Subgroups — #36460040

Order 22784.

918 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151353	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151352	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151352	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151352	C₂	1	1	yes	maximal, characteristic
6	C₄×#15667919	C₂	1	1	yes	maximal, characteristic
7	C₂×#336×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×#10623494	C₂²	1	1	yes	characteristic
9	C₂³×#10623494	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₈₉	—	2	2	no	—
13	C₂×C₈×Dic₈₉	—	2	2	no	—
14	C₂×C₈×Dic₈₉	C₄	1	4	yes	complemented
15	C₂×#15667919	C₄	1	2	yes	—
16	C₂×#15667919	C₄	1	2	yes	—
17	#19151353	—	2	2	no	—
18	#19151352	—	2	2	no	—
19	#19151352	—	2	2	no	—
20	#19151352	C₄	1	4	yes	complemented
21	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
24	#336×C₈₉	—	2	2	no	—
25	C₂³×Dic₈₉	C₂×C₄	1	2	yes	—
26	C₂³×Dic₈₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×Dic₈₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×#10623494	—	2	1	no	—
29	C₂²×#10623494	—	2	1	no	—
30	C₂²×#10623494	—	2	1	no	—
31	C₂²×#10623494	—	2	1	no	—
32	C₂²×#10623494	—	2	1	no	—
33	C₂²×#10623494	—	2	1	no	—
34	C₂²×#10623494	—	2	1	no	—
35	C₂²×#10623494	—	2	1	no	—
36	C₂²×#10623494	—	2	1	no	—
37	C₂²×#10623494	—	2	1	no	—
38	C₂²×#10623494	C₂×C₄	1	2	yes	—
39	C₂²×#10623494	C₂×C₄	1	2	yes	—
40	C₂²×#10623494	D₄	1	2	yes	—
41	C₂²×#10623494	D₄	1	2	yes	—
42	C₂×C₄×Dic₈₉	—	2	1	no	—
43	C₂×C₄×Dic₈₉	—	2	1	no	—
44	C₂×C₄×Dic₈₉	—	2	1	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	C₂×C₄×Dic₈₉	—	2	1	no	—
47	C₂×C₄×Dic₈₉	—	2	1	no	—
48	C₂×C₄×Dic₈₉	—	2	1	no	—
49	C₂×C₄×Dic₈₉	—	2	1	no	—
50	C₂×C₄×Dic₈₉	—	2	1	no	—
51	C₂×C₄×Dic₈₉	—	2	1	no	—
52	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
54	C₈×Dic₈₉	—	2	8	no	—
55	#15667919	—	2	4	no	—
56	#15667919	C₈	1	8	yes	complemented
57	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂²×C₈×C₈₉	—	2	1	no	—
63	C₂²×C₈×C₈₉	—	2	1	no	—
64	C₂²×C₈×C₈₉	—	2	1	no	—
65	C₂²×C₈×C₈₉	—	2	1	no	—
66	C₂²×C₈×C₈₉	—	2	1	no	—
67	C₂²×C₈×C₈₉	—	2	1	no	—
68	C₂²×C₈×C₈₉	—	2	1	no	—
69	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₈₉	D₄	1	2	yes	—
72	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	1	no	—
75	C₂×C₄²×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	—	2	1	no	—
77	C₂×C₄²×C₈₉	—	2	1	no	—
78	C₂×C₄²×C₈₉	—	2	1	no	—
79	C₂²×Dic₈₉	—	2	1	no	—
80	C₂²×Dic₈₉	—	2	1	no	—
81	C₂²×Dic₈₉	—	2	1	no	—
82	C₂²×Dic₈₉	—	2	1	no	—
83	C₂²×Dic₈₉	—	2	2	no	—
84	C₂²×Dic₈₉	—	2	2	no	—
85	C₂²×Dic₈₉	—	2	2	no	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	—	2	2	no	—
88	C₂²×Dic₈₉	—	2	2	no	—
89	C₂²×Dic₈₉	—	2	2	no	—
90	C₂²×Dic₈₉	—	2	2	no	—
91	C₂²×Dic₈₉	C₄²	1	2	yes	—
92	C₂²×Dic₈₉	C₄²	1	2	yes	—
93	C₂²×Dic₈₉	C₂×C₈	1	4	yes	—
94	C₂²×Dic₈₉	C₂×C₈	1	4	yes	—
95	C₂²×Dic₈₉	M₁₆	1	4	yes	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	2	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	—	2	2	no	—
