Finite Group Databasebeta

← #28389839

Subgroups — #28389839

Order 14464.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic226C211yesmaximal, characteristic
2#20298996C211yesmaximal, characteristic, complemented
3#20298884C211yesmaximal, characteristic, complemented
4#20298803C211yesmaximal, characteristic
5#20298345C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic
8C22×Dic226—21no—
9C2×#14268635—21no—
10#16813622C2211yescharacteristic
11#16813622C2211yescharacteristic
12#16813621—21no—
13#16813601—21no—
14#16813599—22no—
15C4×Dic226C2211yescharacteristic
16D4×Dic113—21no—
17#16813554—21no—
18#16813554—22no—
19C4⋊#11744751C2211yescharacteristic
20#16813547—21no—
21#16813545—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—22no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226—42no—
29C2×Dic226—42no—
30C2×Dic226D411yescharacteristic
31C22×Dic113—22no—
32#14268635—42no—
33C2×#11744751—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113D411yescharacteristic
38C4⋊Dic113D412yes—
39#14268626—22no—
40#14268626—21no—
41C22⋊Dic113—22no—
42C4×Dic113—21no—
43C2×D4×C113D411yescharacteristic
44C22×C4×C113—21no—
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51D4×C113—21no—
52D4×C113SD1612yes—
53C2×C4×C113—21no—
54C2×C4×C113—41no—
55C2×C4×C113—41no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113—21no—
61C2×Dic113—22no—
62C2×Dic113—44no—
63C2×Dic113—41no—
64Dic226—21no—
65Dic226—44no—
66Dic226—41no—
67Dic226—41no—
68Dic226—41no—
69Dic226—41no—
70Dic226SD1612yescomplemented
71C8×C113—22no—
72C8×C113—41no—
73#11744751—41no—
74C22×C113—22no—
75C22×C113—41no—
76C22×C113—41no—
77C22×C113#12011yescharacteristic
78C4×C113—21no—
79C4×C113—41no—
80C4×C113C2×SD1611yescharacteristic
81C4×C113C2×SD1611yescharacteristic
82C4×C113AGL(1,ℤ/8)11yescharacteristic
83C4×C113#13711yescharacteristic
84Dic113—22no—
85Dic113—42no—
86Dic113—41no—
87Dic113—81no—
88C2×C113—42no—
89C2×C113#44811yescharacteristic
90C2×C113#45011yescharacteristic
91C2×C113#45611yescharacteristic
92#1651—1131nomaximal, Sylow
93C113#165111yescharacteristic, complemented, Sylow
94D4×Q8—1131no—
95#498—1131no—
96#475—1131no—
97#461—1131no—
98#332—1131no—
99Q8⋊C8—1131no—
100D4⋊C8D11311yescharacteristic
101C22×Q8—2261no—
102C2×SD16—2261no—
103C4⋊Q8—1131no—
104C4⋊Q8—1131no—
105C4⋊Q8—2261no—
106C22⋊Q8—2262no—
107C22⋊Q8—2261no—
108C4×Q8—1131no—
109C4×D4—2261no—
110C4×D4C2×D11311yescharacteristic
111#106—2261no—
112#106—2262no—
113C4⋊C8—1131no—
114C4⋊C8C2×D11311yescharacteristic
115#103—2261no—
116#103—2261no—
117C4×C8C2×D11311yescharacteristic
118C2×Q8—1131no—
119C2×Q8—4522no—
120C2×Q8—4522no—
121C2×Q8—2262no—
122C2×Q8—2261no—
123C2×Q8—2261no—
124C2×D4D45211yescharacteristic
125C22×C4—21no—
126C22×C4—2262no—
127SD16—4522no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2261no—
131C4⋊C4—1131no—
132C4⋊C4—1132no—
133C4⋊C4—2262no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C4⋊C4D45211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—2262no—
141C42—2261no—
142C42C22×D11311yescharacteristic
143C23—21no—
144Q8—1132no—
145Q8—4524no—
146Q8—4521no—
147Q8—4521no—
148Q8—4521no—
149Q8—4521no—
150Q8—2261no—
151D4—21no—
152D4#1426863612yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—4521no—
157C2×C4—4524no—
158C2×C4—2261no—
159C2×C4—2262no—
160C2×C4—2261no—
161C2×C4D4×D11311yescharacteristic
162C2×C4D4×D11311yescharacteristic
163C2×C4C2×D45211yescharacteristic
164C8—22no—
165C8—41no—
166C8—4521no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1681359211yescharacteristic
171C4—21no—
172C4—41no—
173C4—9041no—
174C4—4521no—
175C4—4522no—
176C4—2262no—
177C4SD16×D11311yescharacteristic
178C4C2×#1426863611yescharacteristic
179C4#1681364611yescharacteristic
180C4#1681365511yescharacteristic
181C2—42no—
182C2#2029873911yescharacteristic
183C2#2029875011yescharacteristic
184C2#2029878211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4⋊C8D113
hypocenterC113#1651
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. #20298996C2semidirect
3. #20298884C2semidirect
5. #20298345C2semidirect
6. #20298330C2semidirect
70. Dic226SD16semidirect
93. C113#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2262
#202989962
#202988842
#202988032
#202983452
#202983302
D4⋊C8×C1132
#1651113