Finite Group Databasebeta

← #28391644

Subgroups — #28391644

Order 14464.

510 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×#14268632C212yesmaximal, complemented
2C2×#16813619C211yesmaximal, characteristic, complemented
3C2×#16813542C212yesmaximal, complemented
4#20298353C211yesmaximal, characteristic, complemented
5#390×C113C211yesmaximal, characteristic, complemented
6C22×D452—22no—
7C22×D452C2212yes—
8C2×#14268632—24no—
9C2×#14268632—24no—
10C2×#14268632—24no—
11C22×#11744751C2212yes—
12#16813619—24no—
13#16813542—24no—
14C22×D4×C113C2211yescharacteristic
15C2×C4⋊C4×C113C2211yescharacteristic
16C2×C22⋊C4×C113—22no—
17C2×C42×C113C2211yescharacteristic
18C23×D113—22no—
19C2×D452—22no—
20C2×D452—22no—
21C2×D452—22no—
22C2×D452—22no—
23C2×D452—28no—
24C2×D452—22no—
25C2×D452—44no—
26C2×D452—44no—
27C2×D452D414yes—
28#14268632—216no—
29C2×#11744751—22no—
30C2×#11744751—22no—
31C2×#11744751D414yescomplemented
32C24×C113—21no—
33C2×D4×C113—22no—
34C2×D4×C113—22no—
35C2×D4×C113—21no—
36C2×D4×C113D412yescomplemented
37C22×C4×C113—21no—
38C22×C4×C113D412yes—
39C22×C4×C113C2311yescharacteristic
40C4⋊C4×C113—22no—
41C22⋊C4×C113—44no—
42C42×C113—22no—
43C23×C113—22no—
44C23×C113—41no—
45C23×C113—41no—
46C23×C113—42no—
47C23×C113—42no—
48C23×C113C2×D411yescharacteristic
49C22×D113—24no—
50C22×D113—42no—
51C22×D113—42no—
52C22×D113—44no—
53C22×D113—44no—
54D4×C113—24no—
55D4×C113—42no—
56C2×C4×C113—22no—
57C2×C4×C113—22no—
58C2×C4×C113—41no—
59C2×C4×C113—42no—
60C2×C4×C113D814yescomplemented
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113#4111yescharacteristic
65D452—24no—
66D452—24no—
67D452—416no—
68D452—42no—
69D452—42no—
70#11744751—24no—
71C22×C113—42no—
72C22×C113—44no—
73C22×C113—82no—
74C22×C113—81no—
75C22×C113—81no—
76C22×C113#12011yescharacteristic
77C22×C113#12111yescharacteristic
78C22×C113#12711yescharacteristic
79C22×C113C2×D812yes—
80C22×C113AGL(1,ℤ/8)12yes—
81C2×D113—44no—
82C2×D113—48no—
83C2×D113—84no—
84C2×D113—82no—
85C2×D113—82no—
86C4×C113—24no—
87C4×C113—81no—
88C4×C113#12012yes—
89C4×C113#12112yes—
90C2×C113—82no—
91C2×C113#39211yescharacteristic
92C2×C113#44712yes—
93C2×C113#45912yes—
94C2×C113#49311yescharacteristic
95C2×C113#49611yescharacteristic
96D113—84no—
97#2011—1131nomaximal, Sylow
98C113#201111yescharacteristic, complemented, Sylow
99C22×D8—1132no—
100C2×#127—1131no—
101C2×#102—1132no—
102#390D11311yescharacteristic, complemented
103#336—1131no—
104C22×D4—1132no—
105C22×D4—2262no—
106C22×D4C2×D11311yescharacteristic
107C2×D8—2264no—
108C2×D8—2264no—
109C2×D8—2264no—
110C22×C8—1132no—
111#127—2264no—
112C2×C4⋊C4C2×D11311yescharacteristic
113C2×C22⋊C4—22no—
114C2×C42C2×D11311yescharacteristic
115#102—2264no—
116C24—21no—
117C24—2262no—
118C2×D4—22no—
119C2×D4—22no—
120C2×D4—21no—
121C2×D4—1134no—
122C2×D4—4524no—
123C2×D4—4524no—
124C2×D4—2268no—
125C2×D4—2262no—
126C2×D4—2262no—
127C2×D4—2262no—
128C2×D4—2262no—
129C2×D4—2262no—
130C2×D4D45212yescomplemented
131C22×C4—21no—
132C22×C4C22⋊D11312yes—
133C22×C4C22×D11311yescharacteristic
134D8—22616no—
135C2×C8—1134no—
136C2×C8—2262no—
137C2×C8—2262no—
138C4⋊C4—22no—
139C22⋊C4—44no—
140C42—22no—
141C23—22no—
142C23—41no—
143C23—41no—
144C23—42no—
145C23—42no—
146C23—4522no—
147C23—4522no—
148C23—4524no—
149C23—4524no—
150C23—2264no—
151C23C2×C22⋊D11311yescharacteristic
152D4—24no—
153D4—42no—
154D4—45216no—
155D4—4522no—
156D4—4522no—
157D4—2264no—
158D4—2264no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4#1426863214yescomplemented
164C2×C4D4×D11312yes—
165C2×C4D4×D11312yes—
166C2×C4C2×D45211yescharacteristic
167C2×C4#1426864711yescharacteristic
168C8—2264no—
169C22—42no—
170C22—44no—
171C22—81no—
172C22—82no—
173C22—81no—
174C22—9044no—
175C22—9042no—
176C22—9042no—
177C22—4524no—
178C22—4528no—
179C22#1681359011yescharacteristic
180C22#1681359611yescharacteristic
181C22#1681361811yescharacteristic
182C22C2×#1426863212yes—
183C22#1681364712yes—
184C4—24no—
185C4—81no—
186C4#1681359212yes—
187C4#1681359512yes—
188C2—82no—
189C2—9044no—
190C2#2029850711yescharacteristic
191C2#2029873112yes—
192C2#2029879312yes—
193C2#2029897411yescharacteristic
194C2#2029898811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#390×C113C2
socleC23×C113C2×D4
hypercenter#390D113
hypocenterC113#2011
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C22×#14268632C2semidirect
2. C2×#16813619C2semidirect
3. C2×#16813542C2semidirect
4. #20298353C2semidirect
5. #390×C113C2semidirect
31. C2×#11744751D4semidirect
36. C2×D4×C113D4semidirect
60. C2×C4×C113D8semidirect
98. C113#2011semidirect
102. #390D113semidirect
130. C2×D4D452semidirect
163. C2×C4#14268632semidirect

Maximal subgroups

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

subgroupindex
C22×#142686322
C2×#168136192
C2×#168135422
#202983532
#390×C1132
#2011113