Group #46825749 — subgroups

Subgroups — #46825749

Order 34432.

136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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	#31771628	C₂	1	1	yes	maximal, characteristic
2	D₂₆₉⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#31770660	C₂	1	1	yes	maximal, characteristic
4	C₂×D₂₆₉⋊C₈	C₄	1	2	yes	—
5	#22575520	—	2	1	no	—
6	#22575520	—	2	1	no	—
7	C₄⋊#14524137	—	2	1	no	—
8	#22575510	—	2	1	no	—
9	#22575508	C₄	1	2	yes	—
10	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic
11	#22575382	—	2	1	no	—
12	#22575365	—	2	1	no	—
13	#22575364	C₄	1	1	yes	characteristic
14	#97×C₂₆₉	C₄	1	1	yes	characteristic
15	D₂₆₉⋊C₈	—	4	2	no	—
16	C₂×#14524137	—	2	2	no	—
17	C₂×#14524137	—	2	2	no	—
18	C₂×C₄×D₂₆₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₂₆₉	D₄	1	1	yes	characteristic
20	C₂×C₄×D₂₆₉	Q₈	1	1	yes	characteristic
21	C₂×#14524130	—	2	1	no	—
22	C₄×Dic₂₆₉	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
24	C₄×Dic₂₆₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₂₆₉	—	2	1	no	—
26	C₄²×C₂₆₉	C₂×C₄	1	1	yes	characteristic
27	#14524137	—	4	2	no	—
28	#14524137	—	4	2	no	—
29	C₂²×D₂₆₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×Dic₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₂₆₉	C₄⋊C₄	1	1	yes	characteristic
33	C₄×D₂₆₉	—	2	2	no	—
34	C₄×D₂₆₉	—	2	1	no	—
35	C₄×D₂₆₉	—	2	1	no	—
36	C₄×D₂₆₉	—	4	1	no	—
37	#14524130	—	4	1	no	—
38	C₂×C₄×C₂₆₉	C₄²	1	1	yes	characteristic
39	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₂₆₉	—	4	1	no	—
42	C₂²×C₂₆₉	#95	1	1	yes	characteristic
43	C₂×D₂₆₉	—	2	1	no	—
44	C₂×D₂₆₉	—	2	1	no	—
45	C₂×D₂₆₉	#108	1	2	yes	—
46	C₄×C₂₆₉	—	2	1	no	—
47	C₄×C₂₆₉	—	2	1	no	—
48	C₄×C₂₆₉	—	2	1	no	—
49	Dic₂₆₉	—	2	1	no	—
50	Dic₂₆₉	—	2	1	no	—
51	Dic₂₆₉	#100	1	1	yes	characteristic
52	Dic₂₆₉	#101	1	1	yes	characteristic
53	C₂×C₂₆₉	H(3,ℤ/4)	1	1	yes	characteristic
54	C₂×C₂₆₉	#341	1	1	yes	characteristic
55	C₂×C₂₆₉	#343	1	1	yes	characteristic
56	D₂₆₉	—	2	2	no	—
57	C₂₆₉	#1290	1	1	yes	characteristic, complemented, Sylow
58	#1290	—	269	1	no	maximal, Sylow
59	#432	—	269	1	no	—
60	#432	—	269	1	no	—
61	C₂×C₄⋊C₈	—	269	1	no	—
62	C₂²×C₈	—	269	2	no	—
63	C₂×C₄²	—	269	1	no	—
64	C₄⋊C₈	—	538	1	no	—
65	C₄⋊C₈	—	538	1	no	—
66	C₄⋊C₈	—	538	1	no	—
67	C₄⋊C₈	—	538	1	no	—
68	C₂²⋊C₈	—	538	1	no	—
69	C₂²⋊C₈	—	538	1	no	—
70	#97	—	269	2	no	—
71	#97	—	269	1	no	—
72	#97	#11761640	1	1	yes	characteristic
73	C₂²×C₄	—	269	1	no	—
74	C₂²×C₄	—	269	1	no	—
75	C₂²×C₄	—	269	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	538	2	no	—
78	C₂×C₈	—	538	2	no	—
79	C₂×C₈	—	538	1	no	—
80	C₂×C₈	—	1076	2	no	—
81	C₄²	—	269	1	no	—
82	C₄²	—	269	1	no	—
83	C₄²	—	269	1	no	—
84	C₄²	C₂×#11761640	1	1	yes	characteristic
85	C₂³	—	269	1	no	—
86	C₂×C₄	—	269	1	no	—
87	C₂×C₄	—	269	1	no	—
88	C₂×C₄	—	269	1	no	—
89	C₂×C₄	—	538	1	no	—
90	C₂×C₄	—	538	1	no	—
91	C₂×C₄	—	538	2	no	—
92	C₂×C₄	—	1076	1	no	—
93	C₂×C₄	C₄×#11761640	1	1	yes	characteristic
94	C₂×C₄	C₂²⋊#11761640	1	1	yes	characteristic
95	C₂×C₄	C₄⋊#11761640	1	1	yes	characteristic
96	C₈	—	4	1	no	—
97	C₈	—	1076	1	no	—
98	C₈	—	1076	2	no	—
99	C₈	—	1076	2	no	—
100	C₂²	—	269	2	no	—
101	C₂²	—	538	1	no	—
102	C₂²	—	538	1	no	—
103	C₂²	(C₂×#11761640)⋊C₄	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	269	1	no	—
108	C₄	—	269	1	no	—
109	C₄	—	538	1	no	—
110	C₄	—	538	1	no	—
111	C₂	—	538	2	no	—
112	C₂	#31771472	1	1	yes	characteristic
113	C₂	#31771480	1	1	yes	characteristic
114	C₂	#31771484	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31771628

