Subgroups — C₈₉×#25078 #36402926

Order 22784.

1166 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#465×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2361	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1850	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	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×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×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	—	2	1	no	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	#465×C₈₉	—	2	4	no	—
29	#461×C₈₉	—	2	4	no	—
30	#448×C₈₉	—	2	4	no	—
31	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₈₉	—	2	4	no	—
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×#103×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	#395×C₈₉	—	2	1	no	—
47	#395×C₈₉	—	2	1	no	—
48	#391×C₈₉	C₂²	1	1	yes	characteristic
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#389×C₈₉	C₂²	1	1	yes	characteristic
52	#388×C₈₉	—	2	1	no	—
53	#386×C₈₉	—	2	1	no	—
54	#385×C₈₉	—	2	1	no	—
55	#385×C₈₉	—	2	1	no	—
56	#385×C₈₉	—	2	1	no	—
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
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	1	no	—
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	—	2	2	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	—	2	1	no	—
77	C₂³×C₄×C₈₉	—	2	1	no	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	—	2	2	no	—
80	C₂×SD₁₆×C₈₉	—	2	2	no	—
81	C₂×SD₁₆×C₈₉	—	2	2	no	—
82	C₂×SD₁₆×C₈₉	—	2	2	no	—
83	C₂×SD₁₆×C₈₉	—	2	2	no	—
84	C₂×SD₁₆×C₈₉	—	2	2	no	—
85	C₂×SD₁₆×C₈₉	—	4	1	no	—
86	C₂×SD₁₆×C₈₉	—	4	1	no	—
87	C₂×SD₁₆×C₈₉	—	4	1	no	—
88	C₂²×C₈×C₈₉	—	2	2	no	—
89	C₂²×C₈×C₈₉	—	2	2	no	—
90	C₂²×C₈×C₈₉	—	4	1	no	—
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₈₉	—	2	2	no	—
96	C₄⋊Q₈×C₈₉	—	2	2	no	—
97	C₄⋊Q₈×C₈₉	—	4	1	no	—
98	C₄⋊Q₈×C₈₉	—	4	1	no	—
99	C₂²⋊Q₈×C₈₉	—	2	2	no	—
100	C₂²⋊Q₈×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	2	no	—
102	#121×C₈₉	D₄	1	4	yes	—
103	C₄×D₄×C₈₉	—	2	2	no	—
104	C₄×D₄×C₈₉	—	4	1	no	—
105	C₄×D₄×C₈₉	—	4	4	no	—
106	C₂×C₄⋊C₄×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	—	2	1	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
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	D₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	—	2	1	no	—
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	#106×C₈₉	—	2	2	no	—
130	C₄⋊C₈×C₈₉	—	2	2	no	—
131	C₄⋊C₈×C₈₉	—	4	1	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	—	2	2	no	—
137	#103×C₈₉	—	2	2	no	—
138	#103×C₈₉	—	2	2	no	—
139	#103×C₈₉	—	4	1	no	—
140	#103×C₈₉	D₄	1	4	yes	complemented
141	#102×C₈₉	—	2	2	no	—
142	C₂²⋊C₈×C₈₉	—	2	2	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	—	2	1	no	—
149	#95×C₈₉	D₄	1	1	yes	characteristic
150	#95×C₈₉	D₄	1	1	yes	characteristic
151	C₂⁴×C₈₉	—	2	1	no	—
152	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	—	2	8	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	—	2	1	no	—
167	C₂×Q₈×C₈₉	—	2	1	no	—
168	C₂×Q₈×C₈₉	—	2	1	no	—
169	C₂×Q₈×C₈₉	—	2	1	no	—
170	C₂×Q₈×C₈₉	—	4	2	no	—
171	C₂×Q₈×C₈₉	—	4	2	no	—
172	C₂×Q₈×C₈₉	—	4	4	no	—
173	C₂×Q₈×C₈₉	—	4	4	no	—
174	C₂×Q₈×C₈₉	—	4	4	no	—
175	C₂×Q₈×C₈₉	—	4	2	no	—
176	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₈₉	#41	1	2	yes	—
178	C₂×D₄×C₈₉	—	2	4	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	—	2	1	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	—	4	2	no	—
186	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₈₉	—	2	1	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	—	4	2	no	—
199	C₂²×C₄×C₈₉	—	4	2	no	—
200	C₂²×C₄×C₈₉	—	4	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	2	no	—
203	C₂²×C₄×C₈₉	—	4	2	no	—
204	C₂²×C₄×C₈₉	—	4	2	no	—
205	C₂²×C₄×C₈₉	—	8	1	no	—
