Finite Group Databasebeta

← #28389682

Subgroups — #28389682

Order 14464.

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

normal subgroups only

This group has 216 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#20299318C211yesmaximal, characteristic, complemented
2#20298944C211yesmaximal, characteristic, complemented
3#20298795C211yesmaximal, characteristic, complemented
4#20298345C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7#459×C113C211yesmaximal, characteristic
8C2×#14268635—21no—
9#16813622C2211yescharacteristic
10#16813615—22no—
11#16813609—21no—
12#16813601—21no—
13C4×Dic226C2211yescharacteristic
14#16813587—21no—
15#16813581—21no—
16C4⋊#11744751C2211yescharacteristic
17#16813543—21no—
18#16813543—22no—
19C4×#11744751C2211yescharacteristic
20C2×D8×C113—21no—
21#127×C113C2211yescharacteristic
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24#102×C113—21no—
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27#14268635—42no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113D411yescharacteristic
32C4⋊Dic113D412yes—
33#14268626—22no—
34#14268626—21no—
35C22⋊Dic113—22no—
36C22⋊Dic113—22no—
37C4×Dic113—22no—
38C4×Dic113—21no—
39C2×D4×C113—21no—
40C2×D4×C113—21no—
41C2×D4×C113—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44D8×C113—42no—
45C2×C8×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113C2311yescharacteristic
49C23×C113—21no—
50C23×C113—41no—
51D4×C113—21no—
52D4×C113—21no—
53D4×C113—42no—
54D4×C113—41no—
55D4×C113—41no—
56D4×C113—41no—
57D4×C113—41no—
58C2×C4×C113—21no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C2×Dic113—21no—
65C2×Dic113—21no—
66C2×Dic113—22no—
67Dic226—21no—
68Dic226—21no—
69Dic226—41no—
70Dic226—41no—
71C8×C113—41no—
72#11744751—41no—
73#11744751—41no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113—81no—
78C22×C113—81no—
79C22×C113—81no—
80C22×C113#12011yescharacteristic
81C4×C113—21no—
82C4×C113—41no—
83C4×C113#13511yescharacteristic
84C4×C113#13511yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87Dic113—41no—
88Dic113—42no—
89Dic113—41no—
90C2×C113—81no—
91C2×C113—161no—
92C2×C113#44911yescharacteristic
93C2×C113#44911yescharacteristic
94C2×C113#45411yescharacteristic
95#1628—1131nomaximal, Sylow
96C113#162811yescharacteristic, complemented, Sylow
97#556—1131no—
98#486—1131no—
99#460—1131no—
100#459D11311yescharacteristic
101#332—1131no—
102Q8⋊C8—1131no—
103D4⋊C8—1131no—
104C2×SD16—2261no—
105C2×D8—21no—
106C4⋊Q8—1131no—
107#127C2×D11311yescharacteristic
108#126—2262no—
109#124—2261no—
110C22⋊Q8—2261no—
111C4×Q8—1131no—
112C4×Q8—2261no—
113C4×D4C2×D11311yescharacteristic
114#117—2261no—
115C4⋊C8—1131no—
116C4⋊C8C2×D11311yescharacteristic
117#102—21no—
118#102—2261no—
119#102—2262no—
120C4×C8—1131no—
121C2×Q8—1131no—
122C2×Q8—2261no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D11311yescharacteristic
127C22×C4—21no—
128SD16—4522no—
129D8—42no—
130C2×C8—21no—
131C2×C8—2261no—
132C2×C8—2261no—
133C4⋊C4—1131no—
134C4⋊C4—1132no—
135C4⋊C4—2262no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C4⋊C4C22⋊D11311yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—2262no—
141C22⋊C4—2262no—
142C42—2262no—
143C42—2261no—
144C42C22×D11311yescharacteristic
145C23—21no—
146C23—41no—
147Q8—4521no—
148Q8—4521no—
149Q8—2261no—
150Q8—2261no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2261no—
162C2×C4—2262no—
163C2×C4—2261no—
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C2×C4C2×C22⋊D11311yescharacteristic
167C8—41no—
168C8—4521no—
169C8—4521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1681359011yescharacteristic
177C4—21no—
178C4—41no—
179C4—4521no—
180C4—4521no—
181C4—4522no—
182C4#1681364111yescharacteristic
183C4#1681364211yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681364811yescharacteristic
186C2—81no—
187C2—161no—
188C2#2029874011yescharacteristic
189C2#2029874111yescharacteristic
190C2#2029876911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radical#459×C113C2
socleC22×C113#120
hypercenter#459D113
hypocenterC113#1628
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. #20299318C2semidirect
2. #20298944C2semidirect
3. #20298795C2semidirect
4. #20298345C2semidirect
5. #20298328C2semidirect
6. D4⋊#11744751C2semidirect
96. C113#1628semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202989442
#202987952
#202983452
#202983282
D4⋊#117447512
#459×C1132
#1628113