Finite Group Databasebeta

← #28377932

Subgroups — #28377932

Order 13952.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#20295997C211yesmaximal, characteristic
2#20295968C211yesmaximal, characteristic
3#20294989C211yesmaximal, characteristic
4C2×#13182039—21no—
5C2×C4⋊#89137—21no—
6C2×C22⋊#89137C412yes—
7#16812756—21no—
8C22⋊#11724786C412yescomplemented
9(C2×#89137)⋊C4—21no—
10C22×C4×D109C2211yescharacteristic
11C2×#13182013C411yescharacteristic, complemented
12#16812611—21no—
13#16812611—21no—
14C2×M16×C109C411yescharacteristic, complemented
15C22×#89137—22no—
16#13182039—41no—
17#13182039—41no—
18C2×#11724786—22no—
19C4⋊#89137—41no—
20C4⋊#89137—41no—
21C22⋊#89137—42no—
22C23×D109C2×C411yescharacteristic
23C22×Dic109C2×C411yescharacteristic
24C2×C4×D109—41no—
25C2×C4×D109—41no—
26C2×C4×D109D411yescharacteristic
27C2×C4×D109D411yescharacteristic
28C2×C4×D109D411yescharacteristic
29C2×C4×D109Q811yescharacteristic
30#13182013—41no—
31C2×#11724784—21no—
32C22×C4×C109C2×C411yescharacteristic
33M16×C109—41no—
34C2×C8×C109—21no—
35C23×C109C4211yescharacteristic
36C22×D109—21no—
37C22×D109—21no—
38C22×D109—41no—
39C22×D109—41no—
40C22×D109C22⋊C411yescharacteristic
41C22×D109C4⋊C411yescharacteristic
42C2×#89137—42no—
43C2×#89137—42no—
44C2×#89137—42no—
45C2×C4×C109—21no—
46C2×C4×C109—21no—
47C2×C4×C109C22⋊C411yescharacteristic
48C2×C4×C109C4⋊C411yescharacteristic
49C2×Dic109—41no—
50C2×Dic109C22⋊C411yescharacteristic
51C2×Dic109C4⋊C411yescharacteristic
52C4×D109—21no—
53C4×D109—21no—
54C4×D109—21no—
55C4×D109—21no—
56C4×D109—41no—
57C4×D109—41no—
58#11724786—42no—
59C8×C109—41no—
60#11724784—41no—
61C22×C109—21no—
62C22×C109—21no—
63C22×C109—21no—
64C22×C109#9511yescharacteristic
65C2×D109—21no—
66C2×D109—21no—
67C2×D109—21no—
68C2×D109—21no—
69C2×D109—21no—
70C2×D109—42no—
71C2×D109—42no—
72C2×D109#10011yescharacteristic
73C2×D109#10111yescharacteristic
74#89137—82no—
75C4×C109—21no—
76C4×C109#9911yescharacteristic
77C4×C109#9911yescharacteristic
78Dic109—21no—
79Dic109—21no—
80C2×C109—41no—
81C2×C109#34211yescharacteristic
82C2×C109#34311yescharacteristic
83C2×C109#34411yescharacteristic
84D109—21no—
85D109—21no—
86D109—41no—
87#1305—1091nomaximal, Sylow
88C109#130511yescharacteristic, complemented, Sylow
89#407—1091no—
90#407—1091no—
91#380—1091no—
92C23×C4—1091no—
93C2×M16—1091no—
94C2×M16—2181no—
95C2×M16#8913711yescharacteristic, complemented
96C2×C4⋊C4—2181no—
97C2×C22⋊C4—1092no—
98C22⋊C8—1092no—
99C22⋊C8—2181no—
100C22⋊C8—2181no—
101C22⋊C8—2181no—
102#95—2181no—
103C24—1091no—
104C22×C4—1091no—
105C22×C4—1091no—
106C22×C4—1091no—
107C22×C4—1091no—
108C22×C4—1091no—
109C22×C4—4361no—
110C22×C4—4361no—
111C22×C4—2182no—
112C22×C4C2×#8913711yescharacteristic
113M16—41no—
114M16—4361no—
115M16—4361no—
116M16—4361no—
117C2×C8—21no—
118C2×C8—2182no—
119C2×C8—2181no—
120C4⋊C4—4361no—
121C4⋊C4—4361no—
122C22⋊C4—4362no—
123C23—1091no—
124C23—1091no—
125C23—4361no—
126C23—4361no—
127C23—2181no—
128C23—2181no—
129C23C4×#8913711yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—1091no—
133C2×C4—1091no—
134C2×C4—4361no—
135C2×C4—4361no—
136C2×C4—4362no—
137C2×C4—4362no—
138C2×C4—4362no—
139C2×C4—4361no—
140C2×C4—2181no—
141C2×C4—2181no—
142C2×C4—2181no—
143C2×C4—2181no—
144C2×C4C22⋊#8913711yescharacteristic
145C2×C4C4⋊#8913711yescharacteristic
146C8—41no—
147C8—4362no—
148C8—4361no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—1091no—
153C22—1091no—
154C22—4362no—
155C22—4362no—
156C22—2181no—
157C22—2181no—
158C22—2181no—
159C22—2181no—
160C22—2181no—
161C22(C2×#89137)⋊C411yescharacteristic
162C4—21no—
163C4—8722no—
164C4—2181no—
165C4—2181no—
166C4#1681275711yescharacteristic
167C4#1681275811yescharacteristic
168C2—41no—
169C2—4361no—
170C2—2181no—
171C2—2181no—
172C2#2029590411yescharacteristic
173C2#2029590511yescharacteristic
174C2#2029590911yescharacteristic
subgroupG/H
centerC22(C2×#89137)⋊C4
commutatorC23×C109C42
FrattiniC22×C4C2×#89137
FittingC2×M16×C109C4
socleC22×C109#95
prime radicalC23×D109C2×C4
cosocleC22×C4×D109C22
hypercenterC2×M16#89137
hypocenterC109#1305
LCSG ▷ C23×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#11724786C4semidirect
11. C2×#13182013C4semidirect
14. C2×M16×C109C4semidirect
88. C109#1305semidirect
95. C2×M16#89137semidirect

Maximal subgroups

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

subgroupindex
#202959972
#202959682
#202949892
#1305109