Subgroups — C₈₉×#60490 #36438338

Order 22784.

2178 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	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3081	C₂	1	16	yes	maximal, complemented
4	C₈₉×#3077	C₂	1	8	yes	maximal, complemented
5	C₈₉×#2911	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#418×C₈₉	C₂	1	2	yes	maximal
8	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
10	#544×C₈₉	—	2	2	no	—
11	#544×C₈₉	C₂²	1	8	yes	complemented
12	#543×C₈₉	—	2	2	no	—
13	#533×C₈₉	—	2	4	no	—
14	#533×C₈₉	C₂²	1	4	yes	complemented
15	#518×C₈₉	—	2	4	no	—
16	#518×C₈₉	C₂²	1	8	yes	—
17	C₂×C₄×D₄×C₈₉	—	2	2	no	—
18	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
19	C₂×#117×C₈₉	C₂²	1	2	yes	—
20	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₈₉	—	2	2	no	—
23	#478×C₈₉	C₂²	1	32	yes	complemented
24	#476×C₈₉	C₂²	1	16	yes	complemented
25	#474×C₈₉	C₂²	1	16	yes	complemented
26	#428×C₈₉	C₂²	1	8	yes	complemented
27	#428×C₈₉	C₂²	1	8	yes	complemented
28	#427×C₈₉	C₂²	1	8	yes	complemented
29	#424×C₈₉	C₂²	1	8	yes	complemented
30	#423×C₈₉	C₂²	1	4	yes	complemented
31	#418×C₈₉	C₂²	1	8	yes	—
32	#418×C₈₉	C₂²	1	8	yes	—
33	C₂×#102×C₈₉	C₂²	1	8	yes	—
34	C₂⁵×C₈₉	—	2	1	no	—
35	C₂²×D₄×C₈₉	—	2	1	no	—
36	C₂²×D₄×C₈₉	—	2	2	no	—
37	C₂²×D₄×C₈₉	—	2	4	no	—
38	C₂²×D₄×C₈₉	Q₈	1	8	yes	complemented
39	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
40	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₈₉	—	2	4	no	—
42	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₈₉	—	2	8	no	—
44	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
45	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
46	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₈₉	—	2	8	no	—
48	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
49	#125×C₈₉	—	2	8	no	—
50	#125×C₈₉	C₂³	1	8	yes	complemented
51	C₂²⋊Q₈×C₈₉	—	2	8	no	—
52	C₂²⋊Q₈×C₈₉	—	2	16	no	—
53	C₄×Q₈×C₈₉	—	2	8	no	—
54	C₄×D₄×C₈₉	—	2	16	no	—
55	C₄×D₄×C₈₉	—	2	8	no	—
56	C₄×D₄×C₈₉	C₂³	1	16	yes	—
57	#117×C₈₉	—	2	2	no	—
58	#117×C₈₉	—	2	2	no	—
59	#117×C₈₉	—	2	2	no	—
60	#117×C₈₉	D₄	1	4	yes	—
61	#117×C₈₉	C₂³	1	4	yes	—
62	#117×C₈₉	C₂³	1	4	yes	—
63	#117×C₈₉	C₂³	1	4	yes	—
64	#117×C₈₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
72	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	2	no	—
75	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
76	#107×C₈₉	C₂³	1	16	yes	complemented
77	#106×C₈₉	C₂³	1	16	yes	complemented
78	C₄⋊C₈×C₈₉	C₂³	1	16	yes	complemented
79	#102×C₈₉	C₂³	1	32	yes	—
80	C₂⁴×C₈₉	—	2	2	no	—
81	C₂⁴×C₈₉	—	2	8	no	—
82	C₂⁴×C₈₉	—	2	4	no	—
83	C₂⁴×C₈₉	—	8	4	no	—
84	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₈₉	—	2	8	no	—
86	C₂×D₄×C₈₉	—	2	8	no	—
87	C₂×D₄×C₈₉	—	2	16	no	—
88	C₂×D₄×C₈₉	—	2	2	no	—
89	C₂×D₄×C₈₉	—	2	4	no	—
90	C₂×D₄×C₈₉	—	2	8	no	—
91	C₂×D₄×C₈₉	—	2	4	no	—
92	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
93	C₂×D₄×C₈₉	C₂×Q₈	1	16	yes	—
94	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	—	2	16	no	—
98	C₂²×C₄×C₈₉	—	8	8	no	—
99	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₈₉	#41	1	4	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
106	M₁₆×C₈₉	—	2	8	no	—
107	M₁₆×C₈₉	—	2	8	no	—
108	C₂×C₈×C₈₉	—	2	8	no	—
109	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
110	C₄⋊C₄×C₈₉	—	2	2	no	—
111	C₄⋊C₄×C₈₉	—	2	4	no	—
112	C₄⋊C₄×C₈₉	—	2	8	no	—
113	C₄⋊C₄×C₈₉	—	2	16	no	—
114	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
115	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
116	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
117	C₂²⋊C₄×C₈₉	—	2	4	no	—
118	C₂²⋊C₄×C₈₉	—	2	4	no	—
119	C₂²⋊C₄×C₈₉	—	2	4	no	—
120	C₂²⋊C₄×C₈₉	—	2	16	no	—
121	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
122	C₄²×C₈₉	—	2	4	no	—
123	C₄²×C₈₉	—	2	4	no	—
124	C₄²×C₈₉	—	2	4	no	—
125	C₄²×C₈₉	C₂×D₄	1	4	yes	—
126	C₄²×C₈₉	C₂⁴	1	4	yes	—
127	C₂³×C₈₉	—	2	8	no	—
128	C₂³×C₈₉	—	2	4	no	—
129	C₂³×C₈₉	—	2	16	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	—	4	8	no	—
132	C₂³×C₈₉	—	8	8	no	—
133	C₂³×C₈₉	—	8	16	no	—
134	C₂³×C₈₉	C₂²⋊Q₈	1	4	yes	—
135	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
