Group #49159539 — subgroups

Subgroups — #49159539

Order 37504.

200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22627560	C₂	1	1	yes	maximal, characteristic
2	#34036156	C₂	1	2	yes	maximal
3	C₂×#22627534	C₂	1	1	yes	maximal, characteristic
4	#34035888	C₂	1	2	yes	maximal
5	#427×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#17989786	C₂²	1	2	yes	—
7	C₂²×#14556873	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉₃	C₂²	1	1	yes	characteristic
9	#22627560	—	2	2	no	—
10	C₄⋊#14556873	—	2	4	no	—
11	#22627534	—	2	2	no	—
12	C₂²×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
13	#117×C₂₉₃	C₂²	1	2	yes	—
14	#107×C₂₉₃	C₄	1	2	yes	complemented
15	#106×C₂₉₃	C₄	1	2	yes	complemented
16	C₂²×Dic₂₉₃	—	2	1	no	—
17	#17989786	—	2	2	no	—
18	#17989786	—	2	2	no	—
19	C₂×#14556873	—	2	1	no	—
20	C₂×#14556873	—	2	2	no	—
21	C₂×#14556873	—	2	1	no	—
22	C₂×#14556873	D₄	1	2	yes	—
23	C₄×Dic₂₉₃	—	2	1	no	—
24	C₄×Dic₂₉₃	Q₈	1	2	yes	—
25	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
26	C₂×C₈×C₂₉₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₂₉₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₂₉₃	D₄	1	2	yes	—
29	C₂×C₈×C₂₉₃	Q₈	1	2	yes	—
30	C₄⋊C₄×C₂₉₃	C₂×C₄	1	4	yes	—
31	C₂²⋊C₄×C₂₉₃	—	2	2	no	—
32	C₄²×C₂₉₃	—	2	2	no	—
33	C₂×Dic₂₉₃	—	2	2	no	—
34	C₂×Dic₂₉₃	—	4	2	no	—
35	#14556873	—	2	2	no	—
36	#14556873	—	4	2	no	—
37	C₂³×C₂₉₃	#41	1	1	yes	characteristic
38	C₂×C₄×C₂₉₃	—	2	4	no	—
39	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₂₉₃	#41	1	1	yes	characteristic
45	C₈×C₂₉₃	C₄⋊C₄	1	2	yes	—
46	C₈×C₂₉₃	C₄⋊C₄	1	2	yes	—
47	C₂²×C₂₉₃	—	2	2	no	—
48	C₂²×C₂₉₃	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₂₉₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₂₉₃	#125	1	1	yes	characteristic
51	C₄×C₂₉₃	—	4	4	no	—
52	C₄×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₂₉₃	C₄×Q₈	1	1	yes	characteristic
54	C₄×C₂₉₃	#121	1	1	yes	characteristic
55	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₂₉₃	—	4	2	no	—
57	C₂×C₂₉₃	—	2	1	no	—
58	C₂×C₂₉₃	—	2	1	no	—
59	C₂×C₂₉₃	#389	1	1	yes	characteristic
60	C₂×C₂₉₃	#444	1	2	yes	—
61	C₂₉₃	#1946	1	1	yes	characteristic, complemented, Sylow
62	#1946	—	293	1	no	maximal, Sylow
63	C₂×#108	—	293	1	no	—
64	#427	D₂₉₃	1	1	yes	characteristic
65	#424	—	293	2	no	—
66	C₂×#97	—	293	1	no	—
67	#339	—	293	2	no	—
68	C₂×M₁₆	—	293	2	no	—
69	C₂²×C₈	—	293	1	no	—
70	C₂²×C₈	C₂×D₂₉₃	1	1	yes	characteristic
71	#117	C₂×D₂₉₃	1	2	yes	—
72	C₂×C₄²	—	293	1	no	—
73	#108	—	586	2	no	—
74	#107	Dic₂₉₃	1	2	yes	complemented
75	#106	Dic₂₉₃	1	2	yes	complemented
76	C₄⋊C₈	—	586	4	no	—
77	#97	—	586	2	no	—
78	C₂²×C₄	—	586	1	no	—
79	C₂²×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
80	M₁₆	—	586	2	no	—
81	M₁₆	—	586	2	no	—
82	C₂×C₈	—	293	2	no	—
83	C₂×C₈	—	586	1	no	—
84	C₂×C₈	—	586	1	no	—
85	C₂×C₈	—	586	2	no	—
86	C₂×C₈	C₂×Dic₂₉₃	1	1	yes	characteristic
87	C₂×C₈	C₂×Dic₂₉₃	1	1	yes	characteristic
88	C₂×C₈	D₁₁₇₂	1	2	yes	—
89	C₂×C₈	Dic₅₈₆	1	2	yes	—
90	C₄⋊C₄	C₂×Dic₂₉₃	1	4	yes	—
91	C₂²⋊C₄	—	2	2	no	—
92	C₄²	—	2	2	no	—
93	C₄²	—	293	2	no	—
94	C₄²	—	586	1	no	—
95	C₂³	#17989801	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	586	2	no	—
98	C₂×C₄	—	1172	2	no	—
99	C₂×C₄	C₂²×Dic₂₉₃	1	1	yes	characteristic
100	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
101	C₂×C₄	C₂×D₁₁₇₂	1	1	yes	characteristic
102	C₂×C₄	Q₈×D₂₉₃	1	1	yes	characteristic
103	C₂×C₄	C₂×Dic₅₈₆	1	1	yes	characteristic
104	C₂×C₄	#17989803	1	1	yes	characteristic
105	C₈	—	586	2	no	—
106	C₈	—	1172	2	no	—
107	C₈	C₄⋊Dic₂₉₃	1	2	yes	—
108	C₈	C₄⋊Dic₂₉₃	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	D₄×Dic₂₉₃	1	1	yes	characteristic
111	C₂²	#22627604	1	1	yes	characteristic
112	C₂²	#22627615	1	1	yes	characteristic
113	C₄	—	4	4	no	—
114	C₄	—	1172	2	no	—
115	C₄	C₂×C₄⋊Dic₂₉₃	1	1	yes	characteristic
116	C₄	Q₈×Dic₂₉₃	1	1	yes	characteristic
117	C₄	#22627599	1	1	yes	characteristic
118	C₄	#22627623	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#34036028	1	1	yes	characteristic
122	C₂	#34036251	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22627560

