Subgroups — C₂×#11927118 #14576952

Order 2432.

1512 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64541	C₂	1	1	yes	maximal, characteristic
2	#11927118	C₂	1	16	yes	maximal, direct product factor
3	C₂×#10597390	C₂	1	2	yes	maximal, complemented
4	C₂×#10597393	C₂	1	2	yes	maximal, complemented
5	C₂×#10597375	C₂	1	4	yes	maximal, complemented
6	C₂×#10597392	C₂	1	4	yes	maximal, complemented
7	C₂×#10597372	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×C₁₉	—	2	8	no	—
10	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
12	C₂²×Q₈×C₁₉	C₂²	1	8	yes	complemented
13	C₂³×C₄×C₁₉	C₂²	1	2	yes	—
14	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
16	C₂×#64541	—	2	8	no	—
17	C₂×#64541	C₂²	1	8	yes	—
18	C₂²×D₇₆	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
20	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
22	#10597393	C₂²	1	16	yes	complemented
23	#10597392	C₂²	1	32	yes	complemented
24	#10597390	C₂²	1	16	yes	complemented
25	#10597375	C₂²	1	32	yes	complemented
26	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	8	yes	—
27	#10597372	C₂²	1	8	yes	complemented
28	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	C₂²	1	8	yes	—
30	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
31	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×D₁₉	C₂³	1	2	yes	—
33	C₂×Q₈×C₁₉	—	2	8	no	—
34	C₂×Q₈×C₁₉	—	2	8	no	—
35	C₂×Q₈×C₁₉	—	2	32	no	—
36	C₂×Q₈×C₁₉	C₂³	1	8	yes	—
37	C₂×Q₈×C₁₉	C₂³	1	8	yes	—
38	C₂²×C₄×C₁₉	—	2	8	no	—
39	C₂²×C₄×C₁₉	D₄	1	8	yes	—
40	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂²×C₄×C₁₉	C₂³	1	8	yes	—
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
45	C₂×C₂²⋊D₁₉	—	2	8	no	—
46	C₂×C₂²⋊D₁₉	C₂³	1	8	yes	—
47	C₂²×Dic₁₉	C₂³	1	4	yes	—
48	C₂²×Dic₁₉	C₂³	1	2	yes	—
49	#64541	—	2	32	no	—
50	C₂×D₇₆	—	2	4	no	—
51	C₂×D₇₆	C₂³	1	4	yes	—
52	C₂×C₄×D₁₉	—	2	8	no	—
53	C₂×C₄×D₁₉	C₂³	1	8	yes	—
54	C₂×Dic₃₈	—	2	4	no	—
55	C₂×Dic₃₈	C₂³	1	4	yes	—
56	C₂²⋊Dic₁₉	C₂³	1	8	yes	—
57	(C₂×D₁₉)⋊C₄	C₂³	1	32	yes	—
58	C₄⋊Dic₁₉	C₂³	1	8	yes	—
59	Dic₁₉⋊C₄	C₂³	1	32	yes	—
60	C₄×Dic₁₉	C₂³	1	8	yes	—
61	C₂³×C₁₉	—	2	4	no	—
62	C₂³×C₁₉	C₂×D₄	1	4	yes	—
63	C₂³×C₁₉	C₂⁴	1	2	yes	—
64	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
65	C₂²×D₁₉	—	2	4	no	—
66	C₂²×D₁₉	—	2	8	no	—
67	C₂²×D₁₉	C₂⁴	1	4	yes	—
68	Q₈×C₁₉	—	2	16	no	—
69	Q₈×C₁₉	—	2	16	no	—
70	C₂×C₄×C₁₉	—	2	16	no	—
71	C₂×C₄×C₁₉	—	2	8	no	—
72	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
73	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×D₄	1	16	yes	—
75	C₂×C₄×C₁₉	C₂⁴	1	8	yes	—
