Subgroups — C₈₉×#22875 #36400723

Order 22784.

1182 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2361	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	—	2	1	no	—
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	#448×C₈₉	C₄	1	8	yes	complemented
27	C₄×SD₁₆×C₈₉	—	2	4	no	—
28	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₈₉	—	2	4	no	—
31	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
42	#391×C₈₉	—	2	1	no	—
43	#391×C₈₉	—	2	1	no	—
44	#391×C₈₉	C₂²	1	1	yes	characteristic
45	#391×C₈₉	C₂²	1	1	yes	characteristic
46	#390×C₈₉	C₂²	1	1	yes	characteristic
47	#389×C₈₉	C₂²	1	1	yes	characteristic
48	#388×C₈₉	—	2	1	no	—
49	#386×C₈₉	—	2	1	no	—
50	#385×C₈₉	—	2	1	no	—
51	#380×C₈₉	—	2	1	no	—
52	#380×C₈₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₈₉	—	2	1	no	—
63	C₂²×Q₈×C₈₉	—	2	2	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	2	no	—
66	C₂²×Q₈×C₈₉	—	4	1	no	—
67	C₂²×Q₈×C₈₉	—	4	1	no	—
68	C₂²×Q₈×C₈₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₈₉	—	2	1	no	—
72	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	—	2	1	no	—
74	C₂³×C₄×C₈₉	—	2	1	no	—
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×SD₁₆×C₈₉	—	2	2	no	—
78	C₂×SD₁₆×C₈₉	—	2	2	no	—
79	C₂×SD₁₆×C₈₉	—	4	1	no	—
80	C₂×SD₁₆×C₈₉	—	4	1	no	—
81	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
82	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
83	C₂²×C₈×C₈₉	—	2	2	no	—
84	C₂²×C₈×C₈₉	—	2	2	no	—
85	C₂²×C₈×C₈₉	—	4	1	no	—
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	#121×C₈₉	—	2	2	no	—
91	#121×C₈₉	C₂×C₄	1	4	yes	—
92	C₄×Q₈×C₈₉	—	2	2	no	—
93	C₄×Q₈×C₈₉	—	2	2	no	—
94	C₄×Q₈×C₈₉	—	4	1	no	—
95	C₄×Q₈×C₈₉	—	4	1	no	—
96	C₄×D₄×C₈₉	—	2	2	no	—
97	C₄×D₄×C₈₉	—	4	1	no	—
98	C₄×D₄×C₈₉	—	4	4	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	—	2	1	no	—
118	C₂×C₄²×C₈₉	—	2	1	no	—
119	C₂×C₄²×C₈₉	—	2	1	no	—
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	#106×C₈₉	—	2	2	no	—
123	#106×C₈₉	—	4	1	no	—
124	#103×C₈₉	—	2	2	no	—
125	#103×C₈₉	—	2	2	no	—
126	#103×C₈₉	—	2	2	no	—
127	#103×C₈₉	C₂×C₄	1	4	yes	complemented
128	#103×C₈₉	C₂×C₄	1	4	yes	complemented
129	#103×C₈₉	D₄	1	4	yes	complemented
130	#102×C₈₉	—	2	2	no	—
131	#102×C₈₉	—	4	1	no	—
132	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
133	C₄×C₈×C₈₉	—	2	2	no	—
134	C₄×C₈×C₈₉	—	4	1	no	—
135	#95×C₈₉	—	2	1	no	—
136	#95×C₈₉	—	2	1	no	—
137	#95×C₈₉	—	2	1	no	—
138	#95×C₈₉	—	2	1	no	—
139	#95×C₈₉	—	2	1	no	—
140	#95×C₈₉	—	2	1	no	—
141	#95×C₈₉	—	2	1	no	—
142	#95×C₈₉	D₄	1	1	yes	characteristic
143	#95×C₈₉	D₄	1	1	yes	characteristic
144	C₂⁴×C₈₉	—	2	1	no	—
145	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₈₉	—	2	4	no	—
147	C₂×Q₈×C₈₉	—	2	1	no	—
148	C₂×Q₈×C₈₉	—	2	1	no	—
149	C₂×Q₈×C₈₉	—	2	1	no	—
150	C₂×Q₈×C₈₉	—	2	1	no	—
151	C₂×Q₈×C₈₉	—	2	8	no	—
152	C₂×Q₈×C₈₉	—	2	1	no	—
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	1	no	—