101	C₂×#10623494	—	2	2	no	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	—	4	1	no	—
106	C₂×#10623494	—	4	1	no	—
107	C₂×#10623494	—	4	1	no	—
108	C₂×#10623494	—	4	1	no	—
109	C₂×#10623494	C₂²⋊C₄	1	4	yes	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₄×Dic₈₉	—	2	2	no	—
112	C₄×Dic₈₉	—	2	2	no	—
113	C₄×Dic₈₉	—	2	2	no	—
114	C₄×Dic₈₉	—	4	1	no	—
115	C₄×Dic₈₉	—	4	1	no	—
116	C₄×Dic₈₉	—	4	1	no	—
117	C₄×Dic₈₉	—	4	1	no	—
118	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	—	2	2	no	—
121	C₂²×C₄×C₈₉	—	2	2	no	—
122	C₂²×C₄×C₈₉	—	2	2	no	—
123	C₂²×C₄×C₈₉	—	2	2	no	—
124	C₂²×C₄×C₈₉	—	2	2	no	—
125	C₂²×C₄×C₈₉	C₂×C₈	1	4	yes	—
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₂×C₈×C₈₉	—	2	2	no	—
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	4	1	no	—
150	C₂×C₈×C₈₉	—	4	1	no	—
151	C₂×C₈×C₈₉	—	4	1	no	—
152	C₂×C₈×C₈₉	—	4	1	no	—
153	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
154	C₄²×C₈₉	—	4	1	no	—
155	C₄²×C₈₉	—	4	1	no	—
156	C₄²×C₈₉	—	4	1	no	—
157	C₄²×C₈₉	—	4	1	no	—
158	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
159	C₂³×C₈₉	#117	1	1	yes	characteristic
160	C₂³×C₈₉	#117	1	1	yes	characteristic
161	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₈₉	C₄×Q₈	1	1	yes	characteristic
165	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
166	C₂³×C₈₉	C₂×M₁₆	1	2	yes	—
167	C₂³×C₈₉	#131	1	2	yes	—
168	C₂³×C₈₉	#131	1	2	yes	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	4	no	—
171	C₂×C₄×C₈₉	—	2	4	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	2	no	—
176	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
180	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
193	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
194	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
195	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
196	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
197	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
198	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
199	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
200	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
201	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
202	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
203	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
204	C₂×Dic₈₉	—	2	2	no	—
205	C₂×Dic₈₉	—	2	2	no	—
206	C₂×Dic₈₉	—	2	2	no	—
207	C₂×Dic₈₉	—	2	2	no	—
208	C₂×Dic₈₉	—	2	4	no	—
209	C₂×Dic₈₉	—	2	4	no	—
210	C₂×Dic₈₉	—	2	4	no	—
211	C₂×Dic₈₉	—	2	4	no	—
212	C₂×Dic₈₉	—	2	4	no	—
213	C₂×Dic₈₉	—	2	4	no	—
214	C₂×Dic₈₉	—	2	4	no	—
215	C₂×Dic₈₉	—	4	2	no	—
216	C₂×Dic₈₉	—	4	2	no	—
217	C₂×Dic₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	4	2	no	—
219	C₂×Dic₈₉	C₄×C₈	1	4	yes	—
220	C₂×Dic₈₉	#97	1	4	yes	—
221	C₈×C₈₉	—	2	4	no	—
222	C₈×C₈₉	—	4	2	no	—
223	#10623494	—	2	4	no	—
224	#10623494	—	4	2	no	—
225	C₂²×C₈₉	#376	1	1	yes	characteristic
226	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₈₉	#387	1	1	yes	characteristic
229	C₂²×C₈₉	#387	1	1	yes	characteristic
