Subgroups — #45691997

Order 33516.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30660667	C₂	1	1	yes	maximal, characteristic
2	#26013942	—	3	1	no	maximal
3	C₁₉×#10596885	C₃	1	1	yes	maximal, characteristic, complemented
4	#22552728	C₄	1	1	yes	characteristic, complemented, Hall
5	#19150309	—	2	1	no	—
6	C₁₉×#64425	C₂×C₃	1	1	yes	characteristic
7	#19150286	D₃	1	1	yes	characteristic
8	C₁₉×#5997	—	3	1	no	Hall
9	C₁₉×#3862	C₃×C₄	1	1	yes	characteristic, complemented
10	#14584115	Dic₃	1	1	yes	characteristic, complemented
11	C₇×#87705	—	2	1	no	—
12	AGL(1,𝔽₇)×C₁₉⋊C₃	—	14	1	no	—
13	C₁₉×C₇⋊D₇	C₃×D₃	1	1	yes	characteristic
14	#10596885⋊C₃	—	19	1	no	maximal, Hall
15	ΓL(1,𝔽₈)×C₁₉⋊C₃	—	14	1	no	—
16	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	ΓL(1,𝔽₈)⋊AGL(1,𝔽₇)	—	19	1	no	—
18	#11716326	—	14	1	no	—
19	#11716325	—	14	1	no	—
20	#11716325	—	42	1	no	—
21	C₁₉×AGL(1,𝔽₇)	—	14	1	no	—
22	D₇×C₁₉⋊C₃	—	14	1	no	—
23	Dic₃×C₁₉⋊C₃	—	49	1	no	maximal, Hall
24	#5997⋊C₃	—	57	1	no	—
25	#10596885	C₁₉⋊C₃	1	1	yes	characteristic, complemented
26	ΓL(1,𝔽₈)²	—	19	1	no	Hall
27	#87705	—	2	1	no	—
28	#87704	—	14	1	no	—
29	#87704	—	42	1	no	—
30	C₇×C₁₉⋊C₃	—	14	1	no	—
31	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
32	C₂×C₃×C₁₉⋊C₃	—	49	1	no	—
33	#64425	C₂×C₁₉⋊C₃	1	1	yes	characteristic
34	#64424	—	19	1	no	—
35	ΓL(1,𝔽₈)⋊D₇	—	38	1	no	—
36	D₇×C₁₉	—	14	1	no	—
37	D₇×C₁₉	—	42	1	no	—
38	Dic₃×C₁₉	—	49	1	no	—
39	C₄×C₁₉⋊C₃	—	147	1	no	—
40	#5997	—	3	1	no	Hall
41	C₃×C₁₉⋊C₃	—	49	1	no	Hall
42	#3862	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
43	#3861	—	19	1	no	—
44	C₇×ΓL(1,𝔽₈)	—	38	1	no	—
45	C₇×C₁₉	—	2	1	no	—
46	C₇×C₁₉	—	6	1	no	—
47	C₃×AGL(1,𝔽₇)	—	266	1	no	—
48	C₂×C₃×C₁₉	—	49	1	no	—
49	C₂×C₁₉⋊C₃	—	49	1	no	—
50	C₂×C₁₉⋊C₃	—	98	1	no	—
51	C₇⋊D₇	D₃×C₁₉⋊C₃	1	1	yes	characteristic
52	C₄×C₁₉	—	147	1	no	Hall
53	C₃×ΓL(1,𝔽₈)	—	266	1	no	—
54	C₃×C₁₉	—	49	1	no	—
55	C₁₉⋊C₃	—	14	1	no	—
56	C₁₉⋊C₃	—	49	1	no	—
57	C₇²	Dic₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₃×D₇	—	266	1	no	—
59	AGL(1,𝔽₇)	—	266	1	no	—
60	AGL(1,𝔽₇)	—	266	1	no	—
61	AGL(1,𝔽₇)	—	14	1	no	—
62	AGL(1,𝔽₇)	—	798	1	no	—
63	C₂×C₁₉	—	49	1	no	—
64	C₃×Dic₃	—	931	1	no	Hall
65	C₃×C₇	—	266	1	no	—
66	ΓL(1,𝔽₈)	—	266	1	no	—
67	ΓL(1,𝔽₈)	—	14	1	no	—
68	ΓL(1,𝔽₈)	—	798	1	no	—
69	ΓL(1,𝔽₈)	—	38	1	no	—
70	C₁₉	#10596885⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃²	—	931	1	no	—
72	D₇	—	14	1	no	—
73	D₇	—	42	1	no	—
74	C₃×C₄	—	2793	1	no	—
75	Dic₃	—	49	1	no	—
76	C₃²	—	931	1	no	Sylow
77	C₇	—	2	1	no	—
78	C₇	—	6	1	no	—
79	C₂×C₃	—	49	1	no	—
80	C₂×C₃	—	1862	1	no	—
81	C₂×C₃	—	931	1	no	—
82	C₄	—	147	1	no	Sylow
83	C₃	—	266	1	no	—
84	C₃	—	49	1	no	—
85	C₃	—	931	1	no	—
86	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₁₉×#3862	C₃×C₄
Fitting, socle	C₇²×C₁₉	C₃×Dic₃
prime radical	#30660667	C₂
cosocle	C₁₉×#64425	C₂×C₃
LCS	G ▷ C₁₉×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₁₉×#10596885	C₃	semidirect
4. #22552728	C₄	semidirect
9. C₁₉×#3862	C₃×C₄	semidirect
10. #14584115	Dic₃	semidirect
16. C₇²×C₁₉	C₃×Dic₃	semidirect
25. #10596885	C₁₉⋊C₃	semidirect
42. #3862	C₄×C₁₉⋊C₃	semidirect
57. C₇²	Dic₃×C₁₉⋊C₃	semidirect
70. C₁₉	#10596885⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#30660667	2
#26013942	3
C₁₉×#10596885	3
#10596885⋊C₃	19
Dic₃×C₁₉⋊C₃	49