Finite Group Databasebeta

← #27194327

Subgroups — #27194327

Order 13184.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268527C211yesmaximal, characteristic
2#20268073C211yesmaximal, characteristic, complemented
3#20267998C211yesmaximal, characteristic, complemented
4#20267535C211yesmaximal, characteristic
5#20267523C211yesmaximal, characteristic, complemented
6#20267523C211yesmaximal, characteristic, complemented
7#486×C103C211yesmaximal, characteristic
8C2×#13110095—21no—
9#15693008—21no—
10#15693008—21no—
11#15693002—22no—
12C4×Dic206C2211yescharacteristic
13C4×Dic206C2211yescharacteristic
14D4×Dic103—21no—
15D4×Dic103—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692945—21no—
20#15692944—21no—
21C4⋊Q8×C103C2211yescharacteristic
22#127×C103C2211yescharacteristic
23#102×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206D411yescharacteristic
26C2×Dic206D411yescharacteristic
27C22×Dic103—22no—
28#13110095—42no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103D411yescharacteristic
32C4⋊Dic103D411yescharacteristic
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35C22⋊Dic103—22no—
36C22⋊Dic103—22no—
37C22⋊Dic103—22no—
38C4×Dic103—21no—
39C4×Dic103—21no—
40C2×Q8×C103—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103D412yes—
44C2×C8×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—22no—
49Q8×C103—41no—
50Q8×C103—41no—
51D4×C103—42no—
52D4×C103—41no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—82no—
65Dic206—21no—
66Dic206—21no—
67Dic206—21no—
68Dic206—21no—
69C8×C103—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—42no—
73C22×C103—42no—
74C22×C103—42no—
75C22×C103#12011yescharacteristic
76C4×C103—21no—
77C4×C103—81no—
78C4×C103#13511yescharacteristic
79C4×C103#13511yescharacteristic
80C4×C103AGL(1,ℤ/8)11yescharacteristic
81C4×C103#13711yescharacteristic
82Dic103—41no—
83Dic103—41no—
84Dic103—41no—
85Dic103—41no—
86C2×C103—82no—
87C2×C103#44911yescharacteristic
88C2×C103#45211yescharacteristic
89C2×C103#45511yescharacteristic
90#1640—1031nomaximal, Sylow
91C103#164011yescharacteristic, complemented, Sylow
92#559—1031no—
93#486D10311yescharacteristic
94#475—1031no—
95#462—1031no—
96#331—1031no—
97Q8⋊C8—1031no—
98Q8⋊C8—1031no—
99C2×Q16—2061no—
100C4⋊Q8C2×D10311yescharacteristic
101#127C2×D10311yescharacteristic
102#124—2061no—
103#124—2061no—
104#123—2062no—
105C4×Q8—1031no—
106C4×Q8—1031no—
107C4×D4—2061no—
108C4×D4—2061no—
109#106—2061no—
110C4⋊C8—1031no—
111C4⋊C8—1031no—
112#103—2061no—
113#103—2061no—
114#102—22no—
115C4×C8C2×D10311yescharacteristic
116C2×Q8—21no—
117C2×Q8—1031no—
118C2×Q8—1031no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D10312yes—
122C22×C4—2062no—
123Q16—4122no—
124C2×C8—21no—
125C2×C8—2061no—
126C2×C8—2061no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1031no—
130C4⋊C4—1031no—
131C4⋊C4—2061no—
132C4⋊C4—2061no—
133C22⋊C4—2062no—
134C22⋊C4—2062no—
135C22⋊C4—2062no—
136C42—2061no—
137C42—2061no—
138C42C22×D10311yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—2061no—
143Q8—2061no—
144Q8—2061no—
145Q8—2061no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—8242no—
153C2×C4—2061no—
154C2×C4—2061no—
155C2×C4—2061no—
156C2×C4—2061no—
157C2×C4D4×D10311yescharacteristic
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C8—41no—
161C8—4121no—
162C8—4121no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1569298911yescharacteristic
167C4—21no—
168C4—81no—
169C4—4121no—
170C4—4121no—
171C4—4121no—
172C4—4121no—
173C4#1569304011yescharacteristic
174C4#1569304211yescharacteristic
175C4#1569304511yescharacteristic
176C4#1569305011yescharacteristic
177C2—82no—
178C2#2026793311yescharacteristic
179C2#2026795011yescharacteristic
180C2#2026796811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#486×C103C2
socleC22×C103#120
prime radical#127×C103C22
hypercenter#486D103
hypocenterC103#1640
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #20268073C2semidirect
3. #20267998C2semidirect
5. #20267523C2semidirect
6. #20267523C2semidirect
91. C103#1640semidirect

Maximal subgroups

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

subgroupindex
#202685272
#202680732
#202679982
#202675352
#202675232
#486×C1032
#1640103