230	C₂²×C₈₉	#388	1	1	yes	characteristic
231	C₂²×C₈₉	#388	1	1	yes	characteristic
232	C₂²×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
233	C₂²×C₈₉	C₂×#97	1	1	yes	characteristic
234	C₂²×C₈₉	#405	1	1	yes	characteristic
235	C₂²×C₈₉	#405	1	1	yes	characteristic
236	C₂²×C₈₉	#431	1	2	yes	—
237	C₂²×C₈₉	#431	1	2	yes	—
238	C₂²×C₈₉	#433	1	2	yes	—
239	C₂²×C₈₉	#433	1	2	yes	—
240	C₂²×C₈₉	C₈×D₄	1	2	yes	—
241	C₂²×C₈₉	C₈×D₄	1	2	yes	—
242	C₂²×C₈₉	C₈×D₄	1	2	yes	—
243	C₂²×C₈₉	#435	1	2	yes	—
244	C₂²×C₈₉	#435	1	2	yes	—
245	C₂²×C₈₉	#436	1	2	yes	—
246	C₂²×C₈₉	C₈×Q₈	1	2	yes	—
247	C₂²×C₈₉	#446	1	2	yes	—
248	C₄×C₈₉	—	4	4	no	—
249	C₄×C₈₉	#380	1	1	yes	characteristic
250	C₄×C₈₉	#381	1	1	yes	characteristic
251	C₄×C₈₉	#382	1	1	yes	characteristic
252	C₄×C₈₉	#383	1	1	yes	characteristic
253	C₄×C₈₉	#387	1	1	yes	characteristic
254	C₄×C₈₉	#387	1	1	yes	characteristic
255	C₄×C₈₉	#388	1	1	yes	characteristic
256	C₄×C₈₉	#388	1	1	yes	characteristic
257	Dic₈₉	—	2	4	no	—
258	Dic₈₉	—	2	4	no	—
259	Dic₈₉	—	4	4	no	—
260	#10797	—	89	1	no	maximal, Sylow
261	C₂×C₈₉	#1434	1	1	yes	characteristic
262	C₂×C₈₉	#1744	1	1	yes	characteristic
263	C₂×C₈₉	#1746	1	1	yes	characteristic
264	C₂×C₈₉	C₈×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₈₉	#1752	1	1	yes	characteristic
266	C₂×C₈₉	C₈×C₄⋊C₄	1	1	yes	characteristic
267	C₂×C₈₉	#1770	1	1	yes	characteristic
268	C₂×C₈₉	#1916	1	2	yes	—
269	C₂×C₈₉	#1916	1	2	yes	—
270	C₂×C₈₉	#1923	1	2	yes	—
271	C₂×C₈₉	#1923	1	2	yes	—
272	C₂²×C₄×C₈	—	89	1	no	—
273	C₂×#336	—	89	1	no	—
274	C₂×#336	—	89	1	no	—
275	C₂×#336	—	89	1	no	—
276	C₂×#336	—	89	1	no	—
277	C₂×#336	D₈₉	1	1	yes	characteristic
278	C₄×#95	—	89	1	no	—
279	C₈₉	#10797	1	1	yes	characteristic, complemented, Sylow
280	C₂³×C₈	—	89	1	no	—
281	C₂³×C₈	—	89	1	no	—
282	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
283	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
284	C₂²×C₄²	—	89	1	no	—
285	C₂²×C₄²	—	89	1	no	—
286	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
287	C₂×C₄×C₈	—	89	4	no	—
288	C₂×C₄×C₈	—	178	2	no	—
289	C₂×C₄×C₈	—	178	2	no	—
290	C₂×#95	—	89	2	no	—
291	C₂×#95	—	89	2	no	—
292	#336	—	2	2	no	—
293	#336	—	89	4	no	—
294	#336	—	178	2	no	—
295	#336	—	178	2	no	—
296	#336	—	178	2	no	—
297	C₂³×C₄	—	89	1	no	—
298	C₂³×C₄	—	89	1	no	—
299	C₂³×C₄	—	89	2	no	—
300	C₂³×C₄	C₄×D₈₉	1	2	yes	—
301	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	89	2	no	—
313	C₂²×C₈	—	89	2	no	—
314	C₂²×C₈	—	89	2	no	—
315	C₂²×C₈	—	89	2	no	—
316	C₂²×C₈	—	178	1	no	—
317	C₂²×C₈	—	178	1	no	—
318	C₂²×C₈	—	178	1	no	—
319	C₂²×C₈	—	178	1	no	—
320	C₂²×C₈	—	178	1	no	—
321	C₂²×C₈	—	178	1	no	—
322	C₂²×C₈	—	178	1	no	—
323	C₂²×C₈	—	178	1	no	—
324	C₂²×C₈	—	178	1	no	—
325	C₂²×C₈	—	178	1	no	—
326	C₂²×C₈	Dic₁₇₈	1	2	yes	—
327	C₂²×C₈	C₄×D₈₉	1	2	yes	—
328	C₂²×C₈	C₄×D₈₉	1	2	yes	—
329	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	89	2	no	—
337	C₂×C₄²	—	89	2	no	—
338	C₂×C₄²	—	178	1	no	—
339	C₂×C₄²	—	178	1	no	—
340	C₂×C₄²	—	178	1	no	—
341	C₂×C₄²	—	178	1	no	—
342	C₂×C₄²	—	178	1	no	—
