Subgroups — C₈₉×#25510 #36403358

Order 22784.

1134 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#466×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2624	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#542×C₈₉	—	2	4	no	—
21	#542×C₈₉	—	2	4	no	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#126×C₈₉	—	2	1	no	—
24	C₂×#124×C₈₉	—	2	1	no	—
25	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₈₉	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	#468×C₈₉	—	2	4	no	—
35	#466×C₈₉	—	2	4	no	—
36	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#107×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×#103×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
46	#399×C₈₉	—	2	1	no	—
47	#397×C₈₉	—	2	1	no	—
48	#394×C₈₉	—	2	1	no	—
49	#394×C₈₉	—	2	1	no	—
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#380×C₈₉	C₂²	1	1	yes	characteristic
55	#340×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	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×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	1	no	—
64	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₈₉	—	2	1	no	—
66	C₂²×D₄×C₈₉	—	2	1	no	—
67	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₈₉	—	2	1	no	—
70	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂×SD₁₆×C₈₉	—	2	2	no	—
72	C₂×SD₁₆×C₈₉	—	2	2	no	—
73	C₂×SD₁₆×C₈₉	—	4	1	no	—
74	C₂×D₈×C₈₉	—	2	2	no	—
75	C₂×D₈×C₈₉	—	2	2	no	—
76	C₂×D₈×C₈₉	—	4	1	no	—
77	C₂×M₁₆×C₈₉	—	2	2	no	—
78	C₂×M₁₆×C₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	—	4	1	no	—
80	C₂²×C₈×C₈₉	—	2	2	no	—
81	C₂²×C₈×C₈₉	—	2	2	no	—
82	C₂²×C₈×C₈₉	—	4	1	no	—
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₈₉	—	2	2	no	—
88	C₄⋊Q₈×C₈₉	—	2	2	no	—
89	#126×C₈₉	—	2	8	no	—
90	#124×C₈₉	—	2	8	no	—
91	#124×C₈₉	—	2	2	no	—
92	#124×C₈₉	—	2	2	no	—
93	#123×C₈₉	—	2	8	no	—
94	C₂²⋊Q₈×C₈₉	—	2	8	no	—
95	C₂²⋊Q₈×C₈₉	—	2	2	no	—
96	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	—
97	#121×C₈₉	—	2	2	no	—
98	#121×C₈₉	—	2	2	no	—
99	#121×C₈₉	—	2	2	no	—
100	#121×C₈₉	D₄	1	4	yes	—
101	C₄×Q₈×C₈₉	—	2	2	no	—
102	C₄×Q₈×C₈₉	—	2	2	no	—
103	C₄×D₄×C₈₉	—	2	2	no	—
104	C₄×D₄×C₈₉	—	2	2	no	—
105	#117×C₈₉	—	2	2	no	—
106	#117×C₈₉	—	2	2	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	—	2	1	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	—	2	1	no	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	#107×C₈₉	—	2	2	no	—
136	#107×C₈₉	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	—	2	2	no	—
139	#103×C₈₉	—	4	1	no	—
140	#102×C₈₉	—	2	2	no	—
141	#102×C₈₉	—	2	2	no	—
142	#102×C₈₉	—	2	2	no	—
143	#102×C₈₉	—	2	2	no	—
144	#102×C₈₉	—	4	1	no	—
145	#95×C₈₉	—	2	1	no	—
146	#95×C₈₉	—	2	1	no	—
147	#95×C₈₉	—	2	1	no	—
148	C₂⁴×C₈₉	—	2	1	no	—
149	C₂⁴×C₈₉	—	2	1	no	—
150	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₈₉	—	2	4	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	—	2	1	no	—
157	C₂×Q₈×C₈₉	—	8	1	no	—
158	C₂×Q₈×C₈₉	—	8	1	no	—
159	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₈₉	—	2	4	no	—
161	C₂×D₄×C₈₉	—	2	1	no	—
162	C₂×D₄×C₈₉	—	2	1	no	—
163	C₂×D₄×C₈₉	—	2	1	no	—
164	C₂×D₄×C₈₉	—	2	1	no	—
165	C₂×D₄×C₈₉	—	2	1	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	—	2	1	no	—
172	C₂×D₄×C₈₉	—	4	2	no	—
173	C₂×D₄×C₈₉	—	8	1	no	—
174	C₂×D₄×C₈₉	—	8	1	no	—
175	C₂×D₄×C₈₉	—	8	1	no	—
176	C₂×D₄×C₈₉	—	8	1	no	—
177	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₈₉	—	2	1	no	—
179	C₂²×C₄×C₈₉	—	2	1	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	4	no	—
186	C₂²×C₄×C₈₉	—	2	1	no	—
187	C₂²×C₄×C₈₉	—	2	1	no	—
188	C₂²×C₄×C₈₉	—	2	1	no	—
189	C₂²×C₄×C₈₉	—	8	1	no	—
190	C₂²×C₄×C₈₉	—	8	1	no	—
