Subgroups — #16845842

Order 3968.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14520915	C₂	1	2	yes	maximal
2	#14520812	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
5	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
7	C₄×C₈×C₃₁	C₄	1	4	yes	complemented
8	C₃₁⋊#95	—	2	4	no	—
9	C₂²×C₄×C₃₁	D₄	1	2	yes	—
10	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
11	C₂²×Dic₃₁	—	2	4	no	—
12	C₂×C₈×C₃₁	—	2	4	no	—
13	C₂×C₈×C₃₁	C₂×C₄	1	4	yes	—
14	C₄²×C₃₁	C₂×C₄	1	2	yes	—
15	C₄²×C₃₁	Q₈	1	2	yes	—
16	C₄⋊Dic₃₁	—	2	8	no	—
17	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	—	2	4	no	—
19	C₂×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₃₁	#41	1	4	yes	—
23	C₂×Dic₃₁	—	4	4	no	—
24	C₂×Dic₃₁	—	4	8	no	—
25	C₈×C₃₁	—	2	4	no	—
26	#1835	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₃₁	#124	1	2	yes	—
29	C₂²×C₃₁	#135	1	4	yes	—
30	C₄×C₃₁	—	2	4	no	—
31	C₄×C₃₁	#117	1	2	yes	—
32	C₄×C₃₁	#125	1	2	yes	—
33	Dic₃₁	—	8	4	no	—
34	C₂×C₄×C₈	D₃₁	1	1	yes	characteristic
35	#382	—	31	2	no	—
36	#340	—	31	4	no	—
37	C₂×C₃₁	#382	1	1	yes	characteristic
38	C₂×C₃₁	#427	1	2	yes	—
39	C₂×C₃₁	#488	1	4	yes	—
40	C₂²×C₈	C₂×D₃₁	1	2	yes	—
41	C₂×C₄⋊C₄	—	31	4	no	—
42	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
43	C₄×C₈	Dic₃₁	1	4	yes	complemented
44	#95	—	62	4	no	—
45	C₃₁	#1835	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	—	62	4	no	—
47	C₂²×C₄	D₁₂₄	1	2	yes	—
48	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	C₂×Dic₃₁	1	4	yes	—
51	C₄⋊C₄	—	62	8	no	—
52	C₄²	Dic₆₂	1	2	yes	—
53	C₄²	C₂×Dic₃₁	1	2	yes	—
54	C₂³	C₂×D₁₂₄	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	124	4	no	—
57	C₂×C₄	—	124	8	no	—
58	C₂×C₄	C₄⋊Dic₃₁	1	4	yes	—
59	C₂×C₄	C₂×Dic₆₂	1	1	yes	characteristic
60	C₂×C₄	#92495	1	4	yes	—
61	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₂²	#11758452	1	2	yes	—
64	C₂²	#11758481	1	4	yes	—
65	C₂²	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
66	C₄	—	2	4	no	—
67	C₄	—	248	4	no	—
68	C₄	#11758447	1	2	yes	—
69	C₄	#11758503	1	2	yes	—
70	C₂	#14520915	1	1	yes	characteristic
71	C₂	#14521087	1	2	yes	—
72	C₂	#14521404	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₂₄
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₄×C₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂×D₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×C₄×C₈	D₃₁
hypocenter	C₃₁	#1835
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
7. C₄×C₈×C₃₁	C₄	semidirect
43. C₄×C₈	Dic₃₁	semidirect
45. C₃₁	#1835	semidirect

Maximal subgroups

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

subgroup	index
#14520915	2
#14520812	2
C₂×C₄×C₈×C₃₁	2
#1835	31