Finite Group Databasebeta

← #28393171

Subgroups — #28393171

Order 14464.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×#14268624C211yesmaximal, characteristic
2#20298490C214yesmaximal, complemented
3#20298488C214yesmaximal, complemented
4#20298458C211yesmaximal, characteristic, complemented
5#20298453C212yesmaximal
6C22⋊C4×Dic113C212yesmaximal, complemented
7#380×C113C211yesmaximal, characteristic, complemented
8C24×D113C2211yescharacteristic
9C23×Dic113C2211yescharacteristic
10C2×C4⋊Dic113C2212yescomplemented
11C2×C22⋊Dic113C2212yes—
12C2×#14268624C418yescomplemented
13C2×#14268624C2214yes—
14C2×#14268624C2214yes—
15C2×#14268624C2212yes—
16C2×#14268624C2212yes—
17C2×C4×Dic113C2214yescomplemented
18#16813529C2214yescomplemented
19#16813529C2212yescomplemented
20C23×C4×C113C2211yescharacteristic
21C2×C4⋊C4×C113C2212yescomplemented
22C2×C22⋊C4×C113C2212yes—
23#95×C113C2212yescomplemented
24C23×D113—22no—
25C23×D113—22no—
26C23×D113—42no—
27C23×D113—42no—
28C23×D113C2×C414yes—
29C23×D113C2312yes—
30C22×Dic113—42no—
31C22×Dic113C2×C414yes—
32C22×Dic113C2314yes—
33C22×Dic113C2312yes—
34C4⋊Dic113—42no—
35C22⋊Dic113—24no—
36#14268624—44no—
37#14268624—44no—
38#14268624C2×C418yes—
39#14268624C2×C418yes—
40C4×Dic113—44no—
41C24×C113C2311yescharacteristic
42C22×C4×C113—42no—
43C22×C4×C113C2×C414yes—
44C22×C4×C113C2314yes—
45C22×C4×C113C2311yescharacteristic
46C22×C4×C113C2311yescharacteristic
47C4⋊C4×C113—42no—
48C22⋊C4×C113—24no—
49C23×C113—22no—
50C23×C113—22no—
51C23×C113C22×C412yes—
52C23×C113#4112yes—
53C23×C113#4112yes—
54C23×C113C2411yescharacteristic
55C22×D113—28no—
56C22×D113—22no—
57C22×D113—22no—
58C22×D113—24no—
59C22×D113—24no—
60C22×D113—44no—
61C22×D113—44no—
62C22×D113—48no—
63C22×D113—48no—
64C22×D113C22×C414yes—
65C2×C4×C113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—24no—
68C2×C4×C113—24no—
69C2×C4×C113—24no—
70C2×C4×C113—44no—
71C2×C4×C113C22×C412yes—
72C2×C4×C113C22×C412yes—
73C2×Dic113—24no—
74C2×Dic113—24no—
75C2×Dic113—24no—
76C2×Dic113—24no—
77C2×Dic113—44no—
78C2×Dic113C22×C414yes—
79C22×C113—22no—
80C22×C113—22no—
81C22×C113—24no—
82C22×C113—24no—
83C22×C113#11714yes—
84C22×C113C23×C411yescharacteristic
85C22×C113C2×#4111yescharacteristic
86C22×C113C2×#4111yescharacteristic
87C22×C113H(5,𝔽2)12yes—
88C22×C113H(5,𝔽2)12yes—
89C2×D113—24no—
90C2×D113—24no—
91C2×D113—24no—
92C2×D113—416no—
93C2×D113—44no—
94C2×D113—44no—
95C4×C113—22no—
96C4×C113—22no—
97C4×C113—44no—
98Dic113—24no—
99Dic113—44no—
100C2×C113—24no—
101C2×C113C2×#11711yescharacteristic
102C2×C113#51811yescharacteristic
103C2×C113#51811yescharacteristic
104C2×C113#53812yes—
105C2×C113#53812yes—
106D113—44no—
107#2312—1131nomaximal, Sylow
108C113#231211yescharacteristic, complemented, Sylow
109C22×C22⋊C4—1131no—
