Subgroups — C₂²×#22552710 #45691703

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22552710	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	#22552710	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	3	yes	—
5	C₂²×#11924777	—	7	8	no	maximal
6	C₂²×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
8	C₂×#11924777	—	7	24	no	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	3	yes	complemented
10	C₂²×#89204	—	19	1	no	maximal, Hall
11	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	—
12	#11924777	—	7	8	no	—
13	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×#89204	—	19	3	no	—
15	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	24	yes	—
16	C₂²×#4294	—	49	1	no	Hall
17	C₂²×C₃×C₇²	C₁₉⋊C₃	1	1	yes	characteristic
18	C₂²×C₇×C₁₉	C₇⋊C₉	1	8	yes	complemented
19	#89204	—	19	1	no	Hall
20	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	8	yes	—
21	C₂×#4294	—	49	3	no	—
22	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	3	yes	—
23	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	24	yes	complemented
24	C₂²×C₇⋊C₉	—	133	8	no	—
25	C₂²×C₃×C₁₉	#3861	1	1	yes	characteristic
26	C₂²×C₇²	#4294	1	1	yes	characteristic, complemented, Hall
27	#4294	—	49	1	no	Hall
28	C₃×C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
29	C₇×C₁₉	C₂²×C₇⋊C₉	1	8	yes	complemented
30	C₂×C₇⋊C₉	—	133	24	no	—
31	C₂×C₃×C₁₉	C₂×#3861	1	3	yes	—
32	C₂×C₇²	C₂×#4294	1	3	yes	complemented
33	C₂²×C₃×C₇	#87705	1	8	yes	—
34	C₂²×C₁₉	#89204	1	1	yes	characteristic, complemented, Hall
35	C₇⋊C₉	—	133	8	no	—
36	C₃×C₁₉	C₂²×#3861	1	1	yes	characteristic
37	C₇²	C₂²×#4294	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	C₂×#87705	1	24	yes	—
39	C₂×C₁₉	C₂×#89204	1	3	yes	complemented
40	C₂²×C₉	—	931	1	no	Hall
41	C₂²×C₇	#11924777	1	8	yes	complemented
42	C₃×C₇	C₂²×#87705	1	8	yes	—
43	C₁₉	C₂²×#89204	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	931	3	no	—
45	C₂×C₇	C₂×#11924777	1	24	yes	complemented
46	C₂²×C₃	#14584116	1	1	yes	characteristic
47	C₉	—	931	1	no	Sylow
48	C₇	C₂²×#11924777	1	8	yes	complemented
49	C₂×C₃	C₂×#14584116	1	3	yes	—
50	C₂²	#22552710	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×#14584116	1	1	yes	characteristic
52	C₂	C₂×#22552710	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	#14584116
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₂²×#14584116
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×#22552710	C₂	direct (N × H)
3. #22552710	C₂²	direct (N × H)
6. C₂²×C₇²×C₁₉	C₉	semidirect
9. C₂×C₇²×C₁₉	C₂×C₉	semidirect
13. C₇²×C₁₉	C₂²×C₉	semidirect
18. C₂²×C₇×C₁₉	C₇⋊C₉	semidirect
23. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
26. C₂²×C₇²	#4294	semidirect
29. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
32. C₂×C₇²	C₂×#4294	semidirect
34. C₂²×C₁₉	#89204	semidirect
37. C₇²	C₂²×#4294	semidirect
39. C₂×C₁₉	C₂×#89204	semidirect
41. C₂²×C₇	#11924777	semidirect
43. C₁₉	C₂²×#89204	semidirect
45. C₂×C₇	C₂×#11924777	semidirect
48. C₇	C₂²×#11924777	semidirect
50. C₂²	#22552710	direct (N × H)
52. C₂	C₂×#22552710	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×#22552710	2
C₂²×C₃×C₇²×C₁₉	3
C₂²×#11924777	7
C₂²×#89204	19

Subgroups — C22×#22552710 #45691703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#22552710 #45691703