Finite Group Databasebeta

← #28391020

Subgroups — #28391020

Order 14464.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16813581C211yesmaximal, characteristic, complemented
3C2×#16813548C212yesmaximal, complemented
4#20298359C212yesmaximal, complemented
5#407×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7#16813605—21no—
8#16813601C412yescomplemented
9#16813596C412yescomplemented
10#16813591—21no—
11C4×C22⋊D113—22no—
12#16813581—24no—
13#16813581C2211yescharacteristic
14C2×C4⋊Dic113—21no—
15C2×C22⋊Dic113—21no—
16C2×C4×Dic113C2212yes—
17#16813548—24no—
18C23×C4×C113C2211yescharacteristic
19C2×M16×C113C2212yes—
20C22⋊C8×C113—22no—
21#14268647—22no—
22#14268647—22no—
23C2×Dic226C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113—22no—
26C2×C22⋊D113—21no—
27C22×Dic113—22no—
28C2×C4×D113—21no—
29C4⋊Dic113—24no—
30C4⋊Dic113C2×C412yes—
31#14268626—22no—
32C22⋊Dic113—24no—
33C22⋊Dic113—22no—
34C22⋊Dic113—21no—
35#14268624—22no—
36C4×Dic113—22no—
37C4×Dic113—21no—
38C4×Dic113D414yescomplemented
39C24×C113D411yescharacteristic
40C22×C4×C113—22no—
41C22×C4×C113—22no—
42C22×C4×C113C2×C412yes—
43C22×C4×C113D411yescharacteristic
44C22×C4×C113D412yes—
45C22×C4×C113C2311yescharacteristic
46M16×C113—22no—
47M16×C113—22no—
48C2×C8×C113—22no—
49C23×C113—21no—
50C23×C113—21no—
51C23×C113—42no—
52C23×C113C22⋊C412yes—
53C23×C113C2×D411yescharacteristic
54C22×D113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—24no—
58C2×C4×C113—24no—
59C2×C4×C113C22⋊C412yes—
60C2×C4×C113C22×C411yescharacteristic
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113#4112yes—
64C22⋊D113—44no—
65C22⋊D113—41no—
66C22⋊D113—41no—
67C2×Dic113—22no—
68C2×Dic113—21no—
69C2×Dic113—24no—
70C2×Dic113—44no—
71D452—22no—
72C4×D113—42no—
73Dic226—22no—
74C8×C113—42no—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—22no—
78C22×C113—22no—
79C22×C113—42no—
80C22×C113—42no—
81C22×C113C2×C22⋊C411yescharacteristic
82C22×C113#12011yescharacteristic
83C22×C113#12311yescharacteristic
84C2×D113—41no—
85C2×D113—42no—
86C4×C113—22no—
87C4×C113C4×D412yes—
88C4×C113#12112yes—
89Dic113—44no—
90Dic113—41no—
91Dic113—42no—
92C2×C113—21no—
93C2×C113—21no—
94C2×C113—42no—
95C2×C113#38611yescharacteristic
96C2×C113#42112yes—
97D113—81no—
98#1897—1131nomaximal, Sylow
99C113#189711yescharacteristic, complemented, Sylow
100#525—1131no—
101C2×#117—1131no—
102C2×#104—1132no—
103#407D11311yescharacteristic, complemented
104#339—1132no—
105C2×#41—1131no—
106C23×C4C2×D11311yescharacteristic
107C2×M16C2×D11312yes—
108#123—2261no—
109C22⋊Q8—1132no—
110#121—1132no—
111#120—2261no—
112C4×D4—2262no—
113#117—1131no—
114#117—2264no—
115C2×C4⋊C4—2261no—
116C2×C22⋊C4—2261no—
117C2×C42—1132no—
118#104—2264no—
119C22⋊C8—22no—
120C24D45211yescharacteristic
121#41—2262no—
122#41—2262no—
123C2×Q8—1131no—
124C2×D4—1131no—
125C2×D4—2262no—
126C2×D4—2261no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—2262no—
130C22×C4—2261no—
131C22×C4C4×D11312yes—
132C22×C4D45211yescharacteristic
133C22×C4C22⋊D11312yes—
134C22×C4C22×D11311yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—1132no—
139C4⋊C4—2264no—
140C4⋊C4—2262no—
141C22⋊C4—2264no—
142C22⋊C4—2262no—
143C22⋊C4—2261no—
144C22⋊C4—2262no—
145C42—1134no—
146C42—2262no—
147C42—2261no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2261no—
152C23#1426862412yes—
153C23C2×D45211yescharacteristic
154Q8—2262no—
155D4—4524no—
156D4—4521no—
157D4—4521no—
158D4—2262no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—4524no—
164C2×C4—4522no—
165C2×C4—2262no—
166C2×C4—2261no—
167C2×C4—2264no—
168C2×C4#1426862412yes—
169C2×C4C2×C4×D11311yescharacteristic
170C2×C4D4×D11312yes—
171C2×C4C2×C22⋊D11311yescharacteristic
172C2×C4#1426864612yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—4522no—
181C22—4521no—
182C22C2×#1426862411yescharacteristic
183C22#1681359211yescharacteristic
184C22#1681360611yescharacteristic
185C4—22no—
186C4—4524no—
187C4—4522no—
188C4—4521no—
189C4#1681358212yes—
190C4#1681359412yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—9041no—
195C2#2029847511yescharacteristic
196C2#2029861412yes—
subgroupG/H
centerC2×C4C2×C22⋊D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#407×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299109C2
cosocleC22×C4×C113C23
hypercenter#407D113
hypocenterC113#1897
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#16813581C2semidirect
3. C2×#16813548C2semidirect
4. #20298359C2semidirect
5. #407×C113C2semidirect
8. #16813601C4semidirect
9. #16813596C4semidirect
38. C4×Dic113D4semidirect
99. C113#1897semidirect
103. #407D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×#168135812
C2×#168135482
#202983592
#407×C1132
#1897113