Group #49158947 — subgroups

Subgroups — #49158947

Order 37504.

248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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×#22627557	C₂	1	2	yes	maximal
2	C₂×#22627555	C₂	1	2	yes	maximal
3	C₂×C₄×#14556873	C₂	1	1	yes	maximal, characteristic
4	#34035995	C₂	1	1	yes	maximal, characteristic
5	#382×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14556873	C₂²	1	1	yes	characteristic
7	C₂²×#14556873	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₂₉₃	C₂²	1	2	yes	—
9	#22627557	—	2	4	no	—
10	#22627555	—	2	4	no	—
11	C₄×#14556873	C₄	1	4	yes	complemented
12	#22627531	—	2	2	no	—
13	C₂×C₄⋊C₄×C₂₉₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₂₉₃	C₂²	1	1	yes	characteristic
15	#95×C₂₉₃	—	2	2	no	—
16	C₂²×Dic₂₉₃	—	2	2	no	—
17	C₂×#14556873	C₂×C₄	1	2	yes	—
18	C₂×#14556873	C₂×C₄	1	2	yes	—
19	C₂×#14556873	D₄	1	2	yes	—
20	C₂×#14556873	D₄	1	2	yes	—
21	C₂×#14556873	Q₈	1	2	yes	—
22	C₂×#14556873	Q₈	1	2	yes	—
23	C₄⋊Dic₂₉₃	—	2	2	no	—
24	C₄⋊Dic₂₉₃	—	2	2	no	—
25	C₂²×C₄×C₂₉₃	—	2	2	no	—
26	C₂²×C₄×C₂₉₃	D₄	1	2	yes	—
27	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₂₉₃	—	2	2	no	—
29	C₄⋊C₄×C₂₉₃	—	2	2	no	—
30	C₄²×C₂₉₃	C₂×C₄	1	2	yes	—
31	C₄²×C₂₉₃	Q₈	1	2	yes	—
32	C₂×Dic₂₉₃	—	4	2	no	—
33	C₂×Dic₂₉₃	—	4	4	no	—
34	#14556873	C₄⋊C₄	1	4	yes	—
35	#14556873	C₄⋊C₄	1	4	yes	—
36	C₂³×C₂₉₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉₃	—	2	4	no	—
38	C₂×C₄×C₂₉₃	—	4	2	no	—
39	C₂×C₄×C₂₉₃	—	4	4	no	—
40	C₂×C₄×C₂₉₃	C₄⋊C₄	1	4	yes	—
41	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₂₉₃	#127	1	1	yes	characteristic
49	C₂²×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
50	C₂²×C₂₉₃	#135	1	4	yes	—
51	C₄×C₂₉₃	—	2	4	no	—
52	C₄×C₂₉₃	—	8	2	no	—
53	C₄×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
56	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
57	Dic₂₉₃	—	8	2	no	—
58	C₂×C₂₉₃	#384	1	1	yes	characteristic
59	C₂×C₂₉₃	#427	1	2	yes	—
60	C₂×C₂₉₃	#495	1	2	yes	—
61	C₂×C₂₉₃	#499	1	2	yes	—
