Finite Group Databasebeta

← #34101303

Subgroups — #34101303

Order 20096.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#23757899C211yesmaximal, characteristic
2#23757136C212yesmaximal
3#23757040C211yesmaximal, characteristic
4#23757039C212yesmaximal
5#381×C157C211yesmaximal, characteristic
6#19097750—22no—
7#19097748—24no—
8C2×C22⋊Dic157C2212yes—
9C2×C22⋊Dic157C2212yes—
10#19097678—24no—
11C23×C4×C157C2211yescharacteristic
12C2×C22⋊C4×C157C2211yescharacteristic
13C2×C22⋊C4×C157C2211yescharacteristic
14#95×C157—22no—
15C2×Dic314—22no—
16C22×Dic157—22no—
17C22×Dic157D414yes—
18C4⋊Dic157—22no—
19#14578933—24no—
20C22⋊Dic157—22no—
21C22⋊Dic157—22no—
22C22⋊Dic157—22no—
23C22⋊Dic157—22no—
24C24×C157C2311yescharacteristic
25C22×C4×C157—21no—
26C22×C4×C157—22no—
27C22×C4×C157—22no—
28C22×C4×C157—21no—
29C22×C4×C157—21no—
30C22×C4×C157D412yes—
31C22×C4×C157Q812yescomplemented
32C22⋊C4×C157—22no—
33C22⋊C4×C157—22no—
34Dic314—82no—
35C2×Dic157—24no—
36C2×Dic157—44no—
37C2×Dic157—44no—
38C2×Dic157—42no—
39C23×C157—42no—
40C23×C157C2×D412yes—
41C23×C157C2×D411yescharacteristic
42C23×C157C2×Q811yescharacteristic
43C23×C157#4112yes—
44C23×C157#4111yescharacteristic
45C2×C4×C157—22no—
46C2×C4×C157—24no—
47C2×C4×C157—22no—
48C2×C4×C157—41no—
49C2×C4×C157—42no—
50C2×C4×C157—41no—
51C2×C4×C157—42no—
52C2×C4×C157—42no—
53C2×C4×C157—41no—
54C22×C157—22no—
55C22×C157—24no—
56C22×C157—41no—
57C22×C157—42no—
58C22×C157—41no—
59C22×C157#12011yescharacteristic
60C22×C157C22⋊Q812yes—
61C22×C157C22⋊Q811yescharacteristic
62C22×C157#12412yes—
63C22×C157#12411yescharacteristic
64C4×C157—42no—
65C4×C157—42no—
66C4×C157—81no—
67Dic157—44no—
68Dic157—82no—
69C2×C157—22no—
70C2×C157—21no—
71C2×C157—22no—
72C2×C157—21no—
73C2×C157#39311yescharacteristic
74C2×C157#45812yes—
75C157#203011yescharacteristic, complemented, Sylow
76#2030—1571nomaximal, Sylow
77#543—1571no—
78#381—1572no—
79#381D15711yescharacteristic
80#342—1572no—
81#342—1571no—
82C23×C4C2×D15711yescharacteristic
83C22⋊Q8—3144no—
84C22⋊Q8—3142no—
85C2×C22⋊C4—1572no—
86C2×C22⋊C4—1572no—
87C2×C22⋊C4C2×D15711yescharacteristic
88C2×C22⋊C4C2×D15711yescharacteristic
89#95—22no—
90#95—3144no—
91C24C22×D15711yescharacteristic
92C2×Q8—3142no—
93C22×C4—22no—
94C22×C4—21no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—3142no—
99C22×C4—1574no—
100C22×C4C22⋊D15712yes—
101C22×C4Dic31412yescomplemented
102C4⋊C4—3144no—
103C4⋊C4—3142no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—3142no—
107C22⋊C4—3142no—
108C22⋊C4—3142no—
109C22⋊C4—3142no—
110C23—42no—
111C23D4×D15712yes—
112C23C2×C22⋊D15711yescharacteristic
113C23C2×Dic31411yescharacteristic
114C23#1457895312yes—
115C23#1457895411yescharacteristic
116Q8—12562no—
117C2×C4—22no—
118C2×C4—24no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—3144no—
127C2×C4—6284no—
128C2×C4—6284no—
129C2×C4—6282no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—42no—
134C22—41no—
135C22#1909773911yescharacteristic
136C22#1909774812yes—
137C22#1909775011yescharacteristic
138C22#1909775712yes—
139C22#1909775811yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—6284no—
144C4—12562no—
145C2—21no—
146C2—22no—
147C2—22no—
148C2—21no—
149C2#2375718511yescharacteristic
150C2#2375746212yes—
subgroupG/H
centerC22#19097739
commutator, prime radical, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#381×C157C2
socleC22×C157#120
hypercenter#381D157
hypocenterC157#2030
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
31. C22×C4×C157Q8semidirect
75. C157#2030semidirect
101. C22×C4Dic314semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237571362
#237570402
#237570392
#381×C1572
#2030157