Subgroups — C₈₉×#25149 #36402997

Order 22784.

1086 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#451×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2426	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2033	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	#464×C₈₉	—	2	4	no	—
28	#451×C₈₉	—	2	4	no	—
29	#448×C₈₉	—	2	4	no	—
30	C₄×Q₁₆×C₈₉	—	2	4	no	—
31	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×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×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#396×C₈₉	—	2	1	no	—
46	#394×C₈₉	—	2	1	no	—
47	#391×C₈₉	—	2	1	no	—
48	#391×C₈₉	—	2	1	no	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	—	2	1	no	—
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#388×C₈₉	—	2	1	no	—
55	#380×C₈₉	—	2	1	no	—
56	#380×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	#340×C₈₉	C₂²	1	1	yes	characteristic
60	#340×C₈₉	C₂²	1	1	yes	characteristic
61	#336×C₈₉	C₂²	1	1	yes	characteristic
62	#336×C₈₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₈₉	—	2	2	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	1	no	—
66	C₂²×Q₈×C₈₉	—	2	2	no	—
67	C₂²×Q₈×C₈₉	—	2	2	no	—
68	C₂²×Q₈×C₈₉	—	4	1	no	—
69	C₂²×Q₈×C₈₉	—	4	1	no	—
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₈₉	—	2	1	no	—
74	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	—	2	1	no	—
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₈₉	—	2	2	no	—
78	C₂×Q₁₆×C₈₉	—	2	2	no	—
79	C₂×Q₁₆×C₈₉	—	2	2	no	—
80	C₂×Q₁₆×C₈₉	—	2	2	no	—
81	C₂×Q₁₆×C₈₉	—	4	1	no	—
82	C₂×Q₁₆×C₈₉	D₄	1	4	yes	complemented
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	2	2	no	—
85	C₂×SD₁₆×C₈₉	—	2	2	no	—
86	C₂×SD₁₆×C₈₉	—	2	2	no	—
87	C₂×SD₁₆×C₈₉	—	2	2	no	—
88	C₂×SD₁₆×C₈₉	—	4	1	no	—
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	#124×C₈₉	—	2	2	no	—
94	#124×C₈₉	—	4	1	no	—
95	C₂²⋊Q₈×C₈₉	—	2	2	no	—
96	C₂²⋊Q₈×C₈₉	—	4	1	no	—
97	#121×C₈₉	—	2	2	no	—
98	#121×C₈₉	—	4	1	no	—
99	C₄×Q₈×C₈₉	—	2	2	no	—
100	C₄×Q₈×C₈₉	—	2	2	no	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	4	1	no	—
103	C₄×Q₈×C₈₉	—	4	1	no	—
104	C₄×Q₈×C₈₉	—	4	1	no	—
105	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₈₉	—	2	1	no	—
124	C₂×C₄²×C₈₉	—	2	1	no	—
125	C₂×C₄²×C₈₉	—	2	1	no	—
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	#107×C₈₉	—	2	2	no	—
129	#106×C₈₉	—	4	1	no	—
130	C₄⋊C₈×C₈₉	—	2	2	no	—
131	#103×C₈₉	—	2	2	no	—
132	#103×C₈₉	—	2	2	no	—
133	#103×C₈₉	—	2	2	no	—
134	#103×C₈₉	—	2	2	no	—
135	#103×C₈₉	—	2	2	no	—
136	#103×C₈₉	D₄	1	4	yes	—
137	#102×C₈₉	—	2	2	no	—
138	#102×C₈₉	—	4	1	no	—
139	C₂²⋊C₈×C₈₉	—	2	2	no	—
140	C₂²⋊C₈×C₈₉	—	2	2	no	—
141	C₄×C₈×C₈₉	—	2	2	no	—
142	#95×C₈₉	—	2	1	no	—
143	#95×C₈₉	—	2	1	no	—
144	#95×C₈₉	—	2	1	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	#95×C₈₉	D₄	1	1	yes	characteristic
149	#95×C₈₉	D₄	1	1	yes	characteristic
150	C₂⁴×C₈₉	—	2	1	no	—
151	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₈₉	—	2	4	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	—	2	1	no	—
157	C₂×Q₈×C₈₉	—	2	1	no	—
158	C₂×Q₈×C₈₉	—	2	1	no	—
159	C₂×Q₈×C₈₉	—	2	1	no	—
160	C₂×Q₈×C₈₉	—	2	1	no	—
