Group #34175452 — subgroups

Subgroups — #34175452

Order 20224.

208 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098384	C₂	1	2	yes	maximal
2	C₇₉×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579101	—	2	2	no	—
4	#19098384	—	2	2	no	—
5	#19098384	C₄	1	4	yes	—
6	C₂×#108×C₇₉	—	2	2	no	—
7	#423×C₇₉	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	#14579101	—	2	4	no	—
10	#14579101	—	4	2	no	—
11	C₂×C₇₉⋊C₁₆	—	4	2	no	—
12	C₂×M₁₆×C₇₉	—	2	2	no	—
13	C₂²×C₈×C₇₉	D₄	1	2	yes	—
14	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
15	#108×C₇₉	—	4	2	no	—
16	#108×C₇₉	—	4	2	no	—
17	C₄⋊C₈×C₇₉	—	4	2	no	—
18	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₇₉	Q₈	1	1	yes	characteristic
21	C₇₉⋊C₁₆	—	4	4	no	—
22	C₂²×C₄×C₇₉	—	2	1	no	—
23	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₇₉	—	4	4	no	—
25	C₂×C₈×C₇₉	—	4	2	no	—
26	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₇₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₇₉	D₈	1	2	yes	—
29	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
30	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
31	C₂×C₈×C₇₉	Q₁₆	1	2	yes	—
32	C₄²×C₇₉	—	2	1	no	—
33	C₄²×C₇₉	C₄²	1	1	yes	characteristic
34	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂³×C₇₉	#101	1	1	yes	characteristic
36	C₂×C₄×C₇₉	—	2	1	no	—
37	C₂×C₄×C₇₉	—	2	1	no	—
38	C₂×C₄×C₇₉	—	4	2	no	—
39	C₂×C₄×C₇₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₇₉	#100	1	1	yes	characteristic
41	C₂×C₄×C₇₉	#102	1	2	yes	—
42	C₂×C₄×C₇₉	#103	1	2	yes	—
43	C₈×C₇₉	—	8	2	no	—
44	C₈×C₇₉	#102	1	2	yes	—
45	C₈×C₇₉	#103	1	2	yes	—
46	C₈×C₇₉	#106	1	2	yes	—
47	C₈×C₇₉	#107	1	2	yes	—
48	C₂²×C₇₉	—	4	1	no	—
49	C₂²×C₇₉	#332	1	2	yes	—
50	C₂²×C₇₉	#343	1	1	yes	characteristic
51	C₄×C₇₉	—	2	2	no	—
52	C₄×C₇₉	—	4	1	no	—
53	C₄×C₇₉	#331	1	1	yes	characteristic
54	C₄×C₇₉	#333	1	1	yes	characteristic
55	C₄×C₇₉	#340	1	2	yes	—
56	#7273	—	79	1	no	maximal, Sylow
57	C₂×C₇₉	—	2	1	no	—
58	C₂×C₇₉	—	2	2	no	—
59	C₂×C₇₉	#1296	1	1	yes	characteristic
60	C₂×#364	—	79	2	no	—
61	#1848	D₇₉	1	1	yes	characteristic
62	C₇₉	#7273	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₃₂	—	158	2	no	—
64	C₂×#108	—	2	2	no	—
65	#423	Dic₇₉	1	2	yes	—
66	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
67	#364	—	79	4	no	—
68	#364	—	158	2	no	—
69	C₂×M₁₆	—	2	2	no	—
70	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
71	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
72	M₃₂	—	316	2	no	—
73	M₃₂	—	158	4	no	—
74	C₂×C₁₆	—	316	2	no	—
75	#108	—	4	2	no	—
76	#108	—	4	2	no	—
77	C₄⋊C₈	—	4	2	no	—
78	C₄×C₈	Dic₁₅₈	1	1	yes	characteristic
79	C₄×C₈	C₄×D₇₉	1	2	yes	—
80	C₄×C₈	D₃₁₆	1	1	yes	characteristic
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
83	M₁₆	—	4	4	no	—
84	C₂×C₈	—	4	2	no	—
85	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
86	C₂×C₈	Dic₇₉⋊C₄	1	2	yes	—
87	C₂×C₈	#11929609	1	2	yes	—
88	C₂×C₈	#11929611	1	2	yes	—
89	C₂×C₈	#11929612	1	2	yes	—
90	C₂×C₈	#11929614	1	2	yes	—
91	C₄²	—	2	1	no	—
92	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
93	C₄²	C₄⋊Dic₇₉	1	1	yes	characteristic
94	C₁₆	—	316	4	no	—
95	C₂³	#14579080	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	C₇₉⋊#95	1	1	yes	characteristic
100	C₂×C₄	#14579078	1	1	yes	characteristic
101	C₂×C₄	#14579082	1	2	yes	—
102	C₂×C₄	#14579085	1	2	yes	—
103	C₈	—	8	2	no	—
104	C₈	#14579081	1	2	yes	—
105	C₈	#14579084	1	2	yes	—
106	C₈	#14579092	1	2	yes	—
107	C₈	#14579094	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#19098309	1	2	yes	—
110	C₂²	#19098332	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	4	1	no	—
113	C₄	#19098307	1	1	yes	characteristic
114	C₄	#19098312	1	1	yes	characteristic
115	C₄	#19098325	1	2	yes	—
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	#23761283	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098384

