Subgroups — D₄×#10596842 #17989701

Order 4672.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10596842	C₂	1	2	yes	maximal, complemented
2	C₄⋊#10596842	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#10596842	C₂	1	2	yes	maximal, complemented
4	C₄×#10596842	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#64408	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596842	—	2	4	no	—
7	C₂×#10596842	C₂²	1	1	yes	characteristic
8	C₂×#10596842	C₂²	1	2	yes	—
9	C₂×#10596842	C₂²	1	1	yes	characteristic
10	C₂²×#64408	C₂²	1	2	yes	—
11	C₄⋊#64408	C₄	1	1	yes	characteristic
12	C₂²⋊#64408	C₄	1	2	yes	—
13	C₄×#64408	C₂²	1	1	yes	characteristic
14	D₄×D₇₃	C₄	1	1	yes	characteristic
15	C₂²×D₇₃	C₂×C₄	1	2	yes	—
16	C₂×#64408	—	2	2	no	—
17	C₂×#64408	—	2	2	no	—
18	C₂×#64408	C₂×C₄	1	1	yes	characteristic
19	C₂×#64408	C₂×C₄	1	2	yes	—
20	C₂×#64408	C₂³	1	1	yes	characteristic
21	#10596842	—	2	2	no	—
22	#10596842	—	2	1	no	—
23	#10596842	D₄	1	2	yes	direct product factor
24	D₄×C₇₃	C₈	1	1	yes	characteristic, complemented
25	C₂²⋊D₇₃	C₈	1	2	yes	complemented
26	D₂₉₂	C₈	1	1	yes	characteristic, complemented
27	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₇₃	C₂×C₈	1	2	yes	complemented
29	C₂×D₇₃	—	2	2	no	—
30	C₂×D₇₃	—	2	2	no	—
31	C₂×D₇₃	C₂×C₈	1	2	yes	complemented
32	C₂×D₇₃	C₂²×C₄	1	1	yes	characteristic
33	#64408	—	2	2	no	—
34	#64408	—	2	1	no	—
35	#64408	C₂×D₄	1	1	yes	characteristic
36	#64408	#41	1	1	yes	characteristic
37	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
38	Dic₇₃	C₂×C₈	1	1	yes	characteristic, complemented
39	C₂×C₇₃	—	2	2	no	—
40	C₂×C₇₃	C₂²×C₈	1	1	yes	characteristic
41	D₇₃	—	2	2	no	—
42	D₇₃	C₄×D₄	1	1	yes	characteristic
43	D₇₃	#131	1	1	yes	characteristic
44	C₇₃	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₈×D₄	—	73	1	no	maximal, Sylow
46	C₂²×C₈	—	73	2	no	—
47	C₄×D₄	—	73	1	no	—
48	C₄⋊C₈	—	73	1	no	—
49	C₂²⋊C₈	—	73	2	no	—
50	C₄×C₈	—	73	1	no	—
51	C₂×D₄	—	73	1	no	—
52	C₂²×C₄	—	73	2	no	—
53	C₂×C₈	—	73	1	no	—
54	C₂×C₈	—	73	1	no	—
55	C₂×C₈	—	73	2	no	—
56	C₂×C₈	—	146	4	no	—
57	C₄⋊C₄	—	73	1	no	—
58	C₂²⋊C₄	—	73	2	no	—
59	C₄²	—	73	1	no	—
60	C₂³	—	73	2	no	—
61	D₄	—	73	2	no	—
62	D₄	—	73	1	no	—
63	D₄	#10596842	1	1	yes	characteristic, direct product factor
64	C₂×C₄	—	73	1	no	—
65	C₂×C₄	—	73	1	no	—
66	C₂×C₄	—	73	1	no	—
67	C₂×C₄	—	73	2	no	—
68	C₂×C₄	—	146	2	no	—
69	C₂×C₄	—	146	2	no	—
70	C₈	—	73	2	no	—
71	C₈	—	146	2	no	—
72	C₈	—	146	1	no	—
73	C₂²	—	73	1	no	—
74	C₂²	—	73	2	no	—
75	C₂²	—	146	2	no	—
76	C₂²	—	146	2	no	—
77	C₂²	C₂×#10596842	1	2	yes	complemented
78	C₄	—	73	1	no	—
79	C₄	—	73	1	no	—
80	C₄	—	73	1	no	—
81	C₄	—	146	2	no	—
82	C₄	—	146	1	no	—
83	C₄	C₂×#10596842	1	1	yes	characteristic, complemented
84	C₂	—	2	2	no	—
85	C₂	—	73	1	no	—
86	C₂	—	73	1	no	—
87	C₂	—	146	2	no	—
88	C₂	C₂²×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₈
Fitting	D₄×C₇₃	C₈
prime radical	D₄×D₇₃	C₄
cosocle	C₂×#64408	C₂³
hypercenter	D₄	#10596842
hypocenter	C₇₃	C₈×D₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#10596842	C₂	semidirect
2. C₄⋊#10596842	C₂	semidirect
3. C₂²⋊#10596842	C₂	semidirect
4. C₄×#10596842	C₂	semidirect
23. #10596842	D₄	direct (N × H)
24. D₄×C₇₃	C₈	semidirect
25. C₂²⋊D₇₃	C₈	semidirect
26. D₂₉₂	C₈	semidirect
28. C₂²×C₇₃	C₂×C₈	semidirect
31. C₂×D₇₃	C₂×C₈	semidirect
37. C₄×C₇₃	C₂×C₈	semidirect
38. Dic₇₃	C₂×C₈	semidirect
44. C₇₃	C₈×D₄	semidirect
63. D₄	#10596842	direct (N × H)
77. C₂²	C₂×#10596842	semidirect
83. C₄	C₂×#10596842	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10596842	2
C₄⋊#10596842	2
C₂²⋊#10596842	2
C₄×#10596842	2
D₄×#64408	2
C₈×D₄	73

Subgroups — D4×#10596842 #17989701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#10596842 #17989701