Subgroups — #36459640

Order 22784.

842 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151553	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151553	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151370	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151368	C₂	1	1	yes	maximal, characteristic
5	#26019990	C₂	1	1	yes	maximal, characteristic
6	#26019984	C₂	1	1	yes	maximal, characteristic
7	C₂×#405×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#13083558	C₂²	1	1	yes	characteristic
9	C₂²×#13083558	C₂²	1	1	yes	characteristic
10	C₂×#15667971	C₂²	1	1	yes	characteristic
11	C₂×#15667971	C₂²	1	1	yes	characteristic
12	#19151553	—	2	1	no	—
13	#19151553	—	2	1	no	—
14	#19151553	—	2	1	no	—
15	#19151553	—	2	1	no	—
16	#19151553	—	2	2	no	—
17	#19151553	C₄	1	4	yes	complemented
18	C₂×#15667922	—	2	1	no	—
19	C₂×#15667922	C₄	1	2	yes	complemented
20	C₂×C₈×Dic₈₉	—	2	1	no	—
21	C₂×C₈×Dic₈₉	C₄	1	2	yes	complemented
22	#19151370	C₄	1	4	yes	complemented
23	#19151368	C₄	1	4	yes	complemented
24	#19151366	C₄	1	4	yes	complemented
25	#19151364	C₄	1	4	yes	—
26	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	#405×C₈₉	—	2	2	no	—
30	#405×C₈₉	C₄	1	4	yes	complemented
31	C₂×#97×C₈₉	—	2	1	no	—
32	C₂×C₄×C₈×C₈₉	—	2	1	no	—
33	C₂×#13083558	—	2	1	no	—
34	C₂×#13083558	—	2	1	no	—
35	C₂×#13083558	—	2	1	no	—
36	C₂×#13083558	—	2	1	no	—
37	C₂×#13083558	—	2	1	no	—
38	C₂×#13083558	—	2	1	no	—
39	C₂×#13083558	—	2	1	no	—
40	C₂×#13083558	C₂×C₄	1	2	yes	—
41	C₂×#13083558	C₂×C₄	1	2	yes	—
42	C₂×#13083558	C₂×C₄	1	2	yes	—
43	C₂×#13083558	C₂×C₄	1	2	yes	—
44	C₂×#13083558	C₂×C₄	1	2	yes	—
45	C₂²×#10623494	—	2	1	no	—
46	C₂²×#10623494	C₂×C₄	1	2	yes	—
47	#15667971	—	2	1	no	—
48	#15667971	—	2	1	no	—
49	#15667971	—	2	1	no	—
50	#15667971	—	2	1	no	—
51	#15667971	—	2	1	no	—
52	#15667971	—	2	1	no	—
53	#15667971	C₂×C₄	1	2	yes	—
54	#15667971	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊Dic₈₉	—	2	1	no	—
56	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₈₉	—	2	1	no	—
60	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
61	#15667922	—	2	4	no	—
62	#15667922	—	2	2	no	—
63	#15667922	—	2	2	no	—
64	C₈×Dic₈₉	—	2	4	no	—
65	C₈×Dic₈₉	—	2	2	no	—
66	C₈×Dic₈₉	—	2	2	no	—
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₈₉	—	2	1	no	—
69	C₂×M₁₆×C₈₉	—	2	1	no	—
70	C₂×M₁₆×C₈₉	—	2	1	no	—
71	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
73	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	D₄	1	2	yes	—
84	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
85	#117×C₈₉	—	2	1	no	—
86	#117×C₈₉	—	2	1	no	—
87	#117×C₈₉	C₂×C₄	1	2	yes	—
88	#117×C₈₉	C₂×C₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₈₉	—	2	1	no	—
92	#97×C₈₉	—	2	4	no	—
93	C₄×C₈×C₈₉	—	2	4	no	—
94	C₂²×Dic₈₉	—	2	2	no	—
95	C₂²×Dic₈₉	C₄²	1	4	yes	—
96	#13083558	—	2	2	no	—
97	#13083558	—	2	2	no	—
98	#13083558	—	2	2	no	—
99	#13083558	—	2	2	no	—
100	#13083558	—	2	2	no	—
101	#13083558	—	2	2	no	—
102	#13083558	—	2	2	no	—
103	#13083558	C₄²	1	4	yes	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	2	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	C₄²	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	C₂²⋊Dic₈₉	—	2	2	no	—
115	C₂²⋊Dic₈₉	—	2	2	no	—
116	C₂²⋊Dic₈₉	—	2	2	no	—
117	C₂²⋊Dic₈₉	C₄²	1	4	yes	—
118	C₄×Dic₈₉	—	2	2	no	—
119	C₄×Dic₈₉	—	2	2	no	—
120	C₄×Dic₈₉	—	2	2	no	—
121	C₄×Dic₈₉	—	2	2	no	—
