Subgroups — #18075467

Order 4864.

486 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563627	C₂	1	2	yes	maximal
2	#14562394	C₂	1	2	yes	maximal, complemented
3	#14561510	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	C₂×#10597290	—	2	2	no	—
7	#11926313	—	2	2	no	—
8	#11926297	—	2	2	no	—
9	#11926297	—	2	2	no	—
10	C₂³×C₈×C₁₉	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₈×D₄×C₁₉	—	2	2	no	—
13	C₈×D₄×C₁₉	—	2	2	no	—
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₉	—	2	2	no	—
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	4	4	no	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×#64520	—	2	4	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₂²⋊C₈	—	2	4	no	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	C₄×C₈×C₁₉	D₄	1	2	yes	—
35	#10597290	—	4	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
38	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
39	C₂×D₄×C₁₉	—	2	2	no	—
40	C₂×D₄×C₁₉	—	2	2	no	—
41	C₂×D₄×C₁₉	D₈	1	2	yes	—
42	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	—	4	2	no	—
47	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	—	4	4	no	—
55	C₂×C₈×C₁₉	—	4	4	no	—
56	C₂×C₈×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	#64520	—	4	4	no	—
65	#64520	—	4	4	no	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	#8616	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	—	2	2	no	—
69	C₂³×C₁₉	—	2	2	no	—
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	—	4	2	no	—
72	C₂³×C₁₉	#107	1	4	yes	—
73	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	D₄×C₁₉	—	2	4	no	—
75	D₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	2	yes	—
87	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₈×C₁₉	—	2	1	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₈×C₁₉	—	4	2	no	—
94	C₈×C₁₉	#100	1	2	yes	complemented
95	C₁₉⋊C₈	—	8	4	no	—
96	C₂×C₈×D₄	D₁₉	1	1	yes	characteristic
97	#1800	—	19	2	no	—
98	#1567	—	19	2	no	—
99	#1292	—	19	2	no	—
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	4	no	—
103	C₂²×C₁₉	—	4	4	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	—	4	2	no	—
106	C₂²×C₁₉	—	4	2	no	—
107	C₂²×C₁₉	#380	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
109	C₂²×C₁₉	#427	1	1	yes	characteristic
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	4	2	no	—
113	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
114	C₄×C₁₉	#413	1	1	yes	characteristic
115	C₄×C₁₉	#466	1	2	yes	—
116	C₄×C₁₉	#467	1	2	yes	—
117	C₂³×C₈	Dic₁₉	1	2	yes	—
118	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
119	C₈×D₄	—	2	2	no	—
120	C₈×D₄	—	2	2	no	—
121	#423	—	19	4	no	—
122	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₂×#100	—	38	2	no	—
124	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
125	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
126	#343	—	38	2	no	—
127	#335	—	38	2	no	—
128	#335	—	38	2	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	—	4	4	no	—
132	C₂×C₁₉	#1800	1	1	yes	characteristic
133	C₂×C₁₉	#1808	1	1	yes	characteristic
134	C₂×C₁₉	#1813	1	1	yes	characteristic
135	C₂²×D₄	D₇₆	1	1	yes	characteristic
136	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
137	C₂×M₁₆	—	38	4	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	—	2	2	no	—
140	C₂²×C₈	—	4	4	no	—
141	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
143	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
144	C₄×D₄	—	2	2	no	—
145	C₄×D₄	—	2	2	no	—
146	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
147	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
148	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	38	4	no	—
151	C₄⋊C₈	—	38	4	no	—
152	#100	—	76	4	no	—
153	C₂²⋊C₈	—	2	4	no	—
154	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
155	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
156	C₁₉	#8616	1	1	yes	characteristic, complemented, Sylow
157	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	D₁₅₂	1	2	yes	—
161	C₂×D₄	Dic₇₆	1	2	yes	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	4	2	no	—
165	C₂²×C₄	—	4	2	no	—
166	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
167	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
168	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
169	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
170	M₁₆	—	76	4	no	—
171	M₁₆	—	76	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	4	no	—
176	C₂×C₈	—	4	4	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	76	4	no	—
179	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
180	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
181	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	4	no	—
184	C₄²	#64541	1	2	yes	—
185	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
186	C₂³	—	2	2	no	—
187	C₂³	—	2	2	no	—
188	C₂³	—	4	2	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#10597275	1	4	yes	—
191	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
192	D₄	—	2	4	no	—
193	D₄	—	2	4	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
203	C₂×C₄	#10597350	1	2	yes	—
204	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
205	C₂×C₄	#10597370	1	2	yes	—
206	C₂×C₄	#10597372	1	1	yes	characteristic
207	C₂×C₄	#10597376	1	2	yes	—
208	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₈	—	2	2	no	—
210	C₈	—	2	1	no	—
211	C₈	—	4	2	no	—
212	C₈	—	152	4	no	—
213	C₈	#10597290	1	2	yes	complemented
214	C₂²	—	2	1	no	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	4	4	no	—
218	C₂²	—	4	4	no	—
219	C₂²	—	4	2	no	—
220	C₂²	—	4	2	no	—
221	C₂²	#11926404	1	1	yes	characteristic
222	C₂²	C₂×#10597275	1	1	yes	characteristic
223	C₂²	#11926582	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	2	no	—
226	C₄	—	4	2	no	—
227	C₄	C₂×#10597290	1	1	yes	characteristic
228	C₄	#11926528	1	1	yes	characteristic
229	C₄	#11926780	1	2	yes	—
230	C₄	#11926785	1	2	yes	—
231	C₂	—	2	1	no	—
232	C₂	—	2	1	no	—
233	C₂	—	4	4	no	—
234	C₂	#14563627	1	1	yes	characteristic
235	C₂	#14563664	1	1	yes	characteristic
236	C₂	#14563685	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈×D₄×C₁₉	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈×D₄	D₁₉
hypocenter	C₁₉	#8616
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #14562394	C₂	semidirect
3. #14561510	C₂	semidirect
94. C₈×C₁₉	#100	semidirect
156. C₁₉	#8616	semidirect
213. C₈	#10597290	semidirect

Maximal subgroups

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

subgroup	index
#14563627	2
#14562394	2
#14561510	2
C₂×C₈×D₄×C₁₉	2
#8616	19