Finite Group Databasebeta

← #26127463

Subgroups — #26127463

Order 12032.

296 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 75 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#20254038C211yesmaximal, characteristic
2#20245204C211yesmaximal, characteristic, complemented
3#20241420C214yesmaximal, complemented
4C47×#2110C211yesmaximal, characteristic, complemented
5#15689728C412yes—
6#15689525C411yescharacteristic
7#15689500C411yescharacteristic
8#15689488C2212yes—
9#15689376—21no—
10#15689359—21no—
11#15689236—21no—
12C4×D376—21no—
13#15688944—21no—
14#15688905—21no—
15#15688901C2212yes—
16C2×M32×C47—21no—
17C47×#405C2211yescharacteristic
18C47×#347—21no—
19C47×#347C2212yes—
20C2×D376—21no—
21C2×D376—21no—
22#13094021C2×C412yes—
23#13094016C2×C412yes—
24#13094009—42no—
25#13093998—22no—
26#13093997—42no—
27C4×D188—22no—
28#13093964—22no—
29#13093958—21no—
30#13093956—21no—
31#13093946—22no—
32#13093946—22no—
33C2×M16×C47D411yescharacteristic
34C22×C8×C47D411yescharacteristic
35#117×C47C2×C411yescharacteristic
36M32×C47—22no—
37M32×C47—22no—
38C2×C16×C47—22no—
39#97×C47D411yescharacteristic
40#97×C47C2311yescharacteristic
41C4×C8×C47C2×C411yescharacteristic
42C4×C8×C47D411yescharacteristic
43C22×C4×C47C22⋊C411yescharacteristic
44C2×C22⋊D47—42no—
45C2×D188—22no—
46C2×D188—42no—
47C2×C4×D47—42no—
48M16×C47—41no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C2×C8×C47C22⋊C411yescharacteristic
52C2×C8×C47C22⋊C411yescharacteristic
53C2×C8×C47C2×D411yescharacteristic
54C2×C8×C47C2×D411yescharacteristic
55C4⋊C4×C47—21no—
56C22⋊C4×C47—21no—
57C42×C47C22⋊C411yescharacteristic
58C42×C47C22×C411yescharacteristic
59(C2×D47)⋊C4—42no—
60(C2×D47)⋊C4—42no—
61C4⋊Dic47—22no—
62Dic47⋊C4—42no—
63D376—42no—
64D376—41no—
65D376—41no—
66C16×C47—24no—
67C47⋊C16—42no—
68C23×C47#10011yescharacteristic
69C22×D47—42no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47#10011yescharacteristic
75C2×C4×C47C2×C22⋊C411yescharacteristic
76C22⋊D47—162no—
77C2×Dic47—42no—
78D188—42no—
79D188—42no—
80D188—162no—
81C4×D47—162no—
82C8×C47—21no—
83C8×C47—21no—
84C8×C47—21no—
85C8×C47#10411yescharacteristic
86C8×C47#10411yescharacteristic
87#11913—471nomaximal, Sylow
88C22×C47—21no—
89C22×C47—41no—
90C22×C47C2×#10011yescharacteristic
91C2×D47—82no—
92C2×D47—82no—
93C2×D47—82no—
94C4×C47—21no—
95C4×C47—41no—
96C4×C47—41no—
97C4×C47C2×#10411yescharacteristic
98C4×C47#42111yescharacteristic
99Dic47—82no—
100#3176—471no—
101#2166—471no—
102#2110D4711yescharacteristic, complemented
103#1355—474no—
104C2×C47—21no—
105C2×C47—41no—
106C2×C47#153011yescharacteristic
107D47—162no—
108#540—472no—
109C2×M32—21no—
110#499—471no—
111#493—471no—
112#490—472no—
113#469—941no—
114#466—941no—
115#442—941no—
116C4×D8—941no—
117#405C2×D4711yescharacteristic
118#364—941no—
119#349—941no—
120#347—21no—
121#347—472no—
122#347C2×D4712yes—
123C47#1191311yescharacteristic, complemented, Sylow
124C2×D8—941no—
125C2×D8—941no—
126C2×M16D18811yescharacteristic
127C22×C8C22⋊D4711yescharacteristic
128#127—472no—
129#125—472no—
130#123—1882no—
131#121—942no—
132#121—1882no—
133C4×D4—942no—
134#117C4×D4711yescharacteristic
135M32—22no—
136M32—22no—
137M32—942no—
138C2×C16—22no—
139#107—941no—
140#106—941no—
141#102—942no—
142#102—942no—
143#97C22⋊D4711yescharacteristic
144#97C22×D4711yescharacteristic
145C4×C8C4×D4711yescharacteristic
146C4×C8D18811yescharacteristic
147C2×D4—942no—
148C2×D4—1882no—
149C2×D4—1882no—
150C22×C4—1882no—
151C22×C4(C2×D47)⋊C411yescharacteristic
152D8—1882no—
153D8—1881no—
154D8—1881no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8(C2×D47)⋊C411yescharacteristic
159C2×C8(C2×D47)⋊C411yescharacteristic
160C2×C8C2×D18811yescharacteristic
161C2×C8C2×C22⋊D4711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—942no—
164C4⋊C4—1882no—
165C22⋊C4—21no—
166C22⋊C4—1882no—
167C22⋊C4—1882no—
168C42(C2×D47)⋊C411yescharacteristic
169C42C2×C4×D4711yescharacteristic
170C16—24no—
171C16—1882no—
172C23—1882no—
173C23#1309394011yescharacteristic
174D4—1882no—
175D4—1882no—
176D4—7522no—
177D4—7522no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—1882no—
183C2×C4—7522no—
184C2×C4#1309394011yescharacteristic
185C2×C4C2×(C2×D47)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8#1309395211yescharacteristic
190C8#1309395211yescharacteristic
191C22—21no—
192C22—41no—
193C22—3762no—
194C22—3762no—
195C22—3762no—
196C22C2×#1309394011yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—3762no—
201C4C2×#1309395211yescharacteristic
202C4#1568913911yescharacteristic
203C2—21no—
204C2—41no—
205C2—7522no—
206C2#2024199811yescharacteristic
subgroupG/H
centerC2#20241998
commutatorC42×C47C22×C4
Frattini#97C22×D47
FittingC47×#2110C2
socleC2×C47#1530
prime radical#20254038C2
cosocle#97×C47C23
hypercenter#2110D47
hypocenterC47#11913
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2110

Complements

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

NH ≅ G/Ntype
2. #20245204C2semidirect
3. #20241420C2semidirect
4. C47×#2110C2semidirect
102. #2110D47semidirect
123. C47#11913semidirect

Maximal subgroups

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

subgroupindex
#202540382
#202452042
#202414202
C47×#21102
#1191347