Subgroups — #18081091

Order 4864.

382 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564353	C₂	1	2	yes	maximal
2	C₄×#10597274	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
4	#14561475	C₂	1	2	yes	maximal
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597274	C₄	1	1	yes	characteristic
7	C₂×#10597274	C₄	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×Dic₁₉⋊C₈	—	2	2	no	—
10	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	#11926307	C₄	1	2	yes	—
12	#11926298	—	2	2	no	—
13	#11926297	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	2	1	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	—	2	1	no	—
29	C₄×C₈×C₁₉	—	2	1	no	—
30	C₄×C₈×C₁₉	—	2	1	no	—
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	C₄×C₈×C₁₉	Q₈	1	2	yes	—
33	C₄×C₈×C₁₉	Q₈	1	2	yes	—
34	C₁₉⋊#95	—	2	2	no	—
35	#10597274	—	2	2	no	—
36	#10597274	C₈	1	4	yes	complemented
37	Dic₁₉⋊C₈	—	4	4	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂²×Dic₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	1	no	—
47	C₂×C₈×C₁₉	—	2	1	no	—
48	C₂×C₈×C₁₉	—	2	1	no	—
49	C₂×C₈×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
57	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₁₉	#41	1	1	yes	characteristic
61	C₄⋊Dic₁₉	—	2	2	no	—
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	C₂×C₈	1	4	yes	—
65	C₄×Dic₁₉	—	4	2	no	—
66	C₄×Dic₁₉	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	#9596	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
83	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×C₄×C₁₉	#137	1	2	yes	—
85	C₂×Dic₁₉	—	2	4	no	—
86	C₂×Dic₁₉	—	4	2	no	—
87	C₂×Dic₁₉	—	4	2	no	—
88	C₂×Dic₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	4	2	no	—
90	C₂×Dic₁₉	—	4	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₈×C₁₉	—	4	1	no	—
94	C₈×C₁₉	—	4	1	no	—
95	C₈×C₁₉	C₄⋊C₈	1	4	yes	complemented
96	C₁₉⋊C₈	—	8	2	no	—
97	#1939	—	19	2	no	—
98	C₄×#106	—	19	1	no	—
99	C₂×#335	—	19	1	no	—
100	C₂×#322	D₁₉	1	1	yes	characteristic
101	#1279	—	19	2	no	—
102	C₂²×C₁₉	#389	1	1	yes	characteristic
103	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
104	C₂²×C₁₉	#436	1	1	yes	characteristic
105	C₂²×C₁₉	#440	1	2	yes	—
106	C₂²×C₁₉	#444	1	2	yes	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
110	C₄×C₁₉	#424	1	1	yes	characteristic
111	C₄×C₁₉	C₈×Q₈	1	1	yes	characteristic
112	C₄×C₁₉	#446	1	1	yes	characteristic
113	C₄×C₁₉	#469	1	1	yes	characteristic
114	C₄×C₁₉	#470	1	1	yes	characteristic
115	C₄×C₁₉	#501	1	2	yes	—
116	Dic₁₉	—	4	4	no	—
117	Dic₁₉	—	8	2	no	—
118	C₂×#106	—	19	1	no	—
119	C₂×#106	—	19	1	no	—
120	C₂×C₄⋊C₈	—	19	2	no	—
121	C₂×C₄⋊C₈	—	38	2	no	—
122	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
125	C₄×C₄⋊C₄	—	19	2	no	—
126	#340	—	19	2	no	—
127	#336	—	38	2	no	—
128	#335	—	38	2	no	—
129	#322	—	2	2	no	—
130	C₂×C₁₉	SD₁₆⋊C₈	1	2	yes	—
131	C₂×C₁₉	#1592	1	2	yes	—
132	C₂×C₁₉	#1939	1	1	yes	characteristic
133	C₂×C₁₉	#1944	1	1	yes	characteristic
134	C₂×C₁₉	#1946	1	1	yes	characteristic
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	—	38	2	no	—
137	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
138	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
139	C₂²×C₈	D₇₆	1	1	yes	characteristic
