Subgroups — #45691504

Order 33516.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552710	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×Dic₁₉	C₃	1	1	yes	maximal, characteristic
3	#22552710	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	#18012091	—	7	8	no	maximal
6	C₇²×Dic₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×#11924777	—	7	8	no	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
10	C₄×#89204	—	19	1	no	maximal, Hall
11	C₃×C₇×Dic₁₉	ΓL(1,𝔽₈)	1	8	yes	—
12	#11924777	—	7	8	no	—
13	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×#89204	—	19	1	no	—
15	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	—
16	#4294⋊C₄	—	49	1	no	Hall
17	C₃×C₄×C₇²	—	19	1	no	—
18	C₇×Dic₁₉	C₇⋊C₉	1	8	yes	complemented
19	#89204	—	19	1	no	Hall
20	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	8	yes	—
21	C₂×#4294	—	49	1	no	—
22	C₂×C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic
23	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	8	yes	—
24	C₄×C₇⋊C₉	—	133	8	no	—
25	C₃×Dic₁₉	#3861	1	1	yes	characteristic
26	C₄×C₇²	—	19	1	no	Hall
27	#4294	—	49	1	no	Hall
28	C₃×C₇²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic
29	C₇×C₁₉	C₄×C₇⋊C₉	1	8	yes	complemented
30	C₂×C₇⋊C₉	—	133	8	no	—
31	C₂×C₃×C₁₉	C₂×#3861	1	1	yes	characteristic
32	C₂×C₇²	#4294⋊C₂	1	1	yes	characteristic
33	C₃×C₄×C₇	—	19	8	no	—
34	Dic₁₉	#89204	1	1	yes	characteristic, complemented, Hall
35	C₇⋊C₉	—	133	8	no	—
36	C₃×C₁₉	C₄×#3861	1	1	yes	characteristic
37	C₇²	#4294⋊C₄	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	#11716322	1	8	yes	—
39	C₂×C₁₉	C₂×#89204	1	1	yes	characteristic
40	C₄×C₉	—	931	1	no	Hall
41	C₄×C₇	—	19	8	no	—
42	C₃×C₇	#13097583	1	8	yes	—
43	C₁₉	C₄×#89204	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	931	1	no	—
45	C₂×C₇	#14558781	1	8	yes	—
46	C₃×C₄	—	19	1	no	—
47	C₉	—	931	1	no	Sylow
48	C₇	#18012091	1	8	yes	complemented
49	C₂×C₃	#19150312	1	1	yes	characteristic
50	C₄	—	19	1	no	Sylow
51	C₃	#26013845	1	1	yes	characteristic
52	C₂	#30660600	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	#19150312
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. #22552710	C₄	semidirect
6. C₇²×Dic₁₉	C₉	semidirect
13. C₇²×C₁₉	C₄×C₉	semidirect
18. C₇×Dic₁₉	C₇⋊C₉	semidirect
29. C₇×C₁₉	C₄×C₇⋊C₉	semidirect
34. Dic₁₉	#89204	semidirect
37. C₇²	#4294⋊C₄	semidirect
43. C₁₉	C₄×#89204	semidirect
48. C₇	#18012091	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22552710	2
C₃×C₇²×Dic₁₉	3
#18012091	7
C₄×#89204	19