Subgroups — #14563247

Order 2432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926895	C₂	1	3	yes	maximal, complemented
2	#11926891	C₂	1	3	yes	maximal
3	C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597320	C₂²	1	1	yes	characteristic
5	#10597315	C₂²	1	3	yes	—
6	C₄×C₈×C₁₉	C₂²	1	3	yes	—
7	#10597278	—	2	6	no	—
8	#10597273	—	2	6	no	—
9	C₂×D₇₆	—	2	3	no	—
10	C₂×Dic₃₈	—	2	3	no	—
11	C₂×C₈×C₁₉	D₄	1	6	yes	—
12	C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₁₉	—	2	3	no	—
14	C₄⋊Dic₁₉	—	2	3	no	—
15	C₂²×D₁₉	—	4	1	no	—
16	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
17	C₂×Dic₁₉	—	4	3	no	—
18	D₇₆	—	4	6	no	—
19	Dic₃₈	—	4	6	no	—
20	C₈×C₁₉	—	2	6	no	—
21	#1711	—	19	1	no	maximal, Sylow
22	C₂²×C₁₉	#127	1	1	yes	characteristic
23	C₂×D₁₉	—	8	3	no	—
24	C₄×C₁₉	#135	1	6	yes	—
25	Dic₁₉	—	8	3	no	—
26	#487	—	19	3	no	—
27	#486	—	19	3	no	—
28	C₈²	D₁₉	1	1	yes	characteristic, complemented
29	C₂×C₁₉	#495	1	3	yes	—
30	D₁₉	—	16	1	no	—
31	C₄⋊Q₈	—	19	3	no	—
32	#127	—	19	1	no	—
33	#103	—	38	6	no	—
34	#102	—	38	6	no	—
35	C₄×C₈	C₂×D₁₉	1	3	yes	—
36	C₁₉	#1711	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	38	3	no	—
38	C₂×D₄	—	38	3	no	—
39	C₂×C₈	D₇₆	1	6	yes	—
40	C₄⋊C₄	—	38	3	no	—
41	C₄⋊C₄	—	38	3	no	—
42	C₄²	C₂²×D₁₉	1	1	yes	characteristic
43	C₂³	—	76	1	no	—
44	Q₈	—	76	6	no	—
45	D₄	—	76	6	no	—
46	C₂×C₄	—	76	3	no	—
47	C₂×C₄	C₂×D₇₆	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	152	3	no	—
50	C₂²	#10597320	1	1	yes	characteristic
51	C₄	—	152	3	no	—
52	C₄	#10597350	1	6	yes	—
53	C₂	—	304	1	no	—
54	C₂	#11926928	1	3	yes	—

	subgroup	G/H
center	C₂²	#10597320
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₈²×C₁₉	C₂
socle	C₂²×C₁₉	#127
prime radical	#10597320	C₂²
hypercenter	C₈²	D₁₉
hypocenter	C₁₉	#1711
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #11926895	C₂	semidirect
3. C₈²×C₁₉	C₂	semidirect
28. C₈²	D₁₉	semidirect
36. C₁₉	#1711	semidirect

Maximal subgroups

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

subgroup	index
#11926895	2
#11926891	2
C₈²×C₁₉	2
#1711	19