Finite Group Databasebeta

← #28379331

Subgroups — #28379331

Order 13952.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#20296012C212yesmaximal, complemented
2#20295934C214yesmaximal, complemented
3#20295593C211yesmaximal, characteristic
4D109⋊M16—22no—
5#16812760C2214yescomplemented
6#16812759—22no—
7C2×#13182029C2211yescharacteristic
8#16812695C412yes—
9#16812686C2212yes—
10#16812670—22no—
11#16812668—22no—
12#16812658C411yescharacteristic
13C22×D4×C109C411yescharacteristic
14#13182039—42no—
15#13182038—24no—
16D109⋊C8—42no—
17#13182029—42no—
18C2×Dic218C2311yescharacteristic
19C2×D436C2×C411yescharacteristic
20C2×C22⋊D109—24no—
21C2×C22⋊D109D412yes—
22C2×C4×D109D412yes—
23C4⋊Dic109—21no—
24C22⋊Dic109—21no—
25C22⋊Dic109—24no—
26C4×Dic109C2×C412yes—
27C24×C109—21no—
28C2×D4×C109—21no—
29C2×D4×C109—42no—
30C2×D4×C109C2×C412yes—
31C22×C4×C109C2×C411yescharacteristic
32C23×C109—22no—
33C23×C109—42no—
34C23×C109—82no—
35C23×C109C22⋊C411yescharacteristic
36C22×D109C22⋊C412yes—
37D4×C109—42no—
38D4×C109—42no—
39C2×C4×C109—22no—
40C2×C4×C109C22⋊C411yescharacteristic
41C2×C4×C109C22×C411yescharacteristic
42C22⋊D109—42no—
43C22⋊D109—84no—
44C2×Dic109—22no—
45C2×Dic109C2×D412yes—
46D436—41no—
47C4×D109—22no—
48C4×D109—22no—
49Dic218—41no—
50#11724786—44no—
51C22×C109—21no—
52C22×C109—41no—
53C22×C109—44no—
54C22×C109—42no—
55C22×C109—84no—
56C22×C109C2×C22⋊C411yescharacteristic
57C2×D109—22no—
58C2×D109—42no—
59C4×C109—21no—
60C4×C109#9912yes—
61Dic109—22no—
62Dic109—42no—
63C2×C109—21no—
64C2×C109—41no—
65C2×C109—82no—
66C2×C109C2×#9911yescharacteristic
67D109—42no—
68#2134—1091nomaximal, Sylow
69C109#213411yescharacteristic, complemented, Sylow
70#535—1091no—
71#413—1092no—
72#355—1094no—
73C2×#41—1091no—
74C22×D4#8913711yescharacteristic
75C2×M16—2182no—
76#127—1092no—
77#124—1092no—
78#121—2182no—
79#120—2182no—
80#117—1091no—
81#101—1094no—
82#100—2182no—
83C24—21no—
84#41—4362no—
85C2×Q8—1091no—
86C2×D4—21no—
87C2×D4—42no—
88C2×D4—1092no—
89C2×D4—1091no—
90C2×D4—2184no—
91C2×D4C2×#8913712yes—
92C22×C4—1092no—
93C22×C4C2×#8913711yescharacteristic
94M16—4362no—
95M16—2184no—
96C2×C8—4362no—
97C4⋊C4—2181no—
98C22⋊C4—2184no—
99C22⋊C4—2181no—
100C42—1092no—
101C23—22no—
102C23—42no—
103C23—82no—
104C23—1092no—
105C23C22⋊#8913711yescharacteristic
106Q8—4361no—
107D4—42no—
108D4—42no—
109D4—8724no—
110D4—4361no—
111D4—4362no—
112C2×C4—22no—
113C2×C4—1092no—
114C2×C4—2182no—
115C2×C4—2182no—
116C2×C4—2182no—
117C2×C4C22⋊#8913711yescharacteristic
118C2×C4C22×#8913711yescharacteristic
119C8—4364no—
120C22—21no—
121C22—41no—
122C22—44no—
123C22—42no—
124C22—84no—
125C22—4362no—
126C22—2182no—
127C22C2×C22⋊#8913711yescharacteristic
128C4—21no—
129C4—4362no—
130C4—2182no—
131C4#1681275712yes—
132C2—21no—
133C2—41no—
134C2—82no—
135C2—4362no—
136C2C2×#1681275711yescharacteristic
subgroupG/H
centerC2C2×#16812757
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC22×D4×C109C4
socleC2×C109C2×#99
prime radical#20295593C2
cosocleC2×Dic218C23
hypercenterC22×D4#89137
hypocenterC109#2134
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20296012C2semidirect
2. #20295934C2semidirect
5. #16812760C22semidirect
69. C109#2134semidirect

Maximal subgroups

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

subgroupindex
#202960122
#202959342
#202955932
#2134109