206	C₂²×C₄×C₈₉	—	8	1	no	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	#41	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	SD₁₆×C₈₉	—	4	4	no	—
216	SD₁₆×C₈₉	—	4	4	no	—
217	SD₁₆×C₈₉	—	4	4	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	—	2	1	no	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	1	no	—
225	C₂×C₈×C₈₉	—	2	1	no	—
226	C₂×C₈×C₈₉	—	2	1	no	—
227	C₂×C₈×C₈₉	—	2	1	no	—
228	C₂×C₈×C₈₉	—	2	1	no	—
229	C₂×C₈×C₈₉	—	4	4	no	—
230	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₈₉	—	2	1	no	—
232	C₄⋊C₄×C₈₉	—	2	1	no	—
233	C₄⋊C₄×C₈₉	—	2	1	no	—
234	C₄⋊C₄×C₈₉	—	2	1	no	—
235	C₄⋊C₄×C₈₉	—	2	1	no	—
236	C₄⋊C₄×C₈₉	—	2	1	no	—
237	C₄⋊C₄×C₈₉	—	4	2	no	—
238	C₄⋊C₄×C₈₉	—	4	2	no	—
239	C₄⋊C₄×C₈₉	—	4	2	no	—
240	C₄⋊C₄×C₈₉	—	4	2	no	—
241	C₄⋊C₄×C₈₉	—	4	2	no	—
242	C₄⋊C₄×C₈₉	—	4	2	no	—
243	C₄⋊C₄×C₈₉	—	4	2	no	—
244	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₈₉	—	2	2	no	—
247	C₂²⋊C₄×C₈₉	—	2	4	no	—
248	C₂²⋊C₄×C₈₉	—	4	2	no	—
249	C₂²⋊C₄×C₈₉	—	4	2	no	—
250	C₂²⋊C₄×C₈₉	—	4	2	no	—
251	C₂²⋊C₄×C₈₉	—	8	1	no	—
252	C₂²⋊C₄×C₈₉	SD₁₆	1	4	yes	complemented
253	C₄²×C₈₉	—	2	1	no	—
254	C₄²×C₈₉	—	2	1	no	—
255	C₄²×C₈₉	—	2	1	no	—
256	C₄²×C₈₉	—	2	1	no	—
257	C₄²×C₈₉	—	4	2	no	—
258	C₂³×C₈₉	—	2	1	no	—
259	C₂³×C₈₉	—	2	1	no	—
260	C₂³×C₈₉	—	2	1	no	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	2	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	#121	1	2	yes	—
270	C₂³×C₈₉	C₂×SD₁₆	1	2	yes	—
271	C₂³×C₈₉	#137	1	2	yes	—
272	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₈₉	—	2	2	no	—
274	Q₈×C₈₉	—	2	2	no	—
275	Q₈×C₈₉	—	2	2	no	—
276	Q₈×C₈₉	—	2	2	no	—
277	Q₈×C₈₉	—	4	8	no	—
278	Q₈×C₈₉	—	4	1	no	—
279	Q₈×C₈₉	—	4	1	no	—
280	Q₈×C₈₉	—	4	1	no	—
281	Q₈×C₈₉	—	4	1	no	—
282	Q₈×C₈₉	—	4	1	no	—
283	Q₈×C₈₉	—	4	1	no	—
284	Q₈×C₈₉	—	4	1	no	—
285	Q₈×C₈₉	—	4	1	no	—
286	D₄×C₈₉	—	2	2	no	—
287	D₄×C₈₉	—	2	2	no	—
288	D₄×C₈₉	—	4	8	no	—
289	D₄×C₈₉	—	4	1	no	—
290	D₄×C₈₉	—	4	1	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	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	1	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	4	8	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	—	4	1	no	—
327	C₂×C₄×C₈₉	—	4	1	no	—
328	C₂×C₄×C₈₉	—	4	1	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	4	no	—
331	C₂×C₄×C₈₉	#121	1	2	yes	—
332	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
333	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₈₉	—	2	2	no	—
341	C₈×C₈₉	—	4	1	no	—
342	C₈×C₈₉	—	4	1	no	—
343	C₈×C₈₉	—	4	1	no	—
344	C₂²×C₈₉	—	2	2	no	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	8	1	no	—
354	C₂²×C₈₉	—	8	1	no	—
355	C₂²×C₈₉	—	8	1	no	—
356	C₂²×C₈₉	—	8	1	no	—
357	C₂²×C₈₉	#461	1	4	yes	complemented
358	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
359	C₂²×C₈₉	D₄²	1	1	yes	characteristic
360	C₂²×C₈₉	#546	1	1	yes	characteristic
361	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
362	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
363	C₂²×C₈₉	#577	1	1	yes	characteristic
364	C₂²×C₈₉	#578	1	1	yes	characteristic
365	C₄×C₈₉	—	2	2	no	—
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	2	2	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	1	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	1	no	—
374	C₄×C₈₉	—	8	1	no	—
375	C₄×C₈₉	—	8	1	no	—
376	C₄×C₈₉	—	8	1	no	—
377	C₄×C₈₉	#525	1	1	yes	characteristic
378	C₄×C₈₉	#538	1	1	yes	characteristic
379	C₄×C₈₉	D₄²	1	1	yes	characteristic
380	C₄×C₈₉	#546	1	1	yes	characteristic
381	#25078	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂×C₈₉	—	2	4	no	—
383	C₂×C₈₉	—	8	2	no	—
384	C₂×C₈₉	#2424	1	1	yes	characteristic
385	C₂×C₈₉	C₂×#461	1	1	yes	characteristic
386	C₂×C₈₉	#3046	1	1	yes	characteristic
387	C₂×C₈₉	#3270	1	1	yes	characteristic
388	C₂×C₈₉	D₄×SD₁₆	1	1	yes	characteristic
389	C₂×C₈₉	#3298	1	1	yes	characteristic
390	C₂×C₈₉	#3320	1	1	yes	characteristic
