Finite Group Databasebeta

← #26113668

Subgroups — #26113668

Order 12032.

574 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 135 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×#2982C211yesmaximal, 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
17C8×Q8×C47—24no—
18C47×#431—22no—
19C47×#431C2212yes—
20C22×D188—21no—
21C22×D188—21no—
22C22×D188C2×C412yes—
23C2×#10625329—22no—
24#13094021—22no—
25#13094021—22no—
26#13094013—42no—
27#13094013—42no—
28C2×C4⋊Dic47—21no—
29C2×(C2×D47)⋊C4—24no—
30C2×(C2×D47)⋊C4—24no—
31C2×C4×Dic47—21no—
32C4⋊(C47⋊C8)—22no—
33C4⋊(C47⋊C8)—22no—
34#13093943—42no—
35C47⋊#95C2×C412yes—
36C22×Q8×C47D411yescharacteristic
37C4×Q8×C47—22no—
38C4×Q8×C47—22no—
39C2×C4⋊C4×C47C2×C412yes—
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C42×C47D412yes—
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47—24no—
44C4⋊C8×C47D414yes—
45C22⋊C8×C47—22no—
46C4×C8×C47—24no—
47C4×C8×C47—22no—
48C23×D47—22no—
49C2×Q8×C47—22no—
50C2×Q8×C47—22no—
51C2×Q8×C47D812yes—
52C2×Q8×C47SD1612yes—
53C22×C4×C47C22⋊C412yes—
54C22×C4×C47C22⋊C412yes—
55C22×C4×C47C22×C411yescharacteristic
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47C2×D411yescharacteristic
58C22×Dic47—22no—
59C2×D188—24no—
60C2×D188—44no—
61C2×D188—41no—
62C2×D188—42no—
63C2×D188—41no—
64C2×D188—41no—
65C2×D188—41no—
66C2×D188—42no—
67C2×D188—82no—
68C2×C8×C47—24no—
69C4⋊C4×C47—24no—
70C4⋊C4×C47—22no—
71C42×C47—22no—
72C42×C47—22no—
73C42×C47C2×D412yes—
74C42×C47#4112yes—
75(C2×D47)⋊C4—48no—
76(C2×D47)⋊C4—84no—
77C4⋊Dic47—42no—
78C4×Dic47—41no—
79C4×Dic47—41no—
80#10625329—42no—
81#10625329—42no—
82C2×C47⋊C8—42no—
83C23×C47C2×C22⋊C411yescharacteristic
84C22×D47—44no—
85C22×D47—44no—
86C22×D47—42no—
87C22×D47—42no—
88C22×D47—42no—
89Q8×C47—24no—
90Q8×C47—24no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—41no—
96C2×C4×C47—42no—
97C2×C4×C47#10214yes—
98C2×C4×C47C4×D412yes—
99C2×C4×C47#12011yescharacteristic
100C2×C4×C47#12112yes—
101C2×C4×C47#12311yescharacteristic
102C2×C4×C47C2×D811yescharacteristic
103C2×C4×C47C2×SD1611yescharacteristic
104C2×C4×C47#13512yes—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108D188—84no—
109D188—82no—
110D188—82no—
111D188—82no—
112D188—82no—
113C8×C47—44no—
114C47⋊C8—82no—
115#9398—471nomaximal, Sylow
116C22×C47—21no—
117C22×C47—21no—
118C22×C47#38611yescharacteristic
119C22×C47C2×#10211yescharacteristic
120C22×C47#41611yescharacteristic
121C2×D47—84no—
122C2×D47—84no—
123C2×D47—82no—
124C2×D47—82no—
125C2×D47—82no—
126C4×C47—21no—
127C4×C47—24no—
128C4×C47—22no—
129C4×C47—42no—
130C4×C47#45412yes—
131C4×C47#46512yes—
132C4×C47#46612yes—
133Dic47—82no—
134#2982D4711yescharacteristic, complemented
135#2548—471no—
136#1801—471no—
137#1545—472no—
138#1303—472no—
139C2×C47—21no—
140C2×C47—21no—
141C2×C47#188811yescharacteristic
142C2×C47#189311yescharacteristic
143C2×C47#191411yescharacteristic
144D47—162no—
145C2×#127—471no—
146C2×#124—941no—