110#388—1134no—
111#388—1134no—
112#380—1131no—
113#380D11311yescharacteristic, complemented
114#379—1132no—
115C4×C22⋊C4—1132no—
116C25—1131no—
117C23×C4—1131no—
118C23×C4C2×D11311yescharacteristic
119C2×C4⋊C4—1132no—
120C2×C4⋊C4C2×D11312yescomplemented
121C2×C22⋊C4—1138no—
122C2×C22⋊C4—1132no—
123C2×C22⋊C4—1132no—
124C2×C22⋊C4—1134no—
125C2×C22⋊C4—1134no—
126C2×C22⋊C4—1132no—
127C2×C22⋊C4C2×D11312yes—
128C2×C42—1134no—
129#95—1134no—
130#95—1132no—
131#95C2×D11312yescomplemented
132C24—1134no—
133C24—1132no—
134C24—4522no—
135C24—4522no—
136C24—2262no—
137C24—2262no—
138C24C22×D11311yescharacteristic
139C22×C4—42no—
140C22×C4—1134no—
141C22×C4—1132no—
142C22×C4—1134no—
143C22×C4—4522no—
144C22×C4C4×D11314yes—
145C22×C4C22×D11314yes—
146C22×C4C22×D11311yescharacteristic
147C22×C4C22×D11311yescharacteristic
148C4⋊C4—42no—
149C4⋊C4—4522no—
150C22⋊C4—24no—
151C22⋊C4—1138no—
152C22⋊C4—1138no—
153C22⋊C4—4524no—
154C22⋊C4—4524no—
155C22⋊C4—2264no—
156C42—4524no—
157C23—22no—
158C23—22no—
159C23—1134no—
160C23—4528no—
161C23—4528no—
162C23—4524no—
163C23—4524no—
164C23—2268no—
165C23—2262no—
166C23—2262no—
167C23—2264no—
168C23—2264no—
169C23C2×C4×D11312yes—
170C23#1426864612yes—
171C23#1426864812yes—
172C23C23×D11311yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—44no—
179C2×C4—1134no—
180C2×C4—4524no—
181C2×C4—2264no—
182C2×C4—2264no—
183C2×C4—2264no—
184C2×C4—2264no—
185C2×C4C2×C4×D11312yes—
186C2×C4C2×C4×D11312yes—
187C22—22no—
188C22—22no—
189C22—24no—
190C22—24no—
191C22—45216no—
192C22—4524no—
193C22—4524no—
194C22—2264no—
195C22—2264no—
196C22—2264no—
197C22#1681358014yes—
198C22C22×C4×D11311yescharacteristic
199C22C2×#1426864611yescharacteristic
200C22C2×#1426864811yescharacteristic
201C22#1681366712yes—
202C22#1681366812yes—
203C4—22no—
204C4—22no—
205C4—44no—
206C4—4524no—
207C4—2264no—
208C2—24no—
209C2—4524no—
210C2C2×#1681358011yescharacteristic
211C2#2029907111yescharacteristic
212C2#2029907211yescharacteristic
213C2#2029918512yes—
214C2#2029918812yes—
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#380×C113C2
socle, cosocleC23×C113C24
prime radicalC24×D113C22
hypercenter#380D113
hypocenterC113#2312
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #20298490C2semidirect
3. #20298488C2semidirect
4. #20298458C2semidirect
6. C22⋊C4×Dic113C2semidirect
7. #380×C113C2semidirect
10. C2×C4⋊Dic113C22semidirect
12. C2×#14268624C4semidirect
17. C2×C4×Dic113C22semidirect
18. #16813529C22semidirect
19. #16813529C22semidirect
21. C2×C4⋊C4×C113C22semidirect
23. #95×C113C22semidirect
108. C113#2312semidirect
113. #380D113semidirect
120. C2×C4⋊C4C2×D113semidirect
131. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686242
#202984902
#202984882
#202984582
#202984532
C22⋊C4×Dic1132
#380×C1132
#2312113