Subgroups — #14572581

Order 2432.

356 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927097	C₂	1	1	yes	maximal, characteristic
2	#11926673	C₂	1	2	yes	maximal, complemented
3	#11926673	C₂	1	2	yes	maximal, complemented
4	#11926671	C₂	1	2	yes	maximal, complemented
5	#11926668	C₂	1	2	yes	maximal, complemented
6	#11926572	C₂	1	1	yes	maximal, characteristic
7	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
8	#11926500	C₂	1	1	yes	maximal, characteristic
9	#11926499	C₂	1	1	yes	maximal, characteristic
10	M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#424	C₂	1	1	yes	maximal, characteristic
12	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#117	C₂²	1	1	yes	characteristic
15	#10597372	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#10597336	C₄	1	1	yes	characteristic
20	#10597336	C₄	1	1	yes	characteristic
21	#10597334	C₄	1	1	yes	characteristic
22	#10597334	C₄	1	1	yes	characteristic
23	#10597324	C₄	1	2	yes	—
24	#10597324	C₄	1	2	yes	—
25	C₄×Dic₃₈	C₂²	1	2	yes	—
26	C₄×Dic₃₈	C₂²	1	2	yes	—
27	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
28	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
29	#10597272	C₂²	1	2	yes	—
30	#10597272	C₂²	1	2	yes	—
31	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
32	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
33	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
34	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
35	Dic₁₉⋊C₈	C₂²	1	2	yes	—
36	Dic₁₉⋊C₈	C₂²	1	2	yes	—
37	C₈×Dic₁₉	C₂²	1	2	yes	—
38	C₈×Dic₁₉	C₂²	1	2	yes	—
39	#10597260	C₂²	1	2	yes	—
40	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
45	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
46	M₁₆×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂³	1	2	yes	—
51	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
54	C₄²×C₁₉	C₂³	1	2	yes	—
55	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
56	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
57	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
58	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
59	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
60	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
61	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
62	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
63	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
64	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₄×Dic₁₉	C₂³	1	2	yes	—
68	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
69	#64520	Q₈	1	4	yes	complemented
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
74	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
79	C₂×C₄×C₁₉	#41	1	2	yes	—
80	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂×Dic₁₉	—	2	2	no	—
82	C₂×Dic₁₉	—	4	1	no	—
83	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
87	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
88	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
89	Dic₃₈	—	2	4	no	—
90	Dic₃₈	—	4	2	no	—
91	C₈×C₁₉	—	2	1	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	—	2	2	no	—
94	C₁₉⋊C₈	—	2	1	no	—
95	C₁₉⋊C₈	—	2	1	no	—
96	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
97	#2962	—	19	1	no	maximal, Sylow
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	C₄×Q₈	1	2	yes	—
101	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	C₄×Q₈	1	2	yes	—
105	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
107	Dic₁₉	—	2	2	no	—
108	Dic₁₉	—	2	1	no	—
109	Dic₁₉	—	2	1	no	—
110	Dic₁₉	—	2	2	no	—
111	Dic₁₉	—	2	1	no	—
112	Dic₁₉	#131	1	2	yes	—
113	#533	—	19	1	no	—
114	#446	—	19	2	no	—
115	#446	—	19	2	no	—
116	#446	—	19	2	no	—
117	C₈×Q₈	—	19	2	no	—
118	#424	—	19	1	no	—
119	#424	D₁₉	1	1	yes	characteristic
120	C₂×C₄⋊C₈	—	19	1	no	—
121	#405	—	19	1	no	—
122	#405	—	19	1	no	—
123	C₄×M₁₆	—	19	1	no	—
