉	—	2	4	no	—
86	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
88	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₈₉	#41	1	4	yes	—
91	C₄⋊C₄×C₈₉	C₄²	1	4	yes	—
92	C₄⋊C₄×C₈₉	M₁₆	1	8	yes	complemented
93	C₂²⋊C₄×C₈₉	—	2	8	no	—
94	C₂²⋊C₄×C₈₉	C₄²	1	8	yes	—
95	C₄²×C₈₉	—	2	8	no	—
96	C₄²×C₈₉	—	2	4	no	—
97	C₄²×C₈₉	—	2	2	no	—
98	C₄²×C₈₉	—	2	2	no	—
99	C₄²×C₈₉	—	2	2	no	—
100	C₄²×C₈₉	—	4	2	no	—
101	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
102	C₄²×C₈₉	C₂×D₄	1	2	yes	—
103	C₄²×C₈₉	#41	1	2	yes	—
104	C₂³×C₈₉	—	2	2	no	—
105	C₂³×C₈₉	—	2	2	no	—
106	C₂³×C₈₉	—	2	4	no	—
107	C₂³×C₈₉	—	2	4	no	—
108	C₂³×C₈₉	C₂×C₄²	1	4	yes	—
109	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
110	D₄×C₈₉	—	2	8	no	—
111	C₂×C₄×C₈₉	—	2	4	no	—
112	C₂×C₄×C₈₉	—	2	2	no	—
113	C₂×C₄×C₈₉	—	2	2	no	—
114	C₂×C₄×C₈₉	—	2	2	no	—
115	C₂×C₄×C₈₉	—	2	2	no	—
116	C₂×C₄×C₈₉	—	2	2	no	—
117	C₂×C₄×C₈₉	—	2	4	no	—
118	C₂×C₄×C₈₉	—	2	8	no	—
119	C₂×C₄×C₈₉	—	2	8	no	—
120	C₂×C₄×C₈₉	—	2	2	no	—
121	C₂×C₄×C₈₉	—	2	2	no	—
122	C₂×C₄×C₈₉	—	2	2	no	—
123	C₂×C₄×C₈₉	—	4	16	no	—
124	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₈₉	C₂×C₄²	1	4	yes	—
126	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
128	C₂×C₄×C₈₉	C₂×M₁₆	1	8	yes	—
129	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
130	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
133	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
134	C₈×C₈₉	—	2	8	no	—
135	C₈×C₈₉	—	2	4	no	—
136	C₈×C₈₉	C₄×D₄	1	8	yes	complemented
137	C₂²×C₈₉	—	2	4	no	—
138	C₂²×C₈₉	—	2	4	no	—
139	C₂²×C₈₉	—	2	4	no	—
140	C₂²×C₈₉	—	4	4	no	—
141	C₂²×C₈₉	—	4	4	no	—
142	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
143	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
145	C₂²×C₈₉	C₂²×M₁₆	1	2	yes	—
146	C₂²×C₈₉	#568	1	2	yes	—
147	C₄×C₈₉	—	2	2	no	—
148	C₄×C₈₉	—	2	4	no	—
149	C₄×C₈₉	—	2	8	no	—
150	C₄×C₈₉	—	2	4	no	—
151	C₄×C₈₉	—	4	2	no	—
152	C₄×C₈₉	C₄×M₁₆	1	4	yes	complemented
153	C₄×C₈₉	C₂×C₄×D₄	1	2	yes	—
154	C₄×C₈₉	C₄×#41	1	2	yes	—
155	#20494	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂×C₈₉	—	4	4	no	—
157	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
158	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
159	C₂×C₈₉	#2875	1	1	yes	characteristic
160	C₂×C₈₉	D₄×M₁₆	1	2	yes	—
161	C₂×C₈₉	#2971	1	2	yes	—
162	C₂×#436	C₂×C₈₉	1	2	yes	—
163	C₂×C₄×M₁₆	C₂×C₈₉	1	2	yes	complemented
164	C₄²×D₄	C₂×C₈₉	1	1	yes	characteristic
165	C₈×C₄⋊C₄	C₂×C₈₉	1	2	yes	complemented
166	#1767	C₂×C₈₉	1	1	yes	characteristic, complemented
167	#1753	C₂×C₈₉	1	4	yes	complemented
168	#1749	C₂×C₈₉	1	2	yes	complemented
169	C₄×#97	C₂×C₈₉	1	1	yes	characteristic, complemented
170	C₈₉	#20494	1	1	yes	characteristic, direct product factor, Sylow