343	C₂×C₄²	—	178	1	no	—
344	C₂×C₄²	—	178	1	no	—
345	C₂×C₄²	—	178	1	no	—
346	C₂×C₄²	—	178	1	no	—
347	C₂×C₄²	—	178	1	no	—
348	C₄×C₈	—	178	8	no	—
349	#95	—	89	8	no	—
350	#95	—	178	4	no	—
351	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	89	4	no	—
359	C₂²×C₄	—	89	4	no	—
360	C₂²×C₄	—	89	2	no	—
361	C₂²×C₄	—	89	2	no	—
362	C₂²×C₄	—	89	4	no	—
363	C₂²×C₄	—	178	2	no	—
364	C₂²×C₄	—	178	2	no	—
365	C₂²×C₄	—	178	2	no	—
366	C₂²×C₄	—	178	2	no	—
367	C₂²×C₄	—	178	2	no	—
368	C₂²×C₄	—	178	2	no	—
369	C₂²×C₄	—	178	1	no	—
370	C₂²×C₄	—	178	1	no	—
371	C₂²×C₄	—	178	1	no	—
372	C₂²×C₄	—	178	1	no	—
373	C₂²×C₄	—	178	2	no	—
374	C₂²×C₄	—	178	2	no	—
375	C₂²×C₄	C₈×D₈₉	1	4	yes	—
376	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
379	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
382	C₂²×C₄	#13083573	1	1	yes	characteristic
383	C₂²×C₄	#13083573	1	1	yes	characteristic
384	C₂²×C₄	#13083573	1	1	yes	characteristic
385	C₂²×C₄	#13083573	1	1	yes	characteristic
386	C₂²×C₄	#13083574	1	1	yes	characteristic
387	C₂²×C₄	#13083574	1	1	yes	characteristic
388	C₂²×C₄	#13083575	1	1	yes	characteristic
389	C₂²×C₄	#13083575	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	89	4	no	—
404	C₂×C₈	—	356	1	no	—
405	C₂×C₈	—	356	1	no	—
406	C₂×C₈	—	356	1	no	—
407	C₂×C₈	—	356	1	no	—
408	C₂×C₈	—	178	2	no	—
409	C₂×C₈	—	178	2	no	—
410	C₂×C₈	—	178	2	no	—
411	C₂×C₈	—	178	2	no	—
412	C₂×C₈	—	178	2	no	—
413	C₂×C₈	—	178	2	no	—
414	C₂×C₈	—	178	2	no	—
415	C₂×C₈	—	178	2	no	—
416	C₂×C₈	—	178	2	no	—
417	C₂×C₈	#13083553	1	4	yes	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	356	1	no	—
423	C₄²	—	356	1	no	—
424	C₄²	—	356	1	no	—
425	C₄²	—	356	1	no	—
426	C₄²	—	178	2	no	—
427	C₄²	—	178	2	no	—
428	C₄²	—	178	2	no	—
429	C₄²	—	178	2	no	—
430	C₂³	C₄²×D₈₉	1	1	yes	characteristic
431	C₂³	#15667968	1	1	yes	characteristic
432	C₂³	#15667970	1	1	yes	characteristic
433	C₂³	#15667972	1	1	yes	characteristic
434	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
435	C₂³	#15667974	1	1	yes	characteristic
436	C₂³	C₄×Dic₁₇₈	1	1	yes	characteristic
437	C₂³	C₂×C₈×D₈₉	1	2	yes	—
438	C₂³	M₁₆×D₈₉	1	2	yes	—
439	C₂³	#15668018	1	2	yes	—
440	C₂³	#15668020	1	2	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	89	4	no	—
449	C₂×C₄	—	89	4	no	—
450	C₂×C₄	—	356	2	no	—
451	C₂×C₄	—	356	2	no	—
452	C₂×C₄	—	356	2	no	—
453	C₂×C₄	—	356	2	no	—
454	C₂×C₄	—	178	4	no	—
455	C₂×C₄	—	178	4	no	—
456	C₂×C₄	—	178	4	no	—
457	C₂×C₄	—	178	4	no	—
458	C₂×C₄	—	178	4	no	—
459	C₂×C₄	—	178	4	no	—
460	C₂×C₄	—	178	4	no	—
461	C₂×C₄	—	178	2	no	—
462	C₂×C₄	—	178	2	no	—
463	C₂×C₄	—	178	2	no	—
464	C₂×C₄	—	178	2	no	—
465	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
467	C₂×C₄	#15667968	1	1	yes	characteristic
468	C₂×C₄	#15667968	1	1	yes	characteristic
469	C₂×C₄	#15667969	1	1	yes	characteristic
470	C₂×C₄	#15667970	1	1	yes	characteristic
471	C₂×C₄	#15667970	1	1	yes	characteristic
472	C₂×C₄	#15667970	1	1	yes	characteristic
473	C₂×C₄	#15667972	1	1	yes	characteristic
