Group #34202941 — subgroups

Subgroups — #34202941

Order 20224.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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	#23765682	C₂	1	1	yes	maximal, characteristic
2	#23765627	C₂	1	2	yes	maximal
3	#23762994	C₂	1	2	yes	maximal
4	#23761316	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2247	C₂	1	1	yes	maximal, characteristic
6	#19098968	C₂²	1	2	yes	—
7	#19098959	—	2	2	no	—
8	#19098915	—	2	2	no	—
9	#19098391	—	2	2	no	—
10	#19098367	—	2	4	no	—
11	C₄×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×Q₃₂×C₇₉	—	2	2	no	—
14	#494×C₇₉	C₂²	1	2	yes	—
15	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	#14579161	—	2	2	no	—
17	C₂×C₇₉⋊C₁₆	D₄	1	2	yes	—
18	#14579095	—	2	2	no	—
19	#14579095	—	2	2	no	—
20	#14579092	—	4	4	no	—
21	#14579084	—	4	4	no	—
22	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
23	C₂×Q₁₆×C₇₉	—	2	2	no	—
24	C₂×Q₁₆×C₇₉	—	2	2	no	—
25	C₄⋊Q₈×C₇₉	—	2	2	no	—
26	Q₃₂×C₇₉	—	4	4	no	—
27	C₂×C₁₆×C₇₉	D₄	1	2	yes	—
28	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
29	C₂×Dic₁₅₈	—	4	2	no	—
30	C₂×C₇₉⋊C₈	D₈	1	4	yes	—
31	C₄⋊Dic₇₉	—	4	2	no	—
32	C₄⋊Dic₇₉	—	4	2	no	—
33	C₇₉⋊C₁₆	—	2	2	no	—
34	C₂×Q₈×C₇₉	—	4	2	no	—
35	Q₁₆×C₇₉	—	4	4	no	—
36	Q₁₆×C₇₉	—	4	4	no	—
37	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₄⋊C₄×C₇₉	—	4	2	no	—
40	C₄⋊C₄×C₇₉	—	4	2	no	—
41	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₁₆×C₇₉	SD₁₆	1	4	yes	—
43	Q₈×C₇₉	—	8	2	no	—
44	Q₈×C₇₉	—	8	2	no	—
45	C₂×C₄×C₇₉	—	8	2	no	—
46	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
47	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
48	C₂×Dic₇₉	—	8	2	no	—
49	Dic₁₅₈	—	8	4	no	—
50	C₈×C₇₉	C₂×SD₁₆	1	2	yes	—
51	C₈×C₇₉	#135	1	2	yes	—
52	C₇₉⋊C₈	—	2	4	no	—
53	C₂²×C₇₉	#493	1	1	yes	characteristic
54	C₄×C₇₉	—	16	2	no	—
55	C₄×C₇₉	#492	1	1	yes	characteristic
56	C₄×C₇₉	#495	1	1	yes	characteristic
57	C₄×C₇₉	#510	1	4	yes	—
58	Dic₇₉	—	16	2	no	—
59	#12507	—	79	1	no	maximal, Sylow
60	C₂×C₇₉	#1706	1	1	yes	characteristic
61	C₂×C₇₉	#2251	1	2	yes	—
62	#2254	—	79	1	no	—
63	#2247	D₇₉	1	1	yes	characteristic
64	#2241	—	79	2	no	—
65	#1707	—	79	2	no	—
66	#1311	—	79	1	no	—
67	C₇₉	#12507	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₃₂	—	2	2	no	—
69	#500	—	79	2	no	—
70	#498	—	158	2	no	—
71	#494	C₂×D₇₉	1	2	yes	—
72	#487	—	158	2	no	—
73	#367	—	158	2	no	—
74	#358	—	158	4	no	—
75	C₄×C₁₆	—	79	1	no	—
76	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
77	C₈²	—	79	1	no	—
78	C₂×Q₁₆	—	2	2	no	—
79	C₂×Q₁₆	—	2	2	no	—
80	C₄⋊Q₈	—	2	2	no	—
81	C₄⋊Q₈	—	158	2	no	—
82	Q₃₂	—	4	4	no	—
83	C₂×C₁₆	—	79	2	no	—
84	C₂×C₁₆	C₂²⋊D₇₉	1	2	yes	—
85	#107	—	158	2	no	—
86	#107	—	158	2	no	—
87	#106	—	316	4	no	—
88	#103	—	316	4	no	—
89	C₄×C₈	—	79	2	no	—
90	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
91	C₂×Q₈	—	4	2	no	—
92	C₂×Q₈	—	316	2	no	—
93	Q₁₆	—	4	4	no	—
94	Q₁₆	—	4	4	no	—
95	C₂×C₈	—	79	4	no	—
96	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
97	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
98	C₄⋊C₄	—	4	2	no	—
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	316	2	no	—
101	C₄⋊C₄	—	316	2	no	—
102	C₄²	D₄×D₇₉	1	1	yes	characteristic
103	C₁₆	—	158	2	no	—
104	C₁₆	#11929612	1	4	yes	—
105	Q₈	—	8	2	no	—
106	Q₈	—	8	2	no	—
107	Q₈	—	632	4	no	—
108	C₂×C₄	—	8	2	no	—
109	C₂×C₄	—	632	2	no	—
110	C₂×C₄	#14579157	1	1	yes	characteristic
111	C₂×C₄	D₈×D₇₉	1	2	yes	—
112	C₈	—	158	4	no	—
113	C₈	C₂×#11929612	1	2	yes	—
114	C₈	#14579180	1	2	yes	—
115	C₂²	#19098938	1	1	yes	characteristic
116	C₄	—	16	2	no	—
117	C₄	—	1264	2	no	—
118	C₄	#19098935	1	1	yes	characteristic
119	C₄	#19098946	1	1	yes	characteristic
120	C₄	#19099005	1	4	yes	—
121	C₂	#23762989	1	1	yes	characteristic
122	C₂	#23765668	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23765682

