Group #23763102 — subgroups

Subgroups — #338×D₇₉ #23763102

Order 10112.

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

normal subgroups only

This group has 372 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	C₂×M₁₆×D₇₉	C₂	1	3	yes	maximal
2	C₇₉⋊#338	C₂	1	3	yes	maximal, complemented
3	#338×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
5	C₂×#11929608	C₂²	1	3	yes	—
6	C₂×#11929607	C₄	1	6	yes	—
7	M₁₆×D₇₉	—	2	6	no	—
8	M₁₆×D₇₉	—	2	6	no	—
9	C₂×C₈×D₇₉	C₄	1	6	yes	—
10	C₂×M₁₆×C₇₉	C₂²	1	3	yes	—
11	C₂³×D₇₉	Q₈	1	1	yes	characteristic
12	C₂²×Dic₇₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×D₇₉	C₂×C₄	1	3	yes	—
14	C₂×C₄×D₇₉	C₂×C₄	1	3	yes	—
15	C₂×C₄×D₇₉	D₄	1	3	yes	—
16	C₂×C₄×D₇₉	D₄	1	3	yes	—
17	#11929608	—	2	6	no	—
18	#11929607	—	2	12	no	—
19	C₂×C₇₉⋊C₈	C₂×C₄	1	6	yes	—
20	C₈×D₇₉	—	2	6	no	—
21	C₈×D₇₉	—	2	6	no	—
22	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₇₉	—	2	6	no	—
24	C₂×C₈×C₇₉	C₂×C₄	1	6	yes	—
25	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
26	C₂²×D₇₉	—	4	2	no	—
27	C₂²×D₇₉	C₄⋊C₄	1	3	yes	—
28	C₂²×D₇₉	C₄⋊C₄	1	3	yes	—
29	C₂×C₄×C₇₉	C₂²×C₄	1	3	yes	—
30	C₂×C₄×C₇₉	C₂×D₄	1	3	yes	—
31	C₂×Dic₇₉	C₄⋊C₄	1	3	yes	—
32	C₂×Dic₇₉	C₄⋊C₄	1	3	yes	—
33	C₄×D₇₉	C₄²	1	3	yes	—
34	C₄×D₇₉	C₄²	1	1	yes	characteristic
35	C₄×D₇₉	C₂²⋊C₄	1	3	yes	—
36	C₄×D₇₉	C₂²⋊C₄	1	3	yes	—
37	C₄×D₇₉	C₂²⋊C₄	1	6	yes	—
38	C₈×C₇₉	—	2	6	no	—
39	C₇₉⋊C₈	—	2	6	no	—
40	C₂²×C₇₉	—	4	1	no	—
41	C₂²×C₇₉	C₂×C₄⋊C₄	1	3	yes	—
42	C₂×D₇₉	—	2	6	no	—
43	C₂×D₇₉	—	4	3	no	—
44	C₂×D₇₉	#95	1	3	yes	—
45	C₂×D₇₉	#95	1	1	yes	characteristic
46	C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₇₉	C₂×C₂²⋊C₄	1	3	yes	—
48	Dic₇₉	#95	1	1	yes	characteristic
49	Dic₇₉	#95	1	3	yes	—
50	C₂×C₇₉	—	2	3	no	—
51	C₂×C₇₉	C₂×#95	1	1	yes	characteristic
52	D₇₉	—	2	3	no	—
53	D₇₉	#338	1	2	yes	direct product factor
54	C₂×#338	—	79	1	no	maximal, Sylow
55	C₇₉	C₂×#338	1	1	yes	characteristic, complemented, Sylow
56	C₂²×M₁₆	—	79	3	no	—
57	#338	—	79	3	no	—
58	#338	D₇₉	1	1	yes	characteristic, direct product factor
59	C₂³×C₄	—	79	1	no	—
60	C₂×M₁₆	—	79	3	no	—
61	C₂×M₁₆	—	79	6	no	—
62	C₂×M₁₆	—	158	6	no	—
63	C₂×M₁₆	—	158	6	no	—
64	C₂×M₁₆	C₂×D₇₉	1	3	yes	—
65	C₂²×C₈	—	79	6	no	—
66	C₂⁴	—	79	1	no	—
67	C₂²×C₄	—	79	1	no	—
68	C₂²×C₄	—	79	3	no	—
69	C₂²×C₄	—	79	3	no	—
70	C₂²×C₄	—	79	3	no	—
71	C₂²×C₄	—	79	3	no	—
72	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
73	M₁₆	—	2	6	no	—
74	M₁₆	—	158	12	no	—
75	M₁₆	—	158	6	no	—
76	C₂×C₈	—	79	6	no	—
77	C₂×C₈	—	158	6	no	—
78	C₂×C₈	—	158	6	no	—
79	C₂×C₈	C₄×D₇₉	1	6	yes	—
80	C₂³	—	316	2	no	—
81	C₂³	—	79	3	no	—
82	C₂³	—	79	3	no	—
83	C₂³	Q₈×D₇₉	1	1	yes	characteristic
84	C₂×C₄	—	79	3	no	—
85	C₂×C₄	—	79	3	no	—
86	C₂×C₄	—	79	1	no	—
87	C₂×C₄	—	79	3	no	—
88	C₂×C₄	—	79	3	no	—
89	C₂×C₄	—	79	3	no	—
90	C₂×C₄	—	79	6	no	—
91	C₂×C₄	C₂×C₄×D₇₉	1	3	yes	—
92	C₂×C₄	D₄×D₇₉	1	3	yes	—
93	C₈	—	2	6	no	—
94	C₈	—	158	6	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	316	3	no	—
97	C₂²	—	79	1	no	—
98	C₂²	—	79	3	no	—
99	C₂²	—	158	6	no	—
100	C₂²	C₄⋊C₄×D₇₉	1	3	yes	—
101	C₄	—	79	1	no	—
102	C₄	—	79	3	no	—
103	C₄	C₄²×D₇₉	1	1	yes	characteristic
104	C₄	C₂²⋊C₄×D₇₉	1	3	yes	—
105	C₂	—	2	3	no	—
106	C₂	—	79	2	no	—
107	C₂	—	158	3	no	—
108	C₂	#95×D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×M₁₆×D₇₉

