Subgroups — #18091326

Order 4864.

886 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926306	C₂	1	4	yes	maximal
2	C₂×#11926299	C₂	1	1	yes	maximal, characteristic
3	#14561865	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
7	C₂×C₁₉⋊#95	—	2	1	no	—
8	C₂×C₁₉⋊#95	—	2	1	no	—
9	#11926306	—	2	8	no	—
10	#11926299	—	2	2	no	—
11	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#384	—	2	2	no	—
16	C₁₉×#384	C₄	1	4	yes	complemented
17	C₂³×C₄×C₁₉	—	2	2	no	—
18	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂³×Dic₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₉	—	2	4	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄⋊Dic₁₉	—	2	4	no	—
35	C₂×C₄⋊Dic₁₉	—	2	4	no	—
36	C₂×C₄⋊Dic₁₉	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	D₄	1	4	yes	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₂²×C₁₉⋊C₈	—	2	4	no	—
40	C₂²×C₁₉⋊C₈	—	2	4	no	—
41	C₂²×C₁₉⋊C₈	—	2	2	no	—
42	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
43	C₁₉⋊#95	—	4	2	no	—
44	C₁₉⋊#95	—	4	2	no	—
45	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	4	4	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	D₈	1	2	yes	—
58	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
59	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
65	C₂²×C₄×C₁₉	#41	1	4	yes	—
66	C₂²×C₄×C₁₉	#41	1	2	yes	—
67	C₂²×C₄×C₁₉	#41	1	2	yes	—
68	C₂²×Dic₁₉	—	2	4	no	—
69	C₂²×Dic₁₉	—	4	2	no	—
70	C₂²×Dic₁₉	—	4	2	no	—
71	C₂²×Dic₁₉	—	4	2	no	—
72	C₂²×Dic₁₉	—	4	2	no	—
73	C₂²×Dic₁₉	—	4	2	no	—
74	C₂²×Dic₁₉	—	4	2	no	—
75	C₄⋊C₄×C₁₉	—	2	8	no	—
76	C₄⋊C₄×C₁₉	—	4	8	no	—
77	C₄⋊C₄×C₁₉	—	4	8	no	—
78	C₄⋊C₄×C₁₉	—	4	2	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	—	2	4	no	—
81	C₄²×C₁₉	—	2	4	no	—
82	C₄⋊Dic₁₉	—	2	8	no	—
83	C₄⋊Dic₁₉	—	4	4	no	—
84	C₂×C₁₉⋊C₈	—	2	4	no	—
85	C₂×C₁₉⋊C₈	—	2	8	no	—
86	C₂×C₁₉⋊C₈	—	4	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#11357	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂³×C₁₉	#121	1	2	yes	—
92	C₂³×C₁₉	#123	1	2	yes	—
93	C₂³×C₁₉	#124	1	1	yes	characteristic
94	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
95	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
96	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
97	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₂³×C₁₉	#137	1	2	yes	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	4	no	—
106	C₂×C₄×C₁₉	—	2	4	no	—
107	C₂×C₄×C₁₉	—	2	4	no	—
108	C₂×C₄×C₁₉	—	2	4	no	—
109	C₂×C₄×C₁₉	—	4	4	no	—
110	C₂×C₄×C₁₉	—	4	4	no	—
111	C₂×C₄×C₁₉	—	4	4	no	—
112	C₂×C₄×C₁₉	—	8	4	no	—
113	C₂×C₄×C₁₉	—	8	4	no	—
114	C₂×C₄×C₁₉	#102	1	4	yes	—
115	C₂×C₄×C₁₉	#103	1	4	yes	—
116	C₂×C₄×C₁₉	#117	1	2	yes	—
117	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
119	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
120	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
121	C₂×C₄×C₁₉	#123	1	4	yes	—
122	C₂×C₄×C₁₉	#123	1	2	yes	—
123	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
124	C₂×C₄×C₁₉	#125	1	4	yes	—
125	C₂×C₄×C₁₉	#126	1	4	yes	—
126	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
127	C₂×Dic₁₉	—	4	4	no	—
128	C₂×Dic₁₉	—	4	4	no	—
129	C₂×Dic₁₉	—	4	4	no	—
130	C₂×Dic₁₉	—	8	2	no	—
131	C₂×Dic₁₉	—	8	2	no	—
132	C₂×Dic₁₉	—	8	2	no	—
133	C₂×Dic₁₉	—	8	2	no	—
134	C₁₉⋊C₈	—	4	4	no	—
135	C₂×#384	D₁₉	1	1	yes	characteristic
136	C₂×#340	—	19	4	no	—
137	C₂×#336	—	19	1	no	—