391	C₂×#465	C₂×C₈₉	1	1	yes	characteristic
392	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₂×#448	C₂×C₈₉	1	1	yes	characteristic
394	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2434	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2361	C₂×C₈₉	1	1	yes	characteristic
397	#2066	C₂×C₈₉	1	1	yes	characteristic, complemented
398	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
399	#2043	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2013	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#1981	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#1927	C₂×C₈₉	1	1	yes	characteristic, complemented
403	#1877	C₂×C₈₉	1	1	yes	characteristic, complemented
404	#1872	C₂×C₈₉	1	1	yes	characteristic, complemented
405	#1850	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₈₉	#25078	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
409	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
411	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×C₄×D₄	—	2	1	no	—
417	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
419	#465	—	2	4	no	—
420	#461	—	2	4	no	—
421	#448	—	2	4	no	—
422	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#103	—	2	4	no	—
426	C₂×#103	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×#103	C₂²×C₈₉	1	1	yes	characteristic
431	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
432	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
437	#395	—	2	1	no	—
438	#395	—	2	1	no	—
439	#391	C₂²×C₈₉	1	1	yes	characteristic
440	#391	C₂²×C₈₉	1	1	yes	characteristic
441	#390	C₂²×C₈₉	1	1	yes	characteristic
442	#389	C₂²×C₈₉	1	1	yes	characteristic
443	#388	—	2	1	no	—
444	#386	—	2	1	no	—
445	#385	—	2	1	no	—
446	#385	—	2	1	no	—
447	#385	—	2	1	no	—
448	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
450	#340	C₂²×C₈₉	1	1	yes	characteristic
451	#340	C₂²×C₈₉	1	1	yes	characteristic
452	#336	C₂²×C₈₉	1	1	yes	characteristic
453	#336	C₂²×C₈₉	1	1	yes	characteristic
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	—	2	2	no	—
456	C₂²×Q₈	—	2	2	no	—
457	C₂²×Q₈	—	2	2	no	—
458	C₂²×Q₈	—	2	2	no	—
459	C₂²×Q₈	—	4	1	no	—
460	C₂²×Q₈	—	4	1	no	—
461	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	2	2	no	—
472	C₂×SD₁₆	—	2	2	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	4	1	no	—
477	C₂×SD₁₆	—	4	1	no	—
478	C₂×SD₁₆	—	4	1	no	—
479	C₂²×C₈	—	2	2	no	—
480	C₂²×C₈	—	2	2	no	—
481	C₂²×C₈	—	4	1	no	—
482	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	4	1	no	—
489	C₄⋊Q₈	—	4	1	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	D₄×C₈₉	1	4	yes	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	4	1	no	—
496	C₄×D₄	—	4	4	no	—
497	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	4	1	no	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	D₄×C₈₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
520	#106	—	2	2	no	—
521	C₄⋊C₈	—	2	2	no	—
522	C₄⋊C₈	—	4	1	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#103	—	4	1	no	—
531	#103	D₄×C₈₉	1	4	yes	complemented
532	#102	—	2	2	no	—
533	C₂²⋊C₈	—	2	2	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	D₄×C₈₉	1	1	yes	characteristic
541	#95	D₄×C₈₉	1	1	yes	characteristic
542	C₂⁴	—	2	1	no	—
543	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	8	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	2	no	—
563	C₂×Q₈	—	4	4	no	—
564	C₂×Q₈	—	4	4	no	—
565	C₂×Q₈	—	4	4	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
568	C₂×Q₈	#41×C₈₉	1	2	yes	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
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	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	8	1	no	—
597	C₂²×C₄	—	8	1	no	—
598	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
602	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
