Group #14577262 — subgroups

Subgroups — #14577262

Order 2432.

1202 conjugacy classes of subgroups; only the 491 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 491 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	#11927260	C₂	1	9	yes	maximal, complemented
2	#11927216	C₂	1	6	yes	maximal, complemented
3	#11927095	C₂	1	9	yes	maximal, complemented
4	C₄×#64545	C₂	1	6	yes	maximal, complemented
5	Q₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64545	C₂²	1	6	yes	—
7	C₂×#64545	C₂²	1	6	yes	—
8	C₁₉×C₄⋊Q₈	C₂²	1	9	yes	—
9	C₄×Q₈×C₁₉	C₂²	1	6	yes	—
10	#10597393	C₂²	1	18	yes	—
11	Q₈×Dic₁₉	C₂²	1	2	yes	—
12	#10597341	C₂²	1	36	yes	—
13	#10597339	C₂²	1	18	yes	—
14	#10597338	C₂²	1	18	yes	—
15	#10597320	C₂²	1	9	yes	—
16	C₄×D₇₆	C₂²	1	18	yes	—
17	C₄²×D₁₉	C₂²	1	9	yes	—
18	C₂×Q₈×C₁₉	C₂³	1	6	yes	—
19	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
20	#64545	—	2	24	no	—
21	#64545	—	4	12	no	—
22	C₂×D₇₆	C₂³	1	18	yes	—
23	C₂×D₇₆	C₂³	1	18	yes	—
24	C₂×C₄×D₁₉	C₂³	1	9	yes	—
25	C₂×C₄×D₁₉	C₂³	1	18	yes	—
26	C₄⋊C₄×C₁₉	C₂³	1	18	yes	—
27	C₄²×C₁₉	C₂³	1	9	yes	—
28	(C₂×D₁₉)⋊C₄	C₂³	1	36	yes	—
29	C₄⋊Dic₁₉	C₂³	1	6	yes	—
30	C₄×Dic₁₉	C₂³	1	6	yes	—
31	C₄×Dic₁₉	C₂³	1	9	yes	—
32	C₂²×D₁₉	C₂⁴	1	9	yes	—
33	Q₈×C₁₉	—	4	6	no	—
34	Q₈×C₁₉	#41	1	8	yes	complemented
35	C₂×C₄×C₁₉	C₂⁴	1	9	yes	—
36	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
37	C₂×Dic₁₉	C₂⁴	1	6	yes	—
38	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
39	D₇₆	—	2	36	no	—
40	D₇₆	—	4	18	no	—
41	C₄×D₁₉	—	2	36	no	—
42	C₄×D₁₉	—	2	18	no	—
43	#3483	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
45	C₂×D₁₉	—	2	18	no	—
46	C₂×D₁₉	—	2	9	no	—
47	C₄×C₁₉	—	2	9	no	—
48	C₄×C₁₉	C₂×#41	1	12	yes	—
49	Dic₁₉	—	2	6	no	—
50	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
51	Q₈²	D₁₉	1	1	yes	characteristic, complemented
52	#555	—	19	9	no	—
53	#550	—	19	6	no	—
54	#532	—	19	9	no	—
55	C₄×#41	—	19	6	no	—
56	C₂×C₁₉	C₂²×#41	1	2	yes	—
57	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
58	D₁₉	—	4	9	no	—
59	C₂×#41	—	19	6	no	—
60	C₂×#41	—	19	6	no	—
61	C₄⋊Q₈	C₂×D₁₉	1	9	yes	—
62	#127	—	19	9	no	—
63	#124	—	19	18	no	—
64	#121	—	19	36	no	—
65	C₄×Q₈	—	19	2	no	—
66	C₄×Q₈	C₂×D₁₉	1	6	yes	—
67	C₄×D₄	—	19	18	no	—
68	C₄×D₄	—	19	18	no	—
69	#117	—	19	18	no	—
70	C₂×C₄²	—	19	9	no	—
71	C₁₉	#3483	1	1	yes	characteristic, complemented, Sylow
72	#41	—	38	24	no	—
73	#41	—	76	12	no	—
74	C₂×Q₈	C₂²×D₁₉	1	6	yes	—
75	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
76	C₂×D₄	—	19	18	no	—
77	C₂×D₄	—	19	18	no	—
78	C₂²×C₄	—	19	18	no	—
79	C₂²×C₄	—	19	9	no	—
80	C₄⋊C₄	—	19	6	no	—
81	C₄⋊C₄	C₂²×D₁₉	1	18	yes	—
82	C₂²⋊C₄	—	19	36	no	—
83	C₄²	—	19	6	no	—
84	C₄²	—	19	9	no	—
85	C₄²	C₂²×D₁₉	1	9	yes	—
86	C₂³	—	19	9	no	—
87	Q₈	—	4	6	no	—
88	Q₈	#64545	1	8	yes	complemented
89	D₄	—	38	36	no	—
90	D₄	—	76	18	no	—
91	C₂×C₄	—	19	1	no	—
92	C₂×C₄	—	19	6	no	—
93	C₂×C₄	—	38	18	no	—
94	C₂×C₄	—	38	36	no	—
95	C₂×C₄	C₂³×D₁₉	1	9	yes	—
96	C₂×C₄	C₂³×D₁₉	1	6	yes	—
97	C₂²	—	38	18	no	—
98	C₂²	—	38	9	no	—
99	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
100	C₄	—	2	9	no	—
101	C₄	—	19	2	no	—
102	C₄	—	38	6	no	—
103	C₄	C₂×#64545	1	12	yes	—
104	C₂	—	76	9	no	—
105	C₂	C₂²×#64545	1	2	yes	—
106	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927260

