Subgroups — #18073068

Order 4864.

506 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926498	C₂	1	1	yes	maximal, characteristic
2	#14561947	C₂	1	2	yes	maximal
3	#14561918	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561479	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64515	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₉	C₄	1	1	yes	characteristic
8	C₂×#10597318	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	2	yes	—
10	#11926498	—	2	1	no	—
11	#11926498	—	2	1	no	—
12	#11926498	—	2	1	no	—
13	#11926498	—	2	1	no	—
14	C₂×#10597260	C₂²	1	1	yes	characteristic
15	C₂×#10597272	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
17	#11926269	C₄	1	4	yes	—
18	#11926267	C₄	1	4	yes	—
19	#11926265	—	2	1	no	—
20	C₈×C₁₉⋊C₈	—	2	1	no	—
21	C₁₉×#431	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#322	—	2	1	no	—
24	C₈²×C₁₉	—	2	1	no	—
25	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₂×#64515	—	2	1	no	—
35	C₂×#64515	—	2	1	no	—
36	C₂×#64515	—	2	2	no	—
37	C₂×#64515	C₈	1	4	yes	complemented
38	C₂×C₈×D₁₉	—	2	1	no	—
39	C₂×C₈×D₁₉	—	2	1	no	—
40	C₂×C₈×D₁₉	—	2	2	no	—
41	C₂×C₈×D₁₉	C₈	1	4	yes	complemented
42	#10597318	—	2	1	no	—
43	#10597318	—	2	1	no	—
44	#10597318	—	2	2	no	—
45	C₁₉×C₄⋊C₈	—	2	2	no	—
46	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
47	C₄×C₈×C₁₉	—	2	2	no	—
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
53	#10597272	—	2	1	no	—
54	#10597272	—	2	1	no	—
55	C₈×Dic₁₉	—	2	1	no	—
56	C₈×Dic₁₉	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	#10597260	—	2	1	no	—
59	#10597260	—	2	1	no	—
60	C₄×C₁₉⋊C₈	—	2	2	no	—
61	C₂³×D₁₉	C₄²	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₉	C₄²	1	1	yes	characteristic
65	C₂²×Dic₁₉	C₄²	1	2	yes	—
66	C₂×C₄×D₁₉	—	2	1	no	—
67	C₂×C₄×D₁₉	—	2	1	no	—
68	C₂×C₄×D₁₉	—	2	1	no	—
69	C₂×C₄×D₁₉	—	2	1	no	—
70	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
71	C₂×C₄×D₁₉	C₂×C₈	1	2	yes	—
72	C₂×C₈×C₁₉	—	2	4	no	—
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
78	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
79	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
80	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	#41	1	2	yes	—
84	(C₂×D₁₉)⋊C₄	—	2	2	no	—
85	(C₂×D₁₉)⋊C₄	—	2	2	no	—
86	Dic₁₉⋊C₄	—	2	2	no	—
87	Dic₁₉⋊C₄	—	2	2	no	—
88	C₄×Dic₁₉	—	2	1	no	—
89	C₄×Dic₁₉	—	2	1	no	—
90	C₂×C₁₉⋊C₈	—	2	1	no	—
91	C₂×C₁₉⋊C₈	—	2	1	no	—
92	C₂×C₁₉⋊C₈	—	2	1	no	—
93	C₂×C₁₉⋊C₈	—	2	1	no	—
94	C₂×C₁₉⋊C₈	—	2	4	no	—
95	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
96	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
97	#64515	—	2	4	no	—
98	#64515	—	2	4	no	—
99	C₈×D₁₉	—	2	4	no	—
100	C₈×D₁₉	—	2	4	no	—
101	#8156	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
103	C₂²×D₁₉	—	2	1	no	—
104	C₂²×D₁₉	—	2	1	no	—
105	C₂²×D₁₉	—	4	2	no	—
106	C₂²×D₁₉	C₄×C₈	1	2	yes	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
113	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
116	C₂×Dic₁₉	—	2	1	no	—
117	C₂×Dic₁₉	—	2	1	no	—
118	C₂×Dic₁₉	—	2	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	C₂×Dic₁₉	C₄×C₈	1	2	yes	—
121	C₄×D₁₉	—	2	2	no	—
122	C₄×D₁₉	—	2	2	no	—
