Subgroups — #14521445

Order 1984.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#11758446	C₂	1	1	yes	maximal, characteristic
3	#11758396	C₂	1	4	yes	maximal
4	C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₃₁	—	2	1	no	—
6	C₂×Dic₆₂	—	2	1	no	—
7	C₄⋊C₄×C₃₁	—	2	1	no	—
8	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
9	C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₁	—	2	1	no	—
11	C₄⋊Dic₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
13	Q₈×C₃₁	—	4	2	no	—
14	C₂×C₄×C₃₁	—	2	2	no	—
15	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
18	C₂×Dic₃₁	—	2	2	no	—
19	Dic₆₂	—	4	2	no	—
20	C₃₁⋊C₈	Q₈	1	4	yes	complemented
21	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₁	—	4	2	no	—
23	C₄×C₃₁	SD₁₆	1	2	yes	—
24	C₄×C₃₁	SD₁₆	1	2	yes	—
25	C₄×C₃₁	C₂×Q₈	1	2	yes	—
26	Dic₃₁	—	4	2	no	—
27	#498	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
30	C₂×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
31	C₄⋊Q₈	—	31	1	no	—
32	C₄⋊Q₈	D₃₁	1	1	yes	characteristic
33	#106	—	31	4	no	—
34	C₄×C₈	—	31	1	no	—
35	C₃₁	#498	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	62	1	no	—
38	C₂×C₈	—	31	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	31	2	no	—
41	C₄⋊C₄	—	62	1	no	—
42	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
43	C₄²	C₂×D₃₁	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	124	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	62	2	no	—
48	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
51	C₈	—	31	4	no	—
52	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	124	2	no	—
55	C₄	#92480	1	2	yes	—
56	C₄	#92481	1	2	yes	—
57	C₄	Q₈×D₃₁	1	2	yes	—
58	C₂	C₂×#92480	1	1	yes	characteristic
59	C₂	C₂×#92481	1	1	yes	characteristic
60	C₂	#11758521	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	C₄⋊Q₈	D₃₁
hypocenter	C₃₁	#498
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
20. C₃₁⋊C₈	Q₈	semidirect
35. C₃₁	#498	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×C₄⋊Q₈	2
#11758446	2
#11758396	2
C₄×C₃₁⋊C₈	2
#498	31