156	C₂×Q₈×C₈₉	—	4	2	no	—
157	C₂×Q₈×C₈₉	—	4	2	no	—
158	C₂×Q₈×C₈₉	—	4	4	no	—
159	C₂×Q₈×C₈₉	—	4	4	no	—
160	C₂×Q₈×C₈₉	—	4	4	no	—
161	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
162	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
163	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
164	C₂×Q₈×C₈₉	#41	1	2	yes	—
165	C₂×D₄×C₈₉	—	2	4	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂×D₄×C₈₉	—	4	2	no	—
172	C₂×D₄×C₈₉	—	4	2	no	—
173	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₈₉	—	2	1	no	—
175	C₂²×C₄×C₈₉	—	2	1	no	—
176	C₂²×C₄×C₈₉	—	2	1	no	—
177	C₂²×C₄×C₈₉	—	2	1	no	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	4	no	—
180	C₂²×C₄×C₈₉	—	2	1	no	—
181	C₂²×C₄×C₈₉	—	2	1	no	—
182	C₂²×C₄×C₈₉	—	2	1	no	—
183	C₂²×C₄×C₈₉	—	2	1	no	—
184	C₂²×C₄×C₈₉	—	2	1	no	—
185	C₂²×C₄×C₈₉	—	2	1	no	—
186	C₂²×C₄×C₈₉	—	4	2	no	—
187	C₂²×C₄×C₈₉	—	4	2	no	—
188	C₂²×C₄×C₈₉	—	4	2	no	—
189	C₂²×C₄×C₈₉	—	4	2	no	—
190	C₂²×C₄×C₈₉	—	4	2	no	—
191	C₂²×C₄×C₈₉	—	4	2	no	—
192	C₂²×C₄×C₈₉	—	8	1	no	—
193	C₂²×C₄×C₈₉	—	8	1	no	—
194	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₈₉	#41	1	2	yes	—
201	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
202	SD₁₆×C₈₉	—	2	8	no	—
203	SD₁₆×C₈₉	—	4	4	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	2	1	no	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	2	1	no	—
210	C₂×C₈×C₈₉	—	2	1	no	—
211	C₂×C₈×C₈₉	—	2	1	no	—
212	C₂×C₈×C₈₉	—	2	1	no	—
213	C₂×C₈×C₈₉	—	4	4	no	—
214	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
215	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
216	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₈₉	—	2	1	no	—
218	C₄⋊C₄×C₈₉	—	2	1	no	—
219	C₄⋊C₄×C₈₉	—	2	1	no	—
220	C₄⋊C₄×C₈₉	—	2	1	no	—
221	C₄⋊C₄×C₈₉	—	2	1	no	—
222	C₄⋊C₄×C₈₉	—	2	1	no	—
223	C₄⋊C₄×C₈₉	—	2	1	no	—
224	C₄⋊C₄×C₈₉	—	2	1	no	—
225	C₄⋊C₄×C₈₉	—	4	2	no	—
226	C₄⋊C₄×C₈₉	—	4	2	no	—
227	C₄⋊C₄×C₈₉	—	4	2	no	—
228	C₄⋊C₄×C₈₉	—	4	2	no	—
229	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₈₉	—	2	2	no	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	4	2	no	—
234	C₂²⋊C₄×C₈₉	—	4	2	no	—
235	C₂²⋊C₄×C₈₉	—	4	2	no	—
236	C₂²⋊C₄×C₈₉	—	8	1	no	—
237	C₂²⋊C₄×C₈₉	SD₁₆	1	4	yes	complemented
238	C₄²×C₈₉	—	2	1	no	—
239	C₄²×C₈₉	—	2	1	no	—
240	C₄²×C₈₉	—	2	1	no	—
241	C₄²×C₈₉	—	2	1	no	—
242	C₄²×C₈₉	—	4	2	no	—
243	C₄²×C₈₉	—	4	2	no	—
244	C₄²×C₈₉	—	4	2	no	—
245	C₂³×C₈₉	—	2	1	no	—
246	C₂³×C₈₉	—	2	1	no	—
247	C₂³×C₈₉	—	2	1	no	—
248	C₂³×C₈₉	—	2	1	no	—
249	C₂³×C₈₉	—	2	2	no	—
250	C₂³×C₈₉	—	4	1	no	—
251	C₂³×C₈₉	—	4	1	no	—
252	C₂³×C₈₉	—	4	1	no	—
253	C₂³×C₈₉	—	4	1	no	—
254	C₂³×C₈₉	—	4	1	no	—
255	C₂³×C₈₉	—	4	1	no	—
256	C₂³×C₈₉	C₄×D₄	1	2	yes	—
257	C₂³×C₈₉	C₂×SD₁₆	1	2	yes	—
258	C₂³×C₈₉	#135	1	2	yes	—
259	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₈₉	—	2	2	no	—
261	Q₈×C₈₉	—	2	2	no	—
262	Q₈×C₈₉	—	2	2	no	—
263	Q₈×C₈₉	—	2	2	no	—
264	Q₈×C₈₉	—	2	2	no	—
