Finite Group Databasebeta

← #26130687

Subgroups — #26130687

Order 12032.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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#20245633C211yesmaximal, characteristic, complemented
2#20245565C211yesmaximal, characteristic
3#20245466C211yesmaximal, characteristic
4#20245229C211yesmaximal, characteristic
5#20241455C211yesmaximal, characteristic, complemented
6#20241450C211yesmaximal, characteristic, complemented
7C47×#1358C211yesmaximal, characteristic, complemented
8#15689564—21no—
9#15689541—21no—
10#15689525C2211yescharacteristic
11#15689241C2211yescharacteristic
12#15688946—21no—
13#15688944C2211yescharacteristic
14#15688939—21no—
15#15688934—21no—
16#15688927—21no—
17#15688927—21no—
18#15688908—21no—
19#15688899C2211yescharacteristic
20C47×#494C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#364C2211yescharacteristic
23#13094046D411yescharacteristic
24#13094030—21no—
25#13094016—21no—
26#13093970—41no—
27#13093967—41no—
28#13093964—21no—
29#13093963—41no—
30C2×C47⋊C16D411yescharacteristic
31C2×C47⋊C16D411yescharacteristic
32C16×D47—41no—
33#13093960D411yescharacteristic
34#13093958—21no—
35#13093956—21no—
36#13093952—21no—
37C2×Q16×C47—21no—
38C2×Q16×C47—21no—
39C4⋊Q8×C47—21no—
40M32×C47—21no—
41M32×C47—21no—
42C4×C8×C47C2311yescharacteristic
43C2×Q8×C47—41no—
44#10625350—21no—
45Q16×C47—41no—
46Q16×C47—41no—
47Q16×C47—41no—
48Q16×C47—41no—
49C2×C8×C47C2×D411yescharacteristic
50C2×C8×C47C2×D411yescharacteristic
51C4⋊C4×C47—81no—
52C42×C47#4111yescharacteristic
53C4⋊Dic47—41no—
54Dic47⋊C4—81no—
55#10625329—21no—
56Dic188SD1611yescharacteristic
57D376SD1611yescharacteristic
58#10625325—21no—
59#10625324—41no—
60C8×D47—41no—
61C16×C47—41no—
62C16×C47—41no—
63C47⋊C16—21no—
64C47⋊C16—21no—
65C47⋊C16—41no—
66Q8×C47—81no—
67Q8×C47—81no—
68C2×C4×C47—21no—
69C2×C4×C47—81no—
70C2×C4×C47#12111yescharacteristic
71C22⋊D47—41no—
72C2×Dic47—81no—
73D188—21no—
74C4×D47—41no—
75Dic94—21no—
76C8×C47C2×SD1611yescharacteristic
77C8×C47#13511yescharacteristic
78C8×C47#13511yescharacteristic
79C8×C47AGL(1,ℤ/8)11yescharacteristic
80C47⋊C8—41no—
81#12466—471nomaximal, Sylow
82C22×C47#47211yescharacteristic
83C2×D47—41no—
84C4×C47—41no—
85C4×C47—161no—
86C4×C47#46311yescharacteristic
87C4×C47#46511yescharacteristic
88Dic47—41no—
89Dic47—161no—
90#2245—471no—
91#2231—471no—
92#2214—471no—
93#2171—471no—
94#1369—471no—
95#1366—471no—
96#1358D4711yescharacteristic, complemented
97C2×C47—21no—
98C2×C47#167711yescharacteristic
99D47—81no—
100#510—941no—
101#504—941no—
102#499—471no—
103#494C2×D4711yescharacteristic
104#443—471no—
105#365—941no—
106#364—471no—
107#364C2×D4711yescharacteristic
108#364C2×D4711yescharacteristic
109#362—941no—
110#360—941no—
111#358—941no—
112#358—941no—
113#350—941no—
114#346—471no—
115C47#1246611yescharacteristic, complemented, Sylow
116#135—471no—
117C2×Q16—21no—
118C2×Q16—21no—
119#131—941no—
120C4⋊Q8—21no—
121#125—941no—
122Q32—1881no—
123SD32—1881no—
124M32—21no—
125M32—21no—
126M32—941no—
127M32—1881no—
128C2×C16—471no—
129C2×C16—471no—
130C2×C16—1881no—
131#108—471no—
132#107—941no—
133#106—941no—
134#104—941no—
135C4×C8C22×D4711yescharacteristic
136#41—941no—
137C2×Q8—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—41no—
142Q16—471no—
143SD16—941no—
144D8—471no—
145M16—941no—
146M16—1881no—
147C2×C8—1881no—
148C2×C8D4×D4711yescharacteristic
149C2×C8D4×D4711yescharacteristic
150C4⋊C4—81no—
151C4⋊C4—3761no—
152C4⋊C4—1881no—
153C42#1062535011yescharacteristic
154C16—41no—
155C16—41no—
156C16—941no—
157C16—941no—
158C16—1881no—
159Q8—81no—
160Q8—81no—
161Q8—941no—
162D4—941no—
163D4—1881no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—3761no—
167C2×C4—1881no—
168C2×C4#1309399711yescharacteristic
169C8—1881no—
170C8SD16×D4711yescharacteristic
171C8#1309404311yescharacteristic
172C8#1309404511yescharacteristic
173C8#1309404811yescharacteristic
174C22—1881no—
175C22#1568939211yescharacteristic
176C4—41no—
177C4—161no—
178C4—1881no—
179C4—7521no—
180C4#1568933711yescharacteristic
181C4#1568935111yescharacteristic
182C2—21no—
183C2—3761no—
184C2#2024279611yescharacteristic
subgroupG/H
centerC2#20242796
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1358C2
socleC2×C47#1677
prime radical#13094046D4
hypercenter#1358D47
hypocenterC47#12466
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #20245633C2semidirect
5. #20241455C2semidirect
6. #20241450C2semidirect
7. C47×#1358C2semidirect
96. #1358D47semidirect
115. C47#12466semidirect

Maximal subgroups

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

subgroupindex
#202456332
#202455652
#202454662
#202452292
#202414552
#202414502
C47×#13582
#1246647