Group #16835416 — subgroups

Subgroups — #16835416

Order 3712.

188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 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	#14272167	C₂	1	2	yes	maximal
2	#14272039	C₂	1	4	yes	maximal
3	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#90796	C₂²	1	4	yes	—
5	C₂×C₈×D₂₉	C₂²	1	2	yes	—
6	C₄²×D₂₉	C₂²	1	1	yes	characteristic
7	C₄⋊#6599	—	2	2	no	—
8	C₄⋊#6599	—	2	2	no	—
9	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₄×#6597	C₄	1	1	yes	characteristic
12	C₂×C₄×D₂₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×D₂₉	Q₈	1	1	yes	characteristic
14	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
15	C₂×#6599	—	2	4	no	—
16	#90796	—	2	8	no	—
17	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
18	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₂₉	D₄	1	1	yes	characteristic
21	C₄×Dic₂₉	D₄	1	1	yes	characteristic
22	C₂×#6597	C₂×C₄	1	2	yes	—
23	C₈×D₂₉	—	2	4	no	—
24	C₂²×D₂₉	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
31	C₄×D₂₉	—	2	2	no	—
32	C₄×D₂₉	—	2	2	no	—
33	C₄×D₂₉	#41	1	4	yes	—
34	#6599	—	4	4	no	—
35	C₈×C₂₉	—	2	2	no	—
36	#6597	—	2	2	no	—
37	#1837	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×D₂₉	—	2	1	no	—
40	C₂×D₂₉	—	2	1	no	—
41	C₂×D₂₉	#125	1	2	yes	—
42	C₄×C₂₉	#108	1	2	yes	—
43	C₄×C₂₉	#108	1	2	yes	—
44	C₄×C₂₉	#117	1	2	yes	—
45	Dic₂₉	—	2	1	no	—
46	Dic₂₉	—	2	1	no	—
47	Dic₂₉	#124	1	2	yes	—
48	#423	—	29	2	no	—
49	C₂×C₄×C₈	—	29	1	no	—
50	#341	—	29	4	no	—
51	C₂×C₂₉	#382	1	1	yes	characteristic
52	C₂×C₂₉	C₂×#108	1	1	yes	characteristic
53	C₂×C₂₉	C₂×#108	1	1	yes	characteristic
54	D₂₉	—	2	2	no	—
55	C₂×M₁₆	—	29	4	no	—
56	C₂²×C₈	—	29	2	no	—
57	C₂×C₄²	—	29	1	no	—
58	C₄⋊C₈	—	58	2	no	—
59	C₄⋊C₈	—	58	2	no	—
60	C₄×C₈	—	29	2	no	—
61	C₄×C₈	—	29	1	no	—
62	C₄×C₈	#1181	1	1	yes	characteristic
63	C₂₉	#1837	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	29	1	no	—
65	C₂²×C₄	—	29	1	no	—
66	C₂²×C₄	—	29	1	no	—
67	M₁₆	—	58	8	no	—
68	C₂×C₈	—	29	2	no	—
69	C₂×C₈	—	58	4	no	—
70	C₂×C₈	—	58	4	no	—
71	C₂×C₈	C₂×#1181	1	2	yes	—
72	C₄²	—	29	1	no	—
73	C₄²	—	29	1	no	—
74	C₄²	—	29	1	no	—
75	C₄²	C₂×#1181	1	1	yes	characteristic
76	C₂³	—	29	1	no	—
77	C₂×C₄	—	29	1	no	—
78	C₂×C₄	—	29	4	no	—
79	C₂×C₄	—	29	1	no	—
80	C₂×C₄	—	29	1	no	—
81	C₂×C₄	—	58	2	no	—
82	C₂×C₄	—	58	2	no	—
83	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
84	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
85	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	58	2	no	—
88	C₈	—	116	4	no	—
89	C₂²	—	29	2	no	—
90	C₂²	—	58	1	no	—
91	C₂²	—	58	1	no	—
92	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
93	C₄	—	29	2	no	—
94	C₄	—	58	1	no	—
95	C₄	—	58	1	no	—
96	C₄	#11745211	1	2	yes	—
97	C₄	#11745212	1	2	yes	—
98	C₄	#11745345	1	2	yes	—
99	C₂	—	58	2	no	—
100	C₂	#14272107	1	1	yes	characteristic
101	C₂	C₂×#11745211	1	1	yes	characteristic
102	C₂	C₂×#11745212	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272167

C₂

yes

maximal

#14272039

C₂

yes

maximal

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×#90796

C₂²

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

C₄⋊#6599

—

C₄⋊#6599

—

C₄×C₈×C₂₉

C₄

yes

characteristic

C₈×Dic₂₉

C₄

yes

—

C₄×#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

characteristic

C₂×C₄×D₂₉

Q₈

yes

characteristic

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×#6599

—

#90796

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

—

C₂²×D₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

#41

yes

—

#6599

—

C₈×C₂₉

—

#6597

—

#1837

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

#125

yes

—

C₄×C₂₉

#108

yes

—

C₄×C₂₉

#108

yes

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#124

yes

—

#423

—

C₂×C₄×C₈

—

#341

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#1181

yes

characteristic

C₂₉

#1837

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#1181

yes

characteristic

C₈

—

C₈

—

C₈

—

116

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₄⋊#1181

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#11745211

yes

—

C₄

#11745212

yes

—

C₄

#11745345

yes

—

C₂

—

100

C₂

#14272107

yes

characteristic

101

C₂

C₂×#11745211

yes

characteristic

102

C₂

C₂×#11745212

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₂×Q₈
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1837
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₄×C₈×C₂₉

C₄

socle

C₂²×C₂₉

C₂×C₄⋊C₄

prime radical

C₂²×D₂₉

C₂×Q₈

cosocle

C₂×C₄×D₂₉

C₂³

C₄×C₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
63. C₂₉	#1837	semidirect

H ≅ G/N

type

63. C₂₉

#1837

semidirect

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

subgroup	index
#14272167	2
#14272039	2
C₄×C₈×D₂₉	2
#1837	29

subgroup

index

#14272167

#14272039

C₄×C₈×D₂₉

#1837

Subgroups — #16835416

Conjugacy classes of subgroups

Complements

Maximal subgroups