Group #16815480 — subgroups

Subgroups — C₄×C₂₉×C₄⋊C₈ #16815480

Order 3712.

316 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 240 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×C₂₉×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₉	C₂	1	2	yes	maximal
3	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#336	C₂	1	2	yes	maximal
5	C₂²×C₈×C₂₉	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₉	C₄	1	2	yes	—
7	C₂×C₄²×C₂₉	C₄	1	2	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×C₄⋊C₈	C₄	1	8	yes	direct product factor
12	C₄×C₈×C₂₉	—	2	4	no	—
13	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₂₉	—	2	4	no	—
19	C₂×C₈×C₂₉	—	2	4	no	—
20	C₂×C₈×C₂₉	C₂×C₄	1	8	yes	—
21	C₄²×C₂₉	—	2	4	no	—
22	C₄²×C₂₉	—	2	2	no	—
23	C₄²×C₂₉	C₈	1	8	yes	complemented
24	C₄²×C₂₉	C₂×C₄	1	4	yes	—
25	C₄²×C₂₉	D₄	1	2	yes	—
26	C₄²×C₂₉	Q₈	1	2	yes	—
27	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	2	no	—
29	C₂×C₄×C₂₉	—	2	2	no	—
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	C₄²	1	2	yes	—
32	C₂×C₄×C₂₉	C₄²	1	2	yes	—
33	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
34	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
35	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
37	C₂×C₄×C₂₉	M₁₆	1	4	yes	—
38	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#41	1	2	yes	—
42	C₈×C₂₉	—	2	8	no	—
43	C₄×C₄⋊C₈	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
45	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₂₉	#117	1	1	yes	characteristic
47	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
48	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
49	C₄×C₂₉	—	2	2	no	—
50	C₄×C₂₉	—	2	4	no	—
51	C₄×C₂₉	C₄×C₈	1	4	yes	complemented
52	C₄×C₂₉	C₄⋊C₈	1	8	yes	direct product factor
53	C₄×C₂₉	C₄×D₄	1	2	yes	—
54	C₄×C₂₉	C₄×Q₈	1	2	yes	—
55	C₂×C₄⋊C₈	C₂×C₂₉	1	2	yes	—
56	C₂×C₄×C₈	C₂×C₂₉	1	2	yes	—
57	C₄³	C₂×C₂₉	1	1	yes	characteristic
58	#336	C₂×C₂₉	1	2	yes	—
59	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
61	C₂×C₂₉	C₄×M₁₆	1	1	yes	characteristic
62	C₂×C₂₉	C₂×C₄⋊C₈	1	2	yes	—
63	C₂×C₂₉	#431	1	2	yes	—
64	C₂²×C₈	C₂²×C₂₉	1	4	yes	—
65	C₂×C₄²	C₄×C₂₉	1	2	yes	—
66	C₂×C₄²	C₄×C₂₉	1	2	yes	—
67	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
68	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
69	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
70	C₄⋊C₈	C₄×C₂₉	1	8	yes	direct product factor
71	C₄×C₈	—	2	4	no	—
72	C₂₉	C₄×C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
74	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
75	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
76	C₂²×C₄	C₂×C₄×C₂₉	1	2	yes	—
77	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	C₂×C₄×C₂₉	1	8	yes	—
81	C₄²	—	2	4	no	—
82	C₄²	—	2	2	no	—
83	C₄²	C₈×C₂₉	1	8	yes	complemented
84	C₄²	C₂×C₄×C₂₉	1	4	yes	—
85	C₄²	D₄×C₂₉	1	2	yes	—
86	C₄²	Q₈×C₂₉	1	2	yes	—
87	C₂³	C₂²×C₄×C₂₉	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₄²×C₂₉	1	2	yes	—
92	C₂×C₄	C₄²×C₂₉	1	2	yes	—
93	C₂×C₄	C₄⋊C₄×C₂₉	1	4	yes	—
94	C₂×C₄	C₂×C₈×C₂₉	1	4	yes	—
95	C₂×C₄	C₂×C₈×C₂₉	1	4	yes	—
96	C₂×C₄	C₂×C₈×C₂₉	1	4	yes	—
97	C₂×C₄	M₁₆×C₂₉	1	4	yes	—
98	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
99	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
100	C₂×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
101	C₂×C₄	#41×C₂₉	1	2	yes	—
102	C₈	—	2	8	no	—
103	C₂²	C₂×C₄²×C₂₉	1	1	yes	characteristic
104	C₂²	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
105	C₂²	C₂₉×#117	1	1	yes	characteristic
106	C₂²	C₂²×C₈×C₂₉	1	2	yes	—
107	C₂²	C₂×M₁₆×C₂₉	1	2	yes	—
108	C₄	—	2	4	no	—
109	C₄	—	2	2	no	—
110	C₄	C₄×C₈×C₂₉	1	4	yes	complemented
111	C₄	C₂₉×C₄⋊C₈	1	8	yes	direct product factor
112	C₄	C₄×D₄×C₂₉	1	2	yes	—
113	C₄	C₄×Q₈×C₂₉	1	2	yes	—
114	C₂	C₄×C₄⋊C₄×C₂₉	1	1	yes	characteristic
115	C₂	C₂×C₄×C₈×C₂₉	1	1	yes	characteristic
116	C₂	C₄×M₁₆×C₂₉	1	1	yes	characteristic
117	C₂	C₂×C₂₉×C₄⋊C₈	1	2	yes	—
118	C₂	C₂₉×#431	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₉×C₄⋊C₈