147C2×C4×Q8C2×D4711yescharacteristic
148C8×Q8—24no—
149#431—22no—
150#431C2×D4712yes—
151#423—472no—
152C2×#101—941no—
153#394—474no—
154#390—941no—
155#390—942no—
156C4×C4⋊C4—471no—
157#343—941no—
158#331—944no—
159C47#939811yescharacteristic, complemented, Sylow
160C22×Q8D18811yescharacteristic
161C22×D4—472no—
162C22×D4—941no—
163C22×D4—941no—
164C2×M16—942no—
165#127—942no—
166#127—942no—
167#124—1882no—
168#124—1882no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—941no—
172C2×C4⋊C4C4×D4712yes—
173C2×C4⋊C4D18811yescharacteristic
174C2×C22⋊C4—944no—
175C2×C22⋊C4—944no—
176C2×C42—941no—
177C2×C42C22⋊D4712yes—
178C2×C42C22×D4711yescharacteristic
179C4⋊C8—24no—
180C4⋊C8—942no—
181C4⋊C8—942no—
182C4⋊C8C22⋊D4714yes—
183#101—1882no—
184C22⋊C8—22no—
185C4×C8—24no—
186C4×C8—22no—
187#95—472no—
188C24—942no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8#1062532512yes—
192C2×Q8D37612yes—
193C2×D4—944no—
194C2×D4—3762no—
195C2×D4—1884no—
196C2×D4—1881no—
197C2×D4—1882no—
198C2×D4—1881no—
199C2×D4—1881no—
200C2×D4—1881no—
201C2×D4—1882no—
202C22×C4—942no—
203C22×C4(C2×D47)⋊C412yes—
204C22×C4(C2×D47)⋊C412yes—
205C22×C4C2×C4×D4711yescharacteristic
206C22×C4C2×D18811yescharacteristic
207C22×C4C2×C22⋊D4711yescharacteristic
208M16—1882no—
209M16—1882no—
210C2×C8—24no—
211C2×C8—1882no—
212C4⋊C4—24no—
213C4⋊C4—22no—
214C4⋊C4—1882no—
215C22⋊C4—3764no—
216C22⋊C4—1888no—
217C42—22no—
218C42—22no—
219C42—1881no—
220C42—1881no—
221C42#1062535012yes—
222C42C2×C22⋊D4712yes—
223C23—1884no—
224C23—1884no—
225C23—1882no—
226C23—1882no—
227C23—1882no—
228C23C2×(C2×D47)⋊C411yescharacteristic
229Q8—24no—
230Q8—24no—
231D4—3764no—
232D4—3762no—
233D4—3762no—
234D4—3762no—
235D4—3762no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—1882no—
243C2×C4—1882no—
244C2×C4—1882no—
245C2×C4#1309394614yes—
246C2×C4C4×C22⋊D4712yes—
247C2×C4#1309399311yescharacteristic
248C2×C4#1309399812yes—
249C2×C4#1309400711yescharacteristic
250C2×C4C2×D37611yescharacteristic
251C2×C4C2×#1062532511yescharacteristic
252C2×C4#1309404612yes—
253C8—44no—
254C8—3762no—
255C22—21no—
256C22—21no—
257C22—3764no—
258C22—3764no—
259C22—3762no—
260C22—3762no—
261C22—3762no—
262C22#1568900211yescharacteristic
263C22C2×#1309394611yescharacteristic
264C22#1568912011yescharacteristic
265C4—21no—
266C4—24no—
267C4—22no—
268C4—42no—
269C4—3762no—
270C4#1568929612yes—
271C4#1568935212yes—
272C4#1568935912yes—
273C2—21no—
274C2—21no—
275C2—7522no—
276C2#2024379111yescharacteristic
277C2#2024381611yescharacteristic
278C2#2024393511yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2982C2
socleC22×C47#386
prime radicalC2×#13094021C22
cosocleC2×C42×C47C23
hypercenter#2982D47
hypocenterC47#9398
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #20243384C2semidirect
4. #20241290C2semidirect
5. C47×#2982C2semidirect
134. #2982D47semidirect
159. C47#9398semidirect

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×#29822
#939847