Finite Group Databasebeta

← #34099146

Subgroups — #34099146

Order 20096.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757904C211yesmaximal, characteristic
2#23757604C212yesmaximal
3#23757203C211yesmaximal, characteristic
4#23757011C212yesmaximal
5#324×C157C211yesmaximal, characteristic
6#19097770—22no—
7#19097762—22no—
8#19097750—21no—
9#19097750C2212yes—
10#19097730—21no—
11C2×C4⋊Dic157C2211yescharacteristic
12C2×#14578933—21no—
13#19097703—22no—
14#19097696—22no—
15#19097678—21no—
16#19097678C2211yescharacteristic
17C2×C4⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C2×Dic314—21no—
20C2×Dic314D412yes—
21C22×Dic157—21no—
22C22×Dic157—21no—
23C4⋊Dic157—21no—
24C4⋊Dic157—21no—
25C4⋊Dic157—21no—
26C4⋊Dic157—22no—
27C4⋊Dic157D412yes—
28#14578933—22no—
29#14578933—22no—
30#14578933—42no—
31C22⋊Dic157—22no—
32C4×Dic157—22no—
33C22×C4×C157D411yescharacteristic
34C22×C4×C157D411yescharacteristic
35C22×C4×C157C2311yescharacteristic
36C2×C8×C157—22no—
37C4⋊C4×C157—22no—
38Dic314—42no—
39Dic314—81no—
40C2×Dic157—22no—
41C2×Dic157—22no—
42C2×Dic157—22no—
43C2×Dic157—41no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157—41no—
48C23×C157C2×D411yescharacteristic
49C2×C4×C157—21no—
50C2×C4×C157—21no—
51C2×C4×C157—21no—
52C2×C4×C157—41no—
53C2×C4×C157—41no—
54C2×C4×C157SD1612yes—
55C2×C4×C157C2×D412yes—
56C8×C157—42no—
57C22×C157—21no—
58C22×C157—21no—
59C22×C157#12011yescharacteristic
60C22×C157C2×SD1611yescharacteristic
61C22×C157#13711yescharacteristic
62C4×C157—22no—
63C4×C157—22no—
64C4×C157—41no—
65Dic157—42no—
66Dic157—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#544—1571no—
77#483—1572no—
78#398—1571no—
79#328—1572no—
80#324D15711yescharacteristic
81C4⋊Q8—3142no—
82#125—3142no—
83C22⋊Q8—3141no—
84C22⋊Q8—1572no—
85#117—3141no—
86C2×C4⋊C4—3141no—
87C2×C4⋊C4—1571no—
88C2×C4⋊C4C2×D15711yescharacteristic
89#106—3142no—
90#103—3142no—
91C22⋊C8C2×D15712yes—
92#95—3141no—
93#95—1571no—
94C2×Q8—3141no—
95C2×Q8—1572no—
96C22×C4—3141no—
97C22×C4—3141no—
98C22×C4D62811yescharacteristic
99C22×C4D62811yescharacteristic
100C22×C4C22×D15711yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—3141no—
104C4⋊C4—3141no—
105C4⋊C4—3141no—
106C4⋊C4—3142no—
107C4⋊C4—3142no—
108C4⋊C4—3142no—
109C4⋊C4—6282no—
110C4⋊C4—1572no—
111C22⋊C4—3142no—
112C42—3142no—
113C23C2×D62811yescharacteristic
114Q8—6282no—
115Q8—12561no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—3142no—
122C2×C4—3142no—
123C2×C4—3142no—
124C2×C4—6281no—
125C2×C4—6281no—
126C2×C4—6281no—
127C2×C4—6281no—
128C2×C4—6281no—
129C2×C4#1457894312yes—
130C2×C4D4×D15712yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1909774111yescharacteristic
135C22C2×#1457894311yescharacteristic
136C22#1909780411yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—6282no—
141C4—6282no—
142C4—6282no—
143C4—12561no—
144C2—21no—
145C2—21no—
146C2#2375741411yescharacteristic
147C2#2375745811yescharacteristic
148C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#324D157
hypocenterC157#1611
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

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
#237579042
#237576042
#237572032
#237570112
#324×C1572
#1611157