Subgroups — #11926344

Order 1216.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇₆	—	2	1	no	—
5	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₁₉	—	2	1	no	—
7	D₁₅₂	—	2	1	no	—
8	D₁₅₂	C₄	1	2	yes	complemented
9	C₁₉⋊C₁₆	—	2	1	no	—
10	C₂²×D₁₉	—	4	1	no	—
11	C₂×C₄×C₁₉	—	4	1	no	—
12	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
13	D₇₆	—	2	2	no	—
14	D₇₆	—	4	1	no	—
15	C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₁₉	D₈	1	1	yes	characteristic
18	C₂×D₁₉	—	4	2	no	—
19	C₂×D₁₉	—	8	1	no	—
20	C₂×D₁₉	—	8	1	no	—
21	C₄×C₁₉	—	8	1	no	—
22	C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₁₉	SD₁₆	1	1	yes	characteristic
24	#357	—	19	1	no	maximal, Sylow
25	C₂×C₁₉	#102	1	1	yes	characteristic
26	C₂×C₁₉	D₁₆	1	1	yes	characteristic
27	C₂×C₁₉	SD₃₂	1	1	yes	characteristic
28	D₁₉	—	8	2	no	—
29	C₂×D₈	—	19	1	no	—
30	C₂×C₁₆	—	19	1	no	—
31	#107	D₁₉	1	1	yes	characteristic, complemented
32	C₁₉	#357	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₄	—	38	1	no	—
34	D₈	—	19	2	no	—
35	D₈	—	38	1	no	—
36	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
37	C₄⋊C₄	—	2	1	no	—
38	C₁₆	—	38	1	no	—
39	C₂³	—	76	1	no	—
40	D₄	—	38	2	no	—
41	D₄	—	76	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
44	C₈	C₄×D₁₉	1	1	yes	characteristic
45	C₈	D₇₆	1	1	yes	characteristic
46	C₂²	—	76	2	no	—
47	C₂²	—	152	1	no	—
48	C₂²	—	152	1	no	—
49	C₂²	#64525	1	1	yes	characteristic
50	C₄	—	8	1	no	—
51	C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
52	C₄	#64527	1	1	yes	characteristic
53	C₂	—	152	2	no	—
54	C₂	#10597266	1	1	yes	characteristic
55	C₂	#10597283	1	1	yes	characteristic
56	C₂	#10597285	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64525
commutator	C₈×C₁₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₉
Fitting	C₁₉×#107	C₂
socle	C₂²×C₁₉	D₈
prime radical	C₂×D₁₅₂	C₂
cosocle	C₂×C₈×C₁₉	C₂²
hypercenter	#107	D₁₉
hypocenter	C₁₉	#357
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
2. C₁₉×#107	C₂	semidirect
3. C₂×C₁₉⋊C₁₆	C₂	semidirect
8. D₁₅₂	C₄	semidirect
31. #107	D₁₉	semidirect
32. C₁₉	#357	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₅₂	2
C₁₉×#107	2
C₂×C₁₉⋊C₁₆	2
#357	19