Subgroups — #18073167

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926276	C₂	1	2	yes	maximal
4	#14561475	C₂	1	2	yes	maximal
5	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₄	1	2	yes	—
7	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×#10597260	—	2	1	no	—
10	C₄×Dic₁₉⋊C₄	—	2	1	no	—
11	C₄×Dic₁₉⋊C₄	—	2	2	no	—
12	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₄²×Dic₁₉	—	2	1	no	—
15	#11926299	—	2	1	no	—
16	#11926276	C₄	1	8	yes	complemented
17	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	2	no	—
20	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	—	2	2	no	—
30	C₂×Dic₁₉⋊C₄	—	2	1	no	—
31	C₂×C₄×Dic₁₉	—	2	2	no	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	C₂×C₄×Dic₁₉	—	2	2	no	—
34	C₂×C₄×Dic₁₉	—	2	1	no	—
35	C₂²×C₁₉⋊C₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	4	no	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	4	no	—
39	C₄×Dic₃₈	C₂×C₄	1	4	yes	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
46	#10597260	—	4	2	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₉	—	2	1	no	—
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	—	2	2	no	—
55	C₂×Dic₃₈	—	2	1	no	—
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂×Dic₃₈	C₄²	1	2	yes	—
58	C₂×Dic₃₈	M₁₆	1	4	yes	—
59	C₂×C₈×C₁₉	—	2	4	no	—
60	C₂×C₈×C₁₉	—	4	4	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	2	no	—
63	C₄²×C₁₉	—	2	2	no	—
64	C₄²×C₁₉	—	4	2	no	—
65	C₄²×C₁₉	SD₁₆	1	2	yes	—
66	C₄²×C₁₉	Q₁₆	1	2	yes	—
67	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	2	1	no	—
70	C₄⋊Dic₁₉	—	2	2	no	—
71	C₄⋊Dic₁₉	C₄²	1	2	yes	—
72	C₄⋊Dic₁₉	M₁₆	1	4	yes	—
73	Dic₁₉⋊C₄	—	2	8	no	—
74	Dic₁₉⋊C₄	—	2	4	no	—
75	C₄×Dic₁₉	—	2	8	no	—
76	C₄×Dic₁₉	—	2	4	no	—
77	C₄×Dic₁₉	—	4	4	no	—
78	C₄×Dic₁₉	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	#8175	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	#103	1	4	yes	—
91	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
96	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#135	1	2	yes	—
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	—	2	4	no	—
102	C₂×Dic₁₉	—	2	2	no	—
103	C₂×Dic₁₉	—	2	4	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	Dic₃₈	—	2	2	no	—
108	Dic₃₈	—	2	4	no	—
109	Dic₃₈	#97	1	4	yes	complemented
110	C₈×C₁₉	—	4	4	no	—
111	C₁₉⋊C₈	—	4	4	no	—
112	C₄²×Q₈	—	19	1	no	—
113	#1767	—	19	1	no	—
114	#1744	D₁₉	1	1	yes	characteristic
115	C₂×Q₈⋊C₈	—	19	2	no	—
116	#1279	—	19	2	no	—
117	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₁₉	#407	1	2	yes	—
119	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
120	C₂²×C₁₉	#416	1	1	yes	characteristic
121	C₂²×C₁₉	#421	1	2	yes	—
122	C₄×C₁₉	—	2	4	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	—	4	2	no	—
125	C₄×C₁₉	C₂×#97	1	1	yes	characteristic
126	C₄×C₁₉	C₄×M₁₆	1	1	yes	characteristic
127	C₄×C₁₉	#432	1	2	yes	—
128	C₄×C₁₉	C₄×SD₁₆	1	2	yes	—
129	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
130	Dic₁₉	—	2	4	no	—
131	Dic₁₉	—	4	4	no	—
132	Dic₁₉	—	4	2	no	—
133	C₂×C₄×Q₈	—	19	2	no	—
134	C₂×C₄×Q₈	—	19	1	no	—
135	C₂×C₄⋊C₈	—	19	2	no	—
136	C₂×#97	—	38	1	no	—
137	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
138	C₄×C₄⋊C₄	—	19	2	no	—
139	C₄×C₄⋊C₄	—	19	1	no	—
140	C₄×C₄⋊C₄	—	38	1	no	—
141	C₄×C₄⋊C₄	—	38	2	no	—
142	C₄³	—	38	1	no	—
143	C₄³	C₂×D₁₉	1	1	yes	characteristic
144	#336	—	2	2	no	—
145	#336	—	38	1	no	—
146	Q₈⋊C₈	—	19	8	no	—
147	C₂×C₁₉	#1487	1	2	yes	—
148	C₂×C₁₉	#1488	1	2	yes	—
149	C₂×C₁₉	#1749	1	1	yes	characteristic
150	C₂×C₁₉	#1759	1	1	yes	characteristic
