Subgroups — #14568058

Order 2432.

468 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597344	C₂	1	2	yes	maximal
2	#11926486	C₂	1	2	yes	maximal, complemented
3	#11926473	C₂	1	2	yes	maximal
4	#11926443	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926425	C₂	1	2	yes	maximal, complemented
6	#11926413	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926401	C₂	1	1	yes	maximal, characteristic
8	#11926401	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
18	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
19	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
26	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
27	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
28	#10597344	—	2	8	no	—
29	C₁₉×#95	C₂²	1	2	yes	—
30	C₁₉⋊#95	C₂²	1	1	yes	characteristic
31	C₁₉⋊#95	C₂²	1	1	yes	characteristic
32	C₁₉⋊#95	C₂²	1	2	yes	—
33	C₁₉⋊#95	C₂²	1	2	yes	—
34	C₁₉⋊#95	C₂²	1	2	yes	—
35	C₁₉⋊#95	C₂²	1	2	yes	—
36	C₂³×D₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Dic₁₉	C₂³	1	2	yes	—
44	C₂²×Dic₁₉	C₂³	1	2	yes	—
45	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
47	C₂×C₄×D₁₉	—	2	2	no	—
48	C₂×C₄×D₁₉	—	2	2	no	—
49	C₂×C₄×D₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₄²×C₁₉	—	2	2	no	—
54	(C₂×D₁₉)⋊C₄	—	2	4	no	—
55	(C₂×D₁₉)⋊C₄	—	2	4	no	—
56	(C₂×D₁₉)⋊C₄	—	2	2	no	—
57	(C₂×D₁₉)⋊C₄	D₄	1	4	yes	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	C₄⋊Dic₁₉	—	2	4	no	—
61	Dic₁₉⋊C₄	—	2	4	no	—
62	Dic₁₉⋊C₄	—	2	4	no	—
63	C₄×Dic₁₉	—	2	4	no	—
64	C₄×Dic₁₉	—	2	2	no	—
65	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
66	C₂²×D₁₉	—	2	1	no	—
67	C₂²×D₁₉	—	2	1	no	—
68	C₂²×D₁₉	—	2	1	no	—
69	C₂²×D₁₉	—	2	1	no	—
70	C₂²×D₁₉	—	2	1	no	—
71	C₂²×D₁₉	—	2	1	no	—
72	C₂²×D₁₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#41	1	2	yes	—
86	C₂×C₄×C₁₉	#41	1	2	yes	—
87	C₂×C₄×C₁₉	#41	1	2	yes	—
88	C₂×Dic₁₉	—	2	1	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	1	no	—
91	C₂×Dic₁₉	—	2	1	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	no	—
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	2	1	no	—
98	C₂×Dic₁₉	—	2	1	no	—
99	C₂×Dic₁₉	—	2	1	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
102	C₂×Dic₁₉	#41	1	2	yes	—
103	C₄×D₁₉	—	4	4	no	—
104	#2496	—	19	1	no	maximal, Sylow
105	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
110	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
111	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
112	C₂×D₁₉	—	2	2	no	—
113	C₂×D₁₉	—	2	2	no	—
114	C₂×D₁₉	—	2	2	no	—
115	C₂×D₁₉	—	4	1	no	—
116	C₂×D₁₉	—	4	1	no	—
117	C₂×D₁₉	—	4	1	no	—
118	C₂×D₁₉	—	4	1	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	—	4	1	no	—
123	C₄×C₁₉	#126	1	4	yes	complemented
124	Dic₁₉	—	2	2	no	—
125	Dic₁₉	—	2	2	no	—
126	Dic₁₉	—	4	1	no	—
127	Dic₁₉	—	4	2	no	—
128	Dic₁₉	—	4	2	no	—
129	C₂×#126	—	19	2	no	—
130	#400	—	19	2	no	—
131	#397	—	19	2	no	—
132	#389	—	19	1	no	—
133	#389	D₁₉	1	1	yes	characteristic, complemented
134	#387	—	19	2	no	—
135	#384	—	19	1	no	—
136	#380	—	19	1	no	—
137	#380	—	19	1	no	—
138	C₄×C₄⋊C₄	—	19	1	no	—
139	C₄×C₂²⋊C₄	—	19	1	no	—
140	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
141	C₂×C₁₉	#532	1	1	yes	characteristic
142	C₂×C₁₉	#541	1	1	yes	characteristic
143	C₂×C₁₉	#547	1	1	yes	characteristic
144	C₂×C₁₉	#547	1	1	yes	characteristic
145	C₂×C₁₉	#552	1	1	yes	characteristic
146	C₂×C₁₉	#556	1	1	yes	characteristic
147	D₁₉	—	4	2	no	—
148	C₂³×C₄	—	19	1	no	—
149	#126	—	38	8	no	—
150	C₂×C₄⋊C₄	—	19	2	no	—
151	C₂×C₄⋊C₄	—	19	2	no	—
152	C₂×C₄⋊C₄	—	19	1	no	—
153	C₂×C₄⋊C₄	—	19	1	no	—
154	C₂×C₄⋊C₄	—	19	2	no	—
155	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
