Finite Group Databasebeta

← #26129074

Subgroups — #26129074

Order 12032.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#20249053C211yesmaximal, characteristic
2#20242413C212yesmaximal
3#20241411C212yesmaximal
4#20241318C211yesmaximal, characteristic
5C47×#2030C211yesmaximal, characteristic
6#15689456—22no—
7#15689059C2212yes—
8#15689035—21no—
9#15689027—22no—
10#15689010—22no—
11C4×C22⋊Dic47—21no—
12#15688860—22no—
13#15688847C2212yes—
14C47×#543C2211yescharacteristic
15C47×#381—21no—
16C47×#381C2211yescharacteristic
17C47×#342—21no—
18C47×#342C2211yescharacteristic
19C22×Dic94—21no—
20C2×C4⋊Dic47D412yes—
21C2×Dic47⋊C4—22no—
22C2×C22⋊Dic47—22no—
23C2×C4×Dic47—21no—
24C2×C4×Dic47—21no—
25#13093957—42no—
26#13093948—42no—
27C22⋊(C47⋊C8)—22no—
28C47⋊#95—22no—
29C47⋊#95—21no—
30C47⋊#95—22no—
31C47⋊#95D412yes—
32C23×C4×C47D411yescharacteristic
33C22⋊Q8×C47—22no—
34C22⋊Q8×C47—42no—
35C2×C22⋊C4×C47—21no—
36C2×C22⋊C4×C47—21no—
37C2×C22⋊C4×C47D411yescharacteristic
38C2×C22⋊C4×C47C2311yescharacteristic
39#95×C47—22no—
40#95×C47—42no—
41C24×C47C2×D411yescharacteristic
42C2×Q8×C47—22no—
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47—22no—
47C22×C4×C47—41no—
48C22×C4×C47—41no—
49C22×C4×C47—41no—
50C22×C4×C47Q1612yes—
51C22×C4×C47C2×D412yes—
52C22×Dic47—22no—
53C22×Dic47—22no—
54C2×Dic94—44no—
55C2×Dic94—81no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—42no—
58C22⋊C4×C47—41no—
59C22⋊C4×C47—41no—
60C22⋊C4×C47—41no—
61C22⋊C4×C47—41no—
62C22⋊C4×C47—41no—
63C22⋊C4×C47—41no—
64C22⋊Dic47—44no—
65C4⋊Dic47—42no—
66Dic47⋊C4—44no—
67C4×Dic47—81no—
68C4×Dic47—81no—
69C2×C47⋊C8—42no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47—42no—
73C23×C47#12011yescharacteristic
74C23×C47C2×Q1611yescharacteristic
75C23×C47#13711yescharacteristic
76Q8×C47—82no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—41no—
85C2×C4×C47—42no—
86C2×C4×C47—81no—
87C2×C4×C47—82no—
88C2×C4×C47—81no—
89C2×C4×C47—82no—
90C2×Dic47—24no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—42no—
96Dic94—84no—
97C47⋊C8—82no—
98#12216—471nomaximal, Sylow
99C22×C47—22no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—42no—
105C22×C47—81no—
106C22×C47#45111yescharacteristic
107C22×C47#45511yescharacteristic
108C22×C47B(4,𝔽2)11yescharacteristic
109C4×C47—42no—
110C4×C47—42no—
111C4×C47—81no—
112C4×C47—82no—
113C4×C47—161no—
114Dic47—44no—
115Dic47—82no—
116#2607—471no—
117#2030D4711yescharacteristic
118#1614—472no—
119#1352—472no—
120#1317—471no—
121C2×C47—21no—
122C2×C47—21no—
123C2×C47—41no—
124C2×C47—41no—
125C2×C47#160211yescharacteristic
126C2×C47#219812yes—
127#543C2×D4711yescharacteristic
128#484—942no—
129#399—472no—
130#393—941no—
131#391—942no—
132#387—942no—
133#381—21no—
134#381C2×D4711yescharacteristic
135C4×C22⋊C4—941no—
136#342—21no—
137#342C2×D4711yescharacteristic
138#328—942no—
139#323—472no—
140C47#1221611yescharacteristic, complemented, Sylow
141C22×Q8—941no—
142C23×C4C22⋊D4711yescharacteristic
143C22⋊Q8—22no—
144C22⋊Q8—42no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—942no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—942no—
150C2×C22⋊C4C22⋊D4711yescharacteristic
151C2×C22⋊C4C22×D4711yescharacteristic
152C2×C42—941no—
153C2×C42—941no—
154#107—1882no—
155#103—1882no—
156C22⋊C8—942no—
157#95—22no—
158#95—42no—
159#95—472no—
160#95—942no—
161#95—941no—
162#95—942no—
163C24C2×C22⋊D4711yescharacteristic
164C2×Q8—22no—
165C2×Q8—3761no—
166C2×Q8—1884no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—942no—
175C22×C4—942no—
176C22×C4#1062533712yes—
177C22×C4D4×D4712yes—
178C2×C8—1882no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—1882no—
182C4⋊C4—1884no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—41no—
189C22⋊C4—1884no—
190C42—3761no—
191C42—3761no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23#1309399211yescharacteristic
196C23C2×#1062533711yescharacteristic
197C23#1309405411yescharacteristic
198Q8—82no—
199Q8—3764no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—82no—
213C2×C4—944no—
214C2×C4—1882no—
215C2×C4—1882no—
216C2×C4—1882no—
217C2×C4—1882no—
218C2×C4—1882no—
219C8—3762no—
220C22—22no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22#1568927811yescharacteristic
228C22#1568930011yescharacteristic
229C22#1568930911yescharacteristic
230C4—42no—
231C4—42no—
232C4—81no—
233C4—82no—
234C4—161no—
235C4—3762no—
236C4—1884no—
237C2—21no—
238C2—21no—
239C2—41no—
240C2—41no—
241C2#2024234411yescharacteristic
242C2#2024538212yes—
subgroupG/H
centerC22#15689309
commutator, cosocleC2×C22⋊C4×C47C23
FrattiniC2×C22⋊C4C22×D47
FittingC47×#2030C2
socleC22×C47B(4,𝔽2)
prime radicalC24×C47C2×D4
hypercenter#2030D47
hypocenterC47#12216
LCSG ▷ C2×C22⋊C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
140. C47#12216semidirect

Maximal subgroups

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

subgroupindex
#202490532
#202424132
#202414112
#202413182
C47×#20302
#1221647