Group #16818216 — subgroups

Subgroups — #16818216

Order 3712.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#14271219	C₂	1	2	yes	maximal
3	#14270912	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270911	C₂	1	2	yes	maximal, complemented
5	C₂₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₂₉	C₄	1	2	yes	—
7	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	#11745306	C₄	1	2	yes	—
9	C₄⋊C₄×D₂₉	—	2	2	no	—
10	#11745250	—	2	2	no	—
11	C₄²×D₂₉	C₂²	1	1	yes	characteristic
12	#11745231	C₂²	1	1	yes	characteristic
13	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
14	#11745168	—	2	2	no	—
15	#11745163	—	2	2	no	—
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
18	Q₈×D₂₉	—	4	4	no	—
19	C₂×C₄×D₂₉	—	2	2	no	—
20	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₂₉	D₄	1	2	yes	—
22	C₂×Dic₅₈	—	2	2	no	—
23	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₂₉	—	2	2	no	—
25	C₄⋊C₄×C₂₉	—	2	2	no	—
26	C₄²×C₂₉	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₂₉	—	2	2	no	—
28	#90779	—	2	4	no	—
29	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₉	D₄	1	2	yes	—
31	C₂×#6597	—	2	2	no	—
32	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
33	Q₈×C₂₉	—	4	2	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
37	C₂×Dic₂₉	—	2	2	no	—
38	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×D₂₉	—	2	2	no	—
41	C₄×D₂₉	—	2	2	no	—
42	C₄×D₂₉	—	2	2	no	—
43	C₄×D₂₉	—	4	4	no	—
44	Dic₅₈	—	4	4	no	—
45	Dic₅₈	—	4	2	no	—
46	C₈×C₂₉	—	4	2	no	—
47	#6597	—	4	2	no	—
48	#1558	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂×D₂₉	—	2	2	no	—
51	C₂×D₂₉	#100	1	2	yes	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	—	4	2	no	—
54	C₄×C₂₉	#137	1	2	yes	—
55	C₄×C₂₉	#137	1	2	yes	—
56	Dic₂₉	—	2	1	no	—
57	Dic₂₉	—	2	2	no	—
58	Dic₂₉	—	4	2	no	—
59	C₂×C₄⋊Q₈	—	29	1	no	—
60	#432	—	29	2	no	—
61	#333	—	29	1	no	—
62	#333	—	29	2	no	—
63	#333	D₂₉	1	1	yes	characteristic, complemented
64	C₂×C₂₉	C₂×#100	1	1	yes	characteristic
65	C₂×C₂₉	#419	1	2	yes	—
66	D₂₉	—	2	2	no	—
67	C₂²×Q₈	—	29	2	no	—
68	C₄⋊Q₈	—	29	2	no	—
69	C₄⋊Q₈	—	29	1	no	—
70	C₄⋊Q₈	—	58	2	no	—
71	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
72	C₂×C₄⋊C₄	—	58	2	no	—
73	C₂×C₄²	—	29	1	no	—
74	C₄⋊C₈	—	29	2	no	—
75	C₄⋊C₈	C₂×D₂₉	1	2	yes	—
76	C₂²⋊C₈	—	58	2	no	—
77	#97	—	58	2	no	—
78	C₂₉	#1558	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	29	2	no	—
80	C₂×Q₈	—	58	2	no	—
81	C₂×Q₈	—	116	4	no	—
82	C₂×Q₈	C₄×D₂₉	1	2	yes	—
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	2	no	—
85	C₂²×C₄	—	58	2	no	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	58	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	58	4	no	—
90	C₄⋊C₄	—	58	2	no	—
91	C₄²	—	29	1	no	—
92	C₄²	—	29	2	no	—
93	C₄²	C₂²×D₂₉	1	1	yes	characteristic
94	C₂³	—	29	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	116	2	no	—
97	Q₈	—	116	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	29	2	no	—
100	C₂×C₄	—	29	1	no	—
101	C₂×C₄	—	58	2	no	—
102	C₂×C₄	—	58	2	no	—
103	C₂×C₄	—	58	2	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	—	116	4	no	—
106	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
107	C₂×C₄	D₄×D₂₉	1	2	yes	—
108	C₈	—	4	2	no	—
109	C₈	—	116	2	no	—
110	C₂²	—	29	2	no	—
111	C₂²	—	58	2	no	—
112	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	2	no	—
115	C₄	—	58	1	no	—
116	C₄	—	58	2	no	—
117	C₄	—	116	2	no	—
118	C₄	#11745277	1	2	yes	—
119	C₄	#11745280	1	2	yes	—
120	C₂	—	58	2	no	—
121	C₂	#100×D₂₉	1	1	yes	characteristic
122	C₂	#14271170	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₂₉

C₂

yes

maximal, characteristic

#14271219

C₂

yes

maximal

#14270912

C₂

yes

maximal, characteristic, complemented

#14270911

C₂

yes

maximal, complemented

C₂₉×#333

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₂₉

C₄

yes

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

#11745306

C₄

yes

—

C₄⋊C₄×D₂₉

—

#11745250

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₂²

yes

—

#11745168

—

#11745163

—

C₄⋊#6597

C₂²

yes

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

Q₈×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

#90779

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

—

C₂×#6597

—

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1558

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

#100

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#137

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

C₂×C₄⋊Q₈

—

—

—

—

D₂₉

yes

characteristic, complemented

C₂×C₂₉

C₂×#100

yes

characteristic

C₂×C₂₉

#419

yes

—

D₂₉

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₂₉

yes

—

C₂²⋊C₈

—

#97

—

C₂₉

#1558

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

116

—

C₂×Q₈

C₄×D₂₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

116

—

106

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

107

C₂×C₄

D₄×D₂₉

yes

—

108

C₈

—

109

C₈

—

116

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂²⋊C₄×D₂₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

116

—

118

C₄

#11745277

yes

—

119

C₄

#11745280

yes

—

120

C₂

—

121

C₂

#100×D₂₉

yes

characteristic

122

C₂

#14271170

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#333	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄²×C₂₉	C₂³
hypercenter	#333	D₂₉
hypocenter	C₂₉	#1558
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉

Fitting

C₂₉×#333

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄²×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
3. #14270912	C₂	semidirect
4. #14270911	C₂	semidirect
5. C₂₉×#333	C₂	semidirect
63. #333	D₂₉	semidirect
78. C₂₉	#1558	semidirect

H ≅ G/N

type

3. #14270912

C₂

semidirect

4. #14270911

C₂

semidirect

5. C₂₉×#333

C₂

semidirect

63. #333

D₂₉

semidirect

78. C₂₉

#1558

semidirect

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

subgroup	index
C₄⋊Q₈×D₂₉	2
#14271219	2
#14270912	2
#14270911	2
C₂₉×#333	2
#1558	29

subgroup

index

C₄⋊Q₈×D₂₉

C₂₉×#333

Subgroups — #16818216

Conjugacy classes of subgroups

Complements

Maximal subgroups