Subgroups — #18081441

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	#14564571	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926276	C₂	1	2	yes	maximal
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
8	C₄×Dic₇₆	—	2	2	no	—
9	C₄×Dic₇₆	—	2	2	no	—
10	C₂×#10597275	C₄	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#10597273	C₄	1	2	yes	—
13	#11926298	—	2	4	no	—
14	#11926295	—	2	2	no	—
15	#11926276	—	2	4	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#322	—	2	2	no	—
20	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂×Dic₁₉⋊C₄	—	2	2	no	—
28	C₂×C₄×Dic₁₉	—	2	2	no	—
29	C₂²×C₁₉⋊C₈	—	2	2	no	—
30	C₂×Dic₇₆	—	2	4	no	—
31	C₂×Dic₇₆	—	2	2	no	—
32	C₄×Dic₃₈	—	2	2	no	—
33	C₄×Dic₃₈	—	2	2	no	—
34	C₄×Dic₃₈	—	2	2	no	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	1	no	—
37	C₄×C₈×C₁₉	—	2	1	no	—
38	C₄×C₈×C₁₉	—	2	1	no	—
39	C₄×C₈×C₁₉	D₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	#10597275	—	2	2	no	—
43	#10597273	—	2	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂²×Dic₁₉	—	2	2	no	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂×Dic₃₈	—	2	2	no	—
52	C₂×Dic₃₈	—	2	2	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	—	2	2	no	—
55	C₂×Dic₃₈	—	2	2	no	—
56	C₂×Dic₃₈	M₁₆	1	4	yes	—
57	C₂×C₈×C₁₉	—	2	4	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	4	no	—
63	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄⋊Dic₁₉	—	2	2	no	—
70	C₄⋊Dic₁₉	—	2	2	no	—
71	Dic₁₉⋊C₄	—	4	2	no	—
72	Dic₁₉⋊C₄	—	4	2	no	—
73	C₄×Dic₁₉	—	4	2	no	—
74	C₄×Dic₁₉	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	4	no	—
77	Dic₇₆	—	2	8	no	—
78	#9664	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
88	C₂×C₄×C₁₉	#131	1	2	yes	—
89	C₂×C₄×C₁₉	#137	1	4	yes	—
90	C₂×Dic₁₉	—	2	4	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	4	no	—
95	Dic₃₈	—	2	4	no	—
96	Dic₃₈	—	2	4	no	—
97	Dic₃₈	—	4	2	no	—
98	Dic₃₈	—	4	2	no	—
99	C₈×C₁₉	—	2	4	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₈×C₁₉	—	2	2	no	—
102	C₈×C₁₉	—	4	2	no	—
103	C₁₉⋊C₈	—	8	2	no	—
104	C₂×C₄×Q₁₆	—	19	1	no	—
105	#1984	—	19	2	no	—
106	C₂×#334	—	19	1	no	—
107	C₂×Q₈⋊C₈	—	19	2	no	—
108	C₂×#322	D₁₉	1	1	yes	characteristic
109	C₂²×C₁₉	#390	1	1	yes	characteristic
110	C₂²×C₁₉	#435	1	2	yes	—
111	C₂²×C₁₉	#441	1	2	yes	—
112	C₂²×C₁₉	#443	1	2	yes	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	#407	1	1	yes	characteristic
116	C₄×C₁₉	#408	1	1	yes	characteristic
117	C₄×C₁₉	#435	1	2	yes	—
118	C₄×C₁₉	#470	1	2	yes	—
119	C₄×C₁₉	#497	1	2	yes	—
120	Dic₁₉	—	4	4	no	—
121	Dic₁₉	—	8	2	no	—
122	C₂²×Q₁₆	—	19	1	no	—
123	C₂×C₄×Q₈	—	19	2	no	—
124	C₄×Q₁₆	—	38	2	no	—
125	C₄×Q₁₆	—	38	2	no	—
126	C₂×#107	—	19	1	no	—
127	C₂×C₄⋊C₈	—	19	2	no	—
128	C₂×#103	—	19	2	no	—
129	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
132	#336	—	38	4	no	—
133	#334	—	38	2	no	—
134	Q₈⋊C₈	—	38	4	no	—
135	#322	—	2	2	no	—
136	C₂×C₁₉	#1587	1	4	yes	—
137	C₂×C₁₉	#1955	1	1	yes	characteristic
138	C₂×C₁₉	#1971	1	1	yes	characteristic
139	C₂×C₁₉	#1974	1	1	yes	characteristic
140	C₂²×Q₈	—	19	2	no	—
