Subgroups — C₃⋊((C₁₉⋊C₃)⋊#5997) #45692262

Order 33516.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉⋊C₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#5997)	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₁₉⋊C₃)⋊#5997	—	3	1	no	maximal
4	C₃×C₇²×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₁₉⋊C₃×C₇⋊D₇	—	2	1	no	—
7	C₁₉⋊C₃×C₇⋊D₇	D₃	1	1	yes	characteristic
8	C₁₉⋊#5997	—	3	1	no	Hall
9	C₇²×C₁₉⋊C₃	—	2	1	no	—
10	C₇²×C₁₉⋊C₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×D₇×C₁₉⋊C₃	—	14	4	no	—
13	C₁₉×C₇⋊D₇	C₃×D₃	1	1	yes	characteristic
14	C₃×C₃⋊#5997	—	19	1	no	maximal, Hall
15	C₃×C₇×C₁₉⋊C₃	—	2	4	no	—
16	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃²×C₇⋊D₇	—	19	1	no	—
18	C₃×D₇×C₁₉	—	14	4	no	—
19	D₇×C₁₉⋊C₃	—	14	4	no	—
20	D₇×C₁₉⋊C₃	—	14	8	no	—
21	C₃⋊((C₁₉⋊C₃)⋊C₄)	—	49	1	no	maximal, Hall
22	C₃⋊#5997	—	19	1	no	—
23	C₃×#5997	—	57	1	no	—
24	C₃²×C₇²	—	19	1	no	Hall
25	C₃×C₇×C₁₉	—	2	4	no	—
26	C₇×C₁₉⋊C₃	—	2	8	no	—
27	C₇×C₁₉⋊C₃	—	2	4	no	—
28	C₂×C₃×C₁₉⋊C₃	—	49	1	no	—
29	C₃×C₇⋊D₇	—	19	1	no	—
30	C₃×C₇⋊D₇	—	38	1	no	—
31	C₃×C₇⋊D₇	D₁₉⋊C₃	1	1	yes	characteristic
32	D₇×C₁₉	—	14	4	no	—
33	Dic₅₇	—	49	1	no	—
34	(C₁₉⋊C₃)⋊C₄	—	147	1	no	—
35	#5997	—	57	1	no	Hall
36	C₃×C₁₉⋊C₃	#5997	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	—	19	1	no	—
38	C₃×C₇²	—	38	1	no	—
39	C₃×C₇²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
40	C₇×C₁₉	—	2	4	no	—
41	C₃²×D₇	—	266	4	no	—
42	C₂×C₃×C₁₉	—	49	1	no	—
43	C₂×C₁₉⋊C₃	—	49	1	no	—
44	C₂×C₁₉⋊C₃	—	98	1	no	—
45	C₇⋊D₇	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
46	Dic₁₉	—	147	1	no	Hall
47	C₃²×C₇	—	38	4	no	—
48	C₃×C₁₉	C₃×#5997	1	1	yes	characteristic, complemented
49	C₁₉⋊C₃	—	2	1	no	—
50	C₁₉⋊C₃	C₃⋊#5997	1	1	yes	characteristic, complemented
51	C₇²	C₃⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
52	C₃×D₇	—	266	8	no	—
53	C₃×D₇	—	266	4	no	—
54	C₃×D₇	—	14	4	no	—
55	C₂×C₁₉	—	49	1	no	—
56	C₃×Dic₃	—	931	1	no	Hall
57	C₃×C₇	—	2	4	no	—
58	C₃×C₇	—	38	4	no	—
59	C₃×C₇	—	38	8	no	—
60	C₁₉	C₃×C₃⋊#5997	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃²	—	931	1	no	—
62	D₇	—	14	4	no	—
63	C₃×C₄	—	2793	1	no	—
64	Dic₃	—	931	1	no	—
65	C₃²	—	19	1	no	Sylow
66	C₇	—	2	4	no	—
67	C₂×C₃	—	49	1	no	—
68	C₂×C₃	—	1862	1	no	—
69	C₂×C₃	—	931	1	no	—
70	C₄	—	2793	1	no	Sylow
71	C₃	—	19	1	no	—
72	C₃	—	38	1	no	—
73	C₃	(C₁₉⋊C₃)⋊#5997	1	1	yes	characteristic, complemented
74	C₂	—	49	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₁₉⋊#5997)	C₃	semidirect
4. C₃×C₇²×C₁₉⋊C₃	C₄	semidirect
10. C₇²×C₁₉⋊C₃	Dic₃	semidirect
11. C₃×C₇²×C₁₉	C₃×C₄	semidirect
16. C₇²×C₁₉	C₃×Dic₃	semidirect
36. C₃×C₁₉⋊C₃	#5997	semidirect
39. C₃×C₇²	(C₁₉⋊C₃)⋊C₄	semidirect
48. C₃×C₁₉	C₃×#5997	semidirect
50. C₁₉⋊C₃	C₃⋊#5997	semidirect
51. C₇²	C₃⋊((C₁₉⋊C₃)⋊C₄)	semidirect
60. C₁₉	C₃×C₃⋊#5997	semidirect
73. C₃	(C₁₉⋊C₃)⋊#5997	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉⋊C₃×C₇⋊D₇	2
C₃⋊(C₁₉⋊#5997)	3
(C₁₉⋊C₃)⋊#5997	3
C₃×C₃⋊#5997	19
C₃⋊((C₁₉⋊C₃)⋊C₄)	49

Subgroups — C3⋊((C19⋊C3)⋊#5997) #45692262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₁₉⋊C₃)⋊#5997) #45692262