Subgroups — C₄×#10597433 #14576847

Order 2432.

1492 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597433	C₂	1	1	yes	maximal, characteristic
2	#11927026	C₂	1	4	yes	maximal, complemented
3	#11927025	C₂	1	6	yes	maximal, complemented
4	#11927022	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927020	C₂	1	4	yes	maximal, complemented
6	C₄×#64545	C₂	1	4	yes	maximal, complemented
7	C₄×#64541	C₂	1	6	yes	maximal, complemented
8	C₄×Q₈×D₁₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597433	C₄	1	16	yes	direct product factor
12	C₂×#64545	C₂²	1	4	yes	—
13	C₂×Q₈×D₁₉	C₂²	1	4	yes	—
14	C₂×#64541	C₂²	1	6	yes	—
15	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
16	C₄×Q₈×C₁₉	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
18	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
19	Q₈×Dic₁₉	C₂²	1	4	yes	—
20	Q₈×Dic₁₉	C₂²	1	4	yes	—
21	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	—
22	C₄×C₂²⋊D₁₉	C₂²	1	12	yes	—
23	#10597372	C₂²	1	6	yes	—
24	#10597339	C₂²	1	12	yes	—
25	#10597338	C₂²	1	12	yes	—
26	C₄⋊C₄×D₁₉	C₂²	1	12	yes	—
27	#10597333	C₂²	1	12	yes	—
28	C₄×D₇₆	C₂²	1	6	yes	—
29	C₄×D₇₆	C₂²	1	6	yes	—
30	#10597318	C₂²	1	12	yes	—
31	C₄²×D₁₉	C₂²	1	12	yes	—
32	C₄×Dic₃₈	C₂²	1	6	yes	—
33	C₄×Dic₃₈	C₂²	1	6	yes	—
34	C₂×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
35	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
39	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
40	#64545	C₂×C₄	1	32	yes	complemented
41	Q₈×D₁₉	C₂×C₄	1	32	yes	complemented
42	#64541	C₂×C₄	1	48	yes	complemented
43	C₂×D₇₆	C₂³	1	6	yes	—
44	C₂×C₄×D₁₉	C₂³	1	4	yes	—
45	C₂×C₄×D₁₉	C₂³	1	12	yes	—
46	C₂×C₄×D₁₉	C₂³	1	12	yes	—
47	C₂×Dic₃₈	C₂³	1	6	yes	—
48	C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
49	C₄²×C₁₉	C₂³	1	6	yes	—
50	C₄²×C₁₉	C₂³	1	6	yes	—
51	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
52	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
53	(C₂×D₁₉)⋊C₄	C₂³	1	12	yes	—
54	C₄⋊Dic₁₉	C₂³	1	6	yes	—
55	C₄⋊Dic₁₉	C₂³	1	6	yes	—
56	Dic₁₉⋊C₄	C₂³	1	4	yes	—
57	Dic₁₉⋊C₄	C₂³	1	12	yes	—
58	C₄×Dic₁₉	C₂³	1	12	yes	—
59	C₄×Dic₁₉	C₂³	1	4	yes	—
60	C₄×Dic₁₉	C₂³	1	12	yes	—
61	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
62	C₂²×D₁₉	C₂⁴	1	4	yes	—
63	Q₈×C₁₉	C₂²×C₄	1	16	yes	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	4	3	no	—
66	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	—
67	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
68	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
70	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂²⋊D₁₉	C₂²×C₄	1	16	yes	—
72	C₂×Dic₁₉	C₂⁴	1	4	yes	—
73	C₂×Dic₁₉	C₂⁴	1	4	yes	—
74	C₂×Dic₁₉	C₂⁴	1	4	yes	—
75	D₇₆	C₂²×C₄	1	24	yes	—
76	C₄×D₁₉	—	2	8	no	—
77	C₄×D₁₉	—	4	12	no	—
78	C₄×D₁₉	C₂²×C₄	1	48	yes	—
79	Dic₃₈	C₂²×C₄	1	24	yes	—
80	C₄×2₋¹⁺⁴	—	19	1	no	maximal, Sylow
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	2	1	no	—
83	C₂²×C₁₉	C₂³×C₄	1	2	yes	—
84	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
85	C₂×D₁₉	—	2	4	no	—
86	C₂×D₁₉	—	2	4	no	—
87	C₂×D₁₉	C₂³×C₄	1	8	yes	—
88	C₄×C₁₉	—	2	1	no	—
89	C₄×C₁₉	—	2	6	no	—
90	C₄×C₁₉	C₂³×C₄	1	12	yes	—
91	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	complemented
92	Dic₁₉	—	2	4	no	—
93	Dic₁₉	—	2	4	no	—
94	Dic₁₉	C₂³×C₄	1	8	yes	—
95	C₂×2₋¹⁺⁴	—	19	1	no	—
96	#520	—	19	4	no	—
97	#520	—	19	6	no	—
98	#519	—	19	1	no	—
99	#519	—	19	4	no	—
100	C₄×#41	—	19	4	no	—
101	C₄×#41	—	19	6	no	—
102	C₂×C₄×Q₈	—	19	4	no	—
103	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
104	C₂×C₁₉	—	2	2	no	—
105	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
