Finite Group Databasebeta

← #28390647

Subgroups — #28390647

Order 14464.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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×C22⋊C4×D113C211yesmaximal, characteristic
2#20298453C212yesmaximal
3#20298365C211yesmaximal, characteristic, complemented
4#20298364C212yesmaximal, complemented
5#342×C113C211yesmaximal, characteristic, complemented
6C24×D113C2211yescharacteristic
7C22×C4×D113C412yescomplemented
8C2×C22⋊Dic113C2212yes—
9C2×C22⋊Dic113C2211yescharacteristic
10C2×#14268624—24no—
11C2×#14268624C412yescomplemented
12C22⋊C4×D113—24no—
13C2×C22⋊C4×C113C2212yes—
14C2×C22⋊C4×C113C2211yescharacteristic
15C23×D113—21no—
16C23×D113—22no—
17C23×D113—21no—
18C23×D113—44no—
19C23×D113C2×C411yescharacteristic
20C23×D113C2×C411yescharacteristic
21C23×D113D414yes—
22C22×Dic113—22no—
23C22×Dic113C2×C412yes—
24C2×C4×D113—22no—
25C2×C4×D113—22no—
26C2×C4×D113—44no—
27C22⋊Dic113—22no—
28C22⋊Dic113—22no—
29C22⋊Dic113—22no—
30#14268624—24no—
31#14268624—48no—
32C24×C113C2311yescharacteristic
33C22×C4×C113—22no—
34C22×C4×C113C2×C412yes—
35C22⋊C4×C113—22no—
36C22⋊C4×C113—22no—
37C22⋊C4×C113—22no—
38C23×C113—42no—
39C23×C113C22×C411yescharacteristic
40C23×C113C2×D412yes—
41C23×C113#4111yescharacteristic
42C23×C113#4112yes—
43C23×C113#4111yescharacteristic
44C22×D113—21no—
45C22×D113—21no—
46C22×D113—24no—
47C22×D113—21no—
48C22×D113—21no—
49C22×D113—24no—
50C22×D113—24no—
51C22×D113—28no—
52C22×D113—42no—
53C22×D113—44no—
54C22×D113—44no—
55C22×D113—48no—
56C22×D113—44no—
57C22×D113C22⋊C412yes—
58C22×D113C22⋊C412yes—
59C2×C4×C113—22no—
60C2×C4×C113—42no—
61C2×C4×C113—44no—
62C2×C4×C113—42no—
63C2×Dic113—22no—
64C2×Dic113—42no—
65C2×Dic113—44no—
66C2×Dic113—42no—
67C4×D113—44no—
68C4×D113—44no—
69C22×C113—22no—
70C22×C113—24no—
71C22×C113—41no—
72C22×C113—42no—
73C22×C113—41no—
74C22×C113C2×C22⋊C411yescharacteristic
75C22×C113#11711yescharacteristic
76C22×C113#11711yescharacteristic
77C22×C113#12312yes—
78C22×C113#12312yes—
79C2×D113—24no—
80C2×D113—24no—
81C2×D113—22no—
82C2×D113—22no—
83C2×D113—22no—
84C2×D113—24no—
85C2×D113—48no—
86C2×D113—48no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113#9914yes—
90C4×C113—42no—
91C4×C113—82no—
92Dic113—42no—
93Dic113—82no—
94C2×C113—22no—
95C2×C113—22no—
96C2×C113—21no—
97C2×C113—21no—
98C2×C113#38111yescharacteristic
99C2×C113C2×#9912yes—
100D113—24no—
101D113—42no—
102#1819—1131nomaximal, Sylow
103C113#181911yescharacteristic, complemented, Sylow
104C22×C22⋊C4—1131no—
105#379—1132no—
106#342—1132no—
107#342—1131no—
108#342D11311yescharacteristic, complemented
109C25—1131no—
110C23×C4—1132no—
111C2×C22⋊C4—1131no—
112C2×C22⋊C4—1132no—
113C2×C22⋊C4—1132no—
114C2×C22⋊C4—2264no—
115C2×C22⋊C4—2264no—
116C2×C22⋊C4C2×D11312yes—
117C2×C22⋊C4C2×D11311yescharacteristic
118C24—1131no—
119C24—1134no—
120C24—1131no—
121C24—4524no—
122C24—2261no—
123C24—2262no—
124C24—2261no—
125C24C22×D11311yescharacteristic
126C22×C4—22no—
127C22×C4—1132no—
128C22×C4—4524no—
129C22×C4—2262no—
130C22×C4—2262no—
131C22×C4—2262no—
132C22×C4C4×D11312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—4528no—
137C22⋊C4—2264no—
138C22⋊C4—2262no—
139C22⋊C4—2262no—
140C22⋊C4—2262no—
141C23—42no—
142C23—1132no—
143C23—1132no—
144C23—4522no—
145C23—4524no—
146C23—4524no—
147C23—4528no—
148C23—4524no—
149C23—2268no—
150C23—2264no—
151C23—2261no—
152C23—2261no—
153C23—2264no—
154C23—2264no—
155C23—2261no—
156C23—2261no—
157C23C2×C4×D11311yescharacteristic
158C23D4×D11312yes—
159C23#1426864611yescharacteristic
160C23#1426864712yes—
161C23#1426864811yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—4524no—
167C2×C4—4524no—
168C2×C4—4524no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—2262no—
172C22—22no—
173C22—24no—
174C22—41no—
175C22—42no—
176C22—41no—
177C22—1134no—
178C22—4522no—
179C22—4522no—
180C22—4528no—
181C22—4528no—
182C22—2264no—
183C22—2264no—
184C22—2264no—
185C22—2262no—
186C22—2262no—
187C22—2262no—
188C22C22⋊C4×D11311yescharacteristic
189C22#1681357911yescharacteristic
190C22#1681358011yescharacteristic
191C22#1681360412yes—
192C22#1681360712yes—
193C4—42no—
194C4—82no—
195C4—9042no—
196C4—4522no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—4522no—
202C2—2264no—
203C2#2029846011yescharacteristic
204C2#99×D11312yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC24C22×D113
Fitting#342×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC24×D113C22
cosocleC24×C113C23
hypercenter#342D113
hypocenterC113#1819
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #20298365C2semidirect
4. #20298364C2semidirect
5. #342×C113C2semidirect
7. C22×C4×D113C4semidirect
11. C2×#14268624C4semidirect
103. C113#1819semidirect
108. #342D113semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1132
#202984532
#202983652
#202983642
#342×C1132
#1819113