Subgroups — #36551924

Order 22784.

1042 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151555	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151552	C₂	1	1	yes	maximal, characteristic
3	#26022591	C₂	1	1	yes	maximal, characteristic
4	#26020004	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020002	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020002	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020000	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019999	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019997	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019996	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019947	C₂	1	1	yes	maximal, characteristic
12	#26019947	C₂	1	1	yes	maximal, characteristic
13	#26019944	C₂	1	1	yes	maximal, characteristic
14	#336×D₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#13083557	C₂²	1	1	yes	characteristic
17	C₂²×#13083557	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×#15667969	C₂²	1	1	yes	characteristic
21	C₂×#15667969	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
23	#19151555	C₄	1	8	yes	complemented
24	#19151552	C₄	1	8	yes	complemented
25	C₂×#15667923	C₂²	1	1	yes	characteristic
26	C₂×#15667922	C₂²	1	1	yes	characteristic
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151449	C₄	1	2	yes	—
32	#19151449	C₄	1	2	yes	—
33	#19151445	C₄	1	2	yes	—
34	#19151445	C₄	1	2	yes	—
35	#19151444	C₂²	1	1	yes	characteristic
36	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
37	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
38	#19151353	C₂²	1	1	yes	characteristic
39	#19151353	C₂²	1	1	yes	characteristic
40	#19151353	C₂²	1	1	yes	characteristic
41	#19151353	C₂²	1	1	yes	characteristic
42	#19151352	C₂²	1	1	yes	characteristic
43	#19151352	C₂²	1	1	yes	characteristic
44	#19151352	C₂²	1	1	yes	characteristic
45	#19151352	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	#19151352	C₂²	1	1	yes	characteristic
50	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
52	#376×C₈₉	C₂²	1	1	yes	characteristic
53	#336×C₈₉	C₂²	1	1	yes	characteristic
54	#336×C₈₉	C₂²	1	1	yes	characteristic
55	#336×C₈₉	C₂²	1	1	yes	characteristic
56	#336×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
59	C₂×#13083557	—	2	2	no	—
60	C₂×#13083557	—	2	2	no	—
61	C₂×#13083557	—	2	2	no	—
62	C₂×#13083557	—	2	2	no	—
63	C₂×#13083557	C₂×C₄	1	4	yes	—
64	C₂×#13083557	C₂×C₄	1	4	yes	—
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	1	yes	characteristic
67	C₂²×#10623494	C₂³	1	1	yes	characteristic
68	C₂²×#10623494	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₈₉	—	2	2	no	—
70	C₂×C₈×D₈₉	—	2	2	no	—
71	C₂×C₈×D₈₉	—	2	2	no	—
72	C₂×C₈×D₈₉	—	2	2	no	—
73	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
74	C₂×C₈×D₈₉	C₂×C₄	1	4	yes	—
75	#15667969	—	2	2	no	—
76	#15667969	—	2	2	no	—
77	#15667969	C₂×C₄	1	4	yes	—
78	#15667969	C₂×C₄	1	4	yes	—
79	C₂×#13083553	C₂×C₄	1	2	yes	—
80	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
81	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