156	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
157	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
158	C₂×C₂²⋊C₄	—	19	1	no	—
159	C₂×C₂²⋊C₄	—	19	2	no	—
160	C₂×C₂²⋊C₄	—	19	2	no	—
161	C₂×C₂²⋊C₄	—	19	1	no	—
162	C₂×C₄²	—	19	2	no	—
163	C₂×C₄²	—	19	1	no	—
164	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
165	#95	—	19	1	no	—
166	#95	—	19	1	no	—
167	#95	—	19	2	no	—
168	#95	—	19	2	no	—
169	#95	—	19	2	no	—
170	#95	—	19	2	no	—
171	#95	C₂×D₁₉	1	2	yes	—
172	C₁₉	#2496	1	1	yes	characteristic, complemented, Sylow
173	C₂⁴	—	19	1	no	—
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	19	1	no	—
176	C₂²×C₄	—	19	1	no	—
177	C₂²×C₄	—	19	2	no	—
178	C₂²×C₄	—	19	2	no	—
179	C₂²×C₄	—	38	2	no	—
180	C₂²×C₄	—	38	2	no	—
181	C₂²×C₄	—	38	2	no	—
182	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
183	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
184	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
185	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	4	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	38	4	no	—
191	C₄⋊C₄	—	38	4	no	—
192	C₄⋊C₄	—	38	4	no	—
193	C₄⋊C₄	—	38	2	no	—
194	C₄⋊C₄	—	38	2	no	—
195	C₂²⋊C₄	—	19	4	no	—
196	C₂²⋊C₄	—	38	2	no	—
197	C₂²⋊C₄	—	38	4	no	—
198	C₂²⋊C₄	—	38	4	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	38	4	no	—
201	C₄²	—	38	2	no	—
202	C₂³	—	19	2	no	—
203	C₂³	—	38	1	no	—
204	C₂³	—	38	1	no	—
205	C₂³	—	38	1	no	—
206	C₂³	—	38	1	no	—
207	C₂³	—	38	1	no	—
208	C₂³	—	38	1	no	—
209	C₂³	C₂³×D₁₉	1	1	yes	characteristic
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	19	2	no	—
222	C₂×C₄	—	19	2	no	—
223	C₂×C₄	—	38	1	no	—
224	C₂×C₄	—	38	1	no	—
225	C₂×C₄	—	38	1	no	—
226	C₂×C₄	—	38	1	no	—
227	C₂×C₄	—	38	2	no	—
228	C₂×C₄	—	38	1	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	38	2	no	—
231	C₂×C₄	—	38	1	no	—
232	C₂×C₄	—	38	2	no	—
233	C₂×C₄	—	38	1	no	—
234	C₂×C₄	—	38	2	no	—
235	C₂×C₄	—	38	2	no	—
236	C₂×C₄	—	76	4	no	—
237	C₂×C₄	#64541	1	2	yes	—
238	C₂×C₄	D₄×D₁₉	1	2	yes	—
239	C₂×C₄	#64543	1	2	yes	—
240	C₂×C₄	#64545	1	2	yes	—
241	C₂²	—	38	2	no	—
242	C₂²	—	38	2	no	—
243	C₂²	—	38	2	no	—
244	C₂²	—	76	1	no	—
245	C₂²	—	76	1	no	—
246	C₂²	—	76	1	no	—
247	C₂²	—	76	1	no	—
248	C₂²	C₂×#64541	1	1	yes	characteristic
249	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
250	C₂²	C₂×#64543	1	1	yes	characteristic
251	C₂²	C₂×#64545	1	1	yes	characteristic
252	C₂²	#10597433	1	1	yes	characteristic
253	C₂²	#41×D₁₉	1	1	yes	characteristic
254	C₂²	#10597436	1	1	yes	characteristic
255	C₄	—	2	2	no	—
256	C₄	—	4	2	no	—
257	C₄	—	4	2	no	—
258	C₄	—	4	1	no	—
259	C₄	—	38	2	no	—
260	C₄	—	38	2	no	—
261	C₄	—	76	1	no	—
262	C₄	—	76	2	no	—
263	C₄	—	76	2	no	—
264	C₄	#10597344	1	4	yes	complemented
265	C₂	—	76	2	no	—
266	C₂	C₂×#10597344	1	1	yes	characteristic
267	C₂	#11927091	1	1	yes	characteristic
268	C₂	#11927152	1	1	yes	characteristic
269	C₂	#11927194	1	1	yes	characteristic
270	C₂	#11927197	1	1	yes	characteristic
271	C₂	#11927232	1	1	yes	characteristic
272	C₂	#11927265	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#389	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	#389	D₁₉
hypocenter	C₁₉	#2496
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
2. #11926486	C₂	semidirect
4. #11926443	C₂	semidirect
5. #11926425	C₂	semidirect
6. #11926413	C₂	semidirect
9. C₄×C₄⋊Dic₁₉	C₂	semidirect
11. C₁₉×#389	C₂	semidirect
123. C₄×C₁₉	#126	semidirect
133. #389	D₁₉	semidirect
172. C₁₉	#2496	semidirect
264. C₄	#10597344	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597344	2
#11926486	2
#11926473	2
#11926443	2
#11926425	2
#11926413	2
#11926401	2
C₄×C₄⋊Dic₁₉	2
C₄×(C₂×D₁₉)⋊C₄	2
C₁₉×#389	2
#2496	19