122	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	—	2	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂×Q₈	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	M₁₆×C₈₉	—	2	2	no	—
139	M₁₆×C₈₉	—	2	2	no	—
140	M₁₆×C₈₉	—	2	2	no	—
141	M₁₆×C₈₉	C₄²	1	4	yes	—
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	C₄²	1	2	yes	—
146	C₂×C₈×C₈₉	C₄²	1	2	yes	—
147	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
149	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
152	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
154	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
155	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
156	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
157	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
158	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
159	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
161	C₄⋊C₄×C₈₉	—	2	2	no	—
162	C₄⋊C₄×C₈₉	—	2	2	no	—
163	C₂²⋊C₄×C₈₉	—	2	2	no	—
164	C₂²⋊C₄×C₈₉	C₄²	1	4	yes	—
165	C₄²×C₈₉	—	2	2	no	—
166	C₄²×C₈₉	—	2	2	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
169	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
171	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂³×C₈₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₈₉	—	2	4	no	—
176	C₂×C₄×C₈₉	—	4	4	no	—
177	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
192	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
205	C₂×Dic₈₉	—	2	4	no	—
206	C₂×Dic₈₉	—	2	4	no	—
207	C₂×Dic₈₉	—	4	4	no	—
208	C₂×Dic₈₉	—	4	4	no	—
209	C₈×C₈₉	—	2	4	no	—
210	C₈×C₈₉	#95	1	2	yes	—
211	C₈×C₈₉	#95	1	2	yes	—
212	C₈×C₈₉	#95	1	2	yes	—
213	C₈×C₈₉	#95	1	2	yes	—
214	#10623494	—	2	4	no	—
215	#10623494	—	2	4	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	C₄³	1	1	yes	characteristic
224	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×C₈₉	C₄×C₂²⋊C₄	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	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
230	C₄×C₈₉	—	4	4	no	—
231	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
232	C₄×C₈₉	#376	1	1	yes	characteristic
233	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
234	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
236	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
239	Dic₈₉	—	4	4	no	—
240	Dic₈₉	—	4	4	no	—
241	#10711	—	89	1	no	maximal, Sylow
242	C₂×C₈₉	—	2	1	no	—
243	C₂×C₈₉	—	2	1	no	—
244	C₂×C₈₉	—	2	1	no	—
245	C₂×C₈₉	—	2	1	no	—
246	C₂×C₈₉	—	2	1	no	—
247	C₂×C₈₉	—	2	1	no	—
248	C₂×C₈₉	C₄×#95	1	1	yes	characteristic
249	C₂×C₈₉	#1757	1	2	yes	—
250	C₂×#405	—	89	1	no	—
251	C₂×#405	—	89	1	no	—
252	C₂×#405	D₈₉	1	1	yes	characteristic
253	C₂×#344	—	89	1	no	—
254	C₂×#344	—	89	1	no	—
255	#1742	—	89	1	no	—
256	#1740	—	89	1	no	—
257	C₈₉	#10711	1	1	yes	characteristic, complemented, Sylow
258	C₂²×M₁₆	—	89	1	no	—
259	C₂²×M₁₆	—	89	1	no	—
260	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
261	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
262	C₂×#117	—	89	1	no	—
263	C₂×#117	—	89	1	no	—
264	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
265	#405	—	2	2	no	—
266	#405	—	89	4	no	—
267	#405	—	178	1	no	—
268	#405	—	178	1	no	—
269	#405	—	178	1	no	—
270	#405	—	178	2	no	—
271	#405	—	178	1	no	—
272	#405	Dic₈₉	1	4	yes	complemented
273	C₂×#97	—	2	1	no	—
274	C₂×#97	—	89	2	no	—
275	C₂×#97	—	178	1	no	—
276	C₂×C₄×C₈	—	2	1	no	—
277	C₂×C₄×C₈	—	89	2	no	—
278	C₂×C₄×C₈	—	178	1	no	—
279	#344	—	89	4	no	—
280	#344	—	89	4	no	—
281	#343	—	89	4	no	—
