Group #16818263 — subgroups

Subgroups — #16818263

Order 3712.

168 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14271187	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#6597	C₂	1	1	yes	maximal, characteristic
3	#14270914	C₂	1	4	yes	maximal, complemented
4	C₂₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90777	—	2	1	no	—
7	C₂²×#6597	—	2	1	no	—
8	C₂₉×C₄⋊C₈	C₄	1	2	yes	—
9	C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	2	yes	—
11	C₄⋊#6597	—	2	1	no	—
12	C₄⋊#6597	—	2	1	no	—
13	C₄⋊#6597	C₂²	1	2	yes	—
14	C₄⋊#6597	C₂²	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	Q₈	1	1	yes	characteristic
18	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
19	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₉	D₄	1	1	yes	characteristic
21	C₄²×C₂₉	Q₈	1	1	yes	characteristic
22	C₄²×C₂₉	C₂³	1	1	yes	characteristic
23	#90777	—	4	2	no	—
24	C₂×#6597	—	2	2	no	—
25	C₂×#6597	—	2	2	no	—
26	C₂×#6597	—	4	2	no	—
27	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	2	no	—
29	C₂×C₄×C₂₉	—	4	1	no	—
30	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
34	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₈×C₂₉	—	2	4	no	—
39	#6597	—	4	2	no	—
40	#6597	—	4	2	no	—
41	#1570	—	29	1	no	maximal, Sylow
42	C₂²×C₂₉	—	2	1	no	—
43	C₂²×C₂₉	—	2	1	no	—
44	C₂²×C₂₉	#106	1	2	yes	—
45	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₂₉	—	2	1	no	—
47	C₄×C₂₉	—	2	1	no	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	#106	1	2	yes	—
50	C₄×C₂₉	#131	1	2	yes	—
51	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
52	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
53	#431	D₂₉	1	1	yes	characteristic
54	#423	—	29	1	no	—
55	C₂×C₄⋊C₈	—	29	1	no	—
56	#334	—	29	4	no	—
57	C₂×C₂₉	—	2	2	no	—
58	C₂×C₂₉	#424	1	1	yes	characteristic
59	C₂×C₂₉	C₂×#106	1	1	yes	characteristic
60	C₂×C₂₉	#430	1	1	yes	characteristic
61	C₂×M₁₆	—	58	1	no	—
62	C₂²×C₈	—	58	1	no	—
63	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
64	C₄⋊C₈	—	29	2	no	—
65	C₄⋊C₈	—	29	2	no	—
66	C₄⋊C₈	—	58	1	no	—
67	C₄⋊C₈	—	58	1	no	—
68	C₄⋊C₈	Dic₂₉	1	2	yes	—
69	C₂²⋊C₈	Dic₂₉	1	2	yes	—
70	C₄×C₈	C₂×D₂₉	1	2	yes	—
71	C₂₉	#1570	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	Dic₅₈	1	1	yes	characteristic
73	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
74	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
75	M₁₆	—	116	2	no	—
76	C₂×C₈	—	58	2	no	—
77	C₂×C₈	—	58	2	no	—
78	C₂×C₈	—	116	2	no	—
79	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
80	C₄²	Dic₅₈	1	1	yes	characteristic
81	C₄²	D₁₁₆	1	1	yes	characteristic
82	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
83	C₄²	C₂²×D₂₉	1	1	yes	characteristic
84	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	#90773	1	2	yes	—
88	C₂×C₄	#90773	1	2	yes	—
89	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
90	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
91	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
92	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
93	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
95	C₈	—	2	4	no	—
96	C₈	—	116	2	no	—
97	C₈	—	116	2	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	#11745165	1	2	yes	—
101	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	#11745165	1	2	yes	—
106	C₄	C₂×#90773	1	1	yes	characteristic
107	C₄	C₂×#90773	1	1	yes	characteristic
108	C₄	#11745310	1	2	yes	—
109	C₂	—	2	2	no	—
110	C₂	#14271190	1	1	yes	characteristic
111	C₂	C₂×#11745165	1	1	yes	characteristic
112	C₂	#14271212	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271187

C₂

yes

maximal, characteristic

C₂×C₄⋊#6597

C₂

yes

maximal, characteristic

#14270914

C₂

yes

maximal, complemented

C₂₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

—

C₂²×#6597

—

C₂₉×C₄⋊C₈

C₄

yes

—

C₂₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₂₉

C₂²

yes

—

C₄⋊#6597

—

C₄⋊#6597

—

C₄⋊#6597

C₂²

yes

—

C₄⋊#6597

C₂²

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

Q₈

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

Q₈

yes

characteristic

C₄²×C₂₉

C₂³

yes

—

—

—

—

C₂³×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

SD₁₆

yes

—

C₂×C₄×C₂₉

SD₁₆

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#106

yes

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#106

yes

—

C₄×C₂₉

#131

yes

—

C₄×C₂₉

C₂×SD₁₆

yes

characteristic

C₄×C₂₉

C₂×SD₁₆

yes

characteristic

#431

D₂₉

yes

characteristic

#423

—

C₂×C₄⋊C₈

—

#334

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

Dic₂₉

yes

—

C₂²⋊C₈

Dic₂₉

yes

—

C₄×C₈

C₂×D₂₉

yes

—

C₂₉

#1570

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₅₈

yes

characteristic

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₂₉

yes

characteristic

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

116

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₄²

Dic₅₈

yes

characteristic

C₄²

D₁₁₆

yes

characteristic

C₄²

C₂×Dic₂₉

yes

characteristic

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#90773

yes

—

C₂×C₄

#90773

yes

—

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

C₂×C₄

C₂×Dic₅₈

yes

characteristic

C₂×C₄

C₂×D₁₁₆

yes

characteristic

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

C₈

—

C₈

—

116

—

C₈

—

116

—

C₂²

—

C₂²

—

100

C₂²

#11745165

yes

—

101

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#11745165

yes

—

106

C₄

C₂×#90773

yes

characteristic

107

C₄

C₂×#90773

yes

characteristic

108

C₄

#11745310

yes

—

109

C₂

—

110

C₂

#14271190

yes

characteristic

111

C₂

C₂×#11745165

yes

characteristic

112

C₂

#14271212

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#431	C₂
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂³×C₂₉	C₄⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#431	D₂₉
hypocenter	C₂₉	#1570
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

C₂×D₁₁₆

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#431

C₂

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂³×C₂₉

C₄⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #14270914	C₂	semidirect
71. C₂₉	#1570	semidirect

H ≅ G/N

type

3. #14270914

C₂

semidirect

71. C₂₉

#1570

semidirect

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

subgroup	index
#14271187	2
C₂×C₄⋊#6597	2
#14270914	2
C₂₉×#431	2
#1570	29

subgroup

index

#14271187

C₂×C₄⋊#6597

#14270914

C₂₉×#431

#1570

Subgroups — #16818263

Conjugacy classes of subgroups

Complements

Maximal subgroups