Finite Group Databasebeta

← #26133958

Subgroups — #26133958

Order 12032.

262 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244137C211yesmaximal, characteristic
2#20243269C211yesmaximal, characteristic
3#20241483C211yesmaximal, characteristic
4#20241483C211yesmaximal, characteristic
5#20241482C211yesmaximal, characteristic
6#20241465C211yesmaximal, characteristic
7C47×#2158C211yesmaximal, characteristic
8C22×C47⋊C16C2211yescharacteristic
9C2×#13093960C2211yescharacteristic
10C2×#13093960C2211yescharacteristic
11#15689150—21no—
12#15689079—21no—
13C2×C8×Dic47C2211yescharacteristic
14#15688882—21no—
15#15688882—21no—
16C22×C16×C47C2211yescharacteristic
17C47×#427C2211yescharacteristic
18C47×#427C2211yescharacteristic
19C47×#367C411yescharacteristic, complemented
20C47×#367C411yescharacteristic, complemented
21C47×#366C411yescharacteristic, complemented
22C47×#366C411yescharacteristic, complemented
23C2×#10625329—21no—
24C2×#10625329—21no—
25C22×C47⋊C8D411yescharacteristic
26C2×C4×Dic47D411yescharacteristic
27C2×C47⋊C16—21no—
28C2×C47⋊C16—21no—
29C2×C47⋊C16—21no—
30#13093960—21no—
31#13093960—21no—
32#13093960—21no—
33#13093960Q812yes—
34C4⋊(C47⋊C8)—41no—
35C4⋊(C47⋊C8)—41no—
36#13093935—41no—
37C4×C47⋊C8—41no—
38C8×Dic47—21no—
39C8×Dic47—21no—
40C22×C8×C47C2311yescharacteristic
41#117×C47—21no—
42#117×C47—21no—
43C2×C16×C47—21no—
44C2×C16×C47—21no—
45C2×C16×C47C2×C411yescharacteristic
46C2×C16×C47C2×C411yescharacteristic
47#107×C47C2×C411yescharacteristic
48#107×C47C2×C411yescharacteristic
49#107×C47C2×C411yescharacteristic
50#107×C47C2×C411yescharacteristic
51#106×C47—21no—
52#106×C47—21no—
53C22×C4×C47C2×D411yescharacteristic
54C22×Dic47—21no—
55C2×C8×C47C22×C411yescharacteristic
56C2×C8×C47C2×Q811yescharacteristic
57C2×C8×C47#4111yescharacteristic
58C2×C8×C47#4111yescharacteristic
59C2×C8×C47#4111yescharacteristic
60C2×C8×C47#4111yescharacteristic
61C4⋊C4×C47—21no—
62C4⋊C4×C47—21no—
63C4⋊C4×C47—21no—
64C4⋊C4×C47—21no—
65C22⋊C4×C47—41no—
66C22⋊C4×C47—41no—
67C42×C47—41no—
68C42×C47—41no—
69C4×Dic47—21no—
70C4×Dic47—21no—
71#10625329—22no—
72#10625329—41no—
73#10625329—41no—
74#10625329—41no—
75C2×C47⋊C8—21no—
76C2×C47⋊C8—21no—
77C2×C47⋊C8—41no—
78C2×C47⋊C8—41no—
79C2×C47⋊C8D811yescharacteristic
80C2×C47⋊C8D811yescharacteristic
81C16×C47—21no—
82C16×C47—21no—
83C47⋊C16—41no—
84C23×C47#13511yescharacteristic
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—41no—
89C2×C4×C47C4×D411yescharacteristic
90C2×C4×C47C22⋊Q811yescharacteristic
91C2×C4×C47#12311yescharacteristic
92C2×C4×C47C2×D811yescharacteristic
93C2×C4×C47#13711yescharacteristic
94C2×C4×C47#13711yescharacteristic
95C2×Dic47—22no—
96C2×Dic47—41no—
97C2×Dic47—41no—
98C8×C47#11711yescharacteristic
99C8×C47C4×Q811yescharacteristic
100C8×C47#12511yescharacteristic
101C8×C47#12611yescharacteristic
102C47⋊C8—21no—
103C47⋊C8—21no—
104C47⋊C8—42no—
105C47⋊C8—81no—
106#13113—471nomaximal, Sylow
107C22×C47—21no—
108C22×C47—21no—
109C22×C47C4×D811yescharacteristic
110C22×C47#47911yescharacteristic
111C22×C47#48511yescharacteristic
112C4×C47—81no—
113C4×C47—81no—
114C4×C47—81no—
115C4×C47—81no—
116C4×C47#38711yescharacteristic
117C4×C47#44111yescharacteristic
118C4×C47#47411yescharacteristic
119C4×C47#48011yescharacteristic
120Dic47—42no—
121#2158D4711yescharacteristic
122#1945—471no—
123#1772—471no—
124#1382—471no—
125#1382—471no—
126#1381—471no—
127#1374—471no—