C₂

yes

maximal, characteristic

D₂₆₉⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

#31770660

C₂

yes

maximal, characteristic

C₂×D₂₆₉⋊C₈

C₄

yes

—

—

—

—

—

C₄

yes

—

C₄²×D₂₆₉

C₂²

yes

—

—

C₄

yes

characteristic

#97×C₂₆₉

C₄

yes

characteristic

D₂₆₉⋊C₈

—

C₂×#14524137

—

C₂×#14524137

—

C₂×C₄×D₂₆₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₆₉

D₄

yes

characteristic

C₂×C₄×D₂₆₉

Q₈

yes

characteristic

C₂×#14524130

—

C₄×Dic₂₆₉

C₂×C₄

yes

characteristic

C₄×Dic₂₆₉

D₄

yes

characteristic

C₄×Dic₂₆₉

D₄

yes

characteristic

C₂×C₈×C₂₆₉

—

C₄²×C₂₆₉

C₂×C₄

yes

characteristic

#14524137

—

#14524137

—

C₂²×D₂₆₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₆₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₆₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₆₉

C₄⋊C₄

yes

characteristic

C₄×D₂₆₉

—

C₄×D₂₆₉

—

C₄×D₂₆₉

—

C₄×D₂₆₉

—

#14524130

—

C₂×C₄×C₂₆₉

C₄²

yes

characteristic

C₂×C₄×C₂₆₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₆₉

C₄⋊C₄

yes

characteristic

C₈×C₂₆₉

—

C₂²×C₂₆₉

#95

yes

characteristic

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₂×D₂₆₉

#108

yes

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

Dic₂₆₉

—

Dic₂₆₉

—

Dic₂₆₉

yes

Dic₂₆₉

yes

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

D₂₆₉

—

C₂₆₉

#1290

yes

characteristic, complemented, Sylow

#1290

—

269

maximal, Sylow

#432

—

269

—

#432

—

269

—

C₂×C₄⋊C₈

—

269

—

C₂²×C₈

—

269

—

C₂×C₄²

—

269

—

C₄⋊C₈

—

538

—

C₄⋊C₈

—

538

—

C₄⋊C₈

—

538

—

C₄⋊C₈

—

538

—

C₂²⋊C₈

—

538

—

C₂²⋊C₈

—

538

—

#97

—

269

—

#97

—

269

—

#97

#11761640

yes

characteristic

C₂²×C₄

—

269

—

C₂²×C₄

—

269

—

C₂²×C₄

—

269

—

C₂×C₈

—

C₂×C₈

—

538

—

C₂×C₈

—

538

—

C₂×C₈

—

538

—

C₂×C₈

—

1076

—

C₄²

—

269

—

C₄²

—

269

—

C₄²

—

269

—

C₄²

C₂×#11761640

yes

characteristic

C₂³

—

269

—

C₂×C₄

—

269

—

C₂×C₄

—

269

—

C₂×C₄

—

269

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

—

1076

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

1076

—

C₈

—

1076

—

C₈

—

1076

—

100

C₂²

—

269

—

101

C₂²

—

538

—

102

C₂²

—

538

—

103

C₂²

(C₂×#11761640)⋊C₄

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

269

—

108

C₄

—

269

—

109

C₄

—

538

—

110

C₄

—

538

—

111

C₂

—

538

—

112

C₂

#31771472

yes

characteristic

113

C₂

#31771480

yes

characteristic

114

C₂

#31771484

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#11761640)⋊C₄
commutator	C₂×C₄×C₂₆₉	C₄²
Frattini	C₄²	C₂×#11761640
Fitting	#97×C₂₆₉	C₄
socle	C₂²×C₂₆₉	#95
prime radical	C₂²×D₂₆₉	C₄⋊C₄
cosocle	C₄²×D₂₆₉	C₂²
hypercenter	#97	#11761640
hypocenter	C₂₆₉	#1290
LCS	G ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#11761640)⋊C₄

commutator

C₂×C₄×C₂₆₉

C₄²

Frattini

C₄²

C₂×#11761640

Fitting

#97×C₂₆₉

C₄

socle

C₂²×C₂₆₉

#95

prime radical

C₂²×D₂₆₉

C₄⋊C₄

cosocle

C₄²×D₂₆₉

C₂²

C₂₆₉

G ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
57. C₂₆₉	#1290	semidirect

H ≅ G/N

type

57. C₂₆₉

#1290

semidirect

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

subgroup	index
#31771628	2
D₂₆₉⋊(C₄⋊C₈)	2
#31770660	2
#1290	269

subgroup

index

#31771628

D₂₆₉⋊(C₄⋊C₈)

#31770660

#1290

269

Subgroups — #46825749

Conjugacy classes of subgroups

Complements

Maximal subgroups