Finite Group Databasebeta

← #26120450

Subgroups — #26120450

Order 12032.

402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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#20254769C211yesmaximal, characteristic
2#20242121C212yesmaximal, complemented
3#20241840C212yesmaximal, complemented
4C47⋊#1309C211yesmaximal, characteristic, complemented
5C47×#1848C211yesmaximal, characteristic, complemented
6#15689673C2212yes—
7#15689414—22no—
8#15689376—22no—
9#15689319—22no—
10#15689147C2212yes—
11#15688871—22no—
12#15688866—22no—
13#15688852—24no—
14C2×#108×C47—22no—
15C47×#423C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×C4×C8×C47C2211yescharacteristic
18C2×#10625350—22no—
19C2×D376—22no—
20C2×#10625329—22no—
21#13094024D412yes—
22#13094021D412yes—
23#13094012—22no—
24#13093998—22no—
25#13093998—22no—
26C4×D188—22no—
27C4×D188—22no—
28#13093956—22no—
29C4⋊(C47⋊C8)—22no—
30C4⋊(C47⋊C8)—22no—
31#13093946—24no—
32C2×M16×C47—21no—
33C2×M16×C47D412yes—
34C22×C8×C47—21no—
35C2×C42×C47C2311yescharacteristic
36#108×C47—44no—
37C4⋊C8×C47—22no—
38C4⋊C8×C47—22no—
39C4×C8×C47—21no—
40C4×C8×C47D412yes—
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47#4112yes—
43C2×C22⋊D47—42no—
44#10625350—82no—
45#10625350—82no—
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—22no—
49C2×C4×D47—42no—
50C2×Dic94—22no—
51M16×C47—42no—
52M16×C47—42no—
53C2×C8×C47—22no—
54C2×C8×C47—22no—
55C2×C8×C47—22no—
56C2×C8×C47—22no—
57C2×C8×C47—41no—
58C42×C47C2×D412yes—
59C42×C47C2×D411yescharacteristic
60C42×C47#4111yescharacteristic
61(C2×D47)⋊C4—42no—
62(C2×D47)⋊C4—42no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65#10625329—82no—
66C2×C47⋊C8—42no—
67D376—82no—
68C23×C47#12411yescharacteristic
69C22×D47—42no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47#12011yescharacteristic
75C2×C4×C47#12111yescharacteristic
76C2×C4×C47#12112yes—
77C2×C4×C47#12312yes—
78C22⋊D47—84no—
79C2×Dic47—42no—
80D188—42no—
81D188—42no—
82D188—42no—
83D188—42no—
84D188—82no—
85C4×D47—82no—
86C4×D47—82no—
87Dic94—82no—
88C8×C47—24no—
89C8×C47—42no—
90C8×C47—81no—
91C47⋊C8—82no—
92#10530—471nomaximal, Sylow
93C22×C47—22no—
94C22×C47—21no—
95C22×C47#39411yescharacteristic
96C2×D47—82no—
97C2×D47—82no—
98C2×D47—82no—
99C4×C47—22no—
100C4×C47—21no—
101C4×C47#45311yescharacteristic
102C4×C47#45611yescharacteristic
103C4×C47#47112yes—
104C4×C47#47212yes—
105Dic47—82no—
106#3253—471no—
107#1848D4711yescharacteristic, complemented
108#1560—472no—
109#1492—472no—
110#1309—471no—
111C2×C47—41no—
112C2×C47#203911yescharacteristic
113C2×C47#205112yes—
114D47—162no—
115#532—472no—
116#476—942no—
117#469—942no—
118#459—942no—
119C2×#108—22no—
120#423—472no—
121#423C2×D4711yescharacteristic
122#423C2×D4711yescharacteristic
123C2×C4×C8C2×D4711yescharacteristic
124#333—942no—
125#331—942no—
126D4⋊C8—944no—
127C47#1053011yescharacteristic, complemented, Sylow
128C2×#41—942no—
129C2×D8—942no—
130C2×M16—21no—
131C2×M16—942no—
132C2×M16C22⋊D4712yes—
133C22×C8—21no—
134C4⋊Q8—472no—
135#127—472no—
136#124—942no—
137#121—942no—
138#121—942no—
139C4×D4—942no—
140C4×D4—942no—
141C2×C42C22×D4711yescharacteristic
142#108—44no—
143#106—942no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—942no—
147C4⋊C8—942no—
148#102—944no—
149C4×C8—21no—
150C4×C8D18812yes—
151#41—3762no—
152#41—3762no—
153C2×Q8—942no—
154C2×D4—942no—
155C2×D4—942no—
156C2×D4—942no—
157C2×D4—1882no—
158C22×C4—1882no—
159C22×C4#1062535412yes—
160C22×C4C2×C22⋊D4711yescharacteristic
161D8—3762no—
162M16—42no—
163M16—42no—
164M16—3762no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—1882no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C22⋊C4—1882no—
174C22⋊C4—1882no—
175C42C2×D18811yescharacteristic
176C42#1062535011yescharacteristic
177C42D4×D4712yes—
178C23—1882no—
179C23#1309401311yescharacteristic
180Q8—3762no—
181D4—3762no—
182D4—3764no—
183D4—1882no—
184D4—1882no—
185D4—1882no—
186D4—1882no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—3762no—
192C2×C4—3762no—
193C2×C4—1882no—
194C2×C4#1309399211yescharacteristic
195C2×C4#1309399811yescharacteristic
196C2×C4#1309399912yes—
197C2×C4#1309400912yes—
198C8—24no—
199C8—42no—
200C8—81no—
201C8—3762no—
202C22—21no—
203C22—22no—
204C22—3762no—
205C22—3762no—
206C22—3762no—
207C22#1568904011yescharacteristic
208C4—21no—
209C4—22no—
210C4—3762no—
211C4#1568929011yescharacteristic
212C4#1568930511yescharacteristic
213C4#1568938712yes—
214C4#1568939412yes—
215C2—41no—
216C2—7522no—
217C2#2024461211yescharacteristic
218C2#2024468212yes—
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1848C2
socleC22×C47#394
prime radical#20254769C2
hypercenter#1848D47
hypocenterC47#10530
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
2. #20242121C2semidirect
3. #20241840C2semidirect
4. C47⋊#1309C2semidirect
5. C47×#1848C2semidirect
107. #1848D47semidirect
127. C47#10530semidirect

Maximal subgroups

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

subgroupindex
#202547692
#202421212
#202418402
C47⋊#13092
C47×#18482
#1053047