Subgroups — #16847504

Order 3968.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758386	C₂	1	1	yes	maximal, characteristic
2	#108×D₃₁	C₂	1	2	yes	maximal
3	#14520879	C₂	1	1	yes	maximal, characteristic, complemented
4	#14520878	C₂	1	2	yes	maximal, complemented
5	C₃₁×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×D₃₁	—	2	2	no	—
7	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#108	C₂²	1	2	yes	—
10	#11758410	—	2	2	no	—
11	#11758407	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	#11758386	C₄	1	4	yes	—
14	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
15	M₁₆×C₃₁	—	2	2	no	—
16	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
17	#92474	—	2	2	no	—
18	C₂×C₃₁⋊C₈	D₄	1	1	yes	characteristic
19	#92469	—	4	2	no	—
20	C₈×D₃₁	—	4	2	no	—
21	C₈×D₃₁	C₂×C₄	1	2	yes	—
22	C₈×D₃₁	Q₈	1	2	yes	—
23	C₁₆×C₃₁	C₂×C₄	1	2	yes	—
24	C₃₁⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×D₃₁	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₁	Q₁₆	1	1	yes	characteristic
28	C₄×D₃₁	C₄⋊C₄	1	2	yes	—
29	C₄×D₃₁	D₈	1	2	yes	—
30	C₈×C₃₁	—	4	2	no	—
31	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
33	C₃₁⋊C₈	—	4	2	no	—
34	C₃₁⋊C₈	C₄⋊C₄	1	2	yes	—
35	#2161	—	31	1	no	maximal, Sylow
36	C₂²×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×D₃₁	—	4	1	no	—
38	C₂×D₃₁	#107	1	2	yes	—
39	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
41	Dic₃₁	#107	1	2	yes	—
42	C₂×M₃₂	—	31	1	no	—
43	C₂×#108	—	31	2	no	—
44	#368	—	31	1	no	—
45	#368	—	31	2	no	—
46	#368	D₃₁	1	1	yes	characteristic, complemented
47	C₂×C₃₁	—	2	1	no	—
48	C₂×C₃₁	C₂×#107	1	1	yes	characteristic
49	D₃₁	—	2	2	no	—
50	C₂×M₁₆	—	62	2	no	—
51	C₂²×C₈	—	31	1	no	—
52	M₃₂	—	31	4	no	—
53	C₂×C₁₆	—	31	1	no	—
54	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
55	#108	—	31	2	no	—
56	#108	—	62	2	no	—
57	#108	C₂×D₃₁	1	2	yes	—
58	C₃₁	#2161	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄	—	31	1	no	—
60	M₁₆	—	2	2	no	—
61	M₁₆	—	62	2	no	—
62	M₁₆	—	124	2	no	—
63	C₂×C₈	—	31	1	no	—
64	C₂×C₈	—	31	2	no	—
65	C₂×C₈	—	31	2	no	—
66	C₂×C₈	—	124	2	no	—
67	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
68	C₁₆	—	31	2	no	—
69	C₁₆	C₄×D₃₁	1	2	yes	—
70	C₂³	—	31	1	no	—
71	C₂×C₄	—	31	1	no	—
72	C₂×C₄	—	31	2	no	—
73	C₂×C₄	—	31	2	no	—
74	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
75	C₈	—	4	2	no	—
76	C₈	—	31	2	no	—
77	C₈	—	124	2	no	—
78	C₈	C₂×C₄×D₃₁	1	1	yes	characteristic
79	C₈	Q₈×D₃₁	1	1	yes	characteristic
80	C₂²	—	31	2	no	—
81	C₂²	—	124	1	no	—
82	C₂²	Q₁₆×D₃₁	1	1	yes	characteristic
83	C₄	—	31	2	no	—
84	C₄	C₄⋊C₄×D₃₁	1	1	yes	characteristic
85	C₄	D₈×D₃₁	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	62	2	no	—
88	C₂	#107×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₃₁
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₃₁×#368	C₂
socle	C₂×C₃₁	C₂×#107
prime radical	C₂²×D₃₁	Q₁₆
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	#368	D₃₁
hypocenter	C₃₁	#2161
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
3. #14520879	C₂	semidirect
4. #14520878	C₂	semidirect
5. C₃₁×#368	C₂	semidirect
46. #368	D₃₁	semidirect
58. C₃₁	#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758386	2
#108×D₃₁	2
#14520879	2
#14520878	2
C₃₁×#368	2
#2161	31