265	Q₈×C₈₉	—	4	8	no	—
266	Q₈×C₈₉	—	4	1	no	—
267	Q₈×C₈₉	—	4	1	no	—
268	Q₈×C₈₉	C₄×D₄	1	4	yes	complemented
269	D₄×C₈₉	—	2	2	no	—
270	D₄×C₈₉	—	2	2	no	—
271	D₄×C₈₉	—	4	8	no	—
272	D₄×C₈₉	—	4	1	no	—
273	D₄×C₈₉	—	4	1	no	—
274	C₂×C₄×C₈₉	—	2	2	no	—
275	C₂×C₄×C₈₉	—	2	1	no	—
276	C₂×C₄×C₈₉	—	2	2	no	—
277	C₂×C₄×C₈₉	—	2	1	no	—
278	C₂×C₄×C₈₉	—	2	1	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	1	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	1	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	1	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	1	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	4	8	no	—
297	C₂×C₄×C₈₉	—	4	1	no	—
298	C₂×C₄×C₈₉	—	4	1	no	—
299	C₂×C₄×C₈₉	—	4	1	no	—
300	C₂×C₄×C₈₉	—	4	1	no	—
301	C₂×C₄×C₈₉	—	4	1	no	—
302	C₂×C₄×C₈₉	—	4	1	no	—
303	C₂×C₄×C₈₉	—	4	1	no	—
304	C₂×C₄×C₈₉	—	4	1	no	—
305	C₂×C₄×C₈₉	—	4	1	no	—
306	C₂×C₄×C₈₉	—	4	1	no	—
307	C₂×C₄×C₈₉	—	4	1	no	—
308	C₂×C₄×C₈₉	—	4	1	no	—
309	C₂×C₄×C₈₉	—	4	1	no	—
310	C₂×C₄×C₈₉	—	4	1	no	—
311	C₂×C₄×C₈₉	—	4	1	no	—
312	C₂×C₄×C₈₉	—	8	4	no	—
313	C₂×C₄×C₈₉	—	8	4	no	—
314	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
316	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
317	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
323	C₈×C₈₉	—	2	2	no	—
324	C₈×C₈₉	—	2	2	no	—
325	C₈×C₈₉	—	2	2	no	—
326	C₈×C₈₉	—	4	1	no	—
327	C₂²×C₈₉	—	2	2	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	2	no	—
330	C₂²×C₈₉	—	2	2	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	2	no	—
333	C₂²×C₈₉	—	4	2	no	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	2	no	—
336	C₂²×C₈₉	—	8	1	no	—
337	C₂²×C₈₉	—	8	1	no	—
338	C₂²×C₈₉	—	8	1	no	—
339	C₂²×C₈₉	—	8	1	no	—
340	C₂²×C₈₉	C₄×SD₁₆	1	4	yes	complemented
341	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂²×C₈₉	D₄²	1	1	yes	characteristic
343	C₂²×C₈₉	#546	1	1	yes	characteristic
344	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
345	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
346	C₂²×C₈₉	#577	1	1	yes	characteristic
347	C₂²×C₈₉	#578	1	1	yes	characteristic
348	C₄×C₈₉	—	2	2	no	—
349	C₄×C₈₉	—	2	4	no	—
350	C₄×C₈₉	—	2	2	no	—
351	C₄×C₈₉	—	2	2	no	—
352	C₄×C₈₉	—	4	2	no	—
353	C₄×C₈₉	—	4	2	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	1	no	—
356	C₄×C₈₉	—	4	1	no	—
357	C₄×C₈₉	—	8	1	no	—
358	C₄×C₈₉	—	8	1	no	—
359	C₄×C₈₉	—	8	1	no	—
360	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
361	C₄×C₈₉	#518	1	1	yes	characteristic
362	C₄×C₈₉	#546	1	1	yes	characteristic
363	C₄×C₈₉	#551	1	1	yes	characteristic
364	#22875	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂×C₈₉	—	2	4	no	—
366	C₂×C₈₉	—	8	2	no	—
367	C₂×C₈₉	#2358	1	1	yes	characteristic
368	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
369	C₂×C₈₉	#2947	1	1	yes	characteristic
370	C₂×C₈₉	D₄×SD₁₆	1	1	yes	characteristic
371	C₂×C₈₉	#3285	1	1	yes	characteristic
