Finite Group Databasebeta

← #27194312

Subgroups — #27194312

Order 13184.

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

normal subgroups only

This group has 228 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
1D4×Dic206C211yesmaximal, characteristic
2#20268142C211yesmaximal, characteristic, complemented
3#20268087C211yesmaximal, characteristic, complemented
4#20268081C211yesmaximal, characteristic
5#20267538C211yesmaximal, characteristic, complemented
6#20267523C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic
8C22×Dic206—21no—
9#15693021C2211yescharacteristic
10#15693021C2211yescharacteristic
11#15693020—21no—
12#15693000—21no—
13#15692998—22no—
14C4×Dic206C2211yescharacteristic
15D4×Dic103—21no—
16#15692955—21no—
17#15692952—21no—
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692946—21no—
20#15692946—22no—
21#15692942—21no—
22C4×D4×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4×C8×C103C2211yescharacteristic
25C2×Dic206—22no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—42no—
29C2×Dic206—42no—
30C2×Dic206D411yescharacteristic
31C22×Dic103—22no—
32C2×C103⋊C8—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103D412yes—
37C4⋊Dic103D411yescharacteristic
38Dic103⋊C4—22no—
39Dic103⋊C4—21no—
40C22⋊Dic103—22no—
41C4×Dic103—21no—
42C2×D4×C103D411yescharacteristic
43C22×C4×C103—21no—
44C2×C8×C103—21no—
45C2×C8×C103—21no—
46C4⋊C4×C103D411yescharacteristic
47C22⋊C4×C103—21no—
48C42×C103C2311yescharacteristic
49C23×C103—21no—
50D4×C103—21no—
51D4×C103Q1612yes—
52C2×C4×C103—21no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×Dic103—21no—
59C2×Dic103—21no—
60C2×Dic103—22no—
61C2×Dic103—44no—
62C2×Dic103—41no—
63Dic206—21no—
64Dic206—44no—
65Dic206—41no—
66Dic206—41no—
67Dic206—42no—
68Dic206SD1612yes—
69C8×C103—41no—
70C8×C103—41no—
71C103⋊C8—41no—
72C22×C103—22no—
73C22×C103—41no—
74C22×C103—41no—
75C22×C103#12011yescharacteristic
76C4×C103—21no—
77C4×C103—41no—
78C4×C103C2×SD1611yescharacteristic
79C4×C103C2×Q1611yescharacteristic
80C4×C103AGL(1,ℤ/8)11yescharacteristic
81C4×C103#13711yescharacteristic
82Dic103—22no—
83Dic103—42no—
84Dic103—41no—
85Dic103—81no—
86C2×C103—42no—
87C2×C103#45011yescharacteristic
88C2×C103#45111yescharacteristic
89C2×C103#45411yescharacteristic
90#1637—1031nomaximal, Sylow
91C103#163711yescharacteristic, complemented, Sylow
92D4×Q8—1031no—
93#487—1031no—
94#477—1031no—
95#476—1031no—
96#332—1031no—
97Q8⋊C8—1031no—
98D4⋊C8D10311yescharacteristic
99C22×Q8—2061no—
100C4⋊Q8—1031no—
101C4⋊Q8—1031no—
102C4⋊Q8—2061no—
103C22⋊Q8—2062no—
104C22⋊Q8—2061no—
105C4×Q8—1031no—
106C4×D4—2061no—
107C4×D4C2×D10311yescharacteristic
108#107—2061no—
109#106—2061no—
110C4⋊C8—1031no—
111C4⋊C8C2×D10311yescharacteristic
112#103—2062no—
113#103—2061no—
114#102—2061no—
115C4×C8C2×D10311yescharacteristic
116C2×Q8—1031no—
117C2×Q8—4122no—
118C2×Q8—4122no—
119C2×Q8—2062no—
120C2×Q8—2061no—
121C2×Q8—2061no—
122C2×D4D41211yescharacteristic
123C22×C4—21no—
124C22×C4—2062no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2061no—
128C4⋊C4—1032no—
129C4⋊C4—1031no—
130C4⋊C4—2062no—
131C4⋊C4—2061no—
132C4⋊C4—2061no—
133C4⋊C4—2061no—
134C4⋊C4—2061no—
135C4⋊C4D41211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2062no—
138C42—2061no—
139C42C22×D10311yescharacteristic
140C23—21no—
141Q8—1032no—
142Q8—4122no—
143Q8—4124no—
144Q8—4121no—
145Q8—4121no—
146Q8—2061no—
147D4—21no—
148D4Dic41212yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—4121no—
153C2×C4—4124no—
154C2×C4—2061no—
155C2×C4—2062no—
156C2×C4—2061no—
157C2×C4D4×D10311yescharacteristic
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×D41211yescharacteristic
160C8—41no—
161C8—41no—
162C8—4121no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1569299111yescharacteristic
167C4—21no—
168C4—41no—
169C4—8241no—
170C4—4122no—
171C4—4121no—
172C4—2062no—
173C4SD16×D10311yescharacteristic
174C4C2×Dic41211yescharacteristic
175C4#1569304511yescharacteristic
176C4#1569305411yescharacteristic
177C2—42no—
178C2#2026794311yescharacteristic
179C2#2026794911yescharacteristic
180C2#2026796511yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenterD4⋊C8D103
hypocenterC103#1637
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20268142C2semidirect
3. #20268087C2semidirect
5. #20267538C2semidirect
6. #20267523C2semidirect
91. C103#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2062
#202681422
#202680872
#202680812
#202675382
#202675232
D4⋊C8×C1032
#1637103