Group #23761547 — subgroups

Subgroups — #23761547

Order 10112.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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	#19098740	C₂	1	1	yes	maximal, characteristic
2	#19098303	C₂	1	1	yes	maximal, characteristic, complemented
3	#355×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579206	C₄	1	1	yes	characteristic
5	#14579192	—	2	1	no	—
6	#14579089	—	2	1	no	—
7	#14579078	C₄	1	1	yes	characteristic
8	#14579072	—	2	1	no	—
9	#124×C₇₉	C₂²	1	1	yes	characteristic
10	#101×C₇₉	—	2	1	no	—
11	#11929624	—	2	1	no	—
12	#11929623	—	4	1	no	—
13	C₂×C₂²⋊D₇₉	—	4	1	no	—
14	D₄×D₇₉	—	4	1	no	—
15	#11929614	—	4	1	no	—
16	#11929611	—	4	1	no	—
17	#11929608	—	2	1	no	—
18	C₂×C₇₉⋊C₈	—	4	1	no	—
19	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
20	C₂×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
21	M₁₆×C₇₉	—	4	1	no	—
22	C₂²⋊C₄×C₇₉	—	4	1	no	—
23	C₄²×C₇₉	D₄	1	1	yes	characteristic
24	C₂³×C₇₉	—	2	1	no	—
25	C₂²×D₇₉	—	4	1	no	—
26	Q₈×C₇₉	—	4	1	no	—
27	D₄×C₇₉	—	4	1	no	—
28	C₂×C₄×C₇₉	—	2	1	no	—
29	C₂×C₄×C₇₉	—	2	1	no	—
30	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²⋊D₇₉	—	4	2	no	—
32	C₂²⋊D₇₉	—	4	1	no	—
33	C₂×Dic₇₉	—	4	1	no	—
34	D₃₁₆	—	2	1	no	—
35	C₄×D₇₉	—	4	1	no	—
36	Dic₁₅₈	—	2	1	no	—
37	C₈×C₇₉	—	8	1	no	—
38	C₇₉⋊C₈	—	4	1	no	—
39	C₇₉⋊C₈	—	4	2	no	—
40	C₂²×C₇₉	—	4	1	no	—
41	C₂²×C₇₉	—	8	1	no	—
42	C₂²×C₇₉	#99	1	1	yes	characteristic
43	C₂×D₇₉	—	4	1	no	—
44	C₂×D₇₉	—	16	1	no	—
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	—	4	1	no	—
47	C₄×C₇₉	—	4	1	no	—
48	Dic₇₉	—	4	1	no	—
49	C₂×C₇₉	—	2	1	no	—
50	C₂×C₇₉	—	8	1	no	—
51	C₂×C₇₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
52	D₇₉	—	8	1	no	—
53	#1403	—	79	1	no	maximal, Sylow
54	C₇₉	#1403	1	1	yes	characteristic, complemented, Sylow
55	#455	—	79	1	no	—
56	#355	D₇₉	1	1	yes	characteristic, complemented
57	#329	—	79	1	no	—
58	H(5,𝔽₂)	—	79	1	no	—
59	#137	—	158	1	no	—
60	#124	C₂×D₇₉	1	1	yes	characteristic
61	#104	—	158	1	no	—
62	#101	—	2	1	no	—
63	#100	—	79	1	no	—
64	#97	—	158	1	no	—
65	#41	—	316	1	no	—
66	#41	—	158	1	no	—
67	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
68	C₂×D₄	—	316	1	no	—
69	C₂×D₄	—	316	1	no	—
70	C₂×D₄	C₄×D₇₉	1	1	yes	characteristic
71	Q₁₆	—	316	1	no	—
72	SD₁₆	—	316	1	no	—
73	M₁₆	—	4	1	no	—
74	M₁₆	—	158	1	no	—
75	C₂×C₈	—	316	1	no	—
76	C₂²⋊C₄	—	4	1	no	—
77	C₄²	D₃₁₆	1	1	yes	characteristic
78	C₂³	—	2	1	no	—
79	C₂³	—	316	1	no	—
80	Q₈	—	4	1	no	—
81	Q₈	—	158	1	no	—
82	D₄	—	4	1	no	—
83	D₄	—	316	2	no	—
84	D₄	—	316	1	no	—
85	D₄	—	158	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	316	1	no	—
89	C₂×C₄	—	316	1	no	—
90	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
91	C₈	—	8	1	no	—
92	C₈	—	316	1	no	—
93	C₈	—	316	2	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	8	1	no	—
96	C₂²	—	316	1	no	—
97	C₂²	—	1264	1	no	—
98	C₂²	#14579075	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	316	1	no	—
103	C₂	—	2	1	no	—
104	C₂	—	8	1	no	—
105	C₂	—	632	1	no	—
106	C₂	#19098349	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098740

