Subgroups — C₄×#11926307 #18087720

Order 4864.

1182 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	C₂×C₄×C₄⋊Dic₁₉	C₂	1	2	yes	maximal
2	C₂×#11926307	C₂	1	4	yes	maximal
3	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊Dic₁₉	C₂²	1	4	yes	—
5	C₂²×C₄×Dic₁₉	—	2	2	no	—
6	C₄×C₄⋊Dic₁₉	—	2	4	no	—
7	C₄×C₄⋊Dic₁₉	C₄	1	8	yes	complemented
8	C₂×C₁₉⋊#95	—	2	2	no	—
9	#11926307	C₄	1	16	yes	direct product factor
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₉	—	2	4	no	—
13	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	complemented
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂³×Dic₁₉	—	2	4	no	—
18	C₂²×C₈×C₁₉	—	2	4	no	—
19	C₂²×C₈×C₁₉	—	2	4	no	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₉	D₄	1	4	yes	—
25	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
26	C₂×C₄⋊Dic₁₉	—	2	4	no	—
27	C₂×C₄⋊Dic₁₉	—	2	8	no	—
28	C₂×C₄⋊Dic₁₉	C₂×C₄	1	16	yes	—
29	C₂×C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
30	C₂×C₄×Dic₁₉	—	2	8	no	—
31	C₂×C₄×Dic₁₉	—	4	4	no	—
32	C₂×C₄×Dic₁₉	—	4	4	no	—
33	C₄×C₈×C₁₉	—	2	8	no	—
34	C₁₉⋊#95	—	2	8	no	—
35	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₉	D₈	1	2	yes	—
42	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
43	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
46	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	4	yes	—
50	C₂²×Dic₁₉	—	2	8	no	—
51	C₂²×Dic₁₉	—	2	16	no	—
52	C₂²×Dic₁₉	—	4	4	no	—
53	C₂²×Dic₁₉	—	4	4	no	—
54	C₂²×Dic₁₉	—	4	8	no	—
55	C₂×C₈×C₁₉	—	2	4	no	—
56	C₂×C₈×C₁₉	—	2	4	no	—
57	C₂×C₈×C₁₉	—	2	16	no	—
58	C₂×C₈×C₁₉	C₄²	1	8	yes	complemented
59	C₄²×C₁₉	C₄²	1	4	yes	—
60	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
61	C₄²×C₁₉	C₄⋊C₄	1	8	yes	—
62	C₄⋊Dic₁₉	—	2	8	no	—
63	C₄⋊Dic₁₉	—	2	16	no	—
64	C₄⋊Dic₁₉	C₄²	1	16	yes	complemented
65	C₄×Dic₁₉	—	4	16	no	—
66	C₄×#340	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
68	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂³×C₁₉	C₄×D₄	1	4	yes	—
70	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
71	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
72	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
73	C₂³×C₁₉	#135	1	4	yes	—
74	C₂×C₄×C₁₉	—	2	8	no	—
75	C₂×C₄×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	#95	1	4	yes	—
77	C₂×C₄×C₁₉	#95	1	4	yes	—
78	C₂×C₄×C₁₉	#102	1	8	yes	—
79	C₂×C₄×C₁₉	#103	1	8	yes	—
80	C₂×C₄×C₁₉	#106	1	4	yes	—
81	C₂×C₄×C₁₉	#107	1	4	yes	—
82	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
83	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
87	C₂×C₄×C₁₉	#117	1	4	yes	—
88	C₂×C₄×C₁₉	#117	1	2	yes	—
89	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
90	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
91	C₂×Dic₁₉	—	2	16	no	—
92	C₂×Dic₁₉	—	4	8	no	—
93	C₂×Dic₁₉	—	4	8	no	—
94	C₂×Dic₁₉	—	4	16	no	—
95	C₂×Dic₁₉	—	4	16	no	—
96	C₈×C₁₉	—	2	8	no	—
97	C₂²×C₄×C₈	D₁₉	1	1	yes	characteristic
98	C₂×C₄×C₄⋊C₄	—	19	2	no	—
99	C₂×#340	—	19	4	no	—
