Finite Group Databasebeta

← #28389857

Subgroups — #28389857

Order 14464.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299252C211yesmaximal, characteristic
2#20298994C211yesmaximal, characteristic, complemented
3#20298800C211yesmaximal, characteristic, complemented
4#20298345C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#474×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9C2×#14268634—21no—
10#16813622C2211yescharacteristic
11#16813606—22no—
12#16813602—21no—
13#16813596—21no—
14C4×D452C2211yescharacteristic
15C2×C4⋊Dic113—21no—
16#16813553—22no—
17C4⋊#11744751C2211yescharacteristic
18#16813546—21no—
19C4×#11744751C2211yescharacteristic
20C4⋊Q8×C113C2211yescharacteristic
21C4×D4×C113C2211yescharacteristic
22#107×C113—21no—
23C4⋊C8×C113C2211yescharacteristic
24#102×C113—21no—
25#14268646—42no—
26#14268646—42no—
27C2×Dic226—21no—
28C2×D452D411yescharacteristic
29C2×C22⋊D113—22no—
30C22×Dic113—22no—
31C2×C4×D113—21no—
32#14268634—42no—
33C2×#11744751—21no—
34C2×#11744751—21no—
35C4⋊Dic113—22no—
36C4⋊Dic113—21no—
37C4⋊Dic113D411yescharacteristic
38C4⋊Dic113D412yes—
39#14268624—22no—
40#14268624—21no—
41C2×Q8×C113—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C22×D113—21no—
52Q8×C113—41no—
53Q8×C113—41no—
54D4×C113—21no—
55D4×C113SD1612yescomplemented
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113—41no—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C2×C4×C113C2×D411yescharacteristic
63C22⋊D113—44no—
64C2×Dic113—21no—
65C2×Dic113—22no—
66C2×Dic113—44no—
67D452—21no—
68D452—21no—
69C4×D113—41no—
70C4×D113—41no—
71Dic226—41no—
72Dic226—41no—
73C8×C113—41no—
74#11744751—22no—
75#11744751—41no—
76C22×C113—22no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113#12011yescharacteristic
80C2×D113—41no—
81C2×D113—41no—
82C2×D113—41no—
83C4×C113—21no—
84C4×C113—41no—
85C4×C113—81no—
86C4×C113C2×SD1611yescharacteristic
87C4×C113#13511yescharacteristic
88C4×C113AGL(1,ℤ/8)11yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90Dic113—42no—
91Dic113—41no—
92C2×C113—42no—
93C2×C113#44911yescharacteristic
94C2×C113#45011yescharacteristic
95C2×C113#45611yescharacteristic
96D113—81no—
97#1654—1131nomaximal, Sylow
98C113#165411yescharacteristic, complemented, Sylow
99#547—1131no—
100#498—1131no—
101#474D11311yescharacteristic, complemented
102#461—1131no—
103#332—1131no—
104D4⋊C8—1131no—
105D4⋊C8—1131no—
106C2×#41—2261no—
107C2×SD16—2261no—
108C4⋊Q8—1131no—
109C4⋊Q8C2×D11311yescharacteristic
110#123—2262no—
111C22⋊Q8—2261no—
112#121—2261no—
113C4×D4—1131no—
114C4×D4C2×D11311yescharacteristic
115C2×C4⋊C4—2261no—
116#107—21no—
117#106—2262no—
118C4⋊C8—1131no—
119C4⋊C8C2×D11311yescharacteristic
120#103—2261no—
121#102—21no—
122C4×C8—1131no—
123#41—4522no—
124#41—4522no—
125C2×Q8—21no—
126C2×Q8—2261no—
127C2×D4—1131no—
128C2×D4—2262no—
129C2×D4C22⋊D11311yescharacteristic
130C22×C4—21no—
131C22×C4—2262no—
132C22×C4—2261no—
133SD16—4522no—
134C2×C8—21no—
135C2×C8—2261no—
136C2×C8—2261no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—1131no—
140C4⋊C4—1132no—
141C4⋊C4—2262no—
142C4⋊C4—2261no—
143C4⋊C4C22⋊D11311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—2262no—
146C22⋊C4—2261no—
147C42C22×D11311yescharacteristic
148C23—21no—
149C23—2261no—
150Q8—41no—
151Q8—41no—
152Q8—4521no—
153Q8—4521no—
154D4—21no—
155D4—4524no—
156D4—2261no—
157D4—2261no—
158D4#1426863412yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—4524no—
164C2×C4—4521no—
165C2×C4—4521no—
166C2×C4—2261no—
167C2×C4—2262no—
168C2×C4D4×D11311yescharacteristic
169C2×C4D4×D11311yescharacteristic
170C2×C4C2×C22⋊D11311yescharacteristic
171C8—41no—
172C8—4521no—
173C8—2262no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—4521no—
178C22—4521no—
179C22—4521no—
180C22#1681359011yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—4521no—
185C4—4522no—
186C4C2×#1426863411yescharacteristic
187C4#1681364111yescharacteristic
188C4#1681364611yescharacteristic
189C4#1681364711yescharacteristic
190C2—42no—
191C2—9041no—
192C2#2029874011yescharacteristic
193C2#2029874811yescharacteristic
194C2#2029877911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#474×C113C2
socleC22×C113#120
prime radical#20299252C2
hypercenter#474D113
hypocenterC113#1654
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #20298994C2semidirect
3. #20298800C2semidirect
4. #20298345C2semidirect
5. D4⋊#11744751C2semidirect
6. #20298325C2semidirect
7. #474×C113C2semidirect
55. D4×C113SD16semidirect
98. C113#1654semidirect
101. #474D113semidirect
158. D4#14268634semidirect

Maximal subgroups

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

subgroupindex
#202992522
#202989942
#202988002
#202983452
D4⋊#117447512
#202983252
#474×C1132
#1654113