Group #18010927 — subgroups

Subgroups — C₂×#14558454 #18010927

Order 4736.

184 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₂²×#10596927	C₂	1	2	yes	maximal
2	#14558454	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	4	no	—
5	C₂×#10596927	C₂²	1	4	yes	—
6	C₂²×#64436	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic
8	C₈×Dic₃₇	C₄	1	2	yes	—
9	C₈×Dic₃₇	C₂²	1	2	yes	—
10	C₂²×C₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₃₇	C₈	1	1	yes	characteristic
13	C₂²×Dic₃₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₃₇	—	2	2	no	—
15	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
16	C₄×Dic₃₇	C₈	1	2	yes	—
17	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
18	C₂×#64436	C₂×C₄	1	1	yes	characteristic
19	C₂×#64436	D₄	1	2	yes	—
20	C₂×#64436	Q₈	1	2	yes	—
21	C₂×#64436	C₂³	1	1	yes	characteristic
22	#10596927	—	2	4	no	—
23	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
27	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	2	2	no	—
29	C₂×Dic₃₇	C₁₆	1	4	yes	complemented
30	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
31	C₂×Dic₃₇	C₂×C₈	1	2	yes	—
32	C₈×C₃₇	—	2	2	no	—
33	#64436	C₄⋊C₄	1	2	yes	—
34	#64436	C₂×D₄	1	1	yes	characteristic
35	#64436	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₃₇	C₄⋊C₈	1	2	yes	—
37	C₂²×C₃₇	C₂×C₁₆	1	2	yes	—
38	C₂²×C₃₇	M₃₂	1	2	yes	—
39	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₃₇	C₄⋊C₈	1	2	yes	—
41	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
43	Dic₃₇	—	2	2	no	—
44	Dic₃₇	C₂×C₁₆	1	4	yes	complemented
45	C₂×C₄⋊C₁₆	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	C₄⋊C₁₆	1	4	yes	complemented
47	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
48	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
49	C₂×C₃₇	C₂×M₃₂	1	1	yes	characteristic
50	C₂²×C₁₆	—	37	2	no	—
51	C₂×C₄×C₈	—	37	1	no	—
52	C₄⋊C₁₆	—	37	4	no	—
53	C₃₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	37	1	no	—
55	C₂²×C₈	#3866	1	1	yes	characteristic
56	C₂×C₄²	—	37	1	no	—
57	C₂×C₁₆	—	37	4	no	—
58	C₂×C₁₆	—	74	4	no	—
59	C₄×C₈	—	37	2	no	—
60	C₄×C₈	—	37	2	no	—
61	C₂²×C₄	—	37	1	no	—
62	C₂²×C₄	—	37	1	no	—
63	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
64	C₂×C₈	—	2	2	no	—
65	C₂×C₈	—	37	2	no	—
66	C₂×C₈	—	37	2	no	—
67	C₂×C₈	—	37	1	no	—
68	C₂×C₈	—	37	1	no	—
69	C₂×C₈	C₂×#3866	1	2	yes	—
70	C₄²	—	37	2	no	—
71	C₄²	—	37	2	no	—
72	C₁₆	—	74	4	no	—
73	C₂³	D₃₇⋊C₈	1	1	yes	characteristic
74	C₂×C₄	—	37	4	no	—
75	C₂×C₄	—	37	2	no	—
76	C₂×C₄	—	37	2	no	—
77	C₂×C₄	—	74	2	no	—
78	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
79	C₂×C₄	C₄⋊#3866	1	2	yes	—
80	C₂×C₄	#10596957	1	2	yes	—
81	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	37	1	no	—
84	C₈	—	37	2	no	—
85	C₈	—	37	1	no	—
86	C₂²	#11924603	1	2	yes	—
87	C₂²	D₃₇⋊C₁₆	1	2	yes	—
88	C₂²	#11924611	1	2	yes	—
89	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
90	C₄	—	37	4	no	—
91	C₄	—	74	2	no	—
92	C₄	#11924603	1	2	yes	—
93	C₄	C₂×C₄⋊#3866	1	1	yes	characteristic
94	C₄	C₂×#10596957	1	1	yes	characteristic
95	C₂	#14558454	1	4	yes	direct product factor
96	C₂	C₂×#11924603	1	1	yes	characteristic
97	C₂	C₂×D₃₇⋊C₁₆	1	1	yes	characteristic
98	C₂	C₂×#11924611	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10596927