C₂

yes

maximal

C₂×C₄×C₈×C₂₉

C₂

yes

maximal

C₄³×C₂₉

C₂

yes

maximal, characteristic

C₂₉×#336

C₂

yes

maximal

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₄

yes

—

C₂×C₄²×C₂₉

C₄

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₄

yes

direct product factor

C₄×C₈×C₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₈

yes

complemented

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₈×C₂₉

—

C₄×C₄⋊C₈

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₂²×C₂₉

C₂²×C₈

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×C₈

yes

complemented

C₄×C₂₉

C₄⋊C₈

yes

direct product factor

C₄×C₂₉

C₄×D₄

yes

—

C₄×C₂₉

C₄×Q₈

yes

—

C₂×C₄⋊C₈

C₂×C₂₉

yes

—

C₂×C₄×C₈

C₂×C₂₉

yes

—

C₄³

C₂×C₂₉

yes

characteristic

#336

C₂×C₂₉

yes

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

C₂×C₄×C₈

yes

characteristic

C₂×C₂₉

C₄×M₁₆

yes

characteristic

C₂×C₂₉

C₂×C₄⋊C₈

yes

—

C₂×C₂₉

#431

yes

—

C₂²×C₈

C₂²×C₂₉

yes

—

C₂×C₄²

C₄×C₂₉

yes

—

C₂×C₄²

C₄×C₂₉

yes

—

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₂×C₄²

C₂²×C₂₉

yes

characteristic

C₄⋊C₈

C₄×C₂₉

yes

direct product factor

C₄×C₈

—

C₂₉

C₄×C₄⋊C₈

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₂×C₄×C₂₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₂₉

