Subgroups — C₄²×#11924040 #34034030

Order 18688.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11924040	C₂	1	6	yes	maximal
2	C₄²×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11924040	C₂²	1	4	yes	—
4	C₄×#11924040	C₄	1	24	yes	direct product factor
5	C₂×C₄×#10596833	C₄	1	3	yes	—
6	C₂×C₄×#10596833	C₂²	1	3	yes	—
7	C₄²×Dic₇₃	C₄	1	1	yes	characteristic
8	C₂×#11924040	C₂×C₄	1	24	yes	—
9	C₂²×#10596833	C₂×C₄	1	3	yes	—
10	C₂²×#10596833	C₂³	1	1	yes	characteristic
11	C₄×#10596833	C₈	1	12	yes	—
12	C₄×#10596833	C₂×C₄	1	12	yes	—
13	C₂×C₄×Dic₇₃	C₈	1	3	yes	—
14	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	—
15	C₂×C₄²×C₇₃	C₈	1	1	yes	characteristic
16	#11924040	C₄²	1	16	yes	direct product factor
17	C₂×#10596833	C₄²	1	6	yes	—
18	C₂×#10596833	C₂×C₈	1	12	yes	—
19	C₂×#10596833	C₂²×C₄	1	6	yes	—
20	C₂²×Dic₇₃	C₂×C₈	1	3	yes	—
21	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	C₁₆	1	12	yes	complemented
23	C₄×Dic₇₃	C₄²	1	6	yes	—
24	C₄×Dic₇₃	C₂×C₈	1	6	yes	—
25	C₂²×C₄×C₇₃	C₂×C₈	1	3	yes	—
26	C₄²×C₇₃	C₁₆	1	4	yes	complemented
27	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₄×C₈	1	6	yes	—
29	C₂×C₄×C₇₃	C₂×C₁₆	1	6	yes	—
30	C₂×C₄×C₇₃	C₂×C₁₆	1	6	yes	—
31	C₂×Dic₇₃	C₄×C₈	1	6	yes	—
32	C₂×Dic₇₃	C₂×C₁₆	1	12	yes	—
33	C₂×Dic₇₃	C₂×C₄²	1	3	yes	—
34	C₂×Dic₇₃	C₂²×C₈	1	3	yes	—
35	#10596833	C₄×C₈	1	12	yes	—
36	#10596833	C₂×C₄²	1	4	yes	—
37	C₂²×C₇₃	C₂×C₄×C₈	1	3	yes	—
38	C₂²×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
39	C₂²×C₇₃	C₂²×C₁₆	1	3	yes	—
40	C₄×C₇₃	C₄×C₁₆	1	12	yes	complemented
41	Dic₇₃	C₄×C₁₆	1	12	yes	complemented
42	Dic₇₃	C₄³	1	1	yes	characteristic
43	Dic₇₃	C₂×C₄×C₈	1	3	yes	—
44	C₄²×C₁₆	—	73	1	no	maximal, Sylow
45	C₂×C₇₃	C₄²×C₈	1	1	yes	characteristic
46	C₂×C₇₃	C₂×C₄×C₁₆	1	3	yes	—
47	C₂×C₇₃	C₂×C₄×C₁₆	1	3	yes	—
48	C₂×C₄×C₁₆	—	73	6	no	—
49	C₄²×C₈	—	73	1	no	—
50	C₇₃	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₁₆	—	73	4	no	—
52	C₂×C₄×C₈	—	73	3	no	—
53	C₂×C₄×C₈	—	73	3	no	—
54	C₄³	—	73	1	no	—
55	C₄×C₁₆	—	73	24	no	—
56	C₂²×C₈	—	73	3	no	—
57	C₂²×C₈	—	73	1	no	—
58	C₂×C₄²	—	73	3	no	—
59	C₂×C₄²	—	73	3	no	—
60	C₂×C₄²	#10596842	1	1	yes	characteristic
61	C₂×C₁₆	—	73	24	no	—
62	C₄×C₈	—	73	12	no	—
63	C₄×C₈	—	73	12	no	—
64	C₂²×C₄	—	73	3	no	—
65	C₂²×C₄	—	73	1	no	—
66	C₂²×C₄	C₂×#10596842	1	3	yes	—
67	C₂×C₈	—	73	6	no	—
68	C₂×C₈	—	73	12	no	—
69	C₂×C₈	—	73	6	no	—
70	C₄²	—	73	6	no	—
71	C₄²	—	73	6	no	—
72	C₄²	—	73	12	no	—
73	C₄²	#11924040	1	4	yes	direct product factor
74	C₁₆	—	73	16	no	—
75	C₂³	C₂²×#10596842	1	1	yes	characteristic
76	C₂×C₄	—	73	3	no	—
77	C₂×C₄	—	73	3	no	—
78	C₂×C₄	—	73	6	no	—
79	C₂×C₄	—	73	12	no	—
80	C₂×C₄	C₄×#10596842	1	6	yes	—
81	C₂×C₄	C₂×#11924040	1	6	yes	—
82	C₂×C₄	#14556686	1	6	yes	—
83	C₈	—	73	4	no	—
84	C₈	—	73	12	no	—
85	C₂²	C₂×C₄×#10596842	1	3	yes	—
86	C₂²	C₂²×#11924040	1	1	yes	characteristic
87	C₂²	C₂×#14556686	1	3	yes	—
88	C₄	—	73	12	no	—
89	C₄	—	73	1	no	—
90	C₄	—	73	3	no	—
91	C₄	C₄×#11924040	1	12	yes	direct product factor
92	C₂	C₄²×#10596842	1	1	yes	characteristic
93	C₂	C₂×C₄×#11924040	1	3	yes	—
94	C₂	C₄×#14556686	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#10596842
commutator, hypocenter	C₇₃	C₄²×C₁₆
Frattini	C₂³	C₂²×#10596842
Fitting	C₂×C₄²×C₇₃	C₈
socle, prime radical	C₂³×C₇₃	C₂²×C₈
cosocle	C₂²×#10596833	C₂³
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. C₄×#11924040	C₄	direct (N × H)
16. #11924040	C₄²	direct (N × H)
22. C₄×Dic₇₃	C₁₆	semidirect
26. C₄²×C₇₃	C₁₆	semidirect
40. C₄×C₇₃	C₄×C₁₆	semidirect
41. Dic₇₃	C₄×C₁₆	semidirect
50. C₇₃	C₄²×C₁₆	semidirect
73. C₄²	#11924040	direct (N × H)
91. C₄	C₄×#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
C₂×C₄×#11924040	2
C₄²×#10596833	2
C₄²×C₁₆	73

Subgroups — C42×#11924040 #34034030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#11924040 #34034030