Finite Group Databasebeta

← #28378133

Subgroups — #28378133

Order 13952.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#20296012C211yesmaximal, characteristic
2#20296005C211yesmaximal, characteristic
3#20294994C211yesmaximal, characteristic
4D109⋊M16—21no—
5#16812778—21no—
6#16812760C412yescomplemented
7#16812759—21no—
8#16812758C412yes—
9#16812757—21no—
10C2×#13182029C2211yescharacteristic
11C22×#11724784C411yescharacteristic, complemented
12#16812611—21no—
13#16812611—21no—
14C2×M16×C109C411yescharacteristic, complemented
15#13182039—41no—
16#13182038—22no—
17D109⋊C8—41no—
18C4⋊#89137—41no—
19C22⋊#89137—22no—
20C4×#89137—41no—
21#13182029—41no—
22#13182029—41no—
23C2×Dic218C2×C411yescharacteristic
24C2×D436C2×C411yescharacteristic
25C2×C22⋊D109D411yescharacteristic
26C2×C22⋊D109Q811yescharacteristic
27C2×C4×D109D411yescharacteristic
28C2×C4×D109D411yescharacteristic
29C2×#11724784—21no—
30C2×#11724784—41no—
31C22×C4×C109C2×C411yescharacteristic
32M16×C109—41no—
33C2×C8×C109—21no—
34C23×C109C4⋊C411yescharacteristic
35C22×D109C22⋊C411yescharacteristic
36C22×D109C4⋊C411yescharacteristic
37C2×#89137—42no—
38C2×C4×C109—21no—
39C2×C4×C109—21no—
40C2×C4×C109C4211yescharacteristic
41C2×C4×C109C22⋊C411yescharacteristic
42C22⋊D109—41no—
43C22⋊D109—41no—
44C2×Dic109C22⋊C411yescharacteristic
45C2×Dic109C4⋊C411yescharacteristic
46D436—41no—
47C4×D109—21no—
48C4×D109—21no—
49C4×D109—21no—
50C4×D109—21no—
51Dic218—41no—
52#11724786—42no—
53C8×C109—41no—
54#11724784—41no—
55C22×C109—21no—
56C22×C109—41no—
57C22×C109#9511yescharacteristic
58C2×D109—21no—
59C2×D109—21no—
60C2×D109—41no—
61C2×D109—41no—
62#89137—82no—
63C4×C109—21no—
64C4×C109#9911yescharacteristic
65C4×C109#9911yescharacteristic
66Dic109—21no—
67Dic109—21no—
68C2×C109—21no—
69C2×C109—41no—
70C2×C109#34211yescharacteristic
71D109—41no—
72D109—41no—
73#1395—1091nomaximal, Sylow
74C109#139511yescharacteristic, complemented, Sylow
75#413—1091no—
76#410—1091no—
77#408—1091no—
78C2×#41—1091no—
79C2×M16—2181no—
80C2×M16#8913711yescharacteristic, complemented
81C22×C8—1091no—
82#117—2181no—
83#101—1092no—
84#100—2181no—
85#99—1092no—
86#99—2181no—
87C22⋊C8—2181no—
88C22⋊C8—2181no—
89#41—4361no—
90#41—4361no—
91C2×Q8—1091no—
92C2×D4—1091no—
93C2×D4—1091no—
94C2×D4—1091no—
95C22×C4—1091no—
96C22×C4—1091no—
97C22×C4C2×#8913711yescharacteristic
98M16—41no—
99M16—4361no—
100M16—2182no—
101C2×C8—21no—
102C2×C8—4361no—
103C2×C8—4361no—
104C2×C8—2181no—
105C4⋊C4—4361no—
106C22⋊C4—2182no—
107C42—4361no—
108C23—1091no—
109C23—1091no—
110C23C4⋊#8913711yescharacteristic
111Q8—4361no—
112D4—4361no—
113D4—4361no—
114D4—4361no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—1091no—
118C2×C4—1091no—
119C2×C4—4362no—
120C2×C4—2181no—
121C2×C4—2181no—
122C2×C4—2181no—
123C2×C4—2181no—
124C2×C4C4×#8913711yescharacteristic
125C2×C4C22⋊#8913711yescharacteristic
126C8—41no—
127C8—4362no—
128C8—4361no—
129C22—21no—
130C22—41no—
131C22—4361no—
132C22—4361no—
133C22—2181no—
134C22—2181no—
135C22(C2×#89137)⋊C411yescharacteristic
136C4—21no—
137C4—8722no—
138C4—2181no—
139C4—2181no—
140C4#1681275711yescharacteristic
141C4#1681275811yescharacteristic
142C2—21no—
143C2—41no—
144C2—4361no—
145C2—4361no—
146C2#2029590411yescharacteristic
subgroupG/H
centerC4#16812757
commutatorC2×C4×C109C42
FrattiniC22×C4C2×#89137
FittingC2×M16×C109C4
socleC2×C109#342
prime radical, cosocleC2×#13182029C22
hypercenterC2×M16#89137
hypocenterC109#1395
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #16812760C4semidirect
11. C22×#11724784C4semidirect
14. C2×M16×C109C4semidirect
74. C109#1395semidirect
80. C2×M16#89137semidirect

Maximal subgroups

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

subgroupindex
#202960122
#202960052
#202949942
#1395109