Group #34175904 — subgroups

Subgroups — #34175904

Order 20224.

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

normal subgroups only

This group has 132 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	#23765653	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₃₂	—	2	1	no	—
5	C₂×Dic₆₃₂	C₄	1	2	yes	—
6	#19098943	—	2	1	no	—
7	C₂×C₇₉⋊C₃₂	—	2	1	no	—
8	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
9	#335×C₇₉	—	2	1	no	—
10	C₂×Dic₃₁₆	—	2	2	no	—
11	C₂×Dic₃₁₆	—	4	1	no	—
12	#14579161	—	4	1	no	—
13	Dic₆₃₂	—	4	1	no	—
14	Dic₆₃₂	—	4	1	no	—
15	Dic₆₃₂	—	4	2	no	—
16	C₇₉⋊C₃₂	—	4	1	no	—
17	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
19	C₄⋊C₈×C₇₉	—	4	1	no	—
20	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	4	2	no	—
22	Dic₃₁₆	—	4	2	no	—
23	Dic₃₁₆	—	4	2	no	—
24	Dic₃₁₆	—	8	2	no	—
25	C₄⋊Dic₇₉	—	8	1	no	—
26	C₄⋊Dic₇₉	—	8	1	no	—
27	C₂×C₈×C₇₉	—	8	1	no	—
28	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₉	SD₁₆	1	1	yes	characteristic
30	C₄²×C₇₉	D₈	1	1	yes	characteristic
31	C₁₆×C₇₉	—	2	1	no	—
32	C₁₆×C₇₉	D₈	1	1	yes	characteristic
33	C₁₆×C₇₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
35	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
36	C₂×C₄×C₇₉	SD₃₂	1	1	yes	characteristic
37	C₂×Dic₇₉	—	8	2	no	—
38	Dic₁₅₈	—	8	2	no	—
39	Dic₁₅₈	—	8	2	no	—
40	C₈×C₇₉	—	2	1	no	—
41	C₈×C₇₉	—	16	1	no	—
42	C₈×C₇₉	#100	1	1	yes	characteristic
43	C₈×C₇₉	#102	1	1	yes	characteristic
44	C₂²×C₇₉	#357	1	1	yes	characteristic
45	C₄×C₇₉	—	2	1	no	—
46	C₄×C₇₉	#331	1	1	yes	characteristic
47	C₄×C₇₉	#361	1	1	yes	characteristic
48	C₄×C₇₉	SD₆₄	1	1	yes	characteristic
49	C₄×C₇₉	Q₆₄	1	1	yes	characteristic
50	Dic₇₉	—	16	2	no	—
51	#7445	—	79	1	no	maximal, Sylow
52	C₂×C₇₉	#1361	1	1	yes	characteristic
53	C₂×C₇₉	#1416	1	1	yes	characteristic
54	C₂×C₇₉	#1420	1	1	yes	characteristic
55	#2247	—	79	1	no	—
56	C₄⋊C₃₂	—	79	1	no	—
57	#1371	D₇₉	1	1	yes	characteristic
58	C₇₉	#7445	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₃₂	—	79	2	no	—
60	C₂×Q₃₂	—	158	1	no	—
61	#494	—	158	1	no	—
62	C₂×C₃₂	—	158	1	no	—
63	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
64	#335	—	2	1	no	—
65	C₂×Q₁₆	—	316	1	no	—
66	C₂×Q₁₆	—	158	2	no	—
67	C₄⋊Q₈	—	316	1	no	—
68	Q₃₂	—	316	2	no	—
69	Q₃₂	—	316	1	no	—
70	Q₃₂	—	316	1	no	—
71	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
72	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
73	C₄⋊C₈	—	4	1	no	—
74	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
75	C₃₂	—	316	1	no	—
76	C₂×Q₈	—	316	2	no	—
77	Q₁₆	—	316	2	no	—
78	Q₁₆	—	316	2	no	—
79	Q₁₆	—	632	2	no	—
80	C₂×C₈	—	8	1	no	—
81	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
82	C₂×C₈	#11929611	1	1	yes	characteristic
83	C₄⋊C₄	—	632	1	no	—
84	C₄⋊C₄	—	632	1	no	—
85	C₄²	#11929609	1	1	yes	characteristic
86	C₁₆	—	2	1	no	—
87	C₁₆	D₆₃₂	1	1	yes	characteristic
88	C₁₆	#11929613	1	1	yes	characteristic
89	Q₈	—	632	2	no	—
90	Q₈	—	632	2	no	—
91	C₂×C₄	—	632	2	no	—
92	C₂×C₄	#14579081	1	1	yes	characteristic
93	C₂×C₄	#14579102	1	1	yes	characteristic
94	C₂×C₄	#14579104	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	16	1	no	—
97	C₈	#14579077	1	1	yes	characteristic
98	C₈	#14579083	1	1	yes	characteristic
99	C₂²	#19098363	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	1264	2	no	—
102	C₄	#19098306	1	1	yes	characteristic
103	C₄	#19098375	1	1	yes	characteristic
104	C₄	#19098401	1	1	yes	characteristic
105	C₄	#19098403	1	1	yes	characteristic
106	C₂	#23761445	1	1	yes	characteristic
107	C₂	#23761580	1	1	yes	characteristic
108	C₂	#23761592	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23765653