76	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
77	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
78	C₂²⋊D₁₉	—	2	16	no	—
79	C₂×Dic₁₉	—	2	4	no	—
80	C₂×Dic₁₉	—	2	8	no	—
81	C₂×Dic₁₉	C₂⁴	1	8	yes	—
82	C₂×Dic₁₉	C₂⁴	1	4	yes	—
83	D₇₆	—	2	8	no	—
84	C₄×D₁₉	—	2	16	no	—
85	Dic₃₈	—	2	8	no	—
86	C₂×#536	—	19	1	no	maximal, Sylow
87	C₂²×C₁₉	—	2	8	no	—
88	C₂²×C₁₉	—	2	4	no	—
89	C₂²×C₁₉	C₂²×D₄	1	4	yes	—
90	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
91	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
92	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
93	C₂×D₁₉	—	2	4	no	—
94	C₂×D₁₉	—	2	8	no	—
95	C₂×D₁₉	—	4	8	no	—
96	C₄×C₁₉	—	2	8	no	—
97	C₄×C₁₉	C₂²×D₄	1	4	yes	—
98	C₄×C₁₉	C₂²×D₄	1	4	yes	—
99	Dic₁₉	—	2	4	no	—
100	Dic₁₉	—	2	8	no	—
101	C₂²×#41	—	19	1	no	—
102	C₂³×Q₈	D₁₉	1	1	yes	characteristic, complemented
103	#536	—	19	16	no	—
104	C₂×C₄⋊Q₈	—	19	2	no	—
105	C₂×#124	—	19	2	no	—
106	C₂×#123	—	19	4	no	—
107	C₂×C₂²⋊Q₈	—	19	4	no	—
108	C₂×#117	—	19	1	no	—
109	C₂×C₁₉	—	2	4	no	—
110	C₂×C₁₉	#536	1	4	yes	complemented
111	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
112	C₂×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
113	D₁₉	—	4	4	no	—
114	C₂×#41	—	19	8	no	—
115	C₂×#41	—	38	8	no	—
116	C₂²×Q₈	—	2	8	no	—
117	C₂²×Q₈	—	19	1	no	—
118	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
119	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
120	C₂²×Q₈	C₂×D₁₉	1	8	yes	complemented
121	C₂²×D₄	—	19	2	no	—
122	C₂²×D₄	—	19	1	no	—
123	C₂³×C₄	—	19	2	no	—
124	C₂³×C₄	C₂×D₁₉	1	2	yes	—
125	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
126	C₄⋊Q₈	—	19	16	no	—
127	#124	—	19	16	no	—
128	#123	—	19	32	no	—
129	C₂²⋊Q₈	—	19	32	no	—
130	#117	—	19	8	no	—
131	C₂×C₄⋊C₄	—	19	2	no	—
132	C₂×C₄⋊C₄	—	19	8	no	—
133	C₂×C₂²⋊C₄	—	19	2	no	—
134	C₂×C₂²⋊C₄	—	19	8	no	—
135	C₂×C₄²	—	19	2	no	—
136	C₁₉	C₂×#536	1	1	yes	characteristic, complemented, Sylow
137	C₂⁴	—	19	2	no	—
138	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
139	#41	—	38	32	no	—
140	C₂×Q₈	—	2	8	no	—
141	C₂×Q₈	—	2	8	no	—
142	C₂×Q₈	—	2	32	no	—
143	C₂×Q₈	—	19	4	no	—
144	C₂×Q₈	—	38	4	no	—
145	C₂×Q₈	C₂²×D₁₉	1	8	yes	—
146	C₂×Q₈	C₂²×D₁₉	1	8	yes	—
147	C₂×D₄	—	19	8	no	—
148	C₂×D₄	—	19	4	no	—
149	C₂×D₄	—	38	8	no	—
150	C₂×D₄	—	38	4	no	—
151	C₂²×C₄	—	2	8	no	—
152	C₂²×C₄	—	19	4	no	—
153	C₂²×C₄	—	19	2	no	—
154	C₂²×C₄	—	19	8	no	—
155	C₂²×C₄	—	38	8	no	—
156	C₂²×C₄	C₂²⋊D₁₉	1	8	yes	—
157	C₂²×C₄	C₂²×D₁₉	1	8	yes	—
158	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
159	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