128C2×C47—21no—
129C2×C47—21no—
130C2×C47#191811yescharacteristic
131C2×C47#217811yescharacteristic
132C2×C47#217911yescharacteristic
133C22×C16—471no—
134C22×C16C2×D4711yescharacteristic
135C2×#108—471no—
136C2×#108—471no—
137#427C2×D4711yescharacteristic
138#427C2×D4711yescharacteristic
139#424—941no—
140#405—941no—
141C2×C4×C8—471no—
142#367Dic4711yescharacteristic, complemented
143#367Dic4711yescharacteristic, complemented
144#366Dic4711yescharacteristic, complemented
145#366Dic4711yescharacteristic, complemented
146#339—941no—
147#339—941no—
148C47#1311311yescharacteristic, complemented, Sylow
149C2×M16—941no—
150C2×M16—941no—
151C22×C8—471no—
152C22×C8C22×D4711yescharacteristic
153#117—21no—
154#117—21no—
155C2×C42—471no—
156C2×C16—21no—
157C2×C16—21no—
158C2×C16—941no—
159C2×C16—941no—
160C2×C16—941no—
161C2×C16C2×Dic4711yescharacteristic
162C2×C16C2×Dic4711yescharacteristic
163#108—472no—
164#108—941no—
165#108—941no—
166#108—941no—
167#107C2×Dic4711yescharacteristic
168#107C2×Dic4711yescharacteristic
169#107C2×Dic4711yescharacteristic
170#107C2×Dic4711yescharacteristic
171#106—21no—
172#106—21no—
173C4⋊C8—1881no—
174C4⋊C8—1881no—
175#97—1881no—
176C4×C8—941no—
177C4×C8—941no—
178C4×C8—1881no—
179C22×C4—941no—
180C22×C4D4×D4711yescharacteristic
181M16—942no—
182M16—1881no—
183M16—1881no—
184M16—1881no—
185C2×C8—471no—
186C2×C8—471no—
187C2×C8—941no—
188C2×C8—941no—
189C2×C8—1881no—
190C2×C8—1881no—
191C2×C8#1062535011yescharacteristic
192C2×C8#1062535011yescharacteristic
193C2×C8#1062535211yescharacteristic
194C2×C8Q8×D4711yescharacteristic
195C2×C8#1062535411yescharacteristic
196C2×C8C22×Dic4711yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C42—41no—
204C42—41no—
205C42—941no—
206C42—941no—
207C16—21no—
208C16—21no—
209C16—1881no—
210C23#1309404311yescharacteristic
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—942no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4D4×Dic4711yescharacteristic
219C2×C4#1309400211yescharacteristic
220C2×C4#1309400911yescharacteristic
221C2×C4D8×D4711yescharacteristic
222C2×C4#1309405611yescharacteristic
223C2×C4#1309405611yescharacteristic
224C8—941no—
225C8—941no—
226C8—3761no—
227C8—1882no—
228C8#1309398311yescharacteristic
229C8Q8×Dic4711yescharacteristic
230C8#1309401411yescharacteristic
231C8#1309401911yescharacteristic
232C22—21no—
233C22—21no—
234C22D8×Dic4711yescharacteristic
235C22#1568942911yescharacteristic
236C22#1568946611yescharacteristic
237C4—81no—
238C4—81no—
239C4—81no—
240C4—81no—
241C4—1882no—
242C4#1568900911yescharacteristic
243C4#1568923011yescharacteristic
244C4#1568940211yescharacteristic
245C4#1568943811yescharacteristic
246C2—21no—
247C2—21no—
248C2#2024396111yescharacteristic
249C2#2024526911yescharacteristic
250C2#2024527411yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2158C2
socleC22×C47C4×D8
prime radicalC23×C47#135
cosocleC22×C8×C47C23
hypercenter#2158D47
hypocenterC47#13113
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
19. C47×#367C4semidirect
20. C47×#367C4semidirect
21. C47×#366C4semidirect
22. C47×#366C4semidirect
142. #367Dic47semidirect
143. #367Dic47semidirect
144. #366Dic47semidirect
145. #366Dic47semidirect
148. C47#13113semidirect

Maximal subgroups

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

subgroupindex
#202441372
#202432692
#202414832
#202414822
#202414652
C47×#21582
#1311347