Group #19128200 — subgroups

Subgroups — C₂×#14581772 #19128200

Order 5312.

322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic₁₆₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₈₃	C₂	1	1	yes	maximal, characteristic
3	#14581772	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₈₃	C₂	1	2	yes	maximal, complemented
5	C₂×(C₂×D₈₃)⋊C₄	C₂	1	2	yes	maximal
6	C₂×C₄⋊C₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₈₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₆₆	—	2	4	no	—
9	C₂×Dic₁₆₆	C₂²	1	4	yes	complemented
10	C₂²×Dic₈₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₈₃	C₂²	1	2	yes	—
12	C₂×C₄×D₈₃	—	2	4	no	—
13	C₂×C₄×D₈₃	C₂²	1	4	yes	—
14	C₄⋊Dic₈₃	C₂²	1	8	yes	complemented
15	(C₂×D₈₃)⋊C₄	C₂²	1	8	yes	—
16	C₂²×C₄×C₈₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₈₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₈₃	C₂²	1	4	yes	complemented
19	C₂³×C₈₃	C₂³	1	1	yes	characteristic
20	C₂²×D₈₃	—	2	2	no	—
21	C₂²×D₈₃	—	2	2	no	—
22	C₂²×D₈₃	Q₈	1	4	yes	complemented
23	C₂²×D₈₃	C₂³	1	2	yes	—
24	C₂×C₄×C₈₃	—	2	4	no	—
25	C₂×C₄×C₈₃	D₄	1	4	yes	—
26	C₂×C₄×C₈₃	C₂³	1	4	yes	—
27	C₂×C₄×C₈₃	C₂³	1	2	yes	—
28	C₂×Dic₈₃	—	2	2	no	—
29	C₂×Dic₈₃	—	2	4	no	—
30	C₂×Dic₈₃	C₂³	1	4	yes	—
31	C₂×Dic₈₃	C₂³	1	2	yes	—
32	C₄×D₈₃	—	2	8	no	—
33	Dic₁₆₆	—	2	8	no	—
34	C₂²×C₈₃	C₂×D₄	1	2	yes	—
35	C₂²×C₈₃	C₂×Q₈	1	2	yes	—
36	C₂²×C₈₃	#41	1	2	yes	—
37	C₂²×C₈₃	C₂⁴	1	1	yes	characteristic
38	C₂×D₈₃	—	2	8	no	—
39	C₂×D₈₃	—	2	2	no	—
40	C₂×D₈₃	—	2	2	no	—
41	C₂×D₈₃	C₂×Q₈	1	4	yes	complemented
42	C₄×C₈₃	—	2	4	no	—
43	C₄×C₈₃	C₂×D₄	1	4	yes	—
44	Dic₈₃	—	2	4	no	—
45	Dic₈₃	—	2	2	no	—
