Subgroups — #36571825

Order 22784.

804 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26020818	C₂	1	2	yes	maximal, complemented
2	#26020811	C₂	1	2	yes	maximal, complemented
3	#26020437	C₂	1	2	yes	maximal
4	#26020395	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020369	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020320	C₂	1	1	yes	maximal, characteristic
7	#26020105	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020036	C₂	1	2	yes	maximal
9	#26019998	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019946	C₂	1	1	yes	maximal, characteristic
11	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#13083558	C₂²	1	2	yes	—
13	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
14	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
15	C₂×C₂²⋊#10623494	C₂²	1	2	yes	—
16	C₂×#15667923	C₂²	1	2	yes	—
17	C₂×C₄×#10623494	C₂²	1	2	yes	—
18	#19151353	C₂²	1	1	yes	characteristic
19	#19151353	C₂²	1	1	yes	characteristic
20	#19151353	C₂²	1	1	yes	characteristic
21	#19151353	C₂²	1	2	yes	—
22	#19151353	C₂²	1	2	yes	—
23	#19151353	C₂²	1	1	yes	characteristic
24	#19151353	C₂²	1	2	yes	—
25	#19151353	C₂²	1	2	yes	—
26	#19151353	C₂²	1	2	yes	—
27	#19151353	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	C₄	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₄	1	1	yes	characteristic
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₈₉	C₄	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₈₉	C₄	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	#376×C₈₉	C₄	1	1	yes	characteristic
40	#376×C₈₉	C₄	1	1	yes	characteristic
41	C₄³×C₈₉	C₂²	1	1	yes	characteristic
42	C₄³×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083558	—	2	4	no	—
44	C₂×#13083558	—	2	4	no	—
45	C₂×#13083558	—	4	2	no	—
46	C₂²×#10623494	C₂³	1	2	yes	—
47	C₂²×#10623494	C₂³	1	2	yes	—
48	C₂²×#10623494	C₂³	1	2	yes	—
49	C₂²×#10623494	C₂³	1	2	yes	—
50	C₄⋊#10623494	—	2	4	no	—
51	C₄⋊#10623494	—	4	2	no	—
52	C₂²⋊#10623494	—	2	4	no	—
53	#15667923	—	4	2	no	—
54	C₄×#10623494	—	2	4	no	—
55	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	#117×C₈₉	—	2	4	no	—
59	#117×C₈₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	—	2	4	no	—
69	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
85	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
86	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
87	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
88	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
90	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
91	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
92	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
93	#13083558	—	4	8	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
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	#41	1	4	yes	—
106	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	—	2	2	no	—
108	C₂²×C₄×C₈₉	—	2	2	no	—
109	C₂²×C₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	1	no	—
112	C₂²×C₄×C₈₉	—	2	1	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	—	4	1	no	—
116	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	4	yes	—
130	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₈₉	—	2	2	no	—
132	C₄⋊C₄×C₈₉	—	2	2	no	—
133	C₄⋊C₄×C₈₉	—	2	2	no	—
134	C₄⋊C₄×C₈₉	M₁₆	1	4	yes	complemented
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₂²⋊C₄×C₈₉	—	2	2	no	—
137	C₂²⋊C₄×C₈₉	—	2	2	no	—
138	C₂²⋊C₄×C₈₉	—	2	2	no	—
139	C₄²×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	—	2	2	no	—
141	C₄²×C₈₉	—	2	2	no	—
142	C₄²×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	4	1	no	—
155	C₄²×C₈₉	—	4	1	no	—
156	C₄²×C₈₉	M₁₆	1	4	yes	complemented
157	C₂³×C₈₉	—	2	1	no	—
158	C₂³×C₈₉	—	2	1	no	—
159	C₂³×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	—	2	1	no	—
161	C₂³×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	—	2	1	no	—
163	C₂³×C₈₉	#117	1	2	yes	—
