Subgroups — #18090987

Order 4864.

790 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926299	C₂	1	3	yes	maximal
2	C₂×#11926299	C₂	1	3	yes	maximal
3	C₄×C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₉⋊C₈	C₂²	1	3	yes	—
5	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
6	#11926299	—	2	6	no	—
7	#11926299	—	2	6	no	—
8	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
9	C₂×C₁₉×#95	C₄	1	3	yes	—
10	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	C₂×C₄	1	3	yes	—
12	C₂³×C₄×C₁₉	C₂×C₄	1	3	yes	—
13	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	—	2	3	no	—
15	C₂×C₄²×C₁₉	—	2	3	no	—
16	C₂×C₄²×C₁₉	—	2	3	no	—
17	C₂×C₄²×C₁₉	—	2	3	no	—
18	C₂×C₄²×C₁₉	—	2	3	no	—
19	C₂×C₄²×C₁₉	—	2	3	no	—
20	C₂²×C₁₉⋊C₈	—	2	3	no	—
21	C₂²×C₁₉⋊C₈	—	2	3	no	—
22	C₂²×C₁₉⋊C₈	—	2	3	no	—
23	C₂²×C₁₉⋊C₈	—	2	3	no	—
24	C₂²×C₁₉⋊C₈	—	2	3	no	—
25	C₂²×C₁₉⋊C₈	—	2	3	no	—
26	C₂²×C₁₉⋊C₈	—	2	3	no	—
27	C₂²×C₁₉⋊C₈	—	2	3	no	—
28	C₂²×C₁₉⋊C₈	D₄	1	6	yes	—
29	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
30	C₁₉×#95	—	2	6	no	—
31	C₁₉×#95	C₈	1	4	yes	complemented
32	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	—	2	3	no	—
34	C₂²×C₄×C₁₉	—	2	3	no	—
35	C₂²×C₄×C₁₉	—	2	3	no	—
36	C₂²×C₄×C₁₉	—	2	3	no	—
37	C₂²×C₄×C₁₉	—	2	3	no	—
38	C₂²×C₄×C₁₉	—	2	3	no	—
39	C₂²×C₄×C₁₉	—	2	3	no	—
40	C₂²×C₄×C₁₉	—	2	3	no	—
41	C₂²×C₄×C₁₉	—	2	3	no	—
42	C₂²×C₄×C₁₉	—	2	3	no	—
43	C₂²×C₄×C₁₉	—	2	3	no	—
44	C₂²×C₄×C₁₉	—	2	3	no	—
45	C₂²×C₄×C₁₉	C₂×C₈	1	6	yes	—
46	C₂²×C₄×C₁₉	M₁₆	1	6	yes	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
48	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	3	yes	—
50	C₂²×C₄×C₁₉	#41	1	3	yes	—
51	C₂²×C₄×C₁₉	#41	1	3	yes	—
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₄²×C₁₉	—	4	3	no	—
54	C₄²×C₁₉	—	4	3	no	—
55	C₄²×C₁₉	—	4	3	no	—
56	C₄²×C₁₉	—	4	3	no	—
57	C₂×C₁₉⋊C₈	—	2	6	no	—
58	C₂×C₁₉⋊C₈	—	2	6	no	—
59	C₂×C₁₉⋊C₈	—	2	6	no	—
60	C₂×C₁₉⋊C₈	—	2	6	no	—
61	C₂×C₁₉⋊C₈	—	4	3	no	—
62	C₂×C₁₉⋊C₈	—	4	3	no	—
63	C₂×C₁₉⋊C₈	—	4	3	no	—
64	C₂×C₁₉⋊C₈	—	4	1	no	—
65	C₂×C₁₉⋊C₈	—	4	3	no	—
66	C₂×C₁₉⋊C₈	—	4	3	no	—
67	#11298	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#117	1	3	yes	—
69	C₂³×C₁₉	C₄×D₄	1	3	yes	—
70	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
71	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
72	C₂³×C₁₉	C₂×M₁₆	1	3	yes	—
73	C₂³×C₁₉	#131	1	3	yes	—
74	C₂³×C₁₉	#131	1	1	yes	characteristic
75	C₂×C₄×C₁₉	—	2	6	no	—
76	C₂×C₄×C₁₉	—	2	6	no	—
77	C₂×C₄×C₁₉	—	2	6	no	—
78	C₂×C₄×C₁₉	—	2	6	no	—
79	C₂×C₄×C₁₉	—	2	6	no	—
80	C₂×C₄×C₁₉	—	2	6	no	—
81	C₂×C₄×C₁₉	—	4	3	no	—
82	C₂×C₄×C₁₉	—	4	3	no	—
83	C₂×C₄×C₁₉	—	4	3	no	—
84	C₂×C₄×C₁₉	—	4	3	no	—
