Finite Group Databasebeta

← #28392526

Subgroups — #28392526

Order 14464.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#20299395C211yesmaximal, characteristic
2#20299041C211yesmaximal, characteristic, complemented
3#20299038C211yesmaximal, characteristic, complemented
4#20298857C211yesmaximal, characteristic, complemented
5#20298407C211yesmaximal, characteristic, complemented
6#20298379C211yesmaximal, characteristic, complemented
7#360×C113C211yesmaximal, characteristic, complemented
8#41×D113—21no—
9#16813654—21no—
10#16813651—21no—
11#16813649—21no—
12#16813646—21no—
13#16813644C2211yescharacteristic
14#16813642—21no—
15C2×Dic452C2211yescharacteristic, complemented
16C2×#14268630C2211yescharacteristic
17#16813602—21no—
18Dic904—21no—
19#16813568—21no—
20#16813567—21no—
21#16813566—21no—
22#16813562C2211yescharacteristic, complemented
23#16813545—21no—
24#135×C113C2211yescharacteristic
25M32×C113C2211yescharacteristic, complemented
26#106×C113C2211yescharacteristic, complemented
27#14268648—21no—
28#14268647—21no—
29#14268647—41no—
30#14268646—21no—
31#14268646—41no—
32C2×Dic226—21no—
33Q8×D113—21no—
34D4×D113—21no—
35D4×D113—41no—
36C2×C4×D113—41no—
37C2×C4×D113D411yescharacteristic
38Dic452—21no—
39Dic452—21no—
40Dic452D411yescharacteristic
41#14268637—21no—
42#14268636—21no—
43#14268635—21no—
44#14268634—21no—
45D904D411yescharacteristic
46#14268632—21no—
47#14268630—21no—
48#14268630—21no—
49C2×#11744751D411yescharacteristic
50C4⋊Dic113—41no—
51#14268624—41no—
52#14268622—21no—
53#41×C113—21no—
54Q16×C113D411yescharacteristic
55SD16×C113—21no—
56D8×C113D411yescharacteristic
57C2×C8×C113C2311yescharacteristic
58C4⋊C4×C113—21no—
59C16×C113—21no—
60C22×D113—41no—
61C22×D113D811yescharacteristic
62Q8×C113—21no—
63D4×C113—21no—
64D4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113C2×D411yescharacteristic
68C22⋊D113—41no—
69C22⋊D113—41no—
70C22⋊D113—41no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73C2×Dic113D811yescharacteristic
74D452—21no—
75D452—41no—
76C4×D113—21no—
77C4×D113—21no—
78C4×D113—41no—
79C4×D113—41no—
80C4×D113—41no—
81Dic226—21no—
82Dic226—41no—
83Dic226—41no—
84Dic226—41no—
85C8×C113C2×D411yescharacteristic
86C8×C113C2×D411yescharacteristic
87#11744751—21no—
88C22×C113—41no—
89C22×C113C2×D811yescharacteristic
90C2×D113—21no—
91C2×D113—41no—
92C2×D113—41no—
93C2×D113—82no—
94C4×C113—41no—
95C4×C113—81no—
96C4×C113#12011yescharacteristic
97C4×C113AGL(1,ℤ/8)11yescharacteristic
98Dic113—21no—
99Dic113—41no—
100Dic113—81no—
101C2×C113—21no—
102C2×C113—81no—
103C2×C113#44711yescharacteristic
104D113—41no—
105D113—81no—
106#2191—1131nomaximal, Sylow
107C113#219111yescharacteristic, complemented, Sylow
108#575—1131no—
109#510—1131no—
110#510—1131no—
111#470—1131no—
112#360—1131no—
113#360D11311yescharacteristic, complemented
114#349—1131no—
115C2×#41—2261no—
116#137—2261no—
117#137—2261no—
118AGL(1,ℤ/8)—2261no—
119AGL(1,ℤ/8)—2261no—
120#135—1131no—
121#135—2261no—
122#135C2×D11311yescharacteristic
123C2×Q16—1131no—
124C2×M16—1131no—
125C22⋊Q8—2261no—
126Q32—2261no—
127Q32—2261no—
128SD32—2261no—
129SD32—2261no—
130M32—1131no—
131M32C2×D11311yescharacteristic, complemented
132#106C2×D11311yescharacteristic, complemented
133#103—2261no—
134#41—21no—
135#41—4521no—
136#41—4521no—
137#41—2261no—
138#41—2261no—
139#41—2261no—
140C2×Q8—2261no—
141C2×Q8—2261no—
142C2×D4—4521no—
143C2×D4—2261no—
144C22×C4—1131no—
145C22×C4—4521no—
146Q16—1131no—
147Q16—2261no—
148Q16—2261no—
149Q16—2261no—
150Q16D45211yescharacteristic
151SD16—21no—
152SD16—2261no—
153SD16—2261no—
154SD16—2261no—
155D8—1131no—
156D8—2261no—
157D8D45211yescharacteristic
158M16—2261no—
159M16—2261no—
160C2×C8—1131no—
161C2×C8C22×D11311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—4521no—
164C22⋊C4—4521no—
165C16—21no—
166C16—2261no—
167C23—1131no—
168C23—4521no—
169Q8—21no—
170Q8—4521no—
171Q8—4521no—
172Q8—4521no—
173Q8—2261no—
174D4—21no—
175D4—41no—
176D4—4521no—
177D4—4521no—
178D4—4521no—
179D4—4521no—
180D4—2261no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—1131no—
184C2×C4—4521no—
185C2×C4—4521no—
186C2×C4—4521no—
187C2×C4—4521no—
188C2×C4—4521no—
189C2×C4—2261no—
190C2×C4—2261no—
191C2×C4D4×D11311yescharacteristic
192C8—2261no—
193C8D4×D11311yescharacteristic
194C8C2×D45211yescharacteristic
195C22—41no—
196C22—9042no—
197C22—4521no—
198C22—4521no—
199C22—2261no—
200C22D8×D11311yescharacteristic
201C4—41no—
202C4—81no—
203C4—9041no—
204C4—4521no—
205C4—2261no—
206C4#1681359211yescharacteristic
207C4#1681364911yescharacteristic
208C2—21no—
209C2—81no—
210C2—9041no—
211C2—4521no—
212C2#2029873311yescharacteristic
subgroupG/H
centerC2#20298733
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
Fitting#360×C113C2
socleC2×C113#447
prime radical#20299395C2
hypercenter#360D113
hypocenterC113#2191
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #20299041C2semidirect
3. #20299038C2semidirect
4. #20298857C2semidirect
5. #20298407C2semidirect
6. #20298379C2semidirect
7. #360×C113C2semidirect
15. C2×Dic452C22semidirect
22. #16813562C22semidirect
25. M32×C113C22semidirect
26. #106×C113C22semidirect
107. C113#2191semidirect
113. #360D113semidirect
131. M32C2×D113semidirect
132. #106C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993952
#202990412
#202990382
#202988572
#202984072
#202983792
#360×C1132
#2191113