604	C₂²×C₄	#41×C₈₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
606	SD₁₆	—	4	4	no	—
607	SD₁₆	—	4	4	no	—
608	SD₁₆	—	4	4	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	4	4	no	—
621	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	8	1	no	—
643	C₂²⋊C₄	SD₁₆×C₈₉	1	4	yes	complemented
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	4	2	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	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	—	4	1	no	—
660	C₂³	#121×C₈₉	1	2	yes	—
661	C₂³	C₂×SD₁₆×C₈₉	1	2	yes	—
662	C₂³	#137×C₈₉	1	2	yes	—
663	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
664	Q₈	—	2	2	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	8	no	—
669	Q₈	—	4	1	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	4	1	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	8	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	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	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	8	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	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	#121×C₈₉	1	2	yes	—
723	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
724	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
727	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
728	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
729	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
730	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₈	—	4	1	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	#461×C₈₉	1	4	yes	complemented
749	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
750	C₂²	D₄²×C₈₉	1	1	yes	characteristic
751	C₂²	#546×C₈₉	1	1	yes	characteristic
752	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
753	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
754	C₂²	#577×C₈₉	1	1	yes	characteristic
755	C₂²	#578×C₈₉	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	8	1	no	—
766	C₄	—	8	1	no	—
767	C₄	—	8	1	no	—
768	C₄	#525×C₈₉	1	1	yes	characteristic
769	C₄	#538×C₈₉	1	1	yes	characteristic
770	C₄	D₄²×C₈₉	1	1	yes	characteristic
771	C₄	#546×C₈₉	1	1	yes	characteristic
772	C₂	—	2	4	no	—
773	C₂	—	8	2	no	—
774	C₂	C₈₉×#2424	1	1	yes	characteristic
775	C₂	C₂×#461×C₈₉	1	1	yes	characteristic
776	C₂	C₈₉×#3046	1	1	yes	characteristic
777	C₂	C₈₉×#3270	1	1	yes	characteristic
778	C₂	D₄×SD₁₆×C₈₉	1	1	yes	characteristic
779	C₂	C₈₉×#3298	1	1	yes	characteristic
780	C₂	C₈₉×#3320	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
2. C₂×#461×C₈₉	C₂	semidirect
4. C₂²×#103×C₈₉	C₂	semidirect
5. C₈₉×#2434	C₂	semidirect
7. C₈₉×#2066	C₂	semidirect
8. C₈₉×#2055	C₂	semidirect
9. C₈₉×#2043	C₂	semidirect
10. C₈₉×#2013	C₂	semidirect
11. C₈₉×#1981	C₂	semidirect
12. C₈₉×#1927	C₂	semidirect
13. C₈₉×#1877	C₂	semidirect
14. C₈₉×#1872	C₂	semidirect
15. C₈₉×#1850	C₂	semidirect
140. #103×C₈₉	D₄	semidirect
252. C₂²⋊C₄×C₈₉	SD₁₆	semidirect
357. C₂²×C₈₉	#461	semidirect
381. #25078	C₈₉	direct (N × H)
392. C₂×#461	C₂×C₈₉	semidirect
394. C₂²×#103	C₂×C₈₉	semidirect
395. #2434	C₂×C₈₉	semidirect
397. #2066	C₂×C₈₉	semidirect
398. #2055	C₂×C₈₉	semidirect
399. #2043	C₂×C₈₉	semidirect
400. #2013	C₂×C₈₉	semidirect
401. #1981	C₂×C₈₉	semidirect
402. #1927	C₂×C₈₉	semidirect
403. #1877	C₂×C₈₉	semidirect
404. #1872	C₂×C₈₉	semidirect
405. #1850	C₂×C₈₉	semidirect
406. C₈₉	#25078	direct (N × H)
531. #103	D₄×C₈₉	semidirect
643. C₂²⋊C₄	SD₁₆×C₈₉	semidirect
748. C₂²	#461×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#465×C₈₉	2
C₂×#461×C₈₉	2
C₂×#448×C₈₉	2
C₂²×#103×C₈₉	2
C₈₉×#2434	2
C₈₉×#2361	2
C₈₉×#2066	2
C₈₉×#2055	2
C₈₉×#2043	2
C₈₉×#2013	2
C₈₉×#1981	2
C₈₉×#1927	2
C₈₉×#1877	2
C₈₉×#1872	2
C₈₉×#1850	2
#25078	89

Subgroups — C89×#25078 #36402926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25078 #36402926