Subgroups — #14572583

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	#11927098	C₂	1	1	yes	maximal, characteristic
2	#11926672	C₂	1	2	yes	maximal, complemented
3	#11926671	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926671	C₂	1	2	yes	maximal, complemented
5	Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926569	C₂	1	2	yes	maximal
8	C₄⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
9	#11926501	C₂	1	2	yes	maximal
10	C₄×#64515	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	#10597392	C₄	1	1	yes	characteristic
14	#10597390	C₄	1	1	yes	characteristic
15	C₂×#64515	C₂²	1	1	yes	characteristic
16	C₂×#64515	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₁₉	C₂²	1	2	yes	—
18	#10597343	C₄	1	1	yes	characteristic
19	#10597342	C₄	1	2	yes	—
20	#10597335	C₄	1	2	yes	—
21	#10597334	C₄	1	1	yes	characteristic
22	#10597318	C₂²	1	2	yes	—
23	C₄²×D₁₉	C₂²	1	1	yes	characteristic
24	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
25	C₄×Dic₃₈	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	#10597272	C₂²	1	1	yes	characteristic
31	#10597272	C₂²	1	2	yes	—
32	#10597272	C₂²	1	1	yes	characteristic
33	Dic₁₉⋊C₈	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	2	yes	—
39	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
41	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
45	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
47	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
52	C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₄²×C₁₉	C₂³	1	2	yes	—
54	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
55	(C₂×D₁₉)⋊C₄	C₂×C₄	1	2	yes	—
56	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
57	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
58	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
59	Dic₁₉⋊C₄	C₂×C₄	1	2	yes	—
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	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₉	C₂³	1	2	yes	—
66	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
68	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
70	#64515	—	2	2	no	—
71	#64515	Q₈	1	4	yes	complemented
72	C₈×D₁₉	—	2	4	no	—
73	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
74	Q₈×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
80	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
83	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
84	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₄×D₁₉	—	2	2	no	—
86	C₄×D₁₉	—	4	1	no	—
87	C₄×D₁₉	C₂×Q₈	1	2	yes	—
88	C₄×D₁₉	#41	1	2	yes	—
89	Dic₃₈	—	2	2	no	—
90	Dic₃₈	—	4	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	C₂×Q₈	1	2	yes	—
94	C₁₉⋊C₈	—	2	2	no	—
95	C₁₉⋊C₈	—	2	1	no	—
96	C₁₉⋊C₈	C₂×Q₈	1	2	yes	—
97	#2962	—	19	1	no	maximal, Sylow
98	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
99	C₂×D₁₉	—	2	1	no	—
100	C₂×D₁₉	—	2	1	no	—
101	C₂×D₁₉	C₄×Q₈	1	2	yes	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	#131	1	2	yes	—
106	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
108	Dic₁₉	—	2	2	no	—
109	Dic₁₉	—	2	1	no	—
110	Dic₁₉	—	2	1	no	—
111	Dic₁₉	—	2	2	no	—
112	Dic₁₉	C₄×Q₈	1	2	yes	—
113	#533	—	19	1	no	—
114	#446	—	19	1	no	—
115	#446	—	19	2	no	—
116	#446	—	19	2	no	—
117	#446	D₁₉	1	1	yes	characteristic, complemented
118	C₈×Q₈	—	19	1	no	—
119	C₈×Q₈	—	19	1	no	—
120	#424	—	19	2	no	—
121	C₂×C₄⋊C₈	—	19	1	no	—
122	#405	—	19	2	no	—
123	C₄×M₁₆	—	19	1	no	—
124	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