164	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	—	2	8	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	4	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	2	1	no	—
197	C₂×C₄×C₈₉	—	2	1	no	—
198	C₂×C₄×C₈₉	—	2	1	no	—
199	C₂×C₄×C₈₉	—	4	4	no	—
200	C₂×C₄×C₈₉	#117	1	2	yes	—
201	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
202	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
203	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
205	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
206	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₈₉	#131	1	2	yes	—
208	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
210	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
212	#10623494	—	2	4	no	—
213	#10623494	—	4	2	no	—
214	#10623494	—	4	2	no	—
215	#10623494	—	4	2	no	—
216	C₂²×C₈₉	—	2	2	no	—
217	C₂²×C₈₉	—	2	2	no	—
218	C₂²×C₈₉	—	2	2	no	—
219	C₂²×C₈₉	—	4	1	no	—
220	C₂²×C₈₉	—	4	1	no	—
221	C₂²×C₈₉	—	4	1	no	—
222	C₂²×C₈₉	—	4	1	no	—
223	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
224	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
225	C₂²×C₈₉	#520	1	1	yes	characteristic
226	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
227	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
228	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
229	C₂²×C₈₉	#568	1	1	yes	characteristic
230	C₄×C₈₉	—	2	2	no	—
231	C₄×C₈₉	—	2	2	no	—
232	C₄×C₈₉	—	2	2	no	—
233	C₄×C₈₉	—	2	2	no	—
234	C₄×C₈₉	—	2	2	no	—
235	C₄×C₈₉	—	2	2	no	—
236	C₄×C₈₉	—	2	2	no	—
237	C₄×C₈₉	—	2	2	no	—
238	C₄×C₈₉	—	4	1	no	—
239	C₄×C₈₉	—	4	1	no	—
240	C₄×C₈₉	—	4	1	no	—
241	C₄×C₈₉	—	4	1	no	—
242	C₄×C₈₉	—	4	1	no	—
243	C₄×C₈₉	#551	1	2	yes	—
244	C₄×C₈₉	#552	1	2	yes	—
245	#22590	—	89	1	no	maximal, Sylow
246	C₂×C₈₉	—	4	2	no	—
247	C₂×C₈₉	#2343	1	1	yes	characteristic
248	C₂×C₈₉	#2920	1	1	yes	characteristic
249	C₂×C₈₉	#2924	1	1	yes	characteristic
250	C₂×C₈₉	#2965	1	1	yes	characteristic
251	C₂×C₈₉	#2970	1	1	yes	characteristic
252	C₂×C₈₉	#2989	1	1	yes	characteristic
253	C₂×C₈₉	#2991	1	1	yes	characteristic
254	C₄×#117	D₈₉	1	1	yes	characteristic
255	#1917	—	89	2	no	—
256	#1916	—	89	2	no	—
257	#1851	—	89	2	no	—
258	#1839	—	89	1	no	—
259	#1831	—	89	1	no	—
260	#1817	—	89	1	no	—
261	#1767	—	89	1	no	—
262	#1753	—	89	2	no	—
263	#1744	—	89	1	no	—
264	#1728	—	89	1	no	—
265	C₈₉	#22590	1	1	yes	characteristic, complemented, Sylow
266	C₂²×M₁₆	—	89	2	no	—
267	C₂×#117	Dic₈₉	1	1	yes	characteristic
268	C₂×#117	Dic₈₉	1	1	yes	characteristic
269	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
270	C₂×C₄⋊C₈	—	89	2	no	—
271	C₂×C₄⋊C₈	—	89	2	no	—
272	C₂×C₂²⋊C₈	—	89	2	no	—
273	C₂×#97	—	89	2	no	—
274	C₂×C₄×C₈	—	89	2	no	—
275	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
278	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	Dic₈₉	1	1	yes	characteristic
280	C₄×C₂²⋊C₄	Dic₈₉	1	1	yes	characteristic
281	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
283	#376	Dic₈₉	1	1	yes	characteristic
284	#376	Dic₈₉	1	1	yes	characteristic
285	C₄³	C₂×D₈₉	1	1	yes	characteristic
286	C₄³	C₂×D₈₉	1	1	yes	characteristic
287	#336	—	89	1	no	—
288	#336	—	89	1	no	—
289	#336	—	89	2	no	—
290	#336	—	89	1	no	—
291	#336	—	89	2	no	—
292	#336	—	89	2	no	—
293	#336	—	89	2	no	—
294	#336	—	89	2	no	—
295	#336	—	89	2	no	—
296	#336	—	89	1	no	—
297	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
298	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
299	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
300	C₂×M₁₆	—	356	2	no	—
301	C₂×M₁₆	—	178	4	no	—
302	C₂×M₁₆	—	178	4	no	—
303	C₂²×C₈	—	89	2	no	—
304	C₂²×C₈	—	89	2	no	—
305	C₂²×C₈	—	89	2	no	—
306	C₂²×C₈	—	89	2	no	—
307	#117	—	2	4	no	—
308	#117	—	2	4	no	—
309	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
319	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
320	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
321	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
