Subgroups — #16854103

Order 3968.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14520940	C₂	1	7	yes	maximal
2	#14520933	C₂	1	7	yes	maximal, complemented
3	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×C₃₁	C₂²	1	7	yes	—
5	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	7	yes	—
6	C₂×Dic₃₁⋊C₄	C₂²	1	7	yes	—
7	C₃₁⋊#95	C₂²	1	14	yes	—
8	C₂³×D₃₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₃₁	C₂³	1	7	yes	—
10	C₂²×Dic₃₁	C₂³	1	7	yes	—
11	C₄²×C₃₁	—	2	14	no	—
12	(C₂×D₃₁)⋊C₄	—	2	14	no	—
13	Dic₃₁⋊C₄	—	2	14	no	—
14	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
15	C₂²×D₃₁	—	2	7	no	—
16	C₂×C₄×C₃₁	—	2	14	no	—
17	C₂×C₄×C₃₁	#41	1	14	yes	—
18	C₂×Dic₃₁	—	2	14	no	—
19	C₂×Dic₃₁	—	2	7	no	—
20	#2866	—	31	1	no	maximal, Sylow
21	C₂²×C₃₁	C₂×#41	1	7	yes	—
22	C₂×D₃₁	—	4	7	no	—
23	C₄×C₃₁	—	2	14	no	—
24	Dic₃₁	—	4	7	no	—
25	#388	—	31	7	no	—
26	#387	—	31	7	no	—
27	C₄³	D₃₁	1	1	yes	characteristic, complemented
28	C₂×C₃₁	#529	1	7	yes	—
29	D₃₁	—	8	1	no	—
30	C₂×C₄⋊C₄	—	31	7	no	—
31	C₂×C₂²⋊C₄	—	31	7	no	—
32	C₂×C₄²	C₂×D₃₁	1	7	yes	—
33	#95	—	31	14	no	—
34	C₃₁	#2866	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	31	1	no	—
36	C₂²×C₄	—	31	7	no	—
37	C₂²×C₄	C₂²×D₃₁	1	7	yes	—
38	C₄⋊C₄	—	62	14	no	—
39	C₂²⋊C₄	—	62	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	62	7	no	—
42	C₂³	C₂³×D₃₁	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	62	7	no	—
45	C₂×C₄	—	62	14	no	—
46	C₂×C₄	#92495	1	14	yes	—
47	C₂²	—	124	7	no	—
48	C₂²	C₂×#92495	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	124	7	no	—
51	C₂	—	248	1	no	—
52	C₂	#14521583	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₄³×C₃₁	C₂
prime radical	C₂³×D₃₁	C₂³
hypercenter	C₄³	D₃₁
hypocenter	C₃₁	#2866
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. #14520933	C₂	semidirect
3. C₄³×C₃₁	C₂	semidirect
27. C₄³	D₃₁	semidirect
34. C₃₁	#2866	semidirect

Maximal subgroups

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

subgroup	index
#14520940	2
#14520933	2
C₄³×C₃₁	2
#2866	31