Finite Group Databasebeta

← #34099435

Subgroups — #34099435

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#23757663C211yesmaximal, characteristic
3#23757638C212yesmaximal, complemented
4#23757014C212yesmaximal, complemented
5#329×C157C211yesmaximal, characteristic, complemented
6C2×#14578941—21no—
7C2×#14578939—21no—
8#19097769—21no—
9#19097768C2211yescharacteristic
10#19097764—22no—
11#19097763C2212yes—
12#19097752—21no—
13#19097748—22no—
14#19097693—22no—
15#19097693—22no—
16#19097682C2211yescharacteristic
17#124×C157C2211yescharacteristic
18#97×C157C2212yes—
19C2×Dic314—21no—
20C2×D628—22no—
21C2×D628—21no—
22C22×Dic157—21no—
23#14578941—42no—
24#14578939—42no—
25C2×#11929434—21no—
26C4⋊Dic157D412yes—
27C4⋊Dic157D412yes—
28#14578933—22no—
29#14578933—22no—
30#14578933—22no—
31C22⋊Dic157—22no—
32C22⋊Dic157—21no—
33C4×Dic157—21no—
34C2×Q8×C157D411yescharacteristic
35C2×D4×C157D411yescharacteristic
36C2×C8×C157—22no—
37C22⋊C4×C157—22no—
38C42×C157C2311yescharacteristic
39C22×D157—41no—
40Dic314—81no—
41D628—44no—
42D628—41no—
43D628—41no—
44C2×Dic157—22no—
45C2×Dic157—22no—
46C2×Dic157—81no—
47#11929434—22no—
48C23×C157—21no—
49Q8×C157—41no—
50D4×C157—41no—
51C2×C4×C157—21no—
52C2×C4×C157C2×D412yes—
53C2×C4×C157C2×D411yescharacteristic
54C8×C157—42no—
55C22×C157—41no—
56C22×C157—42no—
57C22×C157#12011yescharacteristic
58C2×D157—81no—
59C2×D157—82no—
60C4×C157—21no—
61C4×C157—22no—
62C4×C157—41no—
63Dic157—42no—
64Dic157—42no—
65C2×C157—81no—
66C2×C157#45311yescharacteristic
67C2×C157#45412yes—
68D157—161no—
69C157#165711yescharacteristic, complemented, Sylow
70#1657—1571nomaximal, Sylow
71#563—1571no—
72#496—1571no—
73#490—1572no—
74#330—1572no—
75#329D15711yescharacteristic, complemented
76C2×SD16—3141no—
77C2×D8—3141no—
78C4⋊Q8—3141no—
79#127—1571no—
80#126—3142no—
81#125—1572no—
82#124C2×D15711yescharacteristic
83#123—3141no—
84C22⋊Q8—3142no—
85#102—3142no—
86#102—3142no—
87#97—1571no—
88#97C2×D15712yes—
89C2×Q8—3141no—
90C2×Q8D62811yescharacteristic
91C2×D4—3142no—
92C2×D4—3141no—
93C2×D4D62811yescharacteristic
94C22×C4—3141no—
95SD16—6282no—
96D8—6282no—
97C2×C8—22no—
98C2×C8—3141no—
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—6281no—
111Q8—41no—
112Q8—12561no—
113D4—41no—
114D4—6281no—
115D4—6281no—
116D4—6284no—
117C2×C4—21no—
118C2×C4—3142no—
119C2×C4—3142no—
120C2×C4—12561no—
121C2×C4D4×D15712yes—
122C2×C4C2×D62811yescharacteristic
123C8—42no—
124C8—3142no—
125C22—41no—
126C22—42no—
127C22—12561no—
128C22—12562no—
129C22#1909774111yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—6282no—
134C4—6282no—
135C2—81no—
136C2—25121no—
137C2#2375744311yescharacteristic
138C2#2375744712yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157#120
prime radical#23757663C2
hypercenter#329D157
hypocenterC157#1657
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #23758023C2semidirect
3. #23757638C2semidirect
4. #23757014C2semidirect
5. #329×C157C2semidirect
69. C157#1657semidirect
75. #329D157semidirect

Maximal subgroups

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

subgroupindex
#237580232
#237576632
#237576382
#237570142
#329×C1572
#1657157