161	C₂×Q₈×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	—	2	1	no	—
163	C₂×Q₈×C₈₉	—	2	1	no	—
164	C₂×Q₈×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	—	2	1	no	—
166	C₂×Q₈×C₈₉	—	4	2	no	—
167	C₂×Q₈×C₈₉	—	4	2	no	—
168	C₂×Q₈×C₈₉	—	4	4	no	—
169	C₂×Q₈×C₈₉	—	4	4	no	—
170	C₂×Q₈×C₈₉	—	4	4	no	—
171	C₂×Q₈×C₈₉	—	4	4	no	—
172	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
174	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
175	C₂×Q₈×C₈₉	#41	1	2	yes	—
176	C₂×Q₈×C₈₉	#41	1	2	yes	—
177	C₂×D₄×C₈₉	—	2	1	no	—
178	C₂×D₄×C₈₉	—	2	1	no	—
179	C₂×D₄×C₈₉	—	2	1	no	—
180	C₂×D₄×C₈₉	—	2	1	no	—
181	C₂×D₄×C₈₉	—	2	1	no	—
182	C₂×D₄×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	8	1	no	—
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	4	no	—
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	2	1	no	—
190	C₂²×C₄×C₈₉	—	2	1	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	1	no	—
193	C₂²×C₄×C₈₉	—	2	1	no	—
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	4	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	Q₁₆×C₈₉	—	2	8	no	—
209	Q₁₆×C₈₉	—	4	4	no	—
210	SD₁₆×C₈₉	—	4	4	no	—
211	SD₁₆×C₈₉	—	4	4	no	—
212	C₂×C₈×C₈₉	—	2	1	no	—
213	C₂×C₈×C₈₉	—	2	1	no	—
214	C₂×C₈×C₈₉	—	2	1	no	—
215	C₂×C₈×C₈₉	—	2	1	no	—
216	C₂×C₈×C₈₉	—	2	1	no	—
217	C₂×C₈×C₈₉	—	2	1	no	—
218	C₂×C₈×C₈₉	—	2	1	no	—
219	C₂×C₈×C₈₉	—	2	1	no	—
220	C₂×C₈×C₈₉	—	2	1	no	—
221	C₂×C₈×C₈₉	—	2	1	no	—
222	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
223	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
224	C₄⋊C₄×C₈₉	—	2	1	no	—
225	C₄⋊C₄×C₈₉	—	2	1	no	—
226	C₄⋊C₄×C₈₉	—	2	1	no	—
227	C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₄⋊C₄×C₈₉	—	2	1	no	—
229	C₄⋊C₄×C₈₉	—	2	1	no	—
230	C₄⋊C₄×C₈₉	—	2	1	no	—
231	C₄⋊C₄×C₈₉	—	4	2	no	—
232	C₄⋊C₄×C₈₉	—	4	2	no	—
233	C₄⋊C₄×C₈₉	—	4	2	no	—
234	C₄⋊C₄×C₈₉	—	4	2	no	—
235	C₄⋊C₄×C₈₉	—	8	1	no	—
236	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
237	C₂²⋊C₄×C₈₉	—	2	2	no	—
238	C₂²⋊C₄×C₈₉	—	2	2	no	—
239	C₂²⋊C₄×C₈₉	—	4	2	no	—
240	C₂²⋊C₄×C₈₉	—	4	2	no	—
241	C₂²⋊C₄×C₈₉	—	4	2	no	—
242	C₂²⋊C₄×C₈₉	—	4	2	no	—
243	C₂²⋊C₄×C₈₉	—	4	2	no	—
244	C₂²⋊C₄×C₈₉	—	4	2	no	—
245	C₂²⋊C₄×C₈₉	—	8	1	no	—
246	C₄²×C₈₉	—	2	1	no	—
247	C₄²×C₈₉	—	2	1	no	—
248	C₄²×C₈₉	—	2	1	no	—
249	C₄²×C₈₉	—	2	1	no	—
250	C₄²×C₈₉	—	4	2	no	—
251	C₄²×C₈₉	—	4	2	no	—
252	C₄²×C₈₉	—	4	2	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	1	no	—
255	C₂³×C₈₉	—	2	1	no	—
256	C₂³×C₈₉	—	2	1	no	—
257	C₂³×C₈₉	—	2	1	no	—
258	C₂³×C₈₉	—	2	1	no	—
259	C₂³×C₈₉	—	4	1	no	—
260	C₂³×C₈₉	—	4	1	no	—
261	C₂³×C₈₉	—	4	1	no	—
262	C₂³×C₈₉	—	4	1	no	—
263	C₂³×C₈₉	—	4	1	no	—
264	C₂³×C₈₉	—	4	1	no	—
265	C₂³×C₈₉	—	4	1	no	—
266	C₂³×C₈₉	#135	1	2	yes	—
267	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₈₉	—	2	2	no	—
269	Q₈×C₈₉	—	2	2	no	—
270	Q₈×C₈₉	—	2	2	no	—
271	Q₈×C₈₉	—	2	2	no	—
272	Q₈×C₈₉	—	2	2	no	—
273	Q₈×C₈₉	—	2	2	no	—
274	Q₈×C₈₉	—	2	2	no	—
275	Q₈×C₈₉	—	4	8	no	—
276	Q₈×C₈₉	—	4	1	no	—
277	Q₈×C₈₉	—	4	1	no	—
278	Q₈×C₈₉	—	4	1	no	—
279	Q₈×C₈₉	—	4	1	no	—
280	Q₈×C₈₉	#121	1	4	yes	—
281	D₄×C₈₉	—	4	1	no	—
282	D₄×C₈₉	—	4	1	no	—
283	D₄×C₈₉	—	4	1	no	—
