Subgroups — #16845883

Order 3968.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758407	C₂	1	4	yes	maximal
2	#14521073	C₂	1	2	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×#92474	C₂²	1	4	yes	—
7	C₄×C₈×C₃₁	C₄	1	2	yes	—
8	C₄×C₈×C₃₁	C₄	1	2	yes	—
9	#11758407	—	2	8	no	—
10	C₄⋊(C₃₁⋊C₈)	—	2	4	no	—
11	C₂²×C₄×C₃₁	Q₈	1	2	yes	—
12	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₃₁	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₃₁	D₄	1	4	yes	—
15	C₂×C₈×C₃₁	Q₈	1	4	yes	—
16	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₃₁	D₄	1	2	yes	—
19	#92474	—	2	8	no	—
20	C₂×C₃₁⋊C₈	—	2	4	no	—
21	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₃₁	—	2	4	no	—
23	C₂×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
29	C₈×C₃₁	C₄⋊C₄	1	8	yes	—
30	C₃₁⋊C₈	—	4	4	no	—
31	#1848	—	31	1	no	maximal, Sylow
32	C₂²×C₃₁	—	2	2	no	—
33	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₃₁	C₄⋊Q₈	1	2	yes	—
35	C₄×C₃₁	—	2	2	no	—
36	C₄×C₃₁	#108	1	4	yes	complemented
37	C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
38	C₄×C₃₁	#127	1	1	yes	characteristic
39	C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×#108	—	31	4	no	—
41	#423	—	31	2	no	—
42	C₂×C₄×C₈	D₃₁	1	1	yes	characteristic
43	C₂×C₃₁	—	2	2	no	—
44	C₂×C₃₁	#384	1	1	yes	characteristic
45	C₂×C₃₁	C₂×#108	1	2	yes	—
46	C₂×M₁₆	—	31	4	no	—
47	C₂²×C₈	C₂×D₃₁	1	2	yes	—
48	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
49	#108	—	62	8	no	—
50	C₄⋊C₈	—	62	4	no	—
51	C₄×C₈	Dic₃₁	1	2	yes	—
52	C₄×C₈	Dic₃₁	1	2	yes	—
53	C₃₁	#1848	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	Dic₆₂	1	2	yes	—
55	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
56	M₁₆	—	62	8	no	—
57	C₂×C₈	—	62	4	no	—
58	C₂×C₈	Dic₆₂	1	4	yes	—
59	C₂×C₈	D₁₂₄	1	4	yes	—
60	C₂×C₈	C₂×Dic₃₁	1	4	yes	—
61	C₄²	D₁₂₄	1	2	yes	—
62	C₄²	C₂×Dic₃₁	1	1	yes	characteristic
63	C₄²	C₂×Dic₃₁	1	1	yes	characteristic
64	C₂³	C₂×Dic₆₂	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₃₁	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₃₁	1	2	yes	—
68	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
69	C₂×C₄	C₂×D₁₂₄	1	2	yes	—
70	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
72	C₈	—	124	4	no	—
73	C₈	C₄⋊Dic₃₁	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	#11758446	1	2	yes	—
76	C₂²	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	#11758407	1	4	yes	complemented
79	C₄	#11758446	1	1	yes	characteristic
80	C₄	#11758451	1	1	yes	characteristic
81	C₄	C₂×C₄⋊Dic₃₁	1	2	yes	—
82	C₂	—	2	2	no	—
83	C₂	#14520919	1	1	yes	characteristic
84	C₂	C₂×#11758407	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₂₄
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₄×C₈×C₃₁	C₂
socle	C₂²×C₃₁	C₂×C₄⋊C₄
prime radical	C₂³×C₃₁	C₂×Q₈
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×C₄×C₈	D₃₁
hypocenter	C₃₁	#1848
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
36. C₄×C₃₁	#108	semidirect
53. C₃₁	#1848	semidirect
78. C₄	#11758407	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758407	2
#14521073	2
C₂×C₄×C₈×C₃₁	2
#1848	31