Finite Group Databasebeta

← #28402934

Subgroups — #28402934

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#20299308C211yesmaximal, characteristic, complemented
2#20299251C211yesmaximal, characteristic
3#20298994C211yesmaximal, characteristic, complemented
4#20298927C212yesmaximal, complemented
5#20298918C212yesmaximal, complemented
6#20298889C211yesmaximal, characteristic, complemented
7#20298830C212yesmaximal, complemented
8C4×#14268634C211yesmaximal, characteristic, complemented
9#20298663C211yesmaximal, characteristic, complemented
10#106×D113C212yesmaximal, complemented
11#475×C113C211yesmaximal, characteristic, complemented
12C2×#14268648—21no—
13C2×#14268634C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813622C2211yescharacteristic
16#16813614—21no—
17#16813607—22no—
18#16813600—22no—
19#16813598—21no—
20#16813598C2212yes—
21#16813597C2212yes—
22C4×D452—21no—
23C4×D452C2211yescharacteristic
24C4×D452C2211yescharacteristic
25C4⋊C4×D113C2212yes—
26C4⋊C4×D113C2212yes—
27#16813554C2212yes—
28#16813553C2212yes—
29#16813553C2211yescharacteristic
30#16813553C2212yes—
31#16813546C2211yescharacteristic
32#16813544C2212yes—
33#16813542C2211yescharacteristic
34#16813534C2212yes—
35C4×#11744751C2211yescharacteristic
36C4⋊Q8×C113C2211yescharacteristic
37C4×Q8×C113C2211yescharacteristic
38#106×C113C2212yes—
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41#14268648—44no—
42C2×Dic226—21no—
43C2×D452—22no—
44C2×D452D411yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C4×D113—22no—
47C2×C4×D113—21no—
48C2×C4×D113—22no—
49C2×C4×D113C2312yes—
50#14268634—22no—
51C2×#11744751C2311yescharacteristic
52C2×#11744751C2311yescharacteristic
53C8×D113—24no—
54C4⋊Dic113—21no—
55C4⋊Dic113D411yescharacteristic
56C4⋊Dic113C2311yescharacteristic
57C4⋊Dic113C2312yes—
58#14268626—22no—
59#14268626—22no—
60#14268626—22no—
61#14268624—22no—
62#14268624—21no—
63#14268624—22no—
64#14268624D412yes—
65C2×Q8×C113—21no—
66C2×Q8×C113C2311yescharacteristic
67C2×C8×C113C2312yes—
68C4⋊C4×C113—21no—
69C4⋊C4×C113—21no—
70C4⋊C4×C113C2311yescharacteristic
71C4⋊C4×C113C2312yes—
72C42×C113—21no—
73C42×C113C2311yescharacteristic
74C22×D113—21no—
75C22×D113C2×D412yes—
76Q8×C113—21no—
77Q8×C113—21no—
78Q8×C113—42no—
79C2×C4×C113—21no—
80C2×C4×C113—21no—
81C2×C4×C113—22no—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C2×Dic113—22no—
86C2×Dic113—21no—
87C2×Dic113C2×D412yes—
88D452—21no—
89D452—21no—
90D452—44no—
91D452SD1614yescomplemented
92C4×D113—22no—
93C4×D113—22no—
94C4×D113—44no—
95C4×D113—42no—
96C4×D113—82no—
97Dic226—81no—
98C8×C113—22no—
99#11744751—21no—
100#11744751#4112yescomplemented
101C22×C113C22×D411yescharacteristic
102C2×D113—22no—
103C2×D113—22no—
104C2×D113—41no—
105C2×D113—41no—
106C2×D113—41no—
107C2×D113C2×SD1614yes—
108C4×C113—21no—
109C4×C113—41no—
110C4×C113—42no—
111C4×C113—41no—
112C4×C113C2×SD1612yes—
113C4×C113C2×#4111yescharacteristic
114C4×C1132−1+411yescharacteristic
115Dic113—22no—
116Dic113—41no—
117Dic113—42no—
118C2×C113#54711yescharacteristic
119C2×C113C22×SD1611yescharacteristic
120C2×C113#57711yescharacteristic
121D113—24no—
122D113—81no—
123#3335—1131nomaximal, Sylow
124C113#333511yescharacteristic, complemented, Sylow
125#554—1131no—
126#547—1131no—
127#498—1131no—
128#483—1132no—
129#481—1132no—
130#476—1131no—
131#475D11311yescharacteristic, complemented
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×Q8C2×D11311yescharacteristic
148C4×D4—1131no—
149C4×D4—1131no—
150C4×D4—2261no—
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—1131no—
160#103C2×D11312yes—
161#102—1132no—
162#102—1131no—
163C22⋊C8—1132no—
164C4×C8—1131no—
165#41—4524no—
166C2×Q8—21no—
167C2×Q8—2261no—
168C2×Q8C22×D11311yescharacteristic
169C2×D4—1131no—
170C2×D4—1131no—
171C2×D4—2262no—
172C22×C4—1132no—
173C22×C4—2262no—
174C22×C4—2262no—
175C22×C4—2261no—
176SD16—2262no—
177C2×C8—1131no—
178C2×C8—1131no—
179C2×C8—2264no—
180C2×C8C22×D11312yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1131no—
184C4⋊C4—1132no—
185C4⋊C4—1131no—
186C4⋊C4—2262no—
187C4⋊C4—2262no—
188C4⋊C4—2262no—
189C4⋊C4—2261no—
190C4⋊C4C22×D11311yescharacteristic
191C4⋊C4C22×D11312yes—
192C22⋊C4—1132no—
193C22⋊C4—2262no—
194C22⋊C4—2262no—
195C22⋊C4—2261no—
196C42—21no—
197C42C22×D11311yescharacteristic
198C23—1132no—
199C23—2261no—
200Q8—21no—
201Q8—21no—
202Q8—42no—
203Q8—9041no—
204D4—1134no—
205D4—4524no—
206D4—2261no—
207D4—2261no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—1132no—
212C2×C4—9042no—
213C2×C4—4524no—
214C2×C4—4522no—
215C2×C4—2262no—
216C2×C4—2261no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4D4×D11311yescharacteristic
221C2×C4C23×D11311yescharacteristic
222C8—22no—
223C8—1132no—
224C8—2261no—
225C22—1134no—
226C22—4521no—
227C22—4521no—
228C22—4521no—
229C22—2262no—
230C22—2262no—
231C22C2×D4×D11311yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—41no—
236C4—4521no—
237C4—4522no—
238C4—2262no—
239C4SD16×D11312yes—
240C4#41×D11311yescharacteristic
241C4#1681367011yescharacteristic
242C2—9041no—
243C2—2264no—
244C2#2029925011yescharacteristic
245C2C2×SD16×D11311yescharacteristic
246C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#475×C113C2
socleC22×C113C22×D4
prime radical#20299251C2
hypercenter#475D113
hypocenterC113#3335
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #20299308C2semidirect
3. #20298994C2semidirect
4. #20298927C2semidirect
5. #20298918C2semidirect
6. #20298889C2semidirect
7. #20298830C2semidirect
8. C4×#14268634C2semidirect
9. #20298663C2semidirect
10. #106×D113C2semidirect
11. #475×C113C2semidirect
91. D452SD16semidirect
100. #11744751#41semidirect
124. C113#3335semidirect
131. #475D113semidirect

Maximal subgroups

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

subgroupindex
#202993082
#202992512
#202989942
#202989272
#202989182
#202988892
#202988302
C4×#142686342
#202986632
#106×D1132
#475×C1132
#3335113