284	D₄×C₈₉	—	4	1	no	—
285	D₄×C₈₉	—	8	4	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	2	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	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	1	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	1	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	4	8	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	—	4	1	no	—
313	C₂×C₄×C₈₉	—	4	1	no	—
314	C₂×C₄×C₈₉	—	4	1	no	—
315	C₂×C₄×C₈₉	—	4	1	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	1	no	—
321	C₂×C₄×C₈₉	—	4	1	no	—
322	C₂×C₄×C₈₉	—	4	1	no	—
323	C₂×C₄×C₈₉	—	4	1	no	—
324	C₂×C₄×C₈₉	—	4	1	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	#137	1	2	yes	—
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
333	C₈×C₈₉	—	2	2	no	—
334	C₈×C₈₉	—	2	2	no	—
335	C₈×C₈₉	—	4	1	no	—
336	C₈×C₈₉	—	4	1	no	—
337	C₂²×C₈₉	—	2	2	no	—
338	C₂²×C₈₉	—	2	2	no	—
339	C₂²×C₈₉	—	2	2	no	—
340	C₂²×C₈₉	—	4	1	no	—
341	C₂²×C₈₉	—	4	1	no	—
342	C₂²×C₈₉	—	4	1	no	—
343	C₂²×C₈₉	—	4	1	no	—
344	C₂²×C₈₉	—	8	1	no	—
345	C₂²×C₈₉	—	8	1	no	—
346	C₂²×C₈₉	—	8	1	no	—
347	C₂²×C₈₉	—	8	1	no	—
348	C₂²×C₈₉	—	8	1	no	—
349	C₂²×C₈₉	—	8	1	no	—
350	C₂²×C₈₉	—	8	1	no	—
351	C₂²×C₈₉	#525	1	1	yes	characteristic
352	C₂²×C₈₉	D₄²	1	1	yes	characteristic
353	C₂²×C₈₉	D₄²	1	1	yes	characteristic
354	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
355	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
356	C₂²×C₈₉	#577	1	1	yes	characteristic
357	C₂²×C₈₉	#578	1	1	yes	characteristic
358	C₄×C₈₉	—	2	4	no	—
359	C₄×C₈₉	—	2	2	no	—
360	C₄×C₈₉	—	4	1	no	—
361	C₄×C₈₉	—	4	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	1	no	—
364	C₄×C₈₉	—	4	1	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	1	no	—
367	C₄×C₈₉	—	8	1	no	—
368	C₄×C₈₉	—	8	1	no	—
369	C₄×C₈₉	—	8	1	no	—
370	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
371	C₄×C₈₉	#538	1	1	yes	characteristic
372	C₄×C₈₉	#546	1	1	yes	characteristic
373	C₄×C₈₉	#546	1	1	yes	characteristic
374	#25149	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂×C₈₉	—	4	2	no	—
376	C₂×C₈₉	—	16	1	no	—
377	C₂×C₈₉	#2424	1	1	yes	characteristic
378	C₂×C₈₉	#3108	1	1	yes	characteristic
379	C₂×C₈₉	#3121	1	1	yes	characteristic
380	C₂×C₈₉	#3270	1	1	yes	characteristic
381	C₂×C₈₉	#3278	1	1	yes	characteristic
382	C₂×C₈₉	#3282	1	1	yes	characteristic
383	C₂×C₈₉	#3285	1	1	yes	characteristic
384	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
385	C₂×#451	C₂×C₈₉	1	1	yes	characteristic, complemented
386	C₂×#448	C₂×C₈₉	1	1	yes	characteristic
387	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#2426	C₂×C₈₉	1	1	yes	characteristic
389	Q₈×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#2068	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#2035	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#2033	C₂×C₈₉	1	1	yes	characteristic
393	#2015	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#1968	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#1923	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#1865	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₈₉	#25149	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
