Group #34046267 — subgroups

Subgroups — #34046267

Order 19072.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#23749674	C₂	1	1	yes	maximal, characteristic
2	#23749648	C₂	1	1	yes	maximal, characteristic
3	#23749395	C₂	1	2	yes	maximal
4	#23749384	C₂	1	2	yes	maximal
5	H(3,ℤ/4)×C₁₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14558720	C₂²	1	2	yes	—
7	C₂×#14558720	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
9	#18011847	—	2	2	no	—
10	#18011840	—	2	2	no	—
11	C₂×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
12	#117×C₁₄₉	C₂²	1	2	yes	—
13	C₂²×Dic₁₄₉	—	2	1	no	—
14	#14558720	—	2	2	no	—
15	#14558720	—	2	2	no	—
16	#14558720	—	2	2	no	—
17	C₂×#11924746	—	2	1	no	—
18	C₂×#11924746	—	2	2	no	—
19	C₄×Dic₁₄₉	—	2	1	no	—
20	C₄×Dic₁₄₉	Q₈	1	1	yes	characteristic
21	C₄×Dic₁₄₉	Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₁₄₉	—	2	2	no	—
24	C₂×C₈×C₁₄₉	D₄	1	2	yes	—
25	C₄⋊C₄×C₁₄₉	—	2	2	no	—
26	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
27	C₄²×C₁₄₉	—	2	2	no	—
28	C₂×Dic₁₄₉	—	2	1	no	—
29	C₂×Dic₁₄₉	—	2	1	no	—
30	C₂×Dic₁₄₉	—	4	2	no	—
31	#11924746	—	4	1	no	—
32	#11924746	—	4	2	no	—
33	C₂³×C₁₄₉	#41	1	1	yes	characteristic
34	C₂×C₄×C₁₄₉	—	4	2	no	—
35	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₄₉	#41	1	2	yes	—
38	C₂×C₄×C₁₄₉	#41	1	2	yes	—
39	C₈×C₁₄₉	—	2	2	no	—
40	C₂²×C₁₄₉	—	4	1	no	—
41	C₂²×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₁₄₉	#126	1	2	yes	—
43	C₄×C₁₄₉	—	8	2	no	—
44	C₄×C₁₄₉	#123	1	1	yes	characteristic
45	C₄×C₁₄₉	#124	1	1	yes	characteristic
46	C₄×C₁₄₉	#125	1	2	yes	—
47	Dic₁₄₉	—	2	2	no	—
48	Dic₁₄₉	—	4	1	no	—
49	C₂×C₁₄₉	—	2	1	no	—
50	C₂×C₁₄₉	—	2	2	no	—
51	C₂×C₁₄₉	#400	1	1	yes	characteristic
52	C₁₄₉	#2102	1	1	yes	characteristic, complemented, Sylow
53	#2102	—	149	1	no	maximal, Sylow
54	#430	—	149	1	no	—
55	#423	—	149	1	no	—
56	#344	—	149	2	no	—
57	#339	—	149	2	no	—
58	H(3,ℤ/4)	D₁₄₉	1	1	yes	characteristic
59	C₂×M₁₆	—	149	2	no	—
60	C₂×M₁₆	—	149	1	no	—
61	C₂×M₁₆	C₂×D₁₄₉	1	1	yes	characteristic
62	#117	C₂×D₁₄₉	1	2	yes	—
63	C₂×C₄²	—	149	1	no	—
64	#108	—	298	2	no	—
65	C₄⋊C₈	—	298	2	no	—
66	C₂²×C₄	—	298	1	no	—
67	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	298	2	no	—
70	M₁₆	—	298	2	no	—
71	M₁₆	—	298	2	no	—
72	C₂×C₈	—	298	1	no	—
73	C₂×C₈	—	298	2	no	—
74	C₂×C₈	D₅₉₆	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	298	1	no	—
79	C₄²	—	149	1	no	—
80	C₄²	—	149	1	no	—
81	C₂³	#14558735	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	298	1	no	—
84	C₂×C₄	—	298	1	no	—
85	C₂×C₄	—	596	2	no	—
86	C₂×C₄	C₂×D₅₉₆	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₁₄₉	1	1	yes	characteristic
88	C₂×C₄	#14558735	1	2	yes	—
89	C₂×C₄	#14558736	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	596	1	no	—
92	C₈	—	596	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#18011891	1	1	yes	characteristic
95	C₂²	#18011904	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	298	2	no	—
98	C₄	—	596	1	no	—
99	C₄	#18011895	1	1	yes	characteristic
100	C₄	#18011899	1	1	yes	characteristic
101	C₄	#18011901	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#23749565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23749674