C₂

yes

maximal

C₇₉⋊#338

C₂

yes

maximal, complemented

#338×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

—

C₂×#11929607

C₄

yes

—

M₁₆×D₇₉

—

M₁₆×D₇₉

—

C₂×C₈×D₇₉

C₄

yes

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂³×D₇₉

Q₈

yes

characteristic

C₂²×Dic₇₉

Q₈

yes

characteristic

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

C₂×C₄

yes

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

D₄

yes

—

#11929608

—

#11929607

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₈×D₇₉

—

C₈×D₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

C₂×Q₈

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

C₄⋊C₄

yes

—

C₂²×D₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₄×D₇₉

C₄²

yes

—

C₄×D₇₉

C₄²

yes

characteristic

C₄×D₇₉

C₂²⋊C₄

yes

—

C₄×D₇₉

C₂²⋊C₄

yes

—

C₄×D₇₉

C₂²⋊C₄

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

#95

yes

—

C₂×D₇₉

#95

yes

characteristic

C₄×C₇₉

C₂×C₄²

yes

characteristic

C₄×C₇₉

C₂×C₂²⋊C₄

yes

—

Dic₇₉

#95

yes

characteristic

Dic₇₉

#95

yes

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#95

yes

characteristic

D₇₉

—

D₇₉

#338

yes

direct product factor

C₂×#338

—

maximal, Sylow

C₇₉

C₂×#338

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

#338

—

#338

D₇₉

yes

characteristic, direct product factor

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

158

—

C₂×M₁₆

—

158

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

—

C₂³

—

316

—

C₂³

—

C₂³

—

C₂³

Q₈×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

D₄×D₇₉

yes

—

C₈

—

C₈

—

158

—

C₂²

—

C₂²

—

316

—

C₂²

—

C₂²

—

C₂²

—

158

—

100

C₂²

C₄⋊C₄×D₇₉

yes

—

101

C₄

—

102

C₄

—

103

C₄

C₄²×D₇₉

yes

characteristic

104

C₄

C₂²⋊C₄×D₇₉

yes

—

105

C₂

—

106

C₂

—

107

C₂

—

158

—

108

C₂

#95×D₇₉

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₇₉
commutator	C₄×C₇₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#338×C₇₉	C₂
socle	C₂×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	Q₈
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#338	D₇₉
hypocenter	C₇₉	C₂×#338
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ #338

subgroup

G/H

center

C₄

C₄²×D₇₉

commutator

C₄×C₇₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#338×C₇₉

C₂

socle

C₂×C₇₉

C₂×#95

prime radical

C₂³×D₇₉

Q₈

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₇₉

C₁ ◁ C₄ ◁ #338

N	H ≅ G/N	type
2. C₇₉⋊#338	C₂	semidirect
3. #338×C₇₉	C₂	semidirect
53. D₇₉	#338	direct (N × H)
55. C₇₉	C₂×#338	semidirect
58. #338	D₇₉	direct (N × H)

H ≅ G/N

type

2. C₇₉⋊#338

C₂

semidirect

3. #338×C₇₉

C₂

semidirect

53. D₇₉

#338

direct (N × H)

55. C₇₉

C₂×#338

semidirect

58. #338

D₇₉

direct (N × H)

Subgroups — #338×D₇₉ #23763102

Conjugacy classes of subgroups

Complements

Subgroups — #338×D79 #23763102

Conjugacy classes of subgroups

Complements

Subgroups — #338×D₇₉ #23763102