85	C₂×C₄×C₁₉	—	4	3	no	—
86	C₂×C₄×C₁₉	—	4	3	no	—
87	C₂×C₄×C₁₉	—	4	3	no	—
88	C₂×C₄×C₁₉	—	4	3	no	—
89	C₂×C₄×C₁₉	#121	1	3	yes	—
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	3	yes	—
91	C₂×C₄×C₁₉	#123	1	3	yes	—
92	C₂×C₄×C₁₉	#123	1	3	yes	—
93	C₂×C₄×C₁₉	#124	1	3	yes	—
94	C₂×C₄×C₁₉	#125	1	3	yes	—
95	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#126	1	3	yes	—
97	C₂×C₄×C₁₉	#126	1	3	yes	—
98	C₂×C₄×C₁₉	#126	1	3	yes	—
99	C₁₉⋊C₈	—	4	2	no	—
100	C₁₉⋊C₈	—	4	6	no	—
101	C₂×#336	—	19	3	no	—
102	C₂×#336	—	19	3	no	—
103	C₄×#95	D₁₉	1	1	yes	characteristic
104	C₂²×C₁₉	#383	1	1	yes	characteristic
105	C₂²×C₁₉	#387	1	3	yes	—
106	C₂²×C₁₉	#388	1	3	yes	—
107	C₂²×C₁₉	#431	1	3	yes	—
108	C₂²×C₁₉	#432	1	3	yes	—
109	C₂²×C₁₉	#433	1	3	yes	—
110	C₂²×C₁₉	#433	1	3	yes	—
111	C₂²×C₁₉	C₈×D₄	1	3	yes	—
112	C₂²×C₁₉	#435	1	3	yes	—
113	C₂²×C₁₉	#435	1	3	yes	—
114	C₂²×C₁₉	#436	1	3	yes	—
115	C₂²×C₁₉	C₈×Q₈	1	1	yes	characteristic
116	C₂²×C₁₉	#446	1	3	yes	—
117	C₄×C₁₉	—	4	6	no	—
118	C₄×C₁₉	—	4	6	no	—
119	C₄×C₁₉	#396	1	1	yes	characteristic
120	C₄×C₁₉	#397	1	3	yes	—
121	C₄×C₁₉	#400	1	3	yes	—
122	C₄×C₁₉	#401	1	1	yes	characteristic
123	C₂³×C₈	—	19	3	no	—
124	C₂³×C₈	—	19	1	no	—
125	C₂²×C₄²	C₂×D₁₉	1	3	yes	—
126	C₂×#95	Dic₁₉	1	3	yes	—
127	C₂×#95	Dic₁₉	1	1	yes	characteristic
128	#336	—	38	6	no	—
129	#336	—	38	6	no	—
130	C₂×C₁₉	#1443	1	1	yes	characteristic
131	C₂×C₁₉	#1839	1	1	yes	characteristic
132	C₂×C₁₉	#1840	1	1	yes	characteristic
133	C₂×C₁₉	#1916	1	3	yes	—
134	C₂×C₁₉	#1917	1	3	yes	—
135	C₂×C₁₉	#1923	1	3	yes	—
136	C₂×C₁₉	#1924	1	3	yes	—
137	C₂³×C₄	C₂×Dic₁₉	1	3	yes	—
138	C₂³×C₄	C₂×Dic₁₉	1	3	yes	—
139	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
140	C₂²×C₈	—	19	6	no	—
141	C₂²×C₈	—	19	2	no	—
142	C₂²×C₈	—	38	3	no	—
143	C₂²×C₈	—	38	3	no	—
144	C₂²×C₈	—	38	3	no	—
145	C₂²×C₈	—	38	3	no	—
146	C₂²×C₈	—	38	3	no	—
147	C₂²×C₈	—	38	3	no	—
148	C₂²×C₈	—	38	3	no	—
149	C₂²×C₈	—	38	3	no	—
150	C₂×C₄²	—	2	3	no	—
151	C₂×C₄²	—	2	3	no	—
152	C₂×C₄²	—	2	3	no	—
153	C₂×C₄²	—	2	3	no	—
154	C₂×C₄²	—	2	3	no	—
155	C₂×C₄²	—	2	3	no	—
156	#95	—	2	6	no	—
157	#95	C₁₉⋊C₈	1	4	yes	complemented
158	C₁₉	#11298	1	1	yes	characteristic, complemented, Sylow
159	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
160	C₂²×C₄	—	2	3	no	—
161	C₂²×C₄	—	2	3	no	—
162	C₂²×C₄	—	2	3	no	—
163	C₂²×C₄	—	2	3	no	—
164	C₂²×C₄	—	2	3	no	—
165	C₂²×C₄	—	2	3	no	—
166	C₂²×C₄	—	2	3	no	—
167	C₂²×C₄	—	2	3	no	—
168	C₂²×C₄	—	2	3	no	—
169	C₂²×C₄	—	2	3	no	—
170	C₂²×C₄	—	2	3	no	—
171	C₂²×C₄	—	2	3	no	—
172	C₂²×C₄	C₂×C₁₉⋊C₈	1	6	yes	—
173	C₂²×C₄	#64520	1	6	yes	—
174	C₂²×C₄	#64541	1	3	yes	—
175	C₂²×C₄	#64541	1	3	yes	—
176	C₂²×C₄	D₄×D₁₉	1	3	yes	—
