Finite Group Databasebeta

← #26113708

Subgroups — #26113708

Order 12032.

554 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 119 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#20248387C211yesmaximal, characteristic
2#20243384C211yesmaximal, characteristic, complemented
3#20242055C212yesmaximal
4#20241290C212yesmaximal, complemented
5C47×#2983C211yesmaximal, characteristic, complemented
6C2×#13094021C2211yescharacteristic
7C2×#13094013—21no—
8#15689147C2212yes—
9C2×#13093943—21no—
10#15689040C414yes—
11#15689025—22no—
12#15689024—21no—
13C4×C4⋊Dic47C2211yescharacteristic
14#15688892—21no—
15#15688866—24no—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#446—24no—
18C47×#432—22no—
19C47×#431C2212yes—
20C22×D188—21no—
21C22×D188—21no—
22C22×D188C2×C412yes—
23C2×#10625329—22no—
24#13094021—22no—
25#13094021—22no—
26#13094013—44no—
27C2×C4⋊Dic47—21no—
28C2×(C2×D47)⋊C4—24no—
29C2×(C2×D47)⋊C4—24no—
30C2×C4×Dic47—21no—
31C4⋊(C47⋊C8)—22no—
32C4⋊(C47⋊C8)—22no—
33#13093943—42no—
34C47⋊#95C2×C412yes—
35C22×Q8×C47D411yescharacteristic
36C4×Q8×C47—22no—
37C4×Q8×C47—22no—
38C2×C4⋊C4×C47C2×C412yes—
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C42×C47D412yes—
41C2×C42×C47C2311yescharacteristic
42C4⋊C8×C47—24no—
43C4⋊C8×C47D414yes—
44C22⋊C8×C47—22no—
45#97×C47—24no—
46C4×C8×C47—22no—
47C23×D47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47—21no—
50C2×Q8×C47—22no—
51C2×Q8×C47—21no—
52C22×C4×C47C22⋊C412yes—
53C22×C4×C47C22⋊C412yes—
54C22×C4×C47C22×C411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47C2×D411yescharacteristic
57C22×Dic47—22no—
58C2×D188—24no—
59C2×D188—44no—
60C2×D188—41no—
61C2×D188—42no—
62C2×D188—41no—
63C2×D188—42no—
64C2×D188—41no—
65C2×D188—41no—
66C2×D188—82no—
67C2×C8×C47—24no—
68C4⋊C4×C47—24no—
69C4⋊C4×C47—22no—
70C42×C47—22no—
71C42×C47—22no—
72C42×C47C2×D412yes—
73C42×C47#4112yes—
74(C2×D47)⋊C4—48no—
75(C2×D47)⋊C4—84no—
76C4⋊Dic47—42no—
77C4×Dic47—42no—
78#10625329—42no—
79#10625329—42no—
80C2×C47⋊C8—42no—
81C23×C47C2×C22⋊C411yescharacteristic
82C22×D47—44no—
83C22×D47—44no—
84C22×D47—42no—
85C22×D47—42no—
86C22×D47—42no—
87Q8×C47—42no—
88Q8×C47—42no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—41no—
95C2×C4×C47—42no—
96C2×C4×C47C4×D412yes—
97C2×C4×C47#12011yescharacteristic
98C2×C4×C47#12112yes—
99C2×C4×C47#12311yescharacteristic
100C2×C4×C47AGL(1,ℤ/8)12yes—
101C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C47#13711yescharacteristic
103C2×Dic47—42no—
104C2×Dic47—42no—
105C2×Dic47—42no—
106D188—84no—
107D188—82no—
108D188—82no—
109D188—82no—
110D188—82no—
111C8×C47—44no—
112C47⋊C8—82no—
113#9406—471nomaximal, Sylow
114C22×C47—21no—
115C22×C47—21no—
116C22×C47#38611yescharacteristic
117C22×C47#41711yescharacteristic
118C22×C47#41811yescharacteristic
119C2×D47—84no—
120C2×D47—84no—
121C2×D47—82no—
122C2×D47—82no—
123C2×D47—82no—
124C4×C47—21no—
125C4×C47—22no—
126C4×C47—42no—
127C4×C47—42no—
128C4×C47#45412yes—
129C4×C47#46812yes—
130C4×C47#46912yes—
131Dic47—82no—
132#2983D4711yescharacteristic, complemented
133#2548—471no—
134#1801—471no—
135#1545—472no—
136#1303—472no—
