Subgroups — C₈₉×#22737 #36400585

Order 22784.

712 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#446×C₈₉	C₂	1	2	yes	maximal
2	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1940	C₂	1	2	yes	maximal
4	C₈₉×#1940	C₂	1	2	yes	maximal
5	C₈₉×#1939	C₂	1	2	yes	maximal
6	C₈₉×#1832	C₂	1	2	yes	maximal
7	C₈₉×#1831	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1768	C₂	1	2	yes	maximal
9	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	#446×C₈₉	—	2	8	no	—
12	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
18	C₂×#97×C₈₉	C₂²	1	2	yes	—
19	C₂×#97×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
21	#391×C₈₉	C₄	1	1	yes	characteristic
22	#391×C₈₉	C₄	1	1	yes	characteristic
23	#389×C₈₉	C₄	1	1	yes	characteristic
24	#389×C₈₉	C₄	1	1	yes	characteristic
25	#387×C₈₉	C₄	1	2	yes	—
26	#387×C₈₉	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	#376×C₈₉	C₂²	1	2	yes	—
30	C₄³×C₈₉	C₂²	1	1	yes	characteristic
31	#336×C₈₉	C₂²	1	2	yes	—
32	#336×C₈₉	C₂²	1	1	yes	characteristic
33	#336×C₈₉	C₂²	1	1	yes	characteristic
34	#336×C₈₉	C₂²	1	1	yes	characteristic
35	#336×C₈₉	C₂²	1	2	yes	—
36	#336×C₈₉	C₂²	1	2	yes	—
37	#336×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
43	C₄×Q₈×C₈₉	D₄	1	4	yes	—
44	C₄×Q₈×C₈₉	Q₈	1	4	yes	—
45	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
58	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
60	C₄⋊C₈×C₈₉	—	2	4	no	—
61	C₄⋊C₈×C₈₉	—	2	4	no	—
62	C₄⋊C₈×C₈₉	—	2	4	no	—
63	C₄⋊C₈×C₈₉	—	2	4	no	—
64	C₄⋊C₈×C₈₉	—	2	4	no	—
65	C₄⋊C₈×C₈₉	—	2	4	no	—
66	#97×C₈₉	—	2	4	no	—
67	#97×C₈₉	—	2	4	no	—
68	C₄×C₈×C₈₉	—	2	4	no	—
69	#95×C₈₉	C₂×C₄	1	2	yes	—
70	#95×C₈₉	C₂×C₄	1	2	yes	—
71	#95×C₈₉	C₂×C₄	1	2	yes	—
72	#95×C₈₉	C₂×C₄	1	2	yes	—
73	#95×C₈₉	C₂×C₄	1	2	yes	—
74	#95×C₈₉	C₂×C₄	1	2	yes	—
75	#95×C₈₉	C₂×C₄	1	2	yes	—
76	C₂×Q₈×C₈₉	—	4	1	no	—
77	C₂×Q₈×C₈₉	—	4	1	no	—
78	C₂×Q₈×C₈₉	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₈₉	—	2	2	no	—
91	C₂×C₈×C₈₉	—	2	2	no	—
92	C₂×C₈×C₈₉	—	2	2	no	—
93	C₂×C₈×C₈₉	—	2	2	no	—
94	C₂×C₈×C₈₉	—	2	2	no	—
95	C₂×C₈×C₈₉	—	2	2	no	—
96	C₂×C₈×C₈₉	—	2	2	no	—
97	C₂×C₈×C₈₉	—	2	2	no	—
98	C₂×C₈×C₈₉	—	2	2	no	—
99	C₂×C₈×C₈₉	—	2	2	no	—
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	#41	1	4	yes	—
102	C₄⋊C₄×C₈₉	—	2	4	no	—
103	C₄⋊C₄×C₈₉	—	4	1	no	—
104	C₄⋊C₄×C₈₉	—	4	1	no	—
105	C₄⋊C₄×C₈₉	—	4	2	no	—
106	C₄⋊C₄×C₈₉	C₄⋊C₄	1	8	yes	—
107	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
108	C₄²×C₈₉	—	2	2	no	—
109	C₄²×C₈₉	—	2	2	no	—
110	C₄²×C₈₉	—	2	2	no	—
111	C₄²×C₈₉	—	2	2	no	—
112	C₄²×C₈₉	—	2	2	no	—
113	C₄²×C₈₉	—	4	1	no	—
114	C₄²×C₈₉	—	4	1	no	—
115	C₄²×C₈₉	—	4	1	no	—
116	C₄²×C₈₉	C₂×D₄	1	4	yes	—
117	C₄²×C₈₉	C₂×D₄	1	2	yes	—
118	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
119	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
120	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
121	Q₈×C₈₉	—	4	4	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	1	no	—
124	C₂×C₄×C₈₉	—	2	2	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	2	no	—
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₈₉	#131	1	2	yes	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
155	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
156	C₈×C₈₉	—	2	4	no	—
157	C₈×C₈₉	—	4	2	no	—
158	C₈×C₈₉	—	4	2	no	—
159	C₈×C₈₉	—	4	2	no	—
160	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
162	C₂²×C₈₉	#519	1	1	yes	characteristic
163	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
164	C₂²×C₈₉	#568	1	1	yes	characteristic
165	C₂²×C₈₉	#568	1	1	yes	characteristic
166	C₂²×C₈₉	#568	1	1	yes	characteristic
167	C₄×C₈₉	—	2	2	no	—
168	C₄×C₈₉	—	2	4	no	—
169	C₄×C₈₉	—	2	2	no	—
170	C₄×C₈₉	—	2	4	no	—
171	C₄×C₈₉	—	2	2	no	—
172	C₄×C₈₉	—	4	1	no	—
173	C₄×C₈₉	—	4	2	no	—
174	C₄×C₈₉	—	4	2	no	—
175	C₄×C₈₉	—	4	1	no	—
176	C₄×C₈₉	—	4	1	no	—
177	C₄×C₈₉	#548	1	2	yes	—
178	C₄×C₈₉	#557	1	2	yes	—
179	#22737	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₈₉	#2351	1	1	yes	characteristic
181	C₂×C₈₉	#2905	1	1	yes	characteristic
182	C₂×C₈₉	#2906	1	1	yes	characteristic
183	C₂×C₈₉	#2967	1	1	yes	characteristic