124	C₂×C₁₉	—	2	2	no	—
125	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
126	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
127	C₂×C₁₉	#568	1	1	yes	characteristic
128	C₂×M₁₆	—	19	1	no	—
129	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
130	C₂²×C₈	—	19	1	no	—
131	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
132	C₄⋊Q₈	—	19	1	no	—
133	C₄⋊Q₈	—	19	1	no	—
134	#125	—	19	1	no	—
135	#125	—	19	1	no	—
136	C₂²⋊Q₈	—	19	2	no	—
137	C₂²⋊Q₈	—	19	2	no	—
138	C₄×Q₈	—	19	2	no	—
139	C₄×Q₈	—	19	2	no	—
140	#117	—	19	1	no	—
141	#117	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₄²	—	19	1	no	—
143	C₄⋊C₈	—	19	1	no	—
144	C₄⋊C₈	—	19	1	no	—
145	C₄⋊C₈	—	19	1	no	—
146	C₄⋊C₈	—	19	1	no	—
147	C₄⋊C₈	—	19	2	no	—
148	C₄⋊C₈	—	19	2	no	—
149	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
150	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
151	#97	—	19	2	no	—
152	#97	—	19	2	no	—
153	#97	—	19	2	no	—
154	C₄×C₈	—	19	2	no	—
155	C₄×C₈	—	19	2	no	—
156	C₄×C₈	—	19	2	no	—
157	C₁₉	#2962	1	1	yes	characteristic, complemented, Sylow
158	C₂×Q₈	—	19	2	no	—
159	C₂×Q₈	—	19	2	no	—
160	C₂²×C₄	—	19	1	no	—
161	C₂²×C₄	—	19	1	no	—
162	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
163	M₁₆	—	2	2	no	—
164	M₁₆	—	19	4	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	19	2	no	—
167	C₂×C₈	—	19	1	no	—
168	C₂×C₈	—	19	1	no	—
169	C₂×C₈	—	38	2	no	—
170	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
171	C₂×C₈	C₂²×D₁₉	1	2	yes	—
172	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₄	—	19	2	no	—
174	C₄⋊C₄	—	19	2	no	—
175	C₄⋊C₄	—	19	2	no	—
176	C₄⋊C₄	—	19	2	no	—
177	C₄⋊C₄	—	19	1	no	—
178	C₄⋊C₄	—	19	1	no	—
179	C₄⋊C₄	—	19	2	no	—
180	C₄⋊C₄	—	19	2	no	—
181	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
182	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
183	C₂²⋊C₄	—	19	2	no	—
184	C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
185	C₄²	—	19	1	no	—
186	C₄²	—	19	1	no	—
187	C₄²	—	19	1	no	—
188	C₄²	—	19	2	no	—
189	C₄²	—	19	1	no	—
190	C₄²	C₂²×D₁₉	1	2	yes	—
191	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
192	Q₈	—	38	4	no	—
193	Q₈	—	76	2	no	—
194	C₂×C₄	—	19	1	no	—
195	C₂×C₄	—	19	1	no	—
196	C₂×C₄	—	19	1	no	—
197	C₂×C₄	—	19	1	no	—
198	C₂×C₄	—	19	2	no	—
199	C₂×C₄	—	19	2	no	—
200	C₂×C₄	—	38	2	no	—
201	C₂×C₄	—	76	1	no	—
202	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
203	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
204	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
205	C₂×C₄	#64543	1	2	yes	—
206	C₂×C₄	Q₈×D₁₉	1	2	yes	—
207	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
208	C₈	—	2	1	no	—
209	C₈	—	2	1	no	—
210	C₈	—	2	2	no	—
211	C₈	—	19	4	no	—
212	C₈	—	38	1	no	—
213	C₈	—	38	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	—	2	1	no	—
216	C₂²	#10597333	1	2	yes	—
217	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
218	C₄	—	2	2	no	—
219	C₄	—	2	2	no	—
220	C₄	—	19	2	no	—
221	C₄	—	38	1	no	—
222	C₄	—	38	2	no	—
223	C₄	—	38	1	no	—
224	C₄	—	38	1	no	—
225	C₄	—	38	2	no	—
226	C₄	#10597333	1	2	yes	—
227	C₄	C₂×#64543	1	1	yes	characteristic
228	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	C₂×#10597333	1	1	yes	characteristic
231	C₂	#131×D₁₉	1	1	yes	characteristic
232	C₂	#11927309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#424	C₂
prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#424	D₁₉
hypocenter	C₁₉	#2962
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
2. #11926673	C₂	semidirect
3. #11926673	C₂	semidirect
4. #11926671	C₂	semidirect
5. #11926668	C₂	semidirect
69. #64520	Q₈	semidirect
157. C₁₉	#2962	semidirect

Maximal subgroups

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

subgroup	index
#11927097	2
#11926673	2
#11926671	2
#11926668	2
#11926572	2
C₂×Dic₁₉⋊C₈	2
#11926500	2
#11926499	2
M₁₆×Dic₁₉	2
C₁₉×#424	2
#2962	19