137C2×C47—21no—
138C2×C47—21no—
139C2×C47#188811yescharacteristic
140C2×C47#189511yescharacteristic
141C2×C47#191411yescharacteristic
142D47—162no—
143C2×#127—471no—
144C2×#124—941no—
145C2×C4×Q8C2×D4711yescharacteristic
146#446—24no—
147#432—22no—
148#431C2×D4712yes—
149#423—472no—
150C2×#101—941no—
151#394—474no—
152#390—941no—
153#390—942no—
154C4×C4⋊C4—471no—
155#343—941no—
156#331—944no—
157C47#940611yescharacteristic, complemented, Sylow
158C22×Q8D18811yescharacteristic
159C22×D4—472no—
160C22×D4—941no—
161C22×D4—941no—
162C2×M16—942no—
163#127—942no—
164#127—942no—
165#124—1884no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—941no—
169C2×C4⋊C4C4×D4712yes—
170C2×C4⋊C4D18811yescharacteristic
171C2×C22⋊C4—944no—
172C2×C22⋊C4—944no—
173C2×C42—941no—
174C2×C42C22⋊D4712yes—
175C2×C42C22×D4711yescharacteristic
176C4⋊C8—24no—
177C4⋊C8—942no—
178C4⋊C8—942no—
179C4⋊C8C22⋊D4714yes—
180#101—1882no—
181C22⋊C8—22no—
182#97—24no—
183C4×C8—22no—
184#95—472no—
185C24—942no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×D4—944no—
191C2×D4—3762no—
192C2×D4—1884no—
193C2×D4—1881no—
194C2×D4—1882no—
195C2×D4—1881no—
196C2×D4—1882no—
197C2×D4—1881no—
198C2×D4—1881no—
199C22×C4—942no—
200C22×C4(C2×D47)⋊C412yes—
201C22×C4(C2×D47)⋊C412yes—
202C22×C4C2×C4×D4711yescharacteristic
203C22×C4C2×D18811yescharacteristic
204C22×C4C2×C22⋊D4711yescharacteristic
205M16—1882no—
206M16—1882no—
207C2×C8—24no—
208C2×C8—1882no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—1882no—
212C22⋊C4—3764no—
213C22⋊C4—1888no—
214C42—22no—
215C42—22no—
216C42—1882no—
217C42#1062535012yes—
218C42C2×C22⋊D4712yes—
219C23—1884no—
220C23—1884no—
221C23—1882no—
222C23—1882no—
223C23—1882no—
224C23C2×(C2×D47)⋊C411yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—3764no—
228D4—3762no—
229D4—3762no—
230D4—3762no—
231D4—3762no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—1882no—
240C2×C4—1882no—
241C2×C4—1882no—
242C2×C4C4×C22⋊D4712yes—
243C2×C4#1309399311yescharacteristic
244C2×C4#1309399812yes—
245C2×C4#1309400711yescharacteristic
246C2×C4#1309405212yes—
247C2×C4#1309405211yescharacteristic
248C2×C4#1309405711yescharacteristic
249C8—44no—
250C8—3762no—
251C22—21no—
252C22—21no—
253C22—3764no—
254C22—3764no—
255C22—3762no—
256C22—3762no—
257C22—3762no—
258C22#1568900211yescharacteristic
259C22#1568912511yescharacteristic
260C22#1568912911yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—3762no—
266C4#1568929612yes—
267C4#1568936912yes—
268C4#1568937612yes—
269C2—21no—
270C2—21no—
271C2—7522no—
272C2#2024379111yescharacteristic
273C2#2024382611yescharacteristic
274C2#2024393511yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2983C2
socleC22×C47#386
prime radicalC2×#13094021C22
cosocleC2×C42×C47C23
hypercenter#2983D47
hypocenterC47#9406
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #20243384C2semidirect
4. #20241290C2semidirect
5. C47×#2983C2semidirect
132. #2983D47semidirect
157. C47#9406semidirect

Maximal subgroups

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

subgroupindex
#202483872
#202433842
#202420552
#202412902
C47×#29832
#940647