Group #11927279 — subgroups

Subgroups — #11927279

Order 1216.

236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597393	C₂	1	2	yes	maximal, complemented
3	#10597340	C₂	1	4	yes	maximal, complemented
4	#10597339	C₂	1	2	yes	maximal, complemented
5	#10597321	C₂	1	2	yes	maximal, complemented
6	#10597320	C₂	1	1	yes	maximal, characteristic
7	C₄×D₇₆	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×D₇₆	C₂²	1	2	yes	—
11	C₂×D₇₆	C₂²	1	2	yes	—
12	C₂×D₇₆	C₂²	1	2	yes	—
13	C₂×C₄×D₁₉	C₂²	1	4	yes	—
14	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₄²×C₁₉	C₂²	1	2	yes	—
19	(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
20	(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
21	(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
22	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	Dic₁₉⋊C₄	C₂²	1	2	yes	—
24	C₄×Dic₁₉	C₂²	1	2	yes	—
25	C₂²×D₁₉	C₂³	1	4	yes	—
26	Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×Dic₁₉	C₂³	1	2	yes	—
33	C₂×Dic₁₉	C₂³	1	2	yes	—
34	D₇₆	—	2	4	no	—
35	D₇₆	—	2	4	no	—
36	D₇₆	—	4	2	no	—
37	C₄×D₁₉	—	4	4	no	—
38	Dic₃₈	—	2	2	no	—
39	C₂²×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂×D₁₉	—	2	4	no	—
41	C₂×D₁₉	—	2	4	no	—
42	C₂×D₁₉	—	2	4	no	—
43	C₄×C₁₉	—	2	2	no	—
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	#41	1	2	yes	—
47	C₄×C₁₉	#41	1	2	yes	—
48	Dic₁₉	—	2	2	no	—
49	Dic₁₉	—	2	2	no	—
50	#559	—	19	1	no	maximal, Sylow
51	C₂×C₁₉	C₂×#41	1	1	yes	characteristic
52	C₂×C₁₉	C₂×#41	1	1	yes	characteristic
53	C₂×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
54	D₁₉	—	4	4	no	—
55	#127	—	19	1	no	—
56	#124	—	19	2	no	—
57	#124	—	19	2	no	—
58	#123	—	19	4	no	—
59	C₄×Q₈	—	19	1	no	—
60	C₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
61	C₄×D₄	—	19	2	no	—
62	C₄×D₄	—	19	2	no	—
63	C₁₉	#559	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₈	—	19	1	no	—
65	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
66	C₂×D₄	—	19	2	no	—
67	C₂×D₄	—	19	2	no	—
68	C₂×D₄	—	19	2	no	—
69	C₂²×C₄	—	19	4	no	—
70	C₄⋊C₄	—	19	2	no	—
71	C₄⋊C₄	—	19	1	no	—
72	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
74	C₂²⋊C₄	—	19	4	no	—
75	C₂²⋊C₄	—	19	4	no	—
76	C₂²⋊C₄	—	19	4	no	—
77	C₄²	—	19	2	no	—
78	C₄²	C₂×D₁₉	1	2	yes	—
79	C₄²	C₂×D₁₉	1	1	yes	characteristic
80	C₂³	—	19	4	no	—
81	Q₈	—	2	2	no	—
82	Q₈	—	38	2	no	—
83	D₄	—	38	4	no	—
84	D₄	—	38	4	no	—
85	D₄	—	76	2	no	—
86	C₂×C₄	—	19	2	no	—
87	C₂×C₄	—	19	2	no	—
88	C₂×C₄	—	76	4	no	—
89	C₂×C₄	C₂²×D₁₉	1	2	yes	—
90	C₂×C₄	C₂²×D₁₉	1	2	yes	—
91	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
93	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
94	C₂²	—	38	4	no	—
95	C₂²	—	38	4	no	—
96	C₂²	—	38	4	no	—
97	C₂²	C₂³×D₁₉	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	38	2	no	—
102	C₄	—	38	2	no	—
103	C₄	#64541	1	2	yes	—
104	C₄	#64545	1	2	yes	—
105	C₂	—	76	4	no	—
106	C₂	C₂×#64541	1	1	yes	characteristic
107	C₂	C₂×#64545	1	1	yes	characteristic
108	C₂	#10597435	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic, complemented

