Finite Group Databasebeta

← #28393889

Subgroups — #28393889

Order 14464.

1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 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×#16813590C212yesmaximal, complemented
2C22×#14268624C211yesmaximal, characteristic, complemented
3#20298509C212yesmaximal, complemented
4#20298506C212yesmaximal, complemented
5#20298478C212yesmaximal, complemented
6#20298477C214yesmaximal, complemented
7#20298461C211yesmaximal, characteristic, complemented
8C22×#41×C113C211yesmaximal, characteristic, complemented
9C24×D113C2211yescharacteristic
10C22×C22⋊D113C2214yes—
11C23×Dic113C2211yescharacteristic
12#16813590—28no—
13C2×C22⋊Dic113C2212yes—
14C2×C22⋊Dic113C2214yescomplemented
15C2×#14268624—24no—
16C2×#14268624C2212yes—
17C2×#14268624C2214yes—
18C2×#14268624C2212yes—
19#16813529C2212yescomplemented
20#16813529C2214yescomplemented
21#16813529C2212yescomplemented
22C2×#41×C113—28no—
23C2×#41×C113—24no—
24C22×Q8×C113C2211yescharacteristic, complemented
25C22×D4×C113C2212yes—
26C22×D4×C113C2211yescharacteristic, complemented
27C23×C4×C113C2211yescharacteristic
28C23×C4×C113C2212yescomplemented
29C23×D113—22no—
30C23×D113—24no—
31C23×D113—24no—
32C23×D113—42no—
33C23×D113C2312yes—
34C2×C22⋊D113—28no—
35C2×C22⋊D113—28no—
36C2×C22⋊D113—44no—
37C22×Dic113—22no—
38C22×Dic113—42no—
39C22×Dic113C2312yes—
40C22×Dic113C2314yes—
41C22⋊Dic113—24no—
42C22⋊Dic113—44no—
43#14268624—24no—
44#14268624—24no—
45#14268624—28no—
46C24×C113C2312yes—
47C24×C113C2311yescharacteristic
48#41×C113—232no—
49C2×Q8×C113—24no—
50C2×Q8×C113—22no—
51C2×D4×C113—24no—
52C2×D4×C113—24no—
53C2×D4×C113—24no—
54C2×D4×C113—22no—
55C2×D4×C113D418yescomplemented
56C22×C4×C113—24no—
57C22×C4×C113—24no—
58C22×C4×C113—24no—
59C22×C4×C113—24no—
60C22×C4×C113D414yescomplemented
61C22×C4×C113C2311yescharacteristic
62C22×C4×C113C2311yescharacteristic
63C22×C4×C113C2312yes—
64C23×C113—22no—
65C23×C113—22no—
66C23×C113—22no—
67C23×C113—22no—
68C23×C113—24no—
69C23×C113—24no—
70C23×C113C2×D414yes—
71C23×C113C2×D414yes—
72C23×C113C2×D412yes—
73C23×C113C2411yescharacteristic
74C22×D113—28no—
75C22×D113—22no—
76C22×D113—24no—
77C22×D113—22no—
78C22×D113—24no—
79C22×D113—416no—
80C22×D113—44no—
81C22×D113—44no—
82C22×D113#4114yescomplemented
83Q8×C113—28no—
84D4×C113—28no—
85D4×C113—216no—
86C2×C4×C113—216no—
87C2×C4×C113—28no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113C2×D412yes—
93C2×C4×C113C2×D414yes—
94C2×C4×C113C2×D412yes—
95C22⋊D113—416no—
96C2×Dic113—22no—
97C2×Dic113—24no—
98C2×Dic113—24no—
99C2×Dic113—24no—
100C2×Dic113—24no—
101C2×Dic113—44no—
102C22×C113—22no—
103C22×C113—22no—
104C22×C113—28no—
105C22×C113—24no—
106C22×C113—28no—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113—44no—
110C22×C113#12014yes—
111C22×C113C22×D411yescharacteristic
112C22×C113C22×D412yes—
113C22×C113C2×#4112yes—
114C22×C113H(5,𝔽2)12yes—
115C2×D113—24no—
116C2×D113—28no—
117C2×D113—416no—
118C2×D113—42no—
119C2×D113—42no—
120C2×D113—44no—
121C4×C113—22no—
122C4×C113—24no—
123C4×C113—22no—
124Dic113—42no—
125Dic113—44no—
126C2×C113—24no—
127C2×C113—44no—
128C2×C113C2×#12011yescharacteristic
129C2×C113#52511yescharacteristic
130C2×C113#53511yescharacteristic
131C2×C113#54614yes—
132D113—44no—
133#2404—1131nomaximal, Sylow
134C113#240411yescharacteristic, complemented, Sylow
135C22×#41D11311yescharacteristic, complemented
136C2×#120—1132no—
