Finite Group Databasebeta

← #28389609

Subgroups — #28389609

Order 14464.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#20299175C211yesmaximal, characteristic
2#20298916C211yesmaximal, characteristic, complemented
3#20298536C211yesmaximal, characteristic, complemented
4#20298333C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic, complemented
6#20298323C211yesmaximal, characteristic, complemented
7#481×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9#16813600—21no—
10#16813599—21no—
11#16813596C2211yescharacteristic
12#16813595—21no—
13#16813594—21no—
14#16813594—21no—
15C2×#14268626C2211yescharacteristic
16#16813553—21no—
17#16813542—21no—
18C22⋊#11744751C2211yescharacteristic
19#16813529—21no—
20#16813529—21no—
21#16813529C2211yescharacteristic
22#121×C113C2211yescharacteristic
23C2×C4⋊C4×C113C2211yescharacteristic
24#106×C113—21no—
25#102×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27#14268646—42no—
28#14268646—42no—
29C2×Dic226—21no—
30C2×D452D411yescharacteristic
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C22×Dic113—21no—
35C22×Dic113—21no—
36C22×Dic113D411yescharacteristic
37C22×Dic113D411yescharacteristic
38C2×C4×D113—21no—
39C2×#11744751—21no—
40C4⋊Dic113D411yescharacteristic
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44C22⋊Dic113—21no—
45#14268624—21no—
46#14268624—21no—
47C2×D4×C113—21no—
48C2×D4×C113D411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113—21no—
54C4⋊C4×C113D411yescharacteristic
55C22⋊C4×C113—21no—
56C23×C113—21no—
57C23×C113C2×D411yescharacteristic
58C22×D113—21no—
59D4×C113—41no—
60D4×C113—41no—
61D4×C113—41no—
62C2×C4×C113—21no—
63C2×C4×C113—41no—
64C2×C4×C113—42no—
65C2×C4×C113—41no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C22⋊D113—42no—
69C22⋊D113—41no—
70C22⋊D113—41no—
71C22⋊D113—81no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76C2×Dic113—42no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79C2×Dic113—41no—
80C2×Dic113—41no—
81C2×Dic113SD1612yes—
82D452—41no—
83C4×D113—42no—
84Dic226—42no—
85C8×C113—41no—
86#11744751—41no—
87C22×C113—21no—
88C22×C113—21no—
89C22×C113—41no—
90C22×C113—41no—
91C22×C113—41no—
92C22×C113#12011yescharacteristic
93C22×C113C2×SD1611yescharacteristic
94C22×C113AGL(1,ℤ/8)11yescharacteristic
95C2×D113—41no—
96C2×D113—41no—
97C2×D113—41no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—41no—
101C4×C113—81no—
102Dic113—22no—
103Dic113—41no—
104Dic113—41no—
105Dic113—81no—
106C2×C113—21no—
107C2×C113—21no—
108C2×C113—81no—
109C2×C113#45011yescharacteristic
110C2×C113#45411yescharacteristic
111C2×C113#45811yescharacteristic
112D113—81no—
113#1616—1131nomaximal, Sylow
114C113#161611yescharacteristic, complemented, Sylow
115#537—1131no—
116#481—1131no—
117#481D11311yescharacteristic, complemented
118#400—1131no—
119#327—1131no—
120#327—1131no—
121#324—1131no—
122C2×#41—2261no—
123C22⋊Q8—2261no—
124C22⋊Q8—2261no—
125#121—1131no—
126#121—2261no—
127#121—2261no—
128#121—2261no—
129#121C2×D11311yescharacteristic
130C2×C4⋊C4—1131no—
131C2×C4⋊C4C2×D11311yescharacteristic
132#106—21no—
133#106—2261no—
134#102—21no—
135#102—2261no—
136C22⋊C8—1131no—
137C22⋊C8C2×D11311yescharacteristic
138#95—1131no—
139#95—2261no—
140#95—2261no—
141#41—4522no—
142#41—4522no—
143C2×Q8—2261no—
144C2×D4—21no—
145C2×D4—1131no—
146C2×D4—2261no—
147C2×D4—2261no—
148C2×D4—2261no—
149C2×D4C22⋊D11311yescharacteristic
150C22×C4—21no—
151C22×C4—1131no—
152C22×C4—1131no—
153C22×C4—2261no—
154C22×C4—2261no—
155C22×C4—2261no—
156C22×C4C22×D11311yescharacteristic
157C2×C8—21no—
158C2×C8—2261no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1131no—
162C4⋊C4—2261no—
163C4⋊C4—2261no—
164C4⋊C4—2261no—
165C4⋊C4C22⋊D11311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C22⋊C4—2261no—
170C23—21no—
171C23—2261no—
172C23D4×D11311yescharacteristic
173Q8—4522no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—9041no—
178D4—4521no—
179D4—4521no—
180D4—4521no—
181D4—4522no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—1132no—
187C2×C4—4522no—
188C2×C4—4521no—
189C2×C4—4521no—
190C2×C4—4521no—
191C2×C4—4522no—
192C2×C4—4521no—
193C2×C4—2261no—
194C2×C4—2261no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4D4×D11311yescharacteristic
198C2×C4C2×C22⋊D11311yescharacteristic
199C8—41no—
200C8—4521no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—4521no—
207C22—4521no—
208C22—4521no—
209C22#1681359011yescharacteristic
210C22SD16×D11311yescharacteristic
211C22#1681364911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—9041no—
217C4—4521no—
218C4—4521no—
219C4—2262no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—9041no—
224C2#2029874711yescharacteristic
225C2#2029876911yescharacteristic
226C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#481×C113C2
socleC22×C113#120
prime radical#20299175C2
hypercenter#481D113
hypocenterC113#1616
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #20298916C2semidirect
3. #20298536C2semidirect
4. #20298333C2semidirect
5. #20298332C2semidirect
6. #20298323C2semidirect
7. #481×C113C2semidirect
114. C113#1616semidirect
117. #481D113semidirect

Maximal subgroups

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

subgroupindex
#202991752
#202989162
#202985362
#202983332
#202983322
#202983232
#481×C1132
#1616113