191	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
199	SD₁₆×C₈₉	—	4	4	no	—
200	D₈×C₈₉	—	4	4	no	—
201	M₁₆×C₈₉	—	4	4	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	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	—	4	4	no	—
213	C₂×C₈×C₈₉	#41	1	2	yes	—
214	C₂×C₈×C₈₉	#41	1	2	yes	—
215	C₄⋊C₄×C₈₉	—	2	4	no	—
216	C₄⋊C₄×C₈₉	—	2	4	no	—
217	C₄⋊C₄×C₈₉	—	2	4	no	—
218	C₄⋊C₄×C₈₉	—	2	2	no	—
219	C₄⋊C₄×C₈₉	—	2	2	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	—	2	1	no	—
226	C₄⋊C₄×C₈₉	—	2	1	no	—
227	C₄⋊C₄×C₈₉	—	2	1	no	—
228	C₄⋊C₄×C₈₉	—	8	1	no	—
229	C₄⋊C₄×C₈₉	—	8	1	no	—
230	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
232	C₂²⋊C₄×C₈₉	—	2	4	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	4	no	—
236	C₂²⋊C₄×C₈₉	—	2	2	no	—
237	C₂²⋊C₄×C₈₉	—	2	2	no	—
238	C₂²⋊C₄×C₈₉	—	2	4	no	—
239	C₂²⋊C₄×C₈₉	—	4	2	no	—
240	C₂²⋊C₄×C₈₉	—	8	1	no	—
241	C₂²⋊C₄×C₈₉	—	8	1	no	—
242	C₂²⋊C₄×C₈₉	—	8	1	no	—
243	C₂²⋊C₄×C₈₉	—	8	1	no	—
244	C₂²⋊C₄×C₈₉	—	8	1	no	—
245	C₄²×C₈₉	—	2	4	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	C₂³×C₈₉	—	2	1	no	—
251	C₂³×C₈₉	—	2	1	no	—
252	C₂³×C₈₉	—	2	1	no	—
253	C₂³×C₈₉	—	2	1	no	—
254	C₂³×C₈₉	—	2	1	no	—
255	C₂³×C₈₉	—	2	1	no	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	4	1	no	—
258	C₂³×C₈₉	—	4	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	—	4	1	no	—
267	C₂³×C₈₉	—	4	1	no	—
268	C₂³×C₈₉	—	4	1	no	—
269	C₂³×C₈₉	—	4	1	no	—
270	C₂³×C₈₉	#120	1	2	yes	—
271	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₈₉	—	2	2	no	—
273	Q₈×C₈₉	—	2	2	no	—
274	Q₈×C₈₉	—	4	1	no	—
275	Q₈×C₈₉	—	4	1	no	—
276	Q₈×C₈₉	—	8	4	no	—
277	D₄×C₈₉	—	2	2	no	—
278	D₄×C₈₉	—	2	2	no	—
279	D₄×C₈₉	—	4	1	no	—
280	D₄×C₈₉	—	4	1	no	—
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	D₄×C₈₉	—	8	4	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	1	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	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	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	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	—	8	4	no	—
324	C₂×C₄×C₈₉	#120	1	2	yes	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
331	C₈×C₈₉	—	2	2	no	—
332	C₈×C₈₉	—	2	2	no	—
333	C₈×C₈₉	—	4	1	no	—
334	C₈×C₈₉	—	4	1	no	—
335	C₂²×C₈₉	—	2	2	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	2	2	no	—
338	C₂²×C₈₉	—	4	1	no	—
339	C₂²×C₈₉	—	4	1	no	—
340	C₂²×C₈₉	—	4	1	no	—
341	C₂²×C₈₉	—	4	1	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	4	2	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	—	8	1	no	—
352	C₂²×C₈₉	—	8	1	no	—
353	C₂²×C₈₉	—	8	1	no	—
354	C₂²×C₈₉	—	8	1	no	—
355	C₂²×C₈₉	—	8	1	no	—
356	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
357	C₂²×C₈₉	#532	1	1	yes	characteristic
358	C₂²×C₈₉	#537	1	1	yes	characteristic
359	C₂²×C₈₉	#576	1	1	yes	characteristic
360	C₂²×C₈₉	#576	1	1	yes	characteristic
361	C₂²×C₈₉	#577	1	1	yes	characteristic
362	C₂²×C₈₉	#578	1	1	yes	characteristic
363	C₄×C₈₉	—	2	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	—	4	1	no	—
366	C₄×C₈₉	—	4	1	no	—
367	C₄×C₈₉	—	4	2	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	1	no	—
370	C₄×C₈₉	—	4	1	no	—
371	C₄×C₈₉	—	8	1	no	—
372	C₄×C₈₉	—	8	1	no	—
373	C₄×C₈₉	—	8	1	no	—
374	C₄×C₈₉	#546	1	1	yes	characteristic
375	C₄×C₈₉	#546	1	1	yes	characteristic
376	C₄×C₈₉	#547	1	1	yes	characteristic
377	C₄×C₈₉	#547	1	1	yes	characteristic
378	#25510	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₂×C₈₉	—	4	2	no	—
380	C₂×C₈₉	—	8	2	no	—
381	C₂×C₈₉	—	16	1	no	—
382	C₂×C₈₉	#2430	1	1	yes	characteristic
383	C₂×C₈₉	#3008	1	1	yes	characteristic
384	C₂×C₈₉	#3013	1	1	yes	characteristic
385	C₂×C₈₉	#3175	1	1	yes	characteristic
