Finite Group Databasebeta

Subgroups — #14565305

Order 2432.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927107	C₂	1	1	yes	maximal, characteristic
2	#11926516	C₂	1	2	yes	maximal, complemented
3	#11926337	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926336	C₂	1	2	yes	maximal, complemented
5	C₁₉×#353	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64543	C₂²	1	1	yes	characteristic
7	C₂×D₄×D₁₉	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	#10597386	C₂²	1	1	yes	characteristic
10	#10597385	—	2	2	no	—
11	#10597383	—	2	2	no	—
12	#10597382	C₄	1	1	yes	characteristic, complemented
13	#10597323	—	2	2	no	—
14	#10597321	C₄	1	1	yes	characteristic, complemented
15	#10597318	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#99	C₂²	1	2	yes	complemented
17	#10597291	C₂²	1	2	yes	complemented
18	#10597263	—	2	2	no	—
19	C₂³×D₁₉	—	2	1	no	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₂²⋊D₁₉	—	2	2	no	—
24	C₂×C₂²⋊D₁₉	—	2	1	no	—
25	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
26	C₂²×Dic₁₉	D₄	1	2	yes	—
27	#64543	—	4	2	no	—
28	D₄×D₁₉	—	4	2	no	—
29	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
32	C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²⋊Dic₁₉	—	2	2	no	—
35	C₂²⋊Dic₁₉	—	2	2	no	—
36	(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	(C₂×D₁₉)⋊C₄	—	2	2	no	—
38	Dic₁₉⋊C₄	—	2	1	no	—
39	Dic₁₉⋊C₄	—	4	2	no	—
40	C₄×Dic₁₉	—	4	2	no	—
41	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₁₉	—	2	1	no	—
43	C₂³×C₁₉	C₂×D₄	1	2	yes	—
44	C₂²×D₁₉	—	2	1	no	—
45	C₂²×D₁₉	—	4	2	no	—
46	C₂²×D₁₉	—	8	2	no	—
47	C₂²×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	D₄×C₁₉	—	4	1	no	—
49	D₄×C₁₉	—	4	1	no	—
50	D₄×C₁₉	—	8	2	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²⋊D₁₉	—	4	2	no	—
55	C₂²⋊D₁₉	—	4	2	no	—
56	C₂²⋊D₁₉	—	8	2	no	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	2	1	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	C₂×Dic₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	D₇₆	—	4	1	no	—
64	C₄×D₁₉	—	2	2	no	—
65	Dic₃₈	—	4	1	no	—
66	#2128	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	1	no	—
71	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×D₁₉	—	2	1	no	—
73	C₂×D₁₉	—	4	1	no	—
74	C₂×D₁₉	—	4	2	no	—
75	C₂×D₁₉	—	4	1	no	—
76	C₂×D₁₉	—	8	4	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	4	1	no	—
79	C₄×C₁₉	—	8	2	no	—
80	Dic₁₉	—	2	2	no	—
81	Dic₁₉	—	4	1	no	—
82	Dic₁₉	—	8	2	no	—
83	Dic₁₉	#99	1	2	yes	—
84	#535	—	19	1	no	—
85	#410	—	19	2	no	—
86	#353	—	19	1	no	—
87	#353	—	19	2	no	—
88	#353	D₁₉	1	1	yes	characteristic, complemented
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	4	2	no	—
91	C₂×C₁₉	—	8	1	no	—
92	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
93	D₁₉	—	4	1	no	—
94	D₁₉	—	8	1	no	—
95	C₂×#41	—	19	1	no	—
96	C₂²×D₄	—	19	1	no	—
97	#127	—	19	1	no	—