62	C₂₉₃	#1846	1	1	yes	characteristic, complemented, Sylow
63	#1846	—	293	1	no	maximal, Sylow
64	C₂×#107	—	293	2	no	—
65	C₂×#106	—	293	2	no	—
66	C₂×C₄×C₈	—	293	1	no	—
67	#382	—	293	1	no	—
68	#382	D₂₉₃	1	1	yes	characteristic
69	C₂²×C₈	—	293	1	no	—
70	C₂²×C₈	—	293	1	no	—
71	C₂×C₄⋊C₄	—	293	2	no	—
72	C₂×C₄⋊C₄	C₂×D₂₉₃	1	2	yes	—
73	C₂×C₄²	C₂×D₂₉₃	1	1	yes	characteristic
74	#107	—	586	4	no	—
75	#106	—	586	4	no	—
76	C₄×C₈	—	293	4	no	—
77	#95	—	2	2	no	—
78	#95	—	586	2	no	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	586	2	no	—
81	C₂²×C₄	C₂²⋊D₂₉₃	1	2	yes	—
82	C₂²×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
83	C₂×C₈	—	293	2	no	—
84	C₂×C₈	—	293	2	no	—
85	C₂×C₈	—	293	2	no	—
86	C₂×C₈	—	293	2	no	—
87	C₂×C₈	—	293	2	no	—
88	C₂×C₈	—	293	2	no	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	586	2	no	—
92	C₄⋊C₄	—	586	2	no	—
93	C₄²	C₄×D₂₉₃	1	2	yes	—
94	C₄²	Dic₅₈₆	1	2	yes	—
95	C₂³	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	4	4	no	—
99	C₂×C₄	—	1172	2	no	—
100	C₂×C₄	—	1172	4	no	—
101	C₂×C₄	#17989781	1	4	yes	—
102	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
103	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
104	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
105	C₂×C₄	Q₈×D₂₉₃	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₂₉₃	1	1	yes	characteristic
107	C₂×C₄	C₂×Dic₅₈₆	1	1	yes	characteristic
108	C₈	—	293	4	no	—
109	C₈	—	293	4	no	—
110	C₂²	C₂×#17989781	1	1	yes	characteristic
111	C₂²	#22627620	1	1	yes	characteristic
112	C₂²	#22627622	1	1	yes	characteristic
113	C₂²	#22627644	1	4	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	8	2	no	—
116	C₄	—	2344	2	no	—
117	C₄	C₄⋊C₄×D₂₉₃	1	1	yes	characteristic
118	C₄	C₄⋊C₄×D₂₉₃	1	1	yes	characteristic
119	C₄	#22627623	1	1	yes	characteristic
120	C₄	#22627623	1	1	yes	characteristic
121	C₂	#34035998	1	1	yes	characteristic
122	C₂	#34036165	1	2	yes	—
123	C₂	#34036511	1	2	yes	—
124	C₂	#34036528	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22627557

