Group #15672295 — subgroups

Subgroups — #15672295

Order 2944.

152 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 69 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	#13092547	C₂	1	2	yes	maximal
2	C₄×Dic₉₂	C₂	1	1	yes	maximal, characteristic
3	#13092170	C₂	1	1	yes	maximal, characteristic
4	#13092149	C₂	1	2	yes	maximal
5	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₂	C₄	1	1	yes	characteristic
7	C₄×Dic₄₆	C₂²	1	2	yes	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	#10625000	C₄	1	1	yes	characteristic
12	#10624998	C₄	1	2	yes	—
13	#10624997	—	2	2	no	—
14	Dic₂₃⋊C₈	—	2	2	no	—
15	C₄⋊(C₂₃⋊C₈)	C₂²	1	2	yes	—
16	C₂×Dic₄₆	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₃	—	2	1	no	—
18	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
22	C₄²×C₂₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₂₃	C₂×C₄	1	2	yes	—
24	Dic₂₃⋊C₄	—	2	2	no	—
25	C₄×Dic₂₃	—	2	2	no	—
26	C₂×C₂₃⋊C₈	—	2	2	no	—
27	Dic₉₂	—	2	2	no	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₃	#41	1	1	yes	characteristic
31	C₂×Dic₂₃	—	2	2	no	—
32	C₂×Dic₂₃	—	2	2	no	—
33	Dic₄₆	—	2	2	no	—
34	Dic₄₆	—	2	2	no	—
35	C₈×C₂₃	—	2	2	no	—
36	C₈×C₂₃	—	2	1	no	—
37	C₈×C₂₃	—	2	1	no	—
38	C₈×C₂₃	M₁₆	1	2	yes	—
39	C₈×C₂₃	Q₁₆	1	2	yes	complemented
40	C₂₃⋊C₈	—	4	2	no	—
41	#1591	—	23	1	no	maximal, Sylow
42	C₂²×C₂₃	C₄×D₄	1	1	yes	characteristic
43	C₄×C₂₃	—	2	1	no	—
44	C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₂₃	#131	1	1	yes	characteristic
46	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
47	C₄×C₂₃	#135	1	1	yes	characteristic
48	Dic₂₃	—	4	2	no	—
49	Dic₂₃	—	4	2	no	—
50	#446	—	23	2	no	—
51	C₄×Q₁₆	—	23	1	no	—
52	#335	—	23	1	no	—
53	Q₈⋊C₈	—	23	2	no	—
54	C₈²	D₂₃	1	1	yes	characteristic
55	C₂×C₂₃	#436	1	1	yes	characteristic
56	C₂×C₂₃	C₄×Q₁₆	1	1	yes	characteristic
57	C₂×C₂₃	#443	1	1	yes	characteristic
58	C₂×Q₁₆	—	23	1	no	—
59	C₄×Q₈	—	23	2	no	—
60	#107	—	23	1	no	—
61	C₄⋊C₈	—	23	2	no	—
62	C₄⋊C₈	—	46	2	no	—
63	#103	—	23	2	no	—
64	#97	—	46	2	no	—
65	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
66	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
67	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
68	C₂₃	#1591	1	1	yes	characteristic, complemented, Sylow
69	C₂×Q₈	—	23	2	no	—
70	Q₁₆	—	46	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	46	2	no	—
73	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
74	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
75	C₂×C₈	D₉₂	1	1	yes	characteristic
76	C₂×C₈	D₉₂	1	1	yes	characteristic
77	C₄⋊C₄	—	23	2	no	—
78	C₄⋊C₄	—	46	2	no	—
79	C₄²	—	46	2	no	—
80	C₄²	C₂²×D₂₃	1	1	yes	characteristic
81	Q₈	—	46	2	no	—
82	Q₈	—	46	2	no	—
83	C₂×C₄	—	46	2	no	—
84	C₂×C₄	—	46	2	no	—
85	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
86	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
87	C₂×C₄	#67288	1	1	yes	characteristic
88	C₈	—	2	2	no	—
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	92	2	no	—
92	C₈	#67262	1	2	yes	—
93	C₈	Dic₉₂	1	2	yes	complemented
94	C₂²	C₄×D₉₂	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	92	2	no	—
97	C₄	—	92	2	no	—
98	C₄	C₂×#67262	1	1	yes	characteristic
99	C₄	#10625072	1	1	yes	characteristic
100	C₄	#10625075	1	1	yes	characteristic
101	C₄	C₂×Dic₉₂	1	1	yes	characteristic
102	C₂	#13092496	1	1	yes	characteristic
103	C₂	C₄×Dic₉₂	1	1	yes	characteristic
104	C₂	#13092535	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13092547

