Group #34060633 — subgroups

Subgroups — #34060633

Order 19072.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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×#18011982	C₂	1	2	yes	maximal
2	C₂×#18011981	C₂	1	2	yes	maximal
3	#23750630	C₂	1	1	yes	maximal, characteristic
4	#23750629	C₂	1	1	yes	maximal, characteristic
5	#97×D₁₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14558746	C₂²	1	2	yes	—
7	C₂×#14558746	C₂²	1	1	yes	characteristic
8	C₂×#14558746	C₂²	1	1	yes	characteristic
9	#18011982	—	2	4	no	—
10	#18011981	—	2	4	no	—
11	#18011978	—	2	2	no	—
12	C₄⋊#11924753	—	2	2	no	—
13	C₂×C₈×D₁₄₉	C₂²	1	2	yes	—
14	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
15	#18011822	C₄	1	1	yes	characteristic
16	#18011821	C₄	1	2	yes	—
17	#97×C₁₄₉	C₄	1	1	yes	characteristic
18	#14558746	—	2	2	no	—
19	#14558746	—	2	2	no	—
20	#14558746	—	2	2	no	—
21	#14558746	—	2	2	no	—
22	C₂×#11924753	—	2	2	no	—
23	C₂×#11924753	—	2	1	no	—
24	C₂×#11924753	—	2	1	no	—
25	C₂×C₄×D₁₄₉	Q₈	1	2	yes	—
26	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
27	C₂×#11924746	C₂×C₄	1	2	yes	—
28	C₈×D₁₄₉	D₄	1	4	yes	—
29	C₈×D₁₄₉	Q₈	1	4	yes	—
30	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₄₉	D₄	1	2	yes	—
32	C₂×C₈×C₁₄₉	C₂×C₄	1	2	yes	—
33	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
34	#11924753	—	4	2	no	—
35	#11924753	—	4	1	no	—
36	#11924753	—	4	1	no	—
37	C₂²×D₁₄₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×Dic₁₄₉	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
40	C₄×D₁₄₉	—	4	2	no	—
41	C₄×D₁₄₉	C₂×D₄	1	2	yes	—
42	C₄×D₁₄₉	C₂×Q₈	1	2	yes	—
43	#11924746	C₄⋊C₄	1	4	yes	—
44	C₂×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₁₄₉	C₄⋊C₄	1	4	yes	—
47	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₁₄₉	—	2	2	no	—
49	C₂×D₁₄₉	C₄⋊Q₈	1	2	yes	—
50	C₄×C₁₄₉	—	2	2	no	—
51	C₄×C₁₄₉	C₂×C₄⋊C₄	1	2	yes	—
52	Dic₁₄₉	—	2	2	no	—
53	Dic₁₄₉	#127	1	1	yes	characteristic
54	Dic₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
55	C₂×C₁₄₉	#384	1	1	yes	characteristic
56	C₂×C₁₄₉	#430	1	2	yes	—
57	D₁₄₉	—	2	2	no	—
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	2	no	—
62	#423	—	149	1	no	—
63	#423	—	149	1	no	—
64	C₂×#97	—	149	1	no	—
65	C₂×M₁₆	—	149	2	no	—
66	C₂×M₁₆	—	149	1	no	—
67	C₂×M₁₆	—	149	1	no	—
68	C₂²×C₈	—	149	2	no	—
69	C₂×C₄²	—	149	1	no	—
70	#108	—	298	4	no	—
71	#108	—	298	4	no	—
72	C₄⋊C₈	—	298	2	no	—
73	C₄⋊C₈	—	298	2	no	—
74	#97	—	149	2	no	—
75	#97	—	149	1	no	—
76	#97	#10597010	1	1	yes	characteristic
77	C₂²×C₄	—	149	2	no	—
78	C₂²×C₄	—	149	1	no	—
79	M₁₆	—	298	2	no	—
80	M₁₆	—	298	2	no	—
81	M₁₆	—	298	2	no	—
82	M₁₆	—	298	2	no	—
83	C₂×C₈	—	298	2	no	—
84	C₂×C₈	—	298	1	no	—
85	C₂×C₈	—	298	1	no	—
86	C₂×C₈	—	149	2	no	—
87	C₂×C₈	—	149	4	no	—
88	C₂×C₈	—	149	4	no	—
89	C₂×C₈	C₂×#10597010	1	2	yes	—
90	C₄²	—	149	2	no	—
91	C₄²	—	149	1	no	—
92	C₄²	C₂×#10597010	1	1	yes	characteristic
93	C₂³	—	149	1	no	—
94	C₂×C₄	—	596	2	no	—
95	C₂×C₄	—	149	2	no	—
96	C₂×C₄	—	149	1	no	—
97	C₂×C₄	—	149	2	no	—
98	C₂×C₄	—	149	2	no	—
99	C₂×C₄	C₄⋊#10597010	1	2	yes	—
100	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
101	C₈	—	596	2	no	—
102	C₈	—	596	1	no	—
103	C₈	—	596	1	no	—
104	C₈	—	149	4	no	—
105	C₈	C₄⋊#10597010	1	4	yes	—
106	C₂²	—	298	2	no	—
107	C₂²	—	149	2	no	—
108	C₂²	C₂×C₄⋊#10597010	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	298	2	no	—
111	C₄	—	149	1	no	—
112	C₄	—	149	1	no	—
113	C₄	C₂×C₄⋊#10597010	1	2	yes	—
114	C₂	—	298	2	no	—
115	C₂	#23750571	1	1	yes	characteristic
116	C₂	#23750640	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011982