401	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
402	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
403	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
404	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
411	#464	—	2	4	no	—
412	#451	—	2	4	no	—
413	#448	—	2	4	no	—
414	C₄×Q₁₆	—	2	4	no	—
415	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
429	#396	—	2	1	no	—
430	#394	—	2	1	no	—
431	#391	—	2	1	no	—
432	#391	—	2	1	no	—
433	#391	C₂²×C₈₉	1	1	yes	characteristic
434	#391	C₂²×C₈₉	1	1	yes	characteristic
435	#390	—	2	1	no	—
436	#390	C₂²×C₈₉	1	1	yes	characteristic
437	#389	C₂²×C₈₉	1	1	yes	characteristic
438	#388	—	2	1	no	—
439	#380	—	2	1	no	—
440	#380	C₂²×C₈₉	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
443	#340	C₂²×C₈₉	1	1	yes	characteristic
444	#340	C₂²×C₈₉	1	1	yes	characteristic
445	#336	C₂²×C₈₉	1	1	yes	characteristic
446	#336	C₂²×C₈₉	1	1	yes	characteristic
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×Q₈	—	2	2	no	—
452	C₂²×Q₈	—	4	1	no	—
453	C₂²×Q₈	—	4	1	no	—
454	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
456	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
461	C₂×Q₁₆	—	2	2	no	—
462	C₂×Q₁₆	—	2	2	no	—
463	C₂×Q₁₆	—	2	2	no	—
464	C₂×Q₁₆	—	2	2	no	—
465	C₂×Q₁₆	—	4	1	no	—
466	C₂×Q₁₆	D₄×C₈₉	1	4	yes	complemented
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	2	2	no	—
469	C₂×SD₁₆	—	2	2	no	—
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	2	2	no	—
472	C₂×SD₁₆	—	4	1	no	—
473	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
477	#124	—	2	2	no	—
478	#124	—	4	1	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	4	1	no	—
481	#121	—	2	2	no	—
482	#121	—	4	1	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	4	1	no	—
487	C₄×Q₈	—	4	1	no	—
488	C₄×Q₈	—	4	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	—	2	1	no	—
509	C₂×C₄²	—	2	1	no	—
510	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
512	#107	—	2	2	no	—
513	#106	—	4	1	no	—
514	C₄⋊C₈	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#103	—	2	2	no	—
519	#103	—	2	2	no	—
520	#103	D₄×C₈₉	1	4	yes	—
521	#102	—	2	2	no	—
522	#102	—	4	1	no	—
523	C₂²⋊C₈	—	2	2	no	—
524	C₂²⋊C₈	—	2	2	no	—
525	C₄×C₈	—	2	2	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	—	2	1	no	—
532	#95	D₄×C₈₉	1	1	yes	characteristic
533	#95	D₄×C₈₉	1	1	yes	characteristic
534	C₂⁴	—	2	1	no	—
535	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	4	2	no	—
551	C₂×Q₈	—	4	2	no	—
552	C₂×Q₈	—	4	4	no	—
553	C₂×Q₈	—	4	4	no	—
554	C₂×Q₈	—	4	4	no	—
555	C₂×Q₈	—	4	4	no	—
556	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
557	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
558	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
559	C₂×Q₈	#41×C₈₉	1	2	yes	—
560	C₂×Q₈	#41×C₈₉	1	2	yes	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	8	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
592	Q₁₆	—	2	8	no	—
593	Q₁₆	—	4	4	no	—
594	SD₁₆	—	4	4	no	—
595	SD₁₆	—	4	4	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