yes

—

C₂²×C₄

C₂×C₄×C₂₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₂₉

yes

—

C₂²×C₄

C₂³×C₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₄×C₂₉

yes

—

C₄²

—

C₄²

—

C₄²

C₈×C₂₉

yes

complemented

C₄²

C₂×C₄×C₂₉

yes

—

C₄²

D₄×C₂₉

yes

—

C₄²

Q₈×C₂₉

yes

—

C₂³

C₂²×C₄×C₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄²×C₂₉

yes

—

C₂×C₄

C₄²×C₂₉

yes

—

C₂×C₄

C₄⋊C₄×C₂₉

yes

—

C₂×C₄

C₂×C₈×C₂₉

yes

—

C₂×C₄

C₂×C₈×C₂₉

yes

—

C₂×C₄

C₂×C₈×C₂₉

yes

—

C₂×C₄

M₁₆×C₂₉

yes

—

C₂×C₄

C₂²×C₄×C₂₉

yes

—

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

100

C₂×C₄

C₂×Q₈×C₂₉

yes

characteristic

101

C₂×C₄

#41×C₂₉

yes

—

102

C₈

—

103

C₂²

C₂×C₄²×C₂₉

yes

characteristic

104

C₂²

C₂×C₄⋊C₄×C₂₉

yes

characteristic

105

C₂²

C₂₉×#117

yes

characteristic

106

C₂²

C₂²×C₈×C₂₉

yes

—

107

C₂²

C₂×M₁₆×C₂₉

yes

—

108

C₄

—

109

C₄

—

110

C₄

C₄×C₈×C₂₉

yes

complemented

111

C₄

C₂₉×C₄⋊C₈

yes

direct product factor

112

C₄

C₄×D₄×C₂₉

yes

—

113

C₄

C₄×Q₈×C₂₉

yes

—

114

C₂

C₄×C₄⋊C₄×C₂₉

yes

characteristic

115

C₂

C₂×C₄×C₈×C₂₉

yes

characteristic

116

C₂

C₄×M₁₆×C₂₉

yes

characteristic

117

C₂

C₂×C₂₉×C₄⋊C₈

yes

—

118

C₂

C₂₉×#431

yes

—

	subgroup	G/H
center	C₂×C₄²×C₂₉	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₉ ◁ G

subgroup

G/H

center

C₂×C₄²×C₂₉

C₂²

commutator

C₂

C₂×C₄×C₈×C₂₉

Frattini, cosocle

C₂²×C₄

C₂³×C₂₉

socle, prime radical

C₂³×C₂₉

C₂²×C₄

LCS

G ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
11. C₂₉×C₄⋊C₈	C₄	direct (N × H)
23. C₄²×C₂₉	C₈	semidirect
43. C₄×C₄⋊C₈	C₂₉	direct (N × H)
51. C₄×C₂₉	C₄×C₈	semidirect
52. C₄×C₂₉	C₄⋊C₈	direct (N × H)
70. C₄⋊C₈	C₄×C₂₉	direct (N × H)
72. C₂₉	C₄×C₄⋊C₈	direct (N × H)
83. C₄²	C₈×C₂₉	semidirect
110. C₄	C₄×C₈×C₂₉	semidirect
111. C₄	C₂₉×C₄⋊C₈	direct (N × H)

H ≅ G/N

type

11. C₂₉×C₄⋊C₈

C₄

direct (N × H)

23. C₄²×C₂₉

C₈

semidirect

43. C₄×C₄⋊C₈

C₂₉

direct (N × H)

51. C₄×C₂₉

C₄×C₈

semidirect

52. C₄×C₂₉

C₄⋊C₈

direct (N × H)

70. C₄⋊C₈

C₄×C₂₉

direct (N × H)

72. C₂₉

C₄×C₄⋊C₈

direct (N × H)

83. C₄²

C₈×C₂₉

semidirect

110. C₄

C₄×C₈×C₂₉

semidirect

111. C₄

C₂₉×C₄⋊C₈

direct (N × H)

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

subgroup	index
C₂×C₂₉×C₄⋊C₈	2
C₂×C₄×C₈×C₂₉	2
C₄³×C₂₉	2
C₂₉×#336	2
C₄×C₄⋊C₈	29

subgroup

index

C₂×C₂₉×C₄⋊C₈

C₂×C₄×C₈×C₂₉

C₄³×C₂₉

C₂₉×#336

C₄×C₄⋊C₈

Subgroups — C₄×C₂₉×C₄⋊C₈ #16815480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×C29×C4⋊C8 #16815480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₉×C₄⋊C₈ #16815480