Finite Group Databasebeta

← #28362327

Subgroups — #28362327

Order 13952.

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

normal subgroups only

This group has 230 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#20295774C211yesmaximal, characteristic, complemented
2#20295415C212yesmaximal, complemented
3#20295392C211yesmaximal, characteristic, complemented
4#20294765C212yesmaximal, complemented
5#330×C109C211yesmaximal, characteristic, complemented
6C2×#13182018—22no—
7C2×D872—22no—
8#16812696C2211yescharacteristic
9#16812687C2212yes—
10#16812684—22no—
11#16812677—22no—
12#16812674—22no—
13#16812619—22no—
14#16812610C2211yescharacteristic
15#125×C109C2211yescharacteristic
16#97×C109C2212yes—
17C2×Dic218D412yes—
18C2×D436—21no—
19C2×D436—22no—
20C2×D436—22no—
21C2×D436D412yes—
22C2×C4×D109—22no—
23#13182018—44no—
24D872—44no—
25C2×#11724784—21no—
26#13182008—22no—
27#13182006—22no—
28#13182006—22no—
29#13182006—22no—
30C2×C8×C109—22no—
31C4⋊C4×C109—22no—
32C4⋊C4×C109D412yes—
33C42×C109C2311yescharacteristic
34C22×D109—22no—
35C22×D109—41no—
36C2×C4×C109—22no—
37C2×C4×C109C2×D412yes—
38C2×C4×C109C2×D411yescharacteristic
39C2×Dic109—22no—
40D436—42no—
41D436—42no—
42D436—42no—
43D436—42no—
44D436—82no—
45C4×D109—82no—
46Dic218—42no—
47C8×C109—24no—
48#11724784—41no—
49C22×C109#12011yescharacteristic
50C2×D109—42no—
51C2×D109—42no—
52C2×D109—42no—
53C2×D109—82no—
54C2×D109—81no—
55C4×C109—22no—
56C4×C109—21no—
57C4×C109—42no—
58Dic109—42no—
59C2×C109#45312yes—
60C2×C109#45411yescharacteristic
61D109—82no—
62D109—161no—
63#1656—1091nomaximal, Sylow
64C109#165611yescharacteristic, complemented, Sylow
65#562—1091no—
66#496—1092no—
67#490—1091no—
68#330D10911yescharacteristic, complemented
69#329—1092no—
70C2×SD16—2182no—
71C2×D8—2182no—
72#127—1091no—
73#125C2×D10911yescharacteristic
74#124—1092no—
75#123—2182no—
76C22⋊Q8—2182no—
77#121—2182no—
78#102—2182no—
79#97—1091no—
80#97C2×D10912yes—
81C2×Q8—1092no—
82C2×D4—1092no—
83C2×D4—2182no—
84C2×D4—2182no—
85C2×D4—2181no—
86C22×C4—2182no—
87SD16—4364no—
88D8—4364no—
89C2×C8—22no—
90C2×C8—2181no—
91C4⋊C4—22no—
92C4⋊C4—2182no—
93C4⋊C4D43612yes—
94C22⋊C4—2182no—
95C22⋊C4—2182no—
96C22⋊C4—2182no—
97C42C22×D10911yescharacteristic
98C23—4361no—
99C23—2182no—
100Q8—4362no—
101D4—8722no—
102D4—4362no—
103D4—4362no—
104D4—4362no—
105D4—4362no—
106C2×C4—22no—
107C2×C4—8722no—
108C2×C4—2182no—
109C2×C4D4×D10912yes—
110C2×C4C2×D43611yescharacteristic
111C8—24no—
112C8—4361no—
113C22—8722no—
114C22—8721no—
115C22—4362no—
116C22—4362no—
117C22—4362no—
118C22#1681266911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—4362no—
123C2—8722no—
124C2—17441no—
125C2#2029519512yes—
126C2#2029520111yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#330×C109C2
socleC22×C109#120
hypercenter#330D109
hypocenterC109#1656
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #20295774C2semidirect
2. #20295415C2semidirect
3. #20295392C2semidirect
4. #20294765C2semidirect
5. #330×C109C2semidirect
64. C109#1656semidirect
68. #330D109semidirect

Maximal subgroups

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

subgroupindex
#202957742
#202954152
#202953922
#202947652
#330×C1092
#1656109