171	C₂²×M₁₆	C₂²×C₈₉	1	4	yes	—
172	C₂×C₄×D₄	C₄×C₈₉	1	2	yes	—
173	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
175	#436	C₄×C₈₉	1	16	yes	complemented
176	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₈₉	1	4	yes	—
178	C₄×M₁₆	—	2	8	no	—
179	C₂×#97	C₂²×C₈₉	1	2	yes	—
180	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
181	C₂×#97	C₂²×C₈₉	1	2	yes	—
182	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₈₉	1	4	yes	—
184	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
185	C₄×C₄⋊C₄	C₄×C₈₉	1	2	yes	—
186	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
187	C₄×C₂²⋊C₄	C₄×C₈₉	1	4	yes	—
188	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
189	C₄³	C₂²×C₈₉	1	1	yes	characteristic
190	#336	C₂²×C₈₉	1	4	yes	—
191	#336	C₂²×C₈₉	1	2	yes	—
192	C₂²×D₄	C₂×C₄×C₈₉	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₈₉	1	4	yes	—
194	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
195	C₂×M₁₆	—	2	8	no	—
196	C₂×M₁₆	—	2	8	no	—
197	C₂×M₁₆	C₂×C₄×C₈₉	1	16	yes	complemented
198	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
199	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
200	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
201	C₄×D₄	—	2	8	no	—
202	C₄×D₄	C₂×C₄×C₈₉	1	8	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	4	yes	—
206	C₂×C₂²⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	C₂×C₄×C₈₉	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₈₉	1	4	yes	—
211	C₂×C₄²	C₂×C₄×C₈₉	1	2	yes	—
212	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
214	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
216	C₄⋊C₈	C₂×C₄×C₈₉	1	8	yes	complemented
217	C₂²⋊C₈	C₂×C₄×C₈₉	1	16	yes	complemented
218	#97	—	2	4	no	—
219	#97	—	2	4	no	—
220	#97	—	2	2	no	—
221	#97	D₄×C₈₉	1	4	yes	complemented
222	C₄×C₈	—	2	8	no	—
223	C₄×C₈	C₂×C₄×C₈₉	1	8	yes	complemented
224	#95	C₂×C₄×C₈₉	1	2	yes	—
225	#95	C₂×C₄×C₈₉	1	4	yes	—
226	C₂⁴	C₂²×C₄×C₈₉	1	2	yes	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	C₄²×C₈₉	1	4	yes	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
238	C₂²×C₄	C₂²×C₄×C₈₉	1	8	yes	—
239	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
240	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
243	M₁₆	—	2	32	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₈₉	1	8	yes	—
250	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
251	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
252	C₂×C₈	#41×C₈₉	1	4	yes	—
253	C₄⋊C₄	C₄²×C₈₉	1	4	yes	—
254	C₄⋊C₄	M₁₆×C₈₉	1	8	yes	complemented
255	C₂²⋊C₄	—	2	8	no	—
256	C₂²⋊C₄	C₄²×C₈₉	1	8	yes	—
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	4	2	no	—
263	C₄²	C₂²×C₄×C₈₉	1	4	yes	—
264	C₄²	C₂×D₄×C₈₉	1	2	yes	—
