Finite Group Databasebeta

← #28389676

Subgroups — #28389676

Order 14464.

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

normal subgroups only

This group has 250 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, complemented
2#20298944C211yesmaximal, characteristic, complemented
3#20298795C211yesmaximal, characteristic, complemented
4#20298343C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7#459×C113C211yesmaximal, characteristic
8C22×Dic226—21no—
9C2×#14268635—21no—
10#16813622C2211yescharacteristic
11#16813621—21no—
12#16813601—21no—
13#16813599—22no—
14C4×Dic226C2211yescharacteristic
15D4×Dic113—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—22no—
26C2×Dic226—21no—
27C2×Dic226—42no—
28C2×Dic226—42no—
29C2×Dic226D411yescharacteristic
30C22×Dic113—22no—
31#14268635—42no—
32C2×#11744751—21no—
33C2×#11744751—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D412yes—
37#14268626—22no—
38#14268626—21no—
39C22⋊Dic113—22no—
40C4×Dic113—21no—
41C2×D4×C113—21no—
42C2×D4×C113—21no—
43C2×D4×C113—21no—
44C2×D4×C113D411yescharacteristic
45C22×C4×C113—21no—
46D8×C113—42no—
47C2×C8×C113—21no—
48C4⋊C4×C113D411yescharacteristic
49C22⋊C4×C113—21no—
50C42×C113C2311yescharacteristic
51C23×C113—21no—
52C23×C113—41no—
53D4×C113—21no—
54D4×C113—42no—
55D4×C113—41no—
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59D4×C113SD1612yescomplemented
60C2×C4×C113—21no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113C2×D411yescharacteristic
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—22no—
69C2×Dic113—44no—
70Dic226—21no—
71Dic226—44no—
72Dic226—41no—
73Dic226—41no—
74Dic226D812yescomplemented
75C8×C113—41no—
76#11744751—41no—
77#11744751—41no—
78C22×C113—22no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113—81no—
82C22×C113—81no—
83C22×C113—81no—
84C22×C113#12011yescharacteristic
85C4×C113—21no—
86C4×C113—41no—
87C4×C113C2×D811yescharacteristic
88C4×C113C2×SD1611yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90C4×C113#13711yescharacteristic
91Dic113—22no—
92Dic113—42no—
93Dic113—41no—
94C2×C113—42no—
95C2×C113—161no—
96C2×C113#44711yescharacteristic
97C2×C113#44811yescharacteristic
98C2×C113#45411yescharacteristic
99#1627—1131nomaximal, Sylow
100C113#162711yescharacteristic, complemented, Sylow
101D4×Q8—1131no—
102#486—1131no—
103#460—1131no—
104#459D11311yescharacteristic
105#332—1131no—
106Q8⋊C8—1131no—
107D4⋊C8—1131no—
108C22×Q8—2261no—
109C2×SD16—2261no—
110C2×D8—21no—
111C4⋊Q8—1131no—
112C4⋊Q8—2261no—
113#127C2×D11311yescharacteristic
114C22⋊Q8—2262no—
115C22⋊Q8—2261no—
116C4×Q8—1131no—
117C4×D4—2261no—
118C4×D4C2×D11311yescharacteristic
119C4⋊C8—1131no—
120C4⋊C8C2×D11311yescharacteristic
121#102—21no—
122#102—2261no—
123#102—2262no—
124C4×C8—1131no—
125C2×Q8—1131no—
126C2×Q8—4522no—
127C2×Q8—4522no—
128C2×Q8—2262no—
129C2×Q8—2261no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D11311yescharacteristic
134C22×C4—21no—
135C22×C4—2262no—
136SD16—4522no—
137D8—42no—
138C2×C8—21no—
139C2×C8—2261no—
140C2×C8—2261no—
141C4⋊C4—1131no—
142C4⋊C4—1132no—
143C4⋊C4—2262no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4C22⋊D11311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2262no—
149C42—2261no—
150C42C22×D11311yescharacteristic
151C23—21no—
152C23—41no—
153Q8—1132no—
154Q8—4524no—
155Q8—4521no—
156Q8—4521no—
157Q8—2261no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1426863512yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—4524no—
169C2×C4—2261no—
170C2×C4—2262no—
171C2×C4—2261no—
172C2×C4D4×D11311yescharacteristic
173C2×C4D4×D11311yescharacteristic
174C2×C4C2×C22⋊D11311yescharacteristic
175C8—41no—
176C8—4521no—
177C8—4521no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#1681359011yescharacteristic
185C4—21no—
186C4—41no—
187C4—4521no—
188C4—4522no—
189C4—2262no—
190C4D8×D11311yescharacteristic
191C4C2×#1426863511yescharacteristic
192C4#1681364611yescharacteristic
193C4#1681365211yescharacteristic
194C2—42no—
195C2—161no—
196C2#2029873011yescharacteristic
197C2#2029873611yescharacteristic
198C2#2029876911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radical#459×C113C2
socleC22×C113#120
hypercenter#459D113
hypocenterC113#1627
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. D4×Dic226C2semidirect
2. #20298944C2semidirect
3. #20298795C2semidirect
4. #20298343C2semidirect
5. #20298328C2semidirect
6. D4⋊#11744751C2semidirect
59. D4×C113SD16semidirect
74. Dic226D8semidirect
100. C113#1627semidirect
164. D4#14268635semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2262
#202989442
#202987952
#202983432
#202983282
D4⋊#117447512
#459×C1132
#1627113