Group #33473 — subgroups

Subgroups — C₂×#2183 #33473

Order 256.

271 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 271 conjugacy classes of subgroups — too many to draw. Only its 215 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×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	#2183	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₁₆	C₂	1	2	yes	maximal
5	C₂×#346	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Q₈	C₄	1	1	yes	characteristic
8	C₂²×C₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₁₆	C₂²	1	2	yes	—
10	C₂²×C₁₆	C₂²	1	1	yes	characteristic
11	C₈×Q₈	C₄	1	4	yes	—
12	C₈×Q₈	C₂²	1	4	yes	—
13	C₂×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₄⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈	C₂²	1	2	yes	—
17	C₄⋊C₁₆	C₂²	1	4	yes	—
18	C₄⋊C₁₆	C₂²	1	8	yes	—
19	#346	C₂²	1	8	yes	—
20	C₄×C₁₆	C₂²	1	4	yes	—
21	C₂²×Q₈	C₈	1	1	yes	characteristic
22	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₈	C₂³	1	1	yes	characteristic
25	C₄×Q₈	C₈	1	4	yes	—
26	C₄×Q₈	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊C₄	C₈	1	2	yes	—
28	C₂×C₄⋊C₄	C₈	1	1	yes	characteristic
29	C₂×C₄²	C₂×C₄	1	2	yes	—
30	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₆	—	2	2	no	—
32	C₂×C₁₆	—	2	4	no	—
33	C₂×C₁₆	Q₈	1	4	yes	complemented
34	C₂×C₁₆	C₂³	1	2	yes	—
35	C₂×C₁₆	C₂³	1	4	yes	—
36	C₂×C₁₆	C₂³	1	2	yes	—
37	C₄⋊C₈	C₂×C₄	1	8	yes	—
38	C₄⋊C₈	C₂×C₄	1	4	yes	—
39	C₄×C₈	C₂×C₄	1	2	yes	—
40	C₄×C₈	C₂×C₄	1	4	yes	—
41	C₄×C₈	C₂³	1	2	yes	—
42	C₄×C₈	C₂³	1	4	yes	—
43	C₂×Q₈	—	2	4	no	—
44	C₂×Q₈	C₂×C₈	1	4	yes	—
45	C₂²×C₄	C₂×C₈	1	2	yes	—
46	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄	C₂×C₈	1	2	yes	—
48	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
49	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈	—	2	2	no	—
51	C₂×C₈	—	2	4	no	—
52	C₂×C₈	C₂²×C₄	1	2	yes	—
53	C₂×C₈	C₂²×C₄	1	4	yes	—
54	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈	C₂×Q₈	1	2	yes	—
56	C₂×C₈	#41	1	2	yes	—
57	C₂×C₈	C₂⁴	1	1	yes	characteristic
58	C₄⋊C₄	C₂×C₈	1	8	yes	—
59	C₄⋊C₄	C₂×C₈	1	4	yes	—
60	C₄²	C₂×C₈	1	4	yes	—
61	C₄²	C₂×C₈	1	2	yes	—
62	C₄²	C₂²×C₄	1	4	yes	—
63	C₄²	C₂²×C₄	1	2	yes	—
64	C₁₆	—	2	2	no	—
65	C₁₆	—	2	4	no	—
66	C₁₆	C₂×Q₈	1	4	yes	complemented
67	C₂³	C₂²×C₈	1	1	yes	characteristic
68	Q₈	—	2	8	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	M₃₂	1	4	yes	—
73	C₂×C₄	C₄×Q₈	1	2	yes	—
74	C₂×C₄	C₂²×C₈	1	4	yes	—
75	C₂×C₄	C₂²×C₈	1	2	yes	—
76	C₂×C₄	C₂²×C₈	1	4	yes	—
77	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₈	1	2	yes	—
79	C₂×C₄	#131	1	2	yes	—
80	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	2	4	no	—
83	C₈	C₄×Q₈	1	2	yes	—
84	C₈	C₂²×Q₈	1	1	yes	characteristic
85	C₈	C₂×#41	1	1	yes	characteristic
86	C₂²	C₈×Q₈	1	2	yes	—
87	C₂²	C₂×M₃₂	1	2	yes	—
88	C₂²	#504	1	2	yes	—
89	C₂²	C₂³×C₈	1	1	yes	characteristic
90	C₄	—	2	4	no	—
91	C₄	—	2	4	no	—
92	C₄	—	2	2	no	—
93	C₄	C₈×Q₈	1	2	yes	—
94	C₄	C₂×M₃₂	1	4	yes	—
95	C₄	C₂×C₄×Q₈	1	1	yes	characteristic
96	C₄	C₂×#131	1	1	yes	characteristic
97	C₂	#2183	1	4	yes	direct product factor
98	C₂	C₂×C₈×Q₈	1	1	yes	characteristic
99	C₂	C₂²×M₃₂	1	1	yes	characteristic
100	C₂	C₂×#504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Q₈

