Subgroups — #16845882

Order 3968.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758410	C₂	1	4	yes	maximal
2	#14521073	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×#92474	C₂²	1	2	yes	—
8	C₂²×C₃₁⋊C₈	C₂²	1	2	yes	—
9	C₃₁×C₄⋊C₈	—	2	2	no	—
10	#11758410	—	2	8	no	—
11	C₄⋊(C₃₁⋊C₈)	—	2	2	no	—
12	C₄×C₃₁⋊C₈	C₄	1	2	yes	—
13	C₄×C₃₁⋊C₈	C₄	1	2	yes	—
14	C₂²×C₄×C₃₁	Q₈	1	2	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	M₁₆×C₃₁	—	2	4	no	—
17	C₂×C₈×C₃₁	—	2	2	no	—
18	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₃₁	D₄	1	2	yes	—
21	#92474	—	2	4	no	—
22	C₂×C₃₁⋊C₈	—	2	2	no	—
23	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₃₁⋊C₈	D₄	1	4	yes	—
25	C₂×C₃₁⋊C₈	Q₈	1	4	yes	—
26	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₃₁	—	2	4	no	—
28	C₂×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
34	C₈×C₃₁	—	4	2	no	—
35	C₃₁⋊C₈	—	4	2	no	—
36	C₃₁⋊C₈	C₄⋊C₄	1	8	yes	—
37	#1848	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	—	2	2	no	—
39	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₁	C₄⋊Q₈	1	2	yes	—
41	C₄×C₃₁	—	2	2	no	—
42	C₄×C₃₁	#108	1	4	yes	complemented
43	C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
44	C₄×C₃₁	#127	1	1	yes	characteristic
45	C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×#108	—	31	4	no	—
47	#423	—	31	1	no	—
48	#423	D₃₁	1	1	yes	characteristic
49	C₂×C₄×C₈	—	31	1	no	—
50	C₂×C₃₁	—	2	2	no	—
51	C₂×C₃₁	#384	1	1	yes	characteristic
52	C₂×C₃₁	C₂×#108	1	2	yes	—
53	C₂×M₁₆	—	31	2	no	—
54	C₂×M₁₆	C₂×D₃₁	1	2	yes	—
55	C₂²×C₈	—	31	2	no	—
56	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
57	#108	—	62	8	no	—
58	C₄⋊C₈	—	2	2	no	—
59	C₄⋊C₈	—	62	2	no	—
60	C₄×C₈	—	31	2	no	—
61	C₄×C₈	—	31	2	no	—
62	C₃₁	#1848	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	Dic₆₂	1	2	yes	—
64	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
65	M₁₆	—	2	4	no	—
66	M₁₆	—	62	4	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	31	4	no	—
69	C₂×C₈	—	31	4	no	—
70	C₂×C₈	—	31	4	no	—
71	C₂×C₈	—	62	2	no	—
72	C₄²	C₄×D₃₁	1	1	yes	characteristic
73	C₄²	C₄×D₃₁	1	1	yes	characteristic
74	C₄²	C₂²⋊D₃₁	1	2	yes	—
75	C₂³	C₂×Dic₆₂	1	1	yes	characteristic
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	Dic₃₁⋊C₄	1	2	yes	—
78	C₂×C₄	Dic₃₁⋊C₄	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
80	C₂×C₄	D₄×D₃₁	1	2	yes	—
81	C₂×C₄	Q₈×D₃₁	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
83	C₈	—	4	2	no	—
84	C₈	—	31	8	no	—
85	C₈	—	124	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#11758465	1	2	yes	—
88	C₂²	C₂×Dic₃₁⋊C₄	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	#11758410	1	4	yes	complemented
91	C₄	C₄⋊C₄×D₃₁	1	2	yes	—
92	C₄	#11758517	1	1	yes	characteristic
93	C₄	#11758521	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	#14520918	1	1	yes	characteristic
96	C₂	C₂×#11758410	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₃₁×#423	C₂
socle	C₂²×C₃₁	C₂×C₄⋊C₄
prime radical	C₂³×C₃₁	C₂×Q₈
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#423	D₃₁
hypocenter	C₃₁	#1848
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
42. C₄×C₃₁	#108	semidirect
62. C₃₁	#1848	semidirect
90. C₄	#11758410	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758410	2
#14521073	2
C₂×C₄×C₃₁⋊C₈	2
C₃₁×#423	2
#1848	31