Subgroups — #2163×D₈₉ #36707494

Order 22784.

686 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#26022055	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022054	C₂	1	2	yes	maximal, complemented
4	#26022053	C₂	1	2	yes	maximal, complemented
5	#26022052	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₁₆×D₈₉	C₂	1	2	yes	maximal, complemented
7	C₂²⋊C₁₆×D₈₉	C₂	1	2	yes	maximal
8	#346×D₈₉	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2163	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₈₉	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₈₉	C₄	1	1	yes	characteristic
13	C₂×C₁₆×D₈₉	C₂²	1	4	yes	—
14	C₂×C₄×#10623494	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
17	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
18	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
19	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
20	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
21	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
22	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
25	C₄⋊#13083549	C₂²	1	2	yes	complemented
26	#19151416	C₂²	1	4	yes	complemented
27	C₂²⋊#13083549	C₂²	1	2	yes	—
28	#19151377	C₂²	1	4	yes	—
29	#19151374	C₂²	1	2	yes	complemented
30	#19151373	C₂²	1	4	yes	complemented
31	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₄⋊C₁₆×C₈₉	C₂²	1	2	yes	complemented
33	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
34	#346×C₈₉	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₈₉	C₈	1	1	yes	characteristic
36	C₂²×C₄×D₈₉	C₈	1	1	yes	characteristic
37	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
39	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×D₈₉	—	2	4	no	—
41	C₂×C₈×D₈₉	—	2	4	no	—
42	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₈₉	C₈	1	1	yes	characteristic
51	C₂×C₄×Dic₈₉	C₈	1	1	yes	characteristic
52	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₈₉	C₈	1	1	yes	characteristic
54	C₄²×D₈₉	C₈	1	1	yes	characteristic
55	C₄²×D₈₉	C₈	1	1	yes	characteristic
56	C₄²×D₈₉	C₈	1	1	yes	characteristic
57	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×#13083549	C₂³	1	4	yes	—
62	C₁₆×D₈₉	—	2	8	no	—
63	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
64	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
65	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
66	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
74	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₆×C₈₉	C₂³	1	4	yes	—
79	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×D₈₉	C₂×C₈	1	1	yes	characteristic
84	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₈₉	—	2	4	no	—
88	C₂×C₄×D₈₉	—	2	4	no	—
89	C₂×C₄×D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	2	2	no	—
91	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
106	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
109	C₈×D₈₉	—	2	2	no	—
110	C₈×D₈₉	—	2	2	no	—
111	C₈×D₈₉	—	2	2	no	—
112	C₈×D₈₉	—	2	2	no	—
113	C₈×D₈₉	—	2	2	no	—
114	C₈×D₈₉	—	2	2	no	—
115	C₈×D₈₉	M₁₆	1	4	yes	—
116	C₈×D₈₉	#41	1	4	yes	—
117	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
118	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
119	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
120	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
121	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
122	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
123	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
124	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
125	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	#13083549	—	2	4	no	—
130	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
140	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
141	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₁₆×C₈₉	—	2	4	no	—
144	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₈₉	—	2	2	no	—
