Finite Group Databasebeta

← #28392551

Subgroups — #28392551

Order 14464.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#20299411C211yesmaximal, characteristic
2#20299039C211yesmaximal, characteristic, complemented
3#20298870C211yesmaximal, characteristic, complemented
4#20298414C211yesmaximal, characteristic, complemented
5#20298406C211yesmaximal, characteristic, complemented
6#20298381C211yesmaximal, characteristic, complemented
7C2×Q32×C113C211yesmaximal, characteristic, complemented
8#16813670—21no—
9#16813654—22no—
10#16813653—21no—
11#16813653—21no—
12#16813645—21no—
13#16813644C2211yescharacteristic
14Q16×D113—21no—
15#16813628C2211yescharacteristic
16#16813568—21no—
17#16813565—21no—
18#16813562C2211yescharacteristic
19#16813558C2211yescharacteristic
20#16813541—21no—
21C2×Q16×C113C2211yescharacteristic
22C2×Q16×C113C2211yescharacteristic
23Q32×C113—22no—
24C2×C16×C113C2211yescharacteristic
25#14268648—22no—
26#14268648—41no—
27#14268647—21no—
28#14268647—42no—
29#14268647D411yescharacteristic
30Q8×D113—22no—
31Q8×D113—41no—
32Dic452D411yescharacteristic
33#14268637—22no—
34#14268637—41no—
35#14268636—21no—
36#14268634—22no—
37#14268634—41no—
38D904D411yescharacteristic
39#14268631—21no—
40#14268631D411yescharacteristic
41#14268630—21no—
42C8×D113—21no—
43#14268622—21no—
44C2×Q8×C113—21no—
45C2×Q8×C113—21no—
46Q16×C113—21no—
47Q16×C113—21no—
48Q16×C113—21no—
49Q16×C113D412yes—
50C2×C8×C113C2311yescharacteristic
51C16×C113—21no—
52Q8×C113—22no—
53Q8×C113—41no—
54Q8×C113—41no—
55Q8×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113C2×D411yescharacteristic
59C22⋊D113—21no—
60C22⋊D113—41no—
61D452—21no—
62D452—42no—
63D452D811yescharacteristic
64C4×D113—21no—
65C4×D113—42no—
66C4×D113—42no—
67C4×D113—41no—
68Dic226—21no—
69Dic226—42no—
70Dic226D811yescharacteristic
71C8×C113C2×D411yescharacteristic
72C8×C113C2×D411yescharacteristic
73#11744751—21no—
74#11744751—41no—
75C22×C113AGL(1,ℤ/8)11yescharacteristic
76C2×D113—21no—
77C2×D113—41no—
78C4×C113—42no—
79C4×C113—81no—
80C4×C113#12011yescharacteristic
81C4×C113C2×D811yescharacteristic
82Dic113—21no—
83Dic113—41no—
84C2×C113—21no—
85C2×C113#44711yescharacteristic
86D113—41no—
87D113—81no—
88#2195—1131nomaximal, Sylow
89C113#219511yescharacteristic, complemented, Sylow
90#578—1131no—
91#510—1131no—
92C2×Q32D11311yescharacteristic, complemented
93#473—1131no—
94#362—1131no—
95#359—1131no—
96#350—1131no—
972−1+4—2261no—
98#137—2261no—
99#137—2261no—
100#137—2262no—
101#135—1131no—
102#135—2261no—
103C2×Q16—2261no—
104C2×Q16C2×D11311yescharacteristic
105C2×Q16C2×D11311yescharacteristic
106#131—1131no—
107Q32—22no—
108Q32—2261no—
109SD32—2261no—
110M32—1131no—
111C2×C16C2×D11311yescharacteristic
112#108—1131no—
113#101—2261no—
114#41—1131no—
115#41—4522no—
116#41—4521no—
117#41—2262no—
118#41—2261no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—4521no—
122C2×Q8—2262no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—1131no—
127Q16—4521no—
128Q16—2262no—
129Q16C22⋊D11312yes—
130SD16—4521no—
131SD16—2262no—
132SD16—2261no—
133D8—1131no—
134M16—1131no—
135M16—2261no—
136M16—2261no—
137C2×C8—2261no—
138C2×C8C22×D11311yescharacteristic
139C16—21no—
140C16—2261no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—1131no—
146Q8—4522no—
147Q8—2261no—
148D4—1131no—
149D4—4522no—
150D4—4521no—
151D4—2261no—
152D4—2261no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—4521no—
158C2×C4—2261no—
159C2×C4D4×D11311yescharacteristic
160C8—4521no—
161C8—2261no—
162C8D4×D11311yescharacteristic
163C8C2×C22⋊D11311yescharacteristic
164C22—4521no—
165C22—2261no—
166C22#1681364611yescharacteristic
167C4—42no—
168C4—81no—
169C4—4521no—
170C4—2261no—
171C4#1681359011yescharacteristic
172C4D8×D11311yescharacteristic
173C2—21no—
174C2—9041no—
175C2—4521no—
176C2#2029873011yescharacteristic
subgroupG/H
centerC2#20298730
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
FittingC2×Q32×C113C2
socleC2×C113#447
prime radical#20299411C2
hypercenterC2×Q32D113
hypocenterC113#2195
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #20299039C2semidirect
3. #20298870C2semidirect
4. #20298414C2semidirect
5. #20298406C2semidirect
6. #20298381C2semidirect
7. C2×Q32×C113C2semidirect
89. C113#2195semidirect
92. C2×Q32D113semidirect

Maximal subgroups

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

subgroupindex
#202994112
#202990392
#202988702
#202984142
#202984062
#202983812
C2×Q32×C1132
#2195113