125	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
126	C₂×C₁₉	#568	1	1	yes	characteristic
127	D₁₉	—	2	2	no	—
128	C₂×M₁₆	—	19	1	no	—
129	C₂×M₁₆	—	19	1	no	—
130	C₂²×C₈	—	19	2	no	—
131	C₄⋊Q₈	—	19	1	no	—
132	C₄⋊Q₈	—	19	1	no	—
133	#125	—	19	2	no	—
134	C₂²⋊Q₈	—	19	1	no	—
135	C₂²⋊Q₈	—	19	2	no	—
136	C₂²⋊Q₈	—	19	1	no	—
137	C₄×Q₈	—	19	1	no	—
138	C₄×Q₈	—	19	2	no	—
139	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
140	#117	—	19	2	no	—
141	C₂×C₄²	—	19	1	no	—
142	C₄⋊C₈	—	19	2	no	—
143	C₄⋊C₈	—	19	2	no	—
144	C₄⋊C₈	—	19	2	no	—
145	C₄⋊C₈	—	19	1	no	—
146	C₄⋊C₈	—	19	2	no	—
147	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
148	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
149	#97	—	19	1	no	—
150	#97	—	19	1	no	—
151	#97	—	19	2	no	—
152	#97	C₂×D₁₉	1	2	yes	—
153	C₄×C₈	—	19	2	no	—
154	C₄×C₈	—	19	1	no	—
155	C₄×C₈	—	19	2	no	—
156	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
157	C₁₉	#2962	1	1	yes	characteristic, complemented, Sylow
158	C₂×Q₈	—	19	1	no	—
159	C₂×Q₈	—	19	2	no	—
160	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
161	C₂²×C₄	—	19	1	no	—
162	C₂²×C₄	—	19	1	no	—
163	C₂²×C₄	—	19	1	no	—
164	M₁₆	—	19	4	no	—
165	M₁₆	—	38	2	no	—
166	C₂×C₈	—	19	1	no	—
167	C₂×C₈	—	19	2	no	—
168	C₂×C₈	—	19	1	no	—
169	C₂×C₈	—	38	4	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	2	no	—
178	C₄⋊C₄	—	19	2	no	—
179	C₄⋊C₄	—	19	1	no	—
180	C₄⋊C₄	C₄×D₁₉	1	2	yes	—
181	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
182	C₂²⋊C₄	—	19	2	no	—
183	C₂²⋊C₄	—	19	2	no	—
184	C₄²	—	19	1	no	—
185	C₄²	—	19	1	no	—
186	C₄²	—	19	2	no	—
187	C₄²	—	19	1	no	—
188	C₄²	C₂²×D₁₉	1	1	yes	characteristic
189	C₄²	C₂²×D₁₉	1	2	yes	—
190	C₂³	—	19	1	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	38	2	no	—
193	Q₈	—	76	2	no	—
194	C₂×C₄	—	19	1	no	—
195	C₂×C₄	—	19	2	no	—
196	C₂×C₄	—	19	2	no	—
197	C₂×C₄	—	19	1	no	—
198	C₂×C₄	—	19	1	no	—
199	C₂×C₄	—	19	2	no	—
200	C₂×C₄	—	19	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
204	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
205	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
206	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
207	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
208	C₈	—	2	2	no	—
209	C₈	—	2	1	no	—
210	C₈	—	19	2	no	—
211	C₈	—	38	2	no	—
212	C₈	—	38	1	no	—
213	C₈	Q₈×D₁₉	1	2	yes	—
214	C₂²	—	19	2	no	—
215	C₂²	—	38	1	no	—
216	C₂²	—	38	1	no	—
217	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
218	C₄	—	2	2	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	19	2	no	—
222	C₄	—	38	1	no	—
223	C₄	—	38	2	no	—
224	C₄	—	38	1	no	—
225	C₄	—	38	2	no	—
226	C₄	#10597353	1	2	yes	—
227	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
228	C₄	#41×D₁₉	1	1	yes	characteristic
229	C₂	—	38	2	no	—
230	C₂	C₄×Q₈×D₁₉	1	1	yes	characteristic
231	C₂	C₂×#10597353	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×#446	C₂
prime radical	C₂²×D₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#446	D₁₉
hypocenter	C₁₉	#2962
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. #11926672	C₂	semidirect
3. #11926671	C₂	semidirect
4. #11926671	C₂	semidirect
5. Q₈×C₁₉⋊C₈	C₂	semidirect
6. C₈×Dic₃₈	C₂	semidirect
11. C₁₉×#446	C₂	semidirect
71. #64515	Q₈	semidirect
117. #446	D₁₉	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
#11927098	2
#11926672	2
#11926671	2
Q₈×C₁₉⋊C₈	2
C₈×Dic₃₈	2
#11926569	2
C₄⋊C₈×D₁₉	2
#11926501	2
C₄×#64515	2
C₁₉×#446	2
#2962	19