Finite Group Databasebeta

← #27193790

Subgroups — #27193790

Order 13184.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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#20268339C211yesmaximal, characteristic
2#20267843C211yesmaximal, characteristic, complemented
3C4⋊C8×D103C211yesmaximal, characteristic, complemented
4#20267538C211yesmaximal, characteristic, complemented
5#20267536C211yesmaximal, characteristic, complemented
6#20267535C211yesmaximal, characteristic, complemented
7#331×C103C211yesmaximal, characteristic, complemented
8C2×#13110104—21no—
9C2×C8×D103—21no—
10#15693021C2211yescharacteristic
11#15693008—21no—
12#15692992—21no—
13#15692992C412yes—
14D4×Dic103—21no—
15D4×Dic103C412yes—
16C42×D103C2211yescharacteristic
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19Dic103⋊C8—21no—
20(C2×D103)⋊C8—21no—
21C8×Dic103—21no—
22#127×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4⋊C8×C103C2211yescharacteristic
25#13110104—42no—
26#13110104—42no—
27C2×Dic206—21no—
28C2×C22⋊D103—22no—
29C22×Dic103—22no—
30C2×C4×D103C2×C411yescharacteristic
31C2×C4×D103D411yescharacteristic
32C2×C4×D103D411yescharacteristic
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C8×D103—42no—
36C4⋊Dic103—21no—
37C4⋊Dic103C2×C412yes—
38C22⋊Dic103—22no—
39C22⋊Dic103—22no—
40C4×Dic103C2×C411yescharacteristic
41C4×Dic103D411yescharacteristic
42C4×Dic103D411yescharacteristic
43C2×D4×C103—21no—
44C2×D4×C103—21no—
45C2×D4×C103C2×C412yes—
46C2×C8×C103—21no—
47C2×C8×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—22no—
50C22×D103C22⋊C411yescharacteristic
51D4×C103—42no—
52D4×C103—41no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—41no—
56C2×C4×C103C22×C411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C22⋊D103—44no—
60C2×Dic103—22no—
61C2×Dic103—44no—
62C2×Dic103C22⋊C411yescharacteristic
63C2×Dic103C22⋊C411yescharacteristic
64C2×Dic103C22⋊C411yescharacteristic
65C4×D103—21no—
66C4×D103—21no—
67C4×D103—41no—
68C4×D103D812yes—
69C4×D103SD1612yes—
70Dic206—41no—
71Dic206—41no—
72C8×C103—41no—
73C8×C103—41no—
74C103⋊C8—41no—
75C103⋊C8—41no—
76C22×C103—42no—
77C22×C103—42no—
78C22×C103—42no—
79C22×C103C2×C22⋊C411yescharacteristic
80C2×D103—21no—
81C2×D103—21no—
82C2×D103#10212yes—
83C4×C103—21no—
84C4×C103C2×D811yescharacteristic
85C4×C103C2×SD1611yescharacteristic
86C4×C103#13511yescharacteristic
87C4×C103#13511yescharacteristic
88Dic103—21no—
89Dic103—21no—
90Dic103—42no—
91Dic103#10212yes—
92C2×C103—82no—
93C2×C103#41311yescharacteristic
94C2×C103C2×#10211yescharacteristic
95C2×C103#41611yescharacteristic
96D103—22no—
97#1540—1031nomaximal, Sylow
98C103#154011yescharacteristic, complemented, Sylow
99#532—1031no—
100#431—1031no—
101C2×C4⋊C8—1031no—
102#332—1031no—
103#332—1031no—
104#331—1031no—
105#331D10311yescharacteristic, complemented
106C2×#41—2061no—
107C22×C8—2061no—
108C4⋊Q8—1031no—
109#127C2×D10311yescharacteristic
110#124—2061no—
111#121—1032no—
112#121—2061no—
113C4×D4—1032no—
114C4×D4—2061no—
115C2×C42—1031no—
116C4⋊C8—1031no—
117C4⋊C8—1031no—
118C4⋊C8—2061no—
119C4⋊C8C2×D10311yescharacteristic
120C4⋊C8C2×D10311yescharacteristic
121C22⋊C8—2061no—
122C4×C8—2061no—
123#41—4122no—
124#41—4122no—
125C2×Q8—2061no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—2062no—
129C2×D4C4×D10312yes—
130C22×C4—1031no—
131C22×C4—1031no—
132C22×C4—1031no—
133C22×C4—2062no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—4122no—
137C2×C8—2061no—
138C2×C8—2061no—
139C4⋊C4—1032no—
140C4⋊C4—2061no—
141C22⋊C4—2062no—
142C22⋊C4—2062no—
143C42—1031no—
144C42—1031no—
145C42—1031no—
146C42C22×D10311yescharacteristic
147C23—22no—
148C23—1031no—
149Q8—4121no—
150Q8—4121no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—4124no—
157C2×C4—1031no—
158C2×C4—1032no—
159C2×C4—1032no—
160C2×C4—1031no—
161C2×C4—1031no—
162C2×C4—4121no—
163C2×C4—4124no—
164C2×C4—2062no—
165C2×C4—2061no—
166C2×C4—2061no—
167C2×C4C2×C4×D10311yescharacteristic
168C2×C4D4×D10311yescharacteristic
169C2×C4D4×D10311yescharacteristic
170C8—41no—
171C8—41no—
172C8—4121no—
173C8—4121no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—1032no—
178C22—2061no—
179C22—2061no—
180C22C22⋊C4×D10311yescharacteristic
181C4—21no—
182C4—1032no—
183C4—4122no—
184C4—2061no—
185C4—2061no—
186C4D8×D10311yescharacteristic
187C4SD16×D10311yescharacteristic
188C4#1569304011yescharacteristic
189C4#1569304211yescharacteristic
190C2—82no—
191C2—2062no—
192C2#2026777211yescharacteristic
193C2#102×D10311yescharacteristic
194C2#2026778411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#331×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268339C2
cosocleC42×C103C23
hypercenter#331D103
hypocenterC103#1540
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20267843C2semidirect
3. C4⋊C8×D103C2semidirect
4. #20267538C2semidirect
5. #20267536C2semidirect
6. #20267535C2semidirect
7. #331×C103C2semidirect
98. C103#1540semidirect
105. #331D103semidirect

Maximal subgroups

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

subgroupindex
#202683392
#202678432
C4⋊C8×D1032
#202675382
#202675362
#202675352
#331×C1032
#1540103