146	C₂²×D₈₉	—	2	2	no	—
147	C₂²×D₈₉	M₃₂	1	4	yes	—
148	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₈₉	—	2	2	no	—
161	C₂×Dic₈₉	—	2	2	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
168	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
169	C₄×D₈₉	—	2	2	no	—
170	C₄×D₈₉	—	2	2	no	—
171	C₄×D₈₉	—	2	2	no	—
172	C₄×D₈₉	—	2	2	no	—
173	C₄×D₈₉	—	2	2	no	—
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	2	1	no	—
176	C₄×D₈₉	—	2	1	no	—
177	C₄×D₈₉	—	2	2	no	—
178	C₄×D₈₉	—	2	2	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	M₃₂	1	4	yes	—
181	C₄×D₈₉	#117	1	2	yes	—
182	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
183	C₈×C₈₉	—	2	1	no	—
184	C₈×C₈₉	—	2	1	no	—
185	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
186	C₈×C₈₉	C₂×#41	1	2	yes	—
187	#10623494	—	2	1	no	—
188	#10623494	—	2	1	no	—
189	#10623494	#117	1	2	yes	—
190	#10623494	C₂×M₁₆	1	2	yes	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	C₂×M₃₂	1	2	yes	—
194	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
195	C₂×D₈₉	—	2	1	no	—
196	C₂×D₈₉	—	2	1	no	—
197	C₂×D₈₉	—	2	8	no	—
198	C₂×D₈₉	#431	1	2	yes	—
199	C₂×D₈₉	C₂×M₃₂	1	2	yes	—
200	C₂×D₈₉	C₂×M₃₂	1	2	yes	—
201	C₂×D₈₉	C₂×M₃₂	1	2	yes	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	C₂×M₃₂	1	2	yes	—
207	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
208	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
209	Dic₈₉	—	2	1	no	—
210	Dic₈₉	—	2	1	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	#431	1	2	yes	—
214	Dic₈₉	C₂×M₃₂	1	2	yes	—
215	C₂×#2163	—	89	1	no	maximal, Sylow
216	C₂×C₈₉	—	2	2	no	—
217	C₂×C₈₉	C₂×#431	1	1	yes	characteristic
218	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
219	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
220	D₈₉	—	2	2	no	—
221	D₈₉	#2163	1	4	yes	direct product factor
222	C₂²×C₄×C₈	—	89	1	no	—
223	#2163	—	89	1	no	—
224	#2163	—	89	2	no	—
225	#2163	—	89	2	no	—
226	#2163	—	89	2	no	—
227	#2163	D₈₉	1	1	yes	characteristic, direct product factor
228	C₂×C₄⋊C₁₆	—	89	2	no	—
229	C₂×C₂²⋊C₁₆	—	89	2	no	—
230	C₂×#346	—	89	2	no	—
231	C₈₉	C₂×#2163	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₈	—	89	1	no	—
233	C₂³×C₈	—	89	1	no	—
234	C₂²×C₄²	—	89	1	no	—
235	C₂²×C₁₆	—	89	4	no	—
236	C₂×C₄×C₈	—	89	1	no	—
237	C₂×C₄×C₈	—	89	1	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	C₂×C₄×C₈	—	89	1	no	—
241	C₂×C₄×C₈	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	89	1	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	C₂×C₄×C₈	—	89	1	no	—
246	C₂×C₄×C₈	—	89	1	no	—
247	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
248	C₄⋊C₁₆	—	89	4	no	—
249	C₄⋊C₁₆	—	89	2	no	—
250	C₄⋊C₁₆	C₂×D₈₉	1	2	yes	complemented
251	C₂²⋊C₁₆	—	89	2	no	—
252	C₂²⋊C₁₆	—	89	4	no	—
253	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
254	#346	—	89	4	no	—
255	#346	—	89	2	no	—
256	#346	C₂×D₈₉	1	2	yes	complemented
257	C₂³×C₄	—	89	1	no	—
258	C₂³×C₄	—	89	1	no	—
259	C₂³×C₄	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	—	89	1	no	—
265	C₂²×C₈	—	89	1	no	—
266	C₂²×C₈	—	89	1	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	89	1	no	—
270	C₂²×C₈	—	178	4	no	—
271	C₂²×C₈	—	178	4	no	—
272	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
274	C₂×C₄²	—	89	1	no	—
275	C₂×C₄²	—	89	1	no	—
276	C₂×C₄²	—	89	1	no	—
277	C₂×C₄²	—	89	1	no	—
278	C₂×C₄²	—	89	1	no	—
279	C₂×C₄²	—	89	1	no	—
280	C₂×C₄²	—	89	1	no	—
281	C₂×C₄²	—	89	1	no	—
282	C₂×C₄²	—	89	1	no	—
283	C₂×C₄²	—	89	1	no	—
284	C₂×C₄²	—	89	1	no	—
285	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
286	C₂×C₁₆	—	89	4	no	—
287	C₂×C₁₆	—	178	8	no	—
288	C₂×C₁₆	C₂²×D₈₉	1	4	yes	—
289	C₄×C₈	—	89	1	no	—
290	C₄×C₈	—	89	1	no	—
291	C₄×C₈	—	89	1	no	—
292	C₄×C₈	—	89	1	no	—
293	C₄×C₈	—	89	1	no	—
294	C₄×C₈	—	89	1	no	—
295	C₄×C₈	—	89	1	no	—
296	C₄×C₈	—	89	1	no	—
297	C₄×C₈	—	89	1	no	—