82	C₂×#13083551	C₂×C₄	1	2	yes	—
83	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
84	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
86	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
87	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
88	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
89	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
93	C₄²×D₈₉	—	2	2	no	—
94	C₄²×D₈₉	—	2	2	no	—
95	#15667923	C₂×C₄	1	4	yes	complemented
96	#15667922	C₂×C₄	1	4	yes	complemented
97	#15667922	C₂×C₄	1	4	yes	complemented
98	C₄×#10623494	C₂×C₄	1	4	yes	complemented
99	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
100	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
101	#15667919	C₂×C₄	1	2	yes	—
102	#15667919	C₂×C₄	1	2	yes	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	#97×C₈₉	C₂×C₄	1	4	yes	complemented
111	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
112	#95×C₈₉	C₂×C₄	1	2	yes	—
113	#95×C₈₉	C₂×C₄	1	2	yes	—
114	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
119	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₈₉	—	2	4	no	—
121	C₂×C₄×D₈₉	—	2	4	no	—
122	C₂×C₄×D₈₉	—	4	2	no	—
123	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
124	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
125	C₂×C₄×D₈₉	#41	1	2	yes	—
126	C₂×C₄×D₈₉	#41	1	2	yes	—
127	C₂×C₄×D₈₉	#41	1	2	yes	—
128	C₂×C₄×D₈₉	#41	1	2	yes	—
129	#13083557	—	2	8	no	—
130	#13083557	—	2	8	no	—
131	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	2	1	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	—	2	1	no	—
139	C₂×#10623494	C₂²×C₄	1	2	yes	—
140	C₂×#10623494	C₂²×C₄	1	2	yes	—
141	C₂×#10623494	C₂²×C₄	1	2	yes	—
142	C₂×#10623494	C₂²×C₄	1	2	yes	—
143	C₈×D₈₉	—	2	8	no	—
144	C₈×D₈₉	—	2	8	no	—
145	#13083553	—	2	4	no	—
146	#13083553	C₄²	1	4	yes	—
147	#13083553	C₄²	1	4	yes	—
148	#13083551	—	2	4	no	—
149	#13083551	C₄²	1	4	yes	—
150	#13083551	C₄²	1	4	yes	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₄×Dic₈₉	—	2	1	no	—
154	C₄×Dic₈₉	—	2	1	no	—
155	C₄×Dic₈₉	—	2	4	no	—
156	C₄×Dic₈₉	—	2	4	no	—
157	C₄×Dic₈₉	—	2	4	no	—
158	C₄×Dic₈₉	—	4	2	no	—
159	C₄×Dic₈₉	—	4	2	no	—
160	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
161	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₈₉	—	2	1	no	—
168	C₂×C₈×C₈₉	—	2	1	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	1	no	—
171	C₂×C₈×C₈₉	—	2	1	no	—
172	C₂×C₈×C₈₉	—	2	1	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	2	1	no	—
175	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
178	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
179	C₄²×C₈₉	—	2	1	no	—
180	C₄²×C₈₉	—	2	1	no	—
181	C₄²×C₈₉	—	2	1	no	—
182	C₄²×C₈₉	—	2	1	no	—
183	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
184	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
185	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
186	C₂²×D₈₉	—	2	2	no	—
187	C₂²×D₈₉	—	2	2	no	—
188	C₂²×D₈₉	C₂×C₄²	1	2	yes	—
189	C₂²×D₈₉	#117	1	2	yes	—
190	C₂²×D₈₉	#117	1	2	yes	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	—	2	2	no	—
