Finite Group Databasebeta

← #28405474

Subgroups — #28405474

Order 14464.

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#20299569C211yesmaximal, characteristic
2#20299540C211yesmaximal, characteristic
3#20298561C211yesmaximal, characteristic
4C2×#14268657—21no—
5C2×C4⋊#90673—21no—
6C2×C22⋊#90673C412yes—
7#16813679—21no—
8C22⋊#11744753C412yescomplemented
9(C2×#90673)⋊C4—21no—
10C22×C4×D113C2211yescharacteristic
11C2×#14268631C411yescharacteristic, complemented
12#16813534—21no—
13#16813534—21no—
14C2×M16×C113C411yescharacteristic, complemented
15C22×#90673—22no—
16#14268657—41no—
17#14268657—41no—
18C2×#11744753—22no—
19C4⋊#90673—41no—
20C4⋊#90673—41no—
21C22⋊#90673—42no—
22C23×D113C2×C411yescharacteristic
23C22×Dic113C2×C411yescharacteristic
24C2×C4×D113—41no—
25C2×C4×D113—41no—
26C2×C4×D113D411yescharacteristic
27C2×C4×D113D411yescharacteristic
28C2×C4×D113D411yescharacteristic
29C2×C4×D113Q811yescharacteristic
30#14268631—41no—
31C2×#11744751—21no—
32C22×C4×C113C2×C411yescharacteristic
33M16×C113—41no—
34C2×C8×C113—21no—
35C23×C113C4211yescharacteristic
36C22×D113—21no—
37C22×D113—21no—
38C22×D113—41no—
39C22×D113—41no—
40C22×D113C22⋊C411yescharacteristic
41C22×D113C4⋊C411yescharacteristic
42C2×#90673—42no—
43C2×#90673—42no—
44C2×#90673—42no—
45C2×C4×C113—21no—
46C2×C4×C113—21no—
47C2×C4×C113C22⋊C411yescharacteristic
48C2×C4×C113C4⋊C411yescharacteristic
49C2×Dic113—41no—
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C4⋊C411yescharacteristic
52C4×D113—21no—
53C4×D113—21no—
54C4×D113—21no—
55C4×D113—21no—
56C4×D113—41no—
57C4×D113—41no—
58#11744753—42no—
59C8×C113—41no—
60#11744751—41no—
61C22×C113—21no—
62C22×C113—21no—
63C22×C113—21no—
64C22×C113#9511yescharacteristic
65C2×D113—21no—
66C2×D113—21no—
67C2×D113—21no—
68C2×D113—21no—
69C2×D113—21no—
70C2×D113—42no—
71C2×D113—42no—
72C2×D113#10011yescharacteristic
73C2×D113#10111yescharacteristic
74#90673—82no—
75C4×C113—21no—
76C4×C113#9911yescharacteristic
77C4×C113#9911yescharacteristic
78Dic113—21no—
79Dic113—21no—
80C2×C113—41no—
81C2×C113#34211yescharacteristic
82C2×C113#34311yescharacteristic
83C2×C113#34411yescharacteristic
84D113—21no—
85D113—21no—
86D113—41no—
87#1305—1131nomaximal, Sylow
88C113#130511yescharacteristic, complemented, Sylow
89#407—1131no—
90#407—1131no—
91#380—1131no—
92C23×C4—1131no—
93C2×M16—1131no—
94C2×M16—2261no—
95C2×M16#9067311yescharacteristic, complemented
96C2×C4⋊C4—2261no—
97C2×C22⋊C4—1132no—
98C22⋊C8—1132no—
99C22⋊C8—2261no—
100C22⋊C8—2261no—
101C22⋊C8—2261no—
102#95—2261no—
103C24—1131no—
104C22×C4—1131no—
105C22×C4—1131no—
106C22×C4—1131no—
107C22×C4—1131no—
108C22×C4—1131no—
109C22×C4—4521no—
110C22×C4—4521no—
111C22×C4—2262no—
112C22×C4C2×#9067311yescharacteristic
113M16—41no—
114M16—4521no—
115M16—4521no—
116M16—4521no—
117C2×C8—21no—
118C2×C8—2262no—
119C2×C8—2261no—
120C4⋊C4—4521no—
121C4⋊C4—4521no—
122C22⋊C4—4522no—
123C23—1131no—
124C23—1131no—
125C23—4521no—
126C23—4521no—
127C23—2261no—
128C23—2261no—
129C23C4×#9067311yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—1131no—
133C2×C4—1131no—
134C2×C4—4521no—
135C2×C4—4521no—
136C2×C4—4522no—
137C2×C4—4522no—
138C2×C4—4522no—
139C2×C4—4521no—
140C2×C4—2261no—
141C2×C4—2261no—
142C2×C4—2261no—
143C2×C4—2261no—
144C2×C4C22⋊#9067311yescharacteristic
145C2×C4C4⋊#9067311yescharacteristic
146C8—41no—
147C8—4522no—
148C8—4521no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—1131no—
153C22—1131no—
154C22—4522no—
155C22—4522no—
156C22—2261no—
157C22—2261no—
158C22—2261no—
159C22—2261no—
160C22—2261no—
161C22(C2×#90673)⋊C411yescharacteristic
162C4—21no—
163C4—9042no—
164C4—2261no—
165C4—2261no—
166C4#1681368011yescharacteristic
167C4#1681368111yescharacteristic
168C2—41no—
169C2—4521no—
170C2—2261no—
171C2—2261no—
172C2#2029947611yescharacteristic
173C2#2029947711yescharacteristic
174C2#2029948111yescharacteristic
subgroupG/H
centerC22(C2×#90673)⋊C4
commutatorC23×C113C42
FrattiniC22×C4C2×#90673
FittingC2×M16×C113C4
socleC22×C113#95
prime radicalC23×D113C2×C4
cosocleC22×C4×D113C22
hypercenterC2×M16#90673
hypocenterC113#1305
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#11744753C4semidirect
11. C2×#14268631C4semidirect
14. C2×M16×C113C4semidirect
88. C113#1305semidirect
95. C2×M16#90673semidirect

Maximal subgroups

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

subgroupindex
#202995692
#202995402
#202985612
#1305113