184	C₂×C₈₉	#2968	1	1	yes	characteristic
185	C₂×C₈₉	#2985	1	1	yes	characteristic
186	C₂×C₈₉	#2987	1	1	yes	characteristic
187	C₂×#446	C₂×C₈₉	1	2	yes	—
188	#2295	C₂×C₈₉	1	1	yes	characteristic
189	#1940	C₂×C₈₉	1	2	yes	—
190	#1940	C₂×C₈₉	1	2	yes	—
191	#1939	C₂×C₈₉	1	2	yes	—
192	#1832	C₂×C₈₉	1	2	yes	—
193	#1831	C₂×C₈₉	1	1	yes	characteristic
194	#1768	C₂×C₈₉	1	2	yes	—
195	#1767	C₂×C₈₉	1	1	yes	characteristic
196	C₈₉	#22737	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
198	#446	—	2	8	no	—
199	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
205	C₂×#97	C₂²×C₈₉	1	2	yes	—
206	C₂×#97	C₂²×C₈₉	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
208	#391	C₄×C₈₉	1	1	yes	characteristic
209	#391	C₄×C₈₉	1	1	yes	characteristic
210	#389	C₄×C₈₉	1	1	yes	characteristic
211	#389	C₄×C₈₉	1	1	yes	characteristic
212	#387	C₄×C₈₉	1	2	yes	—
213	#387	C₄×C₈₉	1	2	yes	—
214	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
216	#376	C₂²×C₈₉	1	2	yes	—
217	C₄³	C₂²×C₈₉	1	1	yes	characteristic
218	#336	C₂²×C₈₉	1	2	yes	—
219	#336	C₂²×C₈₉	1	1	yes	characteristic
220	#336	C₂²×C₈₉	1	1	yes	characteristic
221	#336	C₂²×C₈₉	1	1	yes	characteristic
222	#336	C₂²×C₈₉	1	2	yes	—
223	#336	C₂²×C₈₉	1	2	yes	—
224	#336	C₂²×C₈₉	1	1	yes	characteristic
225	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
227	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
228	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
229	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
230	C₄×Q₈	D₄×C₈₉	1	4	yes	—
231	C₄×Q₈	Q₈×C₈₉	1	4	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
245	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	#97	—	2	4	no	—
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	C₂×C₄×C₈₉	1	2	yes	—
257	#95	C₂×C₄×C₈₉	1	2	yes	—
258	#95	C₂×C₄×C₈₉	1	2	yes	—
259	#95	C₂×C₄×C₈₉	1	2	yes	—
260	#95	C₂×C₄×C₈₉	1	2	yes	—
261	#95	C₂×C₄×C₈₉	1	2	yes	—
262	#95	C₂×C₄×C₈₉	1	2	yes	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	C₄⋊C₄×C₈₉	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
276	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	#41×C₈₉	1	4	yes	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	C₄⋊C₄×C₈₉	1	8	yes	—
294	C₄⋊C₄	C₄⋊C₄×C₈₉	1	4	yes	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	4	1	no	—
301	C₄²	—	4	1	no	—
302	C₄²	—	4	1	no	—
303	C₄²	C₂×D₄×C₈₉	1	4	yes	—
304	C₄²	C₂×D₄×C₈₉	1	2	yes	—
305	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
306	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
307	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	4	yes	—
335	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
336	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	4	yes	—
337	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	2	yes	—
338	C₂×C₄	#131×C₈₉	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
341	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
342	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
343	C₈	—	2	4	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	C₂²×C₄⋊C₄×C₈₉	1	1	yes	characteristic
348	C₂²	C₄×#41×C₈₉	1	1	yes	characteristic
349	C₂²	#519×C₈₉	1	1	yes	characteristic
350	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
351	C₂²	#568×C₈₉	1	1	yes	characteristic
352	C₂²	#568×C₈₉	1	1	yes	characteristic
353	C₂²	#568×C₈₉	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	#548×C₈₉	1	2	yes	—
365	C₄	#557×C₈₉	1	2	yes	—
366	C₂	C₈₉×#2351	1	1	yes	characteristic
367	C₂	C₈₉×#2905	1	1	yes	characteristic
368	C₂	C₈₉×#2906	1	1	yes	characteristic
369	C₂	C₈₉×#2967	1	1	yes	characteristic
370	C₂	C₈₉×#2968	1	1	yes	characteristic
371	C₂	C₈₉×#2985	1	1	yes	characteristic
372	C₂	C₈₉×#2987	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
179. #22737	C₈₉	direct (N × H)
196. C₈₉	#22737	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×#446×C₈₉	2
C₈₉×#2295	2
C₈₉×#1940	2
C₈₉×#1939	2
C₈₉×#1832	2
C₈₉×#1831	2
C₈₉×#1768	2
C₈₉×#1767	2
#22737	89

Subgroups — C89×#22737 #36400585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22737 #36400585