Finite Group Databasebeta

← #26120354

Subgroups — #26120354

Order 12032.

388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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#20254698C211yesmaximal, characteristic
2#20243507C211yesmaximal, characteristic, complemented
3#20242084C212yesmaximal, complemented
4#20241897C212yesmaximal, complemented
5C47×#1290C211yesmaximal, characteristic, complemented
6#15689673C2212yes—
7#15689404—22no—
8#15689359—22no—
9#15689319—22no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11#15688969C2211yescharacteristic
12#15688877—22no—
13#15688871—22no—
14#15688866—22no—
15#15688858—24no—
16C47×#432C2212yes—
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×#10625350—22no—
19C2×D376—22no—
20C22×C47⋊C8—21no—
21#13094024D412yes—
22#13094021D412yes—
23#13094012—22no—
24#13093998—22no—
25#13093998—22no—
26C4×D188—22no—
27C4×D188—22no—
28C2×C4×Dic47—21no—
29#13093958—22no—
30C4⋊(C47⋊C8)—22no—
31#13093946—24no—
32C47⋊#95—21no—
33C47⋊#95D412yes—
34C22×C8×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38C22⋊C8×C47—22no—
39#97×C47—22no—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47#4111yescharacteristic
43C2×C22⋊D47—42no—
44C22×Dic47—22no—
45#10625350—84no—
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—22no—
49C2×C4×D47—42no—
50C2×Dic94—22no—
51C2×C8×C47—22no—
52C2×C8×C47—42no—
53C2×C8×C47—42no—
54C42×C47C2×D412yes—
55C42×C47#4112yes—
56(C2×D47)⋊C4—42no—
57(C2×D47)⋊C4—42no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4×Dic47—41no—
61C4×Dic47—41no—
62C2×C47⋊C8—42no—
63C2×C47⋊C8—41no—
64D376—82no—
65C23×C47#12111yescharacteristic
66C22×D47—42no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—41no—
71C2×C4×C47#12011yescharacteristic
72C2×C4×C47#12112yes—
73C2×C4×C47#12312yes—
74C2×C4×C47#12411yescharacteristic
75C22⋊D47—84no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80D188—42no—
81D188—42no—
82D188—82no—
83D188—82no—
84C4×D47—84no—
85Dic94—82no—
86C8×C47—42no—
87C8×C47—82no—
88C47⋊C8—81no—
89#10513—471nomaximal, Sylow
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#39411yescharacteristic
93C22×C47#47212yes—
94C2×D47—82no—
95C2×D47—82no—
96C2×D47—82no—
97C4×C47—22no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47#45411yescharacteristic
101C4×C47#45511yescharacteristic
102Dic47—82no—
103Dic47—82no—
104#3245—471no—
105#1832—471no—
106#1551—472no—
107#1505—472no—
108#1290D4711yescharacteristic, complemented
109C2×C47—22no—
110C2×C47#204011yescharacteristic
111C2×C47#204511yescharacteristic
112C2×C47#205311yescharacteristic
113D47—162no—
114#532—472no—
115#474—942no—
116#466—942no—
117#459—942no—
118#432C2×D4712yes—
119C2×C4⋊C8—471no—
120C2×C4⋊C8C2×D4711yescharacteristic
121#376—471no—
122#336—942no—
123#333—942no—
124#331—942no—
125#327—944no—
126C47#1051311yescharacteristic, complemented, Sylow
127C2×#41—942no—
128C2×D8—942no—
129C22×C8—941no—
130C22×C8D18812yes—
131C4⋊Q8—472no—
132#127—472no—
133#124—942no—
134#121—942no—
135#121—942no—
136C4×D4—942no—
137C4×D4—942no—
138C2×C42—941no—
139C2×C42C22×D4711yescharacteristic
140#107—942no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—942no—
144#102—944no—
145C22⋊C8—22no—
146#97—22no—
147#95—472no—
148#95—941no—
149#41—3764no—
150C2×Q8—942no—
151C2×D4—942no—
152C2×D4—942no—
153C2×D4—942no—
154C2×D4—1882no—
155C22×C4—942no—
156C22×C4—1882no—
157C22×C4C2×D18811yescharacteristic
158C22×C4D4×D4711yescharacteristic
159C22×C4#1062535411yescharacteristic
160D8—3762no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—1882no—
165C2×C8—1881no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C22⋊C4—1882no—
169C22⋊C4—1882no—
170C42—1881no—
171C42—1881no—
172C42#1062535012yes—
173C42D4×D4712yes—
174C23—1882no—
175C23#1309399911yescharacteristic
176Q8—3762no—
177D4—3762no—
178D4—3762no—
179D4—3764no—
180D4—1882no—
181D4—1882no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—3764no—
187C2×C4—1882no—
188C2×C4—1882no—
189C2×C4—1882no—
190C2×C4—1882no—
191C2×C4#1309399411yescharacteristic
192C2×C4#1309399712yes—
193C2×C4#1309400912yes—
194C2×C4#1309401211yescharacteristic
195C8—42no—
196C8—82no—
197C8—3761no—
198C22—21no—
199C22—21no—
200C22—3762no—
201C22—3762no—
202C22—3762no—
203C22#1568904111yescharacteristic
204C22#1568939412yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—3762no—
209C4—3762no—
210C4#1568929811yescharacteristic
211C4#1568930311yescharacteristic
212C2—22no—
213C2—7522no—
214C2#2024461811yescharacteristic
215C2#2024464511yescharacteristic
216C2#2024469511yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1290C2
socleC22×C47#394
prime radical#20254698C2
hypercenter#1290D47
hypocenterC47#10513
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #20243507C2semidirect
3. #20242084C2semidirect
4. #20241897C2semidirect
5. C47×#1290C2semidirect
108. #1290D47semidirect
126. C47#10513semidirect

Maximal subgroups

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

subgroupindex
#202546982
#202435072
#202420842
#202418972
C47×#12902
#1051347