265	C₄²	#41×C₈₉	1	2	yes	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	4	no	—
270	C₂³	C₂×C₄²×C₈₉	1	4	yes	—
271	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
272	D₄	—	2	8	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	16	no	—
286	C₂×C₄	C₂×C₄²×C₈₉	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₈₉	1	4	yes	—
288	C₂×C₄	C₂×C₄²×C₈₉	1	2	yes	—
289	C₂×C₄	C₄×D₄×C₈₉	1	4	yes	—
290	C₂×C₄	C₂×M₁₆×C₈₉	1	8	yes	—
291	C₂×C₄	C₂×M₁₆×C₈₉	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
294	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
295	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₈₉	1	8	yes	complemented
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	4	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	C₂²×C₄²×C₈₉	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
306	C₂²	C₄×#41×C₈₉	1	1	yes	characteristic
307	C₂²	C₂²×M₁₆×C₈₉	1	2	yes	—
308	C₂²	#568×C₈₉	1	2	yes	—
309	C₄	—	2	2	no	—
310	C₄	—	2	4	no	—
311	C₄	—	2	8	no	—
312	C₄	—	2	4	no	—
313	C₄	—	4	2	no	—
314	C₄	C₄×M₁₆×C₈₉	1	4	yes	complemented
315	C₄	C₂×C₄×D₄×C₈₉	1	2	yes	—
316	C₄	C₄×#41×C₈₉	1	2	yes	—
317	C₂	—	4	4	no	—
318	C₂	C₄²×D₄×C₈₉	1	1	yes	characteristic
319	C₂	C₂×C₄×M₁₆×C₈₉	1	1	yes	characteristic
320	C₂	C₈₉×#2875	1	1	yes	characteristic
321	C₂	D₄×M₁₆×C₈₉	1	2	yes	—
322	C₂	C₈₉×#2971	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₈₉	C₂	semidirect
4. C₈×C₄⋊C₄×C₈₉	C₂	semidirect
5. C₈₉×#1767	C₂	semidirect
6. C₈₉×#1753	C₂	semidirect
7. C₈₉×#1749	C₂	semidirect
8. C₄×#97×C₈₉	C₂	semidirect
13. #436×C₈₉	C₄	semidirect
35. C₂×M₁₆×C₈₉	C₂×C₄	semidirect
54. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
55. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
59. #97×C₈₉	D₄	semidirect
61. C₄×C₈×C₈₉	C₂×C₄	semidirect
92. C₄⋊C₄×C₈₉	M₁₆	semidirect
136. C₈×C₈₉	C₄×D₄	semidirect
152. C₄×C₈₉	C₄×M₁₆	semidirect
155. #20494	C₈₉	direct (N × H)
163. C₂×C₄×M₁₆	C₂×C₈₉	semidirect
165. C₈×C₄⋊C₄	C₂×C₈₉	semidirect
166. #1767	C₂×C₈₉	semidirect
167. #1753	C₂×C₈₉	semidirect
168. #1749	C₂×C₈₉	semidirect
169. C₄×#97	C₂×C₈₉	semidirect
170. C₈₉	#20494	direct (N × H)
175. #436	C₄×C₈₉	semidirect
197. C₂×M₁₆	C₂×C₄×C₈₉	semidirect
216. C₄⋊C₈	C₂×C₄×C₈₉	semidirect
217. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect
221. #97	D₄×C₈₉	semidirect
223. C₄×C₈	C₂×C₄×C₈₉	semidirect
254. C₄⋊C₄	M₁₆×C₈₉	semidirect
298. C₈	C₄×D₄×C₈₉	semidirect
314. C₄	C₄×M₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#436×C₈₉	2
C₂×C₄×M₁₆×C₈₉	2
C₄²×D₄×C₈₉	2
C₈×C₄⋊C₄×C₈₉	2
C₈₉×#1767	2
C₈₉×#1753	2
C₈₉×#1749	2
C₄×#97×C₈₉	2
#20494	89

Subgroups — C89×#20494 #36398342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#20494 #36398342