Group #34175748 — subgroups

Subgroups — #34175748

Order 20224.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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	#23765308	C₂	1	1	yes	maximal, characteristic
2	#23761534	C₂	1	1	yes	maximal, characteristic
3	C₇₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₅₈	C₄	1	1	yes	characteristic
5	C₂×C₇₉⋊C₃₂	—	2	1	no	—
6	C₄⋊(C₇₉⋊C₁₆)	C₄	1	1	yes	characteristic
7	Dic₇₉⋊C₁₆	—	2	1	no	—
8	#19098338	—	2	1	no	—
9	C₂×C₃₂×C₇₉	—	2	1	no	—
10	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₅₈	C₈	1	1	yes	characteristic
12	C₂×C₇₉⋊C₁₆	—	2	1	no	—
13	C₄⋊(C₇₉⋊C₈)	C₈	1	1	yes	characteristic
14	Dic₇₉⋊C₈	—	2	1	no	—
15	C₈×Dic₇₉	—	2	1	no	—
16	C₇₉⋊C₃₂	—	2	2	no	—
17	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
19	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
20	C₃₂×C₇₉	—	4	1	no	—
21	C₂×Dic₁₅₈	C₁₆	1	1	yes	characteristic
22	C₂×C₇₉⋊C₈	—	2	1	no	—
23	C₄⋊Dic₇₉	C₁₆	1	1	yes	characteristic
24	Dic₇₉⋊C₄	—	2	1	no	—
25	C₄×Dic₇₉	—	2	1	no	—
26	C₇₉⋊C₁₆	—	4	1	no	—
27	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₉	M₁₆	1	1	yes	characteristic
29	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
30	C₁₆×C₇₉	—	2	1	no	—
31	C₁₆×C₇₉	SD₁₆	1	1	yes	characteristic
32	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₉	M₃₂	1	1	yes	characteristic
36	C₂×Dic₇₉	—	2	1	no	—
37	C₂×Dic₇₉	—	2	1	no	—
38	Dic₁₅₈	—	4	1	no	—
39	C₈×C₇₉	—	2	1	no	—
40	C₈×C₇₉	#103	1	1	yes	characteristic
41	C₈×C₇₉	#104	1	1	yes	characteristic
42	C₇₉⋊C₈	—	4	1	no	—
43	C₂²×C₇₉	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₄×C₇₉	—	2	1	no	—
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	Q₈⋊C₈	1	1	yes	characteristic
47	C₄×C₇₉	#350	1	1	yes	characteristic
48	Dic₇₉	—	4	1	no	—
49	Dic₇₉	—	4	1	no	—
50	#7393	—	79	1	no	maximal, Sylow
51	C₂×C₇₉	Q₈⋊C₁₆	1	1	yes	characteristic
52	C₂×C₇₉	#1400	1	1	yes	characteristic
53	C₂×C₇₉	#1401	1	1	yes	characteristic
54	#2183	—	79	1	no	—
55	C₄⋊C₃₂	D₇₉	1	1	yes	characteristic
56	#1397	—	79	1	no	—
57	C₇₉	#7393	1	1	yes	characteristic, complemented, Sylow
58	C₈×Q₈	—	79	1	no	—
59	C₂×C₃₂	—	2	1	no	—
60	C₂×C₃₂	—	158	1	no	—
61	C₄⋊C₁₆	—	79	1	no	—
62	C₄⋊C₁₆	—	158	1	no	—
63	#346	—	158	1	no	—
64	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
65	C₄×Q₈	—	79	1	no	—
66	C₂×C₁₆	—	158	1	no	—
67	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
69	C₄⋊C₈	—	79	1	no	—
70	C₄⋊C₈	—	158	1	no	—
71	C₄×C₈	—	158	1	no	—
72	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
73	C₃₂	—	4	1	no	—
74	C₃₂	—	158	2	no	—
75	C₂×Q₈	—	79	1	no	—
76	C₂×C₈	—	158	1	no	—
77	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
78	C₂×C₈	#11929607	1	1	yes	characteristic
79	C₄⋊C₄	—	79	1	no	—
80	C₄⋊C₄	—	158	1	no	—
81	C₄²	—	158	1	no	—
82	C₄²	C₈×D₇₉	1	1	yes	characteristic
83	C₁₆	—	2	1	no	—
84	C₁₆	—	316	1	no	—
85	C₁₆	#11929612	1	1	yes	characteristic
86	C₁₆	#11929614	1	1	yes	characteristic
87	Q₈	—	316	1	no	—
88	C₂×C₄	—	158	1	no	—
89	C₂×C₄	—	158	1	no	—
90	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
91	C₂×C₄	C₁₆×D₇₉	1	1	yes	characteristic
92	C₂×C₄	#14579100	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	316	1	no	—
95	C₈	#14579084	1	1	yes	characteristic
96	C₈	#14579087	1	1	yes	characteristic
97	C₂²	(C₂×D₇₉)⋊C₁₆	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	316	1	no	—
101	C₄	—	316	1	no	—
102	C₄	#19098293	1	1	yes	characteristic
103	C₄	#19098348	1	1	yes	characteristic
104	C₂	#23761378	1	1	yes	characteristic
105	C₂	#23761539	1	1	yes	characteristic
106	C₂	#23761541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765308

