Finite Group Databasebeta

← #27197128

Subgroups — #27197128

Order 13184.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#20267977C212yesmaximal, complemented
2#20267958C211yesmaximal, characteristic, complemented
3#20267584C211yesmaximal, characteristic, complemented
4#20267578C212yesmaximal, complemented
5D42×C103C211yesmaximal, characteristic, complemented
6#15693066C2211yescharacteristic, complemented
7#15693047—21no—
8#15692990—22no—
9#15692949—21no—
10#15692938C2211yescharacteristic, complemented
11#15692936C2212yescomplemented
12#15692935—22no—
13C22×D4×C103—22no—
14#127×C103C2211yescharacteristic
15#121×C103—22no—
16#120×C103—21no—
17#120×C103C2212yes—
18C4×D4×C103—21no—
19#13110105—21no—
20#13110104—41no—
21C2×C22⋊D103—22no—
22C2×C22⋊D103—42no—
23D4×D103—41no—
24#13110093—41no—
25#13110090—41no—
26#13110089—21no—
27C22⋊Dic103—22no—
28C22⋊Dic103—42no—
29C24×C103—21no—
30C24×C103D412yescomplemented
31C2×D4×C103—21no—
32C2×D4×C103—22no—
33C2×D4×C103—22no—
34C2×D4×C103—22no—
35C2×D4×C103—48no—
36C2×D4×C103D411yescharacteristic, complemented
37C2×D4×C103C2311yescharacteristic
38C22×C4×C103—22no—
39C4⋊C4×C103—21no—
40C22⋊C4×C103—21no—
41C22⋊C4×C103—22no—
42C22⋊C4×C103D412yescomplemented
43C42×C103D411yescharacteristic, complemented
44C23×C103—22no—
45C23×C103—21no—
46C23×C103—44no—
47C23×C103—42no—
48C23×C103—44no—
49C23×C103—81no—
50C23×C103C2×D412yes—
51C22×D103—22no—
52D4×C103—24no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—44no—
56D4×C103—44no—
57D4×C103—44no—
58C2×C4×C103—21no—
59C2×C4×C103—22no—
60C2×C4×C103—44no—
61C2×C4×C103C2×D411yescharacteristic
62C22⋊D103—42no—
63C22⋊D103—41no—
64C22⋊D103—84no—
65C2×Dic103—22no—
66C2×Dic103—42no—
67D412—21no—
68C4×D103—41no—
69Dic206—21no—
70C103⋊C8—41no—
71C22×C103—24no—
72C22×C103—22no—
73C22×C103—42no—
74C22×C103—42no—
75C22×C103—42no—
76C22×C103—44no—
77C22×C103—42no—
78C22×C103—41no—
79C22×C103—82no—
80C22×C103—84no—
81C22×C103#12011yescharacteristic
82C2×D103—41no—
83C2×D103—82no—
84C4×C103—22no—
85C4×C103—21no—
86C4×C103—42no—
87Dic103—41no—
88Dic103—82no—
89C2×C103—21no—
90C2×C103—42no—
91C2×C103—44no—
92C2×C103—81no—
93C2×C103B(4,𝔽2)11yescharacteristic
94D103—81no—
95#2196—1031nomaximal, Sylow
96C103#219611yescharacteristic, complemented, Sylow
97D42D10311yescharacteristic, complemented
98B(4,𝔽2)—1032no—
99#453—1031no—
100#353—1031no—
101AΣL(1,𝔽16)—1032no—
102H(5,𝔽2)—1031no—
103C22×D4—22no—
104AGL(1,ℤ/8)—2061no—
105#127C2×D10311yescharacteristic
106#121—22no—
107#120—21no—
108#120—2062no—
109#120C2×D10312yes—
110C4×D4—21no—
111#104—2061no—
112#100—1031no—
113#99—1032no—
114#99—2062no—
115C24—21no—
116C24C22⋊D10312yescomplemented
117#41—4121no—
118#41—2061no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—4121no—
125C2×D4—4122no—
126C2×D4—2062no—
127C2×D4C22⋊D10311yescharacteristic, complemented
128C2×D4C22×D10311yescharacteristic
129C22×C4—22no—
130SD16—4121no—
131D8—4121no—
132M16—2061no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—4122no—
137C22⋊C4—2062no—
138C22⋊C4C22⋊D10312yescomplemented
139C42C22⋊D10311yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—2062no—
147C23C2×C22⋊D10312yes—
148Q8—2061no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—8244no—
156D4—4122no—
157D4—4121no—
158D4—2061no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—4121no—
163C2×C4—4122no—
164C2×C4—2062no—
165C2×C4C2×C22⋊D10311yescharacteristic
166C8—4121no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—8242no—
178C22—4121no—
179C22#1569299011yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—8242no—
184C4—4121no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—8241no—
190C2#2026797811yescharacteristic
subgroupG/H
centerC2#20267978
commutator, cosocleC2×D4×C103C23
FrattiniC2×D4C22×D103
FittingD42×C103C2
socleC2×C103B(4,𝔽2)
hypercenterD42D103
hypocenterC103#2196
LCSG ▷ C2×D4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20267977C2semidirect
2. #20267958C2semidirect
3. #20267584C2semidirect
4. #20267578C2semidirect
5. D42×C103C2semidirect
6. #15693066C22semidirect
10. #15692938C22semidirect
11. #15692936C22semidirect
30. C24×C103D4semidirect
36. C2×D4×C103D4semidirect
42. C22⋊C4×C103D4semidirect
43. C42×C103D4semidirect
96. C103#2196semidirect
97. D42D103semidirect
116. C24C22⋊D103semidirect
127. C2×D4C22⋊D103semidirect
138. C22⋊C4C22⋊D103semidirect
139. C42C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202679772
#202679582
#202675842
#202675782
D42×C1032
#2196103