Finite Group Databasebeta

← #26129562

Subgroups — #26129562

Order 12032.

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

normal subgroups only

This group has 310 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#20254733C211yesmaximal, characteristic
2#20245590C212yesmaximal
3#20241399C212yesmaximal
4#20241328C211yesmaximal, characteristic
5C47×#2087C211yesmaximal, characteristic
6#15689680—21no—
7#15689419—22no—
8#15689364—21no—
9#15689364C2212yes—
10#15689334—22no—
11#15688948—22no—
12#15688926—22no—
13C22⋊(C47⋊C16)C2212yes—
14C2×#107×C47C2211yescharacteristic
15C2×C4⋊C8×C47C2211yescharacteristic
16C47×#389—21no—
17C47×#340—21no—
18C47×#340C2211yescharacteristic
19C2×Dic188—21no—
20C2×Dic188D412yes—
21#13094024—21no—
22#13094024—21no—
23#13094016—41no—
24#13094003—22no—
25#13094003—41no—
26C4×Dic94—22no—
27C4×Dic94—41no—
28#13093983—41no—
29C2×C47⋊C16—22no—
30#13093958—21no—
31#13093958D412yes—
32#13093949—22no—
33#13093949—22no—
34C22×C8×C47D411yescharacteristic
35C22×C8×C47C2311yescharacteristic
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—41no—
39C2×C42×C47D411yescharacteristic
40#107×C47—22no—
41C4⋊C8×C47—22no—
42#95×C47—41no—
43C22×C4×C47—41no—
44C22×C4×C47—41no—
45C22×C4×C47D811yescharacteristic
46C22×C4×C47D811yescharacteristic
47C22×C4×C47C2×D411yescharacteristic
48C2×Dic94—22no—
49C2×Dic94—41no—
50C2×C8×C47—21no—
51C2×C8×C47—41no—
52C2×C8×C47—41no—
53C2×C8×C47C2×D412yes—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—41no—
57C4⋊C4×C47—41no—
58C4⋊C4×C47—82no—
59C42×C47—21no—
60C42×C47—21no—
61C22⋊Dic47—42no—
62C4⋊Dic47—22no—
63C4⋊Dic47—41no—
64C4⋊Dic47—41no—
65C4⋊Dic47—41no—
66Dic47⋊C4—42no—
67Dic47⋊C4—42no—
68C4×Dic47—42no—
69Dic188—42no—
70Dic188—81no—
71C47⋊C16—42no—
72C23×C47C2×D811yescharacteristic
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—41no—
79C2×C4×C47—42no—
80C2×C4×C47—81no—
81C2×C4×C47—81no—
82C2×C4×C47—81no—
83C2×C4×C47—81no—
84C2×C4×C47—81no—
85C2×C4×C47Q3212yes—
86C2×C4×C47#12011yescharacteristic
87C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
88C2×Dic47—42no—
89C2×Dic47—42no—
90Dic94—42no—
91Dic94—42no—
92Dic94—82no—
93C8×C47—22no—
94C8×C47—41no—
95#12292—471nomaximal, Sylow
96C22×C47—21no—
97C22×C47—21no—
98C22×C47#44711yescharacteristic
99C22×C47C2×Q3211yescharacteristic
100C22×C47#51011yescharacteristic
101C4×C47—21no—
102C4×C47—22no—
103C4×C47—41no—
104C4×C47—82no—
105C4×C47—161no—
106C4×C47#45611yescharacteristic
107C4×C47#45811yescharacteristic
108Dic47—82no—
109Dic47—82no—
110#3249—471no—
111#2236—472no—
112#2087D4711yescharacteristic
113#1348—472no—
114#1322—471no—
115C2×C47—21no—
116C2×C47—21no—
117C2×C47#161011yescharacteristic
118C2×C47#218811yescharacteristic
119C2×C47#219011yescharacteristic
120#533—941no—
121#477—942no—
122#467—472no—
123#467—941no—
124#462—942no—
125C2×#107C2×D4711yescharacteristic
126C2×C4⋊C8C2×D4711yescharacteristic
127#389—21no—
128#366—942no—
129#358—942no—
130C22⋊C16—472no—
131#340—21no—
132#340C2×D4711yescharacteristic
133C47#1229211yescharacteristic, complemented, Sylow
134C2×Q16—472no—
135C2×Q16—941no—
136C22×C8C22⋊D4711yescharacteristic
137C22×C8C22×D4711yescharacteristic
138C4⋊Q8—941no—
139C4⋊Q8—941no—
140#125—1881no—
141C22⋊Q8—942no—
142C22⋊Q8—1881no—
143C4×Q8—942no—
144C4×Q8—1881no—
145#117—1881no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C42C22⋊D4711yescharacteristic
150C2×C16—942no—
151#107—22no—
152#107—472no—
153#107—941no—
154C4⋊C8—22no—
155#103—942no—
156#103—942no—
157#95—41no—
158C2×Q8—942no—
159C2×Q8—1881no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#1062533411yescharacteristic
163C22×C4#1062533411yescharacteristic
164C22×C4C2×C22⋊D4711yescharacteristic
165Q16—3761no—
166Q16—1882no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D4712yes—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—82no—
176C4⋊C4—942no—
177C4⋊C4—1882no—
178C4⋊C4—1881no—
179C4⋊C4—1881no—
180C4⋊C4—1881no—
181C4⋊C4—1882no—
182C22⋊C4—1882no—
183C42—21no—
184C42—21no—
185C42—1882no—
186C16—1882no—
187C23C2×#1062533411yescharacteristic
188Q8—3762no—
189Q8—1882no—
190Q8—1882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—1882no—
204C2×C4—1882no—
205C2×C4#1309397012yes—
206C2×C4#1309399211yescharacteristic
207C2×C4#1309404911yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1568925611yescharacteristic
213C22C2×#1309397011yescharacteristic
214C22#1568956311yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—82no—
219C4—161no—
220C4—3762no—
221C4—3762no—
222C4#1568930511yescharacteristic
223C4#1568931211yescharacteristic
224C2—21no—
225C2—21no—
226C2#2024239011yescharacteristic
227C2#2024532111yescharacteristic
228C2#2024533311yescharacteristic
subgroupG/H
centerC22#15689256
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#2087C2
socleC22×C47#447
prime radicalC23×C47C2×D8
hypercenter#2087D47
hypocenterC47#12292
LCSG ▷ C22×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
133. C47#12292semidirect

Maximal subgroups

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

subgroupindex
#202547332
#202455902
#202413992
#202413282
C47×#20872
#1229247