Subgroups — (C₁₉⋊C₃)⋊(#5997⋊C₃) #45691986

Order 33516.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×#64424	C₂	1	1	yes	maximal, characteristic
2	(C₁₉⋊C₃)⋊#5997	C₃	1	1	yes	maximal, characteristic, complemented
3	#26013944	C₃	1	1	yes	maximal, characteristic, complemented
4	#26013941	C₃	1	1	yes	maximal, characteristic, complemented
5	#26013940	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₉⋊C₃×#3861	C₄	1	1	yes	characteristic, complemented, Hall
7	C₁₉⋊C₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
8	#19150287	C₂×C₃	1	1	yes	characteristic
9	#19150286	C₂×C₃	1	1	yes	characteristic
10	C₁₉×#64424	C₂×C₃	1	1	yes	characteristic
11	C₁₉⋊#5997	C₃²	1	1	yes	characteristic, complemented, Hall
12	#14584116	C₃×C₄	1	1	yes	characteristic, complemented
13	#14584115	C₃×C₄	1	1	yes	characteristic, complemented
14	C₁₉×#3861	C₃×C₄	1	1	yes	characteristic, complemented
15	C₇²×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
16	AGL(1,𝔽₇)×C₁₉⋊C₃	—	14	4	no	—
17	C₁₉×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
18	C₃×#5997⋊C₃	—	19	1	no	maximal, Hall
19	ΓL(1,𝔽₈)×C₁₉⋊C₃	—	14	4	no	—
20	C₇²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
21	C₃×#64424	—	19	1	no	—
22	#11716326	—	14	4	no	—
23	#11716325	—	14	4	no	—
24	C₁₉×AGL(1,𝔽₇)	—	14	4	no	—
25	D₇×C₁₉⋊C₃	—	14	4	no	—
26	C₃×(C₁₉⋊C₃)⋊C₄	—	49	1	no	maximal, Hall
27	C₃×#5997	—	19	1	no	—
28	#5997⋊C₃	—	19	1	no	—
29	#5997⋊C₃	—	19	1	no	—
30	#5997⋊C₃	—	19	1	no	—
31	C₃×#3861	—	19	1	no	Hall
32	#87705	—	14	4	no	—
33	#87704	—	14	4	no	—
34	C₇×C₁₉⋊C₃	—	2	4	no	—
35	C₁₉×ΓL(1,𝔽₈)	—	14	4	no	—
36	C₂×C₃×C₁₉⋊C₃	—	49	1	no	—
37	C₃×C₇⋊D₇	—	19	1	no	—
38	#64424	—	19	1	no	—
39	#64424	—	19	1	no	—
40	#64424	D₁₉⋊C₃	1	1	yes	characteristic
41	D₇×C₁₉	—	14	4	no	—
42	C₃×Dic₁₉	—	49	1	no	—
43	(C₁₉⋊C₃)⋊C₄	—	49	1	no	—
44	(C₁₉⋊C₃)⋊C₄	—	49	1	no	—
45	(C₁₉⋊C₃)⋊C₄	—	49	1	no	—
46	#5997	—	19	1	no	Hall
47	C₃×C₁₉⋊C₃	—	49	1	no	Hall
48	C₃×C₇²	—	19	1	no	—
49	#3861	—	19	1	no	—
50	#3861	—	19	1	no	—
51	#3861	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
52	C₇×C₁₉	—	2	4	no	—
53	C₃×AGL(1,𝔽₇)	—	266	4	no	—
54	C₂×C₃×C₁₉	—	49	1	no	—
55	C₂×C₁₉⋊C₃	—	49	1	no	—
56	C₂×C₁₉⋊C₃	—	49	1	no	—
57	C₂×C₁₉⋊C₃	—	49	1	no	—
58	C₇⋊D₇	C₃×D₁₉⋊C₃	1	1	yes	characteristic
59	Dic₁₉	—	49	1	no	Hall
60	C₃×ΓL(1,𝔽₈)	—	266	4	no	—
61	C₃×C₁₉	—	49	1	no	—
62	C₁₉⋊C₃	—	49	1	no	—
63	C₁₉⋊C₃	—	49	1	no	—
64	C₁₉⋊C₃	#5997⋊C₃	1	1	yes	characteristic, complemented
65	C₇²	C₃×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
66	C₃×D₇	—	266	4	no	—
67	AGL(1,𝔽₇)	—	266	4	no	—
68	AGL(1,𝔽₇)	—	266	4	no	—
69	AGL(1,𝔽₇)	—	14	4	no	—
70	C₂×C₁₉	—	49	1	no	—
71	C₃²×C₄	—	931	1	no	Hall
72	C₃×C₇	—	38	4	no	—
73	ΓL(1,𝔽₈)	—	266	4	no	—
74	ΓL(1,𝔽₈)	—	266	4	no	—
75	ΓL(1,𝔽₈)	—	14	4	no	—
76	C₁₉	C₃×#5997⋊C₃	1	1	yes	characteristic, complemented, Sylow
77	C₂×C₃²	—	931	1	no	—
78	D₇	—	14	4	no	—
79	C₃×C₄	—	931	1	no	—
80	C₃×C₄	—	931	1	no	—
81	C₃×C₄	—	931	1	no	—
82	C₃×C₄	—	931	1	no	—
83	C₃²	—	931	1	no	Sylow
84	C₇	—	2	4	no	—
85	C₂×C₃	—	49	1	no	—
86	C₂×C₃	—	931	1	no	—
87	C₂×C₃	—	931	1	no	—
88	C₂×C₃	—	931	1	no	—
89	C₄	—	931	1	no	Sylow
90	C₃	—	19	1	no	—
91	C₃	—	49	1	no	—
92	C₃	—	931	1	no	—
93	C₃	—	931	1	no	—
94	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₉	C₃²×C₄
prime radical	C₁₉⋊C₃×#64424	C₂
cosocle	C₁₉×C₇⋊D₇	C₂×C₃²
LCS	G ▷ C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. (C₁₉⋊C₃)⋊#5997	C₃	semidirect
3. #26013944	C₃	semidirect
4. #26013941	C₃	semidirect
5. #26013940	C₃	semidirect
6. C₁₉⋊C₃×#3861	C₄	semidirect
11. C₁₉⋊#5997	C₃²	semidirect
12. #14584116	C₃×C₄	semidirect
13. #14584115	C₃×C₄	semidirect
14. C₁₉×#3861	C₃×C₄	semidirect
15. C₇²×C₁₉⋊C₃	C₃×C₄	semidirect
20. C₇²×C₁₉	C₃²×C₄	semidirect
51. #3861	(C₁₉⋊C₃)⋊C₄	semidirect
64. C₁₉⋊C₃	#5997⋊C₃	semidirect
65. C₇²	C₃×(C₁₉⋊C₃)⋊C₄	semidirect
76. C₁₉	C₃×#5997⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×#64424	2
(C₁₉⋊C₃)⋊#5997	3
#26013944	3
#26013941	3
#26013940	3
C₃×#5997⋊C₃	19
C₃×(C₁₉⋊C₃)⋊C₄	49

Subgroups — (C19⋊C3)⋊(#5997⋊C3) #45691986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₁₉⋊C₃)⋊(#5997⋊C₃) #45691986