199	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₂×Dic₈₉	—	2	2	no	—
208	C₂×Dic₈₉	—	2	2	no	—
209	C₂×Dic₈₉	—	2	2	no	—
210	C₂×Dic₈₉	—	2	2	no	—
211	C₂×Dic₈₉	—	2	2	no	—
212	C₂×Dic₈₉	—	2	2	no	—
213	C₂×Dic₈₉	—	2	2	no	—
214	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
215	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
216	C₂×Dic₈₉	C₂×C₄²	1	2	yes	—
217	C₂×Dic₈₉	#117	1	2	yes	—
218	C₂×Dic₈₉	#117	1	2	yes	—
219	C₂×Dic₈₉	#131	1	4	yes	—
220	C₄×D₈₉	—	4	8	no	—
221	C₄×D₈₉	#117	1	4	yes	—
222	C₄×D₈₉	#117	1	4	yes	—
223	C₄×D₈₉	#117	1	4	yes	—
224	C₄×D₈₉	#117	1	4	yes	—
225	C₈×C₈₉	—	2	2	no	—
226	C₈×C₈₉	—	2	2	no	—
227	C₈×C₈₉	—	2	2	no	—
228	C₈×C₈₉	—	2	2	no	—
229	#10623494	—	2	2	no	—
230	#10623494	—	2	2	no	—
231	#10623494	—	2	2	no	—
232	#10623494	—	2	2	no	—
233	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
234	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
235	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
236	C₂²×C₈₉	C₂×#131	1	2	yes	—
237	C₂²×C₈₉	#568	1	2	yes	—
238	C₂×D₈₉	—	2	2	no	—
239	C₂×D₈₉	—	2	2	no	—
240	C₂×D₈₉	—	2	4	no	—
241	C₂×D₈₉	—	2	4	no	—
242	C₂×D₈₉	#376	1	4	yes	—
243	C₄×C₈₉	—	2	2	no	—
244	C₄×C₈₉	—	2	2	no	—
245	C₄×C₈₉	—	4	2	no	—
246	C₄×C₈₉	—	4	2	no	—
247	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
248	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
249	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
250	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
251	Dic₈₉	—	2	2	no	—
252	Dic₈₉	—	2	2	no	—
253	Dic₈₉	—	2	4	no	—
254	Dic₈₉	—	4	2	no	—
255	Dic₈₉	#376	1	4	yes	—
256	#20368	—	89	1	no	maximal, Sylow
257	C₂×C₈₉	C₂×#376	1	1	yes	characteristic
258	C₂×C₈₉	C₄×#131	1	1	yes	characteristic
259	C₂×C₈₉	#2875	1	1	yes	characteristic
260	C₂×C₈₉	#2924	1	2	yes	—
261	C₂×C₈₉	#2925	1	2	yes	—
262	D₈₉	—	2	4	no	—
263	C₂×#405	—	89	1	no	—
264	C₂×#405	—	89	1	no	—
265	C₄×#117	—	89	1	no	—
266	#1746	—	89	1	no	—
267	#1746	—	89	1	no	—
268	#1746	—	89	1	no	—
269	#1746	D₈₉	1	1	yes	characteristic, complemented
270	#1745	—	89	1	no	—
271	#1745	—	89	1	no	—
272	#1744	—	89	1	no	—
273	#1744	—	89	1	no	—
274	#1729	—	89	1	no	—
275	#1729	—	89	1	no	—
276	#1728	—	89	1	no	—
277	C₂×#336	—	89	1	no	—
278	C₈₉	#20368	1	1	yes	characteristic, complemented, Sylow
279	C₂²×M₁₆	—	89	1	no	—
280	C₂²×M₁₆	—	89	1	no	—
281	C₂³×C₈	—	89	1	no	—
282	C₂³×C₈	—	89	1	no	—
283	C₂×#117	—	89	1	no	—
284	C₂×#117	—	89	1	no	—
285	C₂²×C₄²	—	89	1	no	—
286	#405	—	89	8	no	—
287	#405	—	89	8	no	—
288	C₂×#97	—	89	1	no	—
289	C₂×#97	—	89	1	no	—
290	C₂×#97	—	89	1	no	—
291	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
292	C₂×C₄×C₈	—	89	1	no	—
293	C₂×C₄×C₈	—	89	1	no	—
294	C₂×C₄×C₈	—	89	1	no	—
295	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
296	C₄×C₄⋊C₄	—	89	2	no	—
297	C₄×C₄⋊C₄	—	89	2	no	—
298	C₄×C₂²⋊C₄	—	89	2	no	—
299	C₄×C₂²⋊C₄	—	89	2	no	—
300	#376	—	89	1	no	—
301	#376	C₂×D₈₉	1	1	yes	characteristic
302	C₄³	—	89	1	no	—
303	C₄³	—	89	1	no	—
304	#336	—	89	1	no	—
305	#336	—	89	1	no	—
306	#336	—	89	1	no	—
307	#336	—	89	1	no	—
308	#336	—	89	1	no	—