141	C₂×Q₁₆	—	38	4	no	—
142	C₂×Q₁₆	—	38	2	no	—
143	C₂²×C₈	—	2	1	no	—
144	C₂²×C₈	—	38	2	no	—
145	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
146	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
147	C₂²×C₈	D₇₆	1	2	yes	—
148	C₄×Q₈	—	38	2	no	—
149	C₄×Q₈	—	38	2	no	—
150	C₄×Q₈	—	38	2	no	—
151	C₄×Q₈	—	38	2	no	—
152	C₂×C₄⋊C₄	—	19	2	no	—
153	C₂×C₄⋊C₄	—	38	2	no	—
154	C₂×C₄²	—	38	2	no	—
155	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
156	#107	—	38	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	#103	—	38	4	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	—	2	1	no	—
162	C₄×C₈	—	2	1	no	—
163	C₄×C₈	D₇₆	1	2	yes	—
164	C₄×C₈	D₇₆	1	2	yes	—
165	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
166	C₁₉	#9664	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	19	4	no	—
168	C₂×Q₈	—	38	2	no	—
169	C₂×Q₈	—	38	2	no	—
170	C₂×Q₈	—	38	2	no	—
171	C₂×Q₈	—	38	2	no	—
172	C₂×Q₈	—	38	2	no	—
173	C₂²×C₄	—	38	2	no	—
174	C₂²×C₄	—	38	2	no	—
175	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
177	C₂²×C₄	#64541	1	1	yes	characteristic
178	Q₁₆	—	38	8	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	76	2	no	—
186	C₂×C₈	—	76	4	no	—
187	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
188	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	76	2	no	—
192	C₄⋊C₄	—	76	2	no	—
193	C₄²	—	76	2	no	—
194	C₄²	—	76	2	no	—
195	C₄²	C₂×D₇₆	1	1	yes	characteristic
196	C₄²	C₂×D₇₆	1	1	yes	characteristic
197	C₄²	#64541	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂³	C₄×D₇₆	1	1	yes	characteristic
200	Q₈	—	38	4	no	—
201	Q₈	—	38	4	no	—
202	Q₈	—	76	2	no	—
203	Q₈	—	76	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	38	4	no	—
206	C₂×C₄	—	76	2	no	—
207	C₂×C₄	—	76	2	no	—
208	C₂×C₄	—	76	4	no	—
209	C₂×C₄	—	76	2	no	—
210	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
211	C₂×C₄	#10597320	1	1	yes	characteristic
212	C₂×C₄	#10597321	1	1	yes	characteristic
213	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
214	C₂×C₄	#10597353	1	2	yes	—
215	C₂×C₄	#10597355	1	4	yes	—
216	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	#10597376	1	1	yes	characteristic
218	C₂×C₄	#10597376	1	1	yes	characteristic
219	C₈	—	2	4	no	—
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	4	2	no	—
223	C₈	—	152	2	no	—
224	C₂²	#11926446	1	1	yes	characteristic
225	C₂²	#11926617	1	2	yes	—
226	C₂²	#11926652	1	2	yes	—
227	C₂²	#11926662	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	76	4	no	—
231	C₄	—	152	2	no	—
232	C₄	#11926507	1	1	yes	characteristic
233	C₄	#11926512	1	1	yes	characteristic
234	C₄	#11926617	1	2	yes	—
235	C₄	#11926802	1	2	yes	—
236	C₄	#11926938	1	2	yes	—
237	C₂	#14562508	1	4	yes	—
238	C₂	#14564433	1	1	yes	characteristic
239	C₂	#14564506	1	1	yes	characteristic
240	C₂	#14564523	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9664
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
166. C₁₉	#9664	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₇₆	2
#14564571	2
C₂×#11926295	2
C₂×#11926276	2
C₂×C₁₉×#322	2
#9664	19