Finite Group Databasebeta

← #28389568

Subgroups — #28389568

Order 14464.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#20299193C211yesmaximal, characteristic
2#20298928C211yesmaximal, characteristic, complemented
3#20298529C211yesmaximal, characteristic, complemented
4#20298336C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic
6#20298323C211yesmaximal, characteristic, complemented
7#480×C113C211yesmaximal, characteristic
8#16813615—21no—
9#16813612—21no—
10#16813603—21no—
11#16813603—21no—
12#16813601C2211yescharacteristic
13#16813599—21no—
14D4×Dic113—21no—
15C2×#14268626—21no—
16C2×#14268626C2211yescharacteristic
17#16813553—21no—
18#16813545—21no—
19C22⋊#11744751C2211yescharacteristic
20#16813529—21no—
21#16813529C2211yescharacteristic
22#121×C113C2211yescharacteristic
23C2×C4⋊C4×C113C2211yescharacteristic
24#107×C113—21no—
25#102×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27C2×Dic226D411yescharacteristic
28C22×Dic113—21no—
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—42no—
41C22⋊Dic113—21no—
42C22⋊Dic113—21no—
43C22⋊Dic113—21no—
44C22⋊Dic113—21no—
45C4×Dic113—21no—
46C2×D4×C113—21no—
47C2×D4×C113D411yescharacteristic
48C22×C4×C113—21no—
49C22×C4×C113C2311yescharacteristic
50C2×C8×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113D411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113—21no—
56C23×C113C2×D411yescharacteristic
57D4×C113—41no—
58D4×C113—41no—
59D4×C113—41no—
60C2×C4×C113—21no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113C2×D411yescharacteristic
66C2×C4×C113C2×D411yescharacteristic
67C2×Dic113—22no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113—81no—
78Dic226—41no—
79C8×C113—41no—
80#11744751—41no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113—41no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113#12011yescharacteristic
87C22×C113#13511yescharacteristic
88C22×C113AGL(1,ℤ/8)11yescharacteristic
89C4×C113—21no—
90C4×C113—21no—
91C4×C113—41no—
92C4×C113—81no—
93Dic113—42no—
94Dic113—41no—
95Dic113—41no—
96Dic113—41no—
97Dic113—41no—
98C2×C113—21no—
99C2×C113—21no—
100C2×C113—81no—
101C2×C113#44911yescharacteristic
102C2×C113#45611yescharacteristic
103C2×C113#45811yescharacteristic
104#1609—1131nomaximal, Sylow
105C113#160911yescharacteristic, complemented, Sylow
106#539—1131no—
107#483—1131no—
108#480D11311yescharacteristic
109#398—1131no—
110#328—1131no—
111#327—1131no—
112#324—1131no—
113#126—2261no—
114#125—2261no—
115#123—2261no—
116#123—2261no—
117C22⋊Q8—1131no—
118C22⋊Q8—2261no—
119#121C2×D11311yescharacteristic
120C4×D4—2261no—
121C2×C4⋊C4—1131no—
122C2×C4⋊C4—2261no—
123C2×C4⋊C4C2×D11311yescharacteristic
124#107—21no—
125#106—2261no—
126#103—2261no—
127#102—21no—
128C22⋊C8—1131no—
129C22⋊C8C2×D11311yescharacteristic
130#95—1131no—
131#95—2261no—
132C2×Q8—1131no—
133C2×D4—21no—
134C2×D4C22⋊D11311yescharacteristic
135C22×C4—21no—
136C22×C4—1131no—
137C22×C4—1131no—
138C22×C4—2261no—
139C22×C4—2261no—
140C22×C4C22×D11311yescharacteristic
141C2×C8—21no—
142C2×C8—2261no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1131no—
146C4⋊C4—4522no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4—2261no—
151C4⋊C4—2261no—
152C4⋊C4—2261no—
153C4⋊C4C22⋊D11311yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—2261no—
156C22⋊C4—2261no—
157C22⋊C4—2261no—
158C22⋊C4—2261no—
159C42—2261no—
160C23—21no—
161C23D4×D11311yescharacteristic
162Q8—4521no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—9041no—
172C2×C4—4521no—
173C2×C4—4521no—
174C2×C4—4521no—
175C2×C4—2262no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4—2261no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4D4×D11311yescharacteristic
183C2×C4C2×C22⋊D11311yescharacteristic
184C8—41no—
185C8—4521no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1681359011yescharacteristic
192C22#1681364111yescharacteristic
193C22#1681364611yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—81no—
198C4—4522no—
199C4—4521no—
200C4—4521no—
201C4—4521no—
202C4—4521no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2029874011yescharacteristic
207C2#2029877911yescharacteristic
208C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#480×C113C2
socleC22×C113#120
prime radical#121×C113C22
hypercenter#480D113
hypocenterC113#1609
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20298928C2semidirect
3. #20298529C2semidirect
4. #20298336C2semidirect
6. #20298323C2semidirect
105. C113#1609semidirect

Maximal subgroups

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

subgroupindex
#202991932
#202989282
#202985292
#202983362
#202983322
#202983232
#480×C1132
#1609113