Finite Group Databasebeta

← #28362341

Subgroups — #28362341

Order 13952.

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#20295776C211yesmaximal, characteristic
2#20295432C212yesmaximal, complemented
3#20294767C212yesmaximal, complemented
4#20294766C211yesmaximal, characteristic
5#497×C109C211yesmaximal, characteristic
6#16812697—21no—
7#16812692—22no—
8#16812691C2212yes—
9#16812680—21no—
10#16812676—22no—
11#16812632—22no—
12#16812630—22no—
13#16812610C2212yes—
14C2×Q16×C109—21no—
15C2×SD16×C109—21no—
16C4⋊Q8×C109C2211yescharacteristic
17#124×C109C2211yescharacteristic
18#97×C109C2211yescharacteristic
19C2×Dic218—21no—
20C22×Dic109—21no—
21C2×#11724784—22no—
22C4⋊Dic109D412yes—
23C4⋊Dic109D412yes—
24#13182008—22no—
25#13182008—22no—
26#13182008—22no—
27C22⋊Dic109—22no—
28C22⋊Dic109—21no—
29C4×Dic109—21no—
30C2×Q8×C109—21no—
31C2×Q8×C109D411yescharacteristic
32C2×D4×C109D411yescharacteristic
33Q16×C109—42no—
34SD16×C109—42no—
35C2×C8×C109—21no—
36C4⋊C4×C109—22no—
37C22⋊C4×C109—22no—
38C42×C109C2311yescharacteristic
39C23×C109—21no—
40Q8×C109—41no—
41Q8×C109—41no—
42Q8×C109—41no—
43D4×C109—41no—
44C2×C4×C109—21no—
45C2×C4×C109—41no—
46C2×C4×C109C2×D412yes—
47C2×C4×C109C2×D411yescharacteristic
48C2×Dic109—22no—
49C2×Dic109—22no—
50C2×Dic109—81no—
51Dic218—81no—
52C8×C109—22no—
53#11724784—24no—
54C22×C109—41no—
55C22×C109—42no—
56C22×C109#12011yescharacteristic
57C4×C109—21no—
58C4×C109—22no—
59C4×C109—41no—
60C4×C109—81no—
61Dic109—42no—
62Dic109—42no—
63C2×C109—81no—
64C2×C109#45311yescharacteristic
65C2×C109#45612yes—
66#1660—1091nomaximal, Sylow
67C109#166011yescharacteristic, complemented, Sylow
68#563—1091no—
69#501—1092no—
70#497D10911yescharacteristic
71#330—1092no—
72#329—1091no—
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—2181no—
76C4⋊Q8C2×D10911yescharacteristic
77#126—2182no—
78#125—1092no—
79#124C2×D10911yescharacteristic
80#123—2181no—
81C22⋊Q8—2182no—
82#107—2182no—
83#106—2182no—
84#97—1092no—
85#97C2×D10911yescharacteristic
86C2×Q8—21no—
87C2×Q8—2181no—
88C2×Q8C22⋊D10911yescharacteristic
89C2×D4C22⋊D10911yescharacteristic
90C22×C4—2181no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—2182no—
95C4⋊C4—22no—
96C4⋊C4—1092no—
97C4⋊C4—1092no—
98C4⋊C4—2182no—
99C4⋊C4—2182no—
100C4⋊C4—2182no—
101C22⋊C4—22no—
102C22⋊C4—2182no—
103C22⋊C4—2181no—
104C42—2181no—
105C42C22×D10911yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—8721no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—8721no—
115C2×C4—2182no—
116C2×C4—2182no—
117C2×C4D4×D10912yes—
118C2×C4C2×C22⋊D10911yescharacteristic
119C8—22no—
120C8—2184no—
121C22—41no—
122C22—42no—
123C22#1681266711yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—4362no—
129C4—4362no—
130C2—81no—
131C2#2029519311yescharacteristic
132C2#2029520712yes—
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#497×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenter#497D109
hypocenterC109#1660
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #20295432C2semidirect
3. #20294767C2semidirect
67. C109#1660semidirect

Maximal subgroups

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

subgroupindex
#202957762
#202954322
#202947672
#202947662
#497×C1092
#1660109