Subgroups — C₂⁴×#11924040 #34035049

Order 18688.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11924040	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11924040	C₂²	1	140	yes	direct product factor
4	C₂³×#10596833	C₄	1	15	yes	—
5	C₂³×#10596833	C₂²	1	15	yes	—
6	C₂⁴×Dic₇₃	C₄	1	1	yes	characteristic
7	C₂×#11924040	C₂³	1	120	yes	direct product factor
8	C₂²×#10596833	C₂×C₄	1	105	yes	—
9	C₂²×#10596833	C₂³	1	35	yes	—
10	C₂³×Dic₇₃	C₈	1	15	yes	—
11	C₂³×Dic₇₃	C₂×C₄	1	15	yes	—
12	C₂⁵×C₇₃	C₈	1	1	yes	characteristic
13	#11924040	C₂⁴	1	16	yes	direct product factor
14	C₂×#10596833	C₂²×C₄	1	105	yes	—
15	C₂×#10596833	C₂⁴	1	15	yes	—
16	C₂²×Dic₇₃	C₂×C₈	1	105	yes	—
17	C₂²×Dic₇₃	C₂²×C₄	1	35	yes	—
18	C₂⁴×C₇₃	C₁₆	1	16	yes	complemented
19	C₂⁴×C₇₃	C₂×C₈	1	15	yes	—
20	C₂³×C₇₃	C₂×C₁₆	1	120	yes	complemented
21	C₂³×C₇₃	C₂²×C₈	1	35	yes	—
22	C₂×Dic₇₃	C₂²×C₈	1	105	yes	—
23	C₂×Dic₇₃	C₂³×C₄	1	15	yes	—
24	#10596833	C₂³×C₄	1	15	yes	—
25	#10596833	C₂⁵	1	1	yes	characteristic
26	C₂²×C₇₃	C₂²×C₁₆	1	140	yes	complemented
27	C₂²×C₇₃	C₂³×C₈	1	15	yes	—
28	Dic₇₃	C₂³×C₈	1	15	yes	—
29	Dic₇₃	C₂⁴×C₄	1	1	yes	characteristic
30	C₂⁴×C₁₆	—	73	1	no	maximal, Sylow
31	C₂×C₇₃	C₂³×C₁₆	1	30	yes	complemented
32	C₂×C₇₃	C₂⁴×C₈	1	1	yes	characteristic
33	C₂⁴×C₈	—	73	1	no	—
34	C₂³×C₁₆	—	73	30	no	—
35	C₇₃	C₂⁴×C₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂⁴×C₄	—	73	1	no	—
37	C₂³×C₈	—	73	15	no	—
38	C₂³×C₈	—	73	15	no	—
39	C₂²×C₁₆	—	73	140	no	—
40	C₂⁵	#10596842	1	1	yes	characteristic
41	C₂³×C₄	—	73	15	no	—
42	C₂³×C₄	—	73	15	no	—
43	C₂²×C₈	—	73	105	no	—
44	C₂²×C₈	—	73	35	no	—
45	C₂×C₁₆	—	73	120	no	—
46	C₂⁴	#11924040	1	16	yes	direct product factor
47	C₂⁴	C₂×#10596842	1	15	yes	—
48	C₂²×C₄	—	73	105	no	—
49	C₂²×C₄	—	73	35	no	—
50	C₂×C₈	—	73	105	no	—
51	C₂×C₈	—	73	15	no	—
52	C₁₆	—	73	16	no	—
53	C₂³	C₂×#11924040	1	120	yes	direct product factor
54	C₂³	C₂²×#10596842	1	35	yes	—
55	C₂×C₄	—	73	15	no	—
56	C₂×C₄	—	73	105	no	—
57	C₈	—	73	1	no	—
58	C₈	—	73	15	no	—
59	C₂²	C₂²×#11924040	1	140	yes	direct product factor
60	C₂²	C₂³×#10596842	1	15	yes	—
61	C₄	—	73	1	no	—
62	C₄	—	73	15	no	—
63	C₂	C₂³×#11924040	1	30	yes	direct product factor
64	C₂	C₂⁴×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#10596842
commutator, hypocenter	C₇₃	C₂⁴×C₁₆
Frattini	C₂	C₂⁴×#10596842
Fitting, socle, prime radical	C₂⁵×C₇₃	C₈
cosocle	#10596833	C₂⁵
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂³×#11924040	C₂	direct (N × H)
3. C₂²×#11924040	C₂²	direct (N × H)
7. C₂×#11924040	C₂³	direct (N × H)
13. #11924040	C₂⁴	direct (N × H)
18. C₂⁴×C₇₃	C₁₆	semidirect
20. C₂³×C₇₃	C₂×C₁₆	semidirect
26. C₂²×C₇₃	C₂²×C₁₆	semidirect
31. C₂×C₇₃	C₂³×C₁₆	semidirect
35. C₇₃	C₂⁴×C₁₆	semidirect
46. C₂⁴	#11924040	direct (N × H)
53. C₂³	C₂×#11924040	direct (N × H)
59. C₂²	C₂²×#11924040	direct (N × H)
63. C₂	C₂³×#11924040	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11924040	2
C₂⁴×#10596833	2
C₂⁴×C₁₆	73

Subgroups — C24×#11924040 #34035049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#11924040 #34035049