386	C₂×C₈₉	#3179	1	1	yes	characteristic
387	C₂×C₈₉	#3257	1	1	yes	characteristic
388	C₂×C₈₉	#3262	1	1	yes	characteristic
389	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₂×#466	C₂×C₈₉	1	1	yes	characteristic
392	#2624	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#2057	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2042	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2023	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#1895	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#1892	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#1879	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#1863	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#1862	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#1729	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₈₉	#25510	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
406	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
407	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
408	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
409	#542	—	2	4	no	—
410	#542	—	2	4	no	—
411	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×#126	—	2	1	no	—
413	C₂×#124	—	2	1	no	—
414	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×#123	—	2	1	no	—
416	C₂×C₂²⋊Q₈	—	2	1	no	—
417	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
423	#468	—	2	4	no	—
424	#466	—	2	4	no	—
425	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
435	#399	—	2	1	no	—
436	#397	—	2	1	no	—
437	#394	—	2	1	no	—
438	#394	—	2	1	no	—
439	#390	C₂²×C₈₉	1	1	yes	characteristic
440	#390	C₂²×C₈₉	1	1	yes	characteristic
441	#389	C₂²×C₈₉	1	1	yes	characteristic
442	#389	C₂²×C₈₉	1	1	yes	characteristic
443	#380	C₂²×C₈₉	1	1	yes	characteristic
444	#340	C₂²×C₈₉	1	1	yes	characteristic
445	#340	C₂²×C₈₉	1	1	yes	characteristic
446	#340	C₂²×C₈₉	1	1	yes	characteristic
447	#340	C₂²×C₈₉	1	1	yes	characteristic
448	#336	C₂²×C₈₉	1	1	yes	characteristic
449	#336	C₂²×C₈₉	1	1	yes	characteristic
450	#336	C₂²×C₈₉	1	1	yes	characteristic
451	#336	C₂²×C₈₉	1	1	yes	characteristic
452	C₂²×Q₈	—	2	1	no	—
453	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
460	C₂×SD₁₆	—	2	2	no	—
461	C₂×SD₁₆	—	2	2	no	—
462	C₂×SD₁₆	—	4	1	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	2	no	—
465	C₂×D₈	—	4	1	no	—
466	C₂×M₁₆	—	2	2	no	—
467	C₂×M₁₆	—	2	2	no	—
468	C₂×M₁₆	—	4	1	no	—
469	C₂²×C₈	—	2	2	no	—
470	C₂²×C₈	—	2	2	no	—
471	C₂²×C₈	—	4	1	no	—
472	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	#126	—	2	8	no	—
479	#124	—	2	8	no	—
480	#124	—	2	2	no	—
481	#124	—	2	2	no	—
482	#123	—	2	8	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	D₄×C₈₉	1	4	yes	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	#117	—	2	2	no	—
495	#117	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
524	#107	—	2	2	no	—
525	#107	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	2	2	no	—
528	#103	—	4	1	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	4	1	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	—	2	1	no	—
539	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
540	C₂×Q₈	—	2	4	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	—	8	1	no	—
547	C₂×Q₈	—	8	1	no	—
548	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	8	1	no	—
563	C₂×D₄	—	8	1	no	—
564	C₂×D₄	—	8	1	no	—
565	C₂×D₄	—	8	1	no	—
566	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	8	1	no	—
579	C₂²×C₄	—	8	1	no	—
580	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
586	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
588	SD₁₆	—	4	4	no	—
589	D₈	—	4	4	no	—
