Finite Group Databasebeta

← #28401638

Subgroups — #28401638

Order 14464.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299204C211yesmaximal, characteristic, complemented
2#20299168C211yesmaximal, characteristic, complemented
3#20298988C211yesmaximal, characteristic, complemented
4#20298971C211yesmaximal, characteristic, complemented
5#20298968C211yesmaximal, characteristic, complemented
6#20298812C212yesmaximal, complemented
7#20298802C212yesmaximal, complemented
8#20298744C212yesmaximal, complemented
9#20298738C212yesmaximal, complemented
10#20298657C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C2×Q8×D113C2211yescharacteristic
14C2×#14268636C2212yes—
15C2×#14268636C2212yes—
16C2×#14268634C2212yes—
17C2×#14268632C2212yes—
18#16813622C2211yescharacteristic
19#16813620C2211yescharacteristic
20#16813619C2211yescharacteristic
21#16813609C2211yescharacteristic
22#16813607—22no—
23#16813604—22no—
24#16813599—22no—
25#16813597—22no—
26#16813597C2212yes—
27#16813584C2212yes—
28#16813579C2211yescharacteristic
29#16813551C2212yes—
30#16813545C2212yes—
31#16813545C2212yes—
32#16813534C2212yes—
33#16813533C2211yescharacteristic
34#125×C113C2211yescharacteristic
35#124×C113C2211yescharacteristic
36#103×C113C2212yes—
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic
39#14268646—42no—
40C2×Dic226—21no—
41C2×Dic226C2311yescharacteristic
42C2×Dic226C2311yescharacteristic
43Q8×D113—42no—
44C2×D452—22no—
45C2×D452—22no—
46C2×D452C2312yes—
47C2×C22⋊D113—21no—
48C22×Dic113—21no—
49C2×C4×D113—21no—
50C2×C4×D113—22no—
51C2×C4×D113C2311yescharacteristic
52#14268636—42no—
53#14268636—42no—
54#14268634—42no—
55#14268632—42no—
56C2×#11744751C2312yes—
57C4⋊Dic113—22no—
58#14268626—22no—
59#14268626D412yes—
60C22⋊Dic113—22no—
61#14268624—22no—
62#14268624—22no—
63#14268624D412yes—
64C4×Dic113C2311yescharacteristic
65C2×Q8×C113C2311yescharacteristic
66C2×D4×C113C2311yescharacteristic
67C2×C8×C113C2312yes—
68C4⋊C4×C113—22no—
69C4⋊C4×C113C2312yes—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C22×D113—22no—
74C22×D113C2×D411yescharacteristic
75Q8×C113—22no—
76D4×C113—22no—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2411yescharacteristic
81C22⋊D113—42no—
82C2×Dic113—21no—
83C2×Dic113—21no—
84C2×Dic113—42no—
85C2×Dic113C2×D412yes—
86C2×Dic113C2×D411yescharacteristic
87D452—22no—
88D452—22no—
89D452—82no—
90D452—82no—
91C4×D113—22no—
92C4×D113—42no—
93C4×D113—82no—
94Dic226—22no—
95Dic226—22no—
96Dic226—42no—
97C8×C113—22no—
98#11744751—22no—
99C22×C113—41no—
100C22×C113—42no—
101C22×C113C22×D411yescharacteristic
102C2×D113—21no—
103C2×D113—22no—
104C2×D113—42no—
105C2×D113—42no—
106C2×D113—42no—
107C4×C113—22no—
108C4×C113—41no—
109C4×C113—42no—
110C4×C113H(5,𝔽2)12yes—
111Dic113—21no—
112Dic113—22no—
113Dic113—41no—
114Dic113—41no—
115C2×C113—81no—
116C2×C113#53511yescharacteristic
117C2×C113#57712yes—
118D113—41no—
119D113—82no—
120#3221—1131nomaximal, Sylow
121C113#322111yescharacteristic, complemented, Sylow
122#540—1131no—
123#536—1131no—
124#496—1131no—
125#492—1131no—
126#491—1131no—
127#488D11311yescharacteristic, complemented
128#463—1132no—
129#461—1132no—
130#449—1132no—
131#448—1132no—
132#433—1131no—
133C2×#41—1131no—
134C22×Q8—1131no—
135C2×SD16—1132no—
136C2×SD16—1132no—
137C2×SD16—1132no—
138C2×D8—1132no—
139C4⋊Q8—1131no—
140C4⋊Q8—1131no—
141#127—1131no—
142#125C2×D11311yescharacteristic
143#124—1131no—
144#124C2×D11311yescharacteristic
145#123—2262no—
146#123—2262no—
147C22⋊Q8—2262no—
148#121—1132no—
149#121—2262no—
150C4×D4—1132no—
151#117—1131no—
152C4⋊C8—1132no—
153#103—1132no—
154#103—1132no—
155#103C2×D11312yes—
156#102C2×D11312yes—
157C22⋊C8—1132no—
158#97—1131no—
159C4×C8C2×D11311yescharacteristic
160#41—4522no—
161C2×Q8—1131no—
162C2×Q8—1131no—
163C2×Q8—4522no—
164C2×Q8—2261no—
165C2×Q8C22×D11311yescharacteristic
166C2×D4—1132no—
167C2×D4—2262no—
168C2×D4—2261no—
169C2×D4—2262no—
170C2×D4C22×D11311yescharacteristic
171C22×C4—1131no—
172C22×C4—2262no—
173C22×C4—2261no—
174C22×C4—2261no—
175SD16—4522no—
176SD16—4522no—
177SD16—4522no—
178D8—4522no—
179C2×C8—1132no—
180C2×C8C22×D11312yes—
181C4⋊C4—22no—
182C4⋊C4—1132no—
183C4⋊C4—2262no—
184C4⋊C4—2262no—
185C4⋊C4C22×D11312yes—
186C22⋊C4—22no—
187C22⋊C4—1132no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C42—1131no—
192C42C22×D11311yescharacteristic
193C23—21no—
194C23—1131no—
195C23—2262no—
196Q8—22no—
197Q8—4522no—
198Q8—2262no—
199Q8—2262no—
200D4—22no—
201D4—9042no—
202D4—9042no—
203D4—4522no—
204D4—2262no—
205D4—2262no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—1132no—
209C2×C4—1131no—
210C2×C4—9042no—
211C2×C4—4522no—
212C2×C4—4522no—
213C2×C4—2261no—
214C2×C4—2261no—
215C2×C4—2262no—
216C2×C4D4×D11312yes—
217C2×C4C23×D11311yescharacteristic
218C8—22no—
219C8—2262no—
220C22—42no—
221C22—41no—
222C22—4522no—
223C22—4522no—
224C22—4522no—
225C22—2262no—
226C22—2261no—
227C22C2×D4×D11311yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—4521no—
232C4—4521no—
233C4—2262no—
234C4—2261no—
235C4#1681366812yes—
236C2—81no—
237C2—9042no—
238C2—4521no—
239C2#2029916611yescharacteristic
240C2#2029940512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
hypercenter#488D113
hypocenterC113#3221
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299204C2semidirect
2. #20299168C2semidirect
3. #20298988C2semidirect
4. #20298971C2semidirect
5. #20298968C2semidirect
6. #20298812C2semidirect
7. #20298802C2semidirect
8. #20298744C2semidirect
9. #20298738C2semidirect
10. #20298657C2semidirect
11. #488×C113C2semidirect
121. C113#3221semidirect
127. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202992042
#202991682
#202989882
#202989712
#202989682
#202988122
#202988022
#202987442
#202987382
#202986572
#488×C1132
#3221113