322	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
323	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
324	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
325	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
326	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
327	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
329	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
330	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
331	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
334	C₄⋊C₈	—	356	2	no	—
335	C₄⋊C₈	—	178	4	no	—
336	C₂²⋊C₈	—	178	4	no	—
337	#97	—	356	2	no	—
338	C₄×C₈	—	178	4	no	—
339	#95	C₂×Dic₈₉	1	1	yes	characteristic
340	#95	C₂×Dic₈₉	1	1	yes	characteristic
341	#95	C₂×Dic₈₉	1	1	yes	characteristic
342	#95	C₂×Dic₈₉	1	1	yes	characteristic
343	#95	C₂×Dic₈₉	1	1	yes	characteristic
344	#95	C₂×Dic₈₉	1	1	yes	characteristic
345	#95	C₂×Dic₈₉	1	1	yes	characteristic
346	#95	C₂×Dic₈₉	1	1	yes	characteristic
347	C₂⁴	C₂²×Dic₈₉	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
360	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
361	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
363	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
365	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
370	C₂²×C₄	#13083574	1	4	yes	—
371	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
372	M₁₆	—	356	8	no	—
373	C₂×C₈	—	89	4	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	—	178	2	no	—
377	C₂×C₈	—	178	2	no	—
378	C₂×C₈	—	178	2	no	—
379	C₂×C₈	—	178	2	no	—
380	C₂×C₈	—	178	2	no	—
381	C₂×C₈	—	178	2	no	—
382	C₂×C₈	—	178	2	no	—
383	C₂×C₈	—	178	2	no	—
384	C₂×C₈	—	178	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	#13083558	1	4	yes	complemented
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	#13083558	1	4	yes	complemented
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	#15667971	1	2	yes	—
418	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	#15667971	1	2	yes	—
455	C₂×C₄	C₂×#13083558	1	2	yes	—
456	C₂×C₄	C₂×#13083558	1	2	yes	—
457	C₂×C₄	C₂×#13083558	1	2	yes	—
458	C₂×C₄	C₂×#13083558	1	2	yes	—
459	C₂×C₄	C₂×#13083558	1	2	yes	—
460	C₂×C₄	C₂×#13083558	1	2	yes	—
461	C₂×C₄	#15668019	1	2	yes	—
462	C₂×C₄	#41×D₈₉	1	2	yes	—
463	C₂×C₄	C₂×#13083574	1	2	yes	—
464	C₂×C₄	#15668058	1	1	yes	characteristic
465	C₂×C₄	#15668059	1	1	yes	characteristic
466	C₈	—	356	2	no	—
467	C₈	—	356	2	no	—
468	C₈	—	356	2	no	—
469	C₈	—	178	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₂×#15667971	1	1	yes	characteristic
478	C₂²	#41×Dic₈₉	1	1	yes	characteristic
479	C₂²	#19152081	1	1	yes	characteristic
480	C₂²	C₂²×#13083558	1	1	yes	characteristic
481	C₂²	C₂²×#13083558	1	1	yes	characteristic
482	C₂²	C₂×#15668019	1	1	yes	characteristic
483	C₂²	#19152365	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	#19152272	1	2	yes	—
498	C₄	#19152281	1	2	yes	—
499	C₂	—	4	2	no	—
500	C₂	#26023112	1	1	yes	characteristic
501	C₂	#26028885	1	1	yes	characteristic
502	C₂	#26028910	1	1	yes	characteristic
503	C₂	#26029219	1	1	yes	characteristic
504	C₂	#26029266	1	1	yes	characteristic
505	C₂	#26029369	1	1	yes	characteristic
506	C₂	#26029384	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₄×#117×C₈₉	C₂
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#117	D₈₉
hypocenter	C₈₉	#22590
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
1. #26020818	C₂	semidirect
2. #26020811	C₂	semidirect
4. #26020395	C₂	semidirect
5. #26020369	C₂	semidirect
7. #26020105	C₂	semidirect
9. #26019998	C₂	semidirect
134. C₄⋊C₄×C₈₉	M₁₆	semidirect
156. C₄²×C₈₉	M₁₆	semidirect
265. C₈₉	#22590	semidirect
388. C₄⋊C₄	#13083558	semidirect
410. C₄²	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26020818	2
#26020811	2
#26020437	2
#26020395	2
#26020369	2
#26020320	2
#26020105	2
#26020036	2
#26019998	2
#26019946	2
C₄×#117×C₈₉	2
#22590	89