100	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
101	C₂²×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
102	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
103	C₂²×C₁₉	C₂×#102	1	2	yes	—
104	C₂²×C₁₉	C₂×#103	1	2	yes	—
105	C₂²×C₁₉	#416	1	4	yes	—
106	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
108	C₂²×C₁₉	#427	1	2	yes	—
109	C₂²×C₁₉	C₄×D₈	1	4	yes	—
110	C₂²×C₁₉	C₄×SD₁₆	1	8	yes	—
111	C₂²×C₁₉	C₄×Q₁₆	1	4	yes	—
112	C₄×C₁₉	—	2	4	no	—
113	C₄×C₁₉	#340	1	8	yes	complemented
114	C₄×C₁₉	C₄³	1	1	yes	characteristic
115	C₄×C₁₉	#376	1	1	yes	characteristic
116	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
117	C₄×C₁₉	C₄×C₄⋊C₄	1	4	yes	—
118	Dic₁₉	—	4	16	no	—
119	C₂³×C₈	C₂×D₁₉	1	2	yes	—
120	C₂²×C₄⋊C₄	—	19	4	no	—
121	C₂²×C₄²	—	38	2	no	—
122	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₄×C₈	—	2	4	no	—
124	C₂×C₄×C₈	Dic₁₉	1	4	yes	complemented
125	C₄×C₄⋊C₄	—	19	8	no	—
126	C₄×C₄⋊C₄	—	38	4	no	—
127	C₂×#95	—	38	2	no	—
128	#340	—	19	16	no	—
129	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
130	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
131	C₂×C₁₉	#1735	1	1	yes	characteristic
132	C₂×C₁₉	C₄×#102	1	4	yes	—
133	C₂×C₁₉	C₄×#103	1	4	yes	—
134	C₂×C₁₉	C₄×#106	1	2	yes	—
135	C₂×C₁₉	C₄×#107	1	2	yes	—
136	C₂³×C₄	—	38	4	no	—
137	C₂³×C₄	D₇₆	1	1	yes	characteristic
138	C₂³×C₄	D₇₆	1	1	yes	characteristic
139	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
140	C₂²×C₈	—	2	4	no	—
141	C₂²×C₈	—	2	4	no	—
142	C₂²×C₈	C₄×D₁₉	1	8	yes	—
143	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
144	C₂×C₄⋊C₄	—	19	16	no	—
145	C₂×C₄⋊C₄	—	19	8	no	—
146	C₂×C₄⋊C₄	—	38	8	no	—
147	C₂×C₄⋊C₄	—	38	4	no	—
148	C₂×C₄²	—	38	8	no	—
149	C₂×C₄²	—	76	4	no	—
150	C₂×C₄²	—	76	4	no	—
151	C₂×C₄²	Dic₃₈	1	2	yes	—
152	C₂×C₄²	C₄×D₁₉	1	4	yes	—
153	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
154	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
155	C₄×C₈	—	2	8	no	—
156	#95	—	38	8	no	—
157	C₁₉	C₄×#340	1	1	yes	characteristic, complemented, Sylow
158	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	38	16	no	—
161	C₂²×C₄	—	38	8	no	—
162	C₂²×C₄	—	76	4	no	—
163	C₂²×C₄	—	76	4	no	—
164	C₂²×C₄	—	76	8	no	—
165	C₂²×C₄	#64516	1	4	yes	—
166	C₂²×C₄	D₁₅₂	1	2	yes	—
167	C₂²×C₄	Dic₇₆	1	2	yes	—
168	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
169	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
170	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
171	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
172	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
174	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
175	C₂²×C₄	#64541	1	4	yes	—
176	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
177	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	2	16	no	—
181	C₂×C₈	C₄×Dic₁₉	1	8	yes	complemented
182	C₄⋊C₄	—	19	16	no	—
183	C₄⋊C₄	—	38	8	no	—
184	C₄⋊C₄	—	38	16	no	—
185	C₄²	—	76	16	no	—