372	C₂×C₈₉	#3298	1	1	yes	characteristic
373	C₂×C₈₉	#3301	1	1	yes	characteristic
374	C₂×#448	C₂×C₈₉	1	1	yes	characteristic
375	C₂×C₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
376	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
377	#2361	C₂×C₈₉	1	1	yes	characteristic
378	Q₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#1933	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#1927	C₂×C₈₉	1	1	yes	characteristic, complemented
382	#1893	C₂×C₈₉	1	1	yes	characteristic
383	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
384	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#1853	C₂×C₈₉	1	1	yes	characteristic, complemented
387	C₄×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
389	C₈₉	#22875	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
393	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
394	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
395	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
397	C₂×C₄×D₄	—	2	1	no	—
398	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
400	#448	C₄×C₈₉	1	8	yes	complemented
401	C₄×SD₁₆	—	2	4	no	—
402	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
403	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×#103	—	2	4	no	—
405	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
416	#391	—	2	1	no	—
417	#391	—	2	1	no	—
418	#391	C₂²×C₈₉	1	1	yes	characteristic
419	#391	C₂²×C₈₉	1	1	yes	characteristic
420	#390	C₂²×C₈₉	1	1	yes	characteristic
421	#389	C₂²×C₈₉	1	1	yes	characteristic
422	#388	—	2	1	no	—
423	#386	—	2	1	no	—
424	#385	—	2	1	no	—
425	#380	—	2	1	no	—
426	#380	C₂²×C₈₉	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
428	C₄×C₂²⋊C₄	—	2	1	no	—
429	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
430	#340	C₂²×C₈₉	1	1	yes	characteristic
431	#340	C₂²×C₈₉	1	1	yes	characteristic
432	#340	C₂²×C₈₉	1	1	yes	characteristic
433	#340	C₂²×C₈₉	1	1	yes	characteristic
434	#336	C₂²×C₈₉	1	1	yes	characteristic
435	#336	C₂²×C₈₉	1	1	yes	characteristic
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	—	2	2	no	—
438	C₂²×Q₈	—	2	2	no	—
439	C₂²×Q₈	—	2	2	no	—
440	C₂²×Q₈	—	4	1	no	—
441	C₂²×Q₈	—	4	1	no	—
442	C₂²×Q₈	C₂×C₄×C₈₉	1	4	yes	complemented
443	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
451	C₂×SD₁₆	—	2	2	no	—
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×SD₁₆	—	4	1	no	—
454	C₂×SD₁₆	—	4	1	no	—
455	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	complemented
456	C₂×SD₁₆	C₂×C₄×C₈₉	1	4	yes	complemented
457	C₂²×C₈	—	2	2	no	—
458	C₂²×C₈	—	2	2	no	—
459	C₂²×C₈	—	4	1	no	—
460	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
464	#121	—	2	2	no	—
465	#121	C₂×C₄×C₈₉	1	4	yes	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	4	1	no	—
469	C₄×Q₈	—	4	1	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	4	1	no	—
472	C₄×D₄	—	4	4	no	—
