Finite Group Databasebeta

← #34099144

Subgroups — #34099144

Order 20096.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757601C212yesmaximal
2#23757203C211yesmaximal, characteristic
3#23757010C212yesmaximal
4#23756999C211yesmaximal, characteristic
5#544×C157C211yesmaximal, characteristic
6C2×C4⋊Dic157C2211yescharacteristic
7C2×#14578933—21no—
8#19097702—22no—
9#19097695—22no—
10C22⋊#11929434C2212yes—
11#19097678—21no—
12#19097678C2211yescharacteristic
13C4⋊Q8×C157—22no—
14#125×C157—22no—
15C22⋊Q8×C157—21no—
16C22⋊Q8×C157C2212yes—
17#117×C157—21no—
18C2×C4⋊C4×C157C2211yescharacteristic
19C22×Dic157—21no—
20C22×Dic157—21no—
21C2×#11929434—22no—
22C4⋊Dic157—22no—
23#14578933—42no—
24C2×Q8×C157—21no—
25C2×Q8×C157D412yes—
26C22×C4×C157D411yescharacteristic
27C22×C4×C157D411yescharacteristic
28C22×C4×C157C2311yescharacteristic
29C4⋊C4×C157—21no—
30C4⋊C4×C157—21no—
31C4⋊C4×C157—21no—
32C4⋊C4×C157—22no—
33C4⋊C4×C157—22no—
34C4⋊C4×C157—22no—
35C4⋊C4×C157D412yes—
36C22⋊C4×C157—22no—
37C42×C157—22no—
38C2×Dic157—22no—
39C2×Dic157—41no—
40C2×Dic157—41no—
41C2×Dic157—41no—
42C2×Dic157—41no—
43C2×Dic157—41no—
44#11929434—42no—
45C23×C157C2×D411yescharacteristic
46Q8×C157—42no—
47Q8×C157—81no—
48C2×C4×C157—21no—
49C2×C4×C157—21no—
50C2×C4×C157—22no—
51C2×C4×C157—22no—
52C2×C4×C157—21no—
53C2×C4×C157—41no—
54C2×C4×C157—41no—
55C2×C4×C157SD1612yes—
56C2×C4×C157C2×D412yes—
57C22×C157—21no—
58C22×C157—21no—
59C22×C157#12011yescharacteristic
60C22×C157C2×SD1611yescharacteristic
61C22×C157#13711yescharacteristic
62C4×C157—22no—
63C4×C157—22no—
64C4×C157—42no—
65C4×C157—41no—
66C4×C157—42no—
67Dic157—42no—
68Dic157—81no—
69C2×C157—21no—
70C2×C157—21no—
71C2×C157#44811yescharacteristic
72C2×C157#45611yescharacteristic
73C2×C157#45811yescharacteristic
74C157#161111yescharacteristic, complemented, Sylow
75#1611—1571nomaximal, Sylow
76#544D15711yescharacteristic
77#483—1572no—
78#398—1571no—
79#328—1572no—
80#324—1571no—
81C4⋊Q8—22no—
82#125—22no—
83C22⋊Q8—21no—
84C22⋊Q8C2×D15712yes—
85#117—21no—
86C2×C4⋊C4—3141no—
87C2×C4⋊C4—1571no—
88C2×C4⋊C4C2×D15711yescharacteristic
89#106—3142no—
90#103—3142no—
91C22⋊C8—1572no—
92#95—3141no—
93#95—1571no—
94C2×Q8—21no—
95C2×Q8C22⋊D15712yes—
96C22×C4—3141no—
97C22×C4—3141no—
98C22×C4C22⋊D15711yescharacteristic
99C22×C4C22⋊D15711yescharacteristic
100C22×C4C22×D15711yescharacteristic
101C2×C8—3142no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—3142no—
109C4⋊C4—6282no—
110C4⋊C4C22⋊D15712yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D15711yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—3142no—
124C2×C4—6281no—
125C2×C4—6281no—
126C2×C4—6281no—
127C2×C4—6281no—
128C2×C4—6281no—
129C2×C4#1457894112yes—
130C2×C4C2×C22⋊D15712yes—
131C8—6282no—
132C22—21no—
133C22—21no—
134C22#1909774011yescharacteristic
135C22C2×#1457894111yescharacteristic
136C22#1909780211yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—6282no—
143C4—12561no—
144C2—21no—
145C2—21no—
146C2#2375741211yescharacteristic
147C2#2375745611yescharacteristic
148C2#2375746311yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#544×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#544D157
hypocenterC157#1611
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
74. C157#1611semidirect

Maximal subgroups

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

subgroupindex
#237576012
#237572032
#237570102
#237569992
#544×C1572
#1611157