C₂

yes

maximal, characteristic

#2183

C₂

yes

maximal, direct product factor

C₂×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×C₄⋊C₁₆

C₂

yes

maximal

C₂×#346

C₂

yes

maximal

C₂×C₄×C₁₆

C₂

yes

maximal, characteristic

C₂×C₄×Q₈

C₄

yes

characteristic

C₂²×C₁₆

C₂²

yes

characteristic

C₂²×C₁₆

C₂²

yes

—

C₂²×C₁₆

C₂²

yes

characteristic

C₈×Q₈

C₄

yes

—

C₈×Q₈

C₂²

yes

—

C₂×C₄⋊C₈

C₄

yes

—

C₂×C₄⋊C₈

C₄

yes

characteristic

C₂×C₄×C₈

C₂²

yes

characteristic

C₂×C₄×C₈

C₂²

yes

—

C₄⋊C₁₆

C₂²

yes

—

C₄⋊C₁₆

C₂²

yes

—

#346

C₂²

yes

—

C₄×C₁₆

C₂²

yes

—

C₂²×Q₈

C₈

yes

characteristic

C₂²×C₈

C₂×C₄

yes

characteristic

C₂²×C₈

C₂×C₄

yes

—

C₂²×C₈

C₂³

yes

characteristic

C₄×Q₈

C₈

yes

—

C₄×Q₈

C₂×C₄

yes

—

C₂×C₄⋊C₄

C₈

yes

—

C₂×C₄⋊C₄

C₈

yes

characteristic

C₂×C₄²

C₂×C₄

yes

—

C₂×C₄²

C₂×C₄

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

Q₈

yes

complemented

C₂×C₁₆

C₂³

yes

—

C₂×C₁₆

C₂³

yes

—

C₂×C₁₆

C₂³

yes

—

C₄⋊C₈

C₂×C₄

yes

—

C₄⋊C₈

C₂×C₄

yes

—

C₄×C₈

C₂×C₄

yes

—

C₄×C₈

C₂×C₄

yes

—

C₄×C₈

C₂³

yes

—

C₄×C₈

C₂³

yes

—

C₂×Q₈

—

C₂×Q₈

C₂×C₈

yes

—

C₂²×C₄

C₂×C₈

yes

—

C₂²×C₄

C₂×C₈

yes

characteristic

C₂²×C₄

C₂×C₈

yes

—

C₂²×C₄

C₂×C₈

yes

characteristic

C₂²×C₄

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×C₄

yes

—

C₂×C₈

C₂²×C₄

yes

—

C₂×C₈

C₂²×C₄

yes

characteristic

C₂×C₈

C₂×Q₈

yes

—

C₂×C₈

#41

yes

—

C₂×C₈

C₂⁴

yes

characteristic

C₄⋊C₄

C₂×C₈

yes

—

C₄⋊C₄

C₂×C₈

yes

—

C₄²

C₂×C₈

yes

—

C₄²

C₂×C₈

yes

—

C₄²

C₂²×C₄

yes

—

C₄²

C₂²×C₄

yes

—

C₁₆

—

C₁₆

—

C₁₆

C₂×Q₈

yes

complemented

C₂³

C₂²×C₈

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

M₃₂

yes

—

C₂×C₄

C₄×Q₈

yes

—

C₂×C₄

C₂²×C₈

yes

—

C₂×C₄

C₂²×C₈

yes

—

C₂×C₄

C₂²×C₈

yes

—

C₂×C₄

C₂²×C₈

yes

characteristic

C₂×C₄

C₂²×C₈

yes

—

C₂×C₄

#131

yes

—

C₂×C₄

C₂³×C₄

yes

characteristic

C₈

—

C₈

—

C₈

C₄×Q₈

yes

—

C₈

C₂²×Q₈

yes

characteristic

C₈

C₂×#41

yes

characteristic

C₂²

C₈×Q₈

yes

—

C₂²

C₂×M₃₂

yes

—

C₂²

#504

yes

—

C₂²

C₂³×C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₈×Q₈

yes

—

C₄

C₂×M₃₂

yes

—

C₄

C₂×C₄×Q₈

yes

C₄

yes

C₂

yes

direct product factor

C₂

C₂×C₈×Q₈

yes

characteristic

C₂

C₂²×M₃₂

yes

characteristic

100

C₂

C₂×#504

yes

characteristic

	subgroup	G/H
center	C₂²×C₈	C₂³
commutator	C₂²	C₂³×C₈
Frattini, cosocle	C₂×C₈	C₂⁴
socle, prime radical	C₂³	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center

C₂²×C₈

C₂³

commutator

C₂²

C₂³×C₈

Frattini, cosocle

C₂×C₈

C₂⁴

socle, prime radical

C₂³

C₂²×C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₈ ◁ G

LECS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

N	H ≅ G/N	type
2. #2183	C₂	direct (N × H)
33. C₂×C₁₆	Q₈	semidirect
66. C₁₆	C₂×Q₈	semidirect
97. C₂	#2183	direct (N × H)

H ≅ G/N

type

2. #2183

C₂

direct (N × H)

33. C₂×C₁₆

Q₈

semidirect

66. C₁₆

C₂×Q₈

semidirect

97. C₂

#2183

direct (N × H)

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

subgroup	index
C₂×C₈×Q₈	2
#2183	2
C₂×C₄⋊C₁₆	2
C₂×#346	2
C₂×C₄×C₁₆	2

subgroup

index

C₂×C₈×Q₈

#2183

C₂×C₄⋊C₁₆

C₂×#346

C₂×C₄×C₁₆

Subgroups — C₂×#2183 #33473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#2183 #33473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2183 #33473