106	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
107	C₂×C₁₉	#585	1	1	yes	characteristic
108	D₁₉	—	2	8	no	—
109	2₋¹⁺⁴	—	19	16	no	—
110	C₂×#41	—	19	4	no	—
111	C₂×#41	—	19	6	no	—
112	C₂²×Q₈	—	19	4	no	—
113	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
114	C₄×Q₈	—	19	4	no	—
115	C₄×Q₈	—	19	4	no	—
116	C₄×Q₈	—	19	12	no	—
117	C₄×Q₈	—	19	6	no	—
118	C₄×Q₈	—	19	6	no	—
119	C₄×Q₈	C₂×D₁₉	1	4	yes	—
120	C₄×Q₈	C₂×D₁₉	1	4	yes	—
121	C₄×D₄	—	19	4	no	—
122	C₄×D₄	—	19	12	no	—
123	C₄×D₄	—	19	12	no	—
124	C₄×D₄	—	19	6	no	—
125	C₄×D₄	—	19	6	no	—
126	#117	—	19	6	no	—
127	#117	—	19	12	no	—
128	#117	—	19	12	no	—
129	C₂×C₄⋊C₄	—	19	12	no	—
130	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
131	C₂×C₄²	—	19	12	no	—
132	C₂×C₄²	C₂×D₁₉	1	3	yes	—
133	C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
134	#41	—	19	32	no	—
135	#41	—	19	48	no	—
136	C₂×Q₈	—	19	32	no	—
137	C₂×Q₈	—	19	6	no	—
138	C₂×Q₈	C₄×D₁₉	1	8	yes	complemented
139	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
140	C₂×D₄	—	19	4	no	—
141	C₂×D₄	—	19	6	no	—
142	C₂²×C₄	—	19	12	no	—
143	C₂²×C₄	—	19	4	no	—
144	C₂²×C₄	—	19	12	no	—
145	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
146	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
147	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
148	C₄⋊C₄	—	19	12	no	—
149	C₄⋊C₄	—	19	4	no	—
150	C₄⋊C₄	—	19	6	no	—
151	C₄⋊C₄	—	19	6	no	—
152	C₄⋊C₄	C₂²×D₁₉	1	12	yes	—
153	C₂²⋊C₄	—	19	4	no	—
154	C₂²⋊C₄	—	19	12	no	—
155	C₂²⋊C₄	—	19	4	no	—
156	C₄²	—	19	12	no	—
157	C₄²	—	19	12	no	—
158	C₄²	—	19	4	no	—
159	C₄²	C₂²×D₁₉	1	6	yes	—
160	C₄²	C₂²×D₁₉	1	6	yes	—
161	C₂³	—	19	4	no	—
162	C₂³	C₂³×D₁₉	1	1	yes	characteristic
163	Q₈	—	19	24	no	—
164	Q₈	C₂×C₄×D₁₉	1	16	yes	—
165	D₄	—	19	16	no	—
166	D₄	—	19	24	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	3	no	—
169	C₂×C₄	—	19	4	no	—
170	C₂×C₄	—	19	48	no	—
171	C₂×C₄	—	19	4	no	—
172	C₂×C₄	—	19	4	no	—
173	C₂×C₄	—	38	8	no	—
174	C₂×C₄	—	76	12	no	—
175	C₂×C₄	C₂×C₄×D₁₉	1	12	yes	—
176	C₂×C₄	C₂³×D₁₉	1	6	yes	—
177	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂³×D₁₉	1	6	yes	—
179	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	19	8	no	—
183	C₂²	—	38	4	no	—
184	C₂²	—	38	4	no	—
185	C₂²	C₂²×C₄×D₁₉	1	2	yes	—
186	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	6	no	—
189	C₄	—	19	8	no	—
190	C₄	—	38	4	no	—
191	C₄	—	38	4	no	—
192	C₄	C₂²×C₄×D₁₉	1	12	yes	—
193	C₄	#10597433	1	2	yes	direct product factor
194	C₂	—	2	2	no	—
195	C₂	—	38	8	no	—
196	C₂	C₂³×C₄×D₁₉	1	1	yes	characteristic
197	C₂	C₂×#10597433	1	1	yes	characteristic
198	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₄×Q₈×C₁₉	C₂
socle, cosocle	C₂²×C₁₉	C₂⁵
prime radical	C₂×#10597433	C₂
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11927026	C₂	semidirect
3. #11927025	C₂	semidirect
4. #11927022	C₂	semidirect
5. #11927020	C₂	semidirect
6. C₄×#64545	C₂	semidirect
7. C₄×#64541	C₂	semidirect
8. C₄×Q₈×D₁₉	C₂	semidirect
9. C₂×C₄×Q₈×C₁₉	C₂	semidirect
11. #10597433	C₄	direct (N × H)
34. C₂×Q₈×C₁₉	C₂×C₄	semidirect
40. #64545	C₂×C₄	semidirect
41. Q₈×D₁₉	C₂×C₄	semidirect
42. #64541	C₂×C₄	semidirect
91. C₄×C₁₉	2₋¹⁺⁴	semidirect
103. C₂×C₄×Q₈	D₁₉	semidirect
133. C₁₉	C₄×2₋¹⁺⁴	semidirect
138. C₂×Q₈	C₄×D₁₉	semidirect
193. C₄	#10597433	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×#10597433	2
#11927026	2
#11927025	2
#11927022	2
#11927020	2
C₄×#64545	2
C₄×#64541	2
C₄×Q₈×D₁₉	2
C₂×C₄×Q₈×C₁₉	2
C₄×2₋¹⁺⁴	19

Subgroups — C4×#10597433 #14576847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597433 #14576847