C₂

yes

maximal

C₄×Dic₉₂

C₂

yes

maximal, characteristic

#13092170

C₂

yes

maximal, characteristic

#13092149

C₂

yes

maximal

C₈²×C₂₃

C₂

yes

maximal, characteristic

C₂×Dic₉₂

C₄

yes

characteristic

C₄×Dic₄₆

C₂²

yes

—

C₄×C₈×C₂₃

C₂²

yes

characteristic

C₄×C₈×C₂₃

C₂²

yes

characteristic

C₄×C₈×C₂₃

C₂²

yes

characteristic

#10625000

C₄

yes

characteristic

#10624998

C₄

yes

—

#10624997

—

Dic₂₃⋊C₈

—

C₄⋊(C₂₃⋊C₈)

C₂²

yes

—

C₂×Dic₄₆

C₂×C₄

yes

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₃

D₄

yes

characteristic

C₂×C₈×C₂₃

D₄

yes

characteristic

C₄²×C₂₃

C₂³

yes

characteristic

C₄⋊Dic₂₃

C₂×C₄

yes

—

Dic₂₃⋊C₄

—

C₄×Dic₂₃

—

C₂×C₂₃⋊C₈

—

Dic₉₂

—

C₂×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₃

#41

yes

characteristic

C₂×Dic₂₃

—

C₂×Dic₂₃

—

Dic₄₆

—

Dic₄₆

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

M₁₆

yes

—

C₈×C₂₃

Q₁₆

yes

complemented

C₂₃⋊C₈

—

#1591

—

maximal, Sylow

C₂²×C₂₃

C₄×D₄

yes

characteristic

C₄×C₂₃

—

C₄×C₂₃

C₂×M₁₆

yes

characteristic

C₄×C₂₃

#131

yes

characteristic

C₄×C₂₃

C₂×Q₁₆

yes

characteristic

C₄×C₂₃

#135

yes

characteristic

Dic₂₃

—

Dic₂₃

—

#446

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

D₂₃

yes

characteristic

C₂×C₂₃

#436

yes

characteristic

C₂×C₂₃

C₄×Q₁₆

yes

characteristic

C₂×C₂₃

#443

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₂₃

yes

characteristic

C₄×C₈

C₂×D₂₃

yes

characteristic

C₄×C₈

C₂×D₂₃

yes

characteristic

C₂₃

#1591

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₃

yes

characteristic

C₂×C₈

C₄×D₂₃

yes

characteristic

C₂×C₈

D₉₂

yes

characteristic

C₂×C₈

D₉₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₂₃

yes

characteristic

C₂×C₄

C₂×D₉₂

yes

characteristic

C₂×C₄

#67288

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

#67262

yes

—

C₈

Dic₉₂

yes

complemented

C₂²

C₄×D₉₂

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₄

#10625075

yes

characteristic

101

C₄

C₂×Dic₉₂

yes

characteristic

102

C₂

#13092496

yes

characteristic

103

C₂

C₄×Dic₉₂

yes

characteristic

104

C₂

#13092535

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₉₂
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₄²	C₂²×D₂₃
Fitting	C₈²×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₄×D₄
cosocle	C₄²×C₂₃	C₂³
hypercenter	C₈²	D₂₃
hypocenter	C₂₃	#1591
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₄

C₂×D₉₂

commutator

C₂×C₄×C₂₃

C₂²×C₄

Frattini

C₄²

C₂²×D₂₃

Fitting

C₈²×C₂₃

C₂

socle, prime radical

C₂²×C₂₃

C₄×D₄

cosocle

C₄²×C₂₃

C₂³

hypercenter

C₈²

D₂₃

hypocenter

C₂₃

#1591

LCS

G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
39. C₈×C₂₃	Q₁₆	semidirect
68. C₂₃	#1591	semidirect
93. C₈	Dic₉₂	semidirect

H ≅ G/N

type

39. C₈×C₂₃

Q₁₆

semidirect

68. C₂₃

#1591

semidirect

93. C₈

Dic₉₂

semidirect

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

subgroup	index
#13092547	2
C₄×Dic₉₂	2
#13092170	2
#13092149	2
C₈²×C₂₃	2
#1591	23

subgroup

index

C₄×Dic₉₂

C₈²×C₂₃

Subgroups — #15672295

Conjugacy classes of subgroups

Complements

Maximal subgroups