C₂

yes

maximal, characteristic

#34036156

C₂

yes

maximal

C₂×#22627534

C₂

yes

maximal, characteristic

#34035888

C₂

yes

maximal

#427×C₂₉₃

C₂

yes

maximal, characteristic

C₂×#17989786

C₂²

yes

—

C₂²×#14556873

C₂²

yes

characteristic

C₂×C₄×Dic₂₉₃

C₂²

yes

—

—

—

C₂²×C₈×C₂₉₃

C₂²

yes

characteristic

#117×C₂₉₃

C₂²

yes

—

#107×C₂₉₃

C₄

yes

complemented

#106×C₂₉₃

C₄

yes

complemented

C₂²×Dic₂₉₃

—

—

—

—

—

—

D₄

yes

—

C₄×Dic₂₉₃

—

C₄×Dic₂₉₃

Q₈

yes

—

C₂²×C₄×C₂₉₃

C₂³

yes

characteristic

C₂×C₈×C₂₉₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉₃

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉₃

D₄

yes

—

C₂×C₈×C₂₉₃

Q₈

yes

—

C₄⋊C₄×C₂₉₃

C₂×C₄

yes

—

C₂²⋊C₄×C₂₉₃

—

C₄²×C₂₉₃

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

—

#14556873

—

#14556873

—

C₂³×C₂₉₃

#41

yes

characteristic

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉₃

#41

yes

characteristic

C₈×C₂₉₃

C₄⋊C₄

yes

—

C₈×C₂₉₃

C₄⋊C₄

yes

—

C₂²×C₂₉₃

—

C₂²×C₂₉₃

C₄×D₄

yes

characteristic

C₂²×C₂₉₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₉₃

#125

yes

characteristic

C₄×C₂₉₃

—

C₄×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉₃

C₄×Q₈

yes

characteristic

C₄×C₂₉₃

#121

yes

characteristic

C₄×C₂₉₃

C₄⋊Q₈

yes

characteristic

Dic₂₉₃

—

C₂×C₂₉₃

—

C₂×C₂₉₃

—

C₂×C₂₉₃

#389

yes

characteristic

C₂×C₂₉₃

#444

yes

—

C₂₉₃

#1946

yes

characteristic, complemented, Sylow

#1946

—

293

maximal, Sylow

C₂×#108

—

293

—

#427

D₂₉₃

yes

characteristic

#424

—

293

—

C₂×#97

—

293

—

#339

—

293

—

C₂×M₁₆

—

293

—

C₂²×C₈

—

293

—

C₂²×C₈

C₂×D₂₉₃

yes

characteristic

#117

C₂×D₂₉₃

yes

—

C₂×C₄²

—

293

—

#108

—

586

—

#107

Dic₂₉₃

yes

complemented

#106

Dic₂₉₃

yes

complemented

C₄⋊C₈

—

586

—

#97

—

586

—

C₂²×C₄

—

586

—

C₂²×C₄

C₂²×D₂₉₃

yes

characteristic

M₁₆

—

586

—

M₁₆

—

586

—

C₂×C₈

—

293

—

C₂×C₈

—

586

—

C₂×C₈

—

586

—

C₂×C₈

—

586

—

C₂×C₈

C₂×Dic₂₉₃

yes

characteristic

C₂×C₈

C₂×Dic₂₉₃

yes

characteristic

C₂×C₈

D₁₁₇₂

yes

—

C₂×C₈

Dic₅₈₆

