Group #34191035 — subgroups

Subgroups — #34191035

Order 20224.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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	#23774794	C₂	1	3	yes	maximal
2	#23764376	C₂	1	3	yes	maximal
3	C₇₉×#1309	C₂	1	1	yes	maximal, characteristic
4	#19099120	C₂²	1	3	yes	—
5	#19098849	—	2	6	no	—
6	#19098821	—	2	6	no	—
7	#19098774	—	2	6	no	—
8	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
9	#19098324	—	2	6	no	—
10	#423×C₇₉	C₂²	1	3	yes	—
11	C₂×Dic₃₁₆	—	2	6	no	—
12	#14579161	D₄	1	6	yes	—
13	#14579153	—	2	3	no	—
14	#14579140	—	2	6	no	—
15	C₄×Dic₁₅₈	—	2	6	no	—
16	#14579120	—	2	3	no	—
17	C₂×C₄×Dic₇₉	—	2	3	no	—
18	#14579093	—	2	6	no	—
19	#14579086	—	2	12	no	—
20	C₂×M₁₆×C₇₉	D₄	1	6	yes	—
21	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₈×C₇₉	—	2	6	no	—
23	C₂×Dic₁₅₈	—	2	6	no	—
24	C₂²×Dic₇₉	—	4	1	no	—
25	Dic₃₁₆	—	8	6	no	—
26	C₄⋊Dic₇₉	—	2	6	no	—
27	C₄⋊Dic₇₉	—	2	6	no	—
28	Dic₇₉⋊C₄	—	4	6	no	—
29	C₂²⋊Dic₇₉	—	4	3	no	—
30	C₄×Dic₇₉	—	2	6	no	—
31	C₄×Dic₇₉	—	4	3	no	—
32	C₄×Dic₇₉	—	4	3	no	—
33	C₂²×C₄×C₇₉	C₂×D₄	1	3	yes	—
34	M₁₆×C₇₉	—	4	6	no	—
35	C₂×C₈×C₇₉	—	2	6	no	—
36	C₄²×C₇₉	C₂×D₄	1	3	yes	—
37	C₄²×C₇₉	#41	1	1	yes	characteristic
38	C₂³×C₇₉	#127	1	1	yes	characteristic
39	C₂×C₄×C₇₉	—	2	3	no	—
40	C₂×C₄×C₇₉	—	2	3	no	—
41	C₂×C₄×C₇₉	#120	1	3	yes	—
42	C₂×C₄×C₇₉	#121	1	3	yes	—
43	C₂×Dic₇₉	—	4	6	no	—
44	C₂×Dic₇₉	—	4	6	no	—
45	Dic₁₅₈	—	4	6	no	—
46	Dic₁₅₈	—	4	6	no	—
47	C₈×C₇₉	—	4	6	no	—
48	C₂²×C₇₉	—	2	3	no	—
49	C₂²×C₇₉	#392	1	1	yes	characteristic
50	C₄×C₇₉	—	2	3	no	—
51	C₄×C₇₉	#455	1	3	yes	—
52	C₄×C₇₉	#456	1	3	yes	—
53	Dic₇₉	—	4	4	no	—
54	Dic₇₉	—	8	6	no	—
55	#10303	—	79	1	no	maximal, Sylow
56	C₂×C₇₉	—	4	1	no	—
57	C₂×C₇₉	#2007	1	3	yes	—
58	#3255	—	79	3	no	—
59	#1994	—	79	3	no	—
60	#1309	D₇₉	1	1	yes	characteristic
61	C₇₉	#10303	1	1	yes	characteristic, complemented, Sylow
62	#533	—	79	3	no	—
63	#475	—	158	6	no	—
64	#470	—	158	6	no	—
65	#462	—	158	6	no	—
66	#423	C₂×D₇₉	1	3	yes	—
67	C₄³	—	79	1	no	—
68	#339	—	158	6	no	—
69	C₂×Q₁₆	—	158	6	no	—
70	C₂×M₁₆	D₃₁₆	1	6	yes	—
71	C₄⋊Q₈	—	79	6	no	—
72	#125	—	158	3	no	—
73	C₂²⋊Q₈	—	158	6	no	—
74	C₄×Q₈	—	158	6	no	—
75	#117	—	158	3	no	—
76	C₂×C₄²	—	158	3	no	—
77	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
78	#106	—	158	6	no	—
79	C₄⋊C₈	—	2	6	no	—
80	#103	—	158	12	no	—
81	C₂×Q₈	—	158	6	no	—
82	C₂²×C₄	—	316	1	no	—
83	C₂²×C₄	C₂×D₃₁₆	1	3	yes	—
84	Q₁₆	—	632	6	no	—
85	M₁₆	—	4	6	no	—
86	C₂×C₈	—	2	6	no	—
87	C₄⋊C₄	—	316	6	no	—
88	C₄⋊C₄	—	158	6	no	—
89	C₄⋊C₄	—	158	6	no	—
90	C₂²⋊C₄	—	316	3	no	—
91	C₄²	—	316	3	no	—
92	C₄²	—	316	3	no	—
93	C₄²	—	158	6	no	—
94	C₄²	D₄×D₇₉	1	3	yes	—
95	C₄²	#11929625	1	1	yes	characteristic
96	C₂³	#14579158	1	1	yes	characteristic
97	Q₈	—	316	6	no	—
98	Q₈	—	316	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	316	6	no	—
102	C₂×C₄	—	316	6	no	—
103	C₂×C₄	#14579131	1	3	yes	—
104	C₂×C₄	#14579136	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	#19098473	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	316	4	no	—
110	C₄	—	632	6	no	—
111	C₄	#19098743	1	3	yes	—
112	C₄	#19098748	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	#23764449	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23774794