123	C₄×D₁₉	—	2	2	no	—
124	C₄×D₁₉	—	2	2	no	—
125	C₈×C₁₉	—	4	4	no	—
126	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
127	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
128	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
129	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
130	C₁₉⋊C₈	—	2	2	no	—
131	C₁₉⋊C₈	—	2	2	no	—
132	C₁₉⋊C₈	—	4	4	no	—
133	C₂×#405	—	19	1	no	—
134	#1458	—	19	2	no	—
135	#1450	—	19	1	no	—
136	#1450	D₁₉	1	1	yes	characteristic, complemented
137	#1281	—	19	2	no	—
138	C₂²×C₁₉	—	2	2	no	—
139	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
141	C₂²×C₁₉	C₄×M₁₆	1	1	yes	characteristic
142	C₂×D₁₉	—	2	2	no	—
143	C₂×D₁₉	—	4	2	no	—
144	C₂×D₁₉	—	4	2	no	—
145	C₂×D₁₉	—	4	2	no	—
146	C₄×C₁₉	—	2	2	no	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
149	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
150	C₄×C₁₉	#431	1	1	yes	characteristic
151	C₄×C₁₉	#431	1	1	yes	characteristic
152	Dic₁₉	—	2	2	no	—
153	Dic₁₉	—	4	2	no	—
154	C₂²×M₁₆	—	19	1	no	—
155	C₂³×C₈	—	19	1	no	—
156	C₂×#117	—	19	1	no	—
157	#431	—	19	2	no	—
158	#431	C₂×D₁₉	1	2	yes	—
159	#405	—	38	1	no	—
160	#405	—	38	1	no	—
161	#405	—	38	1	no	—
162	#405	—	38	1	no	—
163	C₂×#97	—	19	1	no	—
164	C₂×#97	—	19	1	no	—
165	C₂×C₄×C₈	—	19	1	no	—
166	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
167	#324	—	19	4	no	—
168	#323	—	19	4	no	—
169	#322	—	2	1	no	—
170	#322	—	38	1	no	—
171	C₈²	—	2	1	no	—
172	C₈²	—	38	1	no	—
173	C₂×C₁₉	—	2	1	no	—
174	C₂×C₁₉	—	2	1	no	—
175	C₂×C₁₉	C₄×C₂²⋊C₈	1	1	yes	characteristic
176	C₂×C₁₉	#1757	1	2	yes	—
177	D₁₉	—	4	2	no	—
178	C₂³×C₄	—	19	1	no	—
179	C₂×M₁₆	—	19	4	no	—
180	C₂×M₁₆	—	38	2	no	—
181	C₂×M₁₆	—	38	1	no	—
182	C₂×M₁₆	—	38	1	no	—
183	C₂²×C₈	—	19	1	no	—
184	C₂²×C₈	—	19	1	no	—
185	C₂²×C₈	—	19	4	no	—
186	C₂²×C₈	—	38	2	no	—
187	C₂²×C₈	—	38	1	no	—
188	C₂²×C₈	—	38	1	no	—
189	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
190	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
191	#117	—	38	1	no	—
192	#117	—	38	2	no	—
193	#117	—	38	1	no	—
194	C₂×C₄⋊C₄	—	19	2	no	—
195	C₂×C₂²⋊C₄	—	19	2	no	—
196	C₂×C₄²	—	19	1	no	—
197	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
198	C₄⋊C₈	—	2	2	no	—
199	C₄⋊C₈	—	38	2	no	—
200	C₂²⋊C₈	—	19	4	no	—
201	C₂²⋊C₈	C₄×D₁₉	1	4	yes	—
202	#97	—	38	1	no	—
203	#97	—	38	1	no	—
204	#97	—	38	1	no	—
205	#97	—	38	1	no	—
206	C₄×C₈	—	2	2	no	—
207	C₄×C₈	—	38	1	no	—
208	C₄×C₈	—	38	1	no	—
209	C₄×C₈	—	38	2	no	—
210	C₄×C₈	D₇₆	1	1	yes	characteristic
211	C₄×C₈	D₇₆	1	1	yes	characteristic
212	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
213	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
214	C₁₉	#8156	1	1	yes	characteristic, complemented, Sylow
215	C₂⁴	—	19	1	no	—
216	C₂²×C₄	—	19	1	no	—
217	C₂²×C₄	—	19	2	no	—
218	C₂²×C₄	—	19	2	no	—
219	C₂²×C₄	—	19	2	no	—
220	C₂²×C₄	—	38	1	no	—
221	C₂²×C₄	—	38	1	no	—
222	C₂²×C₄	—	38	1	no	—
223	C₂²×C₄	—	38	1	no	—
224	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
225	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
226	M₁₆	—	38	4	no	—
227	M₁₆	—	38	4	no	—
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	19	2	no	—
