Subgroups — C₄×#10625329 #15689076

Order 3008.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625329	C₂	1	2	yes	maximal
2	#13093935	C₂	1	2	yes	maximal, complemented
3	C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₇	C₄	1	2	yes	—
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₄²×C₄₇	C₄	1	2	yes	—
8	C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	#10625329	C₄	1	8	yes	direct product factor
11	C₂×C₄₇⋊C₈	C₂²	1	4	yes	—
12	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₇	—	2	4	no	—
14	C₂×C₄×C₄₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
20	C₂²×C₄₇	—	2	2	no	—
21	C₂²×C₄₇	C₄²	1	2	yes	—
22	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₄₇	—	2	2	no	—
24	C₄×C₄₇	C₄²	1	2	yes	—
25	C₄×C₄₇	M₁₆	1	4	yes	complemented
26	C₄×C₄₇	C₂²×C₄	1	2	yes	—
27	C₂×C₄₇	—	2	2	no	—
28	C₂×C₄₇	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₄₇	C₂×M₁₆	1	2	yes	—
30	C₄×M₁₆	—	47	1	no	maximal, Sylow
31	C₄₇	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×M₁₆	—	47	2	no	—
33	C₂×C₄²	D₄₇	1	1	yes	characteristic
34	#97	—	47	2	no	—
35	C₄×C₈	—	47	2	no	—
36	C₂²×C₄	Dic₄₇	1	2	yes	—
37	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
38	M₁₆	—	47	8	no	—
39	C₂×C₈	—	47	4	no	—
40	C₄²	Dic₄₇	1	2	yes	—
41	C₄²	C₂×D₄₇	1	1	yes	characteristic
42	C₄²	C₂×D₄₇	1	1	yes	characteristic
43	C₂³	C₂×Dic₄₇	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	C₄×D₄₇	1	4	yes	—
46	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
47	C₂×C₄	C₂×Dic₄₇	1	2	yes	—
48	C₂×C₄	C₂×Dic₄₇	1	1	yes	characteristic
49	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
50	C₈	—	47	8	no	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄×Dic₄₇	1	2	yes	—
53	C₂²	C₂²×Dic₄₇	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#10625329	1	4	yes	direct product factor
56	C₄	C₄×Dic₄₇	1	2	yes	—
57	C₄	C₂×C₄×D₄₇	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄×Dic₄₇	1	1	yes	characteristic
60	C₂	C₂×#10625329	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂×C₄²×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₄
prime radical	C₂³×C₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×C₄²	D₄₇
hypocenter	C₄₇	C₄×M₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #13093935	C₂	semidirect
3. C₄×C₄₇⋊C₈	C₂	semidirect
10. #10625329	C₄	direct (N × H)
19. C₄₇⋊C₈	C₂×C₄	semidirect
25. C₄×C₄₇	M₁₆	semidirect
31. C₄₇	C₄×M₁₆	semidirect
55. C₄	#10625329	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×#10625329	2
#13093935	2
C₄×C₄₇⋊C₈	2
C₂×C₄²×C₄₇	2
C₄×M₁₆	47

Subgroups — C4×#10625329 #15689076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10625329 #15689076