Group #34044864 — subgroups

Subgroups — #34044864

Order 19072.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#18011847	C₂	1	1	yes	maximal, characteristic
2	C₂×#18011846	C₂	1	2	yes	maximal
3	#23749648	C₂	1	2	yes	maximal
4	C₂×#18011821	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₁₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14558720	C₂²	1	2	yes	—
7	C₂²×#11924746	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
9	#18011847	—	2	2	no	—
10	#18011846	—	2	4	no	—
11	#18011840	—	2	4	no	—
12	#18011821	C₄	1	4	yes	—
13	C₂×M₁₆×C₁₄₉	C₂²	1	2	yes	—
14	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
15	#108×C₁₄₉	—	2	2	no	—
16	C₂²×Dic₁₄₉	Q₈	1	2	yes	—
17	#14558720	—	2	2	no	—
18	#14558720	—	2	2	no	—
19	C₂×#11924746	—	2	2	no	—
20	C₂×#11924746	C₂×C₄	1	2	yes	—
21	C₂×#11924746	D₄	1	2	yes	—
22	C₂×#11924746	Q₈	1	2	yes	—
23	C₄×Dic₁₄₉	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₄₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₁₄₉	—	2	2	no	—
27	M₁₆×C₁₄₉	—	2	2	no	—
28	C₂×C₈×C₁₄₉	—	2	2	no	—
29	C₂×C₈×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₁₄₉	D₄	1	2	yes	—
31	C₂×C₈×C₁₄₉	Q₈	1	2	yes	—
32	C₂×Dic₁₄₉	—	4	2	no	—
33	C₂×Dic₁₄₉	C₄⋊C₄	1	4	yes	—
34	#11924746	—	4	2	no	—
35	#11924746	C₄⋊C₄	1	4	yes	—
36	C₂³×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
43	C₈×C₁₄₉	—	4	2	no	—
44	C₈×C₁₄₉	C₄⋊C₄	1	4	yes	—
45	C₂²×C₁₄₉	—	2	2	no	—
46	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
49	C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₁₄₉	#127	1	1	yes	characteristic
52	C₄×C₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₁₄₉	—	2	4	no	—
54	C₂×C₁₄₉	—	2	1	no	—
55	C₂×C₁₄₉	—	2	1	no	—
56	C₂×C₁₄₉	#384	1	1	yes	characteristic
57	C₂×C₁₄₉	#430	1	2	yes	—
58	C₁₄₉	#1849	1	1	yes	characteristic, complemented, Sylow
59	#1849	—	149	1	no	maximal, Sylow
60	C₂×#108	—	149	2	no	—
61	C₂×#108	—	149	1	no	—
62	C₂×#108	D₁₄₉	1	1	yes	characteristic
63	#423	—	149	2	no	—
64	C₂×#97	—	149	1	no	—
65	C₂×M₁₆	—	149	2	no	—
66	C₂×M₁₆	C₂×D₁₄₉	1	2	yes	—
67	C₂²×C₈	—	149	1	no	—
68	C₂²×C₈	C₂×D₁₄₉	1	1	yes	characteristic
69	C₂×C₄²	—	149	1	no	—
70	#108	—	2	2	no	—
71	#108	—	298	4	no	—
72	#108	—	298	2	no	—
73	C₄⋊C₈	—	298	4	no	—
74	#97	—	149	4	no	—
75	C₂²×C₄	—	149	2	no	—
76	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	298	2	no	—
80	M₁₆	—	298	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	298	2	no	—
83	C₂×C₈	—	149	2	no	—
84	C₂×C₈	—	149	2	no	—
85	C₂×C₈	—	149	2	no	—
86	C₂×C₈	C₄×D₁₄₉	1	2	yes	—
87	C₂×C₈	C₂²⋊D₁₄₉	1	2	yes	—
88	C₂×C₈	Dic₂₉₈	1	2	yes	—
89	C₄²	—	149	2	no	—
90	C₄²	—	149	2	no	—
91	C₂³	Q₈×D₁₄₉	1	1	yes	characteristic
92	C₂×C₄	—	596	2	no	—
93	C₂×C₄	—	149	4	no	—
94	C₂×C₄	C₂×C₄×D₁₄₉	1	1	yes	characteristic
95	C₂×C₄	D₄×D₁₄₉	1	1	yes	characteristic
96	C₂×C₄	D₄×D₁₄₉	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₁₄₉	1	1	yes	characteristic
99	C₂×C₄	C₂×Dic₂₉₈	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	596	2	no	—
102	C₈	—	149	4	no	—
103	C₈	#14558715	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₁₄₉	1	1	yes	characteristic
106	C₂²	#18011909	1	1	yes	characteristic
107	C₂²	#18011910	1	1	yes	characteristic
108	C₄	—	298	4	no	—
109	C₄	C₄⋊C₄×D₁₄₉	1	1	yes	characteristic
110	C₄	C₂×#14558715	1	1	yes	characteristic
111	C₄	#18011907	1	1	yes	characteristic
112	C₄	#18011910	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#23749494	1	1	yes	characteristic
116	C₂	#23749672	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011847