140	C₂²×C₈	D₇₆	1	1	yes	characteristic
141	C₂×C₄⋊C₄	—	19	2	no	—
142	C₂×C₄⋊C₄	—	19	2	no	—
143	C₂×C₄²	—	38	2	no	—
144	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
145	#106	—	19	4	no	—
146	#106	—	38	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	38	2	no	—
149	C₄⋊C₈	—	76	4	no	—
150	C₄×C₈	—	2	1	no	—
151	C₄×C₈	—	2	1	no	—
152	C₄×C₈	—	2	1	no	—
153	C₄×C₈	Dic₃₈	1	2	yes	—
154	C₄×C₈	Dic₃₈	1	2	yes	—
155	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
156	#95	—	38	2	no	—
157	C₁₉	#9596	1	1	yes	characteristic, complemented, Sylow
158	C₂²×C₄	—	38	2	no	—
159	C₂²×C₄	—	38	2	no	—
160	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
162	C₂²×C₄	#64541	1	1	yes	characteristic
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	—	76	2	no	—
174	C₂×C₈	C₈×D₁₉	1	2	yes	—
175	C₂×C₈	#64515	1	2	yes	—
176	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
177	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
178	C₄⋊C₄	—	19	4	no	—
179	C₄⋊C₄	—	38	2	no	—
180	C₄⋊C₄	—	38	2	no	—
181	C₄⋊C₄	—	38	2	no	—
182	C₄²	—	76	2	no	—
183	C₄²	—	76	2	no	—
184	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
185	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
186	C₄²	#64541	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂³	C₄×D₇₆	1	1	yes	characteristic
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	38	4	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	—	76	2	no	—
194	C₂×C₄	—	76	2	no	—
195	C₂×C₄	—	76	2	no	—
196	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
197	C₂×C₄	#10597315	1	1	yes	characteristic
198	C₂×C₄	#10597316	1	1	yes	characteristic
199	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
200	C₂×C₄	C₂×#64515	1	1	yes	characteristic
201	C₂×C₄	#10597347	1	1	yes	characteristic
202	C₂×C₄	#10597347	1	1	yes	characteristic
203	C₂×C₄	#10597354	1	2	yes	—
204	C₂×C₄	#10597355	1	2	yes	—
205	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
206	C₂×C₄	#10597370	1	1	yes	characteristic
207	C₂×C₄	#10597376	1	1	yes	characteristic
208	C₈	—	2	2	no	—
209	C₈	—	4	2	no	—
210	C₈	—	4	1	no	—
211	C₈	—	4	1	no	—
212	C₈	—	152	2	no	—
213	C₈	Dic₁₉⋊C₈	1	4	yes	complemented
214	C₂²	#11926442	1	1	yes	characteristic
215	C₂²	C₈×D₇₆	1	1	yes	characteristic
216	C₂²	#11926623	1	1	yes	characteristic
217	C₂²	#11926646	1	2	yes	—
218	C₂²	#11926667	1	2	yes	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	76	4	no	—
222	C₄	—	152	2	no	—
223	C₄	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
224	C₄	#11926570	1	1	yes	characteristic
225	C₄	C₈×Dic₃₈	1	1	yes	characteristic
226	C₄	#11926674	1	1	yes	characteristic
227	C₄	#11926797	1	1	yes	characteristic
228	C₄	#11926802	1	1	yes	characteristic
229	C₄	#11926953	1	2	yes	—
230	C₂	#14562449	1	2	yes	—
231	C₂	#14562539	1	2	yes	—
232	C₂	#14564353	1	1	yes	characteristic
233	C₂	#14564378	1	1	yes	characteristic
234	C₂	#14564388	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9596
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
36. #10597274	C₈	semidirect
95. C₈×C₁₉	C₄⋊C₈	semidirect
157. C₁₉	#9596	semidirect
213. C₈	Dic₁₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#14564353	2
C₄×#10597274	2
C₂×#11926297	2
#14561475	2
C₂×C₁₉×#322	2
#9596	19