Finite Group Databasebeta

← #27194362

Subgroups — #27194362

Order 13184.

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

normal subgroups only

This group has 200 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#20268521C211yesmaximal, characteristic
2#20268073C211yesmaximal, characteristic
3#20267998C211yesmaximal, characteristic
4#20267540C211yesmaximal, characteristic
5#20267523C211yesmaximal, characteristic
6#20267523C211yesmaximal, characteristic
7#487×C103C211yesmaximal, characteristic
8C2×#13110095—21no—
9#15693020—21no—
10#15693020—21no—
11#15693019—22no—
12C4×Dic206C2211yescharacteristic
13C4×Dic206C2211yescharacteristic
14#15692986—21no—
15#15692986—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692945—21no—
20#15692944—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23#103×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—22no—
26C2×Dic206D411yescharacteristic
27C2×Dic206D411yescharacteristic
28#13110095—42no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103D411yescharacteristic
32C4⋊Dic103D411yescharacteristic
33Dic103⋊C4—22no—
34Dic103⋊C4—22no—
35Dic103⋊C4—21no—
36Dic103⋊C4—21no—
37C4×Dic103—22no—
38C4×Dic103—21no—
39C4×Dic103—21no—
40C2×Q8×C103—21no—
41C2×Q8×C103D412yes—
42C2×C8×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48Q8×C103—42no—
49Q8×C103—41no—
50Q8×C103—41no—
51C2×C4×C103—22no—
52C2×C4×C103—41no—
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×D411yescharacteristic
55C2×C4×C103C2×D411yescharacteristic
56C2×Dic103—21no—
57C2×Dic103—21no—
58C2×Dic103—21no—
59C2×Dic103—21no—
60Dic206—21no—
61Dic206—21no—
62Dic206—82no—
63Dic206SD1612yes—
64Dic206Q1612yescomplemented
65C8×C103—41no—
66C103⋊C8—41no—
67C103⋊C8—41no—
68C22×C103#12011yescharacteristic
69C4×C103—21no—
70C4×C103—42no—
71C4×C103—81no—
72C4×C103C2×SD1611yescharacteristic
73C4×C103C2×Q1611yescharacteristic
74C4×C103#13711yescharacteristic
75C4×C103#13711yescharacteristic
76Dic103—22no—
77Dic103—22no—
78Dic103—41no—
79Dic103—41no—
80C2×C103#44811yescharacteristic
81C2×C103#45111yescharacteristic
82C2×C103#45511yescharacteristic
83#1645—1031nomaximal, Sylow
84C103#164511yescharacteristic, complemented, Sylow
85Q82—1031no—
86#487D10311yescharacteristic
87#475—1031no—
88#462—1031no—
89#333—1031no—
90Q8⋊C8—1031no—
91Q8⋊C8—1031no—
92C2×Q16—2061no—
93C4⋊Q8—2061no—
94C4⋊Q8—2061no—
95C4⋊Q8—2062no—
96C4⋊Q8C2×D10311yescharacteristic
97C4⋊Q8C2×D10311yescharacteristic
98C4×Q8—1031no—
99C4×Q8—1031no—
100C4×Q8—2061no—
101C4×Q8—2061no—
102#106—2061no—
103C4⋊C8—1031no—
104C4⋊C8—1031no—
105#103—22no—
106#103—2061no—
107#103—2061no—
108C4×C8C2×D10311yescharacteristic
109C2×Q8—21no—
110C2×Q8—1031no—
111C2×Q8—1031no—
112C2×Q8—2062no—
113C2×Q8C22⋊D10312yes—
114Q16—4122no—
115C2×C8—21no—
116C2×C8—2061no—
117C2×C8—2061no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—1031no—
123C4⋊C4—1031no—
124C4⋊C4—2062no—
125C4⋊C4—2062no—
126C4⋊C4—2061no—
127C4⋊C4—2061no—
128C42—2062no—
129C42—2061no—
130C42—2061no—
131C42C22×D10311yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—8242no—
136Q8—1032no—
137Q8—1032no—
138Q8—2061no—
139Q8—2061no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—2061no—
143C2×C4—2061no—
144C2×C4—2061no—
145C2×C4—2061no—
146C2×C4D4×D10311yescharacteristic
147C2×C4D4×D10311yescharacteristic
148C2×C4C2×C22⋊D10311yescharacteristic
149C8—41no—
150C8—4121no—
151C8—4121no—
152C22#1569298911yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—4121no—
157C4—4121no—
158C4—2062no—
159C4—2062no—
160C4SD16×D10311yescharacteristic
161C4Q16×D10311yescharacteristic
162C4#1569305011yescharacteristic
163C4#1569305311yescharacteristic
164C2#2026792811yescharacteristic
165C2#2026794511yescharacteristic
166C2#2026796811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#487×C103C2
socle, prime radicalC22×C103#120
hypercenter#487D103
hypocenterC103#1645
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
64. Dic206Q16semidirect
84. C103#1645semidirect

Maximal subgroups

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

subgroupindex
#202685212
#202680732
#202679982
#202675402
#202675232
#487×C1032
#1645103