Finite Group Databasebeta

← #28389656

Subgroups — #28389656

Order 14464.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299313C211yesmaximal, characteristic, complemented
2#20298970C211yesmaximal, characteristic, complemented
3#20298790C211yesmaximal, characteristic, complemented
4#20298346C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#459×C113C211yesmaximal, characteristic, complemented
8C2×#14268635—22no—
9C2×#14268632—21no—
10#16813622C2211yescharacteristic
11#16813608—22no—
12#16813596—21no—
13#16813593—21no—
14C4×D452C2211yescharacteristic
15#16813581—21no—
16#16813580—21no—
17C4⋊#11744751C2211yescharacteristic
18#16813543—21no—
19C4×#11744751C2211yescharacteristic
20C2×D8×C113—21no—
21#127×C113C2211yescharacteristic
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24#102×C113—21no—
25C2×Dic226D412yes—
26C2×D452D411yescharacteristic
27C2×C22⋊D113—22no—
28C2×C4×D113—21no—
29#14268635—44no—
30#14268632—42no—
31C2×#11744751—21no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36C22⋊Dic113—22no—
37#14268624—22no—
38#14268624—21no—
39C4×Dic113—22no—
40C2×D4×C113—21no—
41C2×D4×C113—21no—
42C2×D4×C113—21no—
43C2×D4×C113D411yescharacteristic
44C22×C4×C113—21no—
45D8×C113—42no—
46C2×C8×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C23×C113—41no—
52C22×D113—21no—
53D4×C113—21no—
54D4×C113—21no—
55D4×C113—42no—
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59D4×C113—41no—
60C2×C4×C113—21no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113C2×D411yescharacteristic
66C22⋊D113—82no—
67C2×Dic113—21no—
68C2×Dic113—22no—
69D452—21no—
70D452—21no—
71C4×D113—41no—
72C4×D113—41no—
73Dic226—42no—
74C8×C113—41no—
75#11744751—22no—
76#11744751—41no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113—81no—
81C22×C113—81no—
82C22×C113—81no—
83C22×C113#12011yescharacteristic
84C2×D113—41no—
85C2×D113—41no—
86C2×D113—41no—
87C4×C113—21no—
88C4×C113—41no—
89C4×C113#13511yescharacteristic
90C4×C113#13511yescharacteristic
91C4×C113AGL(1,ℤ/8)11yescharacteristic
92C4×C113AGL(1,ℤ/8)11yescharacteristic
93Dic113—41no—
94Dic113—42no—
95C2×C113—81no—
96C2×C113—161no—
97C2×C113#44911yescharacteristic
98C2×C113#44911yescharacteristic
99C2×C113#45311yescharacteristic
100D113—81no—
101#1624—1131nomaximal, Sylow
102C113#162411yescharacteristic, complemented, Sylow
103#555—1131no—
104#492—1131no—
105#459—1131no—
106#459D11311yescharacteristic, complemented
107#333—1131no—
108D4⋊C8—1131no—
109D4⋊C8—1131no—
110C2×SD16—2262no—
111C2×D8—21no—
112C2×D8—2261no—
113C4⋊Q8—1131no—
114#127C2×D11311yescharacteristic
115#124—2262no—
116#121—2261no—
117#121—2261no—
118C4×D4—1131no—
119C4×D4C2×D11311yescharacteristic
120#117—2261no—
121#117—2261no—
122C4⋊C8—1131no—
123C4⋊C8C2×D11311yescharacteristic
124#102—21no—
125#102—2261no—
126C4×C8—1131no—
127C2×Q8—1132no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—1131no—
132C2×D4—2262no—
133C2×D4C22⋊D11311yescharacteristic
134C22×C4—21no—
135C22×C4—2261no—
136SD16—4524no—
137D8—42no—
138D8—4522no—
139C2×C8—21no—
140C2×C8—2261no—
141C2×C8—2261no—
142C4⋊C4—1131no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4C22⋊D11311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—2262no—
148C22⋊C4—2262no—
149C22⋊C4—2261no—
150C42—2262no—
151C42C22×D11311yescharacteristic
152C23—21no—
153C23—41no—
154C23—2261no—
155Q8—4522no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—9042no—
164D4—2261no—
165D4—2261no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—2261no—
172C2×C4—2262no—
173C2×C4D4×D11311yescharacteristic
174C2×C4D4×D11311yescharacteristic
175C2×C4C2×C22⋊D11311yescharacteristic
176C8—41no—
177C8—4521no—
178C8—2262no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—4521no—
186C22—4521no—
187C22—4521no—
188C22#1681359011yescharacteristic
189C4—21no—
190C4—41no—
191C4—4522no—
192C4—4521no—
193C4#1681364111yescharacteristic
194C4#1681364211yescharacteristic
195C4#1681364611yescharacteristic
196C4#1681364811yescharacteristic
197C2—81no—
198C2—161no—
199C2—9041no—
200C2#2029874011yescharacteristic
201C2#2029874111yescharacteristic
202C2#2029876411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#459×C113C2
socleC22×C113#120
hypercenter#459D113
hypocenterC113#1624
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20299313C2semidirect
2. #20298970C2semidirect
3. #20298790C2semidirect
4. #20298346C2semidirect
5. D4⋊#11744751C2semidirect
6. #20298325C2semidirect
7. #459×C113C2semidirect
102. C113#1624semidirect
106. #459D113semidirect

Maximal subgroups

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

subgroupindex
#202993132
#202989702
#202987902
#202983462
D4⋊#117447512
#202983252
#459×C1132
#1624113