Subgroups — C₁₉⋊C₃×C₂²⋊#3861 #45692520

Order 33516.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₂²⋊#3861	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#14584115	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊#14584116	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉⋊C₃×#3861	—	4	1	no	maximal, Hall
6	C₂×C₇²×C₁₉⋊C₃	—	3	1	no	—
7	C₁₉⋊C₃×C₂²⋊ΓL(1,𝔽₈)	—	7	8	no	maximal
8	C₂²×C₇²×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	#14584116	—	4	1	no	—
10	#14584115	—	4	1	no	—
11	C₁₉×#3861	—	4	1	no	—
12	C₇²×C₁₉⋊C₃	A₄	1	1	yes	characteristic, complemented
13	C₂×C₇²×C₁₉	—	3	1	no	—
14	C₃×C₂²⋊#3861	—	19	1	no	maximal, Hall
15	C₂²⋊#87705	—	7	8	no	—
16	C₂²⋊#87704	—	7	8	no	—
17	C₁₉×C₂²⋊ΓL(1,𝔽₈)	—	7	8	no	—
18	C₂²×C₇×C₁₉⋊C₃	ΓL(1,𝔽₈)	1	8	yes	complemented
19	ΓL(1,𝔽₈)×C₁₉⋊C₃	—	28	8	no	—
20	C₇²×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₁₉⋊C₃	—	3	8	no	—
22	A₄×C₁₉⋊C₃	—	49	1	no	Hall
23	C₂²×C₃×C₇²	—	19	1	no	—
24	C₂²⋊#3861	—	19	1	no	—
25	C₂²⋊#3861	—	19	1	no	—
26	C₂²⋊#3861	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
27	C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
28	C₃×#3861	—	76	1	no	Hall
29	#87705	—	28	8	no	—
30	#87704	—	28	8	no	—
31	C₇×C₁₉⋊C₃	C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
32	C₁₉×ΓL(1,𝔽₈)	—	28	8	no	—
33	C₂×C₃×C₇²	—	57	1	no	—
34	C₂×C₇×C₁₉	—	3	8	no	—
35	C₃×C₂²⋊ΓL(1,𝔽₈)	—	133	8	no	—
36	C₂²⋊(C₁₉⋊C₃)	—	49	1	no	—
37	C₂²⋊(C₁₉⋊C₃)	—	49	1	no	—
38	A₄×C₁₉	—	49	1	no	—
39	C₂²×C₁₉⋊C₃	#3861	1	1	yes	characteristic, complemented
40	C₂²×C₇²	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₉⋊C₃	—	196	1	no	Hall
42	C₃×C₇²	—	19	1	no	—
43	#3861	—	4	1	no	—
44	#3861	—	76	1	no	—
45	#3861	—	76	1	no	—
46	C₇×C₁₉	C₃×C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
47	C₂×C₁₉⋊C₃	—	3	1	no	—
48	C₂×C₇²	—	3	1	no	—
49	C₂²×C₃×C₇	—	19	8	no	—
50	C₂²⋊ΓL(1,𝔽₈)	—	7	8	no	—
51	C₂²⋊ΓL(1,𝔽₈)	—	133	8	no	—
52	C₂²⋊ΓL(1,𝔽₈)	—	133	8	no	—
53	C₂²×C₁₉	C₃×#3861	1	1	yes	characteristic, complemented, Hall
54	C₃×ΓL(1,𝔽₈)	—	532	8	no	—
55	C₃×C₁₉	—	196	1	no	—
56	C₁₉⋊C₃	—	196	1	no	—
57	C₁₉⋊C₃	—	196	1	no	—
58	C₁₉⋊C₃	C₂²⋊#3861	1	1	yes	characteristic, direct product factor
59	C₇²	A₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃×C₇	—	57	8	no	—
61	C₂×C₁₉	—	3	1	no	—
62	C₃×A₄	—	931	1	no	Hall
63	C₂²×C₇	ΓL(1,𝔽₈)×C₁₉⋊C₃	1	8	yes	complemented
64	C₃×C₇	—	19	8	no	—
65	ΓL(1,𝔽₈)	—	532	8	no	—
66	ΓL(1,𝔽₈)	—	532	8	no	—
67	ΓL(1,𝔽₈)	—	28	8	no	—
68	C₁₉	C₃×C₂²⋊#3861	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₇	—	3	8	no	—
70	C₂²×C₃	—	19	1	no	—
71	A₄	—	49	1	no	—
72	A₄	—	931	1	no	—
73	A₄	—	931	1	no	—
74	C₃²	—	3724	1	no	Sylow
75	C₇	C₁₉⋊C₃×C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
76	C₂×C₃	—	57	1	no	—
77	C₂²	C₁₉⋊C₃×#3861	1	1	yes	characteristic, complemented, Sylow
78	C₃	—	19	1	no	—
79	C₃	—	3724	1	no	—
80	C₃	—	3724	1	no	—
81	C₃	—	196	1	no	—
82	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₇²×C₁₉	C₃²
LCS	G ▷ C₂²×C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇²×C₁₉⋊C₃	C₃	semidirect
2. C₁₉×C₂²⋊#3861	C₃	semidirect
3. C₂²⋊#14584115	C₃	semidirect
4. C₂²⋊#14584116	C₃	semidirect
8. C₂²×C₇²×C₁₉	C₃²	semidirect
12. C₇²×C₁₉⋊C₃	A₄	semidirect
18. C₂²×C₇×C₁₉⋊C₃	ΓL(1,𝔽₈)	semidirect
20. C₇²×C₁₉	C₃×A₄	semidirect
26. C₂²⋊#3861	C₁₉⋊C₃	direct (N × H)
27. C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)	semidirect
31. C₇×C₁₉⋊C₃	C₂²⋊ΓL(1,𝔽₈)	semidirect
39. C₂²×C₁₉⋊C₃	#3861	semidirect
40. C₂²×C₇²	C₃×C₁₉⋊C₃	semidirect
46. C₇×C₁₉	C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
53. C₂²×C₁₉	C₃×#3861	semidirect
58. C₁₉⋊C₃	C₂²⋊#3861	direct (N × H)
59. C₇²	A₄×C₁₉⋊C₃	semidirect
63. C₂²×C₇	ΓL(1,𝔽₈)×C₁₉⋊C₃	semidirect
68. C₁₉	C₃×C₂²⋊#3861	semidirect
75. C₇	C₁₉⋊C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
77. C₂²	C₁₉⋊C₃×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇²×C₁₉⋊C₃	3
C₁₉×C₂²⋊#3861	3
C₂²⋊#14584115	3
C₂²⋊#14584116	3
C₁₉⋊C₃×#3861	4
C₁₉⋊C₃×C₂²⋊ΓL(1,𝔽₈)	7
C₃×C₂²⋊#3861	19

Subgroups — C19⋊C3×C22⋊#3861 #45692520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×C₂²⋊#3861 #45692520