Finite Group Databasebeta

← #27194096

Subgroups — #27194096

Order 13184.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#20267929C212yesmaximal, complemented
2#20267703C211yesmaximal, characteristic, complemented
3#20267525C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic, complemented
5#534×C103C211yesmaximal, characteristic
6C22×Dic206C2211yescharacteristic, complemented
7C2×#13110093—22no—
8C2×C22⋊Dic103—21no—
9#15692944—22no—
10C22⋊(C103⋊C8)C2212yescomplemented
11C103⋊#95—21no—
12C103⋊#95C2211yescharacteristic, complemented
13C22×D4×C103—21no—
14#123×C103—22no—
15#121×C103—21no—
16#121×C103C2212yes—
17#120×C103—22no—
18C2×C22⋊C4×C103C2211yescharacteristic
19C2×Dic206—22no—
20C2×Dic206—42no—
21C22×Dic103—21no—
22C22×Dic103—21no—
23#13110093—44no—
24C2×C103⋊C8—22no—
25C22⋊Dic103—42no—
26C24×C103—21no—
27C24×C103D411yescharacteristic
28C2×D4×C103—22no—
29C2×D4×C103—22no—
30C2×D4×C103—21no—
31C2×D4×C103—42no—
32C2×D4×C103—42no—
33C2×D4×C103D412yes—
34C22×C4×C103—21no—
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C4⋊C4×C103—21no—
38C4⋊C4×C103D412yes—
39C22⋊C4×C103—22no—
40C22⋊C4×C103—22no—
41C22⋊C4×C103—22no—
42C23×C103—21no—
43C23×C103—21no—
44C23×C103—22no—
45C23×C103—41no—
46C23×C103—41no—
47C23×C103—42no—
48C23×C103—81no—
49C23×C103—81no—
50C23×C103SD1612yescomplemented
51C23×C103C2×D411yescharacteristic
52D4×C103—42no—
53D4×C103—44no—
54D4×C103—42no—
55D4×C103—42no—
56D4×C103—81no—
57C2×C4×C103—21no—
58C2×C4×C103—22no—
59C2×C4×C103—41no—
60C2×C4×C103—42no—
61C2×C4×C103—41no—
62C2×C4×C103C2×D412yes—
63C2×Dic103—22no—
64C2×Dic103—41no—
65C2×Dic103—41no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C2×Dic103—41no—
69Dic206—24no—
70Dic206—42no—
71C103⋊C8—42no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103—22no—
75C22×C103—42no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103—42no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103—81no—
82C22×C103—84no—
83C22×C103#12011yescharacteristic
84C22×C103C2×SD1611yescharacteristic
85C22×C103AGL(1,ℤ/8)11yescharacteristic
86C4×C103—22no—
87C4×C103—42no—
88C4×C103—41no—
89Dic103—42no—
90Dic103—81no—
91C2×C103—21no—
92C2×C103—21no—
93C2×C103—42no—
94C2×C103—82no—
95C2×C103#45011yescharacteristic
96C2×C103#45511yescharacteristic
97C2×C103B(4,𝔽2)11yescharacteristic
98#1601—1031nomaximal, Sylow
99C103#160111yescharacteristic, complemented, Sylow
100#534D10311yescharacteristic
101#448—1032no—
102#393—1031no—
103#327—1032no—
104#323—1031no—
105C22×Q8—1031no—
106C22×D4—21no—
107C2×SD16—2062no—
108#123—22no—
109#121—21no—
110#121C2×D10312yes—
111#120—22no—
112C2×C22⋊C4—2061no—
113C2×C22⋊C4C2×D10311yescharacteristic
114#103—2062no—
115C22⋊C8—1032no—
116#95—1031no—
117#95—2061no—
118C24—21no—
119C24C22⋊D10311yescharacteristic
120C2×Q8—4122no—
121C2×Q8—2062no—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4C22⋊D10312yes—
128C22×C4—21no—
129C22×C4—2061no—
130C22×C4—2061no—
131C22×C4C22⋊D10311yescharacteristic
132C22×C4C22×D10311yescharacteristic
133SD16—4124no—
134C2×C8—2062no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D10312yes—
137C22⋊C4—22no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—4122no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—41no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23#1311009312yescomplemented
150C23C2×C22⋊D10311yescharacteristic
151Q8—4122no—
152Q8—2064no—
153D4—42no—
154D4—44no—
155D4—42no—
156D4—42no—
157D4—81no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—4121no—
164C2×C4—4121no—
165C2×C4—4121no—
166C2×C4—4121no—
167C2×C4—4121no—
168C2×C4—2062no—
169C2×C4C2×C22⋊D10312yes—
170C8—4122no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—81no—
181C22—84no—
182C22#1569299011yescharacteristic
183C22C2×#1311009311yescharacteristic
184C22#1569304711yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—8241no—
189C4—4122no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—82no—
194C2#2026794211yescharacteristic
195C2#2026796911yescharacteristic
196C2#2026797811yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting, prime radical#534×C103C2
socleC22×C103#120
hypercenter#534D103
hypocenterC103#1601
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #20267929C2semidirect
2. #20267703C2semidirect
3. #20267525C2semidirect
4. #20267515C2semidirect
6. C22×Dic206C22semidirect
10. C22⋊(C103⋊C8)C22semidirect
12. C103⋊#95C22semidirect
50. C23×C103SD16semidirect
99. C103#1601semidirect
149. C23#13110093semidirect

Maximal subgroups

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

subgroupindex
#202679292
#202677032
#202675252
#202675152
#534×C1032
#1601103