C₂

yes

maximal, characteristic

#19098303

C₂

yes

maximal, characteristic, complemented

#355×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579206

C₄

yes

—

—

C₄

yes

characteristic

#14579072

—

#124×C₇₉

C₂²

yes

characteristic

#101×C₇₉

—

#11929624

—

#11929623

—

C₂×C₂²⋊D₇₉

—

D₄×D₇₉

—

#11929614

—

#11929611

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×D₄×C₇₉

C₂×C₄

yes

characteristic

M₁₆×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²⋊D₇₉

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#99

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

AΣL(1,𝔽₁₆)

yes

characteristic

D₇₉

—

#1403

—

maximal, Sylow

C₇₉

#1403

yes

characteristic, complemented, Sylow

#455

—

#355

D₇₉

yes

characteristic, complemented

#329

—

H(5,𝔽₂)

—

#137

—

158

—

#124

C₂×D₇₉

yes

characteristic

#104

—

158

—

#101

—

#100

—

#97

—

158

—

#41

—

316

—

#41

—

158

—

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

C₂×D₄

—

316

—

C₂×D₄

—

316

—

C₂×D₄

C₄×D₇₉

yes

characteristic

Q₁₆

—

316

—

SD₁₆

—

316

—

M₁₆

—

M₁₆

—

158

—

C₂×C₈

—

316

—

C₂²⋊C₄

—

C₄²

D₃₁₆

yes

characteristic

C₂³

—

C₂³

—

316

—

Q₈

—

Q₈

—

158

—

D₄

—

D₄

—

316

—

D₄

—

316

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

C₈

—

C₈

—

316

—

C₈

—

316

—

C₂²

—

C₂²

—

C₂²

—

316

—

C₂²

—

1264

—

C₂²

#14579075

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

316

—

103

C₂

—

104

C₂

—

105

C₂

—

632

—

106

C₂

#19098349

yes

characteristic

	subgroup	G/H
center	C₂	#19098349
commutator	C₂×D₄×C₇₉	C₂×C₄
Frattini	#124	C₂×D₇₉
Fitting	#355×C₇₉	C₂
socle	C₂×C₇₉	AΣL(1,𝔽₁₆)
prime radical	#14579206	C₄
cosocle	#124×C₇₉	C₂²
hypercenter	#355	D₇₉
hypocenter	C₇₉	#1403
LCS	G ▷ C₂×D₄×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

subgroup

G/H

center

C₂

#19098349

commutator

C₂×D₄×C₇₉

C₂×C₄

Frattini

#124

C₂×D₇₉

Fitting

#355×C₇₉

C₂

socle

C₂×C₇₉

AΣL(1,𝔽₁₆)

prime radical

#14579206

C₄

cosocle

#124×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×D₄×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

N	H ≅ G/N	type
2. #19098303	C₂	semidirect
3. #355×C₇₉	C₂	semidirect
54. C₇₉	#1403	semidirect
56. #355	D₇₉	semidirect

H ≅ G/N

type

2. #19098303

C₂

semidirect

3. #355×C₇₉

C₂

semidirect

54. C₇₉

#1403

semidirect

56. #355

D₇₉

semidirect

Subgroups — #23761547

Conjugacy classes of subgroups

Complements