Finite Group Databasebeta

← #28389728

Subgroups — #28389728

Order 14464.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299253C211yesmaximal, characteristic
2#20298949C211yesmaximal, characteristic, complemented
3#20298889C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic, complemented
5#20298345C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268647—21no—
9#16813622C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813604—22no—
12#16813601—21no—
13#16813593—21no—
14C4×D452C2211yescharacteristic
15C4⋊C4×D113—21no—
16#16813554—21no—
17#16813553—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813547—22no—
20#16813544—21no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25#14268647—42no—
26#14268647—42no—
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×D452D411yescharacteristic
30C2×C22⋊D113—22no—
31C2×C4×D113—22no—
32C2×C4×D113—21no—
33C2×#11744751—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113D411yescharacteristic
38C4⋊Dic113D412yes—
39#14268626—22no—
40C22⋊Dic113—22no—
41#14268624—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113C2311yescharacteristic
49C23×C113—21no—
50C22×D113—21no—
51D4×C113—21no—
52D4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C22⋊D113—44no—
60C2×Dic113—21no—
61C2×Dic113—22no—
62C2×Dic113—41no—
63D452—21no—
64D452SD1612yes—
65C4×D113—44no—
66C4×D113—41no—
67C4×D113—41no—
68Dic226—41no—
69Dic226—41no—
70Dic226—42no—
71C8×C113—41no—
72C8×C113—41no—
73#11744751—41no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113#12011yescharacteristic
78C2×D113—22no—
79C2×D113—41no—
80C2×D113—41no—
81C4×C113—21no—
82C4×C113—41no—
83C4×C113C2×SD1611yescharacteristic
84C4×C113#13511yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113#13711yescharacteristic
87Dic113—42no—
88Dic113—41no—
89Dic113—81no—
90C2×C113—81no—
91C2×C113#45011yescharacteristic
92C2×C113#45211yescharacteristic
93C2×C113#45411yescharacteristic
94D113—42no—
95#1635—1131nomaximal, Sylow
96C113#163511yescharacteristic, complemented, Sylow
97#547—1131no—
98#487—1131no—
99#476—1131no—
100#476—1131no—
101#332—1131no—
102D4⋊C8—1131no—
103D4⋊C8D11311yescharacteristic, complemented
104C2×#41—2261no—
105C4⋊Q8—1131no—
106C4⋊Q8—1131no—
107#123—2262no—
108C22⋊Q8—2261no—
109#121—2261no—
110C4×D4—1131no—
111C4×D4C2×D11311yescharacteristic
112C2×C4⋊C4—2261no—
113#106—2261no—
114#106—2261no—
115C4⋊C8—1131no—
116C4⋊C8C2×D11311yescharacteristic
117#103—2262no—
118#102—2261no—
119#102—2261no—
120C4×C8C2×D11311yescharacteristic
121#41—4522no—
122#41—4522no—
123C2×Q8—2261no—
124C2×Q8—2261no—
125C2×D4—1131no—
126C2×D4—2262no—
127C2×D4D45211yescharacteristic
128C22×C4—21no—
129C22×C4—2262no—
130C22×C4—2261no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2261no—
134C4⋊C4—1132no—
135C4⋊C4—1131no—
136C4⋊C4—2262no—
137C4⋊C4—2261no—
138C4⋊C4—2261no—
139C4⋊C4—2261no—
140C4⋊C4D45211yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2262no—
143C22⋊C4—2261no—
144C42C22×D11311yescharacteristic
145C23—21no—
146C23—2261no—
147Q8—4522no—
148Q8—4521no—
149Q8—4521no—
150D4—21no—
151D4—21no—
152D4—1132no—
153D4—4524no—
154D4—2261no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—4524no—
159C2×C4—4521no—
160C2×C4—4521no—
161C2×C4—4521no—
162C2×C4—2261no—
163C2×C4—2262no—
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C2×C4C2×D45211yescharacteristic
167C8—41no—
168C8—41no—
169C8—4521no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—4521no—
174C22—4521no—
175C22—2262no—
176C22#1681359211yescharacteristic
177C4—21no—
178C4—41no—
179C4—9041no—
180C4—4521no—
181C4—4522no—
182C4SD16×D11311yescharacteristic
183C4#1681364411yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681365511yescharacteristic
186C2—81no—
187C2—4522no—
188C2#2029875011yescharacteristic
189C2#2029876211yescharacteristic
190C2#2029877211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radical#20299253C2
hypercenterD4⋊C8D113
hypocenterC113#1635
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20298949C2semidirect
3. #20298889C2semidirect
4. #20298888C2semidirect
5. #20298345C2semidirect
6. #20298327C2semidirect
7. D4⋊C8×C113C2semidirect
96. C113#1635semidirect
103. D4⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202992532
#202989492
#202988892
#202988882
#202983452
#202983272
D4⋊C8×C1132
#1635113