Subgroups — C₃²×C₁₃×#5997 #37525567

Order 22932.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#5997	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	4	yes	—
5	C₁₃×#5997	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇²×C₁₃	C₃×C₄	1	4	yes	complemented
7	C₃²×#5997	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₁₃×D₇	—	14	4	no	—
9	C₁₃×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
10	C₃²×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic
11	C₃²×C₇×C₁₃	—	2	4	no	—
12	C₇²×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₃×#5997	C₃×C₁₃	1	4	yes	direct product factor
14	C₃×C₁₃×D₇	—	14	16	no	—
15	C₃²×C₄×C₁₃	—	49	1	no	maximal, Hall
16	C₃²×C₇²	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇⋊D₇	C₂×C₃×C₁₃	1	4	yes	—
18	C₃×C₇×C₁₃	—	2	16	no	—
19	C₂×C₃²×C₁₃	—	49	1	no	—
20	#5997	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₁₃×D₇	—	14	4	no	—
22	C₃×C₄×C₁₃	—	49	4	no	—
23	C₃×C₇²	C₃×C₄×C₁₃	1	4	yes	complemented
24	C₃²×D₇	—	14	4	no	—
25	C₃²×C₁₃	#5997	1	1	yes	characteristic, direct product factor, Hall
26	C₇⋊D₇	C₂×C₃²×C₁₃	1	1	yes	characteristic
27	C₇×C₁₃	—	2	4	no	—
28	C₂×C₃×C₁₃	—	49	4	no	—
29	C₃²×C₇	—	2	4	no	—
30	C₄×C₁₃	—	49	1	no	Hall
31	C₇²	C₃²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	14	16	no	—
33	C₃×C₁₃	C₃×#5997	1	4	yes	direct product factor
34	C₃²×C₄	—	49	1	no	Hall
35	C₂×C₁₃	—	49	1	no	—
36	C₃×C₇	—	2	16	no	—
37	C₂×C₃²	—	49	1	no	—
38	D₇	—	14	4	no	—
39	C₁₃	C₃²×#5997	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	—	49	4	no	—
41	C₃²	C₁₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	4	no	—
44	C₄	—	49	1	no	Sylow
45	C₃	C₃×C₁₃×#5997	1	4	yes	direct product factor
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₃	#5997
commutator, hypocenter	C₇²	C₃²×C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₃²×C₁₃×C₇⋊D₇	C₂
cosocle	C₇⋊D₇	C₂×C₃²×C₁₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃²×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×#5997	C₃	direct (N × H)
3. C₃²×C₇²×C₁₃	C₄	semidirect
5. C₁₃×#5997	C₃²	direct (N × H)
6. C₃×C₇²×C₁₃	C₃×C₄	semidirect
7. C₃²×#5997	C₁₃	direct (N × H)
12. C₇²×C₁₃	C₃²×C₄	semidirect
13. C₃×#5997	C₃×C₁₃	direct (N × H)
16. C₃²×C₇²	C₄×C₁₃	semidirect
20. #5997	C₃²×C₁₃	direct (N × H)
23. C₃×C₇²	C₃×C₄×C₁₃	semidirect
25. C₃²×C₁₃	#5997	direct (N × H)
31. C₇²	C₃²×C₄×C₁₃	semidirect
33. C₃×C₁₃	C₃×#5997	direct (N × H)
39. C₁₃	C₃²×#5997	direct (N × H)
41. C₃²	C₁₃×#5997	direct (N × H)
45. C₃	C₃×C₁₃×#5997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇⋊D₇	2
C₃×C₁₃×#5997	3
C₃²×#5997	13
C₃²×C₄×C₁₃	49

Subgroups — C32×C13×#5997 #37525567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₃×#5997 #37525567