Finite Group Databasebeta

← #28362149

Subgroups — #28362149

Order 13952.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#20295661C211yesmaximal, characteristic
2#20295398C211yesmaximal, characteristic, complemented
3#20295317C212yesmaximal, complemented
4#20294753C212yesmaximal, complemented
5#331×C109C211yesmaximal, characteristic, complemented
6C2×D4×D109—22no—
7C2×#13182017—22no—
8#16812699C2211yescharacteristic, complemented
9#16812670—22no—
10#16812667—22no—
11C4×D436C2212yes—
12#16812631—22no—
13#16812621—22no—
14C4×#11724784C2211yescharacteristic, complemented
15#127×C109C2211yescharacteristic
16C4⋊C8×C109C2212yescomplemented
17C23×D109—22no—
18C2×Dic218—21no—
19C2×D436D412yes—
20C2×C22⋊D109—24no—
21D4×D109—44no—
22D4×D109—44no—
23C2×C4×D109—22no—
24#13182017—44no—
25C2×#11724784—21no—
26C4⋊Dic109—22no—
27C4⋊Dic109D412yes—
28C22⋊Dic109—22no—
29#13182006—22no—
30C2×D4×C109—22no—
31C2×D4×C109D412yes—
32C2×C8×C109—22no—
33C42×C109C2311yescharacteristic
34C23×C109—22no—
35C22×D109—22no—
36C22×D109—48no—
37C22×D109—82no—
38D4×C109—42no—
39D4×C109—42no—
40D4×C109—42no—
41C2×C4×C109C2×D412yes—
42C2×C4×C109C2×D411yescharacteristic
43C22⋊D109—48no—
44C2×Dic109—22no—
45C2×Dic109—41no—
46D436—22no—
47D436SD1614yescomplemented
48C4×D109—42no—
49C4×D109—42no—
50Dic218—42no—
51C8×C109—42no—
52#11724784—22no—
53C22×C109—44no—
54C22×C109—42no—
55C22×C109#12011yescharacteristic
56C2×D109—24no—
57C2×D109—42no—
58C2×D109—42no—
59C2×D109—88no—
60C4×C109—21no—
61C4×C109C2×SD1612yes—
62C4×C109AGL(1,ℤ/8)12yes—
63Dic109—42no—
64Dic109—81no—
65C2×C109—82no—
66C2×C109#45012yes—
67C2×C109#45311yescharacteristic
68D109—44no—
69#1629—1091nomaximal, Sylow
70C109#162911yescharacteristic, complemented, Sylow
71D42—1091no—
72#492—1091no—
73#476—1092no—
74#331D10911yescharacteristic, complemented
75D4⋊C8—1092no—
76C22×D4—2182no—
77C2×SD16—2182no—
78C4⋊Q8—1091no—
79#127C2×D10911yescharacteristic
80#121—2182no—
81#120—2182no—
82C4×D4—1092no—
83#106—2182no—
84C4⋊C8C2×D10912yescomplemented
85#102—2182no—
86C4×C8—1091no—
87C24—2182no—
88C2×Q8—2181no—
89C2×D4—22no—
90C2×D4—1092no—
91C2×D4—4364no—
92C2×D4—4364no—
93C2×D4—2184no—
94C2×D4D43612yes—
95C22×C4—2182no—
96SD16—4364no—
97C2×C8—22no—
98C2×C8—2181no—
99C4⋊C4—1092no—
100C4⋊C4—2182no—
101C22⋊C4—2182no—
102C22⋊C4—2182no—
103C42C22×D10911yescharacteristic
104C23—22no—
105C23—8722no—
106C23—4368no—
107C23—2182no—
108Q8—4362no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—1094no—
113D4—4368no—
114D4—2182no—
115C2×C4—4361no—
116C2×C4—4362no—
117C2×C4—4362no—
118C2×C4—2182no—
119C2×C4D4×D10912yes—
120C2×C4C2×D43611yescharacteristic
121C8—42no—
122C8—2182no—
123C22—44no—
124C22—42no—
125C22—8728no—
126C22—4362no—
127C22—4362no—
128C22—2184no—
129C22#1681266911yescharacteristic
130C4—21no—
131C4—8721no—
132C4—4362no—
133C4SD16×D10912yes—
134C4#1681272312yes—
135C2—82no—
136C2—4364no—
137C2#2029517812yes—
138C2#2029519611yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#331×C109C2
socleC22×C109#120
prime radical#20295661C2
hypercenter#331D109
hypocenterC109#1629
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20295398C2semidirect
3. #20295317C2semidirect
4. #20294753C2semidirect
5. #331×C109C2semidirect
8. #16812699C22semidirect
14. C4×#11724784C22semidirect
16. C4⋊C8×C109C22semidirect
47. D436SD16semidirect
70. C109#1629semidirect
74. #331D109semidirect
84. C4⋊C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956612
#202953982
#202953172
#202947532
#331×C1092
#1629109