Finite Group Databasebeta

← #28399941

Subgroups — #28399941

Order 14464.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16813670C211yesmaximal, characteristic, complemented
2#20299398C212yesmaximal, complemented
3#20299172C211yesmaximal, characteristic, complemented
4#20298783C214yesmaximal, complemented
5#20298773C214yesmaximal, complemented
6#20298614C212yesmaximal, complemented
7C2×#101×C113C211yesmaximal, characteristic, complemented
8#16813670—24no—
9#16813670—22no—
10#16813670C2214yes—
11C2×#14268648—22no—
12C2×#14268647—22no—
13C2×#14268647C2212yes—
14C2×#14268647C2211yescharacteristic
15C2×Q8×D113—22no—
16#16813655—22no—
17#16813655C2214yescomplemented
18#16813650—22no—
19#16813650C2214yescomplemented
20#16813644—24no—
21#16813620C2212yescomplemented
22#16813611C2212yescomplemented
23#16813605—22no—
24#16813598—22no—
25#16813581C2211yescharacteristic
26#16813548C2218yescomplemented
27C22×Q8×C113C2211yescharacteristic
28C2×M16×C113C2212yes—
29#101×C113C2214yescomplemented
30#14268648—28no—
31#14268648—28no—
32#14268647—28no—
33#14268647—28no—
34#14268647—22no—
35#14268647—22no—
36#14268647—22no—
37#14268647—22no—
38#14268647D414yes—
39#14268647C2314yes—
40C2×Dic226—22no—
41C2×Dic226D412yes—
42C2×Dic226C2311yescharacteristic
43Q8×D113—28no—
44Q8×D113—28no—
45C2×D452—22no—
46C2×D452D412yes—
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—22no—
49C2×C22⋊D113—21no—
50C2×C4×D113—24no—
51C2×C4×D113—22no—
52C2×C4×D113—21no—
53Dic452—24no—
54#14268636—24no—
55#14268636—24no—
56D904—24no—
57C4⋊Dic113—21no—
58#14268626—24no—
59C22⋊Dic113—21no—
60#14268624—24no—
61C4×Dic113C2312yes—
62C2×Q8×C113—22no—
63C2×Q8×C113—22no—
64C2×Q8×C113D412yes—
65C2×Q8×C113C2312yes—
66C22×C4×C113D412yes—
67C22×C4×C113C2311yescharacteristic
68M16×C113—22no—
69M16×C113C2314yes—
70C2×C8×C113—22no—
71C23×C113C2×D411yescharacteristic
72C22×D113—22no—
73C22×D113—21no—
74Q8×C113—24no—
75Q8×C113—24no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113C2×D412yes—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D414yes—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—24no—
84C22⋊D113—24no—
85C22⋊D113—41no—
86C22⋊D113—41no—
87C2×Dic113—22no—
88C2×Dic113—22no—
89C2×Dic113—21no—
90D452—28no—
91D452—22no—
92D452—22no—
93D452C2×D414yes—
94C4×D113—216no—
95C4×D113—24no—
96C4×D113—24no—
97C4×D113—42no—
98Dic226—28no—
99Dic226—22no—
100Dic226—22no—
101Dic226C2×D414yes—
102C8×C113—24no—
103C22×C113—41no—
104C22×C113#12011yescharacteristic
105C22×C113#12011yescharacteristic
106C22×C113C22×D411yescharacteristic
107C2×D113—24no—
108C2×D113—44no—
109C2×D113—42no—
110C2×D113—41no—
111C4×C113—24no—
112C4×C113#12012yes—
113C4×C113C22×D412yes—
114Dic113—24no—
115Dic113—42no—
116Dic113—41no—
117C2×C113—21no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113C2×#12011yescharacteristic
121D113—44no—
122D113—81no—
123#3020—1131nomaximal, Sylow
124C113#302011yescharacteristic, complemented, Sylow
125C2×2−1+4—1131no—
126#575—1132no—
