Subgroups — #14572751

Order 2432.

388 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#64545	C₂	1	1	yes	maximal, characteristic
2	#11926675	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926623	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926621	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926617	C₂	1	2	yes	maximal, complemented
6	#11926614	C₂	1	2	yes	maximal, complemented
7	#11926599	C₂	1	2	yes	maximal, complemented
8	#11926595	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926566	C₂	1	2	yes	maximal, complemented
10	C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#64545	C₄	1	1	yes	characteristic
13	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	Q₈×Dic₁₉	C₄	1	1	yes	characteristic
15	C₂×#64515	C₂²	1	2	yes	—
16	C₂×#64515	C₂²	1	2	yes	—
17	C₂×C₈×D₁₉	C₂²	1	2	yes	—
18	#10597339	C₄	1	2	yes	—
19	#10597339	C₄	1	1	yes	characteristic
20	#10597338	C₄	1	2	yes	—
21	#10597338	C₄	1	1	yes	characteristic
22	C₄×D₇₆	C₂²	1	2	yes	—
23	C₄×D₇₆	C₂²	1	1	yes	characteristic
24	C₄²×D₁₉	C₂²	1	1	yes	characteristic
25	C₄²×D₁₉	C₂²	1	2	yes	—
26	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
28	C₁₉×#97	C₂²	1	2	yes	—
29	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
31	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
32	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
33	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
34	Dic₁₉⋊C₈	C₂²	1	2	yes	—
35	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
36	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
38	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
39	#10597260	C₂²	1	2	yes	—
40	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	#64545	—	2	4	no	—
43	C₂×D₇₆	C₂×C₄	1	2	yes	—
44	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
46	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
47	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₄×D₁₉	C₂³	1	2	yes	—
51	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₁₉	C₂³	1	2	yes	—
54	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₄²×C₁₉	C₂³	1	1	yes	characteristic
57	C₄²×C₁₉	C₂³	1	2	yes	—
58	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
59	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
60	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
61	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
62	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₉	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	C₂×C₄	1	2	yes	—
67	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
71	#64515	—	4	2	no	—
72	#64515	—	4	2	no	—
73	C₈×D₁₉	—	4	2	no	—
74	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
75	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
80	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
85	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
86	D₇₆	—	2	4	no	—
87	D₇₆	—	2	2	no	—
88	C₄×D₁₉	—	2	1	no	—
89	C₄×D₁₉	—	2	2	no	—
90	C₄×D₁₉	—	2	1	no	—
91	C₄×D₁₉	—	2	2	no	—
92	C₄×D₁₉	—	2	4	no	—
93	C₄×D₁₉	—	4	1	no	—
94	C₄×D₁₉	—	4	2	no	—
95	C₄×D₁₉	M₁₆	1	4	yes	complemented
96	C₈×C₁₉	—	2	2	no	—
97	C₈×C₁₉	—	2	1	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₁₉⋊C₈	—	2	2	no	—
100	C₁₉⋊C₈	—	2	1	no	—
101	C₁₉⋊C₈	—	2	1	no	—
102	#2989	—	19	1	no	maximal, Sylow
103	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
104	C₂×D₁₉	—	2	1	no	—
105	C₂×D₁₉	—	2	1	no	—
106	C₂×D₁₉	—	2	2	no	—
107	C₂×D₁₉	—	2	2	no	—
108	C₂×D₁₉	—	2	2	no	—
109	C₂×D₁₉	C₂×M₁₆	1	2	yes	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
114	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
115	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
116	Dic₁₉	—	2	1	no	—
117	Dic₁₉	—	2	2	no	—
118	Dic₁₉	—	2	1	no	—
119	Dic₁₉	C₂×M₁₆	1	2	yes	—
120	C₄×#41	—	19	1	no	—
121	#446	—	19	1	no	—
122	#446	D₁₉	1	1	yes	characteristic, complemented
123	#436	—	19	1	no	—
124	#436	—	19	1	no	—
125	#435	—	19	2	no	—
126	#435	—	19	2	no	—
127	#432	—	19	2	no	—
128	#431	—	19	1	no	—
129	#423	—	19	2	no	—
130	C₂×C₄⋊C₈	—	19	1	no	—
131	C₂×C₁₉	#520	1	1	yes	characteristic
