Subgroups — D₃₁×#383 #16848099

Order 3968.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₃₁	C₂	1	1	yes	maximal, characteristic
2	#14520917	C₂	1	1	yes	maximal, characteristic, complemented
3	#14520916	C₂	1	6	yes	maximal, complemented
4	#95×D₃₁	C₂	1	6	yes	maximal
5	C₃₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₃₁	C₂²	1	4	yes	—
7	C₂²×C₄×D₃₁	C₂²	1	3	yes	—
8	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₃₁	C₂²	1	3	yes	—
10	C₄²×D₃₁	C₄	1	8	yes	complemented
11	C₃₁×#95	C₂²	1	6	yes	—
12	C₃₁⋊#95	C₂²	1	12	yes	—
13	C₃₁⋊#95	C₂²	1	6	yes	—
14	C₂³×D₃₁	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
16	C₂²×C₄×C₃₁	C₂³	1	3	yes	—
17	C₂²×Dic₃₁	C₂³	1	4	yes	—
18	C₂²×Dic₃₁	C₂³	1	3	yes	—
19	C₂×C₄×D₃₁	—	2	12	no	—
20	C₂×C₄×D₃₁	—	2	24	no	—
21	C₂×C₄×D₃₁	C₂×C₄	1	12	yes	—
22	C₄²×C₃₁	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₃₁	C₂×C₄	1	12	yes	complemented
24	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
25	C₂²×D₃₁	C₂²×C₄	1	2	yes	—
26	C₂²×D₃₁	#41	1	12	yes	—
27	C₂×C₄×C₃₁	—	2	6	no	—
28	C₂×C₄×C₃₁	—	2	12	no	—
29	C₂×C₄×C₃₁	C₂²×C₄	1	6	yes	—
30	C₂×Dic₃₁	—	2	6	no	—
31	C₂×Dic₃₁	—	2	12	no	—
32	C₂×Dic₃₁	C₂²×C₄	1	6	yes	—
33	C₄×D₃₁	—	2	24	no	—
34	C₄×D₃₁	—	4	16	no	—
35	C₂×#383	—	31	1	no	maximal, Sylow
36	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
37	C₂²×C₃₁	C₂×#41	1	6	yes	—
38	C₂×D₃₁	#117	1	12	yes	—
39	C₂×D₃₁	#126	1	16	yes	—
40	C₄×C₃₁	—	2	6	no	—
41	C₄×C₃₁	—	4	4	no	—
42	Dic₃₁	—	2	6	no	—
43	Dic₃₁	—	4	4	no	—
44	C₂²×C₄²	—	31	1	no	—
45	#383	—	31	1	no	—
46	#383	—	31	6	no	—
47	#383	D₃₁	1	1	yes	characteristic, direct product factor
48	C₂×#95	—	31	6	no	—
49	C₂×C₃₁	C₂×#117	1	3	yes	—
50	C₂×C₃₁	C₂×#126	1	4	yes	—
51	D₃₁	#383	1	8	yes	direct product factor
52	C₂³×C₄	—	31	3	no	—
53	C₂³×C₄	—	31	4	no	—
54	C₂×C₄²	—	31	3	no	—
55	C₂×C₄²	—	31	8	no	—
56	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
57	#95	—	31	12	no	—
58	#95	—	31	6	no	—
59	#95	C₂×D₃₁	1	6	yes	—
60	C₃₁	C₂×#383	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	—	31	1	no	—
62	C₂²×C₄	—	31	3	no	—
63	C₂²×C₄	—	31	12	no	—
64	C₂²×C₄	—	31	4	no	—
65	C₂²×C₄	—	62	12	no	—
66	C₂²×C₄	—	62	24	no	—
67	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
68	C₂²×C₄	C₂²×D₃₁	1	3	yes	—
69	C₄²	—	31	12	no	—
70	C₄²	C₄×D₃₁	1	4	yes	complemented
71	C₂³	—	31	2	no	—
72	C₂³	—	31	12	no	—
73	C₂³	C₂³×D₃₁	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	31	6	no	—
77	C₂×C₄	—	62	24	no	—
78	C₂×C₄	—	62	6	no	—
79	C₂×C₄	—	62	12	no	—
80	C₂×C₄	—	124	16	no	—
81	C₂×C₄	C₂×C₄×D₃₁	1	6	yes	—
82	C₂²	—	31	12	no	—
83	C₂²	—	31	16	no	—
84	C₂²	C₂²×C₄×D₃₁	1	1	yes	characteristic
85	C₂²	#41×D₃₁	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	62	6	no	—
89	C₄	—	124	4	no	—
90	C₂	—	31	8	no	—
91	C₂	#117×D₃₁	1	3	yes	—
92	C₂	#126×D₃₁	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator	C₂²×C₃₁	C₂³×C₄
Fitting	C₃₁×#383	C₂
socle, cosocle	C₂³×C₃₁	C₂⁴
prime radical	C₂³×D₃₁	C₂³
hypercenter	#383	D₃₁
hypocenter	C₃₁	C₂×#383
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #14520917	C₂	semidirect
3. #14520916	C₂	semidirect
5. C₃₁×#383	C₂	semidirect
10. C₄²×D₃₁	C₄	semidirect
22. C₄²×C₃₁	C₂×C₄	semidirect
23. C₄×Dic₃₁	C₂×C₄	semidirect
47. #383	D₃₁	direct (N × H)
51. D₃₁	#383	direct (N × H)
60. C₃₁	C₂×#383	semidirect
70. C₄²	C₄×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₃₁	2
#14520917	2
#14520916	2
#95×D₃₁	2
C₃₁×#383	2
C₂×#383	31

Subgroups — D31×#383 #16848099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×#383 #16848099