Subgroups — #36462689

Order 22784.

886 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×#19151360	C₂	1	2	yes	maximal
2	C₂×#19151360	C₂	1	2	yes	maximal
3	C₂×#19151353	C₂	1	1	yes	maximal, characteristic
4	#26018482	C₂	1	1	yes	maximal, characteristic
5	C₂×#384×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×#10623494	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
9	C₂×#15667919	—	2	1	no	—
10	C₂×#15667919	—	2	1	no	—
11	#19151360	—	2	4	no	—
12	#19151360	—	2	4	no	—
13	#19151353	C₄	1	4	yes	complemented
14	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
18	#384×C₈₉	—	2	4	no	—
19	C₂³×Dic₈₉	—	2	1	no	—
20	C₂³×Dic₈₉	—	2	1	no	—
21	C₂²×#10623494	—	2	2	no	—
22	C₂²×#10623494	—	2	2	no	—
23	C₂²×#10623494	—	2	2	no	—
24	C₂²×#10623494	—	2	2	no	—
25	C₂²×#10623494	—	2	2	no	—
26	C₂²×#10623494	—	2	2	no	—
27	C₂²×#10623494	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₈₉	—	2	2	no	—
29	C₂×C₄⋊Dic₈₉	—	2	2	no	—
30	C₂×C₄⋊Dic₈₉	—	2	2	no	—
31	C₂×C₄⋊Dic₈₉	—	2	2	no	—
32	C₂×C₄⋊Dic₈₉	—	2	1	no	—
33	C₂×C₄⋊Dic₈₉	—	2	1	no	—
34	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
35	C₂×C₄⋊Dic₈₉	Q₈	1	2	yes	—
36	#15667919	—	4	2	no	—
37	#15667919	—	4	2	no	—
38	C₂³×C₄×C₈₉	—	2	2	no	—
39	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
50	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
51	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
52	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
53	C₂×C₄⋊C₄×C₈₉	D₄	1	4	yes	—
54	C₂×C₄²×C₈₉	—	2	2	no	—
55	C₂×C₄²×C₈₉	—	2	2	no	—
56	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₈₉	Q₈	1	2	yes	—
58	C₂²×Dic₈₉	—	2	2	no	—
59	C₂²×Dic₈₉	—	2	2	no	—
60	C₂²×Dic₈₉	—	4	1	no	—
61	C₂²×Dic₈₉	—	4	1	no	—
62	C₂²×Dic₈₉	—	4	1	no	—
63	C₂²×Dic₈₉	—	4	1	no	—
64	C₂²×Dic₈₉	—	4	1	no	—
65	C₂²×Dic₈₉	—	4	1	no	—
66	C₂²×Dic₈₉	—	4	1	no	—
67	C₂²×Dic₈₉	—	4	1	no	—
68	C₂²×Dic₈₉	—	4	1	no	—
69	C₂²×Dic₈₉	—	4	1	no	—
70	C₂²×Dic₈₉	—	4	1	no	—
71	C₂²×Dic₈₉	—	4	1	no	—
72	C₂×#10623494	—	2	4	no	—
73	C₂×#10623494	—	2	4	no	—
74	C₂×#10623494	—	2	4	no	—
75	C₂×#10623494	—	4	2	no	—
76	C₂×#10623494	—	4	2	no	—
77	C₂×#10623494	—	4	2	no	—
78	C₂×#10623494	—	4	2	no	—
79	C₄⋊Dic₈₉	—	2	4	no	—
80	C₄⋊Dic₈₉	—	2	4	no	—
81	C₄⋊Dic₈₉	—	4	2	no	—
82	C₄⋊Dic₈₉	—	4	2	no	—
83	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	—	2	1	no	—
85	C₂²×C₄×C₈₉	—	2	1	no	—
86	C₂²×C₄×C₈₉	—	2	1	no	—
87	C₂²×C₄×C₈₉	—	2	1	no	—
88	C₂²×C₄×C₈₉	—	2	1	no	—
89	C₂²×C₄×C₈₉	—	2	1	no	—
90	C₂²×C₄×C₈₉	—	2	1	no	—
91	C₂²×C₄×C₈₉	—	2	1	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	4	2	no	—
94	C₂²×C₄×C₈₉	—	4	2	no	—
95	C₂²×C₄×C₈₉	—	4	2	no	—
96	C₂²×C₄×C₈₉	—	4	2	no	—
97	C₂²×C₄×C₈₉	—	4	2	no	—
98	C₂²×C₄×C₈₉	—	4	2	no	—
99	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₈₉	D₈	1	2	yes	—
102	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
103	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
104	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	#41	1	2	yes	—
