Finite Group Databasebeta

← #34099432

Subgroups — #34099432

Order 20096.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#23758023C211yesmaximal, characteristic, complemented
2#23757637C212yesmaximal, complemented
3#23757014C212yesmaximal, complemented
4#23757013C211yesmaximal, characteristic, complemented
5#496×C157C211yesmaximal, characteristic
6#19097769—21no—
7#19097764—22no—
8#19097763C2212yes—
9#19097752—21no—
10#19097748—22no—
11#19097692—22no—
12#19097692—22no—
13#19097682C2212yes—
14C2×SD16×C157—21no—
15C2×D8×C157—21no—
16#127×C157C2211yescharacteristic
17#124×C157C2211yescharacteristic
18#97×C157C2211yescharacteristic
19C2×Dic314—21no—
20C22×Dic157—21no—
21C2×#11929434—22no—
22C4⋊Dic157D412yes—
23C4⋊Dic157D412yes—
24#14578933—22no—
25#14578933—22no—
26#14578933—22no—
27C22⋊Dic157—22no—
28C22⋊Dic157—21no—
29C4×Dic157—21no—
30C2×Q8×C157D411yescharacteristic
31C2×D4×C157—21no—
32C2×D4×C157—22no—
33C2×D4×C157D411yescharacteristic
34SD16×C157—42no—
35D8×C157—42no—
36C2×C8×C157—21no—
37C22⋊C4×C157—22no—
38C42×C157C2311yescharacteristic
39Dic314—81no—
40C2×Dic157—22no—
41C2×Dic157—22no—
42C2×Dic157—81no—
43#11929434—42no—
44C23×C157—21no—
45C23×C157—41no—
46Q8×C157—41no—
47D4×C157—41no—
48D4×C157—41no—
49D4×C157—41no—
50D4×C157—44no—
51C2×C4×C157—21no—
52C2×C4×C157C2×D412yes—
53C2×C4×C157C2×D411yescharacteristic
54C8×C157—22no—
55C22×C157—41no—
56C22×C157—42no—
57C22×C157—81no—
58C22×C157—82no—
59C22×C157#12011yescharacteristic
60C4×C157—21no—
61C4×C157—22no—
62C4×C157—41no—
63Dic157—42no—
64Dic157—42no—
65C2×C157—81no—
66C2×C157—161no—
67C2×C157#45311yescharacteristic
68C2×C157#45412yes—
69C157#165711yescharacteristic, complemented, Sylow
70#1657—1571nomaximal, Sylow
71#563—1571no—
72#496D15711yescharacteristic
73#490—1572no—
74#330—1572no—
75#329—1571no—
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—3141no—
79#127C2×D15711yescharacteristic
80#126—3142no—
81#125—1572no—
82#124C2×D15711yescharacteristic
83#123—3141no—
84C22⋊Q8—3142no—
85#102—3142no—
86#102—3142no—
87#97—1572no—
88#97C2×D15711yescharacteristic
89C2×Q8—3141no—
90C2×Q8C22⋊D15711yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D15711yescharacteristic
94C22×C4—3141no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—3142no—
99C4⋊C4—3142no—
100C4⋊C4—3142no—
101C4⋊C4—3142no—
102C4⋊C4—1572no—
103C4⋊C4—1572no—
104C22⋊C4—22no—
105C22⋊C4—3142no—
106C22⋊C4—3141no—
107C42—3141no—
108C42C22×D15711yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—12561no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—3142no—
119C2×C4—3142no—
120C2×C4—12561no—
121C2×C4D4×D15712yes—
122C2×C4C2×C22⋊D15711yescharacteristic
123C8—22no—
124C8—6282no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1909773911yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—6282no—
134C4—6282no—
135C2—81no—
136C2—161no—
137C2#2375744011yescharacteristic
138C2#2375744412yes—
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting, prime radical#496×C157C2
socleC22×C157#120
hypercenter#496D157
hypocenterC157#1657
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23758023C2semidirect
2. #23757637C2semidirect
3. #23757014C2semidirect
4. #23757013C2semidirect
69. C157#1657semidirect

Maximal subgroups

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

subgroupindex
#237580232
#237576372
#237570142
#237570132
#496×C1572
#1657157