138	C₄⋊#95	—	19	1	no	—
139	C₂²×C₁₉	#381	1	1	yes	characteristic
140	C₂²×C₁₉	#390	1	1	yes	characteristic
141	C₂²×C₁₉	#391	1	1	yes	characteristic
142	C₂²×C₁₉	#397	1	2	yes	—
143	C₂²×C₁₉	#398	1	2	yes	—
144	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
145	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
146	C₂²×C₁₉	#418	1	1	yes	characteristic
147	C₂²×C₁₉	#419	1	1	yes	characteristic
148	C₂²×C₁₉	#459	1	2	yes	—
149	C₂²×C₁₉	#460	1	2	yes	—
150	C₂²×C₁₉	#461	1	2	yes	—
151	C₂²×C₁₉	#462	1	2	yes	—
152	C₂²×C₁₉	#480	1	2	yes	—
153	C₂²×C₁₉	#481	1	2	yes	—
154	C₂²×C₁₉	#483	1	2	yes	—
155	C₂²×C₁₉	#484	1	2	yes	—
156	C₂²×C₁₉	#486	1	1	yes	characteristic
157	C₂²×C₁₉	#487	1	1	yes	characteristic
158	C₂²×C₁₉	#489	1	2	yes	—
159	C₂²×C₁₉	#498	1	1	yes	characteristic
160	C₂²×C₁₉	#500	1	1	yes	characteristic
161	C₂²×C₁₉	#501	1	2	yes	—
162	C₄×C₁₉	—	2	4	no	—
163	C₄×C₁₉	—	2	4	no	—
164	C₄×C₁₉	—	8	4	no	—
165	C₄×C₁₉	#387	1	4	yes	—
166	C₄×C₁₉	#399	1	2	yes	—
167	C₄×C₁₉	#400	1	2	yes	—
168	Dic₁₉	—	8	4	no	—
169	C₂³×C₈	—	19	2	no	—
170	C₂²×C₄⋊C₄	—	2	1	no	—
171	C₂²×C₄⋊C₄	—	2	1	no	—
172	C₂²×C₄⋊C₄	—	19	2	no	—
173	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
174	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
175	#384	—	2	2	no	—
176	#384	Dic₁₉	1	4	yes	complemented
177	C₂×#95	—	38	1	no	—
178	C₂×#95	—	38	1	no	—
179	#340	—	38	8	no	—
180	#336	—	38	2	no	—
181	C₂×C₁₉	#1445	1	1	yes	characteristic
182	C₂×C₁₉	#1823	1	1	yes	characteristic
183	C₂×C₁₉	#1824	1	1	yes	characteristic
184	C₂×C₁₉	#1981	1	1	yes	characteristic
185	C₂×C₁₉	#1982	1	1	yes	characteristic
186	C₂×C₁₉	#1990	1	1	yes	characteristic
187	C₂×C₁₉	#1993	1	1	yes	characteristic
188	C₂×C₁₉	#2071	1	2	yes	—
189	C₂×C₁₉	#2072	1	2	yes	—
190	C₂×C₁₉	#2083	1	2	yes	—
191	C₂×C₁₉	#2084	1	2	yes	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	—	38	2	no	—
194	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
195	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
196	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
197	C₂²×C₈	—	19	4	no	—
198	C₂²×C₈	—	38	4	no	—
199	C₂²×C₈	—	38	4	no	—
200	C₂²×C₈	—	38	2	no	—
201	C₂²×C₈	—	38	2	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	4	no	—
204	C₂×C₄⋊C₄	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	4	4	no	—
208	C₂×C₄⋊C₄	—	4	2	no	—
209	C₂×C₄⋊C₄	—	4	2	no	—
210	C₂×C₄⋊C₄	—	19	4	no	—
211	C₂×C₄⋊C₄	—	38	4	no	—
212	C₂×C₄⋊C₄	—	38	4	no	—
213	C₂×C₄⋊C₄	—	38	2	no	—
214	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
215	C₂×C₄²	—	2	4	no	—
216	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
217	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
218	#95	—	76	2	no	—
219	#95	—	76	2	no	—
220	C₁₉	#11357	1	1	yes	characteristic, complemented, Sylow
221	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	—	4	4	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	38	4	no	—
232	C₂²×C₄	—	76	2	no	—
233	C₂²×C₄	—	76	2	no	—
234	C₂²×C₄	—	76	2	no	—
235	C₂²×C₄	—	76	2	no	—
236	C₂²×C₄	—	76	2	no	—
237	C₂²×C₄	—	76	2	no	—
238	C₂²×C₄	#64525	1	2	yes	—
239	C₂²×C₄	#64526	1	2	yes	—
240	C₂²×C₄	#64527	1	2	yes	—
241	C₂²×C₄	#64528	1	2	yes	—
242	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
243	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
244	C₂²×C₄	#64541	1	4	yes	—
245	C₂²×C₄	D₄×D₁₉	1	2	yes	—
246	C₂²×C₄	#64543	1	2	yes	—
