Subgroups — #108×D₃₁ #14521093

Order 1984.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₃₁	C₂	1	2	yes	maximal
2	C₂×C₈×D₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758410	C₂	1	2	yes	maximal, complemented
5	#11758407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁	C₂²	1	1	yes	characteristic
7	M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	#92474	C₂²	1	2	yes	—
10	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
11	#92469	—	2	2	no	—
12	C₈×D₃₁	—	2	2	no	—
13	C₈×D₃₁	C₄	1	2	yes	—
14	C₈×D₃₁	C₄	1	2	yes	—
15	C₂²×D₃₁	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₃₁	Q₈	1	1	yes	characteristic
18	C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
20	C₄×D₃₁	D₄	1	1	yes	characteristic
21	C₄×D₃₁	D₄	1	1	yes	characteristic
22	C₈×C₃₁	—	2	2	no	—
23	C₈×C₃₁	C₂×C₄	1	2	yes	—
24	C₃₁⋊C₈	—	2	2	no	—
25	C₃₁⋊C₈	C₂×C₄	1	2	yes	—
26	C₂²×C₃₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×D₃₁	—	2	2	no	—
28	C₂×D₃₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₃₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
32	Dic₃₁	C₄⋊C₄	1	1	yes	characteristic
33	Dic₃₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×#108	—	31	1	no	maximal, Sylow
35	C₂×C₃₁	—	2	1	no	—
36	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₃₁	—	2	1	no	—
38	D₃₁	#108	1	2	yes	direct product factor
39	C₂×M₁₆	—	31	2	no	—
40	C₂²×C₈	—	31	1	no	—
41	#108	—	31	2	no	—
42	#108	—	31	1	no	—
43	#108	D₃₁	1	1	yes	characteristic, direct product factor
44	C₃₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	—	31	1	no	—
46	M₁₆	—	31	2	no	—
47	M₁₆	—	62	2	no	—
48	M₁₆	C₂×D₃₁	1	2	yes	—
49	C₂×C₈	—	31	1	no	—
50	C₂×C₈	—	31	2	no	—
51	C₂×C₈	—	31	2	no	—
52	C₂×C₈	—	62	2	no	—
53	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
54	C₂³	—	31	1	no	—
55	C₂×C₄	—	31	1	no	—
56	C₂×C₄	—	31	1	no	—
57	C₂×C₄	—	31	1	no	—
58	C₂×C₄	—	31	1	no	—
59	C₂×C₄	—	31	1	no	—
60	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	—	31	2	no	—
63	C₈	—	62	2	no	—
64	C₈	C₄×D₃₁	1	2	yes	—
65	C₂²	—	31	1	no	—
66	C₂²	—	31	1	no	—
67	C₂²	—	62	2	no	—
68	C₂²	Q₈×D₃₁	1	1	yes	characteristic
69	C₄	—	31	1	no	—
70	C₄	—	31	1	no	—
71	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
72	C₄	D₄×D₃₁	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	31	2	no	—
75	C₂	—	62	1	no	—
76	C₂	C₄⋊C₄×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#108	C₂
socle	C₂×C₃₁	C₂×C₄⋊C₄
prime radical	C₂²×D₃₁	Q₈
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	#108	D₃₁
hypocenter	C₃₁	C₂×#108
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₃₁×#108	C₂	semidirect
4. #11758410	C₂	semidirect
5. #11758407	C₂	semidirect
38. D₃₁	#108	direct (N × H)
43. #108	D₃₁	direct (N × H)
44. C₃₁	C₂×#108	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₃₁	2
C₂×C₈×D₃₁	2
C₃₁×#108	2
#11758410	2
#11758407	2
C₂×#108	31

Subgroups — #108×D31 #14521093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #108×D₃₁ #14521093