Finite Group Databasebeta

← #27194409

Subgroups — #27194409

Order 13184.

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

normal subgroups only

This group has 234 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#20268189C211yesmaximal, characteristic, complemented
3#20268077C211yesmaximal, characteristic, complemented
4#20267996C211yesmaximal, characteristic
5#20267538C211yesmaximal, characteristic, complemented
6#20267523C211yesmaximal, characteristic, complemented
7D4⋊C8×C103C211yesmaximal, characteristic
8C22×Dic206—21no—
9C2×#13110093—21no—
10#15693021C2211yescharacteristic
11#15693021C2211yescharacteristic
12#15693020—21no—
13#15693000—21no—
14#15692998—22no—
15C4×Dic206C2211yescharacteristic
16D4×Dic103—21no—
17#15692953—21no—
18#15692953—22no—
19C4⋊(C103⋊C8)C2211yescharacteristic
20#15692946—21no—
21#15692944—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—
32#13110093—42no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37C4⋊Dic103D411yescharacteristic
38C4⋊Dic103D412yes—
39Dic103⋊C4—22no—
40Dic103⋊C4—21no—
41C22⋊Dic103—22no—
42C4×Dic103—21no—
43C2×D4×C103D411yescharacteristic
44C22×C4×C103—21no—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C4⋊C4×C103D411yescharacteristic
48C22⋊C4×C103—21no—
49C42×C103C2311yescharacteristic
50C23×C103—21no—
51D4×C103—21no—
52D4×C103SD1612yes—
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×Dic103—21no—
60C2×Dic103—21no—
61C2×Dic103—22no—
62C2×Dic103—44no—
63C2×Dic103—41no—
64Dic206—21no—
65Dic206—44no—
66Dic206—41no—
67Dic206—41no—
68Dic206—41no—
69Dic206—41no—
70Dic206SD1612yescomplemented
71C8×C103—22no—
72C8×C103—41no—
73C103⋊C8—41no—
74C22×C103—22no—
75C22×C103—41no—
76C22×C103—41no—
77C22×C103#12011yescharacteristic
78C4×C103—21no—
79C4×C103—41no—
80C4×C103C2×SD1611yescharacteristic
81C4×C103C2×SD1611yescharacteristic
82C4×C103AGL(1,ℤ/8)11yescharacteristic
83C4×C103#13711yescharacteristic
84Dic103—22no—
85Dic103—42no—
86Dic103—41no—
87Dic103—81no—
88C2×C103—42no—
89C2×C103#44811yescharacteristic
90C2×C103#45011yescharacteristic
91C2×C103#45611yescharacteristic
92#1651—1031nomaximal, Sylow
93C103#165111yescharacteristic, complemented, Sylow
94D4×Q8—1031no—
95#498—1031no—
96#475—1031no—
97#461—1031no—
98#332—1031no—
99Q8⋊C8—1031no—
100D4⋊C8D10311yescharacteristic
101C22×Q8—2061no—
102C2×SD16—2061no—
103C4⋊Q8—1031no—
104C4⋊Q8—1031no—
105C4⋊Q8—2061no—
106C22⋊Q8—2062no—
107C22⋊Q8—2061no—
108C4×Q8—1031no—
109C4×D4—2061no—
110C4×D4C2×D10311yescharacteristic
111#106—2061no—
112#106—2062no—
113C4⋊C8—1031no—
114C4⋊C8C2×D10311yescharacteristic
115#103—2061no—
116#103—2061no—
117C4×C8C2×D10311yescharacteristic
118C2×Q8—1031no—
119C2×Q8—4122no—
120C2×Q8—4122no—
121C2×Q8—2062no—
122C2×Q8—2061no—
123C2×Q8—2061no—
124C2×D4D41211yescharacteristic
125C22×C4—21no—
126C22×C4—2062no—
127SD16—4122no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2061no—
131C4⋊C4—1031no—
132C4⋊C4—1032no—
133C4⋊C4—2062no—
134C4⋊C4—2061no—
135C4⋊C4—2061no—
136C4⋊C4—2061no—
137C4⋊C4—2061no—
138C4⋊C4D41211yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—2062no—
141C42—2061no—
142C42C22×D10311yescharacteristic
143C23—21no—
144Q8—1032no—
145Q8—4124no—
146Q8—4121no—
147Q8—4121no—
148Q8—4121no—
149Q8—4121no—
150Q8—2061no—
151D4—21no—
152D4#1311009412yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—4121no—
157C2×C4—4124no—
158C2×C4—2061no—
159C2×C4—2062no—
160C2×C4—2061no—
161C2×C4D4×D10311yescharacteristic
162C2×C4D4×D10311yescharacteristic
163C2×C4C2×D41211yescharacteristic
164C8—22no—
165C8—41no—
166C8—4121no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1569299111yescharacteristic
171C4—21no—
172C4—41no—
173C4—8241no—
174C4—4122no—
175C4—4121no—
176C4—2062no—
177C4SD16×D10311yescharacteristic
178C4C2×#1311009411yescharacteristic
179C4#1569304511yescharacteristic
180C4#1569305411yescharacteristic
181C2—42no—
182C2#2026793211yescharacteristic
183C2#2026794311yescharacteristic
184C2#2026797511yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
FittingD4⋊C8×C103C2
socleC22×C103#120
prime radicalC2×D4×C103D4
hypercenterD4⋊C8D103
hypocenterC103#1651
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. #20268189C2semidirect
3. #20268077C2semidirect
5. #20267538C2semidirect
6. #20267523C2semidirect
70. Dic206SD16semidirect
93. C103#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2062
#202681892
#202680772
#202679962
#202675382
#202675232
D4⋊C8×C1032
#1651103