Finite Group Databasebeta

← #34102260

Subgroups — #34102260

Order 20096.

140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097717C211yesmaximal, characteristic, complemented
2#23757691C211yesmaximal, characteristic
3#23757549C211yesmaximal, characteristic
4#23757545C211yesmaximal, characteristic
5#23757102C211yesmaximal, characteristic, complemented
6#23757090C211yesmaximal, characteristic, complemented
7#362×C157C211yesmaximal, characteristic, complemented
8#19097804—21no—
9#19097802—21no—
10C2×Dic628C2211yescharacteristic
11#19097777C2211yescharacteristic
12#19097717—21no—
13#19097717—21no—
14#19097710—21no—
15C2×#14578929C2211yescharacteristic
16C16×D157—21no—
17#19097707C2211yescharacteristic
18#19097690—21no—
19#19097689—21no—
20C2×Q16×C157C2211yescharacteristic
21M32×C157C2211yescharacteristic
22#108×C157C2211yescharacteristic
23#14578954D411yescharacteristic
24C2×Dic314—21no—
25Dic628—21no—
26Dic628—21no—
27Dic628—41no—
28#14578944—41no—
29#14578943—41no—
30#14578941—41no—
31#14578938—21no—
32#14578938D411yescharacteristic
33#14578937—21no—
34C8×D157—21no—
35#14578929D411yescharacteristic
36#14578929D411yescharacteristic
37C2×Q8×C157—21no—
38Q16×C157—21no—
39Q16×C157—21no—
40M16×C157—21no—
41C2×C8×C157C2311yescharacteristic
42C16×C157—21no—
43Dic314—41no—
44Dic314—41no—
45Dic314D811yescharacteristic
46D628D811yescharacteristic
47C22⋊D157—21no—
48C2×Dic157—41no—
49C4×D157—21no—
50#11929434—21no—
51#11929434—41no—
52Q8×C157—41no—
53Q8×C157—41no—
54C2×C4×C157—41no—
55C2×C4×C157C2×D411yescharacteristic
56C8×C157—41no—
57C8×C157C2×D411yescharacteristic
58C8×C157#4111yescharacteristic
59C22×C157#13511yescharacteristic
60C2×D157—21no—
61C4×C157—81no—
62C4×C157#12111yescharacteristic
63C4×C157C2×D811yescharacteristic
64Dic157—21no—
65Dic157—81no—
66C2×C157—21no—
67C2×C157#46611yescharacteristic
68D157—41no—
69C157#222211yescharacteristic, complemented, Sylow
70#2222—1571nomaximal, Sylow
71C2×Q32—1571no—
72#504—1571no—
73#473—1571no—
74#473—1571no—
75#368—1571no—
76#362—1571no—
77#362D15711yescharacteristic, complemented
78#137—3141no—
79#137—3141no—
80C2×Q16—1571no—
81C2×Q16C2×D15711yescharacteristic
82#131—1571no—
83Q32—3141no—
84Q32—3141no—
85M32—3141no—
86M32C2×D15711yescharacteristic
87C2×C16—3141no—
88C2×C16—1571no—
89#108—1571no—
90#108C2×D15711yescharacteristic
91#101—3141no—
92#101—3141no—
93#41—1571no—
94C2×Q8—21no—
95C2×Q8—3141no—
96Q16—21no—
97Q16—21no—
98Q16—3141no—
99Q16—3141no—
100Q16—6281no—
101Q16—6281no—
102SD16—6281no—
103SD16—6281no—
104M16—21no—
105M16—3141no—
106M16—3141no—
107M16—1571no—
108C2×C8—3141no—
109C2×C8C22×D15711yescharacteristic
110C16—21no—
111C16—1571no—
112C16—1571no—
113Q8—41no—
114Q8—41no—
115Q8—6281no—
116Q8—6281no—
117Q8—1571no—
118D4—3141no—
119D4—1571no—
120C2×C4—41no—
121C2×C4—3141no—
122C2×C4—6281no—
123C2×C4D4×D15711yescharacteristic
124C8—41no—
125C8—3141no—
126C8—6281no—
127C8D4×D15711yescharacteristic
128C8#1457895411yescharacteristic
129C22—3141no—
130C22#1909779211yescharacteristic
131C4—81no—
132C4—3141no—
133C4—12561no—
134C4#1909774411yescharacteristic
135C4D8×D15711yescharacteristic
136C2—21no—
137C2—6281no—
138C2#2375750811yescharacteristic
subgroupG/H
centerC2#23757508
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#362×C157C2
socleC2×C157#466
prime radical#14578954D4
hypercenter#362D157
hypocenterC157#2222
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19097717C2semidirect
5. #23757102C2semidirect
6. #23757090C2semidirect
7. #362×C157C2semidirect
69. C157#2222semidirect
77. #362D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977172
#237576912
#237575492
#237575452
#237571022
#237570902
#362×C1572
#2222157