C₂

yes

maximal, characteristic

C₂×#18011846

C₂

yes

maximal

#23749648

C₂

yes

maximal

C₂×#18011821

C₂

yes

maximal, characteristic

C₂×#108×C₁₄₉

C₂

yes

maximal, characteristic

C₂×#14558720

C₂²

yes

—

C₂²×#11924746

C₂²

yes

characteristic

C₂×C₄×Dic₁₄₉

C₂²

yes

—

—

—

C₄

yes

—

C₂×M₁₆×C₁₄₉

C₂²

yes

—

C₂²×C₈×C₁₄₉

C₂²

yes

characteristic

#108×C₁₄₉

—

C₂²×Dic₁₄₉

Q₈

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#11924746

D₄

yes

—

C₂×#11924746

Q₈

yes

—

C₄×Dic₁₄₉

C₂×C₄

yes

—

C₄×Dic₁₄₉

D₄

yes

—

C₂²×C₄×C₁₄₉

C₂³

yes

characteristic

M₁₆×C₁₄₉

—

M₁₆×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

C₂×C₄

yes

—

C₂×C₈×C₁₄₉

D₄

yes

—

C₂×C₈×C₁₄₉

Q₈

yes

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₄⋊C₄

yes

—

#11924746

—

#11924746

C₄⋊C₄

yes

—

C₂³×C₁₄₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₄₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₄₉

C₂×Q₈

yes

characteristic

C₈×C₁₄₉

—

C₈×C₁₄₉

C₄⋊C₄

yes

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₄₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₄₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₄₉

#127

yes

characteristic

C₄×C₁₄₉

C₄⋊Q₈

yes

characteristic

Dic₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

#384

yes

characteristic

C₂×C₁₄₉

#430

yes

—

C₁₄₉

#1849

yes

characteristic, complemented, Sylow

#1849

—

149

maximal, Sylow

C₂×#108

—

149

—

C₂×#108

—

149

—

C₂×#108

D₁₄₉

yes

characteristic

#423

—

149

—

C₂×#97

—

149

—

C₂×M₁₆

—

149

—

C₂×M₁₆

C₂×D₁₄₉

yes

—

C₂²×C₈

—

149

—

C₂²×C₈

C₂×D₁₄₉

yes

characteristic

C₂×C₄²

—

149

—

#108

—

#108

—

298

—

#108

—

298

—

C₄⋊C₈

—

298

—

#97

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂²×D₁₄₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

298

—

M₁₆

—

298

—

C₂×C₈

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

C₄×D₁₄₉

yes

—

C₂×C₈

C₂²⋊D₁₄₉

yes

—

C₂×C₈

Dic₂₉₈

yes

—

C₄²

—

149

—

C₄²

—

149

—

C₂³

Q₈×D₁₄₉

yes

characteristic

C₂×C₄

—

596

—

C₂×C₄

—

149

—

C₂×C₄

C₂×C₄×D₁₄₉

yes

characteristic

C₂×C₄

D₄×D₁₄₉

yes

characteristic

C₂×C₄

D₄×D₁₄₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₄₉

yes

characteristic

C₂×C₄

Q₈×D₁₄₉

yes

characteristic

C₂×C₄

C₂×Dic₂₉₈

yes

characteristic

100

C₈

—

101

C₈

—

596

—

102

C₈

—

149

—

103

C₈

#14558715

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₁₄₉

yes

characteristic

106

C₂²

#18011909

yes

characteristic

107

C₂²

#18011910

yes

characteristic

108

C₄

—

298

—

109

C₄

C₄⋊C₄×D₁₄₉

yes

characteristic

110

C₄

C₂×#14558715

yes

characteristic

111

C₄

#18011907

yes

characteristic

112

C₄

#18011910

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#23749494

yes

characteristic

116

C₂

#23749672

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₄₉
commutator	C₂×C₄×C₁₄₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₄₉
Fitting	C₂×#108×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₄₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₄₉	C₂³
hypercenter	C₂×#108	D₁₄₉
hypocenter	C₁₄₉	#1849
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₄₉

commutator

C₂×C₄×C₁₄₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₄₉

Fitting

C₂×#108×C₁₄₉

C₂

socle

C₂²×C₁₄₉

C₂×C₄⋊C₄

prime radical

C₂³×C₁₄₉

C₂×Q₈

cosocle

C₂²×C₄×C₁₄₉

C₂³

D₁₄₉

C₁₄₉

G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
58. C₁₄₉	#1849	semidirect

H ≅ G/N

type

58. C₁₄₉

#1849

semidirect

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

subgroup	index
C₂×#18011847	2
C₂×#18011846	2
#23749648	2
C₂×#18011821	2
C₂×#108×C₁₄₉	2
#1849	149

subgroup

index

C₂×#108×C₁₄₉

149

Subgroups — #34044864

Conjugacy classes of subgroups

Complements

Maximal subgroups