C₂

yes

maximal, characteristic

#23761534

C₂

yes

maximal, characteristic

C₇₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₈×Dic₁₅₈

C₄

yes

characteristic

C₂×C₇₉⋊C₃₂

—

C₄⋊(C₇₉⋊C₁₆)

C₄

yes

characteristic

Dic₇₉⋊C₁₆

—

#19098338

—

C₂×C₃₂×C₇₉

—

C₄×C₁₆×C₇₉

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₈

yes

characteristic

C₂×C₇₉⋊C₁₆

—

C₄⋊(C₇₉⋊C₈)

C₈

yes

characteristic

Dic₇₉⋊C₈

—

C₈×Dic₇₉

—

C₇₉⋊C₃₂

—

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₃₂×C₇₉

—

C₂×Dic₁₅₈

C₁₆

yes

characteristic

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₁₆

yes

characteristic

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

M₁₆

yes

characteristic

C₄²×C₇₉

C₂×C₈

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

SD₁₆

yes

characteristic

C₁₆×C₇₉

Q₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₉

M₃₂

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

Q₈⋊C₈

yes

characteristic

C₄×C₇₉

#350

yes

characteristic

Dic₇₉

—

Dic₇₉

—

#7393

—

maximal, Sylow

C₂×C₇₉

Q₈⋊C₁₆

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₄⋊C₃₂

D₇₉

yes

characteristic

#1397

—

C₇₉

#7393

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

158

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

158

—

#346

—

158

—

C₄×C₁₆

C₂×D₇₉

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

158

—

C₂×C₁₆

D₃₁₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄×C₈

—

158

—

C₄×C₈

C₄×D₇₉

yes

characteristic

C₃₂

—

C₃₂

—

158

—

C₂×Q₈

—

C₂×C₈

—

158

—

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₈

#11929607

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄²

—

158

—

C₄²

C₈×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

316

—

C₁₆

yes

C₁₆

yes

Q₈

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

C₂×C₄

C₁₆×D₇₉

yes

characteristic

C₂×C₄

#14579100

yes

characteristic

C₈

—

C₈

—

316

—

C₈

yes

C₈

yes

C₂²

(C₂×D₇₉)⋊C₁₆

yes

characteristic

C₄

—

C₄

—

100

C₄

—

316

—

101

C₄

—

316

—

102

C₄

#19098293

yes

characteristic

103

C₄

#19098348

yes

characteristic

104

C₂

#23761378

yes

characteristic

105

C₂

#23761539

yes

characteristic

106

C₂

#23761541

yes

characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₇₉	C₂²⋊C₁₆
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	C₄⋊C₃₂	D₇₉
hypocenter	C₇₉	#7393
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

subgroup

G/H

center

C₂×C₈

(C₂×D₇₉)⋊C₄

commutator

C₂×C₄×C₇₉

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₇₉

Fitting

C₇₉×C₄⋊C₃₂

C₂

socle, prime radical

C₂²×C₇₉

C₂²⋊C₁₆

cosocle

C₄×C₁₆×C₇₉

C₂²

hypercenter

C₄⋊C₃₂

D₇₉

hypocenter

C₇₉

#7393

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

N	H ≅ G/N	type
57. C₇₉	#7393	semidirect

H ≅ G/N

type

57. C₇₉

#7393

semidirect

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

subgroup	index
#23765308	2
#23761534	2
C₇₉×C₄⋊C₃₂	2
#7393	79

subgroup

index

#23765308

#23761534

C₇₉×C₄⋊C₃₂

#7393

Subgroups — #34175748

Conjugacy classes of subgroups

Complements

Maximal subgroups