Finite Group Databasebeta

← #26120349

Subgroups — #26120349

Order 12032.

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

normal subgroups only

This group has 408 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#20243541C211yesmaximal, 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
11C2×Dic47⋊C8—22no—
12#15688969C2211yescharacteristic
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—
31Dic47⋊C8—44no—
32#13093946—24no—
33C47⋊#95—21no—
34C47⋊#95D412yes—
35C22×C8×C47D412yes—
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—22no—
38C4⋊C8×C47—22no—
39C22⋊C8×C47—22no—
40#97×C47—22no—
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47#4111yescharacteristic
44C2×C22⋊D47—42no—
45C22×Dic47—22no—
46#10625350—84no—
47C2×D188—22no—
48C2×D188—22no—
49C2×D188—22no—
50C2×C4×D47—42no—
51C2×Dic94—22no—
52C2×C8×C47—22no—
53C2×C8×C47—42no—
54C2×C8×C47—42no—
55C42×C47C2×D412yes—
56C42×C47#4112yes—
57(C2×D47)⋊C4—42no—
58(C2×D47)⋊C4—42no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4×Dic47—22no—
62C4×Dic47—22no—
63C2×C47⋊C8—42no—
64C2×C47⋊C8—41no—
65D376—82no—
66C23×C47#12111yescharacteristic
67C22×D47—42no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47#12011yescharacteristic
73C2×C4×C47#12112yes—
74C2×C4×C47#12312yes—
75C2×C4×C47#12411yescharacteristic
76C22⋊D47—84no—
77C2×Dic47—24no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81D188—42no—
82D188—42no—
83D188—82no—
84D188—82no—
85C4×D47—84no—
86Dic94—82no—
87C8×C47—42no—
88C8×C47—82no—
89C47⋊C8—81no—
90#10512—471nomaximal, Sylow
91C22×C47—21no—
92C22×C47—21no—
93C22×C47#39411yescharacteristic
94C22×C47#47212yes—
95C2×D47—82no—
96C2×D47—82no—
97C2×D47—82no—
98C4×C47—22no—
99C4×C47—21no—
100C4×C47—22no—
101C4×C47#45311yescharacteristic
102C4×C47#45611yescharacteristic
103Dic47—44no—
104Dic47—82no—
105#3245—471no—
106#1843—471no—
107#1551—472no—
108#1505—472no—
109#1290D4711yescharacteristic, complemented
110C2×C47—22no—
111C2×C47#203911yescharacteristic
112C2×C47#204511yescharacteristic
113C2×C47#205311yescharacteristic
114D47—162no—
115#532—472no—
116#474—942no—
117#466—942no—
118#459—942no—
119#432C2×D4712yes—
120C2×C4⋊C8—471no—
121C2×C4⋊C8—942no—
122C2×C4⋊C8C2×D4711yescharacteristic
123#376—471no—
124#333—942no—
125#331—942no—
126#327—944no—
127C47#1051211yescharacteristic, complemented, Sylow
128C2×#41—942no—
129C2×D8—942no—
130C22×C8—941no—
131C22×C8D18812yes—
132C4⋊Q8—472no—
133#127—472no—
134#124—942no—
135#121—942no—
136#121—942no—
137C4×D4—942no—
138C4×D4—942no—
139C2×C42—941no—
140C2×C42C22×D4711yescharacteristic
141#107—942no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—942no—
145C4⋊C8—1884no—
146#102—944no—
147C22⋊C8—22no—
148#97—22no—
149#95—472no—
150#95—941no—
151#41—3764no—
152C2×Q8—942no—
153C2×D4—942no—
154C2×D4—942no—
155C2×D4—942no—
156C2×D4—1882no—
157C22×C4—942no—
158C22×C4—1882no—
159C22×C4C2×D18811yescharacteristic
160C22×C4D4×D4711yescharacteristic
161C22×C4#1062535411yescharacteristic
162D8—3762no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—1882no—
167C2×C8—1881no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C22⋊C4—1882no—
171C22⋊C4—1882no—
172C42—942no—
173C42—942no—
174C42#1062535012yes—
175C42D4×D4712yes—
176C23—1882no—
177C23#1309399911yescharacteristic
178Q8—3762no—
179D4—3762no—
180D4—3762no—
181D4—3764no—
182D4—1882no—
183D4—1882no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—944no—
189C2×C4—3764no—
190C2×C4—1882no—
191C2×C4—1882no—
192C2×C4—1882no—
193C2×C4#1309399411yescharacteristic
194C2×C4#1309399712yes—
195C2×C4#1309400912yes—
196C2×C4#1309401211yescharacteristic
197C8—42no—
198C8—82no—
199C8—3761no—
200C22—21no—
201C22—21no—
202C22—3762no—
203C22—3762no—
204C22—3762no—
205C22#1568904111yescharacteristic
206C22#1568939412yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—3762no—
211C4—1884no—
212C4#1568929311yescharacteristic
213C4#1568930811yescharacteristic
214C2—22no—
215C2—7522no—
216C2#2024461311yescharacteristic
217C2#2024464511yescharacteristic
218C2#2024469511yescharacteristic
subgroupG/H
centerC22#15689041
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1290C2
socleC22×C47#394
prime radical#20254698C2
hypercenter#1290D47
hypocenterC47#10512
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. #20243541C2semidirect
3. #20242084C2semidirect
4. #20241897C2semidirect
5. C47×#1290C2semidirect
109. #1290D47semidirect
127. C47#10512semidirect

Maximal subgroups

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

subgroupindex
#202546982
#202435412
#202420842
#202418972
C47×#12902
#1051247