Subgroups — C₄×#11926301 #18087704

Order 4864.

954 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597372	C₂	1	2	yes	maximal
2	C₂×#11926301	C₂	1	4	yes	maximal
3	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597372	C₂²	1	4	yes	—
5	C₄×C₄⋊Dic₁₉	—	2	4	no	—
6	C₄×C₂²⋊Dic₁₉	—	2	4	no	—
7	#11926390	C₄	1	4	yes	complemented
8	C₄²×Dic₁₉	C₄	1	4	yes	complemented
9	#11926301	C₄	1	16	yes	direct product factor
10	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₁₉	—	2	4	no	—
13	C₂×C₁₉×#97	C₄	1	2	yes	complemented
14	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	complemented
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	—	2	4	no	—
18	C₂×M₁₆×C₁₉	—	2	4	no	—
19	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	—
20	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	4	yes	—
26	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
27	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
28	#10597372	—	2	8	no	—
29	#10597372	C₂×C₄	1	16	yes	—
30	C₂×C₄⋊Dic₁₉	—	2	4	no	—
31	C₂×C₄×Dic₁₉	—	2	8	no	—
32	C₂×C₄×Dic₁₉	C₂×C₄	1	8	yes	—
33	C₁₉×#97	—	2	4	no	—
34	C₄×C₈×C₁₉	—	2	4	no	—
35	C₁₉⋊#95	—	2	8	no	—
36	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	—	4	4	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
40	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
44	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	#41	1	4	yes	—
48	C₂²×Dic₁₉	—	2	8	no	—
49	M₁₆×C₁₉	—	2	16	no	—
50	C₂×C₈×C₁₉	—	2	4	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	C₄²	1	8	yes	complemented
53	C₄²×C₁₉	C₄²	1	1	yes	characteristic
54	C₄²×C₁₉	C₄²	1	2	yes	—
55	C₄²×C₁₉	C₄²	1	1	yes	characteristic
56	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
59	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
60	C₂²⋊Dic₁₉	—	2	16	no	—
61	C₄⋊Dic₁₉	—	2	16	no	—
62	C₄×Dic₁₉	—	2	8	no	—
63	C₄×Dic₁₉	—	4	16	no	—
64	C₄×Dic₁₉	C₄²	1	16	yes	complemented
65	C₄×H(3,ℤ/4)	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	—	4	2	no	—
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	C₂×C₄×C₁₉	—	2	8	no	—
71	C₂×C₄×C₁₉	—	2	4	no	—
72	C₂×C₄×C₁₉	—	4	4	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	#95	1	2	yes	—
75	C₂×C₄×C₁₉	#95	1	4	yes	—
76	C₂×C₄×C₁₉	#95	1	2	yes	—
77	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
78	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
82	C₂×C₄×C₁₉	#117	1	4	yes	—
83	C₂×C₄×C₁₉	#117	1	2	yes	—
84	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
85	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
86	C₂×Dic₁₉	—	2	16	no	—
87	C₂×Dic₁₉	—	4	16	no	—
88	C₈×C₁₉	—	2	8	no	—
89	C₂×C₄×M₁₆	D₁₉	1	1	yes	characteristic
90	C₄×#117	—	19	2	no	—
91	C₂×H(3,ℤ/4)	—	19	4	no	—
92	C₂²×C₁₉	—	2	4	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	4	4	no	—
95	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
96	C₂²×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
97	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
98	C₄×C₁₉	—	2	4	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	H(3,ℤ/4)	1	4	yes	complemented
101	C₄×C₁₉	C₄³	1	1	yes	characteristic
102	C₄×C₁₉	#376	1	1	yes	characteristic
103	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
104	C₄×C₁₉	C₄×C₄⋊C₄	1	4	yes	—
105	Dic₁₉	—	4	16	no	—
106	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
107	C₂×#117	—	19	4	no	—
108	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
109	C₄×M₁₆	—	2	4	no	—
110	C₂×#97	Dic₁₉	1	2	yes	complemented
111	C₂×C₄×C₈	Dic₁₉	1	2	yes	complemented
112	C₄×C₄⋊C₄	—	38	4	no	—
113	C₄×C₂²⋊C₄	—	38	4	no	—
114	#376	—	19	4	no	—
115	C₄³	—	19	4	no	—
116	H(3,ℤ/4)	—	19	16	no	—
117	C₂×C₁₉	—	2	4	no	—
118	C₂×C₁₉	—	2	2	no	—
119	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
120	C₂×C₁₉	C₂×H(3,ℤ/4)	1	2	yes	—
121	C₂³×C₄	D₇₆	1	2	yes	—
122	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
123	C₂×M₁₆	—	2	4	no	—
124	C₂×M₁₆	—	2	4	no	—
125	C₂×M₁₆	C₄×D₁₉	1	8	yes	—
