Group #16790219 — subgroups

Subgroups — #16790219

Order 3328.

302 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 124 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	#13131168	C₂	1	2	yes	maximal
2	#13129881	C₂	1	4	yes	maximal
3	#13114524	C₂	1	1	yes	maximal, characteristic
4	C₂×#88106	C₂²	1	4	yes	—
5	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
6	C₂×#88055	C₄	1	2	yes	—
7	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
8	#11718593	C₄	1	1	yes	characteristic
9	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
10	C₄⋊#6092	—	2	4	no	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
14	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
15	C₂²×#1055	C₂³	1	1	yes	characteristic
16	#88106	—	2	8	no	—
17	C₂×#6092	—	2	4	no	—
18	C₁₃×#97	C₈	1	4	yes	—
19	#88071	—	2	2	no	—
20	#88055	—	2	4	no	—
21	C₈×Dic₁₃	—	2	4	no	—
22	C₄×#1055	D₄	1	2	yes	—
23	C₄×#1055	Q₈	1	2	yes	—
24	#12884	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
26	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×Dic₁₃	—	2	2	no	—
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₄²×C₁₃	C₂×C₈	1	2	yes	—
33	C₄×Dic₁₃	—	2	2	no	—
34	C₄×Dic₁₃	M₁₆	1	4	yes	—
35	C₂×#1055	—	2	2	no	—
36	C₂×#1055	C₄⋊C₄	1	2	yes	—
37	C₂×#1055	C₂×D₄	1	1	yes	characteristic
38	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
39	C₂×#1055	#41	1	4	yes	—
40	#6092	—	4	4	no	—
41	#2150	—	13	2	no	—
42	#1726	—	13	1	no	—
43	#1376	—	13	4	no	—
44	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	4	2	no	—
46	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
47	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₃	#117	1	2	yes	—
49	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
51	C₂×Dic₁₃	—	2	4	no	—
52	C₂×Dic₁₃	—	4	4	no	—
53	C₈×C₁₃	—	2	4	no	—
54	#1055	—	2	2	no	—
55	#1055	#124	1	2	yes	—
56	#1055	#125	1	2	yes	—
57	C₂×M₃₂	—	13	4	no	—
58	C₂×#97	—	13	2	no	—
59	C₂×#97	#261	1	1	yes	characteristic
60	C₂×C₄×C₈	—	13	1	no	—
61	C₂×C₄×C₈	—	13	2	no	—
62	#376	—	13	1	no	—
63	C₄⋊C₁₆	—	26	4	no	—
64	C₂²×C₁₃	—	2	2	no	—
65	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₂²×C₁₃	#432	1	2	yes	—
67	C₄×C₁₃	—	2	4	no	—
68	C₄×C₁₃	#382	1	1	yes	characteristic
69	C₄×C₁₃	#423	1	1	yes	characteristic
70	C₄×C₁₃	#431	1	2	yes	—
71	Dic₁₃	—	4	4	no	—
72	C₂²×C₈	—	13	1	no	—
73	C₂²×C₈	—	13	1	no	—
74	C₂²×C₈	C₂×#261	1	2	yes	—
75	C₂×C₄²	—	13	2	no	—
76	C₂×C₄²	C₂×#261	1	1	yes	characteristic
77	M₃₂	—	26	8	no	—
78	C₂×C₁₆	—	26	4	no	—
79	#97	—	26	4	no	—
80	#97	#1057	1	4	yes	—
81	C₄×C₈	—	13	2	no	—
82	C₄×C₈	—	13	2	no	—
83	C₄×C₈	—	26	4	no	—
84	#95	—	26	2	no	—
85	C₂×C₁₃	—	2	2	no	—
86	C₂×C₁₃	#1831	1	1	yes	characteristic
87	C₂×C₁₃	#2153	1	2	yes	—
88	C₂²×C₄	—	26	2	no	—
89	C₂²×C₄	#6118	1	2	yes	—
90	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	13	1	no	—
94	C₂×C₈	—	13	1	no	—
95	C₂×C₈	—	13	4	no	—
96	C₂×C₈	—	13	2	no	—
97	C₂×C₈	—	26	2	no	—
98	C₂×C₈	C₂×#1057	1	4	yes	—
99	C₄²	—	13	4	no	—
100	C₄²	—	26	2	no	—
101	C₄²	C₄⋊#261	1	2	yes	—
102	C₄²	C₂×#1057	1	2	yes	—
103	C₁₆	—	52	4	no	—
104	C₁₃	#12884	1	1	yes	characteristic, complemented, Sylow
105	C₂³	C₂×#6118	1	1	yes	characteristic
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	26	4	no	—
108	C₂×C₄	—	52	4	no	—
109	C₂×C₄	C₄⋊#1057	1	4	yes	—
110	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
111	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
112	C₂×C₄	#88237	1	2	yes	—
113	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
114	C₈	—	2	4	no	—
115	C₈	—	13	2	no	—
116	C₈	—	13	2	no	—
117	C₈	—	26	2	no	—
118	C₂²	—	2	2	no	—
119	C₂²	#11719054	1	2	yes	—
120	C₂²	C₂×C₄⋊#1057	1	1	yes	characteristic
121	C₄	—	2	4	no	—
122	C₄	—	52	4	no	—
123	C₄	#11719053	1	1	yes	characteristic
124	C₄	#11719060	1	1	yes	characteristic
125	C₄	#11719119	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#13130751	1	1	yes	characteristic
128	C₂	#13131177	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13131168