136	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₈₉	—	8	8	no	—
138	D₄×C₈₉	—	2	8	no	—
139	D₄×C₈₉	—	2	16	no	—
140	D₄×C₈₉	—	2	4	no	—
141	D₄×C₈₉	C₂²×Q₈	1	8	yes	—
142	C₂×C₄×C₈₉	—	2	4	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	—	4	4	no	—
146	C₂×C₄×C₈₉	—	8	16	no	—
147	C₂×C₄×C₈₉	—	8	4	no	—
148	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
149	C₂×C₄×C₈₉	C₂²⋊Q₈	1	8	yes	—
150	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
155	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
156	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
157	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
158	C₈×C₈₉	—	2	8	no	—
159	C₂²×C₈₉	—	2	2	no	—
160	C₂²×C₈₉	—	2	4	no	—
161	C₂²×C₈₉	—	2	8	no	—
162	C₂²×C₈₉	—	4	4	no	—
163	C₂²×C₈₉	—	4	16	no	—
164	C₂²×C₈₉	—	4	8	no	—
165	C₂²×C₈₉	—	8	16	no	—
166	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
167	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
168	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
169	C₄×C₈₉	—	2	8	no	—
170	C₄×C₈₉	—	4	4	no	—
171	C₄×C₈₉	—	4	8	no	—
172	C₄×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
173	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
174	C₄×C₈₉	C₂³×Q₈	1	1	yes	characteristic
175	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
176	#60490	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₈₉	—	2	2	no	—
178	C₂×C₈₉	—	2	4	no	—
179	C₂×C₈₉	—	4	8	no	—
180	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₈₉	#3585	1	2	yes	—
182	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
183	C₂×#518	C₂×C₈₉	1	1	yes	characteristic
184	#3081	C₂×C₈₉	1	16	yes	complemented
185	#3077	C₂×C₈₉	1	8	yes	complemented
186	#2911	C₂×C₈₉	1	2	yes	complemented
187	#2905	C₂×C₈₉	1	1	yes	characteristic, complemented
188	C₂×#418	C₂×C₈₉	1	2	yes	—
189	C₈₉	#60490	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
191	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
192	#544	—	2	2	no	—
193	#544	C₂²×C₈₉	1	8	yes	complemented
194	#543	—	2	2	no	—
195	#533	—	2	4	no	—
196	#533	C₂²×C₈₉	1	4	yes	complemented
197	#518	—	2	4	no	—
198	#518	C₂²×C₈₉	1	8	yes	—
199	C₂×C₄×D₄	—	2	2	no	—
200	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
201	C₂×#117	C₂²×C₈₉	1	2	yes	—
202	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
203	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
204	C₂²×C₂²⋊C₄	—	2	2	no	—
205	#478	C₂²×C₈₉	1	32	yes	complemented
206	#476	C₂²×C₈₉	1	16	yes	complemented
207	#474	C₂²×C₈₉	1	16	yes	complemented
208	#428	C₂²×C₈₉	1	8	yes	complemented
209	#428	C₂²×C₈₉	1	8	yes	complemented
210	#427	C₂²×C₈₉	1	8	yes	complemented
211	#424	C₂²×C₈₉	1	8	yes	complemented
212	#423	C₂²×C₈₉	1	4	yes	complemented
213	#418	C₂²×C₈₉	1	8	yes	—
214	#418	C₂²×C₈₉	1	8	yes	—
215	C₂×#102	C₂²×C₈₉	1	8	yes	—
216	C₂⁵	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂²×D₄	—	2	2	no	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	Q₈×C₈₉	1	8	yes	complemented
221	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
222	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
223	C₂³×C₄	—	2	4	no	—
224	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
225	C₂×M₁₆	—	2	8	no	—
226	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
227	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
228	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
229	C₄⋊Q₈	—	2	8	no	—
230	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
231	#125	—	2	8	no	—
232	#125	C₂³×C₈₉	1	8	yes	complemented
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	—	2	16	no	—
235	C₄×Q₈	—	2	8	no	—
236	C₄×D₄	—	2	16	no	—
237	C₄×D₄	—	2	8	no	—
238	C₄×D₄	C₂³×C₈₉	1	16	yes	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	D₄×C₈₉	1	4	yes	—
243	#117	C₂³×C₈₉	1	4	yes	—
244	#117	C₂³×C₈₉	1	4	yes	—
245	#117	C₂³×C₈₉	1	4	yes	—
246	#117	C₂³×C₈₉	1	4	yes	—
247	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	16	no	—
254	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
258	#107	C₂³×C₈₉	1	16	yes	complemented
259	#106	C₂³×C₈₉	1	16	yes	complemented
260	C₄⋊C₈	C₂³×C₈₉	1	16	yes	complemented
