Subgroups — #14521089

Order 1984.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	#11758503	C₂	1	1	yes	maximal, characteristic
3	C₂×#92474	C₂	1	1	yes	maximal, characteristic
4	#11758396	C₂	1	2	yes	maximal, complemented
5	#11758395	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₃₁	—	2	1	no	—
7	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₁	—	2	1	no	—
9	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
10	C₂²⋊Dic₃₁	—	2	1	no	—
11	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
13	C₄×Dic₃₁	—	2	1	no	—
14	#92474	C₄	1	4	yes	complemented
15	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₃₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	—	4	2	no	—
19	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	Q₈	1	2	yes	—
22	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₃₁	—	2	1	no	—
24	C₂×Dic₃₁	—	2	1	no	—
25	C₃₁⋊C₈	C₂×C₄	1	4	yes	complemented
26	C₂²×C₃₁	—	2	1	no	—
27	C₂²×C₃₁	—	2	1	no	—
28	C₂²×C₃₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₁	—	4	2	no	—
31	C₄×C₃₁	C₄⋊C₄	1	2	yes	—
32	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₃₁	—	4	1	no	—
35	Dic₃₁	—	4	1	no	—
36	#428	—	31	1	no	maximal, Sylow
37	C₂×C₃₁	—	2	2	no	—
38	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₃₁	#137	1	1	yes	characteristic
41	C₂×M₁₆	—	31	1	no	—
42	#117	—	31	1	no	—
43	C₂×C₄⋊C₄	D₃₁	1	1	yes	characteristic
44	#107	—	31	2	no	—
45	#106	—	31	2	no	—
46	C₃₁	#428	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	2	1	no	—
48	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
49	M₁₆	—	31	4	no	—
50	C₂×C₈	—	31	2	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	31	1	no	—
53	C₄⋊C₄	—	31	1	no	—
54	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
55	C₂²⋊C₄	—	62	1	no	—
56	C₄²	—	62	1	no	—
57	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	—	62	1	no	—
61	C₂×C₄	—	62	1	no	—
62	C₂×C₄	Dic₆₂	1	2	yes	—
63	C₂×C₄	C₄×D₃₁	1	2	yes	—
64	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
66	C₈	—	31	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	Dic₃₁⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	124	1	no	—
73	C₄	—	124	1	no	—
74	C₄	Dic₃₁⋊C₄	1	2	yes	—
75	C₄	C₂×Dic₆₂	1	1	yes	characteristic
76	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×Dic₃₁⋊C₄	1	1	yes	characteristic
79	C₂	#11758509	1	1	yes	characteristic
80	C₂	#11758519	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #11758396	C₂	semidirect
5. #11758395	C₂	semidirect
14. #92474	C₄	semidirect
25. C₃₁⋊C₈	C₂×C₄	semidirect
46. C₃₁	#428	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₃₁	2
#11758503	2
C₂×#92474	2
#11758396	2
#11758395	2
#428	31