126	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
127	#117	—	19	16	no	—
128	#117	—	38	8	no	—
129	C₂×C₄⋊C₄	—	38	4	no	—
130	C₂×C₂²⋊C₄	—	38	4	no	—
131	C₂×C₄²	—	19	8	no	—
132	C₂×C₄²	—	38	8	no	—
133	C₂×C₄²	Dic₃₈	1	2	yes	—
134	C₂×C₄²	C₄×D₁₉	1	2	yes	—
135	C₂×C₄²	C₄×D₁₉	1	2	yes	—
136	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
137	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
138	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
139	#97	—	2	4	no	—
140	C₄×C₈	—	2	4	no	—
141	#95	—	38	8	no	—
142	C₁₉	C₄×H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
143	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
144	C₂²×C₄	—	4	4	no	—
145	C₂²×C₄	—	38	8	no	—
146	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
147	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
148	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
149	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
150	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
152	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
153	C₂²×C₄	#64541	1	4	yes	—
154	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
155	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
156	M₁₆	—	2	16	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	C₄×Dic₁₉	1	8	yes	complemented
160	C₄⋊C₄	—	38	16	no	—
161	C₂²⋊C₄	—	38	16	no	—
162	C₄²	—	19	16	no	—
163	C₄²	—	38	8	no	—
164	C₄²	—	76	16	no	—
165	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
166	C₄²	C₄×Dic₁₉	1	2	yes	—
167	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
168	C₄²	Dic₁₉⋊C₄	1	4	yes	—
169	C₄²	Dic₁₉⋊C₄	1	4	yes	—
170	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
171	C₄²	C₂²⋊Dic₁₉	1	2	yes	—
172	C₂³	—	4	2	no	—
173	C₂³	C₄×D₇₆	1	4	yes	—
174	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
175	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂×C₄	—	2	8	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	38	16	no	—
181	C₂×C₄	—	76	16	no	—
182	C₂×C₄	C₁₉⋊#95	1	2	yes	—
183	C₂×C₄	C₁₉⋊#95	1	4	yes	—
184	C₂×C₄	C₁₉⋊#95	1	2	yes	—
185	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
186	C₂×C₄	C₄²×D₁₉	1	4	yes	—
187	C₂×C₄	#10597318	1	4	yes	—
188	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
189	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
190	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
191	C₂×C₄	#10597372	1	2	yes	—
192	C₂×C₄	C₄×C₂²⋊D₁₉	1	8	yes	—
193	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
194	C₈	—	2	8	no	—
195	C₂²	—	2	4	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	4	4	no	—
198	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
199	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	4	yes	—
200	C₂²	C₄×C₄⋊Dic₁₉	1	2	yes	—
201	C₄	—	2	4	no	—
202	C₄	—	2	2	no	—
203	C₄	—	76	16	no	—
204	C₄	#11926301	1	4	yes	direct product factor
205	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
206	C₄	#11926390	1	1	yes	characteristic
207	C₄	C₄×C₂²⋊Dic₁₉	1	2	yes	—
208	C₄	C₄×Dic₁₉⋊C₄	1	4	yes	—
209	C₂	—	2	4	no	—
210	C₂	—	2	2	no	—
211	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
212	C₂	C₂×#11926301	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₉
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₉
hypocenter	C₁₉	C₄×H(3,ℤ/4)
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
7. #11926390	C₄	semidirect
8. C₄²×Dic₁₉	C₄	semidirect
9. #11926301	C₄	direct (N × H)
13. C₂×C₁₉×#97	C₄	semidirect
14. C₂×C₄×C₈×C₁₉	C₄	semidirect
52. C₂×C₈×C₁₉	C₄²	semidirect
64. C₄×Dic₁₉	C₄²	semidirect
100. C₄×C₁₉	H(3,ℤ/4)	semidirect
110. C₂×#97	Dic₁₉	semidirect
111. C₂×C₄×C₈	Dic₁₉	semidirect
142. C₁₉	C₄×H(3,ℤ/4)	semidirect
159. C₂×C₈	C₄×Dic₁₉	semidirect
204. C₄	#11926301	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10597372	2
C₂×#11926301	2
C₂×C₄×M₁₆×C₁₉	2
C₄×H(3,ℤ/4)	19

Subgroups — C4×#11926301 #18087704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926301 #18087704