Finite Group Databasebeta

← #26136936

Subgroups — #26136936

Order 12032.

324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×D752C211yesmaximal, characteristic
2C2×#15688962C212yesmaximal, complemented
3#20245479C211yesmaximal, characteristic, complemented
4#20241567C212yesmaximal, complemented
5C47×C22⋊C32C211yesmaximal, characteristic, complemented
6C22×D376—21no—
7C2×Dic376C2211yescharacteristic, complemented
8C2×D752—24no—
9C2×D752—21no—
10C2×D752C2212yes—
11#15689364—21no—
12#15688962—24no—
13#15688949C2211yescharacteristic, complemented
14#15688928—21no—
15C22×C16×C47C2211yescharacteristic
16C2×C32×C47C2212yescomplemented
17C22×D188—41no—
18C2×Dic188—21no—
19C2×D376—24no—
20C2×D376—22no—
21C2×D376—42no—
22C2×D376—41no—
23#13094003—41no—
24Dic376—22no—
25D752—24no—
26D752—22no—
27D752D414yes—
28#13093958—21no—
29#13093949—41no—
30C22×C8×C47D411yescharacteristic
31C2×C16×C47—22no—
32C2×C16×C47D411yescharacteristic
33C2×C16×C47C2311yescharacteristic
34C32×C47—22no—
35C23×D47—81no—
36C22×C4×C47D811yescharacteristic
37C2×D188—44no—
38C2×D188—42no—
39C2×D188—82no—
40C2×D188—81no—
41C2×Dic94—41no—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C2×C8×C47D811yescharacteristic
45C2×C8×C47C2×D411yescharacteristic
46C22⋊Dic47—81no—
47C4⋊Dic47—41no—
48Dic47⋊C4—81no—
49Dic188—41no—
50Dic188—41no—
51D376—24no—
52D376—44no—
53D376—42no—
54C16×C47—21no—
55C16×C47C2×D412yes—
56C23×C47D1611yescharacteristic
57C22×D47—84no—
58C22×D47—82no—
59C22×D47—162no—
60C22×D47—162no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47D1611yescharacteristic
64C2×C4×C47C2×D811yescharacteristic
65C2×Dic47—81no—
66C2×Dic47—81no—
67D188—44no—
68D188—84no—
69D188—82no—
70Dic94—81no—
71Dic94—81no—
72C8×C47—21no—
73C8×C47#12011yescharacteristic
74C8×C47AGL(1,ℤ/8)11yescharacteristic
75#13664—471nomaximal, Sylow
76C22×C47—21no—
77C22×C47—21no—
78C22×C47SD6412yescomplemented
79C22×C47C2×D1611yescharacteristic
80C2×D47—84no—
81C2×D47—168no—
82C2×D47—162no—
83C2×D47—162no—
84C4×C47—21no—
85C4×C47#44711yescharacteristic
86C4×C47#50911yescharacteristic
87Dic47—161no—
88Dic47—161no—
89C22×D16—471no—
90C2×SD64—472no—
91#2216—471no—
92#1415—472no—
93C22⋊C32D4711yescharacteristic, complemented
94C2×C47—22no—
95C2×C47#218411yescharacteristic
96C2×C47C2×SD6411yescharacteristic
97C2×C47#226311yescharacteristic
98D47—164no—
99C22×D8—941no—
100C2×Q32—471no—
101C2×D16—472no—
102C2×D16—944no—
103C2×D16—941no—
104C22×C16C2×D4711yescharacteristic
105#467—941no—
106SD64—944no—
107C2×C32C2×D4712yescomplemented
108#366—471no—
109#358—941no—
110C47#1366411yescharacteristic, complemented, Sylow
111C22×D4—1881no—
112C2×Q16—941no—
113C2×D8—944no—
114C2×D8—942no—
115C2×D8—1882no—
116C2×D8—1881no—
117C22×C8D18811yescharacteristic
118C22⋊Q8—1881no—
119Q32—942no—
120D16—474no—
121D16—944no—
122D16—942no—
123C2×C16—22no—
124C2×C16D18811yescharacteristic
125C2×C16C22×D4711yescharacteristic
126#107—941no—
127#103—1881no—
128C32—22no—
129C24—3761no—
130C2×Q8—1881no—
131C2×D4—3762no—
132C2×D4—3761no—
133C2×D4—1884no—
134C2×D4—1882no—
135C22×C4D37611yescharacteristic
136Q16—1881no—
137Q16—1881no—
138D8—944no—
139D8—1884no—
140D8—1882no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8D37611yescharacteristic
144C2×C8C2×D18811yescharacteristic
145C4⋊C4—3761no—
146C4⋊C4—1881no—
147C22⋊C4—3761no—
148C16—21no—
149C16D4×D4712yes—
150C23—3764no—
151C23—3762no—
152C23—7522no—
153C23—7522no—
154C23D75211yescharacteristic
155Q8—3761no—
156Q8—3761no—
157D4—3764no—
158D4—3762no—
159D4—1884no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—3761no—
163C2×C4—3761no—
164C2×C4D75211yescharacteristic
165C2×C4C2×D37611yescharacteristic
166C8—21no—
167C8#1309399411yescharacteristic
168C8#1309405211yescharacteristic
169C22—21no—
170C22—21no—
171C22—3764no—
172C22—7528no—
173C22—7522no—
174C22—7522no—
175C22#1568896212yescomplemented
176C22C2×D75211yescharacteristic
177C4—21no—
178C4—7521no—
179C4—7521no—
180C4#1568925911yescharacteristic
181C4#1568956111yescharacteristic
182C2—22no—
183C2—7524no—
184C2#2024530211yescharacteristic
185C2C2×#1568896211yescharacteristic
186C2#2024570311yescharacteristic
subgroupG/H
centerC22C2×D752
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×C22⋊C32C2
socleC22×C47C2×D16
prime radicalC22×D752C2
hypercenterC22⋊C32D47
hypocenterC47#13664
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22⋊C32

Complements

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

NH ≅ G/Ntype
2. C2×#15688962C2semidirect
3. #20245479C2semidirect
4. #20241567C2semidirect
5. C47×C22⋊C32C2semidirect
7. C2×Dic376C22semidirect
13. #15688949C22semidirect
16. C2×C32×C47C22semidirect
78. C22×C47SD64semidirect
93. C22⋊C32D47semidirect
107. C2×C32C2×D47semidirect
110. C47#13664semidirect
175. C22#15688962semidirect

Maximal subgroups

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

subgroupindex
C22×D7522
C2×#156889622
#202454792
#202415672
C47×C22⋊C322
#1366447