282	#342	—	89	4	no	—
283	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	89	2	no	—
288	C₂×M₁₆	—	89	2	no	—
289	C₂×M₁₆	—	89	2	no	—
290	C₂×M₁₆	—	89	2	no	—
291	C₂×M₁₆	—	89	2	no	—
292	C₂×M₁₆	—	178	1	no	—
293	C₂×M₁₆	—	178	1	no	—
294	C₂×M₁₆	—	178	1	no	—
295	C₂×M₁₆	—	178	1	no	—
296	C₂×M₁₆	—	178	1	no	—
297	C₂×M₁₆	—	178	1	no	—
298	C₂×M₁₆	—	178	1	no	—
299	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
300	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
301	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	89	2	no	—
304	C₂²×C₈	—	178	1	no	—
305	C₂²×C₈	Dic₁₇₈	1	2	yes	—
306	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
307	C₂²×C₈	C₄×D₈₉	1	2	yes	—
308	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
310	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
311	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
312	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
313	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
314	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	89	2	no	—
318	#117	—	89	2	no	—
319	#117	—	178	1	no	—
320	#117	—	178	1	no	—
321	#117	—	178	1	no	—
322	#117	—	178	1	no	—
323	#117	—	178	1	no	—
324	#117	—	178	1	no	—
325	#117	C₄×D₈₉	1	2	yes	—
326	#117	C₂×Dic₈₉	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	89	2	no	—
329	C₂×C₄⋊C₄	—	178	1	no	—
330	C₂×C₂²⋊C₄	—	89	2	no	—
331	C₂×C₂²⋊C₄	—	89	2	no	—
332	C₂×C₂²⋊C₄	C₄×D₈₉	1	2	yes	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	89	2	no	—
335	C₂×C₄²	—	178	1	no	—
336	#97	—	2	4	no	—
337	#97	—	178	2	no	—
338	#97	—	178	2	no	—
339	#97	—	178	4	no	—
340	C₄×C₈	—	2	4	no	—
341	C₄×C₈	—	178	2	no	—
342	C₄×C₈	—	178	4	no	—
343	C₄×C₈	—	178	2	no	—
344	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	89	4	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
357	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
358	C₂²×C₄	#13083574	1	1	yes	characteristic
359	C₂²×C₄	#13083574	1	1	yes	characteristic
360	C₂²×C₄	#13083574	1	1	yes	characteristic
361	C₂²×C₄	#13083574	1	1	yes	characteristic
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	89	4	no	—
366	M₁₆	—	178	2	no	—
367	M₁₆	—	178	2	no	—
368	M₁₆	—	178	2	no	—
369	M₁₆	—	178	2	no	—
370	M₁₆	—	178	2	no	—
371	M₁₆	—	178	2	no	—
372	M₁₆	—	178	2	no	—
373	M₁₆	C₄×Dic₈₉	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	89	4	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	C₄×Dic₈₉	1	2	yes	—
384	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
385	C₂×C₈	#13083551	1	1	yes	characteristic
386	C₂×C₈	#13083551	1	2	yes	—
387	C₂×C₈	#13083551	1	2	yes	—
388	C₂×C₈	#13083551	1	1	yes	characteristic
389	C₂×C₈	#13083551	1	1	yes	characteristic
390	C₂×C₈	#13083551	1	1	yes	characteristic
391	C₂×C₈	C₂²⋊Dic₈₉	1	2	yes	—
392	C₂×C₈	C₂²⋊Dic₈₉	1	2	yes	—
393	C₂×C₈	#13083553	1	2	yes	—
394	C₂×C₈	#13083553	1	2	yes	—
395	C₂×C₈	#13083553	1	2	yes	—
396	C₂×C₈	#13083553	1	2	yes	—
397	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
398	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	178	2	no	—
402	C₄⋊C₄	—	178	2	no	—
403	C₄⋊C₄	—	178	2	no	—
404	C₄⋊C₄	—	178	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	89	4	no	—
407	C₂²⋊C₄	—	178	2	no	—
408	C₂²⋊C₄	—	178	2	no	—
409	C₂²⋊C₄	—	178	2	no	—
410	C₂²⋊C₄	C₄×Dic₈₉	1	4	yes	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	178	2	no	—
414	C₄²	—	178	2	no	—
415	C₄²	—	178	2	no	—
416	C₄²	—	178	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	C₄²×D₈₉	1	1	yes	characteristic
