Finite Group Databasebeta

← #26130689

Subgroups — #26130689

Order 12032.

186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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#20245634C211yesmaximal, characteristic, complemented
2#20245565C211yesmaximal, characteristic
3#20245470C211yesmaximal, characteristic
4#20245231C211yesmaximal, characteristic
5#20241448C211yesmaximal, characteristic, complemented
6#20241426C211yesmaximal, characteristic, complemented
7C47×#1369C211yesmaximal, characteristic, complemented
8#15689566—21no—
9#15689539—21no—
10#15689525C2211yescharacteristic
11#15689503C2211yescharacteristic
12#15689241C2211yescharacteristic
13#15688946—21no—
14#15688944C2211yescharacteristic
15#15688940—21no—
16#15688934—21no—
17#15688928—21no—
18#15688928—21no—
19#15688906—21no—
20C47×#364C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#346C2211yescharacteristic
23#13094046D411yescharacteristic
24C2×Dic188—21no—
25C2×Dic188—21no—
26#13094030—21no—
27#13094024—21no—
28#13094016—21no—
29Dic376—41no—
30#13093969—41no—
31#13093964—21no—
32#13093963—41no—
33C16×D47—41no—
34#13093960D411yescharacteristic
35#13093958—21no—
36#13093956—21no—
37#13093952—21no—
38M32×C47—21no—
39M32×C47—21no—
40C2×C16×C47D411yescharacteristic
41C2×C16×C47D411yescharacteristic
42C4×C8×C47C2311yescharacteristic
43#10625350—21no—
44C2×Dic94—41no—
45C2×C8×C47C2×D411yescharacteristic
46C2×C8×C47C2×D411yescharacteristic
47C42×C47#4111yescharacteristic
48C4⋊Dic47—41no—
49C4⋊Dic47—81no—
50Dic47⋊C4—81no—
51#10625329—21no—
52Dic188—41no—
53Dic188—41no—
54Dic188—41no—
55Dic188—41no—
56Dic188SD1611yescharacteristic
57D376SD1611yescharacteristic
58#10625325—21no—
59#10625324—41no—
60C8×D47—41no—
61C16×C47—21no—
62C16×C47—21no—
63C16×C47—41no—
64C16×C47—41no—
65C47⋊C16—41no—
66C2×C4×C47—21no—
67C2×C4×C47#12111yescharacteristic
68C22⋊D47—41no—
69C2×Dic47—81no—
70C2×Dic47—81no—
71D188—21no—
72C4×D47—41no—
73Dic94—21no—
74Dic94—81no—
75Dic94—81no—
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#46311yescharacteristic
86C4×C47#46511yescharacteristic
87Dic47—41no—
88Dic47—161no—
89Dic47—161no—
90#2245—471no—
91#2231—471no—
92#2214—471no—
93#2171—471no—
94#1369D4711yescharacteristic, complemented
95#1366—471no—
96#1358—471no—
97C2×C47—21no—
98C2×C47#167711yescharacteristic
99D47—81no—
100#510—941no—
101#504—941no—
102#499—471no—
103#494—471no—
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#346C2×D4711yescharacteristic
115C47#1246611yescharacteristic, complemented, Sylow
116#135—471no—
117C2×Q16—941no—
118C2×Q16—941no—
119#131—941no—
120C4⋊Q8—941no—
121#125—941no—
122Q32—1881no—
123SD32—1881no—
124M32—21no—
125M32—21no—
126M32—941no—
127M32—1881no—
128C2×C16—1881no—
129C2×C16D18811yescharacteristic
130C2×C16D18811yescharacteristic
131#108—471no—
132#107—941no—
133#106—941no—
134#104—941no—
135C4×C8C22×D4711yescharacteristic
136#41—941no—
137C2×Q8—1881no—
138Q16—471no—
139Q16—1881no—
140Q16—1881no—
141Q16—1881no—
142Q16—1881no—
143SD16—941no—
144D8—471no—
145M16—941no—
146M16—1881no—
147C2×C8—1881no—
148C2×C8C2×D18811yescharacteristic
149C2×C8D4×D4711yescharacteristic
150C4⋊C4—3761no—
151C4⋊C4—3761no—
152C4⋊C4—1881no—
153C42#1062535411yescharacteristic
154C16—21no—
155C16—21no—
156C16—41no—
157C16—41no—
158C16—1881no—
159Q8—941no—
160Q8—3761no—
161Q8—3761no—
162D4—941no—
163D4—1881no—
164C2×C4—21no—
165C2×C4—3761no—
166C2×C4—3761no—
167C2×C4—1881no—
168C2×C4#1309399911yescharacteristic
169C8—1881no—
170C8SD16×D4711yescharacteristic
171C8#1309404511yescharacteristic
172C8#1309404611yescharacteristic
173C8#1309405211yescharacteristic
174C22—1881no—
175C22#1568939411yescharacteristic
176C4—41no—
177C4—1881no—
178C4—7521no—
179C4—7521no—
180C4#1568933911yescharacteristic
181C4#1568935311yescharacteristic
182C2—21no—
183C2—3761no—
184C2#2024279811yescharacteristic
subgroupG/H
centerC2#20242798
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1369C2
socleC2×C47#1677
prime radical#13094046D4
hypercenter#1369D47
hypocenterC47#12466
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1369

Complements

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

NH ≅ G/Ntype
1. #20245634C2semidirect
5. #20241448C2semidirect
6. #20241426C2semidirect
7. C47×#1369C2semidirect
94. #1369D47semidirect
115. C47#12466semidirect

Maximal subgroups

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

subgroupindex
#202456342
#202455652
#202454702
#202452312
#202414482
#202414262
C47×#13692
#1246647