C₂

yes

maximal, complemented

#11927216

C₂

yes

maximal, complemented

#11927095

C₂

yes

maximal, complemented

C₄×#64545

C₂

yes

maximal, complemented

Q₈²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×#64545

C₂²

yes

—

C₂×#64545

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

#10597393

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

#10597341

C₂²

yes

—

#10597339

C₂²

yes

—

#10597338

C₂²

yes

—

#10597320

C₂²

yes

—

C₄×D₇₆

C₂²

yes

—

C₄²×D₁₉

C₂²

yes

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

C₂³

yes

—

#64545

—

#64545

—

C₂×D₇₆

C₂³

yes

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂²×D₁₉

C₂⁴

yes

—

Q₈×C₁₉

—

Q₈×C₁₉

#41

yes

complemented

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

characteristic

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

#3483

—

maximal, Sylow

C₂²×C₁₉

C₂⁵

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

H(5,𝔽₂)

yes

—

Q₈²

D₁₉

yes

characteristic, complemented

#555

—

#550

—

#532

—

C₄×#41

—

C₂×C₁₉

C₂²×#41

yes

—

C₂×C₁₉

C₂×H(5,𝔽₂)

yes

characteristic

D₁₉

—

C₂×#41

—

C₂×#41

—

C₄⋊Q₈

C₂×D₁₉

yes

—

#127

—

#124

—

#121

—

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

—

C₄×D₄

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₁₉

#3483

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂²×D₁₉

yes

—

C₂×Q₈

C₂²×D₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₉

yes

—

C₂³

—

Q₈

—

Q₈

#64545

yes

complemented

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂³×D₁₉

yes

—

C₂×C₄

C₂³×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₁₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

C₂×#64545

yes

—

104

C₂

—

105

C₂

C₂²×#64545

yes

—

106

C₂

H(5,𝔽₂)×D₁₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	Q₈²×C₁₉	C₂
hypercenter	Q₈²	D₁₉
hypocenter	C₁₉	#3483
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ Q₈²

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₉

commutator, socle, cosocle

C₂²×C₁₉

C₂⁵

Fitting

Q₈²×C₁₉

C₂

hypercenter

Q₈²

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ Q₈²

N	H ≅ G/N	type
1. #11927260	C₂	semidirect
2. #11927216	C₂	semidirect
3. #11927095	C₂	semidirect
4. C₄×#64545	C₂	semidirect
5. Q₈²×C₁₉	C₂	semidirect
34. Q₈×C₁₉	#41	semidirect
51. Q₈²	D₁₉	semidirect
71. C₁₉	#3483	semidirect
88. Q₈	#64545	semidirect

H ≅ G/N

type

1. #11927260

C₂

semidirect

2. #11927216

C₂

semidirect

3. #11927095

C₂

semidirect

4. C₄×#64545

C₂

semidirect

5. Q₈²×C₁₉

C₂

semidirect

34. Q₈×C₁₉

#41

semidirect

51. Q₈²

D₁₉

semidirect

71. C₁₉

#3483

semidirect

88. Q₈

#64545

semidirect

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

subgroup	index
#11927260	2
#11927216	2
#11927095	2
C₄×#64545	2
Q₈²×C₁₉	2
#3483	19

subgroup

index

Q₈²×C₁₉

Subgroups — #14577262

Conjugacy classes of subgroups

Complements

Maximal subgroups