Subgroups — #14572780

Order 2432.

354 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927078	C₂	1	1	yes	maximal, characteristic
2	#11926671	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926668	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926621	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926620	C₂	1	2	yes	maximal, complemented
6	#11926613	C₂	1	2	yes	maximal, complemented
7	#11926609	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926604	C₂	1	2	yes	maximal, complemented
9	#11926597	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926569	C₂	1	2	yes	maximal, complemented
11	C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	#10597376	C₄	1	1	yes	characteristic
15	#10597375	C₄	1	2	yes	—
16	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
17	#10597370	C₄	1	1	yes	characteristic
18	C₂×#64515	C₂²	1	2	yes	—
19	C₂×C₈×D₁₉	C₂²	1	2	yes	—
20	#10597322	C₄	1	2	yes	—
21	#10597321	C₄	1	1	yes	characteristic
22	C₄×D₇₆	C₂²	1	1	yes	characteristic
23	#10597318	C₂²	1	2	yes	—
24	#10597316	C₄	1	1	yes	characteristic
25	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
26	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
27	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
31	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
32	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
33	#10597272	C₂²	1	2	yes	—
34	Dic₁₉⋊C₈	C₂²	1	2	yes	—
35	Dic₁₉⋊C₈	C₂²	1	2	yes	—
36	C₈×Dic₁₉	C₂²	1	2	yes	—
37	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
38	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
39	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊D₁₉	C₂×C₄	1	2	yes	—
45	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×D₁₉	C₂³	1	2	yes	—
47	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
48	M₁₆×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	C₂³	1	2	yes	—
50	C₂×C₈×C₁₉	C₂³	1	2	yes	—
51	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₄²×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
56	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
57	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
58	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
59	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
60	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
61	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
62	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
63	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
64	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
65	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₉	C₂³	1	2	yes	—
67	C₂×C₁₉⋊C₈	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	1	yes	characteristic
71	#64515	—	4	2	no	—
72	C₈×D₁₉	—	4	2	no	—
73	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
85	C₂²⋊D₁₉	—	4	2	no	—
86	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
87	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
88	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
89	D₇₆	—	2	2	no	—
90	C₄×D₁₉	—	2	2	no	—
91	C₄×D₁₉	—	2	2	no	—
92	Dic₃₈	—	2	2	no	—
93	C₈×C₁₉	—	2	2	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₁₉⋊C₈	—	2	1	no	—
96	C₁₉⋊C₈	—	2	1	no	—
97	C₁₉⋊C₈	—	2	1	no	—
98	C₁₉⋊C₈	—	2	1	no	—
99	#2993	—	19	1	no	maximal, Sylow
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
104	C₂×D₁₉	—	2	2	no	—
105	C₂×D₁₉	—	2	2	no	—
106	C₂×D₁₉	—	2	2	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	#131	1	2	yes	—
112	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
113	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
114	Dic₁₉	—	2	2	no	—
115	Dic₁₉	—	2	2	no	—
116	Dic₁₉	—	2	2	no	—
117	#529	—	19	1	no	—
118	#446	—	19	1	no	—
119	C₈×Q₈	—	19	1	no	—
120	#436	—	19	2	no	—
121	#436	—	19	1	no	—
122	#435	—	19	2	no	—
123	C₈×D₄	—	19	1	no	—
124	#433	—	19	2	no	—
125	#431	—	19	1	no	—
126	#424	—	19	2	no	—
127	#423	D₁₉	1	1	yes	characteristic, complemented
