Subgroups — #14520849

Order 1984.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄₈	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₂₄	—	2	1	no	—
5	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₃₁	—	2	1	no	—
7	D₂₄₈	—	2	1	no	—
8	D₂₄₈	C₄	1	2	yes	complemented
9	C₃₁⋊C₁₆	—	2	1	no	—
10	C₂²×D₃₁	—	4	1	no	—
11	C₂×C₄×C₃₁	—	4	1	no	—
12	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
13	D₁₂₄	—	2	2	no	—
14	D₁₂₄	—	4	1	no	—
15	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₁	D₄	1	1	yes	characteristic
17	C₂²×C₃₁	D₈	1	1	yes	characteristic
18	C₂×D₃₁	—	4	2	no	—
19	C₂×D₃₁	—	8	1	no	—
20	C₂×D₃₁	—	8	1	no	—
21	C₄×C₃₁	—	8	1	no	—
22	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₃₁	SD₁₆	1	1	yes	characteristic
24	#357	—	31	1	no	maximal, Sylow
25	C₂×C₃₁	#102	1	1	yes	characteristic
26	C₂×C₃₁	D₁₆	1	1	yes	characteristic
27	C₂×C₃₁	SD₃₂	1	1	yes	characteristic
28	D₃₁	—	8	2	no	—
29	C₂×D₈	—	31	1	no	—
30	C₂×C₁₆	—	31	1	no	—
31	#107	D₃₁	1	1	yes	characteristic, complemented
32	C₃₁	#357	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₄	—	62	1	no	—
34	D₈	—	31	2	no	—
35	D₈	—	62	1	no	—
36	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
37	C₄⋊C₄	—	2	1	no	—
38	C₁₆	—	62	1	no	—
39	C₂³	—	124	1	no	—
40	D₄	—	62	2	no	—
41	D₄	—	124	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
44	C₈	C₄×D₃₁	1	1	yes	characteristic
45	C₈	D₁₂₄	1	1	yes	characteristic
46	C₂²	—	124	2	no	—
47	C₂²	—	248	1	no	—
48	C₂²	—	248	1	no	—
49	C₂²	#92479	1	1	yes	characteristic
50	C₄	—	8	1	no	—
51	C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
52	C₄	#92481	1	1	yes	characteristic
53	C₂	—	248	2	no	—
54	C₂	#11758397	1	1	yes	characteristic
55	C₂	#11758414	1	1	yes	characteristic
56	C₂	#11758416	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#92479
commutator	C₈×C₃₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₁
Fitting	C₃₁×#107	C₂
socle	C₂²×C₃₁	D₈
prime radical	C₂×D₂₄₈	C₂
cosocle	C₂×C₈×C₃₁	C₂²
hypercenter	#107	D₃₁
hypocenter	C₃₁	#357
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
2. C₃₁×#107	C₂	semidirect
3. C₂×C₃₁⋊C₁₆	C₂	semidirect
8. D₂₄₈	C₄	semidirect
31. #107	D₃₁	semidirect
32. C₃₁	#357	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₄₈	2
C₃₁×#107	2
C₂×C₃₁⋊C₁₆	2
#357	31