Finite Group Databasebeta

← #28402928

Subgroups — #28402928

Order 14464.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#20299309C211yesmaximal, characteristic, complemented
2#20299253C211yesmaximal, characteristic
3#20298994C211yesmaximal, characteristic, complemented
4#20298930C212yesmaximal, complemented
5#20298915C212yesmaximal, complemented
6#20298884C211yesmaximal, characteristic, complemented
7#20298826C212yesmaximal, complemented
8C4×#14268635C211yesmaximal, characteristic, complemented
9#20298663C211yesmaximal, characteristic, complemented
10#106×D113C212yesmaximal, complemented
11#476×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C2×#14268635C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813622C2211yescharacteristic
16#16813613—21no—
17#16813604—22no—
18#16813602C2212yes—
19#16813601—21no—
20#16813598—22no—
21#16813593C2212yes—
22C4×Dic226C2211yescharacteristic
23C4×D452C2211yescharacteristic
24#16813584—21no—
25C4⋊C4×D113C2212yes—
26C4⋊C4×D113C2212yes—
27#16813554C2212yes—
28#16813553C2212yes—
29#16813553C2211yescharacteristic
30#16813553C2212yes—
31#16813547C2212yes—
32#16813545C2211yescharacteristic
33#16813543C2211yescharacteristic
34#16813534C2212yes—
35C4×#11744751C2211yescharacteristic
36C4⋊Q8×C113C2211yescharacteristic
37C4×D4×C113C2211yescharacteristic
38#106×C113C2212yes—
39C4⋊C8×C113C2211yescharacteristic
40#102×C113C2212yes—
41#14268647—44no—
42C2×Dic226—21no—
43C2×Dic226C2311yescharacteristic
44C2×D452D411yescharacteristic
45C2×C22⋊D113—22no—
46C2×C4×D113—22no—
47C2×C4×D113—22no—
48C2×C4×D113C2312yes—
49#14268635—22no—
50C2×#11744751C2311yescharacteristic
51C2×#11744751C2311yescharacteristic
52C8×D113—24no—
53C4⋊Dic113—21no—
54C4⋊Dic113—22no—
55C4⋊Dic113D411yescharacteristic
56C4⋊Dic113C2311yescharacteristic
57C4⋊Dic113C2312yes—
58#14268626—21no—
59#14268626—22no—
60#14268626—22no—
61C22⋊Dic113—22no—
62#14268624—22no—
63#14268624D412yes—
64C4×Dic113—21no—
65C2×Q8×C113—21no—
66C2×D4×C113C2311yescharacteristic
67C22×C4×C113—21no—
68C2×C8×C113C2312yes—
69C4⋊C4×C113—21no—
70C4⋊C4×C113C2311yescharacteristic
71C4⋊C4×C113C2312yes—
72C22⋊C4×C113—21no—
73C42×C113C2311yescharacteristic
74C23×C113—21no—
75C22×D113C2×D412yes—
76Q8×C113—81no—
77D4×C113—21no—
78D4×C113—21no—
79C2×C4×C113—21no—
80C2×C4×C113—22no—
81C2×C4×C113—42no—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—44no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—22no—
89C2×Dic113C2×D412yes—
90D452SD1614yescomplemented
91C4×D113—22no—
92C4×D113—22no—
93C4×D113—44no—
94C4×D113—82no—
95Dic226—21no—
96Dic226—21no—
97Dic226—42no—
98C8×C113—22no—
99#11744751—21no—
100#11744751#4112yescomplemented
101C22×C113—41no—
102C22×C113—41no—
103C22×C113—41no—
104C22×C113C22×D411yescharacteristic
105C2×D113—22no—
106C2×D113—22no—
107C2×D113C2×SD1614yes—
108C4×C113—21no—
109C4×C113—41no—
110C4×C113—42no—
111C4×C113C2×SD1612yes—
112C4×C113C2×#4111yescharacteristic
113C4×C1132−1+411yescharacteristic
114Dic113—22no—
115Dic113—41no—
116Dic113—42no—
117Dic113—41no—
118C2×C113—81no—
119C2×C113#54711yescharacteristic
120C2×C113C22×SD1611yescharacteristic
121C2×C113#57711yescharacteristic