419	C₂³	C₄²×D₈₉	1	1	yes	characteristic
420	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
421	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
422	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
423	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
424	C₂³	C₄×Dic₁₇₈	1	1	yes	characteristic
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	356	4	no	—
428	C₂×C₄	—	356	4	no	—
429	C₂×C₄	—	178	4	no	—
430	C₂×C₄	—	178	4	no	—
431	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
432	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
436	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
437	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
438	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
439	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
440	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
441	C₂×C₄	#15667969	1	1	yes	characteristic
442	C₂×C₄	#15667969	1	1	yes	characteristic
443	C₂×C₄	#15667969	1	1	yes	characteristic
444	C₂×C₄	#15667969	1	1	yes	characteristic
445	C₂×C₄	#15667971	1	1	yes	characteristic
446	C₂×C₄	#15667971	1	1	yes	characteristic
447	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
450	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
451	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
454	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
455	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
456	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
457	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
458	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
459	C₈	—	2	4	no	—
460	C₈	—	178	4	no	—
461	C₈	—	178	4	no	—
462	C₈	#15667919	1	2	yes	—
463	C₈	#15667919	1	2	yes	—
464	C₈	#15667919	1	2	yes	—
465	C₈	#15667919	1	2	yes	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	C₄²×Dic₈₉	1	1	yes	characteristic
474	C₂²	C₄×C₂²⋊Dic₈₉	1	1	yes	characteristic
475	C₂²	C₄×#13083551	1	1	yes	characteristic
476	C₂²	C₄×#13083551	1	1	yes	characteristic
477	C₂²	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
478	C₂²	C₄×#13083553	1	1	yes	characteristic
479	C₂²	C₄×#13083553	1	1	yes	characteristic
480	C₄	—	4	4	no	—
481	C₄	—	356	4	no	—
482	C₄	—	356	4	no	—
483	C₄	C₂×#15667919	1	1	yes	characteristic
484	C₄	#19151444	1	1	yes	characteristic
485	C₄	C₄×C₂²⋊Dic₈₉	1	1	yes	characteristic
486	C₄	C₄×#13083551	1	1	yes	characteristic
487	C₄	C₄×#13083551	1	1	yes	characteristic
488	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
489	C₄	C₄×#13083553	1	1	yes	characteristic
490	C₄	C₄×#13083553	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	C₄×#15667919	1	1	yes	characteristic
498	C₂	#26020053	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	#13083551
commutator	C₂²×C₈₉	C₄³
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#405×C₈₉	C₂
socle	C₂²×C₈₉	C₄×C₂²⋊C₄
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#405	D₈₉
hypocenter	C₈₉	#10711
LCS	G ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
17. #19151553	C₄	semidirect
19. C₂×#15667922	C₄	semidirect
21. C₂×C₈×Dic₈₉	C₄	semidirect
22. #19151370	C₄	semidirect
23. #19151368	C₄	semidirect
24. #19151366	C₄	semidirect
30. #405×C₈₉	C₄	semidirect
257. C₈₉	#10711	semidirect
272. #405	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151553	2
C₂×#19151370	2
C₂×#19151368	2
#26019990	2
#26019984	2
C₂×#405×C₈₉	2
#10711	89