137C22×C22⋊C4—1131no—
138#393—1132no—
139#392—1132no—
140#386—1132no—
141#386—1134no—
142#381—1131no—
143C25—1131no—
144C2×#41—28no—
145C2×#41—24no—
146C22×Q8C2×D11311yescharacteristic, complemented
147C22×D4—1134no—
148C22×D4C2×D11312yes—
149C22×D4C2×D11311yescharacteristic, complemented
150C23×C4—1131no—
151C23×C4C2×D11311yescharacteristic
152C23×C4C2×D11312yescomplemented
153#120—2268no—
154C2×C22⋊C4—1134no—
155C2×C22⋊C4—1132no—
156C2×C22⋊C4—1132no—
157C2×C22⋊C4—1132no—
158C2×C22⋊C4—1134no—
159C2×C22⋊C4—2264no—
160#95—1132no—
161#95—1132no—
162#95—1134no—
163C24—1132no—
164C24—4522no—
165C24—2264no—
166C24—2264no—
167C24—2262no—
168C24C22×D11312yes—
169C24C22×D11311yescharacteristic
170#41—232no—
171C2×Q8—24no—
172C2×Q8—22no—
173C2×D4—24no—
174C2×D4—24no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—4524no—
178C2×D4—2268no—
179C2×D4—2268no—
180C2×D4C22⋊D11318yescomplemented
181C22×C4—24no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—1134no—
186C22×C4—1132no—
187C22×C4—4522no—
188C22×C4—2262no—
189C22×C4C22⋊D11314yescomplemented
190C22×C4C22×D11311yescharacteristic
191C22×C4C22×D11311yescharacteristic
192C22×C4C22×D11312yes—
193C22⋊C4—4524no—
194C22⋊C4—2264no—
195C22⋊C4—2264no—
196C22⋊C4—2264no—
197C22⋊C4—2268no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—24no—
203C23—24no—
204C23—1134no—
205C23—4524no—
206C23—45216no—
207C23—4524no—
208C23—2268no—
209C23—2262no—
210C23—2264no—
211C23—2262no—
212C23—2264no—
213C23C2×C22⋊D11314yes—
214C23C2×C22⋊D11314yes—
215C23C2×C22⋊D11312yes—
216C23C23×D11311yescharacteristic
217Q8—28no—
218D4—28no—
219D4—216no—
220D4—45216no—
221C2×C4—216no—
222C2×C4—28no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—4524no—
228C2×C4—2262no—
229C2×C4—2264no—
230C2×C4—2264no—
231C2×C4—2264no—
232C2×C4—2264no—
233C2×C4C2×C22⋊D11312yes—
234C2×C4C2×C22⋊D11314yes—
235C2×C4C2×C22⋊D11312yes—
236C22—22no—
237C22—22no—
238C22—28no—
239C22—24no—
240C22—28no—
241C22—42no—
242C22—42no—
243C22—44no—
244C22—45216no—
245C22—4522no—
246C22—4522no—
247C22—4524no—
248C22—2264no—
249C22—2268no—
250C22#1681359114yes—
251C22C22×C22⋊D11311yescharacteristic
252C22C22×C22⋊D11312yes—
253C22#41×D11312yes—
254C22#1681366812yes—
255C4—22no—
256C4—24no—
257C4—22no—
258C4—4522no—
259C4—4524no—
260C2—24no—
261C2—44no—
262C2—4524no—
263C2C2×#1681359111yescharacteristic
264C2#2029910511yescharacteristic
265C2#2029916211yescharacteristic
266C2#2029923614yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
FittingC22×#41×C113C2
hypercenterC22×#41D113
hypocenterC113#2404
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16813590C2semidirect
2. C22×#14268624C2semidirect
3. #20298509C2semidirect
4. #20298506C2semidirect
5. #20298478C2semidirect
6. #20298477C2semidirect
7. #20298461C2semidirect
8. C22×#41×C113C2semidirect
14. C2×C22⋊Dic113C22semidirect
19. #16813529C22semidirect
20. #16813529C22semidirect
21. #16813529C22semidirect
24. C22×Q8×C113C22semidirect
26. C22×D4×C113C22semidirect
28. C23×C4×C113C22semidirect
55. C2×D4×C113D4semidirect
60. C22×C4×C113D4semidirect
82. C22×D113#41semidirect
134. C113#2404semidirect
135. C22×#41D113semidirect
146. C22×Q8C2×D113semidirect
149. C22×D4C2×D113semidirect
152. C23×C4C2×D113semidirect
180. C2×D4C22⋊D113semidirect
189. C22×C4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135902
C22×#142686242
#202985092
#202985062
#202984782
#202984772
#202984612
C22×#41×C1132
#2404113