Subgroups — #14565512

Order 2432.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₄	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₅₂	C₂	1	2	yes	maximal, complemented
3	#11926372	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926346	C₂	1	2	yes	maximal, complemented
5	C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₅₂	C₂²	1	2	yes	—
7	C₄×D₇₆	—	2	2	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597278	—	2	2	no	—
12	#10597275	C₂²	1	2	yes	—
13	D₃₀₄	C₄	1	4	yes	complemented
14	C₂×D₇₆	—	2	2	no	—
15	C₂×C₄×D₁₉	—	4	2	no	—
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄²×C₁₉	D₄	1	1	yes	characteristic
19	(C₂×D₁₉)⋊C₄	—	4	2	no	—
20	C₄⋊Dic₁₉	—	2	2	no	—
21	D₁₅₂	—	2	2	no	—
22	D₁₅₂	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₁₉	—	2	1	no	—
24	C₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
25	C₂²×D₁₉	—	4	2	no	—
26	C₂×C₄×C₁₉	D₈	1	2	yes	—
27	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₉	—	4	2	no	—
29	D₇₆	—	2	4	no	—
30	D₇₆	—	4	2	no	—
31	C₄×D₁₉	—	8	4	no	—
32	C₈×C₁₉	—	2	1	no	—
33	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₉	#41	1	1	yes	characteristic
35	#2177	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₂×D₁₉	—	4	4	no	—
38	C₂×D₁₉	—	8	2	no	—
39	C₂×D₁₉	—	8	2	no	—
40	C₄×C₁₉	—	2	2	no	—
41	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₁₉	#135	1	1	yes	characteristic
43	Dic₁₉	—	8	2	no	—
44	C₂×D₁₆	—	19	1	no	—
45	C₄×D₈	—	19	2	no	—
46	#367	—	19	1	no	—
47	#357	—	19	2	no	—
48	#346	D₁₉	1	1	yes	characteristic, complemented
49	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
50	C₂×C₁₉	#509	1	2	yes	—
51	D₁₉	—	8	4	no	—
52	C₂×D₈	—	19	2	no	—
53	C₄×D₄	—	38	2	no	—
54	D₁₆	—	19	4	no	—
55	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
56	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
57	#107	—	19	2	no	—
58	#102	—	38	2	no	—
59	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
60	C₁₉	#2177	1	1	yes	characteristic, complemented, Sylow
61	C₂×D₄	—	38	2	no	—
62	C₂²×C₄	—	76	2	no	—
63	D₈	—	19	4	no	—
64	D₈	—	38	2	no	—
65	C₂×C₈	D₇₆	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
67	C₄⋊C₄	—	38	2	no	—
68	C₂²⋊C₄	—	76	2	no	—
69	C₄²	D₇₆	1	1	yes	characteristic
70	C₁₆	—	2	1	no	—
71	C₁₆	C₄×D₁₉	1	2	yes	complemented
72	C₂³	—	76	2	no	—
73	D₄	—	38	4	no	—
74	D₄	—	76	2	no	—
75	C₂×C₄	—	76	2	no	—
76	C₂×C₄	—	152	4	no	—
77	C₂×C₄	D₁₅₂	1	2	yes	—
78	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
79	C₈	—	2	1	no	—
80	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
81	C₈	#64541	1	1	yes	characteristic
82	C₂²	—	76	4	no	—
83	C₂²	—	152	2	no	—
84	C₂²	—	152	2	no	—
85	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	152	2	no	—
88	C₄	C₄×D₇₆	1	1	yes	characteristic
89	C₄	#10597350	1	1	yes	characteristic
90	C₂	—	152	4	no	—
91	C₂	C₄×D₁₅₂	1	1	yes	characteristic
92	C₂	#11926982	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#346	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₃₀₄	C₂
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#346	D₁₉
hypocenter	C₁₉	#2177
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₅₂	C₂	semidirect
3. #11926372	C₂	semidirect
4. #11926346	C₂	semidirect
5. C₁₉×#346	C₂	semidirect
13. D₃₀₄	C₄	semidirect
22. D₁₅₂	C₂×C₄	semidirect
24. C₁₆×C₁₉	C₂×C₄	semidirect
48. #346	D₁₉	semidirect
60. C₁₉	#2177	semidirect
71. C₁₆	C₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₀₄	2
C₄×D₁₅₂	2
#11926372	2
#11926346	2
C₁₉×#346	2
#2177	19