151	C₂×C₁₉	C₄×#103	1	1	yes	characteristic
152	C₂²×Q₈	—	19	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	38	2	no	—
155	C₄×Q₈	—	19	4	no	—
156	C₄×Q₈	—	38	4	no	—
157	C₄×Q₈	—	38	4	no	—
158	C₄×Q₈	—	38	2	no	—
159	C₂×C₄⋊C₄	—	19	1	no	—
160	C₂×C₄⋊C₄	—	19	2	no	—
161	C₂×C₄⋊C₄	—	38	2	no	—
162	C₂×C₄⋊C₄	—	38	1	no	—
163	C₂×C₄²	—	38	2	no	—
164	C₂×C₄²	—	38	1	no	—
165	C₂×C₄²	—	38	2	no	—
166	C₂×C₄²	—	38	1	no	—
167	C₂×C₄²	C₄×D₁₉	1	2	yes	—
168	C₂×C₄²	D₇₆	1	1	yes	characteristic
169	C₂×C₄²	D₇₆	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	19	4	no	—
173	C₄⋊C₈	—	38	2	no	—
174	#97	—	76	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	C₄×D₁₉	1	4	yes	—
177	#95	—	38	2	no	—
178	#95	—	38	1	no	—
179	C₁₉	#8175	1	1	yes	characteristic, complemented, Sylow
180	C₂×Q₈	—	19	2	no	—
181	C₂×Q₈	—	19	4	no	—
182	C₂×Q₈	—	38	1	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂²×C₄	—	38	1	no	—
185	C₂²×C₄	—	38	1	no	—
186	C₂²×C₄	—	38	2	no	—
187	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
188	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
189	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
192	C₂×C₈	—	2	4	no	—
193	C₂×C₈	—	4	4	no	—
194	C₂×C₈	—	38	4	no	—
195	C₂×C₈	—	76	2	no	—
196	C₂×C₈	—	76	2	no	—
197	C₄⋊C₄	—	19	2	no	—
198	C₄⋊C₄	—	19	4	no	—
199	C₄⋊C₄	—	38	8	no	—
200	C₄⋊C₄	—	38	1	no	—
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	38	4	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	4	2	no	—
207	C₄²	—	38	8	no	—
208	C₄²	—	38	4	no	—
209	C₄²	—	76	4	no	—
210	C₄²	—	76	2	no	—
211	C₄²	#64516	1	2	yes	—
212	C₄²	Dic₇₆	1	2	yes	—
213	C₄²	C₂×C₄×D₁₉	1	2	yes	—
214	C₄²	#64541	1	2	yes	—
215	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	Q₈	—	19	4	no	—
217	Q₈	—	38	4	no	—
218	Q₈	—	38	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	38	2	no	—
226	C₂×C₄	—	38	4	no	—
227	C₂×C₄	—	38	2	no	—
228	C₂×C₄	—	38	4	no	—
229	C₂×C₄	—	76	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	#10597273	1	4	yes	—
233	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
234	C₂×C₄	#10597318	1	1	yes	characteristic
235	C₂×C₄	C₄×D₇₆	1	2	yes	—
236	C₂×C₄	C₂×#64516	1	1	yes	characteristic
237	C₂×C₄	#10597350	1	2	yes	—
238	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
239	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
240	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
241	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
242	C₈	—	4	4	no	—
243	C₈	—	76	4	no	—
244	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
245	C₂²	#11926507	1	2	yes	—
246	C₂²	C₂×#10597273	1	1	yes	characteristic
247	C₂²	#11926541	1	1	yes	characteristic
248	C₂²	#11926562	1	2	yes	—
249	C₄	—	2	4	no	—
250	C₄	—	2	2	no	—
251	C₄	—	4	2	no	—
252	C₄	—	38	4	no	—
253	C₄	—	76	4	no	—
254	C₄	—	76	2	no	—
255	C₄	#97×D₁₉	1	1	yes	characteristic
256	C₄	#11926496	1	1	yes	characteristic
257	C₄	#11926599	1	2	yes	—
258	C₄	C₄×#64516	1	2	yes	—
259	C₄	C₄×Dic₇₆	1	2	yes	—
260	C₂	#14562065	1	2	yes	—
261	C₂	#14562070	1	2	yes	—
262	C₂	#14563398	1	1	yes	characteristic
263	C₂	#14563446	1	1	yes	characteristic
264	C₂	C₄×#10597273	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8175
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

Complements

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

N	H ≅ G/N	type
16. #11926276	C₄	semidirect
109. Dic₃₈	#97	semidirect
179. C₁₉	#8175	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₃₈	2
#14563488	2
C₂×#11926276	2
#14561475	2
C₁₉×#1744	2
#8175	19