Finite Group Databasebeta

← #28389858

Subgroups — #28389858

Order 14464.

240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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#20298994C211yesmaximal, characteristic, complemented
2#20298878C211yesmaximal, characteristic, complemented
3#20298803C211yesmaximal, characteristic, complemented
4#20298344C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7#547×C113C211yesmaximal, characteristic
8C2×#14268635—21no—
9#16813622C2211yescharacteristic
10#16813555—21no—
11#16813553—22no—
12C4⋊#11744751C2211yescharacteristic
13C4⋊#11744751C2211yescharacteristic
14#16813545—21no—
15#16813543—21no—
16C4×#11744751C2211yescharacteristic
17C2×#41×C113—21no—
18C4⋊Q8×C113C2211yescharacteristic
19#123×C113—22no—
20C22⋊Q8×C113—21no—
21#121×C113—21no—
22C4×D4×C113C2211yescharacteristic
23C4×D4×C113C2211yescharacteristic
24C2×C4⋊C4×C113—21no—
25C2×Dic226—21no—
26#14268635—42no—
27C2×#11744751—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32#41×C113—42no—
33#41×C113—42no—
34C2×Q8×C113—21no—
35C2×D4×C113—22no—
36C2×D4×C113D411yescharacteristic
37C2×D4×C113D411yescharacteristic
38C22×C4×C113—22no—
39C22×C4×C113—21no—
40C22×C4×C113—21no—
41C4⋊C4×C113—22no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113D411yescharacteristic
44C4⋊C4×C113D411yescharacteristic
45C4⋊C4×C113D412yes—
46C22⋊C4×C113—22no—
47C22⋊C4×C113—21no—
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C23×C113—21no—
52Q8×C113—41no—
53Q8×C113—41no—
54D4×C113—21no—
55D4×C113—21no—
56D4×C113—21no—
57D4×C113—44no—
58D4×C113SD1612yescomplemented
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—22no—
62C2×C4×C113—44no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2×D411yescharacteristic
70C2×Dic113—41no—
71Dic226—41no—
72Dic226—41no—
73#11744751—22no—
74#11744751—41no—
75#11744751—41no—
76C22×C113—22no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113—41no—
82C22×C113#12011yescharacteristic
83C4×C113—21no—
84C4×C113—41no—
85C4×C113—41no—
86C4×C113—42no—
87C4×C113C2×SD1611yescharacteristic
88C4×C113#13511yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90C4×C113AGL(1,ℤ/8)11yescharacteristic
91Dic113—81no—
92C2×C113—42no—
93C2×C113—81no—
94C2×C113#44911yescharacteristic
95C2×C113#45011yescharacteristic
96C2×C113#45611yescharacteristic
97#1654—1131nomaximal, Sylow
98C113#165411yescharacteristic, complemented, Sylow
99#547D11311yescharacteristic
100#498—1131no—
101#474—1131no—
102#461—1131no—
103#332—1131no—
104D4⋊C8—1131no—
105D4⋊C8—1131no—
106C2×#41—21no—
107C2×SD16—2261no—
108C4⋊Q8—1131no—
109C4⋊Q8C2×D11311yescharacteristic
110#123—22no—
111C22⋊Q8—21no—
112#121—21no—
113C4×D4C2×D11311yescharacteristic
114C4×D4C2×D11311yescharacteristic
115C2×C4⋊C4—21no—
116#107—2261no—
117#106—2262no—
118C4⋊C8—1131no—
119C4⋊C8—1131no—
120#103—2261no—
121#102—2261no—
122C4×C8—1131no—
123#41—42no—
124#41—42no—
125C2×Q8—21no—
126C2×Q8—2261no—
127C2×D4—22no—
128C2×D4C22⋊D11311yescharacteristic
129C2×D4C22⋊D11311yescharacteristic
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133SD16—4522no—
134C2×C8—2261no—
135C2×C8—2261no—
136C2×C8—2261no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—2261no—
140C4⋊C4—2261no—
141C4⋊C4C22⋊D11311yescharacteristic
142C4⋊C4C22⋊D11312yes—
143C4⋊C4C22⋊D11311yescharacteristic
144C22⋊C4—22no—
145C22⋊C4—21no—
146C22⋊C4—21no—
147C42C22×D11311yescharacteristic
148C23—21no—
149C23—21no—
150Q8—41no—
151Q8—41no—
152Q8—4521no—
153Q8—4521no—
154D4—21no—
155D4—21no—
156D4—21no—
157D4—44no—
158D4#1426863512yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—4521no—
168C2×C4C2×C22⋊D11311yescharacteristic
169C2×C4C2×C22⋊D11311yescharacteristic
170C2×C4C2×C22⋊D11311yescharacteristic
171C8—4521no—
172C8—4521no—
173C8—2262no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22#1681359111yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—9041no—
186C4C2×#1426863511yescharacteristic
187C4#1681364211yescharacteristic
188C4#1681364711yescharacteristic
189C4#1681364811yescharacteristic
190C2—42no—
191C2—81no—
192C2#2029874311yescharacteristic
193C2#2029874911yescharacteristic
194C2#2029878111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radical#547×C113C2
socleC22×C113#120
hypercenter#547D113
hypocenterC113#1654
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #20298994C2semidirect
2. #20298878C2semidirect
3. #20298803C2semidirect
4. #20298344C2semidirect
5. D4⋊#11744751C2semidirect
6. D4⋊#11744751C2semidirect
58. D4×C113SD16semidirect
98. C113#1654semidirect
158. D4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202989942
#202988782
#202988032
#202983442
D4⋊#117447512
#547×C1132
#1654113