186	C₄²	C₄×Dic₁₉	1	4	yes	—
187	C₄²	Dic₁₉⋊C₄	1	8	yes	—
188	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
189	C₂³	C₄×D₇₆	1	4	yes	—
190	C₂³	C₂×#64516	1	2	yes	—
191	C₂³	C₂×D₁₅₂	1	1	yes	characteristic
192	C₂³	#10597350	1	4	yes	—
193	C₂³	C₂×Dic₇₆	1	1	yes	characteristic
194	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
195	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
196	C₂×C₄	—	2	8	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	38	16	no	—
199	C₂×C₄	—	76	8	no	—
200	C₂×C₄	—	76	8	no	—
201	C₂×C₄	—	76	16	no	—
202	C₂×C₄	—	76	16	no	—
203	C₂×C₄	#10597273	1	8	yes	—
204	C₂×C₄	#10597274	1	4	yes	—
205	C₂×C₄	#10597275	1	4	yes	—
206	C₂×C₄	#10597278	1	8	yes	—
207	C₂×C₄	C₁₉⋊#95	1	4	yes	—
208	C₂×C₄	C₁₉⋊#95	1	4	yes	—
209	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
210	C₂×C₄	C₄²×D₁₉	1	4	yes	—
211	C₂×C₄	#10597318	1	4	yes	—
212	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
213	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
214	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
215	C₂×C₄	#10597372	1	2	yes	—
216	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
217	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
218	C₈	—	2	8	no	—
219	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
220	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	4	yes	—
221	C₂²	C₄×C₄⋊Dic₁₉	1	2	yes	—
222	C₂²	C₂×#10597278	1	2	yes	—
223	C₂²	C₂×#10597273	1	2	yes	—
224	C₂²	#11926541	1	4	yes	—
225	C₂²	C₂×#10597274	1	1	yes	characteristic
226	C₂²	C₂×#10597275	1	1	yes	characteristic
227	C₂²	#11926582	1	2	yes	—
228	C₂²	C₄×D₁₅₂	1	4	yes	—
229	C₂²	C₄×#64516	1	8	yes	—
230	C₂²	C₄×Dic₇₆	1	4	yes	—
231	C₄	—	2	4	no	—
232	C₄	—	76	16	no	—
233	C₄	#11926307	1	8	yes	direct product factor
234	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
235	C₄	#11926390	1	1	yes	characteristic
236	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
237	C₄	C₄×Dic₁₉⋊C₄	1	4	yes	—
238	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
239	C₂	C₂×#11926307	1	1	yes	characteristic
240	C₂	#14563352	1	1	yes	characteristic
241	C₂	C₄×#10597278	1	4	yes	—
242	C₂	C₄×#10597273	1	4	yes	—
243	C₂	C₄×#10597274	1	2	yes	—
244	C₂	C₄×#10597275	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	D₇₆
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄×C₈	D₁₉
hypocenter	C₁₉	C₄×#340
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. C₄×C₄⋊Dic₁₉	C₄	semidirect
9. #11926307	C₄	direct (N × H)
13. C₂×C₄×C₈×C₁₉	C₄	semidirect
58. C₂×C₈×C₁₉	C₄²	semidirect
64. C₄⋊Dic₁₉	C₄²	semidirect
113. C₄×C₁₉	#340	semidirect
124. C₂×C₄×C₈	Dic₁₉	semidirect
157. C₁₉	C₄×#340	semidirect
181. C₂×C₈	C₄×Dic₁₉	semidirect
233. C₄	#11926307	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊Dic₁₉	2
C₂×#11926307	2
C₂²×C₄×C₈×C₁₉	2
C₄×#340	19

Subgroups — C4×#11926307 #18087720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926307 #18087720