Finite Group Databasebeta

← #27194368

Subgroups — #27194368

Order 13184.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic206C211yesmaximal, characteristic
2#20268142C211yesmaximal, characteristic
3#20268076C211yesmaximal, characteristic
4#20268002C211yesmaximal, characteristic
5#20267539C211yesmaximal, characteristic
6#20267523C211yesmaximal, characteristic
7Q8⋊C8×C103C211yesmaximal, characteristic
8C2×Dic412—21no—
9#15693021—21no—
10#15693021C2211yescharacteristic
11#15693021C2211yescharacteristic
12#15693020—22no—
13#15693020—21no—
14Q8×Dic103—21no—
15C4×Dic206—21no—
16C4×Dic206C2211yescharacteristic
17#15692952—21no—
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692946—22no—
20#15692946—21no—
21#15692945—21no—
22C4×Q8×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—21no—
26C2×Dic206—22no—
27C2×Dic206D411yescharacteristic
28C2×Dic206D412yes—
29Dic412—42no—
30C2×C103⋊C8—21no—
31C4⋊Dic103—22no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103D411yescharacteristic
37Dic103⋊C4—22no—
38Dic103⋊C4—21no—
39C4×Dic103—22no—
40C4×Dic103—21no—
41C2×Q8×C103D411yescharacteristic
42C2×C8×C103—21no—
43C2×C8×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C42×C103—21no—
47C42×C103C2311yescharacteristic
48Q8×C103—21no—
49Q8×C103Q1612yescomplemented
50C2×C4×C103—21no—
51C2×C4×C103—21no—
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×D411yescharacteristic
55C2×Dic103—21no—
56C2×Dic103—22no—
57C2×Dic103—21no—
58C2×Dic103—41no—
59Dic206—21no—
60Dic206—42no—
61Dic206—41no—
62Dic206—41no—
63Dic206—82no—
64Dic206SD1612yes—
65C8×C103—41no—
66C8×C103—41no—
67C103⋊C8—41no—
68C22×C103#12011yescharacteristic
69C4×C103—22no—
70C4×C103—21no—
71C4×C103—41no—
72C4×C103C2×SD1611yescharacteristic
73C4×C103C2×Q1611yescharacteristic
74C4×C103#13711yescharacteristic
75C4×C103#13711yescharacteristic
76Dic103—22no—
77Dic103—42no—
78Dic103—41no—
79Dic103—81no—
80C2×C103#44811yescharacteristic
81C2×C103#45111yescharacteristic
82C2×C103#45511yescharacteristic
83#1645—1031nomaximal, Sylow
84C103#164511yescharacteristic, complemented, Sylow
85Q82—1031no—
86#487—1031no—
87#475—1031no—
88#462—1031no—
89#333—1031no—
90Q8⋊C8—1031no—
91Q8⋊C8D10311yescharacteristic
92C2×Q16—2061no—
93C4⋊Q8—1031no—
94C4⋊Q8—1031no—
95C4⋊Q8—2061no—
96C4⋊Q8—2062no—
97C4⋊Q8—2061no—
98C4×Q8—1031no—
99C4×Q8—2061no—
100C4×Q8—2061no—
101C4×Q8C2×D10311yescharacteristic
102#106—2061no—
103C4⋊C8—1031no—
104C4⋊C8C2×D10311yescharacteristic
105#103—2061no—
106#103—2062no—
107#103—2061no—
108C4×C8C2×D10311yescharacteristic
109C2×Q8—1031no—
110C2×Q8—1032no—
111C2×Q8—2062no—
112C2×Q8—2061no—
113C2×Q8D41211yescharacteristic
114Q16—4122no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—2061no—
118C4⋊C4—21no—
119C4⋊C4—1031no—
120C4⋊C4—2062no—
121C4⋊C4—2062no—
122C4⋊C4—2061no—
123C4⋊C4—2061no—
124C4⋊C4—2061no—
125C4⋊C4—2061no—
126C4⋊C4—2061no—
127C4⋊C4D41211yescharacteristic
128C42—21no—
129C42—2062no—
130C42—2061no—
131C42C22×D10311yescharacteristic
132Q8—21no—
133Q8—8242no—
134Q8—1032no—
135Q8—4122no—
136Q8—4121no—
137Q8—4121no—
138Q8—2061no—
139Q8Dic41212yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—4121no—
143C2×C4—2061no—
144C2×C4—2062no—
145C2×C4—2061no—
146C2×C4D4×D10311yescharacteristic
147C2×C4D4×D10311yescharacteristic
148C2×C4C2×D41211yescharacteristic
149C8—41no—
150C8—41no—
151C8—4121no—
152C22#1569299111yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—8241no—
157C4—4121no—
158C4—4122no—
159C4—2062no—
160C4SD16×D10311yescharacteristic
161C4C2×Dic41211yescharacteristic
162C4#1569305311yescharacteristic
163C4#1569305411yescharacteristic
164C2#2026793111yescharacteristic
165C2#2026794911yescharacteristic
166C2#2026797011yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingQ8⋊C8×C103C2
socle, prime radicalC22×C103#120
hypercenterQ8⋊C8D103
hypocenterC103#1645
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
49. Q8×C103Q16semidirect
84. C103#1645semidirect
139. Q8Dic412semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2062
#202681422
#202680762
#202680022
#202675392
#202675232
Q8⋊C8×C1032
#1645103