C₂

yes

maximal

#14558454

C₂

yes

maximal, direct product factor

C₂×C₈×Dic₃₇

C₂

yes

maximal, characteristic

C₂×#10596927

—

C₂×#10596927

C₂²

yes

—

C₂²×#64436

C₂²

yes

characteristic

C₂×C₄×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₄

yes

—

C₈×Dic₃₇

C₂²

yes

—

C₂²×C₈×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₈

yes

characteristic

C₂²×Dic₃₇

C₈

yes

characteristic

C₂×C₈×C₃₇

—

C₂×C₈×C₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₈

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

D₄

yes

—

C₂×#64436

Q₈

yes

—

C₂×#64436

C₂³

yes

characteristic

#10596927

—

C₂³×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

—

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

M₁₆

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

—

C₂×Dic₃₇

C₁₆

yes

complemented

C₂×Dic₃₇

C₂×C₈

yes

—

C₂×Dic₃₇

C₂×C₈

yes

—

C₈×C₃₇

—

#64436

C₄⋊C₄

yes

—

#64436

C₂×D₄

yes

characteristic

#64436

C₂×Q₈

yes

characteristic

C₂²×C₃₇

C₄⋊C₈

yes

—

C₂²×C₃₇

C₂×C₁₆

yes

—

C₂²×C₃₇

M₃₂

yes

—

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₄×C₃₇

C₄⋊C₈

yes

—

C₄×C₃₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₇

C₂×M₁₆

yes

characteristic

Dic₃₇

—

Dic₃₇

C₂×C₁₆

yes

complemented

C₂×C₄⋊C₁₆

—

maximal, Sylow

C₂×C₃₇

C₄⋊C₁₆

yes

complemented

C₂×C₃₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₃₇

C₂²×C₁₆

yes

characteristic

C₂×C₃₇

C₂×M₃₂

yes

characteristic

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₃₇

C₂×C₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

#3866

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#3866

yes

—

C₄²

—

C₄²

—

C₁₆

—

C₂³

D₃₇⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

characteristic

C₂×C₄

C₄⋊#3866

yes

—

C₂×C₄

#10596957

yes

—

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

#11924603

yes

—

C₂²

D₃₇⋊C₁₆

yes

—

C₂²

#11924611

yes

—

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

#11924603

yes

—

C₄

C₂×C₄⋊#3866

yes

C₄

yes

C₂

yes

direct product factor

C₂

C₂×#11924603

yes

characteristic

C₂

C₂×D₃₇⋊C₁₆

yes

characteristic

C₂

C₂×#11924611

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#3866
commutator	C₂×C₃₇	C₂²×C₁₆
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₂²×C₈×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₂²×C₈	#3866
hypocenter	C₃₇	C₂×C₄⋊C₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×#3866

commutator

C₂×C₃₇

C₂²×C₁₆

Frattini

C₂×C₄

C₂²×#3866

Fitting

C₂²×C₈×C₃₇

C₄

socle, prime radical

C₂³×C₃₇

C₂×C₈

C₂³

C₂²×C₈

C₃₇

C₂×C₄⋊C₁₆

LCS

G ▷ C₂×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #14558454	C₂	direct (N × H)
29. C₂×Dic₃₇	C₁₆	semidirect
44. Dic₃₇	C₂×C₁₆	semidirect
46. C₂×C₃₇	C₄⋊C₁₆	semidirect
53. C₃₇	C₂×C₄⋊C₁₆	semidirect
95. C₂	#14558454	direct (N × H)

H ≅ G/N

type

2. #14558454

C₂

direct (N × H)

29. C₂×Dic₃₇

C₁₆

semidirect

44. Dic₃₇

C₂×C₁₆

semidirect

46. C₂×C₃₇

C₄⋊C₁₆

semidirect

53. C₃₇

C₂×C₄⋊C₁₆

semidirect

95. C₂

#14558454

direct (N × H)

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

subgroup	index
C₂²×#10596927	2
#14558454	2
C₂×C₈×Dic₃₇	2
C₂×C₄⋊C₁₆	37

subgroup

index

C₂²×#10596927

#14558454

C₂×C₈×Dic₃₇

C₂×C₄⋊C₁₆

Subgroups — C₂×#14558454 #18010927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14558454 #18010927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558454 #18010927