Finite Group Databasebeta

← #28378945

Subgroups — #28378945

Order 13952.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#16812759C212yesmaximal
2#20295907C214yesmaximal, complemented
3#20295499C211yesmaximal, characteristic
4C2×#13182038C2214yes—
5#16812759—22no—
6#16812759—22no—
7C22×C22⋊D109C2211yescharacteristic
8C4×C22⋊D109—22no—
9#16812659—22no—
10#16812655C2212yes—
11C2×C22⋊Dic109C411yescharacteristic
12C22⋊C4×D109C412yes—
13C2×C22⋊C4×C109C411yescharacteristic
14#13182038—24no—
15#13182038—24no—
16C2×#11724786—24no—
17C23×D109C2×C411yescharacteristic
18C2×C22⋊D109—24no—
19C2×C22⋊D109D412yes—
20C2×C22⋊D109D412yes—
21C22×Dic109—21no—
22C22×Dic109C2311yescharacteristic
23C2×C4×D109—22no—
24#13182008—22no—
25C22⋊Dic109—21no—
26C22⋊Dic109C2×C412yes—
27#13182006—22no—
28C4×Dic109—22no—
29C24×C109C2×C411yescharacteristic
30C22×C4×C109—21no—
31C22⋊C4×C109—21no—
32C22⋊C4×C109C2×C412yes—
33C23×C109—22no—
34C23×C109—81no—
35C23×C109C22⋊C411yescharacteristic
36C23×C109C22⋊C411yescharacteristic
37C23×C109C22×C411yescharacteristic
38C22×D109—22no—
39C22×D109—81no—
40C22×D109C22⋊C412yes—
41C2×C4×C109—22no—
42C2×C4×C109—81no—
43C22⋊D109—24no—
44C22⋊D109—24no—
45C2×Dic109—22no—
46C2×Dic109—81no—
47C2×Dic109C2×D412yes—
48C2×Dic109#4114yes—
49C4×D109—82no—
50#11724786—44no—
51C22×C109—21no—
52C22×C109—21no—
53C22×C109—41no—
54C22×C109—41no—
55C22×C109—41no—
56C22×C109—82no—
57C22×C109C2×C22⋊C411yescharacteristic
58C22×C109#11712yes—
59C2×D109—22no—
60C2×D109—42no—
61C2×D109—82no—
62C4×C109—42no—
63Dic109—42no—
64Dic109#12314yes—
65C2×C109—21no—
66C2×C109—22no—
67C2×C109—41no—
68C2×C109—41no—
69C2×C109#38111yescharacteristic
70D109—42no—
71#1829—1091nomaximal, Sylow
72C109#182911yescharacteristic, complemented, Sylow
73#518—1091no—
74C2×#100—1092no—
75#344—1094no—
76C22×D4—1091no—
77C2×M16—1094no—
78C4×D4—2182no—
79C4×D4—2182no—
80#117—1092no—
81C2×C22⋊C4—1091no—
82C2×C22⋊C4—1092no—
83C2×C22⋊C4#8913711yescharacteristic
84#100—2182no—
85#100—2182no—
86C24—1091no—
87C24C2×#8913711yescharacteristic
88C2×D4—1092no—
89C2×D4—1092no—
90C2×D4—2184no—
91C22×C4—21no—
92C22×C4—1091no—
93C22×C4—2182no—
94C22×C4—2181no—
95M16—2184no—
96M16—2184no—
97C2×C8—2184no—
98C4⋊C4—2182no—
99C22⋊C4—21no—
100C22⋊C4—1092no—
101C22⋊C4—2182no—
102C22⋊C4—2181no—
103C22⋊C4C2×#8913712yes—
104C42—2182no—
105C23—22no—
106C23—81no—
107C23—8721no—
108C23—1092no—
109C23—2182no—
110C23C22⋊#8913711yescharacteristic
111C23C22⋊#8913711yescharacteristic
112C23C22×#8913711yescharacteristic
113D4—2184no—
114D4—2184no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—8722no—
118C2×C4—8721no—
119C2×C4—1092no—
120C2×C4—1094no—
121C2×C4—2182no—
122C8—4364no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—8722no—
130C22—4362no—
131C22—2182no—
132C22C2×C22⋊#8913711yescharacteristic
133C22#1681277812yes—
134C4—42no—
135C4—1094no—
136C4—4362no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—4362no—
142C2#2029596911yescharacteristic
subgroupG/H
centerC2#20295969
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC2×C109#381
prime radicalC22×C22⋊D109C22
cosocleC22×Dic109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109#1829
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20295907C2semidirect
72. C109#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#168127592
#202959072
#202954992
#1829109