Group #49157446 — subgroups

Subgroups — #49157446

Order 37504.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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	#34036680	C₂	1	1	yes	maximal, characteristic
2	#34036181	C₂	1	2	yes	maximal, complemented
3	#34035878	C₂	1	1	yes	maximal, characteristic, complemented
4	#34035872	C₂	1	2	yes	maximal, complemented
5	#333×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17989803	C₄	1	2	yes	—
7	#22627621	C₂²	1	1	yes	characteristic
8	#22627613	C₄	1	2	yes	—
9	#22627599	—	2	2	no	—
10	#22627586	—	2	2	no	—
11	C₄²×D₂₉₃	C₂²	1	1	yes	characteristic
12	C₄⋊#14556873	C₂²	1	2	yes	—
13	#22627536	—	2	2	no	—
14	C₈×Dic₂₉₃	—	2	2	no	—
15	C₄⋊Q₈×C₂₉₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₂₉₃	C₂²	1	2	yes	—
17	#17989803	—	4	4	no	—
18	C₂×D₁₁₇₂	—	2	2	no	—
19	C₂×D₁₁₇₂	—	2	2	no	—
20	C₂×D₁₁₇₂	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₂₉₃	—	2	2	no	—
22	C₂×C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₂₉₃	D₄	1	2	yes	—
24	C₂×#14556873	—	2	2	no	—
25	#17989779	—	2	4	no	—
26	C₄×Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₂₉₃	D₄	1	2	yes	—
28	C₂×Q₈×C₂₉₃	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₂₉₃	—	2	2	no	—
30	C₄⋊C₄×C₂₉₃	—	2	2	no	—
31	C₄²×C₂₉₃	C₂³	1	1	yes	characteristic
32	C₂²×D₂₉₃	—	2	2	no	—
33	C₂²×D₂₉₃	C₂²⋊C₄	1	1	yes	characteristic
34	D₁₁₇₂	—	4	2	no	—
35	D₁₁₇₂	—	4	4	no	—
36	D₁₁₇₂	—	4	2	no	—
37	D₁₁₇₂	—	4	2	no	—
38	C₂×Dic₂₉₃	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₂₉₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×D₂₉₃	—	2	2	no	—
41	C₄×D₂₉₃	—	2	2	no	—
42	C₄×D₂₉₃	—	2	2	no	—
43	C₄×D₂₉₃	—	4	4	no	—
44	#14556873	—	4	2	no	—
45	Q₈×C₂₉₃	—	4	2	no	—
46	C₂×C₄×C₂₉₃	—	2	2	no	—
47	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉₃	C₂×D₄	1	2	yes	—
49	C₈×C₂₉₃	—	4	2	no	—
50	C₂²×C₂₉₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×D₂₉₃	—	2	1	no	—
52	C₂×D₂₉₃	—	2	2	no	—
53	C₂×D₂₉₃	—	4	2	no	—
54	C₂×D₂₉₃	—	4	4	no	—
55	C₄×C₂₉₃	—	2	1	no	—
56	C₄×C₂₉₃	—	4	2	no	—
57	C₄×C₂₉₃	#135	1	2	yes	—
58	C₄×C₂₉₃	#135	1	2	yes	—
59	Dic₂₉₃	—	2	2	no	—
60	Dic₂₉₃	#100	1	2	yes	—
61	C₂×C₂₉₃	C₂×#100	1	1	yes	characteristic
62	C₂×C₂₉₃	#416	1	2	yes	—
63	D₂₉₃	—	4	1	no	—
64	D₂₉₃	—	8	2	no	—
65	C₂₉₃	#1543	1	1	yes	characteristic, complemented, Sylow
66	#1543	—	293	1	no	maximal, Sylow
67	#532	—	293	1	no	—
68	#431	—	293	2	no	—
69	#333	—	293	1	no	—
70	#333	D₂₉₃	1	1	yes	characteristic, complemented
71	#331	—	293	2	no	—
72	C₂×#41	—	293	2	no	—
73	C₄⋊Q₈	C₂×D₂₉₃	1	1	yes	characteristic
74	#127	—	293	1	no	—
75	#124	—	293	2	no	—
76	#121	—	586	2	no	—
77	C₄×D₄	—	586	2	no	—
78	C₂×C₄²	—	293	1	no	—
79	C₄⋊C₈	—	293	2	no	—
80	C₄⋊C₈	C₂×D₂₉₃	1	2	yes	—
81	C₂²⋊C₈	—	586	2	no	—
82	C₄×C₈	—	586	2	no	—
83	#41	—	1172	4	no	—
84	C₂×Q₈	C₄×D₂₉₃	1	2	yes	—
85	C₂×D₄	—	293	2	no	—
86	C₂×D₄	—	586	2	no	—
87	C₂×D₄	—	586	2	no	—
88	C₂²×C₄	—	293	1	no	—
89	C₂²×C₄	—	293	2	no	—
90	C₂²×C₄	—	586	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	586	2	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₂²⋊C₄	—	586	4	no	—
95	C₄²	—	293	1	no	—
96	C₄²	—	293	2	no	—
97	C₄²	C₂²×D₂₉₃	1	1	yes	characteristic
98	C₂³	—	293	1	no	—
99	C₂³	—	586	2	no	—
100	Q₈	—	4	2	no	—
101	D₄	—	1172	2	no	—
102	D₄	—	1172	4	no	—
103	D₄	—	1172	2	no	—
104	D₄	—	1172	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	293	1	no	—
107	C₂×C₄	—	293	2	no	—
108	C₂×C₄	—	586	2	no	—
109	C₂×C₄	—	586	2	no	—
110	C₂×C₄	—	586	2	no	—
111	C₂×C₄	—	1172	4	no	—
112	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
113	C₂×C₄	D₄×D₂₉₃	1	2	yes	—
114	C₈	—	4	2	no	—
115	C₈	—	1172	2	no	—
116	C₂²	—	586	1	no	—
117	C₂²	—	586	2	no	—
118	C₂²	—	1172	2	no	—
119	C₂²	—	1172	4	no	—
120	C₂²	C₂²⋊C₄×D₂₉₃	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	4	2	no	—
123	C₄	—	293	2	no	—
124	C₄	—	586	2	no	—
125	C₄	#22627645	1	2	yes	—
126	C₄	#22627647	1	2	yes	—
127	C₂	—	2344	2	no	—
128	C₂	—	1172	1	no	—
129	C₂	#100×D₂₉₃	1	1	yes	characteristic
130	C₂	#34036124	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#34036680