261	#102	C₂³×C₈₉	1	32	yes	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	8	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	8	4	no	—
266	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
267	C₂×Q₈	—	2	8	no	—
268	C₂×D₄	—	2	8	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
275	C₂×D₄	C₂×Q₈×C₈₉	1	16	yes	—
276	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	16	no	—
280	C₂²×C₄	—	8	8	no	—
281	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
282	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
284	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
285	C₂²×C₄	#41×C₈₉	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
288	M₁₆	—	2	8	no	—
289	M₁₆	—	2	8	no	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
297	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
298	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	16	no	—
303	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	C₂×D₄×C₈₉	1	4	yes	—
308	C₄²	C₂⁴×C₈₉	1	4	yes	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	8	8	no	—
315	C₂³	—	8	16	no	—
316	C₂³	C₂²⋊Q₈×C₈₉	1	4	yes	—
317	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
318	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
319	Q₈	—	8	8	no	—
320	D₄	—	2	8	no	—
321	D₄	—	2	16	no	—
322	D₄	—	2	4	no	—
323	D₄	C₂²×Q₈×C₈₉	1	8	yes	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	16	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
331	C₂×C₄	C₂²⋊Q₈×C₈₉	1	8	yes	—
332	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
333	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
335	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
336	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
337	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
338	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
339	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
340	C₈	—	2	8	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	16	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	8	16	no	—
348	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
349	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
350	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
351	C₄	—	2	8	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	8	no	—
354	C₄	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
355	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
356	C₄	C₂³×Q₈×C₈₉	1	1	yes	characteristic
357	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	2	4	no	—
360	C₂	—	4	8	no	—
361	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
362	C₂	C₈₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3458	C₂	semidirect
3. C₈₉×#3081	C₂	semidirect
4. C₈₉×#3077	C₂	semidirect
5. C₈₉×#2911	C₂	semidirect
6. C₈₉×#2905	C₂	semidirect
11. #544×C₈₉	C₂²	semidirect
14. #533×C₈₉	C₂²	semidirect
23. #478×C₈₉	C₂²	semidirect
24. #476×C₈₉	C₂²	semidirect
25. #474×C₈₉	C₂²	semidirect
26. #428×C₈₉	C₂²	semidirect
27. #428×C₈₉	C₂²	semidirect
28. #427×C₈₉	C₂²	semidirect
29. #424×C₈₉	C₂²	semidirect
30. #423×C₈₉	C₂²	semidirect
38. C₂²×D₄×C₈₉	Q₈	semidirect
48. C₄⋊Q₈×C₈₉	C₂³	semidirect
50. #125×C₈₉	C₂³	semidirect
76. #107×C₈₉	C₂³	semidirect
77. #106×C₈₉	C₂³	semidirect
78. C₄⋊C₈×C₈₉	C₂³	semidirect
176. #60490	C₈₉	direct (N × H)
182. #3458	C₂×C₈₉	semidirect
184. #3081	C₂×C₈₉	semidirect
185. #3077	C₂×C₈₉	semidirect
186. #2911	C₂×C₈₉	semidirect
187. #2905	C₂×C₈₉	semidirect
189. C₈₉	#60490	direct (N × H)
193. #544	C₂²×C₈₉	semidirect
196. #533	C₂²×C₈₉	semidirect
205. #478	C₂²×C₈₉	semidirect
206. #476	C₂²×C₈₉	semidirect
207. #474	C₂²×C₈₉	semidirect
208. #428	C₂²×C₈₉	semidirect
209. #428	C₂²×C₈₉	semidirect
210. #427	C₂²×C₈₉	semidirect
211. #424	C₂²×C₈₉	semidirect
212. #423	C₂²×C₈₉	semidirect
220. C₂²×D₄	Q₈×C₈₉	semidirect
230. C₄⋊Q₈	C₂³×C₈₉	semidirect
232. #125	C₂³×C₈₉	semidirect
258. #107	C₂³×C₈₉	semidirect
259. #106	C₂³×C₈₉	semidirect
260. C₄⋊C₈	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3458	2
C₂×#518×C₈₉	2
C₈₉×#3081	2
C₈₉×#3077	2
C₈₉×#2911	2
C₈₉×#2905	2
C₂×#418×C₈₉	2
#60490	89

Subgroups — C89×#60490 #36438338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60490 #36438338