127#536—1131no—
128#456—1134no—
129#454—1134no—
130#421—1132no—
131C2×#101D11311yescharacteristic, complemented
1322−1+4—1134no—
1332−1+4—2264no—
1342−1+4—2262no—
135C2×#41—1132no—
136C2×#41—1131no—
137C2×#41—2262no—
138C2×#41—2262no—
139C22×Q8—2262no—
140C22×Q8C2×D11311yescharacteristic
141#137—1134no—
142#137—2262no—
143AGL(1,ℤ/8)—1134no—
144AGL(1,ℤ/8)—2262no—
145#135—2264no—
146C2×M16C2×D11312yes—
147C4⋊Q8—1132no—
148#124—1132no—
149#123—2262no—
150C22⋊Q8—2262no—
151#117—1131no—
152#104—1138no—
153#101C2×D11314yescomplemented
154#41—1134no—
155#41—1134no—
156#41—2268no—
157#41—2262no—
158#41—2262no—
159#41—2268no—
160#41—2268no—
161#41—2262no—
162#41—2262no—
163#41—2268no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—1132no—
167C2×Q8—1131no—
168C2×Q8—2262no—
169C2×Q8—2268no—
170C2×Q8—2268no—
171C2×Q8D45212yes—
172C2×Q8C22×D11312yes—
173C2×D4—1132no—
174C2×D4—1131no—
175C2×D4—2262no—
176C2×D4—2261no—
177C2×D4—2262no—
178C22×C4—2264no—
179C22×C4—2261no—
180C22×C4—2262no—
181C22×C4D45212yes—
182C22×C4C22×D11311yescharacteristic
183Q16—2264no—
184SD16—2264no—
185SD16—2264no—
186D8—2264no—
187M16—22no—
188M16C22×D11314yes—
189C2×C8—22no—
190C4⋊C4—2261no—
191C4⋊C4—2264no—
192C22⋊C4—2261no—
193C22⋊C4—2264no—
194C42—1132no—
195C23—2261no—
196C23—2262no—
197C23C2×D45211yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—1134no—
201Q8—2268no—
202Q8—2262no—
203Q8—2262no—
204D4—1134no—
205D4—4521no—
206D4—4521no—
207D4—2268no—
208D4—2264no—
209D4—2264no—
210D4—2262no—
211D4—2262no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—4522no—
215C2×C4—22616no—
216C2×C4—2262no—
217C2×C4—2261no—
218C2×C4—2262no—
219C2×C4—2264no—
220C2×C4—2264no—
221C2×C4D4×D11312yes—
222C2×C4D4×D11312yes—
223C2×C4C2×D45214yes—
224C2×C4C2×D45211yescharacteristic
225C2×C4C23×D11311yescharacteristic
226C8—24no—
227C22—41no—
228C22—4522no—
229C22—4524no—
230C22—4521no—
231C22—2264no—
232C22#1681359211yescharacteristic
233C22#1681359211yescharacteristic
234C22C22×D45211yescharacteristic
235C4—24no—
236C4—4522no—
237C4—4521no—
238C4—2264no—
239C4#1681359212yes—
240C4C2×D4×D11312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—9041no—
245C2—4524no—
246C2C2×#1681359211yescharacteristic
subgroupG/H
centerC2C2×#16813592
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#101×C113C2
socleC2×C113C2×#120
hypercenterC2×#101D113
hypocenterC113#3020
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#16813670C2semidirect
2. #20299398C2semidirect
3. #20299172C2semidirect
4. #20298783C2semidirect
5. #20298773C2semidirect
6. #20298614C2semidirect
7. C2×#101×C113C2semidirect
17. #16813655C22semidirect
19. #16813650C22semidirect
21. #16813620C22semidirect
22. #16813611C22semidirect
26. #16813548C22semidirect
29. #101×C113C22semidirect
124. C113#3020semidirect
131. C2×#101D113semidirect
153. #101C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
#202993982
#202991722
#202987832
#202987732
#202986142
C2×#101×C1132
#3020113