Finite Group Databasebeta

← #34068419

Subgroups — #34068419

Order 19328.

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

normal subgroups only

This group has 196 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#23752962C211yesmaximal, characteristic
2#23752618C212yesmaximal, complemented
3#23751953C212yesmaximal, complemented
4#23751952C211yesmaximal, characteristic
5#497×C151C211yesmaximal, characteristic
6#18012737—21no—
7#18012732—22no—
8#18012731C2212yes—
9#18012720—21no—
10#18012716—22no—
11#18012672—22no—
12#18012670—22no—
13#18012650C2212yes—
14C2×Q16×C151—21no—
15C2×SD16×C151—21no—
16C4⋊Q8×C151C2211yescharacteristic
17#124×C151C2211yescharacteristic
18#97×C151C2211yescharacteristic
19C2×Dic302—21no—
20C22×Dic151—21no—
21C2×C151⋊C8—22no—
22C4⋊Dic151D412yes—
23C4⋊Dic151D412yes—
24Dic151⋊C4—22no—
25Dic151⋊C4—22no—
26Dic151⋊C4—22no—
27C22⋊Dic151—22no—
28C22⋊Dic151—21no—
29C4×Dic151—21no—
30C2×Q8×C151—21no—
31C2×Q8×C151D411yescharacteristic
32C2×D4×C151D411yescharacteristic
33Q16×C151—42no—
34SD16×C151—42no—
35C2×C8×C151—21no—
36C4⋊C4×C151—22no—
37C22⋊C4×C151—22no—
38C42×C151C2311yescharacteristic
39Dic302—81no—
40C2×Dic151—22no—
41C2×Dic151—22no—
42C2×Dic151—81no—
43C151⋊C8—24no—
44C23×C151—21no—
45Q8×C151—41no—
46Q8×C151—41no—
47Q8×C151—41no—
48D4×C151—41no—
49C2×C4×C151—21no—
50C2×C4×C151—41no—
51C2×C4×C151C2×D412yes—
52C2×C4×C151C2×D411yescharacteristic
53C8×C151—22no—
54C22×C151—41no—
55C22×C151—42no—
56C22×C151#12011yescharacteristic
57C4×C151—21no—
58C4×C151—22no—
59C4×C151—41no—
60C4×C151—81no—
61Dic151—42no—
62Dic151—42no—
63C2×C151—81no—
64C2×C151#45311yescharacteristic
65C2×C151#45612yes—
66C151#166011yescharacteristic, complemented, Sylow
67#1660—1511nomaximal, Sylow
68#563—1511no—
69#501—1512no—
70#497D15111yescharacteristic
71#330—1512no—
72#329—1511no—
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—3021no—
76C4⋊Q8C2×D15111yescharacteristic
77#126—3022no—
78#125—1512no—
79#124C2×D15111yescharacteristic
80#123—3021no—
81C22⋊Q8—3022no—
82#107—3022no—
83#106—3022no—
84#97—1512no—
85#97C2×D15111yescharacteristic
86C2×Q8—21no—
87C2×Q8—3021no—
88C2×Q8C22⋊D15111yescharacteristic
89C2×D4C22⋊D15111yescharacteristic
90C22×C4—3021no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—3022no—
95C4⋊C4—22no—
96C4⋊C4—3022no—
97C4⋊C4—3022no—
98C4⋊C4—3022no—
99C4⋊C4—1512no—
100C4⋊C4—1512no—
101C22⋊C4—22no—
102C22⋊C4—3022no—
103C22⋊C4—3021no—
104C42—3021no—
105C42C22×D15111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—12081no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—3022no—
115C2×C4—3022no—
116C2×C4—12081no—
117C2×C4D4×D15112yes—
118C2×C4C2×C22⋊D15111yescharacteristic
119C8—22no—
120C8—3024no—
121C22—41no—
122C22—42no—
123C22#1801270711yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—6042no—
129C4—6042no—
130C2—81no—
131C2#2375237911yescharacteristic
132C2#2375239312yes—
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#497×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenter#497D151
hypocenterC151#1660
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
3. #23751953C2semidirect
66. C151#1660semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237526182
#237519532
#237519522
#497×C1512
#1660151