Subgroups — C₂×#11758395 #14521082

Order 1984.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11758395	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₃₁	—	2	1	no	—
6	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₁	—	2	1	no	—
8	C₄⋊C₄×C₃₁	—	2	1	no	—
9	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
10	C₄⋊Dic₃₁	—	2	1	no	—
11	C₄⋊Dic₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₁	—	2	2	no	—
16	C₂×C₄×C₃₁	—	4	2	no	—
17	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	Q₈	1	2	yes	—
20	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₃₁	—	2	2	no	—
22	C₂×Dic₃₁	—	4	2	no	—
23	C₃₁⋊C₈	C₂×C₄	1	4	yes	complemented
24	C₂²×C₃₁	C₄⋊C₄	1	2	yes	—
25	C₂²×C₃₁	D₈	1	2	yes	—
26	C₂²×C₃₁	Q₁₆	1	2	yes	—
27	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₁	—	4	2	no	—
29	C₄×C₃₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₃₁	—	4	2	no	—
33	C₂×#107	—	31	1	no	maximal, Sylow
34	C₂×C₃₁	#107	1	4	yes	complemented
35	C₂×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
37	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
38	C₂²×C₈	—	31	1	no	—
39	C₂×C₄⋊C₄	—	31	1	no	—
40	C₂×C₄⋊C₄	D₃₁	1	1	yes	characteristic
41	#107	—	31	4	no	—
42	C₃₁	C₂×#107	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	62	1	no	—
45	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
46	C₂×C₈	—	31	4	no	—
47	C₂×C₈	—	31	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	31	2	no	—
50	C₄⋊C₄	—	62	1	no	—
51	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
52	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	62	2	no	—
56	C₂×C₄	—	124	2	no	—
57	C₂×C₄	Dic₆₂	1	2	yes	—
58	C₂×C₄	C₄×D₃₁	1	2	yes	—
59	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
61	C₈	—	31	4	no	—
62	C₂²	Dic₃₁⋊C₄	1	2	yes	—
63	C₂²	#92479	1	2	yes	—
64	C₂²	#92482	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	124	2	no	—
68	C₄	Dic₃₁⋊C₄	1	2	yes	—
69	C₄	C₂×Dic₆₂	1	1	yes	characteristic
70	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
71	C₂	#11758395	1	4	yes	direct product factor
72	C₂	C₂×Dic₃₁⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#92479	1	1	yes	characteristic
74	C₂	C₂×#92482	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂×C₄⋊C₄×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₂×C₄⋊C₄	D₃₁
hypocenter	C₃₁	C₂×#107
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #11758395	C₂	direct (N × H)
12. C₂×C₃₁⋊C₈	C₄	semidirect
23. C₃₁⋊C₈	C₂×C₄	semidirect
34. C₂×C₃₁	#107	semidirect
42. C₃₁	C₂×#107	semidirect
71. C₂	#11758395	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₃₁	2
C₂×C₄⋊Dic₃₁	2
C₂²×C₃₁⋊C₈	2
#11758395	2
C₂×#107	31

Subgroups — C2×#11758395 #14521082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758395 #14521082