Finite Group Databasebeta

← #34101294

Subgroups — #34101294

Order 20096.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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#23757281C212yesmaximal
2#23757178C211yesmaximal, characteristic
3#23757042C211yesmaximal, characteristic
4#23757032C212yesmaximal
5#544×C157C211yesmaximal, characteristic
6C22×Dic314C2211yescharacteristic
7C2×#14578938C2212yes—
8C2×C4×Dic157C2211yescharacteristic
9#19097694—22no—
10#19097694—22no—
11#19097678—22no—
12C4⋊Q8×C157—22no—
13#125×C157—22no—
14C22⋊Q8×C157—22no—
15#117×C157C2212yes—
16C2×C4⋊C4×C157C2211yescharacteristic
17C2×Dic314—22no—
18C2×Dic314—21no—
19C2×Dic314—22no—
20C2×Dic314Q812yescomplemented
21C22×Dic157—21no—
22C22×Dic157—21no—
23#14578938—22no—
24#14578938—22no—
25C2×#11929434—22no—
26C4×Dic157—22no—
27C2×Q8×C157—22no—
28C22×C4×C157D412yes—
29C22×C4×C157C2311yescharacteristic
30C4⋊C4×C157—22no—
31C4⋊C4×C157—24no—
32C4⋊C4×C157—22no—
33C4⋊C4×C157D412yes—
34C4⋊C4×C157D412yes—
35C22⋊C4×C157—22no—
36C42×C157—22no—
37Dic314—24no—
38Dic314—42no—
39C2×Dic157—22no—
40C2×Dic157—22no—
41C2×Dic157—41no—
42C2×Dic157—41no—
43C2×Dic157—41no—
44C2×Dic157—41no—
45#11929434—42no—
46C23×C157C2×D411yescharacteristic
47Q8×C157—82no—
48C2×C4×C157—22no—
49C2×C4×C157—22no—
50C2×C4×C157—22no—
51C2×C4×C157—42no—
52C2×C4×C157C2×D412yes—
53C2×C4×C157C2×Q811yescharacteristic
54C2×C4×C157#4112yes—
55C2×C4×C157#4111yescharacteristic
56C22×C157—21no—
57C22×C157—21no—
58C22×C157#12011yescharacteristic
59C22×C157C22⋊Q811yescharacteristic
60C22×C157#12411yescharacteristic
61C4×C157—42no—
62C4×C157—42no—
63C4×C157—42no—
64C4×C157C22⋊Q812yes—
65C4×C157#12412yes—
66Dic157—42no—
67Dic157—42no—
68C2×C157—21no—
69C2×C157—21no—
70C2×C157#39311yescharacteristic
71C2×C157#45511yescharacteristic
72C2×C157#45611yescharacteristic
73C157#202811yescharacteristic, complemented, Sylow
74#2028—1571nomaximal, Sylow
75#544D15711yescharacteristic
76#419—1572no—
77#391—1571no—
78#343—1571no—
79#339—1572no—
80C22×Q8—1571no—
81C2×M16—1572no—
82C4⋊Q8—22no—
83#125—22no—
84C22⋊Q8—22no—
85#117C2×D15712yes—
86C2×C4⋊C4C2×D15711yescharacteristic
87C2×C42—1571no—
88#103—3142no—
89#103—3142no—
90#95—3142no—
91C2×Q8—22no—
92C2×Q8—3141no—
93C2×Q8—3142no—
94C2×Q8—3142no—
95C2×Q8—1572no—
96C22×C4—3141no—
97C22×C4—3141no—
98C22×C4C22⋊D15712yes—
99C22×C4C22×D15711yescharacteristic
100M16—3142no—
101M16—3142no—
102C2×C8—3142no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4C22⋊D15712yes—
107C4⋊C4C22⋊D15712yes—
108C22⋊C4—22no—
109C42—22no—
110C42—3142no—
111C23C2×C22⋊D15711yescharacteristic
112Q8—82no—
113Q8—3144no—
114Q8—6282no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—3142no—
120C2×C4—3142no—
121C2×C4—6281no—
122C2×C4—6281no—
123C2×C4—6281no—
124C2×C4—6281no—
125C2×C4C2×C22⋊D15712yes—
126C2×C4Q8×D15711yescharacteristic
127C2×C4#1457895512yes—
128C2×C4#1457895511yescharacteristic
129C8—6282no—
130C22—21no—
131C22—21no—
132C22#1909774011yescharacteristic
133C22#1909774711yescharacteristic
134C22#1909776011yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—6282no—
139C4—6282no—
140C4#1909774712yes—
141C4#1909776012yes—
142C2—21no—
143C2—21no—
144C2#2375718411yescharacteristic
145C2#2375745111yescharacteristic
146C2#2375745611yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#544×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#544D157
hypocenterC157#2028
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. C2×Dic314Q8semidirect
73. C157#2028semidirect

Maximal subgroups

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

subgroupindex
#237572812
#237571782
#237570422
#237570322
#544×C1572
#2028157