C₂

yes

maximal

C₂×#22627555

C₂

yes

maximal

C₂×C₄×#14556873

C₂

yes

maximal, characteristic

#34035995

C₂

yes

maximal, characteristic

#382×C₂₉₃

C₂

yes

maximal, characteristic

C₂²×#14556873

C₂²

yes

characteristic

C₂²×#14556873

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉₃

C₂²

yes

—

#22627557

—

#22627555

—

C₄×#14556873

C₄

yes

complemented

#22627531

—

C₂×C₄⋊C₄×C₂₉₃

C₂²

yes

—

C₂×C₄²×C₂₉₃

C₂²

yes

characteristic

#95×C₂₉₃

—

C₂²×Dic₂₉₃

—

C₂×#14556873

C₂×C₄

yes

—

C₂×#14556873

C₂×C₄

yes

—

C₂×#14556873

D₄

yes

—

C₂×#14556873

D₄

yes

—

C₂×#14556873

Q₈

yes

—

C₂×#14556873

Q₈

yes

—

C₄⋊Dic₂₉₃

—

C₄⋊Dic₂₉₃

—

C₂²×C₄×C₂₉₃

—

C₂²×C₄×C₂₉₃

D₄

yes

—

C₂²×C₄×C₂₉₃

C₂³

yes

characteristic

C₄⋊C₄×C₂₉₃

—

C₄⋊C₄×C₂₉₃

—

C₄²×C₂₉₃

C₂×C₄

yes

—

C₄²×C₂₉₃

Q₈

yes

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

—

#14556873

C₄⋊C₄

yes

—

#14556873

C₄⋊C₄

yes

—

C₂³×C₂₉₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

C₄⋊C₄

yes

—

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

C₂×Q₈

yes

characteristic

C₂²×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉₃

#127

yes

characteristic

C₂²×C₂₉₃

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉₃

#135

yes

—

C₄×C₂₉₃

—

C₄×C₂₉₃

—

C₄×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉₃

C₄⋊Q₈

yes

characteristic

C₄×C₂₉₃

C₄⋊Q₈

yes

characteristic

Dic₂₉₃

—

C₂×C₂₉₃

#384

yes

characteristic

C₂×C₂₉₃

#427

yes

—

C₂×C₂₉₃

#495

yes

—

C₂×C₂₉₃

#499

yes

—

C₂₉₃

#1846

yes

characteristic, complemented, Sylow

#1846

—

293

maximal, Sylow

C₂×#107

—

293

—

C₂×#106

—

293

—

C₂×C₄×C₈

—

293

—

#382

—

293

—

#382

D₂₉₃

yes

characteristic

C₂²×C₈

—

293

—

C₂²×C₈

—

293

—

C₂×C₄⋊C₄

—

293

—

C₂×C₄⋊C₄

C₂×D₂₉₃

yes

—

C₂×C₄²

C₂×D₂₉₃

yes

characteristic

#107

—

586

—

#106

—

586

—

C₄×C₈

—

293

—

#95

—

#95

—

586

—

C₂²×C₄

—

C₂²×C₄

—

586

—

C₂²×C₄

C₂²⋊D₂₉₃

yes

—

C₂²×C₄

C₂²×D₂₉₃

yes

characteristic

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

586

—

C₄⋊C₄

—

586

—

C₄²

C₄×D₂₉₃

yes

—

C₄²

Dic₅₈₆

yes

—

C₂³

C₂×C₂²⋊D₂₉₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1172

—

100

C₂×C₄

—

1172

—

101

C₂×C₄

#17989781

yes

—

102

C₂×C₄

C₂×C₄×D₂₉₃

yes

characteristic

103

C₂×C₄

D₄×D₂₉₃

yes

characteristic

104

C₂×C₄

D₄×D₂₉₃

yes

characteristic

105

C₂×C₄

Q₈×D₂₉₃

yes

characteristic

106

C₂×C₄

Q₈×D₂₉₃

yes

characteristic

107

C₂×C₄

C₂×Dic₅₈₆

yes

characteristic

108

C₈

—

293

—

109

C₈

—

293

—

110

C₂²

C₂×#17989781

yes

characteristic

111

C₂²

#22627620

yes

characteristic

112

C₂²

#22627622

yes

characteristic

113

C₂²

#22627644

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

2344

—

117

C₄

C₄⋊C₄×D₂₉₃

yes

characteristic

118

C₄

C₄⋊C₄×D₂₉₃

yes

characteristic

119

C₄

#22627623

yes

characteristic

120

C₄

#22627623

yes

characteristic

121

C₂

#34035998

yes

characteristic

122

C₂

#34036165

yes

—

123

C₂

#34036511

yes

—

124

C₂

#34036528

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉₃
commutator	C₂×C₄×C₂₉₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉₃
Fitting	#382×C₂₉₃	C₂
socle, prime radical	C₂³×C₂₉₃	C₂×D₄
cosocle	C₂²×C₄×C₂₉₃	C₂³
hypercenter	#382	D₂₉₃
hypocenter	C₂₉₃	#1846
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉₃

commutator

C₂×C₄×C₂₉₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉₃

Fitting

#382×C₂₉₃

C₂

socle, prime radical

C₂³×C₂₉₃

C₂×D₄

cosocle

C₂²×C₄×C₂₉₃

C₂³

D₂₉₃

C₂₉₃

G ▷ C₂×C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
11. C₄×#14556873	C₄	semidirect
62. C₂₉₃	#1846	semidirect

H ≅ G/N

type

11. C₄×#14556873

C₄

semidirect

62. C₂₉₃

#1846

semidirect

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

subgroup	index
C₂×#22627557	2
C₂×#22627555	2
C₂×C₄×#14556873	2
#34035995	2
#382×C₂₉₃	2
#1846	293

subgroup

index

#382×C₂₉₃

293

Subgroups — #49158947

Conjugacy classes of subgroups

Complements

Maximal subgroups