Subgroups — #18088148

Order 4864.

838 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	2	yes	maximal
2	C₂×#11926299	C₂	1	2	yes	maximal
3	C₂×#11926299	C₂	1	2	yes	maximal
4	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	4	yes	—
6	#11926299	—	2	4	no	—
7	#11926299	—	2	4	no	—
8	#11926299	C₄	1	8	yes	complemented
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#376	—	2	4	no	—
13	C₂×C₁₉×#95	C₄	1	4	yes	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	—	2	2	no	—
21	C₂×C₄²×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₉	D₄	1	4	yes	—
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
28	C₂²×C₁₉⋊C₈	—	2	4	no	—
29	C₂²×C₁₉⋊C₈	—	2	4	no	—
30	C₂²×C₁₉⋊C₈	—	2	4	no	—
31	C₂²×C₁₉⋊C₈	—	2	4	no	—
32	C₂²×C₁₉⋊C₈	—	2	4	no	—
33	C₂²×C₁₉⋊C₈	—	2	4	no	—
34	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
35	C₁₉×#95	—	2	8	no	—
36	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	2	2	no	—
42	C₂²×C₄×C₁₉	—	2	2	no	—
43	C₂²×C₄×C₁₉	—	2	8	no	—
44	C₂²×C₄×C₁₉	—	2	8	no	—
45	C₂²×C₄×C₁₉	—	2	8	no	—
46	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
48	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	2	yes	—
54	C₂²×C₄×C₁₉	#41	1	2	yes	—
55	C₂²×C₄×C₁₉	#41	1	2	yes	—
56	C₂²×C₄×C₁₉	#41	1	2	yes	—
57	C₄²×C₁₉	—	2	8	no	—
58	C₄²×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	—	2	4	no	—
60	C₄²×C₁₉	—	2	8	no	—
61	C₂×C₁₉⋊C₈	—	2	8	no	—
62	C₂×C₁₉⋊C₈	—	2	8	no	—
63	C₂×C₁₉⋊C₈	—	2	8	no	—
64	C₂×C₁₉⋊C₈	—	4	4	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	#10796	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
70	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂³×C₁₉	#117	1	1	yes	characteristic
73	C₂³×C₁₉	#117	1	1	yes	characteristic
74	C₂³×C₁₉	#117	1	1	yes	characteristic
75	C₂³×C₁₉	#117	1	1	yes	characteristic
76	C₂³×C₁₉	#131	1	8	yes	—
77	C₂×C₄×C₁₉	—	2	4	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	4	no	—
80	C₂×C₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	2	8	no	—
82	C₂×C₄×C₁₉	—	2	8	no	—
83	C₂×C₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	4	4	no	—
86	C₂×C₄×C₁₉	—	4	4	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	4	4	no	—
89	C₂×C₄×C₁₉	#117	1	4	yes	—
90	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
92	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
93	C₂×C₄×C₁₉	#121	1	2	yes	—
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
95	C₂×C₄×C₁₉	#123	1	4	yes	—
96	C₂×C₄×C₁₉	#124	1	2	yes	—
97	C₂×C₄×C₁₉	#125	1	2	yes	—
98	C₂×C₄×C₁₉	#126	1	4	yes	—
99	C₁₉⋊C₈	—	4	8	no	—
100	C₂×#376	D₁₉	1	1	yes	characteristic
101	C₂×#336	—	19	2	no	—
102	C₂×#336	—	19	2	no	—
103	C₂×#336	—	19	2	no	—
104	C₂²×C₁₉	#376	1	1	yes	characteristic
105	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₁₉	#380	1	1	yes	characteristic
108	C₂²×C₁₉	#381	1	1	yes	characteristic
109	C₂²×C₁₉	#382	1	1	yes	characteristic
110	C₂²×C₁₉	#383	1	1	yes	characteristic
111	C₂²×C₁₉	#405	1	4	yes	—
112	C₂²×C₁₉	#408	1	4	yes	—
113	C₂²×C₁₉	#424	1	4	yes	—
114	C₂²×C₁₉	#433	1	4	yes	—
115	C₂²×C₁₉	#433	1	4	yes	—
116	C₂²×C₁₉	#433	1	4	yes	—
117	C₂²×C₁₉	#433	1	4	yes	—
118	C₄×C₁₉	—	4	4	no	—
119	C₄×C₁₉	—	4	4	no	—
120	C₄×C₁₉	—	4	4	no	—
121	C₄×C₁₉	#387	1	4	yes	—
122	C₄×C₁₉	#388	1	4	yes	—
123	C₂³×C₈	—	19	4	no	—
124	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
125	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
126	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
127	#376	—	2	4	no	—
128	C₂×#95	Dic₁₉	1	4	yes	—
129	#336	—	19	8	no	—
130	#336	—	38	4	no	—
131	#336	—	38	4	no	—
132	C₂×C₁₉	#1434	1	1	yes	characteristic
133	C₂×C₁₉	#1746	1	2	yes	—
134	C₂×C₁₉	#1750	1	2	yes	—
135	C₂×C₁₉	#1768	1	2	yes	—