C₂

yes

maximal

C₇₉×#1848

C₂

yes

maximal, characteristic

C₂×#14579101

—

#19098384

—

#19098384

C₄

yes

—

C₂×#108×C₇₉

—

#423×C₇₉

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

#108×C₇₉

—

#108×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

—

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

Q₈

yes

characteristic

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₄⋊C₄

yes

—

C₂×C₈×C₇₉

D₈

yes

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

Q₁₆

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

C₄²

yes

characteristic

C₄²×C₇₉

C₄⋊C₄

yes

characteristic

C₂³×C₇₉

#101

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#103

yes

—

C₈×C₇₉

—

C₈×C₇₉

#102

yes

—

C₈×C₇₉

#103

yes

—

C₈×C₇₉

#106

yes

—

C₈×C₇₉

#107

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

#332

yes

—

C₂²×C₇₉

#343

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

#7273

—

maximal, Sylow

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

D₇₉

yes

characteristic

C₇₉

#7273

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

158

—

C₂×#108

—

#423

Dic₇₉

yes

—

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

#364

—

#364

—

158

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₇₉

yes

—

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

M₃₂

—

316

—

M₃₂

—

158

—

C₂×C₁₆

—

316

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₁₅₈

yes

characteristic

C₄×C₈

C₄×D₇₉

yes

—

C₄×C₈

D₃₁₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₇₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

C₂×C₈

Dic₇₉⋊C₄

yes

—

C₂×C₈

#11929609

yes

—

C₂×C₈

#11929611

yes

—

C₂×C₈

#11929612

yes

—

C₂×C₈

#11929614

yes

—

C₄²

—

C₄²

C₄×Dic₇₉

yes

characteristic

C₄²

C₄⋊Dic₇₉

yes

characteristic

C₁₆

—

316

—

C₂³

#14579080

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₇₉⋊#95

yes

characteristic

100

C₂×C₄

#14579078

yes

characteristic

101

C₂×C₄

#14579082

yes

—

102

C₂×C₄

#14579085

yes

—

103

C₈

—

104

C₈

#14579081

yes

—

105

C₈

#14579084

yes

—

106

C₈

#14579092

yes

—

107

C₈

#14579094

yes

—

108

C₂²

—

109

C₂²

#19098309

yes

—

110

C₂²

#19098332

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

#19098307

yes

characteristic

114

C₄

#19098312

yes

characteristic

115

C₄

#19098325

yes

—

116

C₂

—

117

C₂

—

118

C₂

#23761283

yes

characteristic

	subgroup	G/H
center	C₄	#19098312
commutator	C₄²×C₇₉	C₄²
Frattini	C₂×C₄×C₈	C₂×D₇₉
Fitting	C₇₉×#1848	C₂
socle	C₂×C₇₉	#1296
prime radical	C₂³×C₇₉	#101
cosocle	C₂×C₄×C₈×C₇₉	C₂²
hypercenter	#1848	D₇₉
hypocenter	C₇₉	#7273
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₄

#19098312

commutator

C₄²×C₇₉

C₄²

Frattini

C₂×C₄×C₈

C₂×D₇₉

Fitting

C₇₉×#1848

C₂

C₂×C₇₉

C₂³×C₇₉

C₂×C₄×C₈×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

N	H ≅ G/N	type
62. C₇₉	#7273	semidirect

H ≅ G/N

type

62. C₇₉

#7273

semidirect

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

subgroup	index
C₂×#19098384	2
C₇₉×#1848	2
#7273	79

subgroup

index

C₂×#19098384

C₇₉×#1848

#7273

Subgroups — #34175452

Conjugacy classes of subgroups

Complements

Maximal subgroups