Subgroups — #14521088

Order 1984.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92469	C₂	1	1	yes	maximal, characteristic
2	#11758469	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758406	C₂	1	1	yes	maximal, characteristic, complemented
6	#11758396	C₂	1	1	yes	maximal, characteristic, complemented
7	#11758395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₁	—	2	1	no	—
9	C₂×C₄×D₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
13	(C₂×D₃₁)⋊C₄	—	2	1	no	—
14	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	—	2	1	no	—
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	#92469	C₄	1	4	yes	complemented
20	C₂²×D₃₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₃₁	—	2	1	no	—
25	C₂×Dic₃₁	—	2	1	no	—
26	C₂×Dic₃₁	D₄	1	1	yes	characteristic
27	C₄×D₃₁	—	4	2	no	—
28	C₄×D₃₁	C₂×C₄	1	2	yes	—
29	C₄×D₃₁	Q₈	1	2	yes	—
30	C₈×C₃₁	C₂×C₄	1	2	yes	complemented
31	C₃₁⋊C₈	C₂×C₄	1	2	yes	complemented
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₁	—	2	1	no	—
34	C₂×D₃₁	—	2	1	no	—
35	C₂×D₃₁	C₄⋊C₄	1	2	yes	—
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
40	Dic₃₁	—	4	1	no	—
41	Dic₃₁	—	4	1	no	—
42	Dic₃₁	C₄⋊C₄	1	2	yes	—
43	#428	—	31	1	no	maximal, Sylow
44	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₃₁	#137	1	1	yes	characteristic
47	D₃₁	—	2	2	no	—
48	C₂×M₁₆	—	31	1	no	—
49	#117	—	31	1	no	—
50	C₂×C₄⋊C₄	—	31	1	no	—
51	#107	—	31	1	no	—
52	#107	—	31	1	no	—
53	#106	—	31	1	no	—
54	#106	D₃₁	1	1	yes	characteristic, complemented
55	C₃₁	#428	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	31	1	no	—
57	C₂²×C₄	—	62	1	no	—
58	M₁₆	—	31	4	no	—
59	C₂×C₈	—	31	1	no	—
60	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
61	C₄⋊C₄	—	31	1	no	—
62	C₄⋊C₄	—	31	1	no	—
63	C₄⋊C₄	—	62	1	no	—
64	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
65	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
66	C₂²⋊C₄	—	62	1	no	—
67	C₄²	—	62	1	no	—
68	C₂³	—	31	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	31	1	no	—
72	C₂×C₄	—	31	2	no	—
73	C₂×C₄	—	31	2	no	—
74	C₂×C₄	—	62	1	no	—
75	C₂×C₄	—	62	1	no	—
76	C₂×C₄	—	124	2	no	—
77	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
78	C₈	—	31	2	no	—
79	C₈	C₄×D₃₁	1	2	yes	complemented
80	C₂²	—	31	2	no	—
81	C₂²	—	62	1	no	—
82	C₂²	—	62	1	no	—
83	C₂²	D₄×D₃₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	31	2	no	—
87	C₄	—	124	1	no	—
88	C₄	—	124	1	no	—
89	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
90	C₄	Q₈×D₃₁	1	1	yes	characteristic
91	C₂	—	62	2	no	—
92	C₂	C₄⋊C₄×D₃₁	1	1	yes	characteristic
93	C₂	#11758491	1	1	yes	characteristic
94	C₂	#11758492	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#106	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂²×D₃₁	D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	#106	D₃₁
hypocenter	C₃₁	#428
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
4. C₃₁×#106	C₂	semidirect
5. #11758406	C₂	semidirect
6. #11758396	C₂	semidirect
7. #11758395	C₂	semidirect
19. #92469	C₄	semidirect
30. C₈×C₃₁	C₂×C₄	semidirect
31. C₃₁⋊C₈	C₂×C₄	semidirect
54. #106	D₃₁	semidirect
55. C₃₁	#428	semidirect
79. C₈	C₄×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92469	2
#11758469	2
C₄⋊C₄×D₃₁	2
C₃₁×#106	2
#11758406	2
#11758396	2
#11758395	2
#428	31