111	C₂²×C₄×C₈₉	#41	1	2	yes	—
112	C₂²×C₄×C₈₉	#41	1	2	yes	—
113	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	—	2	4	no	—
116	C₄⋊C₄×C₈₉	—	2	4	no	—
117	C₄⋊C₄×C₈₉	—	4	8	no	—
118	C₄⋊C₄×C₈₉	—	4	8	no	—
119	C₄⋊C₄×C₈₉	—	4	2	no	—
120	C₄⋊C₄×C₈₉	—	4	2	no	—
121	C₄²×C₈₉	—	2	4	no	—
122	C₄²×C₈₉	—	2	4	no	—
123	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₈₉	#120	1	1	yes	characteristic
125	C₂³×C₈₉	#121	1	1	yes	characteristic
126	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₈₉	#123	1	1	yes	characteristic
128	C₂³×C₈₉	#124	1	1	yes	characteristic
129	C₂³×C₈₉	#124	1	1	yes	characteristic
130	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
133	C₂³×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
134	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂³×C₈₉	#137	1	1	yes	characteristic
137	C₂³×C₈₉	#137	1	1	yes	characteristic
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	4	4	no	—
151	C₂×C₄×C₈₉	—	4	4	no	—
152	C₂×C₄×C₈₉	—	4	4	no	—
153	C₂×C₄×C₈₉	—	8	2	no	—
154	C₂×C₄×C₈₉	—	8	2	no	—
155	C₂×C₄×C₈₉	—	8	2	no	—
156	C₂×C₄×C₈₉	—	8	2	no	—
157	C₂×C₄×C₈₉	#106	1	4	yes	—
158	C₂×C₄×C₈₉	#107	1	4	yes	—
159	C₂×C₄×C₈₉	#117	1	2	yes	—
160	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#121	1	2	yes	—
164	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₈₉	#123	1	2	yes	—
167	C₂×C₄×C₈₉	#123	1	2	yes	—
168	C₂×C₄×C₈₉	#124	1	2	yes	—
169	C₂×C₄×C₈₉	#125	1	2	yes	—
170	C₂×C₄×C₈₉	#125	1	2	yes	—
171	C₂×C₄×C₈₉	#125	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#126	1	2	yes	—
173	C₂×C₄×C₈₉	#126	1	2	yes	—
174	C₂×C₄×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
175	C₂×Dic₈₉	—	4	2	no	—
176	C₂×Dic₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	4	2	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	4	2	no	—
181	C₂×Dic₈₉	—	8	1	no	—
182	C₂×Dic₈₉	—	8	1	no	—
183	C₂×Dic₈₉	—	8	1	no	—
184	C₂×Dic₈₉	—	8	1	no	—
185	C₂×Dic₈₉	—	8	1	no	—
186	C₂×Dic₈₉	—	8	1	no	—
187	C₂×Dic₈₉	—	8	1	no	—
188	C₂×Dic₈₉	—	8	1	no	—
189	#10623494	—	4	4	no	—
190	C₂²×C₈₉	#382	1	1	yes	characteristic
191	C₂²×C₈₉	#385	1	1	yes	characteristic
192	C₂²×C₈₉	#389	1	1	yes	characteristic
193	C₂²×C₈₉	#393	1	1	yes	characteristic
194	C₂²×C₈₉	#394	1	1	yes	characteristic
195	C₂²×C₈₉	#397	1	1	yes	characteristic
196	C₂²×C₈₉	#400	1	1	yes	characteristic
197	C₂²×C₈₉	C₂×#106	1	1	yes	characteristic
198	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
199	C₂²×C₈₉	#428	1	1	yes	characteristic
200	C₂²×C₈₉	#428	1	1	yes	characteristic
201	C₂²×C₈₉	#447	1	1	yes	characteristic
202	C₂²×C₈₉	#448	1	1	yes	characteristic
203	C₂²×C₈₉	#450	1	1	yes	characteristic
204	C₂²×C₈₉	#451	1	1	yes	characteristic
205	C₂²×C₈₉	#459	1	1	yes	characteristic
206	C₂²×C₈₉	#460	1	1	yes	characteristic
207	C₂²×C₈₉	#461	1	1	yes	characteristic
208	C₂²×C₈₉	#462	1	1	yes	characteristic
209	C₂²×C₈₉	#474	1	1	yes	characteristic
