Subgroups — #45691483

Order 33516.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552712	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic
3	#22552712	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	#18012095	—	7	1	no	maximal
6	#18012094	—	7	1	no	maximal
7	C₁₉×C₇⋊Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₂×#11924777	—	7	1	no	—
10	C₂×#11924776	—	7	1	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
12	#13183534	—	19	1	no	maximal, Hall
13	C₃×C₁₉×Dic₇	—	7	1	no	—
14	C₃×C₁₉×Dic₇	—	7	1	no	—
15	C₃×C₁₉×Dic₇	—	21	2	no	—
16	#11924777	—	7	1	no	—
17	#11924776	—	7	1	no	—
18	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×#89205	—	19	1	no	—
20	C₂×C₃×C₇×C₁₉	—	3	2	no	—
21	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
23	C₄×#4294	—	49	1	no	Hall
24	C₃×C₇⋊Dic₇	C₁₉⋊C₃	1	1	yes	characteristic
25	C₁₉×Dic₇	—	7	1	no	—
26	C₁₉×Dic₇	—	7	1	no	—
27	C₁₉×Dic₇	—	21	2	no	—
28	#89205	—	19	1	no	Hall
29	C₃×C₇×C₁₉	—	3	2	no	—
30	C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
31	C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
32	C₂×#4294	—	49	1	no	—
33	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂×C₇×C₁₉	—	3	2	no	—
35	C₂×C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic
36	C₂×C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic
37	Dic₇⋊C₉	—	133	1	no	—
38	Dic₇⋊C₉	—	133	1	no	—
39	C₃×C₄×C₁₉	—	49	1	no	—
40	C₇⋊Dic₇	#4294	1	1	yes	characteristic, complemented, Hall
41	#4294	—	49	1	no	Hall
42	C₃×C₇²	C₄×C₁₉⋊C₃	1	1	yes	characteristic
43	C₇×C₁₉	—	3	2	no	—
44	C₇×C₁₉	Dic₇⋊C₉	1	1	yes	characteristic, complemented
45	C₇×C₁₉	Dic₇⋊C₉	1	1	yes	characteristic, complemented
46	C₂×C₇⋊C₉	—	133	1	no	—
47	C₂×C₇⋊C₉	—	133	1	no	—
48	C₂×C₃×C₁₉	#64425	1	1	yes	characteristic
49	C₂×C₇²	C₂×#4294	1	1	yes	characteristic
50	C₃×Dic₇	—	7	1	no	—
51	C₃×Dic₇	—	7	1	no	—
52	C₃×Dic₇	—	21	2	no	—
53	C₄×C₁₉	—	49	1	no	Hall
54	C₇⋊C₉	—	133	1	no	—
55	C₇⋊C₉	—	133	1	no	—
56	C₃×C₁₉	#10596875	1	1	yes	characteristic
57	C₇²	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	3	2	no	—
59	C₂×C₃×C₇	#11716325	1	1	yes	characteristic
60	C₂×C₃×C₇	#11716326	1	1	yes	characteristic
61	C₂×C₁₉	#11725078	1	1	yes	characteristic
62	C₄×C₉	—	931	1	no	Hall
63	Dic₇	—	7	1	no	—
64	Dic₇	—	7	1	no	—
65	Dic₇	—	21	2	no	—
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	#13097586	1	1	yes	characteristic
68	C₃×C₇	#13097587	1	1	yes	characteristic
69	C₁₉	#13183534	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₉	—	931	1	no	—
71	C₂×C₇	—	3	2	no	—
72	C₂×C₇	#14558784	1	1	yes	characteristic
73	C₂×C₇	#14558785	1	1	yes	characteristic
74	C₃×C₄	—	49	1	no	—
75	C₉	—	931	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	#18012094	1	1	yes	characteristic, complemented
78	C₇	#18012095	1	1	yes	characteristic, complemented
79	C₂×C₃	#19150291	1	1	yes	characteristic
80	C₄	—	49	1	no	Sylow
81	C₃	#26013824	1	1	yes	characteristic
82	C₂	#30660579	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	#19150291
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. #22552712	C₄	semidirect
7. C₁₉×C₇⋊Dic₇	C₉	semidirect
18. C₇²×C₁₉	C₄×C₉	semidirect
40. C₇⋊Dic₇	#4294	semidirect
44. C₇×C₁₉	Dic₇⋊C₉	semidirect
45. C₇×C₁₉	Dic₇⋊C₉	semidirect
57. C₇²	C₄×#4294	semidirect
69. C₁₉	#13183534	semidirect
77. C₇	#18012094	semidirect
78. C₇	#18012095	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22552712	2
C₃×C₁₉×C₇⋊Dic₇	3
#18012095	7
#18012094	7
#13183534	19