Group #16854074 — subgroups

Subgroups — #16854074

Order 3968.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758447	C₂	1	2	yes	maximal
2	#14520947	C₂	1	8	yes	maximal
3	#14520919	C₂	1	2	yes	maximal
4	#14520915	C₂	1	2	yes	maximal
5	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₃₁	C₂²	1	8	yes	—
12	C₂×Dic₃₁⋊C₄	C₂²	1	8	yes	—
13	#11758447	—	2	8	no	—
14	C₃₁⋊#95	C₂²	1	8	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
16	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
17	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
19	C₂²×Dic₃₁	C₂³	1	8	yes	—
20	C₄²×C₃₁	—	2	8	no	—
21	C₄²×C₃₁	D₄	1	4	yes	—
22	C₄²×C₃₁	Q₈	1	4	yes	—
23	C₄²×C₃₁	Q₈	1	4	yes	—
24	C₄⋊Dic₃₁	—	2	8	no	—
25	C₄⋊Dic₃₁	—	2	16	no	—
26	Dic₃₁⋊C₄	—	2	16	no	—
27	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₃₁	—	2	4	no	—
29	C₂×C₄×C₃₁	—	2	4	no	—
30	C₂×C₄×C₃₁	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₃₁	#41	1	8	yes	—
37	C₂×Dic₃₁	—	2	8	no	—
38	C₂×Dic₃₁	—	2	16	no	—
39	#2859	—	31	1	no	maximal, Sylow
40	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₃₁	C₂×#41	1	4	yes	—
44	C₄×C₃₁	—	2	4	no	—
45	C₄×C₃₁	—	2	4	no	—
46	C₄×C₃₁	#125	1	8	yes	complemented
47	C₄×C₃₁	C₄⋊Q₈	1	4	yes	—
48	Dic₃₁	—	4	8	no	—
49	C₂×#125	—	31	2	no	—
50	#389	—	31	8	no	—
51	#384	—	31	2	no	—
52	#382	—	31	2	no	—
53	C₄³	D₃₁	1	1	yes	characteristic
54	C₂×C₃₁	C₂×#125	1	2	yes	—
55	C₂×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₃₁	#532	1	2	yes	—
57	C₂×C₃₁	#533	1	2	yes	—
58	#125	—	62	8	no	—
59	C₂×C₄⋊C₄	—	31	4	no	—
60	C₂×C₄⋊C₄	—	31	8	no	—
61	C₂×C₄⋊C₄	—	31	8	no	—
62	C₂×C₄²	C₂×D₃₁	1	4	yes	—
63	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
66	#95	—	31	8	no	—
67	C₃₁	#2859	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	31	8	no	—
69	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
70	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
71	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
73	C₄⋊C₄	—	62	16	no	—
74	C₄⋊C₄	—	62	8	no	—
75	C₄⋊C₄	—	62	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₆₂	1	4	yes	—
78	C₄²	Dic₆₂	1	4	yes	—
79	C₄²	D₁₂₄	1	4	yes	—
80	C₂³	C₂³×D₃₁	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	62	8	no	—
84	C₂×C₄	—	62	16	no	—
85	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
86	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
87	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
88	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
89	C₂×C₄	C₂×D₁₂₄	1	4	yes	—
90	C₂×C₄	C₂×D₁₂₄	1	2	yes	—
91	C₂×C₄	#92495	1	8	yes	—
92	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
93	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
94	C₂²	C₂²×D₁₂₄	1	1	yes	characteristic
95	C₂²	C₂×#92495	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	124	8	no	—
99	C₄	#11758446	1	4	yes	—
100	C₄	#11758447	1	8	yes	complemented
101	C₂	C₂×#11758447	1	2	yes	—
102	C₂	C₂×#11758446	1	1	yes	characteristic
103	C₂	#14521599	1	2	yes	—
104	C₂	#14521606	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758447

C₂

yes

maximal

#14520947

C₂

yes

maximal

#14520919

C₂

yes

maximal

#14520915

C₂

yes

maximal

C₄³×C₃₁

C₂

yes

maximal, characteristic

C₂×C₄²×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×Dic₃₁⋊C₄

C₂²

yes

—

#11758447

—

C₃₁⋊#95

C₂²

yes

—

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×Dic₃₁

C₂³

yes

—

C₄²×C₃₁

—

C₄²×C₃₁

D₄

yes

—

C₄²×C₃₁

Q₈

yes

—

C₄²×C₃₁

Q₈

yes

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

Dic₃₁⋊C₄

—

C₂³×C₃₁

C₂⁴

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×C₄×C₃₁

C₂×D₄

yes

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

#41

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

#2859

—

maximal, Sylow

C₂²×C₃₁

C₂²×D₄

yes

characteristic

C₂²×C₃₁

C₂²×Q₈

yes

characteristic

C₂²×C₃₁

C₂²×Q₈

yes

characteristic

C₂²×C₃₁

C₂×#41

yes

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

#125

yes

complemented

C₄×C₃₁

C₄⋊Q₈

yes

—

Dic₃₁

—

—

—

—

—

C₄³

D₃₁

yes

characteristic

C₂×C₃₁

C₂×#125

yes

—

C₂×C₃₁

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₃₁

#532

yes

—

C₂×C₃₁

#533

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₃₁

yes

—

C₂×C₄²

C₂×D₃₁

yes

characteristic

C₂×C₄²

C₂×D₃₁

yes

characteristic

C₂×C₄²

C₂×D₃₁

yes

characteristic

#95

—

C₃₁

#2859

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂²×C₄

C₂²×D₃₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₆₂

yes

—

C₄²

Dic₆₂

yes

—

C₄²

D₁₂₄

yes

—

C₂³

C₂³×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₆₂

yes

—

C₂×C₄

C₂×Dic₆₂

yes

—

C₂×C₄

C₂×Dic₆₂

yes

—

C₂×C₄

C₂×Dic₆₂

yes

—

C₂×C₄

C₂×D₁₂₄

yes

—

C₂×C₄

C₂×D₁₂₄

yes

—

C₂×C₄

#92495

yes

—

C₂²

C₂²×Dic₆₂

yes

characteristic

C₂²

C₂²×Dic₆₂

yes

characteristic

C₂²

C₂²×D₁₂₄

yes

characteristic

C₂²

C₂×#92495

yes

—

C₄

—

C₄

—

C₄

—

124

—

C₄

#11758446

yes

—

100

C₄

#11758447

yes

complemented

101

C₂

C₂×#11758447

yes

—

102

C₂

C₂×#11758446

yes

characteristic

103

C₂

#14521599

yes

—

104

C₂

#14521606

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₄³×C₃₁	C₂
hypercenter	C₄³	D₃₁
hypocenter	C₃₁	#2859
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₃₁

commutator, socle, prime radical, cosocle

C₂³×C₃₁

C₂⁴

Fitting

C₄³×C₃₁

C₂

hypercenter

C₄³

D₃₁

C₃₁

G ▷ C₂³×C₃₁ ▷ C₃₁

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
46. C₄×C₃₁	#125	semidirect
67. C₃₁	#2859	semidirect
100. C₄	#11758447	semidirect

H ≅ G/N

type

46. C₄×C₃₁

#125

semidirect

67. C₃₁

#2859

semidirect

100. C₄

#11758447

semidirect

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

subgroup	index
C₂×#11758447	2
#14520947	2
#14520919	2
#14520915	2
C₄³×C₃₁	2
#2859	31

subgroup

index

C₄³×C₃₁

Subgroups — #16854074

Conjugacy classes of subgroups

Complements

Maximal subgroups