309	#336	—	89	1	no	—
310	#336	—	89	1	no	—
311	#336	—	89	1	no	—
312	#336	—	89	1	no	—
313	#336	—	89	1	no	—
314	#336	—	89	1	no	—
315	#336	—	89	1	no	—
316	#336	C₂×D₈₉	1	1	yes	characteristic
317	#336	C₂×D₈₉	1	1	yes	characteristic
318	#336	C₂×D₈₉	1	1	yes	characteristic
319	#336	C₂×D₈₉	1	1	yes	characteristic
320	C₂³×C₄	—	89	1	no	—
321	C₂³×C₄	—	89	2	no	—
322	C₂×M₁₆	—	89	4	no	—
323	C₂×M₁₆	—	89	4	no	—
324	C₂×M₁₆	—	178	2	no	—
325	C₂×M₁₆	—	178	2	no	—
326	C₂×M₁₆	—	178	2	no	—
327	C₂×M₁₆	—	178	2	no	—
328	C₂²×C₈	—	89	1	no	—
329	C₂²×C₈	—	89	1	no	—
330	C₂²×C₈	—	89	1	no	—
331	C₂²×C₈	—	89	1	no	—
332	C₂²×C₈	—	89	4	no	—
333	C₂²×C₈	—	89	4	no	—
334	C₂²×C₈	—	178	2	no	—
335	C₂²×C₈	—	178	2	no	—
336	C₂²×C₈	—	178	2	no	—
337	C₂²×C₈	—	178	2	no	—
338	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
342	#117	—	89	4	no	—
343	#117	—	89	4	no	—
344	#117	—	178	2	no	—
345	#117	—	178	2	no	—
346	C₂×C₄⋊C₄	—	89	1	no	—
347	C₂×C₄⋊C₄	—	89	1	no	—
348	C₂×C₄⋊C₄	—	89	2	no	—
349	C₂×C₂²⋊C₄	—	89	1	no	—
350	C₂×C₂²⋊C₄	—	89	1	no	—
351	C₂×C₂²⋊C₄	—	89	2	no	—
352	C₂×C₄²	—	89	1	no	—
353	C₂×C₄²	—	89	2	no	—
354	C₂×C₄²	—	89	2	no	—
355	C₂×C₄²	—	89	2	no	—
356	C₂×C₄²	—	89	2	no	—
357	C₂×C₄²	—	89	2	no	—
358	C₂×C₄²	—	89	1	no	—
359	C₂×C₄²	—	89	1	no	—
360	C₂×C₄²	—	178	2	no	—
361	C₂×C₄²	—	178	2	no	—
362	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
365	#97	—	89	4	no	—
366	#97	—	89	4	no	—
367	#97	—	89	4	no	—
368	#97	C₄×D₈₉	1	4	yes	complemented
369	C₄×C₈	—	89	4	no	—
370	C₄×C₈	—	89	4	no	—
371	C₄×C₈	—	89	4	no	—
372	C₄×C₈	C₄×D₈₉	1	4	yes	complemented
373	#95	—	89	2	no	—
374	#95	—	89	2	no	—
375	#95	C₄×D₈₉	1	2	yes	—
376	#95	C₄×D₈₉	1	2	yes	—
377	C₂⁴	—	89	1	no	—
378	C₂²×C₄	—	89	1	no	—
379	C₂²×C₄	—	89	2	no	—
380	C₂²×C₄	—	89	2	no	—
381	C₂²×C₄	—	89	2	no	—
382	C₂²×C₄	—	89	2	no	—
383	C₂²×C₄	—	89	2	no	—
384	C₂²×C₄	—	89	2	no	—
385	C₂²×C₄	—	89	1	no	—
386	C₂²×C₄	—	89	1	no	—
387	C₂²×C₄	—	89	2	no	—
388	C₂²×C₄	—	89	2	no	—
389	C₂²×C₄	—	356	2	no	—
390	C₂²×C₄	—	178	4	no	—
391	C₂²×C₄	—	178	4	no	—
392	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
393	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
394	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
396	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
397	M₁₆	—	178	8	no	—
398	M₁₆	—	178	8	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	89	2	no	—
408	C₂×C₈	—	89	2	no	—
409	C₂×C₈	—	89	2	no	—
410	C₂×C₈	—	89	2	no	—
411	C₂×C₈	—	178	8	no	—
412	C₂×C₈	—	178	8	no	—
413	C₂×C₈	—	178	1	no	—
414	C₂×C₈	—	178	1	no	—
415	C₂×C₈	—	178	1	no	—
416	C₂×C₈	—	178	1	no	—
417	C₂×C₈	—	178	1	no	—
418	C₂×C₈	—	178	1	no	—
419	C₂×C₈	—	178	1	no	—
420	C₂×C₈	—	178	1	no	—
421	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
425	C₄⋊C₄	—	89	4	no	—
426	C₄⋊C₄	—	89	4	no	—
427	C₄⋊C₄	—	178	4	no	—
428	C₂²⋊C₄	—	89	4	no	—
429	C₂²⋊C₄	—	89	4	no	—
430	C₂²⋊C₄	—	178	4	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	89	2	no	—
436	C₄²	—	89	2	no	—
437	C₄²	—	356	2	no	—
438	C₄²	—	356	2	no	—
439	C₄²	—	178	4	no	—
440	C₄²	—	178	4	no	—
441	C₄²	—	178	4	no	—
442	C₄²	—	178	1	no	—