C₂

yes

maximal

#23764376

C₂

yes

maximal

C₇₉×#1309

C₂

yes

maximal, characteristic

#19099120

C₂²

yes

—

#19098849

—

#19098821

—

#19098774

—

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098324

—

#423×C₇₉

C₂²

yes

—

C₂×Dic₃₁₆

—

#14579161

D₄

yes

—

#14579153

—

#14579140

—

C₄×Dic₁₅₈

—

#14579120

—

C₂×C₄×Dic₇₉

—

#14579093

—

#14579086

—

C₂×M₁₆×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#121

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#392

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#455

yes

—

C₄×C₇₉

#456

yes

—

Dic₇₉

—

Dic₇₉

—

#10303

—

maximal, Sylow

C₂×C₇₉

—

C₂×C₇₉

#2007

yes

—

#3255

—

#1994

—

#1309

D₇₉

yes

characteristic

C₇₉

#10303

yes

characteristic, complemented, Sylow

#533

—

#475

—

158

—

#470

—

158

—

#462

—

158

—

#423

C₂×D₇₉

yes

—

C₄³

—

#339

—

158

—

C₂×Q₁₆

—

158

—

C₂×M₁₆

D₃₁₆

yes

—

C₄⋊Q₈

—

#125

—

158

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

158

—

#117

—

158

—

C₂×C₄²

—

158

—

C₂×C₄²

C₂²×D₇₉

yes

characteristic

#106

—

158

—

C₄⋊C₈

—

#103

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

316

—

C₂²×C₄

C₂×D₃₁₆

yes

—

Q₁₆

—

632

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₂²⋊C₄

—

316

—

C₄²

—

316

—

C₄²

—

316

—

C₄²

—

158

—

C₄²

D₄×D₇₉

yes

—

C₄²

yes

C₂³

yes

Q₈

—

316

—

Q₈

—

316

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

316

—

102

C₂×C₄

—

316

—

103

C₂×C₄

#14579131

yes

—

104

C₂×C₄

#14579136

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

#19098473

yes

characteristic

108

C₄

—

109

C₄

—

316

—

110

C₄

—

632

—

111

C₄

#19098743

yes

—

112

C₄

#19098748

yes

—

113

C₂

—

114

C₂

#23764449

yes

—

	subgroup	G/H
center	C₂²	#19098473
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1309	C₂
socle	C₂²×C₇₉	#392
prime radical	C₂³×C₇₉	#127
hypercenter	#1309	D₇₉
hypocenter	C₇₉	#10303
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#19098473

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1309

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
61. C₇₉	#10303	semidirect

H ≅ G/N

type

61. C₇₉

#10303

semidirect

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

subgroup	index
#23774794	2
#23764376	2
C₇₉×#1309	2
#10303	79

subgroup

index

#23774794

#23764376

C₇₉×#1309

#10303

Subgroups — #34191035

Conjugacy classes of subgroups

Complements

Maximal subgroups