C₂

yes

maximal

#13129881

C₂

yes

maximal

#13114524

C₂

yes

maximal, characteristic

C₂×#88106

C₂²

yes

—

C₂×C₁₃×#97

C₄

yes

characteristic

C₂×#88055

C₄

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

—

#11718593

C₄

yes

characteristic

C₂×C₄×#1055

C₂²

yes

characteristic

C₄⋊#6092

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

characteristic

C₂²×#1055

C₂³

yes

characteristic

#88106

—

C₂×#6092

—

C₁₃×#97

C₈

yes

—

#88071

—

#88055

—

C₈×Dic₁₃

—

C₄×#1055

D₄

yes

—

C₄×#1055

Q₈

yes

—

#12884

—

maximal, Sylow

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

M₁₆

yes

—

C₂×#1055

—

C₂×#1055

C₄⋊C₄

yes

—

C₂×#1055

C₂×D₄

yes

characteristic

C₂×#1055

C₂×Q₈

yes

characteristic

C₂×#1055

#41

yes

—

—

—

—

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

#1055

—

#1055

#124

yes

—

#1055

#125

yes

—

C₂×M₃₂

—

C₂×#97

—

C₂×#97

#261

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₄⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#432

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

characteristic

M₃₂

—

C₂×C₁₆

—

#97

—

#97

#1057

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#1831

yes

characteristic

C₂×C₁₃

#2153

yes

—

C₂²×C₄

—

C₂²×C₄

#6118

yes

—

C₂²×C₄

C₂²×#261

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1057

yes

—

C₄²

—

100

C₄²

—

101

C₄²

C₄⋊#261

yes

—

102

C₄²

C₂×#1057

yes

—

103

C₁₆

—

104

C₁₃

#12884

yes

characteristic, complemented, Sylow

105

C₂³

C₂×#6118

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊#1057

yes

—

110

C₂×C₄

D₁₃⋊M₁₆

yes

—

111

C₂×C₄

C₂×C₄⋊#261

yes

characteristic

112

C₂×C₄

#88237

yes

—

113

C₂×C₄

C₂²×#1057

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₂²

—

119

C₂²

#11719054

yes

—

120

C₂²

C₂×C₄⋊#1057

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

#11719053

yes

characteristic

124

C₄

#11719060

yes

characteristic

125

C₄

#11719119

yes

—

126

C₂

—

127

C₂

#13130751

yes

characteristic

128

C₂

#13131177

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#12884
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂²×C₄

C₂²×#261

Fitting

C₂×C₁₃×#97

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂³×C₁₃

C₂×M₁₆

cosocle

C₂²×#1055

C₂³

C₂×#97

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
104. C₁₃	#12884	semidirect

H ≅ G/N

type

104. C₁₃

#12884

semidirect

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

subgroup	index
#13131168	2
#13129881	2
#13114524	2
#12884	13

subgroup

index

Subgroups — #16790219

Conjugacy classes of subgroups

Complements

Maximal subgroups