210	C₂²×C₈₉	#475	1	1	yes	characteristic
211	C₂²×C₈₉	#476	1	1	yes	characteristic
212	C₂²×C₈₉	#477	1	1	yes	characteristic
213	C₂²×C₈₉	#480	1	1	yes	characteristic
214	C₂²×C₈₉	#481	1	1	yes	characteristic
215	C₂²×C₈₉	#483	1	1	yes	characteristic
216	C₂²×C₈₉	#484	1	1	yes	characteristic
217	C₂²×C₈₉	#486	1	1	yes	characteristic
218	C₂²×C₈₉	#486	1	1	yes	characteristic
219	C₂²×C₈₉	#487	1	1	yes	characteristic
220	C₂²×C₈₉	#487	1	1	yes	characteristic
221	C₂²×C₈₉	#489	1	1	yes	characteristic
222	C₂²×C₈₉	#489	1	1	yes	characteristic
223	C₂²×C₈₉	#490	1	1	yes	characteristic
224	C₂²×C₈₉	#491	1	1	yes	characteristic
225	C₄×C₈₉	—	2	4	no	—
226	C₄×C₈₉	—	2	4	no	—
227	C₄×C₈₉	—	8	4	no	—
228	C₄×C₈₉	#387	1	2	yes	—
229	C₄×C₈₉	#388	1	2	yes	—
230	C₄×C₈₉	#398	1	2	yes	—
231	C₄×C₈₉	#400	1	2	yes	—
232	Dic₈₉	—	8	2	no	—
233	Dic₈₉	—	8	2	no	—
234	#11267	—	89	1	no	maximal, Sylow
235	C₂×C₈₉	#1442	1	1	yes	characteristic
236	C₂×C₈₉	#1834	1	1	yes	characteristic
237	C₂×C₈₉	#1836	1	1	yes	characteristic
238	C₂×C₈₉	#1852	1	1	yes	characteristic
239	C₂×C₈₉	#1853	1	1	yes	characteristic
240	C₂×C₈₉	#1947	1	1	yes	characteristic
241	C₂×C₈₉	#1948	1	1	yes	characteristic
242	C₂×C₈₉	#2023	1	1	yes	characteristic
243	C₂×C₈₉	#2024	1	1	yes	characteristic
244	C₂×C₈₉	#2041	1	1	yes	characteristic
245	C₂×C₈₉	#2043	1	1	yes	characteristic
246	C₂×C₈₉	#2071	1	1	yes	characteristic
247	C₂×C₈₉	#2072	1	1	yes	characteristic
248	C₂×C₈₉	#2099	1	1	yes	characteristic
249	C₂×C₈₉	#2100	1	1	yes	characteristic
250	C₂×#384	D₈₉	1	1	yes	characteristic
251	C₂×#340	—	89	2	no	—
252	C₂×#340	—	89	2	no	—
253	C₂×#336	—	89	1	no	—
254	C₄⋊#95	—	89	1	no	—
255	C₈₉	#11267	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₈	—	89	2	no	—
257	C₂²×C₄⋊C₄	—	2	1	no	—
258	C₂²×C₄⋊C₄	—	2	1	no	—
259	C₂²×C₄⋊C₄	—	89	1	no	—
260	C₂²×C₄⋊C₄	—	89	1	no	—
261	C₂²×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
262	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
263	#384	—	2	4	no	—
264	C₂×#95	—	178	1	no	—
265	C₂×#95	—	178	1	no	—
266	#340	—	178	4	no	—
267	#340	—	178	4	no	—
268	#336	—	89	4	no	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	178	1	no	—
271	C₂³×C₄	—	178	1	no	—
272	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
273	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
275	C₂²×C₈	—	89	4	no	—
276	C₂²×C₈	—	178	2	no	—
277	C₂²×C₈	—	178	2	no	—
278	C₂²×C₈	—	178	2	no	—
279	C₂²×C₈	—	178	2	no	—
280	C₂²×C₈	—	178	2	no	—
281	C₂²×C₈	—	178	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	4	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	4	2	no	—
290	C₂×C₄⋊C₄	—	4	2	no	—
291	C₂×C₄⋊C₄	—	4	2	no	—
292	C₂×C₄⋊C₄	—	4	2	no	—
293	C₂×C₄⋊C₄	—	89	2	no	—
294	C₂×C₄⋊C₄	—	89	2	no	—
295	C₂×C₄⋊C₄	—	178	1	no	—
296	C₂×C₄⋊C₄	—	178	1	no	—
297	C₂×C₄⋊C₄	—	178	2	no	—
298	C₂×C₄⋊C₄	—	178	2	no	—
299	C₂×C₄⋊C₄	—	178	2	no	—
300	C₂×C₄⋊C₄	—	178	2	no	—
301	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	4	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	Dic₁₇₈	1	2	yes	—
