Subgroups — C₂×#11926672 #14572560

Order 2432.

400 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#11926672	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
7	C₂×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₃₈	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
14	C₂×Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×Dic₃₈	C₄	1	4	yes	—
21	C₄×Dic₃₈	C₂²	1	4	yes	—
22	C₁₉×#97	C₂²	1	4	yes	—
23	#10597272	C₂²	1	4	yes	—
24	Dic₁₉⋊C₈	C₂²	1	4	yes	—
25	Dic₁₉⋊C₈	C₂²	1	4	yes	—
26	C₈×Dic₁₉	C₂²	1	4	yes	—
27	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×Dic₃₈	—	2	4	no	—
36	C₂×Dic₃₈	C₂×C₄	1	4	yes	—
37	C₂×C₈×C₁₉	—	2	2	no	—
38	C₂×C₈×C₁₉	Q₈	1	4	yes	complemented
39	C₂×C₈×C₁₉	C₂³	1	2	yes	—
40	C₂×C₈×C₁₉	C₂³	1	2	yes	—
41	C₄²×C₁₉	C₂×C₄	1	2	yes	—
42	C₄²×C₁₉	C₂³	1	2	yes	—
43	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
44	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
45	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
46	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
48	C₄×Dic₁₉	C₂³	1	2	yes	—
49	C₄×Dic₁₉	C₂³	1	2	yes	—
50	C₂×C₁₉⋊C₈	—	2	2	no	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
53	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
54	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
61	C₂×C₄×C₁₉	#41	1	2	yes	—
62	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₁₉	—	2	2	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	M₁₆	1	4	yes	—
67	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
68	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
69	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
70	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
71	Dic₃₈	—	2	8	no	—
72	C₈×C₁₉	—	2	2	no	—
73	C₈×C₁₉	C₂×Q₈	1	4	yes	complemented
74	C₁₉⋊C₈	—	2	2	no	—
75	C₁₉⋊C₈	—	2	2	no	—
76	C₂×#446	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	C₄×Q₈	1	2	yes	—
78	C₂²×C₁₉	C₂×M₁₆	1	2	yes	—
79	C₂²×C₁₉	#131	1	2	yes	—
80	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	C₄×Q₈	1	2	yes	—
84	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
85	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
86	Dic₁₉	—	2	2	no	—
87	Dic₁₉	—	2	2	no	—
88	Dic₁₉	—	2	2	no	—
89	Dic₁₉	C₂×M₁₆	1	4	yes	—
90	C₂×C₄×Q₈	—	19	1	no	—
91	#446	—	19	8	no	—
92	C₂×C₄⋊C₈	—	19	1	no	—
93	C₂×C₄⋊C₈	—	19	1	no	—
94	C₂×C₄⋊C₈	—	19	1	no	—
95	C₂×#97	—	19	1	no	—
96	C₂×#97	D₁₉	1	1	yes	characteristic
97	C₂×C₄×C₈	—	19	1	no	—
98	C₂×C₁₉	#446	1	4	yes	complemented
99	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
100	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
101	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
102	C₂²×Q₈	—	19	1	no	—
103	C₂²×C₈	—	19	1	no	—
104	C₂²×C₈	—	19	1	no	—
105	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
106	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
107	C₄×Q₈	—	19	4	no	—
108	C₄×Q₈	—	19	4	no	—
109	C₂×C₄⋊C₄	—	19	1	no	—
110	C₂×C₄⋊C₄	—	19	1	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄²	—	19	1	no	—
113	C₂×C₄²	—	19	1	no	—
114	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
115	C₄⋊C₈	—	19	4	no	—
116	C₄⋊C₈	—	19	4	no	—
117	C₄⋊C₈	—	19	4	no	—
118	#97	—	19	4	no	—
119	#97	C₂×D₁₉	1	4	yes	—
120	C₄×C₈	—	19	4	no	—
121	C₁₉	C₂×#446	1	1	yes	characteristic, complemented, Sylow
122	C₂×Q₈	—	19	4	no	—
123	C₂×Q₈	—	38	4	no	—
124	C₂²×C₄	—	19	1	no	—
125	C₂²×C₄	—	19	1	no	—
126	C₂²×C₄	—	19	1	no	—
127	C₂²×C₄	—	19	1	no	—
128	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	19	2	no	—
133	C₂×C₈	—	19	2	no	—
134	C₂×C₈	—	38	2	no	—
135	C₂×C₈	—	38	2	no	—
136	C₂×C₈	Dic₃₈	1	4	yes	complemented
137	C₂×C₈	C₂²×D₁₉	1	2	yes	—
138	C₂×C₈	C₂²×D₁₉	1	2	yes	—
139	C₄⋊C₄	—	19	4	no	—
140	C₄⋊C₄	—	19	4	no	—
141	C₄⋊C₄	—	19	4	no	—
142	C₄²	—	19	2	no	—
143	C₄²	—	19	2	no	—
144	C₄²	—	19	2	no	—
145	C₄²	—	19	2	no	—
146	C₄²	C₄×D₁₉	1	2	yes	—
147	C₄²	C₂²×D₁₉	1	2	yes	—
148	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
149	Q₈	—	38	8	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	19	2	no	—
153	C₂×C₄	—	19	4	no	—
154	C₂×C₄	—	19	2	no	—
155	C₂×C₄	—	19	2	no	—
156	C₂×C₄	—	19	2	no	—
157	C₂×C₄	—	38	2	no	—
158	C₂×C₄	—	38	2	no	—
159	C₂×C₄	—	38	2	no	—
160	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
161	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
162	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
163	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
164	C₂×C₄	#64541	1	2	yes	—
165	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
166	C₈	—	2	2	no	—
167	C₈	—	38	2	no	—
168	C₈	—	38	2	no	—
169	C₈	C₂×Dic₃₈	1	4	yes	complemented
170	C₂²	C₄×Dic₃₈	1	2	yes	—
171	C₂²	M₁₆×D₁₉	1	2	yes	—
172	C₂²	#10597353	1	2	yes	—
173	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	2	2	no	—
176	C₄	—	19	4	no	—
177	C₄	—	38	2	no	—
178	C₄	—	38	2	no	—
179	C₄	—	38	2	no	—
180	C₄	C₄×Dic₃₈	1	2	yes	—
181	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
182	C₄	C₂×#64541	1	1	yes	characteristic
183	C₂	#11926672	1	4	yes	direct product factor
184	C₂	C₂×C₄×Dic₃₈	1	1	yes	characteristic
185	C₂	C₂×M₁₆×D₁₉	1	1	yes	characteristic
186	C₂	C₂×#10597353	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	C₂×#446
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
2. #11926672	C₂	direct (N × H)
38. C₂×C₈×C₁₉	Q₈	semidirect
73. C₈×C₁₉	C₂×Q₈	semidirect
98. C₂×C₁₉	#446	semidirect
121. C₁₉	C₂×#446	semidirect
136. C₂×C₈	Dic₃₈	semidirect
169. C₈	C₂×Dic₃₈	semidirect
183. C₂	#11926672	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×Dic₃₈	2
#11926672	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×Dic₁₉⋊C₈	2
C₂×#10597272	2
C₂×C₈×Dic₁₉	2
C₂×C₁₉×#97	2
C₂×#446	19

Subgroups — C2×#11926672 #14572560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926672 #14572560