298	C₄×C₈	—	89	1	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
302	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₂⁴	—	89	1	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	89	1	no	—
311	C₂²×C₄	—	89	1	no	—
312	C₂²×C₄	—	89	1	no	—
313	C₂²×C₄	—	89	1	no	—
314	C₂²×C₄	—	89	1	no	—
315	C₂²×C₄	—	89	1	no	—
316	C₂²×C₄	—	89	1	no	—
317	C₂²×C₄	—	89	1	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	89	1	no	—
320	C₂²×C₄	—	89	1	no	—
321	C₂²×C₄	—	178	2	no	—
322	C₂²×C₄	—	178	2	no	—
323	C₂²×C₄	—	178	4	no	—
324	C₂²×C₄	—	178	4	no	—
325	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
326	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	89	1	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	89	4	no	—
333	C₂×C₈	—	89	4	no	—
334	C₂×C₈	—	89	1	no	—
335	C₂×C₈	—	89	1	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	—	178	2	no	—
340	C₂×C₈	—	178	2	no	—
341	C₂×C₈	—	178	2	no	—
342	C₂×C₈	—	178	2	no	—
343	C₂×C₈	—	178	2	no	—
344	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
348	C₄²	—	89	1	no	—
349	C₄²	—	89	1	no	—
350	C₄²	—	89	1	no	—
351	C₄²	—	89	1	no	—
352	C₄²	—	89	1	no	—
353	C₄²	—	89	1	no	—
354	C₄²	—	89	1	no	—
355	C₄²	—	89	1	no	—
356	C₄²	—	89	1	no	—
357	C₄²	—	89	1	no	—
358	C₄²	—	89	1	no	—
359	C₄²	—	89	1	no	—
360	C₄²	C₈×D₈₉	1	1	yes	characteristic
361	C₄²	C₈×D₈₉	1	1	yes	characteristic
362	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
364	C₁₆	—	2	4	no	—
365	C₁₆	—	178	4	no	—
366	C₂³	—	89	1	no	—
367	C₂³	—	89	4	no	—
368	C₂³	—	89	1	no	—
369	C₂³	—	178	2	no	—
370	C₂³	—	178	2	no	—
371	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	89	1	no	—
377	C₂×C₄	—	89	1	no	—
378	C₂×C₄	—	89	4	no	—
379	C₂×C₄	—	89	2	no	—
380	C₂×C₄	—	89	2	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	89	1	no	—
384	C₂×C₄	—	89	1	no	—
385	C₂×C₄	—	178	2	no	—
386	C₂×C₄	—	178	2	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	—	178	2	no	—
393	C₂×C₄	—	178	2	no	—
394	C₂×C₄	—	178	2	no	—
395	C₂×C₄	—	178	2	no	—
396	C₂×C₄	—	178	2	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
403	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	89	2	no	—
408	C₈	—	89	2	no	—
409	C₈	—	178	1	no	—
410	C₈	—	178	1	no	—
411	C₈	M₁₆×D₈₉	1	2	yes	—
412	C₈	#41×D₈₉	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	89	2	no	—
416	C₂²	—	89	2	no	—
417	C₂²	—	89	2	no	—
418	C₂²	—	89	2	no	—
419	C₂²	—	178	8	no	—
420	C₂²	—	178	1	no	—
421	C₂²	—	178	1	no	—
422	C₂²	M₃₂×D₈₉	1	2	yes	—
423	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	89	2	no	—
429	C₄	—	89	2	no	—
430	C₄	—	178	1	no	—
431	C₄	—	178	1	no	—
432	C₄	—	178	1	no	—
433	C₄	—	178	1	no	—
434	C₄	M₃₂×D₈₉	1	2	yes	—
435	C₄	#117×D₈₉	1	1	yes	characteristic
436	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	89	4	no	—
439	C₂	—	178	2	no	—
440	C₂	#431×D₈₉	1	1	yes	characteristic
441	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic
442	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2163	C₂
prime radical	C₂³×D₈₉	C₂×C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2163	D₈₉
hypocenter	C₈₉	C₂×#2163
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #26022055	C₂	semidirect
3. #26022054	C₂	semidirect
4. #26022053	C₂	semidirect
5. #26022052	C₂	semidirect
6. C₄⋊C₁₆×D₈₉	C₂	semidirect
8. #346×D₈₉	C₂	semidirect
9. C₈₉×#2163	C₂	semidirect
25. C₄⋊#13083549	C₂²	semidirect
26. #19151416	C₂²	semidirect
29. #19151374	C₂²	semidirect
30. #19151373	C₂²	semidirect
32. C₄⋊C₁₆×C₈₉	C₂²	semidirect
34. #346×C₈₉	C₂²	semidirect
221. D₈₉	#2163	direct (N × H)
227. #2163	D₈₉	direct (N × H)
231. C₈₉	C₂×#2163	semidirect
250. C₄⋊C₁₆	C₂×D₈₉	semidirect
256. #346	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₈₉	2
#26022055	2
#26022054	2
#26022053	2
#26022052	2
C₄⋊C₁₆×D₈₉	2
C₂²⋊C₁₆×D₈₉	2
#346×D₈₉	2
C₈₉×#2163	2
C₂×#2163	89

Subgroups — #2163×D89 #36707494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2163×D₈₉ #36707494