247	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
248	C₂²×C₄	#64545	1	2	yes	—
249	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂×C₈	—	38	4	no	—
252	C₂×C₈	—	38	8	no	—
253	C₂×C₈	—	76	2	no	—
254	C₂×C₈	—	76	4	no	—
255	C₂×C₈	—	76	2	no	—
256	C₄⋊C₄	—	2	8	no	—
257	C₄⋊C₄	—	4	8	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	—	4	2	no	—
260	C₄⋊C₄	—	4	8	no	—
261	C₄⋊C₄	—	38	8	no	—
262	C₄⋊C₄	—	76	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₂³	#10597375	1	2	yes	—
266	C₂³	C₂×#64525	1	1	yes	characteristic
267	C₂³	#10597378	1	2	yes	—
268	C₂³	C₂×#64526	1	1	yes	characteristic
269	C₂³	#10597384	1	2	yes	—
270	C₂³	C₂×#64527	1	1	yes	characteristic
271	C₂³	#10597388	1	2	yes	—
272	C₂³	C₂×#64528	1	1	yes	characteristic
273	C₂³	#10597390	1	1	yes	characteristic
274	C₂³	#10597393	1	1	yes	characteristic
275	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	—	4	4	no	—
287	C₂×C₄	—	8	4	no	—
288	C₂×C₄	—	8	4	no	—
289	C₂×C₄	—	76	4	no	—
290	C₂×C₄	—	76	4	no	—
291	C₂×C₄	—	76	4	no	—
292	C₂×C₄	—	152	2	no	—
293	C₂×C₄	—	152	2	no	—
294	C₂×C₄	—	152	2	no	—
295	C₂×C₄	—	152	2	no	—
296	C₂×C₄	#10597289	1	4	yes	—
297	C₂×C₄	#10597292	1	4	yes	—
298	C₂×C₄	#10597335	1	4	yes	—
299	C₂×C₄	#10597340	1	4	yes	—
300	C₂×C₄	#10597342	1	4	yes	—
301	C₂×C₄	#10597344	1	4	yes	—
302	C₂×C₄	#10597372	1	2	yes	—
303	C₂×C₄	#10597375	1	2	yes	—
304	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
305	C₂×C₄	#10597382	1	1	yes	characteristic
306	C₂×C₄	#10597386	1	1	yes	characteristic
307	C₂×C₄	Q₈×Dic₁₉	1	2	yes	—
308	C₂×C₄	#10597392	1	2	yes	—
309	C₈	—	76	4	no	—
310	C₂²	#11926407	1	1	yes	characteristic
311	C₂²	#11926447	1	1	yes	characteristic
312	C₂²	#11926451	1	1	yes	characteristic
313	C₂²	#11926470	1	2	yes	—
314	C₂²	#11926475	1	2	yes	—
315	C₂²	C₂×#10597289	1	1	yes	characteristic
316	C₂²	C₂×#10597292	1	1	yes	characteristic
317	C₂²	#11926549	1	1	yes	characteristic
318	C₂²	#11926553	1	1	yes	characteristic
319	C₂²	#11926736	1	2	yes	—
320	C₂²	#11926741	1	2	yes	—
321	C₂²	#11926746	1	2	yes	—
322	C₂²	#11926751	1	2	yes	—
323	C₂²	#11926857	1	2	yes	—
324	C₂²	#11926862	1	2	yes	—
325	C₂²	#11926874	1	2	yes	—
326	C₂²	#11926879	1	2	yes	—
327	C₂²	#11926892	1	1	yes	characteristic
328	C₂²	#11926896	1	1	yes	characteristic
329	C₂²	#11926906	1	2	yes	—
330	C₂²	#11926940	1	1	yes	characteristic
331	C₂²	#11926947	1	1	yes	characteristic
332	C₂²	#11926950	1	2	yes	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	8	4	no	—
336	C₄	—	152	4	no	—
337	C₄	#11926430	1	4	yes	—
338	C₄	#11926479	1	2	yes	—
339	C₄	#11926482	1	2	yes	—
340	C₂	#14561903	1	1	yes	characteristic
341	C₂	#14563721	1	1	yes	characteristic
342	C₂	#14563725	1	1	yes	characteristic
343	C₂	#14564559	1	1	yes	characteristic
344	C₂	#14564563	1	1	yes	characteristic
345	C₂	#14564597	1	1	yes	characteristic
346	C₂	#14564609	1	1	yes	characteristic
347	C₂	#14565039	1	2	yes	—
348	C₂	#14565044	1	2	yes	—
349	C₂	#14565107	1	2	yes	—
350	C₂	#14565112	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#384	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#384	D₁₉
hypocenter	C₁₉	#11357
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
16. C₁₉×#384	C₄	semidirect
176. #384	Dic₁₉	semidirect
220. C₁₉	#11357	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926306	2
C₂×#11926299	2
#14561865	2
C₂×C₁₉×#384	2
#11357	19