607	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	8	1	no	—
620	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	8	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	2	no	—
636	C₄²	—	4	2	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	#135×C₈₉	1	2	yes	—
651	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	4	8	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	1	no	—
664	Q₈	#121×C₈₉	1	4	yes	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	#137×C₈₉	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
713	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
714	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
715	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
716	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
717	C₈	—	2	2	no	—
718	C₈	—	2	2	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	—	8	1	no	—
735	C₂²	#525×C₈₉	1	1	yes	characteristic
736	C₂²	D₄²×C₈₉	1	1	yes	characteristic
737	C₂²	D₄²×C₈₉	1	1	yes	characteristic
738	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
739	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
740	C₂²	#577×C₈₉	1	1	yes	characteristic
741	C₂²	#578×C₈₉	1	1	yes	characteristic
742	C₄	—	2	4	no	—
743	C₄	—	2	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	8	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
755	C₄	#538×C₈₉	1	1	yes	characteristic
756	C₄	#546×C₈₉	1	1	yes	characteristic
757	C₄	#546×C₈₉	1	1	yes	characteristic
758	C₂	—	4	2	no	—
759	C₂	—	16	1	no	—
760	C₂	C₈₉×#2424	1	1	yes	characteristic
761	C₂	C₈₉×#3108	1	1	yes	characteristic
762	C₂	C₈₉×#3121	1	1	yes	characteristic
763	C₂	C₈₉×#3270	1	1	yes	characteristic
764	C₂	C₈₉×#3278	1	1	yes	characteristic
765	C₂	C₈₉×#3282	1	1	yes	characteristic
766	C₂	C₈₉×#3285	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#121×C₈₉	C₂²
LCS	G ▷ C₂²×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
1. C₂×#464×C₈₉	C₂	semidirect
2. C₂×#451×C₈₉	C₂	semidirect
4. C₂×C₄×Q₁₆×C₈₉	C₂	semidirect
6. Q₈×C₂²⋊C₄×C₈₉	C₂	semidirect
7. C₈₉×#2068	C₂	semidirect
8. C₈₉×#2035	C₂	semidirect
10. C₈₉×#2015	C₂	semidirect
11. C₈₉×#1968	C₂	semidirect
12. C₈₉×#1923	C₂	semidirect
13. C₈₉×#1880	C₂	semidirect
14. C₈₉×#1878	C₂	semidirect
15. C₈₉×#1865	C₂	semidirect
82. C₂×Q₁₆×C₈₉	D₄	semidirect
374. #25149	C₈₉	direct (N × H)
384. C₂×#464	C₂×C₈₉	semidirect
385. C₂×#451	C₂×C₈₉	semidirect
387. C₂×C₄×Q₁₆	C₂×C₈₉	semidirect
389. Q₈×C₂²⋊C₄	C₂×C₈₉	semidirect
390. #2068	C₂×C₈₉	semidirect
391. #2035	C₂×C₈₉	semidirect
393. #2015	C₂×C₈₉	semidirect
394. #1968	C₂×C₈₉	semidirect
395. #1923	C₂×C₈₉	semidirect
396. #1880	C₂×C₈₉	semidirect
397. #1878	C₂×C₈₉	semidirect
398. #1865	C₂×C₈₉	semidirect
399. C₈₉	#25149	direct (N × H)
466. C₂×Q₁₆	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#464×C₈₉	2
C₂×#451×C₈₉	2
C₂×#448×C₈₉	2
C₂×C₄×Q₁₆×C₈₉	2
C₈₉×#2426	2
Q₈×C₂²⋊C₄×C₈₉	2
C₈₉×#2068	2
C₈₉×#2035	2
C₈₉×#2033	2
C₈₉×#2015	2
C₈₉×#1968	2
C₈₉×#1923	2
C₈₉×#1880	2
C₈₉×#1878	2
C₈₉×#1865	2
#25149	89

Subgroups — C89×#25149 #36402997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25149 #36402997