443	C₄²	—	178	1	no	—
444	C₄²	—	178	1	no	—
445	C₄²	—	178	1	no	—
446	C₄²	C₂×C₄×D₈₉	1	2	yes	—
447	C₄²	C₂×C₄×D₈₉	1	2	yes	—
448	C₂³	—	89	2	no	—
449	C₂³	—	89	2	no	—
450	C₂³	—	89	2	no	—
451	C₂³	—	178	2	no	—
452	C₂³	—	178	2	no	—
453	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	89	2	no	—
463	C₂×C₄	—	89	2	no	—
464	C₂×C₄	—	89	2	no	—
465	C₂×C₄	—	89	4	no	—
466	C₂×C₄	—	89	4	no	—
467	C₂×C₄	—	89	4	no	—
468	C₂×C₄	—	89	4	no	—
469	C₂×C₄	—	89	2	no	—
470	C₂×C₄	—	89	2	no	—
471	C₂×C₄	—	89	4	no	—
472	C₂×C₄	—	356	8	no	—
473	C₂×C₄	—	178	2	no	—
474	C₂×C₄	—	178	2	no	—
475	C₂×C₄	—	178	2	no	—
476	C₂×C₄	—	178	2	no	—
477	C₂×C₄	—	178	2	no	—
478	C₂×C₄	—	178	2	no	—
479	C₂×C₄	—	178	2	no	—
480	C₂×C₄	C₄²×D₈₉	1	2	yes	—
481	C₂×C₄	C₄²×D₈₉	1	2	yes	—
482	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
484	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
485	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
486	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
487	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	178	2	no	—
493	C₈	—	178	2	no	—
494	C₈	—	178	2	no	—
495	C₈	—	178	2	no	—
496	C₂²	—	89	4	no	—
497	C₂²	—	178	4	no	—
498	C₂²	—	178	4	no	—
499	C₂²	—	178	2	no	—
500	C₂²	—	178	2	no	—
501	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
502	C₂²	#117×D₈₉	1	1	yes	characteristic
503	C₂²	#117×D₈₉	1	1	yes	characteristic
504	C₂²	#131×D₈₉	1	2	yes	—
505	C₂²	#19152363	1	2	yes	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	89	4	no	—
511	C₄	—	356	2	no	—
512	C₄	—	178	4	no	—
513	C₄	—	178	2	no	—
514	C₄	—	178	2	no	—
515	C₄	#117×D₈₉	1	1	yes	characteristic
516	C₄	#117×D₈₉	1	1	yes	characteristic
517	C₄	#117×D₈₉	1	1	yes	characteristic
518	C₄	#117×D₈₉	1	1	yes	characteristic
519	C₂	—	178	4	no	—
520	C₂	#376×D₈₉	1	1	yes	characteristic
521	C₂	#26028674	1	1	yes	characteristic
522	C₂	#26028679	1	1	yes	characteristic
523	C₂	#26028908	1	2	yes	—
524	C₂	#26028915	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#1746	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1746	D₈₉
hypocenter	C₈₉	#20368
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1746

Complements

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

N	H ≅ G/N	type
4. #26020004	C₂	semidirect
5. #26020002	C₂	semidirect
6. #26020002	C₂	semidirect
7. #26020000	C₂	semidirect
8. #26019999	C₂	semidirect
9. #26019997	C₂	semidirect
10. #26019996	C₂	semidirect
15. C₈₉×#1746	C₂	semidirect
23. #19151555	C₄	semidirect
24. #19151552	C₄	semidirect
95. #15667923	C₂×C₄	semidirect
96. #15667922	C₂×C₄	semidirect
97. #15667922	C₂×C₄	semidirect
98. C₄×#10623494	C₂×C₄	semidirect
99. C₈×Dic₈₉	C₂×C₄	semidirect
100. C₈×Dic₈₉	C₂×C₄	semidirect
110. #97×C₈₉	C₂×C₄	semidirect
111. C₄×C₈×C₈₉	C₂×C₄	semidirect
269. #1746	D₈₉	semidirect
278. C₈₉	#20368	semidirect
368. #97	C₄×D₈₉	semidirect
372. C₄×C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151555	2
C₂×#19151552	2
#26022591	2
#26020004	2
#26020002	2
#26020000	2
#26019999	2
#26019997	2
#26019996	2
#26019947	2
#26019944	2
#336×D₈₉	2
C₈₉×#1746	2
#20368	89