C₂

yes

maximal, characteristic

C₄⋊(C₇₉⋊C₃₂)

C₂

yes

maximal, characteristic

C₇₉×#1371

C₂

yes

maximal, characteristic

C₂×Dic₆₃₂

—

C₂×Dic₆₃₂

C₄

yes

—

#19098943

—

C₂×C₇₉⋊C₃₂

—

C₄×C₁₆×C₇₉

C₂²

yes

characteristic

#335×C₇₉

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

#14579161

—

Dic₆₃₂

—

Dic₆₃₂

—

Dic₆₃₂

—

C₇₉⋊C₃₂

—

C₂×C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₉

D₄

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

SD₁₆

yes

characteristic

C₄²×C₇₉

D₈

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

D₈

yes

characteristic

C₁₆×C₇₉

SD₁₆

yes

characteristic

C₂×C₄×C₇₉

#102

yes

characteristic

C₂×C₄×C₇₉

D₁₆

yes

characteristic

C₂×C₄×C₇₉

SD₃₂

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

SD₆₄

yes

characteristic

C₄×C₇₉

Q₆₄

yes

characteristic

Dic₇₉

—

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₄⋊C₃₂

—

#1371

D₇₉

yes

characteristic

C₇₉

#7445

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

—

158

—

#494

—

158

—

C₂×C₃₂

—

158

—

C₄×C₁₆

C₂×D₇₉

yes

characteristic

#335

—

C₂×Q₁₆

—

316

—

C₂×Q₁₆

—

158

—

C₄⋊Q₈

—

316

—

Q₃₂

—

316

—

Q₃₂

—

316

—

Q₃₂

—

316

—

C₂×C₁₆

C₄×D₇₉

yes

characteristic

C₂×C₁₆

D₃₁₆

yes

characteristic

C₄⋊C₈

—

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

C₃₂

—

316

—

C₂×Q₈

—

316

—

Q₁₆

—

316

—

Q₁₆

—

316

—

Q₁₆

—

632

—

C₂×C₈

—

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

C₂×C₈

#11929611

yes

characteristic

C₄⋊C₄

—

632

—

C₄⋊C₄

—

632

—

C₄²

#11929609

yes

characteristic

C₁₆

—

C₁₆

D₆₃₂

yes

characteristic

C₁₆

#11929613

yes

characteristic

Q₈

—

632

—

Q₈

—

632

—

C₂×C₄

—

632

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

yes

100

C₄

—

101

C₄

—

1264

—

102

C₄

#19098306

yes

characteristic

103

C₄

#19098375

yes

characteristic

104

C₄

#19098401

yes

characteristic

105

C₄

#19098403

yes

characteristic

106

C₂

#23761445

yes

characteristic

107

C₂

#23761580

yes

characteristic

108

C₂

#23761592

yes

characteristic

	subgroup	G/H
center	C₂²	#19098363
commutator	C₂×C₁₆×C₇₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×#1371	C₂
socle, prime radical	C₂²×C₇₉	#357
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	#1371	D₇₉
hypocenter	C₇₉	#7445
LCS	G ▷ C₂×C₁₆×C₇₉ ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

subgroup

G/H

center

C₂²

#19098363

commutator

C₂×C₁₆×C₇₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₇₉

Fitting

C₇₉×#1371

C₂

socle, prime radical

C₂²×C₇₉

#357

cosocle

C₄×C₁₆×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₁₆×C₇₉ ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

N	H ≅ G/N	type
58. C₇₉	#7445	semidirect

H ≅ G/N

type

58. C₇₉

#7445

semidirect

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

subgroup	index
#23765653	2
C₄⋊(C₇₉⋊C₃₂)	2
C₇₉×#1371	2
#7445	79

subgroup

index

#23765653

C₄⋊(C₇₉⋊C₃₂)

C₇₉×#1371

#7445

Subgroups — #34175904

Conjugacy classes of subgroups

Complements

Maximal subgroups