Finite Group Databasebeta

← #34099434

Subgroups — #34099434

Order 20096.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757663C211yesmaximal, characteristic
2#23757639C212yesmaximal, complemented
3#23757015C212yesmaximal, complemented
4#23757013C211yesmaximal, characteristic, complemented
5#563×C157C211yesmaximal, characteristic, complemented
6C2×#14578941—21no—
7C2×#14578939—21no—
8#19097768C2211yescharacteristic
9#19097691—22no—
10#19097691—22no—
11#19097682C2212yes—
12#19097682C2211yescharacteristic
13C4⋊Q8×C157—21no—
14#126×C157—22no—
15#125×C157C2212yes—
16#124×C157C2211yescharacteristic
17#123×C157—21no—
18C22⋊Q8×C157—22no—
19C2×D628—22no—
20C2×D628—21no—
21#14578941—42no—
22#14578939—42no—
23C2×#11929434—21no—
24C2×#11929434—22no—
25C2×Q8×C157—21no—
26C2×Q8×C157D411yescharacteristic
27C2×D4×C157D411yescharacteristic
28C22×C4×C157—21no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157—22no—
31C4⋊C4×C157—22no—
32C4⋊C4×C157D412yes—
33C4⋊C4×C157D412yes—
34C22⋊C4×C157—22no—
35C22⋊C4×C157—21no—
36C22⋊C4×C157—22no—
37C42×C157—21no—
38C42×C157C2311yescharacteristic
39C22×D157—41no—
40D628—44no—
41D628—41no—
42D628—41no—
43#11929434—22no—
44#11929434—42no—
45C23×C157—21no—
46Q8×C157—41no—
47Q8×C157—81no—
48D4×C157—41no—
49C2×C4×C157—22no—
50C2×C4×C157—21no—
51C2×C4×C157—22no—
52C2×C4×C157—81no—
53C2×C4×C157C2×D412yes—
54C2×C4×C157C2×D411yescharacteristic
55C22×C157—41no—
56C22×C157—42no—
57C22×C157#12011yescharacteristic
58C2×D157—81no—
59C2×D157—82no—
60C4×C157—21no—
61C4×C157—22no—
62C4×C157—42no—
63C4×C157—41no—
64C4×C157—42no—
65C2×C157—81no—
66C2×C157#45311yescharacteristic
67C2×C157#45412yes—
68D157—161no—
69C157#165711yescharacteristic, complemented, Sylow
70#1657—1571nomaximal, Sylow
71#563D15711yescharacteristic, complemented
72#496—1571no—
73#490—1572no—
74#330—1572no—
75#329—1571no—
76C2×SD16—3141no—
77C2×D8—3141no—
78C4⋊Q8—21no—
79#127—1571no—
80#126—22no—
81#125C2×D15712yes—
82#124C2×D15711yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—3142no—
86#102—3142no—
87#97—1572no—
88#97—1571no—
89C2×Q8—21no—
90C2×Q8C22⋊D15711yescharacteristic
91C2×D4—3142no—
92C2×D4—3141no—
93C2×D4C22⋊D15711yescharacteristic
94C22×C4—21no—
95SD16—6282no—
96D8—6282no—
97C2×C8—3141no—
98C2×C8—3142no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D15712yes—
103C4⋊C4C22⋊D15712yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D15711yescharacteristic
109C23—21no—
110C23—6281no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—6281no—
115D4—6281no—
116D4—6284no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D15712yes—
122C2×C4C2×C22⋊D15711yescharacteristic
123C8—3142no—
124C8—6282no—
125C22—41no—
126C22—42no—
127C22—12561no—
128C22—12562no—
129C22#1909774011yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—25121no—
137C2#2375744111yescharacteristic
138C2#2375744612yes—
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#563×C157C2
socleC22×C157#120
prime radical#23757663C2
hypercenter#563D157
hypocenterC157#1657
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #23757639C2semidirect
3. #23757015C2semidirect
4. #23757013C2semidirect
5. #563×C157C2semidirect
69. C157#1657semidirect
71. #563D157semidirect

Maximal subgroups

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

subgroupindex
#237576632
#237576392
#237570152
#237570132
#563×C1572
#1657157