C₂

yes

maximal, characteristic

#34036181

C₂

yes

maximal, complemented

#34035878

C₂

yes

maximal, characteristic, complemented

#34035872

C₂

yes

maximal, complemented

#333×C₂₉₃

C₂

yes

maximal, characteristic, complemented

C₂×#17989803

C₄

yes

—

#22627621

C₂²

yes

characteristic

#22627613

C₄

yes

—

#22627599

—

#22627586

—

C₄²×D₂₉₃

C₂²

yes

characteristic

C₄⋊#14556873

C₂²

yes

—

#22627536

—

C₈×Dic₂₉₃

—

C₄⋊Q₈×C₂₉₃

C₂²

yes

characteristic

C₄⋊C₈×C₂₉₃

C₂²

yes

—

#17989803

—

C₂×D₁₁₇₂

—

C₂×D₁₁₇₂

—

C₂×D₁₁₇₂

C₂×C₄

yes

—

C₂×C₄×D₂₉₃

—

C₂×C₄×D₂₉₃

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉₃

D₄

yes

—

C₂×#14556873

—

#17989779

—

C₄×Dic₂₉₃

C₂×C₄

yes

characteristic

C₄×Dic₂₉₃

D₄

yes

—

C₂×Q₈×C₂₉₃

C₂×C₄

yes

—

C₂×C₈×C₂₉₃

—

C₄⋊C₄×C₂₉₃

—

C₄²×C₂₉₃

C₂³

yes

characteristic

C₂²×D₂₉₃

—

C₂²×D₂₉₃

C₂²⋊C₄

yes

characteristic

D₁₁₇₂

—

D₁₁₇₂

—

D₁₁₇₂

—

D₁₁₇₂

—

C₂×Dic₂₉₃

C₂²⋊C₄

yes

—

C₂×Dic₂₉₃

C₂²⋊C₄

yes

characteristic

C₄×D₂₉₃

—

C₄×D₂₉₃

—

C₄×D₂₉₃

—

C₄×D₂₉₃

—

#14556873

—

Q₈×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉₃

C₂×D₄

yes

—

C₈×C₂₉₃

—

C₂²×C₂₉₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉₃

—

C₂×D₂₉₃

—

C₂×D₂₉₃

—

C₂×D₂₉₃

—

C₄×C₂₉₃

—

C₄×C₂₉₃

—

C₄×C₂₉₃

#135

yes

—

C₄×C₂₉₃

#135

yes

—

Dic₂₉₃

—

Dic₂₉₃

#100

yes

—

C₂×C₂₉₃

C₂×#100

yes

characteristic

C₂×C₂₉₃

#416

yes

—

D₂₉₃

—

D₂₉₃

—

C₂₉₃

#1543

yes

characteristic, complemented, Sylow

#1543

—

293

maximal, Sylow

#532

—

293

—

#431

—

293

—

#333

—

293

—

#333

D₂₉₃

yes

characteristic, complemented

#331

—

293

—

C₂×#41

—

293

—

C₄⋊Q₈

C₂×D₂₉₃

yes

characteristic

#127

—

293

—

#124

—

293

—

#121

—

586

—

C₄×D₄

—

586

—

C₂×C₄²

—

293

—

C₄⋊C₈

—

293

—

C₄⋊C₈

C₂×D₂₉₃

yes

—

C₂²⋊C₈

—

586

—

C₄×C₈

—

586

—

#41

—

1172

—

C₂×Q₈

C₄×D₂₉₃

yes

—

C₂×D₄

—

293

—

C₂×D₄

—

586

—

C₂×D₄

—

586

—

C₂²×C₄

—

293

—

C₂²×C₄

—

293

—

C₂²×C₄

—

586

—

C₂×C₈

—

C₂×C₈

—

