Finite Group Databasebeta

← #28362116

Subgroups — #28362116

Order 13952.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20295742C211yesmaximal, characteristic, complemented
2#20295400C211yesmaximal, characteristic, complemented
3#20295222C212yesmaximal, complemented
4#20294753C212yesmaximal, complemented
5#333×C109C211yesmaximal, characteristic, complemented
6C2×#13182016—22no—
7C2×D872—22no—
8#16812696C2211yescharacteristic
9#16812688—22no—
10#16812674—22no—
11C4×D436C2212yes—
12#16812657—22no—
13#16812621—22no—
14C4×#11724784C2211yescharacteristic
15C4⋊Q8×C109C2211yescharacteristic
16C4⋊C8×C109C2212yes—
17C2×D436—22no—
18C2×D436—21no—
19C2×D436—22no—
20C2×D436D412yes—
21C2×C4×D109—22no—
22#13182016—44no—
23D872—44no—
24C2×#11724784—21no—
25C4⋊Dic109D412yes—
26#13182006—24no—
27#13182006—22no—
28C4×Dic109—22no—
29C2×Q8×C109D412yes—
30C2×C8×C109—22no—
31C4⋊C4×C109—22no—
32C42×C109C2311yescharacteristic
33C22×D109—22no—
34C22×D109—41no—
35Q8×C109—42no—
36C2×C4×C109—22no—
37C2×C4×C109C2×D412yes—
38C2×C4×C109C2×D411yescharacteristic
39C2×Dic109—22no—
40D436—22no—
41D436—22no—
42D436—42no—
43D436—42no—
44D436—42no—
45D436—82no—
46C4×D109—42no—
47C4×D109—42no—
48C8×C109—42no—
49#11724784—22no—
50C22×C109#12011yescharacteristic
51C2×D109—42no—
52C2×D109—42no—
53C2×D109—42no—
54C2×D109—82no—
55C2×D109—81no—
56C4×C109—21no—
57C4×C109—42no—
58C4×C109#13512yes—
59C4×C109AGL(1,ℤ/8)12yes—
60Dic109—42no—
61C2×C109#44912yes—
62C2×C109#45311yescharacteristic
63D109—82no—
64D109—161no—
65#1624—1091nomaximal, Sylow
66C109#162411yescharacteristic, complemented, Sylow
67#555—1091no—
68#492—1091no—
69#459—1092no—
70#333D10911yescharacteristic, complemented
71D4⋊C8—1092no—
72C2×SD16—2182no—
73C2×D8—2182no—
74C4⋊Q8C2×D10911yescharacteristic
75#127—1091no—
76#124—2182no—
77#121—2182no—
78C4×D4—1092no—
79#117—2182no—
80C4⋊C8C2×D10912yes—
81#102—2182no—
82C4×C8—1091no—
83C2×Q8D43612yes—
84C2×D4—1092no—
85C2×D4—2182no—
86C2×D4—2182no—
87C2×D4—2181no—
88C22×C4—2182no—
89SD16—4364no—
90D8—4364no—
91C2×C8—22no—
92C2×C8—2181no—
93C4⋊C4—22no—
94C4⋊C4—1092no—
95C22⋊C4—2184no—
96C22⋊C4—2182no—
97C42—2182no—
98C42C22×D10911yescharacteristic
99C23—4361no—
100C23—2182no—
101Q8—42no—
102D4—8722no—
103D4—4362no—
104D4—4362no—
105D4—4362no—
106D4—2182no—
107D4—2182no—
108C2×C4—22no—
109C2×C4—4362no—
110C2×C4—4362no—
111C2×C4—2182no—
112C2×C4D4×D10912yes—
113C2×C4C2×D43611yescharacteristic
114C8—42no—
115C8—2182no—
116C22—8722no—
117C22—8721no—
118C22—4362no—
119C22—4362no—
120C22—4362no—
121C22#1681266911yescharacteristic
122C4—21no—
123C4—42no—
124C4—4362no—
125C4#1681272212yes—
126C4#1681272612yes—
127C2—8722no—
128C2—17441no—
129C2#2029517412yes—
130C2#2029519611yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#333×C109C2
socleC22×C109#120
hypercenter#333D109
hypocenterC109#1624
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #20295742C2semidirect
2. #20295400C2semidirect
3. #20295222C2semidirect
4. #20294753C2semidirect
5. #333×C109C2semidirect
66. C109#1624semidirect
70. #333D109semidirect

Maximal subgroups

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

subgroupindex
#202957422
#202954002
#202952222
#202947532
#333×C1092
#1624109