46	C₂×C₈₃	C₂²⋊Q₈	1	4	yes	complemented
47	C₂×C₈₃	C₂²×D₄	1	1	yes	characteristic
48	C₂×C₈₃	C₂²×Q₈	1	1	yes	characteristic
49	C₂×C₈₃	C₂×#41	1	1	yes	characteristic
50	D₈₃	—	2	4	no	—
51	C₈₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₂²⋊Q₈	—	83	1	no	maximal, Sylow
53	C₂²×Q₈	—	83	1	no	—
54	C₂³×C₄	—	83	1	no	—
55	C₂²⋊Q₈	—	83	8	no	—
56	C₂×C₄⋊C₄	—	83	2	no	—
57	C₂×C₄⋊C₄	D₈₃	1	1	yes	characteristic, complemented
58	C₂×C₂²⋊C₄	—	83	2	no	—
59	C₂⁴	—	83	1	no	—
60	C₂×Q₈	—	83	4	no	—
61	C₂×Q₈	—	166	4	no	—
62	C₂²×C₄	—	83	2	no	—
63	C₂²×C₄	—	83	1	no	—
64	C₂²×C₄	—	83	4	no	—
65	C₂²×C₄	—	166	4	no	—
66	C₂²×C₄	C₂×D₈₃	1	2	yes	—
67	C₂²×C₄	C₂×D₈₃	1	1	yes	characteristic
68	C₄⋊C₄	—	83	8	no	—
69	C₄⋊C₄	C₂×D₈₃	1	4	yes	complemented
70	C₂²⋊C₄	—	83	8	no	—
71	C₂³	—	83	4	no	—
72	C₂³	—	83	2	no	—
73	C₂³	—	166	2	no	—
74	C₂³	—	166	2	no	—
75	C₂³	C₂²×D₈₃	1	1	yes	characteristic
76	Q₈	—	166	8	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	83	4	no	—
79	C₂×C₄	—	83	2	no	—
80	C₂×C₄	—	166	2	no	—
81	C₂×C₄	—	166	4	no	—
82	C₂×C₄	—	166	8	no	—
83	C₂×C₄	D₃₃₂	1	4	yes	—
84	C₂×C₄	C₂²×D₈₃	1	4	yes	—
85	C₂×C₄	C₂²×D₈₃	1	2	yes	—
86	C₂²	—	83	4	no	—
87	C₂²	—	166	8	no	—
88	C₂²	—	166	2	no	—
89	C₂²	—	166	2	no	—
90	C₂²	C₂×D₃₃₂	1	2	yes	—
91	C₂²	Q₈×D₈₃	1	2	yes	—
92	C₂²	#13050589	1	2	yes	—
93	C₂²	C₂³×D₈₃	1	1	yes	characteristic
94	C₄	—	2	4	no	—
95	C₄	—	166	2	no	—
96	C₄	—	166	4	no	—
97	C₄	C₂×D₃₃₂	1	4	yes	—
98	C₂	—	166	4	no	—
99	C₂	#14581772	1	4	yes	direct product factor
100	C₂	C₂²×D₃₃₂	1	1	yes	characteristic
101	C₂	C₂×Q₈×D₈₃	1	1	yes	characteristic
102	C₂	C₂×#13050589	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₆₆