305	C₂×C₄²	C₄×D₈₉	1	2	yes	—
306	#95	—	356	2	no	—
307	#95	—	356	2	no	—
308	C₂⁴	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	356	1	no	—
325	C₂²×C₄	—	356	1	no	—
326	C₂²×C₄	—	356	1	no	—
327	C₂²×C₄	—	356	1	no	—
328	C₂²×C₄	—	356	1	no	—
329	C₂²×C₄	—	356	1	no	—
330	C₂²×C₄	—	356	1	no	—
331	C₂²×C₄	—	356	1	no	—
332	C₂²×C₄	—	356	1	no	—
333	C₂²×C₄	—	356	1	no	—
334	C₂²×C₄	—	356	1	no	—
335	C₂²×C₄	—	356	1	no	—
336	C₂²×C₄	—	178	2	no	—
337	C₂²×C₄	—	178	2	no	—
338	C₂²×C₄	#13083553	1	2	yes	—
339	C₂²×C₄	#13083553	1	2	yes	—
340	C₂²×C₄	#13083559	1	2	yes	—
341	C₂²×C₄	#13083561	1	2	yes	—
342	C₂²×C₄	#13083562	1	2	yes	—
343	C₂²×C₄	#13083564	1	2	yes	—
344	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
347	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
349	C₂²×C₄	#13083573	1	2	yes	—
350	C₂²×C₄	#13083573	1	1	yes	characteristic
351	C₂²×C₄	#13083574	1	2	yes	—
352	C₂²×C₄	#13083575	1	2	yes	—
353	C₂²×C₄	#13083575	1	1	yes	characteristic
354	C₂×C₈	—	356	2	no	—
355	C₂×C₈	—	356	2	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	356	2	no	—
358	C₂×C₈	—	178	4	no	—
359	C₂×C₈	—	178	4	no	—
360	C₂×C₈	—	178	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	8	no	—
364	C₄⋊C₄	—	4	8	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	356	2	no	—
368	C₄⋊C₄	—	356	2	no	—
369	C₄⋊C₄	—	178	4	no	—
370	C₄⋊C₄	—	178	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	4	no	—
373	C₂³	C₂×#13083553	1	1	yes	characteristic
374	C₂³	#15667981	1	1	yes	characteristic
375	C₂³	#15667983	1	1	yes	characteristic
376	C₂³	#15667988	1	1	yes	characteristic
377	C₂³	#15667995	1	1	yes	characteristic
378	C₂³	#15667999	1	1	yes	characteristic
379	C₂³	#15668001	1	1	yes	characteristic
380	C₂³	C₂×#13083559	1	1	yes	characteristic
381	C₂³	C₂×#13083561	1	1	yes	characteristic
382	C₂³	C₂×#13083562	1	1	yes	characteristic
383	C₂³	C₂×#13083564	1	1	yes	characteristic
384	C₂³	#15668038	1	1	yes	characteristic
385	C₂³	#15668038	1	1	yes	characteristic
386	C₂³	#15668043	1	1	yes	characteristic
387	C₂³	#15668043	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	356	2	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	356	2	no	—
412	C₂×C₄	—	356	2	no	—
413	C₂×C₄	—	712	1	no	—
414	C₂×C₄	—	712	1	no	—
415	C₂×C₄	—	712	1	no	—
416	C₂×C₄	—	712	1	no	—
417	C₂×C₄	—	712	1	no	—
418	C₂×C₄	—	712	1	no	—
419	C₂×C₄	—	712	1	no	—
420	C₂×C₄	—	712	1	no	—
421	C₂×C₄	#15667943	1	4	yes	—
422	C₂×C₄	#15667945	1	4	yes	—
423	C₂×C₄	#15667970	1	2	yes	—
424	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
425	C₂×C₄	#15667974	1	1	yes	characteristic
426	C₂×C₄	#15667977	1	1	yes	characteristic
427	C₂×C₄	#15667984	1	2	yes	—
428	C₂×C₄	#15667988	1	2	yes	—
429	C₂×C₄	#15667991	1	2	yes	—
430	C₂×C₄	#15667993	1	2	yes	—
431	C₂×C₄	#15667997	1	2	yes	—
432	C₂×C₄	#15668001	1	2	yes	—
433	C₂×C₄	#15668002	1	2	yes	—
434	C₂×C₄	#15668003	1	2	yes	—
