Finite Group Databasebeta

← #26129483

Subgroups — #26129483

Order 12032.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#20254163C211yesmaximal, characteristic
2#20245585C212yesmaximal, complemented
3#20241399C212yesmaximal, complemented
4#20241312C211yesmaximal, characteristic
5C47×#2075C211yesmaximal, characteristic
6C2×#13094003—21no—
7#15689459—22no—
8#15689364—21no—
9#15689364C2212yes—
10#15689281—22no—
11#15688950—22no—
12#15688926—22no—
13C22⋊(C47⋊C16)C2212yes—
14C2×#107×C47C2211yescharacteristic
15C2×C22⋊C8×C47C2211yescharacteristic
16C47×#380—21no—
17C47×#340—21no—
18C47×#340C2211yescharacteristic
19C22×Dic94—21no—
20C2×Dic188—21no—
21C2×Dic188D412yes—
22#13094003—22no—
23#13094003—22no—
24#13094003—41no—
25#13094003—41no—
26C2×C4⋊Dic47—21no—
27C2×Dic47⋊C4—41no—
28C2×C22⋊Dic47—41no—
29C2×C47⋊C16—22no—
30#13093958—21no—
31#13093958D412yes—
32#13093949—22no—
33#13093949—22no—
34C23×C4×C47D411yescharacteristic
35C22×C8×C47D411yescharacteristic
36C22×C8×C47C2311yescharacteristic
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C22⋊C4×C47—41no—
40#107×C47—22no—
41C22⋊C8×C47—22no—
42#95×C47—41no—
43C24×C47D811yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47—41no—
47C22×C4×C47—41no—
48C22×C4×C47—41no—
49C22×C4×C47—41no—
50C22×C4×C47D811yescharacteristic
51C22×C4×C47C2×D411yescharacteristic
52C22×Dic47—41no—
53C22×Dic47—41no—
54C2×Dic94—22no—
55C2×Dic94—41no—
56C2×Dic94—81no—
57C2×Dic94—81no—
58C2×C8×C47—21no—
59C2×C8×C47—41no—
60C2×C8×C47—41no—
61C2×C8×C47C2×D412yes—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—41no—
65C4⋊C4×C47—41no—
66C22⋊C4×C47—82no—
67C22⋊Dic47—42no—
68C22⋊Dic47—42no—
69C4⋊Dic47—22no—
70C4⋊Dic47—41no—
71Dic47⋊C4—42no—
72Dic47⋊C4—42no—
73Dic188—42no—
74Dic188—81no—
75C47⋊C16—42no—
76C23×C47—21no—
77C23×C47—21no—
78C23×C47—41no—
79C23×C47—41no—
80C23×C47SD3212yes—
81C23×C47C2×D811yescharacteristic
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—81no—
89C2×C4×C47—81no—
90C2×C4×C47—81no—
91C2×C4×C47—81no—
92C2×C4×C47—81no—
93C2×C4×C47—81no—
94C2×C4×C47—81no—
95C2×C4×C47#12011yescharacteristic
96C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
97C2×Dic47—42no—
98C2×Dic47—42no—
99C2×Dic47—82no—
100C2×Dic47—82no—
101Dic94—42no—
102Dic94—42no—
103Dic94—82no—
104C8×C47—22no—
105C8×C47—41no—
106#12279—471nomaximal, Sylow
107C22×C47—21no—
108C22×C47—21no—
109C22×C47—22no—
110C22×C47—42no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—81no—
114C22×C47#44711yescharacteristic
115C22×C47C2×SD3211yescharacteristic
116C22×C47#51011yescharacteristic
117C4×C47—21no—
118C4×C47—41no—
119C4×C47—161no—
120C4×C47—161no—
121C4×C47#45511yescharacteristic
122C4×C47#45811yescharacteristic
123Dic47—82no—
124Dic47—82no—
125#3189—471no—
126#2235—472no—
127#2075D4711yescharacteristic
128#1348—472no—
129#1314—471no—
130C2×C47—21no—
131C2×C47—21no—
132C2×C47—42no—
133C2×C47#160711yescharacteristic
134C2×C47#218511yescharacteristic
135C2×C47#219111yescharacteristic
136C2×C22⋊Q8—941no—
137#484—942no—
138#467—472no—
139#467—941no—
140#451—942no—
141C2×#107C2×D4711yescharacteristic
142C2×C22⋊C8C2×D4711yescharacteristic
143#380—21no—
144#367—942no—
145#358—942no—
146C22⋊C16—472no—
147#340—21no—
148#340C2×D4711yescharacteristic
149C47#1227911yescharacteristic, complemented, Sylow
150C22×Q8—941no—
151C23×C4C22⋊D4711yescharacteristic
152C2×Q16—472no—
153C2×Q16—941no—
154C22×C8C22⋊D4711yescharacteristic
155C22×C8C22×D4711yescharacteristic
156C22⋊Q8—942no—
157C22⋊Q8—942no—
158C22⋊Q8—1881no—
159C22⋊Q8—1881no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—941no—
163C2×C4⋊C4—1881no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—1881no—
166C2×C16—942no—
167#107—22no—
168#107—472no—
169#107—941no—
170#103—942no—
171#103—942no—
172C22⋊C8—22no—
173#95—41no—
174C24#1062533411yescharacteristic
175C2×Q8—942no—
176C2×Q8—3761no—
177C2×Q8—3761no—
178C2×Q8—1881no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—1881no—
186C22×C4—1881no—
187C22×C4#1062533411yescharacteristic
188C22×C4C2×C22⋊D4711yescharacteristic
189Q16—3761no—
190Q16—1882no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8D4×D4712yes—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—942no—
200C4⋊C4—1882no—
201C4⋊C4—1881no—
202C4⋊C4—1882no—
203C22⋊C4—82no—
204C22⋊C4—1882no—
205C22⋊C4—1882no—
206C16—1882no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#1309396812yes—
212C23C2×#1062533411yescharacteristic
213Q8—3762no—
214Q8—1882no—
215Q8—1882no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—3762no—
230C2×C4—3762no—
231C2×C4—1882no—
232C2×C4—1882no—
233C2×C4#1309399211yescharacteristic
234C2×C4#1309404911yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1568925611yescharacteristic
245C22C2×#1309396811yescharacteristic
246C22#1568956311yescharacteristic
247C4—21no—
248C4—41no—
249C4—161no—
250C4—161no—
251C4—3762no—
252C4—3762no—
253C4#1568930011yescharacteristic
254C4#1568931211yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#2024237311yescharacteristic
259C2#2024530411yescharacteristic
260C2#2024533811yescharacteristic
subgroupG/H
centerC22#15689256
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#2075C2
socleC22×C47#447
prime radicalC24×C47D8
hypercenter#2075D47
hypocenterC47#12279
LCSG ▷ C22×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2075

Complements

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

NH ≅ G/Ntype
2. #20245585C2semidirect
3. #20241399C2semidirect
149. C47#12279semidirect

Maximal subgroups

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

subgroupindex
#202541632
#202455852
#202413992
#202413122
C47×#20752
#1227947