yes

—

C₄⋊C₄

C₂×Dic₂₉₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

293

—

C₄²

—

586

—

C₂³

#17989801

yes

characteristic

C₂×C₄

—

C₂×C₄

—

586

—

C₂×C₄

—

1172

—

C₂×C₄

C₂²×Dic₂₉₃

yes

characteristic

100

C₂×C₄

D₄×D₂₉₃

yes

characteristic

101

C₂×C₄

C₂×D₁₁₇₂

yes

characteristic

102

C₂×C₄

Q₈×D₂₉₃

yes

characteristic

103

C₂×C₄

C₂×Dic₅₈₆

yes

characteristic

104

C₂×C₄

#17989803

yes

characteristic

105

C₈

—

586

—

106

C₈

—

1172

—

107

C₈

C₄⋊Dic₂₉₃

yes

—

108

C₈

C₄⋊Dic₂₉₃

yes

—

109

C₂²

—

110

C₂²

D₄×Dic₂₉₃

yes

characteristic

111

C₂²

#22627604

yes

characteristic

112

C₂²

#22627615

yes

characteristic

113

C₄

—

114

C₄

—

1172

—

115

C₄

C₂×C₄⋊Dic₂₉₃

yes

characteristic

116

C₄

Q₈×Dic₂₉₃

yes

characteristic

117

C₄

#22627599

yes

characteristic

118

C₄

#22627623

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#34036028

yes

characteristic

122

C₂

#34036251

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉₃
commutator	C₂×C₄×C₂₉₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉₃
Fitting	#427×C₂₉₃	C₂
socle	C₂²×C₂₉₃	C₄×D₄
prime radical	C₂³×C₂₉₃	#41
cosocle	C₂²×C₄×C₂₉₃	C₂³
hypercenter	#427	D₂₉₃
hypocenter	C₂₉₃	#1946
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₂₉₃

commutator

C₂×C₄×C₂₉₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉₃

Fitting

#427×C₂₉₃

C₂

socle

C₂²×C₂₉₃

C₄×D₄

prime radical

C₂³×C₂₉₃

#41

cosocle

C₂²×C₄×C₂₉₃

C₂³

D₂₉₃

C₂₉₃

G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
14. #107×C₂₉₃	C₄	semidirect
15. #106×C₂₉₃	C₄	semidirect
61. C₂₉₃	#1946	semidirect
74. #107	Dic₂₉₃	semidirect
75. #106	Dic₂₉₃	semidirect

H ≅ G/N

type

14. #107×C₂₉₃

C₄

semidirect

15. #106×C₂₉₃

C₄

semidirect

61. C₂₉₃

#1946

semidirect

74. #107

Dic₂₉₃

semidirect

75. #106

Dic₂₉₃

semidirect

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

subgroup	index
C₂×#22627560	2
#34036156	2
C₂×#22627534	2
#34035888	2
#427×C₂₉₃	2
#1946	293

subgroup

index

#427×C₂₉₃

293

Subgroups — #49159539

Conjugacy classes of subgroups

Complements

Maximal subgroups