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	4	1	no	—
479	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
496	#106	—	2	2	no	—
497	#106	—	4	1	no	—
498	#103	—	2	2	no	—
499	#103	—	2	2	no	—
500	#103	—	2	2	no	—
501	#103	C₂×C₄×C₈₉	1	4	yes	complemented
502	#103	C₂×C₄×C₈₉	1	4	yes	complemented
503	#103	D₄×C₈₉	1	4	yes	complemented
504	#102	—	2	2	no	—
505	#102	—	4	1	no	—
506	C₂²⋊C₈	C₂×C₄×C₈₉	1	4	yes	complemented
507	C₄×C₈	—	2	2	no	—
508	C₄×C₈	—	4	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	D₄×C₈₉	1	1	yes	characteristic
517	#95	D₄×C₈₉	1	1	yes	characteristic
518	C₂⁴	—	2	1	no	—
519	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	8	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	4	2	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂×Q₈	—	4	4	no	—
533	C₂×Q₈	—	4	4	no	—
534	C₂×Q₈	—	4	4	no	—
535	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
536	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
537	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
538	C₂×Q₈	#41×C₈₉	1	2	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	8	1	no	—
567	C₂²×C₄	—	8	1	no	—
568	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
569	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
574	C₂²×C₄	#41×C₈₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
576	SD₁₆	—	2	8	no	—
577	SD₁₆	—	4	4	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	4	4	no	—
588	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
589	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
590	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
604	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	8	1	no	—
611	C₂²⋊C₄	SD₁₆×C₈₉	1	4	yes	complemented
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	4	2	no	—
617	C₄²	—	4	2	no	—
618	C₄²	—	4	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	C₄×D₄×C₈₉	1	2	yes	—
631	C₂³	C₂×SD₁₆×C₈₉	1	2	yes	—
632	C₂³	#135×C₈₉	1	2	yes	—
633	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	4	8	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	4	1	no	—
642	Q₈	C₄×D₄×C₈₉	1	4	yes	complemented
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	8	4	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
689	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
690	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
691	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
693	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
694	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
695	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
696	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	2	2	no	—
700	C₈	—	4	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	C₄×SD₁₆×C₈₉	1	4	yes	complemented
715	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
716	C₂²	D₄²×C₈₉	1	1	yes	characteristic
