Subgroups — #18075408

Order 4864.

368 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14562383	C₂	1	2	yes	maximal, complemented
2	#14561949	C₂	1	2	yes	maximal
3	#14561466	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#433	C₂	1	1	yes	maximal, characteristic
5	#11926597	C₂²	1	4	yes	—
6	#11926297	—	2	2	no	—
7	#11926295	—	2	2	no	—
8	#11926270	—	2	2	no	—
9	#11926268	—	2	2	no	—
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₁₉×#433	—	2	2	no	—
12	C₁₉×#433	—	2	2	no	—
13	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₁₉×#117	—	2	2	no	—
25	C₁₉×#117	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×C₄⋊C₈	—	2	1	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₂²⋊C₈	—	2	1	no	—
36	C₁₉×C₂²⋊C₈	—	2	2	no	—
37	C₁₉×C₂²⋊C₈	—	2	1	no	—
38	C₁₉×#97	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₄×C₁₉⋊C₈	—	2	4	no	—
44	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	1	no	—
58	C₂×C₈×C₁₉	—	2	1	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	#41	1	2	yes	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	#8603	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	—	2	1	no	—
75	C₂³×C₁₉	—	2	2	no	—
76	C₂³×C₁₉	—	4	1	no	—
77	C₂³×C₁₉	—	4	1	no	—
78	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	2	yes	—
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
94	C₂×C₄×C₁₉	#131	1	2	yes	—
95	C₂×C₄×C₁₉	#131	1	2	yes	—
96	C₈×C₁₉	—	2	1	no	—
97	C₈×C₁₉	—	2	2	no	—
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	4	1	no	—
100	C₈×C₁₉	—	4	1	no	—
101	C₁₉⋊C₈	—	8	4	no	—
102	C₂×#433	D₁₉	1	1	yes	characteristic
103	#1564	—	19	2	no	—
104	#1458	—	19	2	no	—
105	#1275	—	19	2	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	4	1	no	—
109	C₂²×C₁₉	—	4	1	no	—
110	C₂²×C₁₉	—	4	1	no	—
111	C₂²×C₁₉	—	8	2	no	—
112	C₂²×C₁₉	#380	1	1	yes	characteristic
113	C₂²×C₁₉	#424	1	2	yes	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	4	1	no	—
117	C₄×C₁₉	—	4	1	no	—
118	C₄×C₁₉	—	4	1	no	—
119	C₄×C₁₉	#408	1	1	yes	characteristic
120	C₄×C₁₉	#408	1	1	yes	characteristic
121	C₄×C₁₉	#433	1	2	yes	—
122	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
123	#433	—	2	2	no	—
124	#433	—	2	2	no	—
125	#431	—	19	4	no	—
126	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
127	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
128	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
129	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
130	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
132	#335	—	38	2	no	—
133	#334	—	38	2	no	—
134	#324	—	38	2	no	—
135	#323	—	38	2	no	—
136	C₂×C₁₉	—	2	2	no	—
137	C₂×C₁₉	—	8	1	no	—
138	C₂×C₁₉	#1798	1	1	yes	characteristic
139	C₂×C₁₉	#1812	1	1	yes	characteristic
140	C₂×C₁₉	#1813	1	1	yes	characteristic
141	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
143	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
144	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
146	#117	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
149	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
151	C₂×C₂²⋊C₄	D₇₆	1	1	yes	characteristic
152	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	38	4	no	—
158	C₂²⋊C₈	—	2	1	no	—
159	C₂²⋊C₈	—	2	2	no	—
160	C₂²⋊C₈	—	2	1	no	—
161	C₂²⋊C₈	—	38	4	no	—
162	#97	—	2	2	no	—
163	C₄×C₈	—	38	4	no	—
164	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
165	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
166	C₁₉	#8603	1	1	yes	characteristic, complemented, Sylow
167	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
173	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
174	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
175	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
177	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	1	no	—
183	C₂×C₈	—	2	1	no	—
184	C₂×C₈	—	76	4	no	—
185	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
186	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	2	no	—
192	C₄²	—	2	1	no	—
193	C₄²	—	2	1	no	—
194	C₄²	#64541	1	2	yes	—
195	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
196	C₂³	—	2	1	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	4	1	no	—
199	C₂³	—	4	1	no	—
200	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	#10597370	1	2	yes	—
213	C₂×C₄	#10597372	1	1	yes	characteristic
214	C₂×C₄	#10597376	1	2	yes	—
215	C₂×C₄	#10597394	1	2	yes	—
216	C₂×C₄	#10597394	1	2	yes	—
217	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
218	C₈	—	2	1	no	—
219	C₈	—	2	2	no	—
220	C₈	—	2	1	no	—
221	C₈	—	4	1	no	—
222	C₈	—	4	1	no	—
223	C₈	—	152	4	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	8	2	no	—
230	C₂²	#11926404	1	1	yes	characteristic
231	C₂²	#11926571	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	4	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	1	no	—
237	C₄	#11926511	1	1	yes	characteristic
238	C₄	#11926511	1	1	yes	characteristic
239	C₄	#11926605	1	2	yes	—
240	C₂	—	2	2	no	—
241	C₂	—	8	1	no	—
242	C₂	#14563619	1	1	yes	characteristic
243	C₂	#14563681	1	1	yes	characteristic
244	C₂	#14563685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597372
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#433	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#433	D₁₉
hypocenter	C₁₉	#8603
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
1. #14562383	C₂	semidirect
3. #14561466	C₂	semidirect
166. C₁₉	#8603	semidirect

Maximal subgroups

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

subgroup	index
#14562383	2
#14561949	2
#14561466	2
C₂×C₁₉×#433	2
#8603	19