Finite Group Databasebeta

← #28401629

Subgroups — #28401629

Order 14464.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299174C211yesmaximal, characteristic, complemented
2#20298985C211yesmaximal, characteristic, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298968C211yesmaximal, characteristic, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298813C212yesmaximal, complemented
7#20298803C212yesmaximal, complemented
8#20298741C212yesmaximal, complemented
9#20298736C212yesmaximal, complemented
10#20298659C211yesmaximal, characteristic, complemented
11#540×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14C2×#14268635C2212yes—
15C2×#14268635C2212yes—
16C2×#14268635C2212yes—
17C2×#14268632C2212yes—
18#16813622C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813610C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813606—22no—
23#16813602—22no—
24C4⋊#11744751C2212yes—
25#16813545C2212yes—
26#16813545C2212yes—
27#16813545C2212yes—
28#16813542C2212yes—
29C22⋊#11744751C2212yes—
30#16813533C2211yescharacteristic
31C4×#11744751C2211yescharacteristic
32#127×C113C2211yescharacteristic
33#125×C113C2211yescharacteristic
34#123×C113—22no—
35#121×C113—22no—
36#121×C113C2212yes—
37C4×D4×C113C2212yes—
38#117×C113C2211yescharacteristic
39#14268647—42no—
40C2×Dic226—21no—
41C2×Dic226—42no—
42C2×Dic226C2311yescharacteristic
43C2×Dic226C2311yescharacteristic
44C2×Dic226C2311yescharacteristic
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47C22×Dic113—21no—
48C2×C4×D113—21no—
49#14268635—42no—
50#14268635—42no—
51#14268635—42no—
52#14268632—42no—
53C2×#11744751C2312yes—
54C2×#11744751C2312yes—
55C4⋊Dic113—22no—
56C4⋊Dic113—22no—
57#14268624—22no—
58#14268624—22no—
59C2×D4×C113—22no—
60C2×D4×C113—22no—
61C2×D4×C113C2312yes—
62C22×C4×C113—22no—
63C22×C4×C113C2311yescharacteristic
64C4⋊C4×C113—22no—
65C4⋊C4×C113D412yes—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C22⋊C4×C113—22no—
69C22⋊C4×C113D412yes—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113—22no—
73C23×C113C2×D411yescharacteristic
74C22×D113—21no—
75D4×C113—22no—
76D4×C113—22no—
77D4×C113—82no—
78D4×C113—82no—
79C2×C4×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—82no—
82C2×C4×C113C2×D412yes—
83C2×C4×C113C2×D412yes—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2411yescharacteristic
86C22⋊D113—42no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113—42no—
91D452—22no—
92C4×D113—42no—
93Dic226—22no—
94Dic226—22no—
95Dic226—22no—
96Dic226—42no—
97#11744751—22no—
98#11744751—22no—
99C22×C113—21no—
100C22×C113—22no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113—42no—
104C22×C113C22×D411yescharacteristic
105C2×D113—41no—
106C2×D113—42no—
107C4×C113—21no—
108C4×C113—22no—
109C4×C113—22no—
110C4×C113—42no—
111C4×C113H(5,𝔽2)12yes—
112Dic113—41no—
113Dic113—41no—
114Dic113—41no—
115C2×C113—41no—
116C2×C113—82no—
117C2×C113#53511yescharacteristic
118C2×C113#57712yes—
119D113—81no—
120#3221—1131nomaximal, Sylow
121C113#322111yescharacteristic, complemented, Sylow
122#540D11311yescharacteristic, complemented
123#536—1131no—
124#496—1131no—
125#492—1131no—
126#491—1131no—
127#488—1131no—
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#127C2×D11311yescharacteristic
142#125C2×D11311yescharacteristic
143#124—1131no—
144#124—1131no—
145#123—22no—
146#123—2262no—
147C22⋊Q8—2262no—
148#121—22no—
149#121C2×D11312yes—
150C4×D4C2×D11312yes—
151#117C2×D11311yescharacteristic
152C4⋊C8—1132no—
153#103—1132no—
154#103—1132no—
155#103—1132no—
156#102—1132no—
157C22⋊C8—1132no—
158#97—1131no—
159C4×C8—1131no—
160#41—4522no—
161C2×Q8—1131no—
162C2×Q8—1131no—
163C2×Q8—1131no—
164C2×Q8—4522no—
165C2×Q8—2261no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—1131no—
169C2×D4—2261no—
170C2×D4C22×D11312yes—
171C22×C4—22no—
172C22×C4—2261no—
173C22×C4—2261no—
174C22×C4C22×D11311yescharacteristic
175SD16—4522no—
176SD16—4522no—
177SD16—4522no—
178D8—4522no—
179C2×C8—1132no—
180C2×C8—1132no—
181C4⋊C4—22no—
182C4⋊C4—2262no—
183C4⋊C4—2262no—
184C4⋊C4C22⋊D11312yes—
185C4⋊C4C22×D11312yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4C22⋊D11312yes—
191C42C22×D11311yescharacteristic
192C42C22×D11311yescharacteristic
193C23—22no—
194C23—2261no—
195C23C2×C22⋊D11311yescharacteristic
196Q8—4522no—
197Q8—2262no—
198Q8—2262no—
199Q8—2262no—
200D4—22no—
201D4—22no—
202D4—82no—
203D4—82no—
204D4—4522no—
205D4—2262no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—4522no—
210C2×C4—4522no—
211C2×C4—2261no—
212C2×C4—2261no—
213C2×C4—2261no—
214C2×C4C2×C22⋊D11312yes—
215C2×C4C2×C22⋊D11312yes—
216C2×C4C2×C22⋊D11311yescharacteristic
217C2×C4C23×D11311yescharacteristic
218C8—2262no—
219C8—2262no—
220C22—22no—
221C22—21no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—4522no—
226C22—4521no—
227C22C22×C22⋊D11311yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—42no—
232C4—4521no—
233C4—4521no—
234C4—4521no—
235C4#1681366812yes—
236C2—41no—
237C2—82no—
238C2—9041no—
239C2#2029916211yescharacteristic
240C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3221
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299174C2semidirect
2. #20298985C2semidirect
3. #20298970C2semidirect
4. #20298968C2semidirect
5. #20298955C2semidirect
6. #20298813C2semidirect
7. #20298803C2semidirect
8. #20298741C2semidirect
9. #20298736C2semidirect
10. #20298659C2semidirect
11. #540×C113C2semidirect
121. C113#3221semidirect
122. #540D113semidirect

Maximal subgroups

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

subgroupindex
#202991742
#202989852
#202989702
#202989682
#202989552
#202988132
#202988032
#202987412
#202987362
#202986592
#540×C1132
#3221113