717	C₂²	#546×C₈₉	1	1	yes	characteristic
718	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
719	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
720	C₂²	#577×C₈₉	1	1	yes	characteristic
721	C₂²	#578×C₈₉	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	4	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	8	1	no	—
732	C₄	—	8	1	no	—
733	C₄	—	8	1	no	—
734	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
735	C₄	#518×C₈₉	1	1	yes	characteristic
736	C₄	#546×C₈₉	1	1	yes	characteristic
737	C₄	#551×C₈₉	1	1	yes	characteristic
738	C₂	—	2	4	no	—
739	C₂	—	8	2	no	—
740	C₂	C₈₉×#2358	1	1	yes	characteristic
741	C₂	C₂×C₄×SD₁₆×C₈₉	1	1	yes	characteristic
742	C₂	C₈₉×#2947	1	1	yes	characteristic
743	C₂	D₄×SD₁₆×C₈₉	1	1	yes	characteristic
744	C₂	C₈₉×#3285	1	1	yes	characteristic
745	C₂	C₈₉×#3298	1	1	yes	characteristic
746	C₂	C₈₉×#3301	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
3. C₂²×#103×C₈₉	C₂	semidirect
5. Q₈×C₂²⋊C₄×C₈₉	C₂	semidirect
6. C₈₉×#1968	C₂	semidirect
7. C₈₉×#1933	C₂	semidirect
8. C₈₉×#1927	C₂	semidirect
10. C₈₉×#1880	C₂	semidirect
11. C₈₉×#1877	C₂	semidirect
12. C₈₉×#1865	C₂	semidirect
13. C₈₉×#1853	C₂	semidirect
14. C₄×#103×C₈₉	C₂	semidirect
15. C₈×C₂²⋊C₄×C₈₉	C₂	semidirect
26. #448×C₈₉	C₄	semidirect
68. C₂²×Q₈×C₈₉	C₂×C₄	semidirect
81. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
82. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
127. #103×C₈₉	C₂×C₄	semidirect
128. #103×C₈₉	C₂×C₄	semidirect
129. #103×C₈₉	D₄	semidirect
132. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
237. C₂²⋊C₄×C₈₉	SD₁₆	semidirect
268. Q₈×C₈₉	C₄×D₄	semidirect
340. C₂²×C₈₉	C₄×SD₁₆	semidirect
364. #22875	C₈₉	direct (N × H)
375. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
376. C₂²×#103	C₂×C₈₉	semidirect
378. Q₈×C₂²⋊C₄	C₂×C₈₉	semidirect
379. #1968	C₂×C₈₉	semidirect
380. #1933	C₂×C₈₉	semidirect
381. #1927	C₂×C₈₉	semidirect
383. #1880	C₂×C₈₉	semidirect
384. #1877	C₂×C₈₉	semidirect
385. #1865	C₂×C₈₉	semidirect
386. #1853	C₂×C₈₉	semidirect
387. C₄×#103	C₂×C₈₉	semidirect
388. C₈×C₂²⋊C₄	C₂×C₈₉	semidirect
389. C₈₉	#22875	direct (N × H)
400. #448	C₄×C₈₉	semidirect
442. C₂²×Q₈	C₂×C₄×C₈₉	semidirect
455. C₂×SD₁₆	C₂×C₄×C₈₉	semidirect
456. C₂×SD₁₆	C₂×C₄×C₈₉	semidirect
501. #103	C₂×C₄×C₈₉	semidirect
502. #103	C₂×C₄×C₈₉	semidirect
503. #103	D₄×C₈₉	semidirect
506. C₂²⋊C₈	C₂×C₄×C₈₉	semidirect
611. C₂²⋊C₄	SD₁₆×C₈₉	semidirect
642. Q₈	C₄×D₄×C₈₉	semidirect
714. C₂²	C₄×SD₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#448×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₂²×#103×C₈₉	2
C₈₉×#2361	2
Q₈×C₂²⋊C₄×C₈₉	2
C₈₉×#1968	2
C₈₉×#1933	2
C₈₉×#1927	2
C₈₉×#1893	2
C₈₉×#1880	2
C₈₉×#1877	2
C₈₉×#1865	2
C₈₉×#1853	2
C₄×#103×C₈₉	2
C₈×C₂²⋊C₄×C₈₉	2
#22875	89

Subgroups — C89×#22875 #36400723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22875 #36400723