C₂

yes

maximal

C₂×#18011981

C₂

yes

maximal

#23750630

C₂

yes

maximal, characteristic

#23750629

C₂

yes

maximal, characteristic

#97×D₁₄₉

C₂

yes

maximal, characteristic

C₂×#14558746

C₂²

yes

—

C₂×#14558746

C₂²

yes

characteristic

C₂×#14558746

C₂²

yes

—

—

—

—

C₂×C₈×D₁₄₉

C₂²

yes

—

C₄²×D₁₄₉

C₂²

yes

characteristic

#18011822

C₄

yes

characteristic

#18011821

C₄

yes

—

#97×C₁₄₉

C₄

yes

—

—

—

—

—

—

—

C₂×C₄×D₁₄₉

Q₈

yes

—

C₂×C₄×D₁₄₉

C₂³

yes

characteristic

C₂×#11924746

C₂×C₄

yes

—

C₈×D₁₄₉

D₄

yes

—

C₈×D₁₄₉

Q₈

yes

—

C₄×Dic₁₄₉

C₂×C₄

yes

characteristic

C₄×Dic₁₄₉

D₄

yes

—

C₂×C₈×C₁₄₉

C₂×C₄

yes

—

C₄²×C₁₄₉

C₂×C₄

yes

—

—

—

C₂²×D₁₄₉

C₂×Q₈

yes

characteristic

C₂×Dic₁₄₉

C₄⋊C₄

yes

—

C₂×Dic₁₄₉

C₂×D₄

yes

characteristic

C₄×D₁₄₉

—

C₄×D₁₄₉

C₂×D₄

yes

—

C₄×D₁₄₉

C₂×Q₈

yes

—

#11924746

C₄⋊C₄

yes

—

C₂×C₄×C₁₄₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₄₉

C₂²×C₄

yes

characteristic

C₈×C₁₄₉

C₄⋊C₄

yes

—

C₂²×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₄₉

—

C₂×D₁₄₉

C₄⋊Q₈

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

C₂×C₄⋊C₄

yes

—

Dic₁₄₉

—

Dic₁₄₉

#127

yes

characteristic

Dic₁₄₉

C₄⋊Q₈

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

D₁₄₉

—

C₁₄₉

#1849

yes

characteristic, complemented, Sylow

#1849

—

149

maximal, Sylow

C₂×#108

—

149

—

C₂×#108

—

149

—

#423

—

149

—

#423

—

149

—

C₂×#97

—

149

—

C₂×M₁₆

—

149

—

C₂×M₁₆

—

149

—

C₂×M₁₆

—

149

—

C₂²×C₈

—

149

—

C₂×C₄²

—

149

—

#108

—

298

—

#108

—

298

—

C₄⋊C₈

—

298

—

C₄⋊C₈

—

298

—

#97

—

149

—

#97

—

149

—

#97

#10597010

yes

characteristic

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

M₁₆

—

298

—

M₁₆

—

298

—

M₁₆

—

298

—

M₁₆

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

C₂×#10597010

yes

—

C₄²

—

149

—

C₄²

—

149

—

C₄²

C₂×#10597010

yes

characteristic

C₂³

—

149

—

C₂×C₄

—

596

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

C₄⋊#10597010

yes

—

100

C₂×C₄

C₂²×#10597010

yes

characteristic

101

C₈

—

596

—

102

C₈

—

596

—

103

C₈

—

596

—

104

C₈

—

149

—

105

C₈

C₄⋊#10597010

yes

—

106

C₂²

—

298

—

107

C₂²

—

149

—

108

C₂²

C₂×C₄⋊#10597010

yes

characteristic

109

C₄

—

110

C₄

—

298

—

111

C₄

—

149

—

112

C₄

—

149

—

113

C₄

C₂×C₄⋊#10597010

yes

—

114

C₂

—

298

—

115

C₂

#23750571

yes

characteristic

116

C₂

#23750640

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10597010
commutator	C₂×C₄×C₁₄₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10597010
Fitting	#97×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂×C₄⋊C₄
prime radical	C₂²×D₁₄₉	C₂×Q₈
cosocle	C₂×C₄×D₁₄₉	C₂³
hypercenter	#97	#10597010
hypocenter	C₁₄₉	#1849
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#10597010

commutator

C₂×C₄×C₁₄₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#10597010

Fitting

#97×C₁₄₉

C₄

socle

C₂²×C₁₄₉

C₂×C₄⋊C₄

prime radical

C₂²×D₁₄₉

C₂×Q₈

cosocle

C₂×C₄×D₁₄₉

C₂³

C₁₄₉

G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

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×#18011982	2
C₂×#18011981	2
#23750630	2
#23750629	2
#97×D₁₄₉	2
#1849	149

subgroup

index

#97×D₁₄₉

149

Subgroups — #34060633

Conjugacy classes of subgroups

Complements

Maximal subgroups