474	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
475	C₂×C₄	#15667974	1	1	yes	characteristic
476	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
477	C₂×C₄	#15667984	1	1	yes	characteristic
478	C₂×C₄	#15667984	1	1	yes	characteristic
479	C₂×C₄	#15667989	1	1	yes	characteristic
480	C₂×C₄	#15667989	1	1	yes	characteristic
481	C₂×C₄	#15667994	1	1	yes	characteristic
482	C₂×C₄	#15667994	1	1	yes	characteristic
483	C₂×C₄	#15667997	1	1	yes	characteristic
484	C₂×C₄	#15667997	1	1	yes	characteristic
485	C₂×C₄	#15667999	1	1	yes	characteristic
486	C₂×C₄	#15668001	1	1	yes	characteristic
487	C₂×C₄	#15668003	1	1	yes	characteristic
488	C₂×C₄	#15668003	1	1	yes	characteristic
489	C₂×C₄	#15668005	1	1	yes	characteristic
490	C₂×C₄	#15668005	1	1	yes	characteristic
491	C₂×C₄	#15668007	1	1	yes	characteristic
492	C₂×C₄	#15668007	1	1	yes	characteristic
493	C₈	—	2	4	no	—
494	C₈	—	4	2	no	—
495	C₈	—	356	2	no	—
496	C₈	—	178	4	no	—
497	C₂²	#19151443	1	1	yes	characteristic
498	C₂²	#19151445	1	1	yes	characteristic
499	C₂²	C₄×#13083553	1	1	yes	characteristic
500	C₂²	#19151481	1	1	yes	characteristic
501	C₂²	#19151485	1	1	yes	characteristic
502	C₂²	#19151488	1	1	yes	characteristic
503	C₂²	#19151492	1	1	yes	characteristic
504	C₂²	C₄×C₈×D₈₉	1	1	yes	characteristic
505	C₂²	#97×D₈₉	1	1	yes	characteristic
506	C₂²	#19151552	1	1	yes	characteristic
507	C₂²	#19151555	1	1	yes	characteristic
508	C₂²	#19151648	1	2	yes	—
509	C₂²	#19151650	1	2	yes	—
510	C₂²	#19151656	1	2	yes	—
511	C₂²	#19151658	1	2	yes	—
512	C₂²	#19151661	1	2	yes	—
513	C₂²	C₈×C₂²⋊D₈₉	1	2	yes	—
514	C₂²	#19151663	1	2	yes	—
515	C₂²	#19151668	1	2	yes	—
516	C₂²	#19151672	1	2	yes	—
517	C₂²	#19151674	1	2	yes	—
518	C₂²	C₈×Dic₁₇₈	1	2	yes	—
519	C₂²	#19151726	1	2	yes	—
520	C₄	—	4	4	no	—
521	C₄	—	356	4	no	—
522	C₄	—	178	4	no	—
523	C₄	—	178	4	no	—
524	C₄	#19151456	1	1	yes	characteristic
525	C₄	#19151460	1	1	yes	characteristic
526	C₄	#19151463	1	1	yes	characteristic
527	C₄	#19151465	1	1	yes	characteristic
528	C₄	#19151481	1	1	yes	characteristic
529	C₄	#19151485	1	1	yes	characteristic
530	C₄	#19151488	1	1	yes	characteristic
531	C₄	#19151492	1	1	yes	characteristic
532	C₂	#26018478	1	1	yes	characteristic
533	C₂	#26019996	1	1	yes	characteristic
534	C₂	#26020002	1	1	yes	characteristic
535	C₂	#26020022	1	1	yes	characteristic
536	C₂	#26020027	1	1	yes	characteristic
537	C₂	C₈×#13083553	1	1	yes	characteristic
538	C₂	#26020120	1	1	yes	characteristic
539	C₂	#26020808	1	2	yes	—
540	C₂	#26020812	1	2	yes	—
541	C₂	#26020857	1	2	yes	—
542	C₂	#26020861	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₈₉
commutator	C₂²×C₈₉	C₂×C₄×C₈
Fitting	C₂×#336×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#336	D₈₉
hypocenter	C₈₉	#10797
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×Dic₈₉	C₄	semidirect
20. #19151352	C₄	semidirect
56. #15667919	C₈	semidirect
279. C₈₉	#10797	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₈₉	2
C₂×#19151353	2
C₂×#19151352	2
C₄×#15667919	2
C₂×#336×C₈₉	2
#10797	89