Finite Group Databasebeta

← #28406737

Subgroups — #28406737

Order 14464.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#16813687C214yesmaximal, complemented
2C4×#14268657C211yesmaximal, characteristic, complemented
3C4×C4⋊#90673C211yesmaximal, characteristic, complemented
4#20299149C211yesmaximal, characteristic
5C2×#14268657C2212yes—
6C2×C4⋊#90673—21no—
7C2×C4×#90673C2212yes—
8#16813687—28no—
9#16813677—21no—
10C4×#11744753—21no—
11(C2×#90673)⋊C4—21no—
12C2×#14268648C2212yes—
13#16813619C411yescharacteristic, complemented
14#16813611C412yescomplemented
15#16813597—21no—
16#16813597—21no—
17#16813584—21no—
18#16813584—21no—
19C42×D113C2211yescharacteristic
20C4⋊Q8×C113C411yescharacteristic, complemented
21C22×#90673—22no—
22#14268657—22no—
23#14268657D414yescomplemented
24C2×#11744753—22no—
25C4⋊#90673—24no—
26C4×#90673—24no—
27#14268648—24no—
28#14268648—24no—
29C2×D452—22no—
30C2×D452—21no—
31C2×D452—21no—
32C2×D452C2×C412yes—
33C2×C4×D113—22no—
34C2×C4×D113D411yescharacteristic
35C2×C4×D113D411yescharacteristic
36C2×C4×D113C2311yescharacteristic
37#14268624—22no—
38#14268624—22no—
39C4×Dic113C2×C411yescharacteristic
40C4×Dic113D411yescharacteristic
41C4×Dic113D411yescharacteristic
42C2×Q8×C113C2×C412yes—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C42×C113C2×C411yescharacteristic
46C22×D113—22no—
47C22×D113C2×D411yescharacteristic
48C2×#90673—24no—
49C2×#90673—42no—
50C2×#90673—42no—
51Q8×C113—24no—
52C2×C4×C113—22no—
53C2×C4×C113C22⋊C411yescharacteristic
54C2×C4×C113C22⋊C411yescharacteristic
55C2×C4×C113C22×C411yescharacteristic
56C2×Dic113C22⋊C411yescharacteristic
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C2×D411yescharacteristic
59D452—24no—
60D452—42no—
61D452—42no—
62D452—42no—
63D452—42no—
64C4×D113—22no—
65C4×D113—41no—
66C4×D113—44no—
67C4×D113C2×D412yes—
68C4×D113#4112yes—
69#11744753—24no—
70C22×C113C2×C22⋊C411yescharacteristic
71C2×D113—21no—
72C2×D113—21no—
73C2×D113—42no—
74C2×D113—42no—
75C2×D113—42no—
76C2×D113#12411yescharacteristic
77C2×D113#12711yescharacteristic
78#90673—44no—
79C4×C113—21no—
80C4×C113—42no—
81C4×C113#10412yescomplemented
82C4×C113C4×D412yes—
83Dic113—21no—
84Dic113—21no—
85Dic113#12112yes—
86C2×C113#39011yescharacteristic
87C2×C113C2×#10411yescharacteristic
88C2×C113#42111yescharacteristic
89D113—21no—
90D113—21no—
91D113—82no—
92#1980—1131nomaximal, Sylow
93C113#198011yescharacteristic, complemented, Sylow
94#532—1131no—
95C2×#104—1134no—
96C4×M16—1131no—
97C4×C4⋊C4—1131no—
98C2×#41—1132no—
99C2×M16—1132no—
100C4⋊Q8#9067311yescharacteristic, complemented
101#127—1131no—
102#124—1132no—
103#121—2261no—
104#121—2261no—
105C4×D4—2261no—
106C4×D4—2261no—
107C2×C4⋊C4—2261no—
108C2×C42—1131no—
109C2×C42—1132no—
110#104—2268no—
111#97—2261no—
112C4×C8—2261no—
113#95—2261no—
114#41—2264no—
115#41—2264no—
116C2×Q8C2×#9067312yes—
117C2×D4—1132no—
118C2×D4—2262no—
119C2×D4—2261no—
120C2×D4—2261no—
121C22×C4—1131no—
122C22×C4—1131no—
123C22×C4—1131no—
124C22×C4—2262no—
125C22×C4—2262no—
126M16—1134no—
127M16—2262no—
128C2×C8—2262no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2264no—
132C22⋊C4—2262no—
133C22⋊C4—2262no—
134C42—1131no—
135C42—1131no—
136C42—1131no—
137C42—2264no—
138C42C2×#9067311yescharacteristic
139C23—1131no—
140C23—2262no—
141Q8—24no—
142D4—4522no—
143D4—4522no—
144D4—4522no—
145D4—4522no—
146D4—2264no—
147C2×C4—22no—
148C2×C4—1131no—
149C2×C4—1132no—
150C2×C4—1132no—
151C2×C4—1131no—
152C2×C4—1131no—
153C2×C4—4521no—
154C2×C4—4524no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—2264no—
158C2×C4—2262no—
159C2×C4C22⋊#9067311yescharacteristic
160C2×C4C22⋊#9067311yescharacteristic
161C2×C4C22×#9067311yescharacteristic
162C8—2264no—
163C22—1131no—
164C22—1131no—
165C22—4522no—
166C22—4522no—
167C22—4522no—
168C22—2261no—
169C22—2261no—
170C22C2×C22⋊#9067311yescharacteristic
171C4—21no—
172C4—42no—
173C4—1132no—
174C4—4524no—
175C4—2261no—
176C4—2261no—
177C4#1681368712yescomplemented
178C4D4×#9067312yes—
179C2—9042no—
180C2—2261no—
181C2—2261no—
182C2#2029955011yescharacteristic
183C2C2×#1681368711yescharacteristic
184C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299149C2
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1980
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16813687C2semidirect
2. C4×#14268657C2semidirect
3. C4×C4⋊#90673C2semidirect
13. #16813619C4semidirect
14. #16813611C4semidirect
20. C4⋊Q8×C113C4semidirect
23. #14268657D4semidirect
81. C4×C113#104semidirect
93. C113#1980semidirect
100. C4⋊Q8#90673semidirect
177. C4#16813687semidirect

Maximal subgroups

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

subgroupindex
C2×#168136872
C4×#142686572
C4×C4⋊#906732
#202991492
#1980113