136	C₂×C₁₉	#1798	1	2	yes	—
137	C₂×C₁₉	#1818	1	2	yes	—
138	C₂×C₁₉	#1832	1	2	yes	—
139	C₂×C₁₉	#1840	1	2	yes	—
140	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
141	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
142	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
143	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
144	C₂²×C₈	—	19	8	no	—
145	C₂²×C₈	—	38	4	no	—
146	C₂²×C₈	—	38	4	no	—
147	C₂²×C₈	—	38	4	no	—
148	C₂²×C₈	—	38	4	no	—
149	C₂²×C₈	—	38	4	no	—
150	C₂²×C₈	—	38	4	no	—
151	C₂×C₄²	—	2	2	no	—
152	C₂×C₄²	—	2	2	no	—
153	C₂×C₄²	—	2	2	no	—
154	C₂×C₄²	—	2	2	no	—
155	C₂×C₄²	—	2	2	no	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	Dic₃₈	1	2	yes	—
158	C₂×C₄²	C₄×D₁₉	1	4	yes	—
159	C₂×C₄²	D₇₆	1	2	yes	—
160	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
161	#95	—	2	8	no	—
162	C₁₉	#10796	1	1	yes	characteristic, complemented, Sylow
163	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
164	C₂²×C₄	—	2	8	no	—
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	2	8	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
174	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
175	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
176	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
178	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
179	C₂²×C₄	#64541	1	2	yes	—
180	C₂²×C₄	#64541	1	2	yes	—
181	C₂²×C₄	#64541	1	2	yes	—
182	C₂²×C₄	#64541	1	2	yes	—
183	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
184	C₂×C₈	—	38	8	no	—
185	C₂×C₈	—	38	8	no	—
186	C₂×C₈	—	38	8	no	—
187	C₂×C₈	—	76	4	no	—
188	C₂×C₈	—	76	4	no	—
189	C₂×C₈	—	76	4	no	—
190	C₂×C₈	—	76	4	no	—
191	C₄²	—	2	4	no	—
192	C₄²	—	2	4	no	—
193	C₄²	—	2	8	no	—
194	C₄²	—	2	8	no	—
195	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
196	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
197	C₂³	#10597372	1	1	yes	characteristic
198	C₂³	#10597372	1	1	yes	characteristic
199	C₂³	#10597372	1	1	yes	characteristic
200	C₂³	#10597372	1	1	yes	characteristic
201	C₂³	#10597394	1	8	yes	—
202	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
216	C₂×C₄	#10597316	1	2	yes	—
217	C₂×C₄	#10597318	1	4	yes	—
218	C₂×C₄	C₄×D₇₆	1	2	yes	—
219	C₂×C₄	#10597321	1	2	yes	—
220	C₂×C₄	#10597322	1	4	yes	—
221	C₂×C₄	#10597370	1	2	yes	—
222	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
223	C₂×C₄	#10597375	1	4	yes	—
224	C₂×C₄	#10597376	1	2	yes	—
225	C₈	—	76	8	no	—
226	C₂²	#11926390	1	1	yes	characteristic
227	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
228	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
229	C₂²	#11926404	1	1	yes	characteristic
230	C₂²	#11926407	1	1	yes	characteristic
231	C₂²	#11926410	1	1	yes	characteristic
232	C₂²	#11926412	1	1	yes	characteristic
233	C₂²	#11926500	1	4	yes	—
234	C₂²	#11926511	1	4	yes	—
235	C₂²	#11926571	1	4	yes	—
236	C₂²	#11926605	1	4	yes	—
237	C₂²	#11926605	1	4	yes	—
238	C₂²	#11926605	1	4	yes	—
239	C₂²	#11926605	1	4	yes	—
240	C₄	—	4	4	no	—
241	C₄	—	4	4	no	—
242	C₄	—	4	4	no	—
243	C₄	#11926428	1	4	yes	—
244	C₄	#11926435	1	4	yes	—
245	C₂	#14561862	1	1	yes	characteristic
246	C₂	#14563387	1	2	yes	—
247	C₂	#14563401	1	2	yes	—
248	C₂	#14563492	1	2	yes	—
249	C₂	#14563619	1	2	yes	—
250	C₂	#14563706	1	2	yes	—
251	C₂	#14563755	1	2	yes	—
252	C₂	#14563780	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Fitting	C₂×C₁₉×#376	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#376	D₁₉
hypocenter	C₁₉	#10796
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
8. #11926299	C₄	semidirect
162. C₁₉	#10796	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
C₂×C₁₉×#376	2
#10796	19