Subgroups — C₂²×#22552712 #45691698

Order 33516.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552712	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	#22552712	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	3	yes	—
5	C₂²×#11924777	—	7	1	no	maximal
6	C₂²×#11924776	—	7	1	no	maximal
7	C₂²×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
9	C₂×#11924777	—	7	3	no	—
10	C₂×#11924776	—	7	3	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	3	yes	complemented
12	C₂²×#89205	—	19	1	no	maximal, Hall
13	C₂²×C₃×C₇×C₁₉	—	3	2	no	—
14	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
16	#11924777	—	7	1	no	—
17	#11924776	—	7	1	no	—
18	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×#89205	—	19	3	no	—
20	C₂×C₃×C₇×C₁₉	—	3	6	no	—
21	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	3	yes	—
22	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	3	yes	—
23	C₂²×#4294	—	49	1	no	Hall
24	C₂²×C₃×C₇²	C₁₉⋊C₃	1	1	yes	characteristic
25	C₂²×C₇×C₁₉	—	3	2	no	—
26	C₂²×C₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
27	C₂²×C₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented
28	#89205	—	19	1	no	Hall
29	C₃×C₇×C₁₉	—	3	2	no	—
30	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₂×#4294	—	49	3	no	—
33	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	3	yes	—
34	C₂×C₇×C₁₉	—	3	6	no	—
35	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	3	yes	complemented
36	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	3	yes	complemented
37	C₂²×C₇⋊C₉	—	133	1	no	—
38	C₂²×C₇⋊C₉	—	133	1	no	—
39	C₂²×C₃×C₁₉	#3862	1	1	yes	characteristic
40	C₂²×C₇²	#4294	1	1	yes	characteristic, complemented, Hall
41	#4294	—	49	1	no	Hall
42	C₃×C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
43	C₇×C₁₉	—	3	2	no	—
44	C₇×C₁₉	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented
45	C₇×C₁₉	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented
46	C₂×C₇⋊C₉	—	133	3	no	—
47	C₂×C₇⋊C₉	—	133	3	no	—
48	C₂×C₃×C₁₉	C₂×#3862	1	3	yes	—
49	C₂×C₇²	C₂×#4294	1	3	yes	complemented
50	C₂²×C₃×C₇	—	3	2	no	—
51	C₂²×C₃×C₇	#87704	1	1	yes	characteristic
52	C₂²×C₃×C₇	#87705	1	1	yes	characteristic
53	C₂²×C₁₉	#89205	1	1	yes	characteristic, complemented, Hall
54	C₇⋊C₉	—	133	1	no	—
55	C₇⋊C₉	—	133	1	no	—
56	C₃×C₁₉	C₂²×#3862	1	1	yes	characteristic
57	C₇²	C₂²×#4294	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	3	6	no	—
59	C₂×C₃×C₇	C₂×#87704	1	3	yes	—
60	C₂×C₃×C₇	C₂×#87705	1	3	yes	—
61	C₂×C₁₉	C₂×#89205	1	3	yes	complemented
62	C₂²×C₉	—	931	1	no	Hall
63	C₂²×C₇	—	3	2	no	—
64	C₂²×C₇	#11924776	1	1	yes	characteristic, complemented
65	C₂²×C₇	#11924777	1	1	yes	characteristic, complemented
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	C₂²×#87704	1	1	yes	characteristic
68	C₃×C₇	C₂²×#87705	1	1	yes	characteristic
69	C₁₉	C₂²×#89205	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₉	—	931	3	no	—
71	C₂×C₇	—	3	6	no	—
72	C₂×C₇	C₂×#11924776	1	3	yes	complemented
73	C₂×C₇	C₂×#11924777	1	3	yes	complemented
74	C₂²×C₃	C₁₉⋊#3862	1	1	yes	characteristic
75	C₉	—	931	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	C₂²×#11924776	1	1	yes	characteristic, complemented
78	C₇	C₂²×#11924777	1	1	yes	characteristic, complemented
79	C₂×C₃	C₂×C₁₉⋊#3862	1	3	yes	—
80	C₂²	#22552712	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	C₂²×C₁₉⋊#3862	1	1	yes	characteristic
82	C₂	C₂×#22552712	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₉⋊#3862
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₂²×C₁₉⋊#3862
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₉	C₃
cosocle	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×#22552712	C₂	direct (N × H)
3. #22552712	C₂²	direct (N × H)
7. C₂²×C₇²×C₁₉	C₉	semidirect
11. C₂×C₇²×C₁₉	C₂×C₉	semidirect
18. C₇²×C₁₉	C₂²×C₉	semidirect
26. C₂²×C₇×C₁₉	C₇⋊C₉	semidirect
27. C₂²×C₇×C₁₉	C₇⋊C₉	semidirect
35. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
36. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
40. C₂²×C₇²	#4294	semidirect
44. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
45. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
49. C₂×C₇²	C₂×#4294	semidirect
53. C₂²×C₁₉	#89205	semidirect
57. C₇²	C₂²×#4294	semidirect
61. C₂×C₁₉	C₂×#89205	semidirect
64. C₂²×C₇	#11924776	semidirect
65. C₂²×C₇	#11924777	semidirect
69. C₁₉	C₂²×#89205	semidirect
72. C₂×C₇	C₂×#11924776	semidirect
73. C₂×C₇	C₂×#11924777	semidirect
77. C₇	C₂²×#11924776	semidirect
78. C₇	C₂²×#11924777	semidirect
80. C₂²	#22552712	direct (N × H)
82. C₂	C₂×#22552712	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22552712	2
C₂²×C₃×C₇²×C₁₉	3
C₂²×#11924777	7
C₂²×#11924776	7
C₂²×#89205	19

Subgroups — C22×#22552712 #45691698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#22552712 #45691698