C₂

yes

maximal, characteristic

#23749648

C₂

yes

maximal, characteristic

#23749395

C₂

yes

maximal

#23749384

C₂

yes

maximal

H(3,ℤ/4)×C₁₄₉

C₂

yes

maximal, characteristic

C₂×#14558720

C₂²

yes

—

C₂×#14558720

C₂²

yes

characteristic

C₂×C₄×Dic₁₄₉

C₂²

yes

characteristic

#18011847

—

#18011840

—

C₂×M₁₆×C₁₄₉

C₂²

yes

characteristic

#117×C₁₄₉

C₂²

yes

—

C₂²×Dic₁₄₉

—

—

—

—

—

—

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

Q₈

yes

characteristic

C₄×Dic₁₄₉

Q₈

yes

characteristic

C₂²×C₄×C₁₄₉

C₂³

yes

characteristic

M₁₆×C₁₄₉

—

C₂×C₈×C₁₄₉

D₄

yes

—

C₄⋊C₄×C₁₄₉

—

C₂²⋊C₄×C₁₄₉

—

C₄²×C₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

#11924746

—

#11924746

—

C₂³×C₁₄₉

#41

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₄₉

#41

yes

—

C₂×C₄×C₁₄₉

#41

yes

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₄₉

#126

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

yes

C₄×C₁₄₉

yes

C₄×C₁₄₉

yes

—

Dic₁₄₉

—

Dic₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

#400

yes

characteristic

C₁₄₉

#2102

yes

characteristic, complemented, Sylow

#2102

—

149

maximal, Sylow

#430

—

149

—

#423

—

149

—

#344

—

149

—

#339

—

149

—

H(3,ℤ/4)

D₁₄₉

yes

characteristic

C₂×M₁₆

—

149

—

C₂×M₁₆

—

149

—

C₂×M₁₆

C₂×D₁₄₉

yes

characteristic

#117

C₂×D₁₄₉

yes

—

C₂×C₄²

—

149

—

#108

—

298

—

C₄⋊C₈

—

298

—

C₂²×C₄

—

298

—

C₂²×C₄

C₂²×D₁₄₉

yes

characteristic

M₁₆

—

M₁₆

—

298

—

M₁₆

—

298

—

M₁₆

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

D₅₉₆

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

298

—

C₄²

—

149

—

C₄²

—

149

—

C₂³

#14558735

yes

characteristic

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

596

—

C₂×C₄

C₂×D₅₉₆

yes

characteristic

C₂×C₄

Q₈×D₁₄₉

yes

characteristic

C₂×C₄

#14558735

yes

—

C₂×C₄

#14558736

yes

—

C₈

—

C₈

—

596

—

C₈

—

596

—

C₂²

—

C₂²

#18011891

yes

characteristic

C₂²

#18011904

yes

—

C₄

—

C₄

—

298

—

C₄

—

596

—

C₄

#18011895

yes

characteristic

100

C₄

#18011899

yes

characteristic

101

C₄

#18011901

yes

—

102

C₂

—

103

C₂

—

104

C₂

#23749565

yes

characteristic

	subgroup	G/H
center	C₄	#18011899
commutator, cosocle	C₂²×C₄×C₁₄₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₄₉
Fitting	H(3,ℤ/4)×C₁₄₉	C₂
socle	C₂×C₁₄₉	#400
prime radical	C₂³×C₁₄₉	#41
hypercenter	H(3,ℤ/4)	D₁₄₉
hypocenter	C₁₄₉	#2102
LCS	G ▷ C₂²×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#18011899

commutator, cosocle

C₂²×C₄×C₁₄₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₄₉

Fitting

H(3,ℤ/4)×C₁₄₉

C₂

C₂×C₁₄₉

C₂³×C₁₄₉

D₁₄₉

C₁₄₉

G ▷ C₂²×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
52. C₁₄₉	#2102	semidirect

H ≅ G/N

type

52. C₁₄₉

#2102

semidirect

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

subgroup	index
#23749674	2
#23749648	2
#23749395	2
#23749384	2
H(3,ℤ/4)×C₁₄₉	2
#2102	149

subgroup

index

H(3,ℤ/4)×C₁₄₉

149

Subgroups — #34046267

Conjugacy classes of subgroups

Complements

Maximal subgroups