Finite Group Databasebeta

← #28392537

Subgroups — #28392537

Order 14464.

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

normal subgroups only

This group has 210 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, complemented
2#20299034C211yesmaximal, characteristic, complemented
3#20298865C211yesmaximal, characteristic, complemented
4#20298414C211yesmaximal, characteristic, complemented
5#20298406C211yesmaximal, characteristic, complemented
6#20298381C211yesmaximal, characteristic, complemented
7C2×SD32×C113C211yesmaximal, characteristic, complemented
8#16813670—21no—
9#16813654—22no—
10#16813653—21no—
11#16813648—21no—
12#16813645—21no—
13#16813644C2211yescharacteristic
14Q16×D113—21no—
15#16813628C2211yescharacteristic
16#16813566—21no—
17#16813563—21no—
18#16813562C2211yescharacteristic
19#16813558C2211yescharacteristic
20#16813539—21no—
21C2×Q16×C113C2211yescharacteristic
22C2×D8×C113C2211yescharacteristic
23SD32×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#14268636—21no—
35#14268635—41no—
36#14268634—22no—
37D904D411yescharacteristic
38#14268632—41no—
39#14268631—21no—
40#14268631D411yescharacteristic
41#14268630—21no—
42C8×D113—21no—
43#14268622—21no—
44C2×Q8×C113—21no—
45C2×D4×C113—21no—
46Q16×C113—21no—
47Q16×C113D412yes—
48D8×C113—21no—
49D8×C113—21no—
50C2×C8×C113C2311yescharacteristic
51C16×C113—21no—
52C23×C113—41no—
53Q8×C113—22no—
54Q8×C113—41no—
55D4×C113—41no—
56D4×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×C113—81no—
76C22×C113—161no—
77C22×C113AGL(1,ℤ/8)11yescharacteristic
78C2×D113—21no—
79C2×D113—41no—
80C4×C113—42no—
81C4×C113#12011yescharacteristic
82C4×C113C2×D811yescharacteristic
83Dic113—21no—
84Dic113—41no—
85C2×C113—21no—
86C2×C113—161no—
87C2×C113#44711yescharacteristic
88D113—41no—
89D113—81no—
90#2193—1131nomaximal, Sylow
91C113#219311yescharacteristic, complemented, Sylow
92#578—1131no—
93#509—1131no—
94C2×SD32D11311yescharacteristic, complemented
95#472—1131no—
96#362—1131no—
97#359—1131no—
98#350—1131no—
992−1+4—2261no—
100#137—2261no—
101#137—2262no—
102AGL(1,ℤ/8)—2261no—
103#135—1131no—
104#135—2261no—
105C2×Q16—2261no—
106C2×Q16C2×D11311yescharacteristic
107C2×D8C2×D11311yescharacteristic
108#131—1131no—
109SD32—22no—
110SD32—2261no—
111D16—2261no—
112M32—1131no—
113C2×C16C2×D11311yescharacteristic
114#108—1131no—
115#100—2261no—
116#41—1131no—
117#41—4522no—
118#41—4521no—
119#41—2262no—
120#41—2261no—
121C2×Q8—21no—
122C2×Q8—4521no—
123C2×Q8—2262no—
124C2×D4—21no—
125Q16—21no—
126Q16—1131no—
127Q16—2262no—
128Q16C22⋊D11312yes—
129SD16—4521no—
130SD16—2262no—
131SD16—2261no—
132D8—21no—
133D8—21no—
134D8—1131no—
135D8—4521no—
136M16—1131no—
137M16—2261no—
138M16—2261no—
139C2×C8—2261no—
140C2×C8C22×D11311yescharacteristic
141C16—21no—
142C16—2261no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—1131no—
147Q8—4522no—
148Q8—2261no—
149D4—41no—
150D4—41no—
151D4—1131no—
152D4—4522no—
153D4—4521no—
154D4—2261no—
155D4—2261no—
156C2×C4—41no—
157C2×C4—4522no—
158C2×C4—4522no—
159C2×C4—4521no—
160C2×C4—2261no—
161C2×C4D4×D11311yescharacteristic
162C8—4521no—
163C8—2261no—
164C8D4×D11311yescharacteristic
165C8C2×C22⋊D11311yescharacteristic
166C22—81no—
167C22—161no—
168C22—4521no—
169C22—2261no—
170C22#1681364611yescharacteristic
171C4—42no—
172C4—4521no—
173C4—2261no—
174C4#1681359011yescharacteristic
175C4D8×D11311yescharacteristic
176C2—21no—
177C2—161no—
178C2—9041no—
179C2—4521no—
180C2#2029873011yescharacteristic
subgroupG/H
centerC2#20298730
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
FittingC2×SD32×C113C2
socleC2×C113#447
hypercenterC2×SD32D113
hypocenterC113#2193
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #20299411C2semidirect
2. #20299034C2semidirect
3. #20298865C2semidirect
4. #20298414C2semidirect
5. #20298406C2semidirect
6. #20298381C2semidirect
7. C2×SD32×C113C2semidirect
91. C113#2193semidirect
94. C2×SD32D113semidirect

Maximal subgroups

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

subgroupindex
#202994112
#202990342
#202988652
#202984142
#202984062
#202983812
C2×SD32×C1132
#2193113