435	C₂×C₄	#15668003	1	1	yes	characteristic
436	C₂×C₄	#15668007	1	2	yes	—
437	C₂×C₄	#15668007	1	2	yes	—
438	C₂×C₄	#15668011	1	1	yes	characteristic
439	C₈	—	356	4	no	—
440	C₂²	#19151463	1	1	yes	characteristic
441	C₂²	#19151471	1	1	yes	characteristic
442	C₂²	#19151494	1	1	yes	characteristic
443	C₂²	#19151509	1	1	yes	characteristic
444	C₂²	#19151512	1	1	yes	characteristic
445	C₂²	#19151524	1	1	yes	characteristic
446	C₂²	#19151536	1	1	yes	characteristic
447	C₂²	C₂×#15667943	1	1	yes	characteristic
448	C₂²	C₂×#15667945	1	1	yes	characteristic
449	C₂²	#19151638	1	1	yes	characteristic
450	C₂²	#19151638	1	1	yes	characteristic
451	C₂²	#19151732	1	1	yes	characteristic
452	C₂²	#19151737	1	1	yes	characteristic
453	C₂²	#19151749	1	1	yes	characteristic
454	C₂²	#19151754	1	1	yes	characteristic
455	C₂²	#19151790	1	1	yes	characteristic
456	C₂²	#19151795	1	1	yes	characteristic
457	C₂²	#19151800	1	1	yes	characteristic
458	C₂²	#19151805	1	1	yes	characteristic
459	C₂²	#19151875	1	1	yes	characteristic
460	C₂²	#19151880	1	1	yes	characteristic
461	C₂²	#19151885	1	1	yes	characteristic
462	C₂²	#19151890	1	1	yes	characteristic
463	C₂²	#19151911	1	1	yes	characteristic
464	C₂²	#19151916	1	1	yes	characteristic
465	C₂²	#19151928	1	1	yes	characteristic
466	C₂²	#19151933	1	1	yes	characteristic
467	C₂²	#19151944	1	1	yes	characteristic
468	C₂²	#19151946	1	1	yes	characteristic
469	C₂²	#19151948	1	1	yes	characteristic
470	C₂²	#19151950	1	1	yes	characteristic
471	C₂²	#19151960	1	1	yes	characteristic
472	C₂²	#19151960	1	1	yes	characteristic
473	C₂²	#19151962	1	1	yes	characteristic
474	C₂²	#19151966	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	4	no	—
478	C₄	—	712	2	no	—
479	C₄	—	712	2	no	—
480	C₄	#19151479	1	2	yes	—
481	C₄	#19151488	1	2	yes	—
482	C₄	#19151531	1	2	yes	—
483	C₄	#19151537	1	2	yes	—
484	C₂	#26018511	1	1	yes	characteristic
485	C₂	#26020379	1	1	yes	characteristic
486	C₂	#26020387	1	1	yes	characteristic
487	C₂	#26020440	1	1	yes	characteristic
488	C₂	#26020445	1	1	yes	characteristic
489	C₂	#26021008	1	1	yes	characteristic
490	C₂	#26021013	1	1	yes	characteristic
491	C₂	#26021385	1	1	yes	characteristic
492	C₂	#26021390	1	1	yes	characteristic
493	C₂	#26021483	1	1	yes	characteristic
494	C₂	#26021495	1	1	yes	characteristic
495	C₂	#26021656	1	1	yes	characteristic
496	C₂	#26021661	1	1	yes	characteristic
497	C₂	#26021809	1	1	yes	characteristic
498	C₂	#26021814	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₈₉
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#384×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂×D₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#384	D₈₉
hypocenter	C₈₉	#11267
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
13. #19151353	C₄	semidirect
255. C₈₉	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151360	2
C₂×#19151353	2
#26018482	2
C₂×#384×C₈₉	2
#11267	89