122D113—24no—
123#3335—1131nomaximal, Sylow
124C113#333511yescharacteristic, complemented, Sylow
125#554—1131no—
126#547—1131no—
127#498—1131no—
128#483—1132no—
129#481—1132no—
130#476D11311yescharacteristic, complemented
131#475—1131no—
132#465—1132no—
133C4×SD16—1131no—
134C8×D4—1131no—
135C2×#106—1132no—
136C2×#41—2261no—
137C2×SD16—1131no—
138C22×C8—1132no—
139C4⋊Q8—1131no—
140C4⋊Q8C2×D11311yescharacteristic
141#125—2261no—
142#123—2262no—
143C22⋊Q8—1132no—
144C22⋊Q8—2262no—
145C22⋊Q8—2261no—
146#121—1132no—
147C4×Q8—1131no—
148C4×D4—1131no—
149C4×D4—2261no—
150C4×D4C2×D11311yescharacteristic
151C2×C4⋊C4—1132no—
152C2×C4⋊C4—1132no—
153#106—1132no—
154#106—1131no—
155#106—1132no—
156#106—1132no—
157#106C2×D11312yes—
158C4⋊C8C2×D11311yescharacteristic
159#103—1132no—
160#103—1131no—
161#102—1131no—
162#102C2×D11312yes—
163C22⋊C8—1132no—
164C4×C8—1131no—
165#41—4524no—
166C2×Q8—21no—
167C2×Q8—1131no—
168C2×Q8—2261no—
169C2×D4—1131no—
170C2×D4—2262no—
171C2×D4C22×D11311yescharacteristic
172C22×C4—21no—
173C22×C4—1132no—
174C22×C4—2262no—
175C22×C4—2262no—
176SD16—2262no—
177C2×C8—1131no—
178C2×C8—1131no—
179C2×C8—2264no—
180C2×C8C22×D11312yes—
181C4⋊C4—21no—
182C4⋊C4—1131no—
183C4⋊C4—1131no—
184C4⋊C4—1132no—
185C4⋊C4—2262no—
186C4⋊C4—2262no—
187C4⋊C4—2262no—
188C4⋊C4—2261no—
189C4⋊C4—2261no—
190C4⋊C4C22×D11312yes—
191C4⋊C4C22×D11311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—1132no—
194C22⋊C4—2262no—
195C22⋊C4—2262no—
196C42—2261no—
197C42C22×D11311yescharacteristic
198C23—21no—
199C23—1132no—
200Q8—81no—
201Q8—4522no—
202Q8—2261no—
203Q8—2261no—
204D4—21no—
205D4—21no—
206D4—1134no—
207D4—4524no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—1132no—
212C2×C4—9042no—
213C2×C4—4524no—
214C2×C4—2261no—
215C2×C4—2261no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4D4×D11311yescharacteristic
221C2×C4C23×D11311yescharacteristic
222C8—22no—
223C8—1132no—
224C8—2261no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—1134no—
229C22—2262no—
230C22—2262no—
231C22C2×D4×D11311yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—4522no—
236C4—4521no—
237C4—4521no—
238C4—2262no—
239C4SD16×D11312yes—
240C4#41×D11311yescharacteristic
241C4#1681367011yescharacteristic
242C2—81no—
243C2—2264no—
244C2#2029925011yescharacteristic
245C2C2×SD16×D11311yescharacteristic
246C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#476×C113C2
socleC22×C113C22×D4
prime radical#20299253C2
hypercenter#476D113
hypocenterC113#3335
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20299309C2semidirect
3. #20298994C2semidirect
4. #20298930C2semidirect
5. #20298915C2semidirect
6. #20298884C2semidirect
7. #20298826C2semidirect
8. C4×#14268635C2semidirect
9. #20298663C2semidirect
10. #106×D113C2semidirect
11. #476×C113C2semidirect
90. D452SD16semidirect
100. #11744751#41semidirect
124. C113#3335semidirect
130. #476D113semidirect

Maximal subgroups

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

subgroupindex
#202993092
#202992532
#202989942
#202989302
#202989152
#202988842
#202988262
C4×#142686352
#202986632
#106×D1132
#476×C1132
#3335113