Group #16818632 — subgroups

Subgroups — #16818632

Order 3712.

206 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14271542	C₂	1	1	yes	maximal, characteristic
2	#14271458	C₂	1	2	yes	maximal
3	#14270912	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊#6597	C₂	1	2	yes	maximal
5	Q₈²×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂₉×C₄⋊Q₈	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	—	2	2	no	—
8	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₂₉	—	2	2	no	—
10	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
11	C₂×#90785	—	2	2	no	—
12	#11745231	C₂²	1	1	yes	characteristic
13	#11745183	—	2	2	no	—
14	#11745155	—	2	2	no	—
15	C₄⋊#6597	C₂²	1	2	yes	—
16	C₄×#6597	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₂₉	—	2	2	no	—
18	C₂×Q₈×C₂₉	D₄	1	2	yes	—
19	C₂×Q₈×C₂₉	D₄	1	2	yes	—
20	C₂×Dic₅₈	—	2	1	no	—
21	C₄⋊C₄×C₂₉	—	2	4	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	2	2	no	—
24	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
25	C₄²×C₂₉	—	2	2	no	—
26	C₄²×C₂₉	—	2	2	no	—
27	C₄²×C₂₉	C₂³	1	1	yes	characteristic
28	#90785	—	4	4	no	—
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₂×#6597	—	2	1	no	—
31	C₂×#6597	—	2	2	no	—
32	Q₈×C₂₉	—	2	2	no	—
33	Q₈×C₂₉	—	4	2	no	—
34	Q₈×C₂₉	—	8	2	no	—
35	Q₈×C₂₉	Q₁₆	1	4	yes	complemented
36	C₂×C₄×C₂₉	—	2	2	no	—
37	C₂×C₄×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
41	C₂×Dic₂₉	—	4	1	no	—
42	Dic₅₈	—	4	2	no	—
43	#6597	—	2	2	no	—
44	#6597	—	4	2	no	—
45	#1633	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	#120	1	1	yes	characteristic
47	C₄×C₂₉	—	2	4	no	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	4	2	no	—
50	C₄×C₂₉	—	4	2	no	—
51	C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
52	C₄×C₂₉	#137	1	2	yes	—
53	Dic₂₉	—	8	1	no	—
54	Q₈²	D₂₉	1	1	yes	characteristic
55	#494	—	29	1	no	—
56	#477	—	29	2	no	—
57	#333	—	29	1	no	—
58	Q₈⋊C₈	—	29	2	no	—
59	C₂×C₂₉	#451	1	2	yes	—
60	C₂×C₂₉	#453	1	1	yes	characteristic
61	C₂×Q₁₆	—	58	2	no	—
62	C₄⋊Q₈	—	2	2	no	—
63	C₄⋊Q₈	—	2	2	no	—
64	C₄⋊Q₈	—	29	1	no	—
65	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
66	C₄×Q₈	—	2	2	no	—
67	C₄×Q₈	C₂×D₂₉	1	2	yes	—
68	#107	—	58	2	no	—
69	C₄⋊C₈	—	29	2	no	—
70	#103	—	58	2	no	—
71	C₄×C₈	—	29	1	no	—
72	C₂₉	#1633	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	58	1	no	—
75	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
76	C₂×Q₈	C₂²⋊D₂₉	1	2	yes	—
77	Q₁₆	—	116	4	no	—
78	C₂×C₈	—	58	1	no	—
79	C₂×C₈	—	58	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄⋊C₄	C₂²⋊D₂₉	1	2	yes	—
85	C₄²	—	2	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	C₂²×D₂₉	1	1	yes	characteristic
88	Q₈	—	2	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	8	2	no	—
91	Q₈	—	116	2	no	—
92	Q₈	#90785	1	4	yes	complemented
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	116	1	no	—
97	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
99	C₈	—	58	2	no	—
100	C₈	—	116	2	no	—
101	C₂²	#11745315	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	2	no	—
106	C₄	—	232	1	no	—
107	C₄	#11745304	1	2	yes	—
108	C₄	C₂×#90785	1	2	yes	—
109	C₂	#14271319	1	2	yes	—
110	C₂	#14271331	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271542

C₂

yes

maximal, characteristic

#14271458

C₂

yes

maximal

#14270912

C₂

yes

maximal, characteristic

Q₈⋊#6597

C₂

yes

maximal

Q₈²×C₂₉

C₂

yes

maximal, characteristic

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×Q₈×C₂₉

—

C₄×Q₈×C₂₉

C₂²

yes

—

C₂×#90785

—

#11745231

C₂²

yes

—

—

C₂²

yes

—

C₄×#6597

C₂²

yes

characteristic

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×Q₈×C₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

#90785

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

Q₁₆

yes

complemented

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

—

Dic₅₈

—

—

—

—

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂×Q₁₆

yes

—

C₄×C₂₉

#137

yes

—

Dic₂₉

—

Q₈²

D₂₉

yes

—

—

—

Q₈⋊C₈

—

C₂×C₂₉

#451

yes

—

C₂×C₂₉

#453

yes

characteristic

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

C₂×D₂₉

yes

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₂₉

#1633

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₂₉

yes

—

C₂×Q₈

C₂²⋊D₂₉

yes

—

Q₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₂₉

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

116

—

Q₈

#90785

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

C₈

—

100

C₈

—

116

—

101

C₂²

#11745315

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

232

—

107

C₄

#11745304

yes

—

108

C₄

C₂×#90785

yes

—

109

C₂

#14271319

yes

—

110

C₂

#14271331

yes

characteristic

	subgroup	G/H
center	C₂²	#11745315
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	Q₈²×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	#120
hypercenter	Q₈²	D₂₉
hypocenter	C₂₉	#1633
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

subgroup

G/H

center

C₂²

#11745315

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting

Q₈²×C₂₉

C₂

socle, prime radical

C₂²×C₂₉

#120

hypercenter

Q₈²

D₂₉

hypocenter

C₂₉

#1633

LCS

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

N	H ≅ G/N	type
35. Q₈×C₂₉	Q₁₆	semidirect
72. C₂₉	#1633	semidirect
92. Q₈	#90785	semidirect

H ≅ G/N

type

35. Q₈×C₂₉

Q₁₆

semidirect

72. C₂₉

#1633

semidirect

92. Q₈

#90785

semidirect

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

subgroup	index
#14271542	2
#14271458	2
#14270912	2
Q₈⋊#6597	2
Q₈²×C₂₉	2
#1633	29

subgroup

index

Q₈²×C₂₉

Subgroups — #16818632

Conjugacy classes of subgroups

Complements

Maximal subgroups