132	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
133	C₂×C₁₉	#568	1	1	yes	characteristic
134	D₁₉	—	2	2	no	—
135	D₁₉	—	4	2	no	—
136	C₂×#41	—	19	1	no	—
137	C₂×M₁₆	—	19	2	no	—
138	C₂×M₁₆	—	19	2	no	—
139	C₂²×C₈	—	19	2	no	—
140	C₄×Q₈	—	19	1	no	—
141	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
142	C₄×D₄	—	19	2	no	—
143	C₄×D₄	—	19	1	no	—
144	C₄×D₄	—	19	2	no	—
145	C₄×D₄	—	19	1	no	—
146	#117	—	19	1	no	—
147	#117	—	19	2	no	—
148	C₂×C₄²	—	19	1	no	—
149	C₂×C₄²	—	19	2	no	—
150	C₄⋊C₈	—	19	2	no	—
151	C₄⋊C₈	—	19	1	no	—
152	C₄⋊C₈	—	19	1	no	—
153	C₄⋊C₈	—	19	1	no	—
154	C₄⋊C₈	—	19	2	no	—
155	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
156	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
157	C₂²⋊C₈	—	19	1	no	—
158	C₂²⋊C₈	—	19	1	no	—
159	C₂²⋊C₈	—	19	2	no	—
160	C₂²⋊C₈	—	19	2	no	—
161	#97	—	19	2	no	—
162	#97	C₂×D₁₉	1	2	yes	—
163	C₄×C₈	—	19	1	no	—
164	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
165	C₁₉	#2989	1	1	yes	characteristic, complemented, Sylow
166	#41	—	38	4	no	—
167	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
168	C₂×D₄	—	19	2	no	—
169	C₂×D₄	—	19	1	no	—
170	C₂²×C₄	—	19	1	no	—
171	C₂²×C₄	—	19	2	no	—
172	C₂²×C₄	—	19	1	no	—
173	C₂²×C₄	—	19	2	no	—
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	19	2	no	—
176	M₁₆	—	76	2	no	—
177	M₁₆	—	76	2	no	—
178	C₂×C₈	—	19	1	no	—
179	C₂×C₈	—	19	1	no	—
180	C₂×C₈	—	19	2	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
183	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
184	C₂×C₈	C₂²×D₁₉	1	2	yes	—
185	C₄⋊C₄	—	19	2	no	—
186	C₄⋊C₄	—	19	1	no	—
187	C₄⋊C₄	C₄×D₁₉	1	2	yes	—
188	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
189	C₂²⋊C₄	—	19	2	no	—
190	C₂²⋊C₄	—	19	2	no	—
191	C₂²⋊C₄	—	19	2	no	—
192	C₄²	—	19	1	no	—
193	C₄²	—	19	2	no	—
194	C₄²	—	19	2	no	—
195	C₄²	—	19	1	no	—
196	C₄²	—	19	1	no	—
197	C₄²	C₂²×D₁₉	1	1	yes	characteristic
198	C₄²	C₂²×D₁₉	1	2	yes	—
199	C₂³	—	19	1	no	—
200	C₂³	—	19	2	no	—
201	Q₈	—	2	2	no	—
202	D₄	—	38	4	no	—
203	D₄	—	38	2	no	—
204	C₂×C₄	—	19	1	no	—
205	C₂×C₄	—	19	4	no	—
206	C₂×C₄	—	19	1	no	—
207	C₂×C₄	—	19	1	no	—
208	C₂×C₄	—	19	2	no	—
209	C₂×C₄	—	38	4	no	—
210	C₂×C₄	—	38	1	no	—
211	C₂×C₄	—	38	2	no	—
212	C₂×C₄	—	38	1	no	—
213	C₂×C₄	—	38	2	no	—
214	C₂×C₄	—	76	1	no	—
215	C₂×C₄	—	76	2	no	—
216	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
217	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
218	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
219	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
220	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
221	C₈	—	2	1	no	—
222	C₈	—	2	2	no	—
223	C₈	—	2	1	no	—
224	C₈	—	38	1	no	—
225	C₈	—	38	2	no	—
226	C₈	—	38	1	no	—
227	C₂²	—	19	2	no	—
228	C₂²	—	38	1	no	—
229	C₂²	—	38	1	no	—
230	C₂²	—	38	2	no	—
231	C₂²	—	38	2	no	—
232	C₂²	—	38	2	no	—
233	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
234	C₄	—	2	2	no	—
235	C₄	—	2	1	no	—
236	C₄	—	2	2	no	—
237	C₄	—	19	2	no	—
238	C₄	—	38	1	no	—
239	C₄	—	38	1	no	—
240	C₄	—	38	2	no	—
241	C₄	M₁₆×D₁₉	1	2	yes	—
242	C₄	#10597433	1	1	yes	characteristic
243	C₄	#10597435	1	1	yes	characteristic
244	C₂	—	38	2	no	—
245	C₂	—	76	2	no	—
246	C₂	#11927026	1	1	yes	characteristic
247	C₂	C₂×M₁₆×D₁₉	1	1	yes	characteristic
248	C₂	#11927309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#446	C₂
prime radical	C₂×#64545	C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#446	D₁₉
hypocenter	C₁₉	#2989
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. #11926675	C₂	semidirect
3. #11926623	C₂	semidirect
4. #11926621	C₂	semidirect
5. #11926617	C₂	semidirect
6. #11926614	C₂	semidirect
7. #11926599	C₂	semidirect
8. #11926595	C₂	semidirect
9. #11926566	C₂	semidirect
10. C₄⋊C₈×D₁₉	C₂	semidirect
11. C₁₉×#446	C₂	semidirect
95. C₄×D₁₉	M₁₆	semidirect
122. #446	D₁₉	semidirect
165. C₁₉	#2989	semidirect

Maximal subgroups

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

subgroup	index
C₄×#64545	2
#11926675	2
#11926623	2
#11926621	2
#11926617	2
#11926614	2
#11926599	2
#11926595	2
#11926566	2
C₄⋊C₈×D₁₉	2
C₁₉×#446	2
#2989	19