Subgroups — #18069103

Order 4864.

344 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563381	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	—	2	1	no	—
5	C₂×#10597260	C₄	1	2	yes	—
6	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
7	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	C₄	1	2	yes	—
10	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#336	—	2	1	no	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	4	2	no	—
25	#10597260	—	2	4	no	—
26	#10597260	—	2	2	no	—
27	#10597260	C₈	1	4	yes	complemented
28	C₄×C₁₉⋊C₈	—	2	4	no	—
29	C₄×C₁₉⋊C₈	—	2	4	no	—
30	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	—	4	2	no	—
39	C₂×C₈×C₁₉	—	4	2	no	—
40	C₄²×C₁₉	—	2	1	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	—	2	2	no	—
43	C₄²×C₁₉	—	2	2	no	—
44	C₄²×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	4	1	no	—
47	C₄²×C₁₉	C₂×C₈	1	2	yes	—
48	C₄²×C₁₉	M₁₆	1	2	yes	—
49	C₂×C₁₉⋊C₈	—	2	4	no	—
50	C₂×C₁₉⋊C₈	—	2	4	no	—
51	C₂×C₁₉⋊C₈	—	2	4	no	—
52	C₂×C₁₉⋊C₈	—	2	4	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	#7030	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	#95	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
73	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#104	1	2	yes	—
76	C₂×C₄×C₁₉	#104	1	2	yes	—
77	C₂×C₄×C₁₉	#104	1	2	yes	—
78	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
79	C₂×C₄×C₁₉	#108	1	2	yes	—
80	C₈×C₁₉	—	8	2	no	—
81	C₁₉⋊C₈	—	2	8	no	—
82	C₁₉⋊C₈	—	4	4	no	—
83	#1831	D₁₉	1	1	yes	characteristic
84	#1744	—	19	1	no	—
85	C₄×#97	—	19	1	no	—
86	C₂²×C₁₉	#336	1	1	yes	characteristic
87	C₂²×C₁₉	#339	1	1	yes	characteristic
88	C₂²×C₁₉	#339	1	1	yes	characteristic
89	C₂²×C₁₉	#339	1	1	yes	characteristic
90	C₂²×C₁₉	#341	1	1	yes	characteristic
91	C₂²×C₁₉	#343	1	1	yes	characteristic
92	C₂²×C₁₉	#344	1	1	yes	characteristic
93	C₄×C₁₉	—	2	1	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	2	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	4	1	no	—
100	C₄×C₁₉	#329	1	2	yes	—
101	C₄×C₁₉	#330	1	2	yes	—
102	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
103	C₂×#97	—	19	2	no	—
104	C₂×#97	—	38	1	no	—
105	C₂×C₄×C₈	—	38	1	no	—
106	C₂×C₄×C₈	—	38	1	no	—
107	C₄³	C₂×D₁₉	1	1	yes	characteristic
108	#336	—	2	1	no	—
109	#336	—	2	1	no	—
110	#336	—	19	2	no	—
111	#336	—	38	1	no	—
112	C₂×C₁₉	#1276	1	1	yes	characteristic
113	C₂×C₁₉	#1278	1	1	yes	characteristic
114	C₂×C₁₉	#1283	1	1	yes	characteristic
115	C₂×C₁₉	#1295	1	1	yes	characteristic
116	C₂×C₁₉	#1299	1	1	yes	characteristic
117	C₂×C₁₉	#1300	1	1	yes	characteristic
118	C₂×C₁₉	#1302	1	1	yes	characteristic
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	38	2	no	—
121	C₂²×C₈	—	38	2	no	—
122	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
123	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
124	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
125	C₂×C₄²	D₇₆	1	1	yes	characteristic
126	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
127	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
129	C₄⋊C₈	—	4	2	no	—
130	#97	—	19	4	no	—
131	#97	—	38	4	no	—
132	#97	—	38	2	no	—
133	C₄×C₈	—	38	4	no	—
134	C₄×C₈	—	38	4	no	—
135	C₁₉	#7030	1	1	yes	characteristic, complemented, Sylow
136	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
137	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
138	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
139	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
140	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
141	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
142	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	—	38	4	no	—
147	C₂×C₈	—	38	4	no	—
148	C₂×C₈	—	38	4	no	—
149	C₂×C₈	—	38	4	no	—
150	C₂×C₈	—	76	2	no	—
151	C₂×C₈	—	76	2	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	2	2	no	—
154	C₄²	—	2	1	no	—
155	C₄²	—	2	1	no	—
156	C₄²	—	2	2	no	—
157	C₄²	—	2	2	no	—
158	C₄²	—	4	1	no	—
159	C₄²	C₈×D₁₉	1	2	yes	—
160	C₄²	#64515	1	2	yes	—
161	C₂³	C₁₉⋊#95	1	1	yes	characteristic
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄	Dic₁₉⋊C₈	1	2	yes	—
177	C₂×C₄	#10597272	1	1	yes	characteristic
178	C₂×C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
179	C₂×C₄	#10597279	1	2	yes	—
180	C₂×C₄	#10597282	1	2	yes	—
181	C₂×C₄	#10597290	1	1	yes	characteristic
182	C₂×C₄	#10597293	1	1	yes	characteristic
183	C₂×C₄	#10597294	1	2	yes	—
184	C₂×C₄	#10597294	1	2	yes	—
185	C₈	—	8	2	no	—
186	C₈	—	38	8	no	—
187	C₈	—	76	4	no	—
188	C₂²	#11926298	1	1	yes	characteristic
189	C₂²	#11926303	1	1	yes	characteristic
190	C₂²	#11926303	1	1	yes	characteristic
191	C₂²	#11926305	1	1	yes	characteristic
192	C₂²	#11926308	1	1	yes	characteristic
193	C₂²	#11926313	1	1	yes	characteristic
194	C₂²	#11926315	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	2	1	no	—
198	C₄	—	2	1	no	—
199	C₄	—	2	2	no	—
200	C₄	—	2	2	no	—
201	C₄	—	4	1	no	—
202	C₄	#11926284	1	2	yes	—
203	C₄	#11926286	1	2	yes	—
204	C₂	#14561467	1	1	yes	characteristic
205	C₂	#14561471	1	1	yes	characteristic
206	C₂	#14561485	1	1	yes	characteristic
207	C₂	#14561516	1	1	yes	characteristic
208	C₂	#14561524	1	1	yes	characteristic
209	C₂	#14561527	1	1	yes	characteristic
210	C₂	#14561533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1831	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1831	D₁₉
hypocenter	C₁₉	#7030
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
27. #10597260	C₈	semidirect
135. C₁₉	#7030	semidirect

Maximal subgroups

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

subgroup	index
#14563381	2
C₄×#10597260	2
C₁₉×#1831	2
#7030	19