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	#520	1	1	yes	characteristic
130	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
131	C₂×C₁₉	#568	1	1	yes	characteristic
132	D₁₉	—	4	2	no	—
133	C₂×M₁₆	—	19	2	no	—
134	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
135	C₂²×C₈	—	19	2	no	—
136	#126	—	19	2	no	—
137	#125	—	19	1	no	—
138	#124	—	19	1	no	—
139	#123	—	19	2	no	—
140	C₂²⋊Q₈	—	19	1	no	—
141	#121	—	19	1	no	—
142	C₄×Q₈	—	19	1	no	—
143	C₄×D₄	—	19	2	no	—
144	C₄×D₄	—	19	1	no	—
145	#117	—	19	2	no	—
146	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
147	C₄⋊C₈	—	19	2	no	—
148	C₄⋊C₈	—	19	2	no	—
149	C₄⋊C₈	—	19	1	no	—
150	C₄⋊C₈	—	19	1	no	—
151	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
152	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
153	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
154	C₂²⋊C₈	—	19	1	no	—
155	C₂²⋊C₈	—	19	1	no	—
156	C₂²⋊C₈	—	19	2	no	—
157	C₂²⋊C₈	—	19	2	no	—
158	#97	—	19	2	no	—
159	C₄×C₈	—	19	2	no	—
160	C₄×C₈	—	19	1	no	—
161	C₄×C₈	—	19	1	no	—
162	C₁₉	#2993	1	1	yes	characteristic, complemented, Sylow
163	C₂×Q₈	—	19	1	no	—
164	C₂×D₄	—	19	2	no	—
165	C₂×D₄	—	19	1	no	—
166	C₂²×C₄	—	19	2	no	—
167	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
168	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
170	M₁₆	—	4	2	no	—
171	M₁₆	—	76	2	no	—
172	C₂×C₈	—	19	1	no	—
173	C₂×C₈	—	19	1	no	—
174	C₂×C₈	—	19	1	no	—
175	C₂×C₈	—	19	1	no	—
176	C₂×C₈	—	76	2	no	—
177	C₂×C₈	C₂²×D₁₉	1	2	yes	—
178	C₂×C₈	C₂²×D₁₉	1	2	yes	—
179	C₄⋊C₄	—	19	2	no	—
180	C₄⋊C₄	—	19	2	no	—
181	C₄⋊C₄	—	19	2	no	—
182	C₄⋊C₄	—	19	2	no	—
183	C₄⋊C₄	—	19	1	no	—
184	C₄⋊C₄	—	19	1	no	—
185	C₂²⋊C₄	—	19	2	no	—
186	C₂²⋊C₄	—	19	2	no	—
187	C₂²⋊C₄	—	19	2	no	—
188	C₂²⋊C₄	—	19	2	no	—
189	C₂²⋊C₄	—	19	2	no	—
190	C₄²	—	19	2	no	—
191	C₄²	C₄×D₁₉	1	1	yes	characteristic
192	C₄²	C₄×D₁₉	1	1	yes	characteristic
193	C₄²	C₂²×D₁₉	1	1	yes	characteristic
194	C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	C₂³	—	19	2	no	—
196	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
197	Q₈	—	38	2	no	—
198	D₄	—	38	2	no	—
199	D₄	—	76	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	19	2	no	—
205	C₂×C₄	—	19	2	no	—
206	C₂×C₄	—	19	2	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
210	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
211	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
212	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
213	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
214	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
215	C₈	—	2	2	no	—
216	C₈	—	2	2	no	—
217	C₈	—	38	1	no	—
218	C₈	—	38	1	no	—
219	C₈	—	38	1	no	—
220	C₈	—	38	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	38	2	no	—
225	C₂²	—	38	2	no	—
226	C₂²	—	38	2	no	—
227	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	38	2	no	—
233	C₄	—	38	2	no	—
234	C₄	—	38	2	no	—
235	C₄	#10597353	1	2	yes	—
236	C₄	#10597430	1	1	yes	characteristic
237	C₄	#10597433	1	1	yes	characteristic
238	C₂	—	4	1	no	—
239	C₂	—	76	2	no	—
240	C₂	#11927025	1	1	yes	characteristic
241	C₂	C₂×#10597353	1	1	yes	characteristic
242	C₂	#11927310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#423	C₂
prime radical	#10597376	C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#423	D₁₉
hypocenter	C₁₉	#2993
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
2. #11926671	C₂	semidirect
3. #11926668	C₂	semidirect
4. #11926621	C₂	semidirect
5. #11926620	C₂	semidirect
6. #11926613	C₂	semidirect
7. #11926609	C₂	semidirect
8. #11926604	C₂	semidirect
9. #11926597	C₂	semidirect
10. #11926569	C₂	semidirect
11. C₁₉×#423	C₂	semidirect
127. #423	D₁₉	semidirect
162. C₁₉	#2993	semidirect

Maximal subgroups

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

subgroup	index
#11927078	2
#11926671	2
#11926668	2
#11926621	2
#11926620	2
#11926613	2
#11926609	2
#11926604	2
#11926597	2
#11926569	2
C₁₉×#423	2
#2993	19