Finite Group Databasebeta

← #26105620

Subgroups — #26105620

Order 12032.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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#20251381C211yesmaximal, characteristic
2#20244927C212yesmaximal
3#20241214C211yesmaximal, characteristic
4#20241213C212yesmaximal
5C47×#2095C211yesmaximal, characteristic
6C2×#13093957—22no—
7C2×#13093947—22no—
8#15689044—22no—
9#15689043—21no—
10#15689030—21no—
11#15689029C2212yes—
12#15689027—22no—
13#15688878C2212yes—
14C2×#107×C47—21no—
15C2×#103×C47—21no—
16C47×#391C2211yescharacteristic
17C47×#384C2211yescharacteristic
18C47×#336C2211yescharacteristic
19C22×Dic94—21no—
20C22×Dic94D412yes—
21C22×C47⋊C8—22no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47D412yes—
24C2×Dic47⋊C4—22no—
25C2×C4×Dic47—21no—
26#13093957—44no—
27#13093947—44no—
28C47⋊#95—21no—
29C47⋊#95—22no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C22×Q8×C47D411yescharacteristic
33C22×C8×C47—21no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47D411yescharacteristic
37C2×C42×C47C2311yescharacteristic
38#107×C47—42no—
39#103×C47—42no—
40#95×C47—22no—
41C2×Q8×C47—21no—
42C2×Q8×C47—41no—
43C2×Q8×C47—41no—
44C2×Q8×C47Q1612yes—
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47—41no—
48C22×C4×C47C2×D412yes—
49C22×C4×C47C2×D411yescharacteristic
50C22×Dic47—22no—
51C22×Dic47—22no—
52C2×Dic94—22no—
53C2×Dic94—42no—
54C2×Dic94—42no—
55C2×Dic94—82no—
56C2×Dic94—81no—
57C2×Dic94Q1614yes—
58C2×C8×C47—22no—
59C2×C8×C47—41no—
60C2×C8×C47—41no—
61C4⋊C4×C47—41no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—42no—
65C4⋊C4×C47—42no—
66C42×C47—41no—
67C4⋊Dic47—42no—
68C4⋊Dic47—81no—
69Dic47⋊C4—82no—
70C4×Dic47—81no—
71C2×C47⋊C8—24no—
72C2×C47⋊C8—42no—
73C2×C47⋊C8—42no—
74C23×C47#12011yescharacteristic
75Q8×C47—42no—
76Q8×C47—81no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—42no—
85C2×C4×C47—41no—
86C2×C4×C47—82no—
87C2×C4×C47—81no—
88C2×C4×C47C2×Q1612yes—
89C2×C4×C47C2×Q1611yescharacteristic
90C2×C4×C47#13711yescharacteristic
91C2×C4×C47#13712yes—
92C2×Dic47—24no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98Dic94—44no—
99Dic94—82no—
100Dic94—84no—
101C8×C47—42no—
102C47⋊C8—44no—
103#7837—471nomaximal, Sylow
104C22×C47#45112yes—
105C22×C47#45111yescharacteristic
106C22×C47#45312yes—
107C22×C47#45311yescharacteristic
108C22×C47#45811yescharacteristic
109C4×C47—22no—
110C4×C47—21no—
111C4×C47—22no—
112C4×C47—21no—
113C4×C47—42no—
114C4×C47—81no—
115C4×C47—161no—
116Dic47—44no—
117Dic47—82no—
118#2811—471no—
119#2095—472no—
120#2095D4711yescharacteristic
121#1272—471no—
122#1272—472no—
123C2×C47#161412yes—
124C2×C47#161411yescharacteristic
125C2×C47#163311yescharacteristic
126C2×C47#163312yes—
127C2×C47#165511yescharacteristic
128C2×#107—21no—
129C2×#107—942no—
130C2×#103—21no—
131C2×#103—942no—
132#395—942no—
133#395—941no—
134#391—472no—
135#391—942no—
136#391—941no—
137#391C2×D4711yescharacteristic
138#384C2×D4711yescharacteristic
139#336—472no—
140#336C2×D4711yescharacteristic
141C47#783711yescharacteristic, complemented, Sylow
142C22×Q8—472no—
143C22×Q8—941no—
144C22×Q8C22⋊D4711yescharacteristic
145C22×C8—21no—
146C22×C8—942no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—472no—
150C2×C4⋊C4—942no—
151C2×C4⋊C4—941no—
152C2×C4⋊C4C22⋊D4711yescharacteristic
153C2×C42—941no—
154C2×C42C22×D4711yescharacteristic
155#107—42no—
156#107—1884no—
157#103—42no—
158#103—1884no—
159#95—22no—
160#95—942no—
161#95—941no—
162#95—942no—
163#95—942no—
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—474no—
168C2×Q8—942no—
169C2×Q8—3762no—
170C2×Q8—3761no—
171C2×Q8—1882no—
172C2×Q8—1882no—
173C2×Q8#1062533712yes—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—942no—
178C22×C4—942no—
179C22×C4D4×D4712yes—
180C22×C4C2×C22⋊D4711yescharacteristic
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—944no—
185C2×C8—1882no—
186C2×C8—1882no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—3762no—
193C4⋊C4—3761no—
194C4⋊C4—1882no—
195C42—41no—
196C42—3761no—
197C23#1309399211yescharacteristic
198Q8—42no—
199Q8—81no—
200Q8—3762no—
201Q8—3764no—
202Q8—1884no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—82no—
213C2×C4—81no—
214C2×C4—944no—
215C2×C4—1882no—
216C2×C4—1882no—
217C2×C4—1882no—
218C2×C4—1882no—
219C2×C4—1882no—
220C2×C4Q16×D4712yes—
221C2×C4C2×#1062533711yescharacteristic
222C2×C4#1309405411yescharacteristic
223C2×C4#1309405612yes—
224C8—42no—
225C8—1884no—
226C22#1568927712yes—
227C22#1568927811yescharacteristic
228C22#1568928912yes—
229C22#1568929011yescharacteristic
230C22#1568931211yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—161no—
238C4—3762no—
239C4—1884no—
240C2#2024241112yes—
241C2#2024241211yescharacteristic
242C2#2024252611yescharacteristic
243C2#2024252712yes—
244C2#2024267611yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2095C2
socle, prime radicalC23×C47#120
hypercenter#2095D47
hypocenterC47#7837
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
141. C47#7837semidirect

Maximal subgroups

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

subgroupindex
#202513812
#202449272
#202412142
#202412132
C47×#20952
#783747