Finite Group Databasebeta

← #28391017

Subgroups — #28391017

Order 14464.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#20299109C211yesmaximal, characteristic
2C2×#16813550C212yesmaximal, complemented
3#20298562C211yesmaximal, characteristic, complemented
4#20298358C212yesmaximal, complemented
5C22×C42×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7C2×#14268631C2212yes—
8#16813605—21no—
9#16813601C412yescomplemented
10#16813596C412yescomplemented
11#16813591—21no—
12C4×C22⋊D113—22no—
13#16813581C2211yescharacteristic
14#16813550—24no—
15C22⋊#11744751—22no—
16C23×C4×C113—21no—
17C23×C4×C113C2211yescharacteristic
18C2×C42×C113—21no—
19C2×C42×C113—24no—
20C2×C42×C113C2212yes—
21#14268647—22no—
22#14268647—22no—
23C2×Dic226C2×C411yescharacteristic, complemented
24C2×D452C2×C411yescharacteristic, complemented
25C2×C22⋊D113—22no—
26C2×C22⋊D113—21no—
27C2×C4×D113—21no—
28#14268631—22no—
29#14268631—22no—
30C2×#11744751—22no—
31C4⋊Dic113C2×C412yescomplemented
32#14268626—22no—
33C22⋊Dic113—22no—
34C22⋊Dic113—21no—
35#14268624—22no—
36C4×Dic113—21no—
37C24×C113D411yescharacteristic
38C22×C4×C113—24no—
39C22×C4×C113—28no—
40C22×C4×C113—22no—
41C22×C4×C113—22no—
42C22×C4×C113—22no—
43C22×C4×C113C2×C412yes—
44C22×C4×C113D412yes—
45C22×C4×C113D411yescharacteristic
46C22×C4×C113C2311yescharacteristic
47C42×C113—24no—
48C42×C113—22no—
49C42×C113D414yescomplemented
50C23×C113—24no—
51C23×C113—21no—
52C23×C113—21no—
53C23×C113C22⋊C412yes—
54C23×C113C2×D411yescharacteristic
55C22×D113—21no—
56C2×C4×C113—216no—
57C2×C4×C113—28no—
58C2×C4×C113—21no—
59C2×C4×C113—24no—
60C2×C4×C113—21no—
61C2×C4×C113—24no—
62C2×C4×C113—24no—
63C2×C4×C113C22⋊C412yes—
64C2×C4×C113C22×C411yescharacteristic
65C2×C4×C113C2×D412yes—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113#4112yes—
68C22⋊D113—44no—
69C22⋊D113—41no—
70C22⋊D113—41no—
71C2×Dic113—22no—
72C2×Dic113—21no—
73D452—22no—
74C4×D113—42no—
75Dic226—22no—
76#11744751—42no—
77C22×C113—24no—
78C22×C113—24no—
79C22×C113—22no—
80C22×C113—22no—
81C22×C113—22no—
82C22×C113#10414yescomplemented
83C22×C113C2×C22⋊C411yescharacteristic
84C22×C113#12011yescharacteristic
85C22×C113#12311yescharacteristic
86C2×D113—41no—
87C2×D113—42no—
88C4×C113—28no—
89C4×C113—22no—
90C4×C113C4×D412yes—
91C4×C113#12112yes—
92Dic113—41no—
93Dic113—42no—
94C2×C113—21no—
95C2×C113—24no—
96C2×C113—21no—
97C2×C113#38611yescharacteristic
98C2×C113C2×#10412yes—
99D113—81no—
100#1896—1131nomaximal, Sylow
101C113#189611yescharacteristic, complemented, Sylow
102#525—1131no—
103C22×C42D11311yescharacteristic, complemented
104C2×#104—1132no—
105#407—1131no—
106#339—1132no—
107C2×#41—1131no—
108C23×C4—21no—
109C23×C4C2×D11311yescharacteristic
110C2×M16—1132no—
111#123—2261no—
112C22⋊Q8—1132no—
113#121—1132no—
114#120—2261no—
115C4×D4—2262no—
116#117—1131no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D11312yes—
120#104—2264no—
121C22⋊C8—2262no—
122C24C22⋊D11311yescharacteristic
123#41—2262no—
124#41—2262no—
125C2×Q8—1131no—
126C2×D4—1131no—
127C2×D4—2262no—
128C2×D4—2261no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—2261no—
135C22×C4C4×D11312yes—
136C22×C4D45212yes—
137C22×C4C22⋊D11311yescharacteristic
138C22×C4C22×D11311yescharacteristic
139M16—2262no—
140M16—2262no—
141C2×C8—2262no—
142C4⋊C4—1132no—
143C4⋊C4—2262no—
144C22⋊C4—2262no—
145C22⋊C4—2261no—
146C22⋊C4—2262no—
147C42—24no—
148C42—22no—
149C42—2261no—
150C42C22⋊D11314yescomplemented
151C23—21no—
152C23—21no—
153C23—24no—
154C23—2261no—
155C23#1426862412yes—
156C23C2×C22⋊D11311yescharacteristic
157Q8—2262no—
158D4—4521no—
159D4—4521no—
160D4—4524no—
161D4—2262no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—4522no—
170C2×C4—2262no—
171C2×C4—2261no—
172C2×C4#1426862412yes—
173C2×C4C2×C4×D11311yescharacteristic
174C2×C4C2×C22⋊D11312yes—
175C2×C4C2×D45211yescharacteristic
176C2×C4#1426864712yes—
177C8—4522no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—4522no—
184C22—4521no—
185C22#1681355014yescomplemented
186C22C2×#1426862411yescharacteristic
187C22#1681359111yescharacteristic
188C22#1681360511yescharacteristic
189C4—28no—
190C4—22no—
191C4—4522no—
192C4—4521no—
193C4C4×C22⋊D11312yes—
194C4#1681359612yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—9041no—
199C2#2029847711yescharacteristic
200C2C2×#1681355012yes—
subgroupG/H
centerC2×C4C2×D452
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC22×C42×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299109C2
cosocleC22×C4×C113C23
hypercenterC22×C42D113
hypocenterC113#1896
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#16813550C2semidirect
3. #20298562C2semidirect
4. #20298358C2semidirect
5. C22×C42×C113C2semidirect
9. #16813601C4semidirect
10. #16813596C4semidirect
23. C2×Dic226C2×C4semidirect
24. C2×D452C2×C4semidirect
31. C4⋊Dic113C2×C4semidirect
49. C42×C113D4semidirect
82. C22×C113#104semidirect
101. C113#1896semidirect
103. C22×C42D113semidirect
150. C42C22⋊D113semidirect
185. C22#16813550semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×#168135502
#202985622
#202983582
C22×C42×C1132
#1896113