98	#127	C₂×D₁₉	1	1	yes	characteristic
99	#124	—	19	1	no	—
100	#124	—	19	1	no	—
101	#121	—	38	2	no	—
102	#120	—	38	2	no	—
103	#117	—	19	1	no	—
104	#117	—	38	2	no	—
105	#99	—	19	2	no	—
106	#99	—	38	2	no	—
107	#99	C₂×D₁₉	1	2	yes	complemented
108	C₁₉	#2128	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	—	38	1	no	—
110	#41	—	76	2	no	—
111	C₂×Q₈	—	19	1	no	—
112	C₂×D₄	—	2	2	no	—
113	C₂×D₄	—	19	2	no	—
114	C₂×D₄	—	19	1	no	—
115	C₂×D₄	—	38	1	no	—
116	C₂×D₄	—	38	2	no	—
117	C₂×D₄	—	76	2	no	—
118	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
119	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
120	C₂²×C₄	—	19	2	no	—
121	C₂²×C₄	—	19	1	no	—
122	C₄⋊C₄	—	38	1	no	—
123	C₄⋊C₄	—	76	2	no	—
124	C₂²⋊C₄	—	2	2	no	—
125	C₂²⋊C₄	—	38	2	no	—
126	C₂²⋊C₄	—	38	1	no	—
127	C₂²⋊C₄	—	38	2	no	—
128	C₂²⋊C₄	—	38	2	no	—
129	C₄²	—	19	1	no	—
130	C₄²	—	76	2	no	—
131	C₄²	C₄×D₁₉	1	1	yes	characteristic
132	C₂³	—	2	1	no	—
133	C₂³	—	19	1	no	—
134	C₂³	—	38	1	no	—
135	C₂³	—	76	2	no	—
136	C₂³	—	152	2	no	—
137	C₂³	D₄×D₁₉	1	2	yes	—
138	Q₈	—	76	1	no	—
139	D₄	—	4	1	no	—
140	D₄	—	4	1	no	—
141	D₄	—	8	2	no	—
142	D₄	—	76	1	no	—
143	D₄	—	76	2	no	—
144	D₄	—	76	2	no	—
145	D₄	—	152	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	19	1	no	—
149	C₂×C₄	—	19	2	no	—
150	C₂×C₄	—	38	2	no	—
151	C₂×C₄	—	38	2	no	—
152	C₂×C₄	—	38	2	no	—
153	C₂×C₄	—	38	1	no	—
154	C₂×C₄	—	76	2	no	—
155	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
156	C₂²	—	2	2	no	—
157	C₂²	—	4	2	no	—
158	C₂²	—	4	2	no	—
159	C₂²	—	4	1	no	—
160	C₂²	—	38	1	no	—
161	C₂²	—	76	1	no	—
162	C₂²	—	76	2	no	—
163	C₂²	—	76	1	no	—
164	C₂²	—	152	4	no	—
165	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
166	C₄	—	2	1	no	—
167	C₄	—	4	1	no	—
168	C₄	—	8	2	no	—
169	C₄	—	19	2	no	—
170	C₄	—	38	2	no	—
171	C₄	—	76	1	no	—
172	C₄	—	152	2	no	—
173	C₂	—	2	1	no	—
174	C₂	—	4	2	no	—
175	C₂	—	8	1	no	—
176	C₂	—	76	1	no	—
177	C₂	—	152	1	no	—
178	C₂	#99×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#99×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂×D₄	C₂²×D₁₉
Fitting	C₁₉×#353	C₂
socle	C₂×C₁₉	C₂×#99
prime radical	#11927107	C₂
cosocle	C₂×D₄×C₁₉	C₂³
hypercenter	#353	D₁₉
hypocenter	C₁₉	#2128
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #353

Complements

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

N	H ≅ G/N	type
2. #11926516	C₂	semidirect
3. #11926337	C₂	semidirect
4. #11926336	C₂	semidirect
5. C₁₉×#353	C₂	semidirect
7. C₂×D₄×D₁₉	C₄	semidirect
12. #10597382	C₄	semidirect
14. #10597321	C₄	semidirect
15. #10597318	C₄	semidirect
16. C₁₉×#99	C₂²	semidirect
17. #10597291	C₂²	semidirect
88. #353	D₁₉	semidirect
107. #99	C₂×D₁₉	semidirect
108. C₁₉	#2128	semidirect

Maximal subgroups

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

subgroup	index
#11927107	2
#11926516	2
#11926337	2
#11926336	2
C₁₉×#353	2
#2128	19