590	M₁₆	—	4	4	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	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	—	4	4	no	—
602	C₂×C₈	#41×C₈₉	1	2	yes	—
603	C₂×C₈	#41×C₈₉	1	2	yes	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	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	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	8	1	no	—
618	C₄⋊C₄	—	8	1	no	—
619	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	8	1	no	—
630	C₂²⋊C₄	—	8	1	no	—
631	C₂²⋊C₄	—	8	1	no	—
632	C₂²⋊C₄	—	8	1	no	—
633	C₂²⋊C₄	—	8	1	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	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	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	#120×C₈₉	1	2	yes	—
660	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	8	4	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	8	4	no	—
675	D₄	—	8	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	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	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	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	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	#120×C₈₉	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
716	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
717	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
718	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
719	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	2	no	—
722	C₈	—	4	1	no	—
723	C₈	—	4	1	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
746	C₂²	#532×C₈₉	1	1	yes	characteristic
747	C₂²	#537×C₈₉	1	1	yes	characteristic
748	C₂²	#576×C₈₉	1	1	yes	characteristic
749	C₂²	#576×C₈₉	1	1	yes	characteristic
750	C₂²	#577×C₈₉	1	1	yes	characteristic
751	C₂²	#578×C₈₉	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	8	1	no	—
761	C₄	—	8	1	no	—
762	C₄	—	8	1	no	—
763	C₄	#546×C₈₉	1	1	yes	characteristic
764	C₄	#546×C₈₉	1	1	yes	characteristic
765	C₄	#547×C₈₉	1	1	yes	characteristic
766	C₄	#547×C₈₉	1	1	yes	characteristic
767	C₂	—	4	2	no	—
768	C₂	—	8	2	no	—
769	C₂	—	16	1	no	—
770	C₂	C₈₉×#2430	1	1	yes	characteristic
771	C₂	C₈₉×#3008	1	1	yes	characteristic
772	C₂	C₈₉×#3013	1	1	yes	characteristic
773	C₂	C₈₉×#3175	1	1	yes	characteristic
774	C₂	C₈₉×#3179	1	1	yes	characteristic
775	C₂	C₈₉×#3257	1	1	yes	characteristic
776	C₂	C₈₉×#3262	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#466×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#542×C₈₉	C₂	semidirect
2. C₂×#468×C₈₉	C₂	semidirect
4. C₈₉×#2624	C₂	semidirect
5. C₈₉×#2057	C₂	semidirect
6. C₈₉×#2042	C₂	semidirect
7. C₈₉×#2023	C₂	semidirect
8. C₈₉×#2012	C₂	semidirect
9. C₈₉×#1895	C₂	semidirect
10. C₈₉×#1892	C₂	semidirect
11. C₈₉×#1880	C₂	semidirect
12. C₈₉×#1879	C₂	semidirect
13. C₈₉×#1863	C₂	semidirect
14. C₈₉×#1862	C₂	semidirect
15. C₈₉×#1729	C₂	semidirect
378. #25510	C₈₉	direct (N × H)
389. C₂×#542	C₂×C₈₉	semidirect
390. C₂×#468	C₂×C₈₉	semidirect
392. #2624	C₂×C₈₉	semidirect
393. #2057	C₂×C₈₉	semidirect
394. #2042	C₂×C₈₉	semidirect
395. #2023	C₂×C₈₉	semidirect
396. #2012	C₂×C₈₉	semidirect
397. #1895	C₂×C₈₉	semidirect
398. #1892	C₂×C₈₉	semidirect
399. #1880	C₂×C₈₉	semidirect
400. #1879	C₂×C₈₉	semidirect
401. #1863	C₂×C₈₉	semidirect
402. #1862	C₂×C₈₉	semidirect
403. #1729	C₂×C₈₉	semidirect
404. C₈₉	#25510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₂×#468×C₈₉	2
C₂×#466×C₈₉	2
C₈₉×#2624	2
C₈₉×#2057	2
C₈₉×#2042	2
C₈₉×#2023	2
C₈₉×#2012	2
C₈₉×#1895	2
C₈₉×#1892	2
C₈₉×#1880	2
C₈₉×#1879	2
C₈₉×#1863	2
C₈₉×#1862	2
C₈₉×#1729	2
#25510	89

Subgroups — C89×#25510 #36403358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25510 #36403358