230	C₂×C₈	—	19	2	no	—
231	C₂×C₈	—	38	1	no	—
232	C₂×C₈	—	38	1	no	—
233	C₂×C₈	—	38	1	no	—
234	C₂×C₈	—	38	1	no	—
235	C₂×C₈	—	38	4	no	—
236	C₂×C₈	—	38	4	no	—
237	C₂×C₈	—	38	4	no	—
238	C₂×C₈	C₈×D₁₉	1	2	yes	—
239	C₂×C₈	C₈×D₁₉	1	2	yes	—
240	C₂×C₈	#64515	1	2	yes	—
241	C₂×C₈	#64515	1	2	yes	—
242	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
243	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
244	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
245	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
246	C₄⋊C₄	—	38	2	no	—
247	C₄⋊C₄	—	38	2	no	—
248	C₂²⋊C₄	—	38	2	no	—
249	C₂²⋊C₄	—	38	2	no	—
250	C₄²	—	38	1	no	—
251	C₄²	—	38	1	no	—
252	C₄²	C₂×D₇₆	1	1	yes	characteristic
253	C₄²	#64541	1	2	yes	—
254	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂³	—	19	2	no	—
256	C₂³	—	38	1	no	—
257	C₂³	—	38	1	no	—
258	C₂³	—	76	2	no	—
259	C₂³	C₄²×D₁₉	1	1	yes	characteristic
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	19	2	no	—
262	C₂×C₄	—	38	1	no	—
263	C₂×C₄	—	38	1	no	—
264	C₂×C₄	—	38	2	no	—
265	C₂×C₄	—	38	2	no	—
266	C₂×C₄	—	38	2	no	—
267	C₂×C₄	—	38	2	no	—
268	C₂×C₄	—	38	2	no	—
269	C₂×C₄	—	76	2	no	—
270	C₂×C₄	#10597318	1	1	yes	characteristic
271	C₂×C₄	C₄×D₇₆	1	2	yes	—
272	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
273	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
274	C₂×C₄	C₂×#64515	1	1	yes	characteristic
275	C₂×C₄	C₂×#64515	1	1	yes	characteristic
276	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
278	C₈	—	4	4	no	—
279	C₈	—	38	2	no	—
280	C₈	—	38	2	no	—
281	C₈	—	76	4	no	—
282	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
283	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
284	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
285	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
286	C₂²	—	2	2	no	—
287	C₂²	—	38	2	no	—
288	C₂²	—	76	2	no	—
289	C₂²	—	76	2	no	—
290	C₂²	—	76	2	no	—
291	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
292	C₂²	C₄×C₈×D₁₉	1	1	yes	characteristic
293	C₂²	C₄×#64515	1	1	yes	characteristic
294	C₄	—	2	2	no	—
295	C₄	—	2	2	no	—
296	C₄	—	38	2	no	—
297	C₄	—	76	2	no	—
298	C₄	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
299	C₄	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
300	C₄	#11926595	1	1	yes	characteristic
301	C₄	#11926595	1	1	yes	characteristic
302	C₂	—	2	1	no	—
303	C₂	—	2	1	no	—
304	C₂	—	76	2	no	—
305	C₂	C₄×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
306	C₂	#14563436	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	(C₂×D₁₉)⋊C₄
commutator	C₂²×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1450	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1450	D₁₉
hypocenter	C₁₉	#8156
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1450

Complements

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

N	H ≅ G/N	type
3. #14561918	C₂	semidirect
4. #14561479	C₂	semidirect
5. C₁₉×#1450	C₂	semidirect
37. C₂×#64515	C₈	semidirect
41. C₂×C₈×D₁₉	C₈	semidirect
136. #1450	D₁₉	semidirect
214. C₁₉	#8156	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926498	2
#14561947	2
#14561918	2
#14561479	2
C₁₉×#1450	2
#8156	19