#10597393

C₂

yes

maximal, complemented

#10597340

C₂

yes

maximal, complemented

#10597339

C₂

yes

maximal, complemented

#10597321

C₂

yes

maximal, complemented

#10597320

C₂

yes

maximal, characteristic

C₄×D₇₆

C₂

yes

maximal, complemented

C₄×Dic₃₈

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×C₁₉

C₂²

yes

characteristic

C₂×D₇₆

C₂²

yes

—

C₂×D₇₆

C₂²

yes

—

C₂×D₇₆

C₂²

yes

—

C₂×C₄×D₁₉

C₂²

yes

—

C₂×Dic₃₈

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₉

C₂²

yes

—

C₄²×C₁₉

C₂²

yes

characteristic

C₄²×C₁₉

C₂²

yes

—

(C₂×D₁₉)⋊C₄

C₂²

yes

—

(C₂×D₁₉)⋊C₄

C₂²

yes

—

(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₄⋊Dic₁₉

C₂²

yes

characteristic

Dic₁₉⋊C₄

C₂²

yes

—

C₄×Dic₁₉

C₂²

yes

—

C₂²×D₁₉

C₂³

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄×C₁₉

C₂³

yes

—

C₂×C₄×C₁₉

C₂³

yes

—

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₁₉

C₂³

yes

—

C₂×Dic₁₉

C₂³

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₂²×C₁₉

C₂⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#41

yes

—

C₄×C₁₉

#41

yes

—

Dic₁₉

—

Dic₁₉

—

#559

—

maximal, Sylow

C₂×C₁₉

C₂×#41

yes

characteristic

C₂×C₁₉

C₂×#41

yes

characteristic

C₂×C₁₉

H(5,𝔽₂)

yes

characteristic

D₁₉

—

—

—

—

—

C₄×Q₈

—

C₄×Q₈

D₁₉

yes

characteristic, complemented

C₄×D₄

—

C₄×D₄

—

C₁₉

#559

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×D₁₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₄⋊C₄

C₂×D₁₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×D₁₉

yes

—

C₄²

C₂×D₁₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₁₉

yes

—

C₂×C₄

C₂²×D₁₉

yes

—

C₂×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₄

C₂²×D₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂³×D₁₉

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#64541

yes

—

104

C₄

#64545

yes

—

105

C₂

—

106

C₂

C₂×#64541

yes

characteristic

107

C₂

C₂×#64545

yes

characteristic

108

C₂

#10597435

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁴
Fitting	C₄×Q₈×C₁₉	C₂
prime radical	#10597320	C₂
hypercenter	C₄×Q₈	D₁₉
hypocenter	C₁₉	#559
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₉

commutator, socle, cosocle

C₂²×C₁₉

C₂⁴

Fitting

C₄×Q₈×C₁₉

C₂

prime radical

#10597320

C₂

hypercenter

C₄×Q₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ C₄×Q₈

N	H ≅ G/N	type
1. C₄×Q₈×C₁₉	C₂	semidirect
2. #10597393	C₂	semidirect
3. #10597340	C₂	semidirect
4. #10597339	C₂	semidirect
5. #10597321	C₂	semidirect
7. C₄×D₇₆	C₂	semidirect
8. C₄×Dic₃₈	C₂	semidirect
60. C₄×Q₈	D₁₉	semidirect
63. C₁₉	#559	semidirect

H ≅ G/N

type

1. C₄×Q₈×C₁₉

C₂

semidirect

2. #10597393

C₂

semidirect

3. #10597340

C₂

semidirect

4. #10597339

C₂

semidirect

5. #10597321

C₂

semidirect

7. C₄×D₇₆

C₂

semidirect

8. C₄×Dic₃₈

C₂

semidirect

60. C₄×Q₈

D₁₉

semidirect

63. C₁₉

#559

semidirect

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

subgroup	index
C₄×Q₈×C₁₉	2
#10597393	2
#10597340	2
#10597339	2
#10597321	2
#10597320	2
C₄×D₇₆	2
C₄×Dic₃₈	2
#559	19

subgroup

index

C₄×Q₈×C₁₉

C₄×D₇₆

C₄×Dic₃₈

#559

Subgroups — #11927279

Conjugacy classes of subgroups

Complements

Maximal subgroups