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₈₃

C₂

yes

maximal, characteristic

#14581772

C₂

yes

maximal, direct product factor

C₂×C₄⋊Dic₈₃

C₂

yes

maximal, complemented

C₂×(C₂×D₈₃)⋊C₄

C₂

yes

maximal

C₂×C₄⋊C₄×C₈₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₈₃

C₂²

yes

characteristic

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

C₂²

yes

complemented

C₂²×Dic₈₃

C₂²

yes

characteristic

C₂²×Dic₈₃

C₂²

yes

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

C₂²

yes

—

C₄⋊Dic₈₃

C₂²

yes

complemented

(C₂×D₈₃)⋊C₄

C₂²

yes

—

C₂²×C₄×C₈₃

C₂²

yes

—

C₂²×C₄×C₈₃

C₂²

yes

characteristic

C₄⋊C₄×C₈₃

C₂²

yes

complemented

C₂³×C₈₃

C₂³

yes

characteristic

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

Q₈

yes

complemented

C₂²×D₈₃

C₂³

yes

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

D₄

yes

—

C₂×C₄×C₈₃

C₂³

yes

—

C₂×C₄×C₈₃

C₂³

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

C₂³

yes

—

C₂×Dic₈₃

C₂³

yes

—

C₄×D₈₃

—

Dic₁₆₆

—

C₂²×C₈₃

C₂×D₄

yes

—

C₂²×C₈₃

C₂×Q₈

yes

—

C₂²×C₈₃

#41

yes

—

C₂²×C₈₃

C₂⁴

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

C₂×Q₈

yes

complemented

C₄×C₈₃

—

C₄×C₈₃

C₂×D₄

yes

—

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

C₂²⋊Q₈

yes

complemented

C₂×C₈₃

C₂²×D₄

yes

characteristic

C₂×C₈₃

C₂²×Q₈

yes

characteristic

C₂×C₈₃

C₂×#41

yes

characteristic

D₈₃

—

C₈₃

C₂×C₂²⋊Q₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊Q₈

—

maximal, Sylow

C₂²×Q₈

—

C₂³×C₄

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₈₃

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

166

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

166

—

C₂²×C₄

C₂×D₈₃

yes

—

C₂²×C₄

C₂×D₈₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×D₈₃

yes

complemented

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

166

—

C₂³

—

166

—

C₂³

C₂²×D₈₃

yes

characteristic

Q₈

—

166

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

D₃₃₂

yes

—

C₂×C₄

C₂²×D₈₃

yes

—

C₂×C₄

C₂²×D₈₃

yes

—

C₂²

—

C₂²

—

166

—

C₂²

—

166

—

C₂²

—

166

—

C₂²

C₂×D₃₃₂

yes

—

C₂²

Q₈×D₈₃

yes

—

C₂²

#13050589

yes

—

C₂²

C₂³×D₈₃

yes

characteristic

C₄

—

C₄

—

166

—

C₄

—

166

—

C₄

C₂×D₃₃₂

yes

—

C₂

—

166

—

C₂

#14581772

yes

direct product factor

100

C₂

C₂²×D₃₃₂

yes

characteristic

101

C₂

C₂×Q₈×D₈₃

yes

characteristic

102

C₂

C₂×#13050589

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²×D₈₃
commutator	C₂²×C₈₃	C₂⁴
Frattini	C₂²	C₂³×D₈₃
Fitting	C₂×C₄⋊C₄×C₈₃	C₂
socle	C₂³×C₈₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₈₃
hypocenter	C₈₃	C₂×C₂²⋊Q₈
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²×D₈₃

commutator

C₂²×C₈₃

C₂⁴

Frattini

C₂²

C₂³×D₈₃

Fitting

C₂×C₄⋊C₄×C₈₃

C₂

socle

C₂³×C₈₃

C₂³

hypercenter

C₂×C₄⋊C₄

D₈₃

hypocenter

C₈₃

C₂×C₂²⋊Q₈

LCS

G ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
1. C₂²×Dic₁₆₆	C₂	semidirect
3. #14581772	C₂	direct (N × H)
4. C₂×C₄⋊Dic₈₃	C₂	semidirect
6. C₂×C₄⋊C₄×C₈₃	C₂	semidirect
9. C₂×Dic₁₆₆	C₂²	semidirect
14. C₄⋊Dic₈₃	C₂²	semidirect
18. C₄⋊C₄×C₈₃	C₂²	semidirect
22. C₂²×D₈₃	Q₈	semidirect
41. C₂×D₈₃	C₂×Q₈	semidirect
46. C₂×C₈₃	C₂²⋊Q₈	semidirect
51. C₈₃	C₂×C₂²⋊Q₈	semidirect
57. C₂×C₄⋊C₄	D₈₃	semidirect
69. C₄⋊C₄	C₂×D₈₃	semidirect
99. C₂	#14581772	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₁₆₆

C₂

semidirect

3. #14581772

C₂

direct (N × H)

4. C₂×C₄⋊Dic₈₃

C₂

semidirect

6. C₂×C₄⋊C₄×C₈₃

C₂

semidirect

9. C₂×Dic₁₆₆

C₂²

semidirect

14. C₄⋊Dic₈₃

C₂²

semidirect

18. C₄⋊C₄×C₈₃

C₂²

semidirect

22. C₂²×D₈₃

Q₈

semidirect

41. C₂×D₈₃

C₂×Q₈

semidirect

46. C₂×C₈₃

C₂²⋊Q₈

semidirect

51. C₈₃

C₂×C₂²⋊Q₈

semidirect

57. C₂×C₄⋊C₄

D₈₃

semidirect

69. C₄⋊C₄

C₂×D₈₃

semidirect

99. C₂

#14581772

direct (N × H)

Subgroups — C₂×#14581772 #19128200

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14581772 #19128200

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14581772 #19128200