C₂

yes

maximal, characteristic

#23765627

C₂

yes

maximal

#23762994

C₂

yes

maximal

#23761316

C₂

yes

maximal, characteristic

C₇₉×#2247

C₂

yes

maximal, characteristic

#19098968

C₂²

yes

—

—

—

—

—

C₄×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₈×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×Q₃₂×C₇₉

—

#494×C₇₉

C₂²

yes

—

C₄×C₁₆×C₇₉

C₂²

yes

characteristic

#14579161

—

C₂×C₇₉⋊C₁₆

D₄

yes

—

—

—

—

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

—

Q₃₂×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

C₂³

yes

characteristic

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

D₈

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₁₆×C₇₉

SD₁₆

yes

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

C₂×SD₁₆

yes

—

C₈×C₇₉

#135

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

#493

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

#2254

—

#2247

D₇₉

yes

—

—

—

C₇₉

#12507

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

#500

—

#498

—

158

—

#494

C₂×D₇₉

yes

—

#487

—

158

—

#367

—

158

—

#358

—

158

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₇₉

yes

characteristic

C₈²

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

158

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₇₉

yes

—

#107

—

158

—

#107

—

158

—

#106

—

316

—

#103

—

316

—

C₄×C₈

—

C₄×C₈

C₂²×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

316

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

D₄×D₇₉

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

316

—

101

C₄⋊C₄

—

316

—

102

C₄²

D₄×D₇₉

yes

characteristic

103

C₁₆

—

158

—

104

C₁₆

#11929612

yes

—

105

Q₈

—

106

Q₈

—

107

Q₈

—

632

—

108

C₂×C₄

—

109

C₂×C₄

—

632

—

110

C₂×C₄

#14579157

yes

characteristic

111

C₂×C₄

D₈×D₇₉

yes

—

112

C₈

—

158

—

113

C₈

C₂×#11929612

yes

—

114

C₈

#14579180

yes

—

115

C₂²

#19098938

yes

characteristic

116

C₄

—

117

C₄

—

1264

—

118

C₄

#19098935

yes

characteristic

119

C₄

#19098946

yes

characteristic

120

C₄

#19099005

yes

—

121

C₂

#23762989

yes

characteristic

122

C₂

#23765668

yes

—

	subgroup	G/H
center	C₂²	#19098938
commutator, cosocle	C₄×C₈×C₇₉	C₂³
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₇₉×#2247	C₂
socle, prime radical	C₂²×C₇₉	#493
hypercenter	#2247	D₇₉
hypocenter	C₇₉	#12507
LCS	G ▷ C₄×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

subgroup

G/H

center

C₂²

#19098938

commutator, cosocle

C₄×C₈×C₇₉

C₂³

Frattini

C₄×C₈

C₂²×D₇₉

Fitting

C₇₉×#2247

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

N	H ≅ G/N	type
67. C₇₉	#12507	semidirect

H ≅ G/N

type

67. C₇₉

#12507

semidirect

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

subgroup	index
#23765682	2
#23765627	2
#23762994	2
#23761316	2
C₇₉×#2247	2
#12507	79

subgroup

index

C₇₉×#2247

Subgroups — #34202941

Conjugacy classes of subgroups

Complements

Maximal subgroups