586

—

C₄⋊C₄

—

C₂²⋊C₄

—

586

—

C₄²

—

293

—

C₄²

—

293

—

C₄²

C₂²×D₂₉₃

yes

characteristic

C₂³

—

293

—

C₂³

—

586

—

100

Q₈

—

101

D₄

—

1172

—

102

D₄

—

1172

—

103

D₄

—

1172

—

104

D₄

—

1172

—

105

C₂×C₄

—

106

C₂×C₄

—

293

—

107

C₂×C₄

—

293

—

108

C₂×C₄

—

586

—

109

C₂×C₄

—

586

—

110

C₂×C₄

—

586

—

111

C₂×C₄

—

1172

—

112

C₂×C₄

C₂×C₄×D₂₉₃

yes

characteristic

113

C₂×C₄

D₄×D₂₉₃

yes

—

114

C₈

—

115

C₈

—

1172

—

116

C₂²

—

586

—

117

C₂²

—

586

—

118

C₂²

—

1172

—

119

C₂²

—

1172

—

120

C₂²

C₂²⋊C₄×D₂₉₃

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

293

—

124

C₄

—

586

—

125

C₄

#22627645

yes

—

126

C₄

#22627647

yes

—

127

C₂

—

2344

—

128

C₂

—

1172

—

129

C₂

#100×D₂₉₃

yes

characteristic

130

C₂

#34036124

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉₃
commutator	C₂×C₄×C₂₉₃	C₂²×C₄
Frattini	C₄²	C₂²×D₂₉₃
Fitting	#333×C₂₉₃	C₂
socle	C₂²×C₂₉₃	C₂×C₂²⋊C₄
prime radical	#34036680	C₂
cosocle	C₄²×C₂₉₃	C₂³
hypercenter	#333	D₂₉₃
hypocenter	C₂₉₃	#1543
LCS	G ▷ C₂×C₄×C₂₉₃ ▷ C₂²×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉₃

commutator

C₂×C₄×C₂₉₃

C₂²×C₄

Frattini

C₄²

C₂²×D₂₉₃

Fitting

#333×C₂₉₃

C₂

socle

C₂²×C₂₉₃

C₂×C₂²⋊C₄

prime radical

#34036680

C₂

cosocle

C₄²×C₂₉₃

C₂³

D₂₉₃

C₂₉₃

G ▷ C₂×C₄×C₂₉₃ ▷ C₂²×C₂₉₃ ▷ C₂₉₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
2. #34036181	C₂	semidirect
3. #34035878	C₂	semidirect
4. #34035872	C₂	semidirect
5. #333×C₂₉₃	C₂	semidirect
65. C₂₉₃	#1543	semidirect
70. #333	D₂₉₃	semidirect

H ≅ G/N

type

2. #34036181

C₂

semidirect

3. #34035878

C₂

semidirect

4. #34035872

C₂

semidirect

5. #333×C₂₉₃

C₂

semidirect

65. C₂₉₃

#1543

semidirect

70. #333

D₂₉₃

semidirect

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

subgroup	index
#34036680	2
#34036181	2
#34035878	2
#34035872	2
#333×C₂₉₃	2
#1543	293

subgroup

index

#333×C₂₉₃

293

Subgroups — #49157446

Conjugacy classes of subgroups

Complements

Maximal subgroups