177	C₂²×C₄	#64543	1	3	yes	—
178	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
179	C₂²×C₄	#64545	1	1	yes	characteristic
180	C₂×C₈	—	38	6	no	—
181	C₂×C₈	—	38	6	no	—
182	C₂×C₈	—	38	6	no	—
183	C₂×C₈	—	38	6	no	—
184	C₂×C₈	—	76	1	no	—
185	C₂×C₈	—	76	3	no	—
186	C₂×C₈	—	76	3	no	—
187	C₂×C₈	—	76	3	no	—
188	C₂×C₈	—	76	3	no	—
189	C₂×C₈	—	76	3	no	—
190	C₄²	—	4	3	no	—
191	C₄²	—	4	3	no	—
192	C₄²	—	4	3	no	—
193	C₄²	—	4	3	no	—
194	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
195	C₂³	C₂×#64520	1	3	yes	—
196	C₂³	#10597372	1	3	yes	—
197	C₂³	D₄×Dic₁₉	1	3	yes	—
198	C₂³	Q₈×Dic₁₉	1	1	yes	characteristic
199	C₂³	#10597394	1	3	yes	—
200	C₂³	#10597394	1	1	yes	characteristic
201	C₂×C₄	—	2	6	no	—
202	C₂×C₄	—	2	6	no	—
203	C₂×C₄	—	2	6	no	—
204	C₂×C₄	—	2	6	no	—
205	C₂×C₄	—	2	6	no	—
206	C₂×C₄	—	2	6	no	—
207	C₂×C₄	—	4	3	no	—
208	C₂×C₄	—	4	3	no	—
209	C₂×C₄	—	4	3	no	—
210	C₂×C₄	—	4	3	no	—
211	C₂×C₄	—	4	3	no	—
212	C₂×C₄	—	4	3	no	—
213	C₂×C₄	—	4	3	no	—
214	C₂×C₄	—	4	3	no	—
215	C₂×C₄	#10597322	1	1	yes	characteristic
216	C₂×C₄	#10597322	1	3	yes	—
217	C₂×C₄	#10597325	1	3	yes	—
218	C₂×C₄	#10597329	1	3	yes	—
219	C₂×C₄	#10597330	1	3	yes	—
220	C₂×C₄	#10597331	1	3	yes	—
221	C₂×C₄	#10597335	1	3	yes	—
222	C₂×C₄	#10597340	1	3	yes	—
223	C₂×C₄	#10597342	1	3	yes	—
224	C₂×C₄	#10597344	1	3	yes	—
225	C₈	—	76	2	no	—
226	C₈	—	76	6	no	—
227	C₂²	#11926412	1	1	yes	characteristic
228	C₂²	#11926430	1	3	yes	—
229	C₂²	#11926437	1	3	yes	—
230	C₂²	#11926597	1	3	yes	—
231	C₂²	#11926601	1	3	yes	—
232	C₂²	#11926605	1	3	yes	—
233	C₂²	#11926605	1	3	yes	—
234	C₂²	D₄×C₁₉⋊C₈	1	3	yes	—
235	C₂²	#11926616	1	3	yes	—
236	C₂²	#11926616	1	3	yes	—
237	C₂²	#11926622	1	3	yes	—
238	C₂²	Q₈×C₁₉⋊C₈	1	1	yes	characteristic
239	C₂²	#11926675	1	3	yes	—
240	C₄	—	4	6	no	—
241	C₄	—	4	6	no	—
242	C₄	#11926468	1	1	yes	characteristic
243	C₄	#11926473	1	3	yes	—
244	C₄	#11926485	1	3	yes	—
245	C₄	C₁₉⋊#401	1	1	yes	characteristic
246	C₂	#14561897	1	1	yes	characteristic
247	C₂	#14563778	1	1	yes	characteristic
248	C₂	#14563780	1	1	yes	characteristic
249	C₂	#14564194	1	3	yes	—
250	C₂	#14564201	1	3	yes	—
251	C₂	#14564243	1	3	yes	—
252	C₂	#14564250	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Fitting	C₄×C₁₉×#95	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₄×#95	D₁₉
hypocenter	C₁₉	#11298
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₄×#95

Complements

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

N	H ≅ G/N	type
31. C₁₉×#95	C₈	semidirect
157. #95	C₁₉⋊C₈	semidirect
158. C₁₉	#11298	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926299	2
C₄×C₁₉×#95	2
#11298	19