Subgroups — C₄×#92482 #14521142

Order 1984.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#92482	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic
4	#11758423	C₂	1	1	yes	maximal, characteristic
5	#11758398	C₂	1	1	yes	maximal, characteristic
6	#11758395	C₂	1	1	yes	maximal, characteristic
7	C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₃₁	—	2	1	no	—
11	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₄²×C₃₁	—	2	1	no	—
13	C₄²×C₃₁	C₂²	1	1	yes	characteristic
14	#92482	C₄	1	4	yes	direct product factor
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	—	2	1	no	—
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
20	Q₈×C₃₁	—	2	1	no	—
21	Q₈×C₃₁	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	—	2	1	no	—
24	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂×Dic₃₁	—	2	1	no	—
28	C₂×Dic₃₁	—	2	1	no	—
29	Dic₆₂	—	2	1	no	—
30	Dic₆₂	C₂×C₄	1	2	yes	—
31	C₃₁⋊C₈	—	2	1	no	—
32	C₃₁⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₁	—	2	2	no	—
35	C₄×C₃₁	—	2	1	no	—
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	Q₁₆	1	2	yes	complemented
38	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₃₁	#41	1	1	yes	characteristic
40	Dic₃₁	—	2	2	no	—
41	Dic₃₁	—	4	1	no	—
42	C₄×Q₁₆	—	31	1	no	maximal, Sylow
43	C₂×C₃₁	C₄×D₄	1	1	yes	characteristic
44	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
45	C₂×C₃₁	#135	1	1	yes	characteristic
46	C₂×Q₁₆	—	31	1	no	—
47	C₄×Q₈	—	31	1	no	—
48	C₄×Q₈	D₃₁	1	1	yes	characteristic
49	#107	—	31	1	no	—
50	#103	—	31	1	no	—
51	#103	—	31	1	no	—
52	C₄×C₈	—	31	1	no	—
53	C₃₁	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	31	1	no	—
55	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
56	Q₁₆	—	31	4	no	—
57	C₂×C₈	—	31	1	no	—
58	C₂×C₈	—	31	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	31	1	no	—
61	C₄⋊C₄	—	62	1	no	—
62	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
63	C₄²	—	2	1	no	—
64	C₄²	—	62	1	no	—
65	C₄²	C₂×D₃₁	1	1	yes	characteristic
66	Q₈	—	2	1	no	—
67	Q₈	—	31	2	no	—
68	Q₈	—	62	1	no	—
69	Q₈	C₄×D₃₁	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	62	1	no	—
73	C₂×C₄	—	62	1	no	—
74	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
77	C₈	—	31	2	no	—
78	C₈	—	62	1	no	—
79	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	2	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	62	2	no	—
84	C₄	—	124	1	no	—
85	C₄	#92482	1	2	yes	direct product factor
86	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
87	C₄	#92495	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₃₁	1	1	yes	characteristic
89	C₂	C₂×#92482	1	1	yes	characteristic
90	C₂	#11758527	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₄×Q₈×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₄×Q₈	D₃₁
hypocenter	C₃₁	C₄×Q₁₆
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
14. #92482	C₄	direct (N × H)
37. C₄×C₃₁	Q₁₆	semidirect
53. C₃₁	C₄×Q₁₆	semidirect
85. C₄	#92482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₃₁	2
C₂×#92482	2
C₄×Dic₆₂	2
#11758423	2
#11758398	2
#11758395	2
C₄×C₃₁⋊C₈	2
C₄×Q₁₆	31

Subgroups — C4×#92482 #14521142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#92482 #14521142