160	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
161	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
162	C₄⋊C₄	—	19	32	no	—
163	C₄⋊C₄	—	19	8	no	—
164	C₂²⋊C₄	—	19	8	no	—
165	C₂²⋊C₄	—	19	32	no	—
166	C₄²	—	19	8	no	—
167	C₂³	—	2	4	no	—
168	C₂³	—	19	4	no	—
169	C₂³	—	38	8	no	—
170	C₂³	—	38	4	no	—
171	C₂³	C₂×C₂²⋊D₁₉	1	4	yes	—
172	C₂³	C₂³×D₁₉	1	2	yes	—
173	C₂³	C₂³×D₁₉	1	1	yes	characteristic
174	Q₈	—	2	16	no	—
175	Q₈	—	2	16	no	—
176	Q₈	—	38	8	no	—
177	D₄	—	38	16	no	—
178	D₄	—	38	8	no	—
179	C₂×C₄	—	2	16	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	19	8	no	—
182	C₂×C₄	—	19	4	no	—
183	C₂×C₄	—	38	8	no	—
184	C₂×C₄	—	38	4	no	—
185	C₂×C₄	—	38	16	no	—
186	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
187	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
188	C₂×C₄	C₂×C₂²⋊D₁₉	1	16	yes	—
189	C₂×C₄	C₂³×D₁₉	1	8	yes	—
190	C₂×C₄	C₂³×D₁₉	1	2	yes	—
191	C₂×C₄	C₂³×D₁₉	1	2	yes	—
192	C₂²	—	2	8	no	—
193	C₂²	—	2	4	no	—
194	C₂²	—	38	4	no	—
195	C₂²	—	38	8	no	—
196	C₂²	—	76	8	no	—
197	C₂²	#10597433	1	4	yes	—
198	C₂²	C₂²×C₂²⋊D₁₉	1	4	yes	—
199	C₂²	C₂²×C₂²⋊D₁₉	1	2	yes	—
200	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
201	C₄	—	2	8	no	—
202	C₄	—	38	4	no	—
203	C₄	—	38	8	no	—
204	C₄	C₂²×C₂²⋊D₁₉	1	4	yes	—
205	C₄	C₂²×C₂²⋊D₁₉	1	4	yes	—
206	C₂	—	2	4	no	—
207	C₂	—	76	4	no	—
208	C₂	#11927118	1	4	yes	direct product factor
209	C₂	C₂³×C₂²⋊D₁₉	1	1	yes	characteristic
210	C₂	C₂×#10597433	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₁₉
commutator, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂³×Q₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂⁴
prime radical	C₂²×#64541	C₂
hypercenter	C₂³×Q₈	D₁₉
hypocenter	C₁₉	C₂×#536
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
2. #11927118	C₂	direct (N × H)
3. C₂×#10597390	C₂	semidirect
4. C₂×#10597393	C₂	semidirect
5. C₂×#10597375	C₂	semidirect
6. C₂×#10597392	C₂	semidirect
7. C₂×#10597372	C₂	semidirect
8. C₂³×Q₈×C₁₉	C₂	semidirect
12. C₂²×Q₈×C₁₉	C₂²	semidirect
22. #10597393	C₂²	semidirect
23. #10597392	C₂²	semidirect
24. #10597390	C₂²	semidirect
25. #10597375	C₂²	semidirect
27. #10597372	C₂²	semidirect
102. C₂³×Q₈	D₁₉	semidirect
110. C₂×C₁₉	#536	semidirect
120. C₂²×Q₈	C₂×D₁₉	semidirect
136. C₁₉	C₂×#536	semidirect
208. C₂	#11927118	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#64541	2
#11927118	2
C₂×#10597390	2
C₂×#10597393	2
C₂×#10597375	2
C₂×#10597392	2
C₂×#10597372	2
C₂³×Q₈×C₁₉	2
C₂×#536	19

Subgroups — C2×#11927118 #14576952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927118 #14576952