Finite Group Databasebeta

← #26105119

Subgroups — #26105119

Order 12032.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#20251376C211yesmaximal, characteristic
2#20244718C212yesmaximal
3#20241214C211yesmaximal, characteristic
4#20241210C212yesmaximal
5C47×#2016C211yesmaximal, characteristic
6C2×#13093955—22no—
7#15689062—21no—
8#15689055—22no—
9#15689030—21no—
10#15689021C2212yes—
11#15689010—22no—
12#15688885—22no—
13#15688878C2212yes—
14C22×Q16×C47—21no—
15C2×C4⋊Q8×C47C2211yescharacteristic
16C2×#103×C47—21no—
17C47×#391C2211yescharacteristic
18C47×#336C2211yescharacteristic
19C22×C47⋊C8—22no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47D412yes—
23C2×C4⋊Dic47D412yes—
24C2×Dic47⋊C4—22no—
25C2×C4×Dic47—21no—
26#13093955—44no—
27C47⋊#95—21no—
28C47⋊#95—22no—
29C47⋊#95—22no—
30C47⋊#95—22no—
31C22×Q8×C47—21no—
32C22×Q8×C47D411yescharacteristic
33C2×Q16×C47—42no—
34C2×Q16×C47—42no—
35C2×Q16×C47—42no—
36C22×C8×C47—21no—
37C4⋊Q8×C47—42no—
38C2×C4⋊C4×C47—22no—
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C42×C47C2311yescharacteristic
41#103×C47—42no—
42#95×C47—22no—
43C2×Q8×C47—21no—
44C2×Q8×C47—22no—
45C2×Q8×C47—41no—
46C2×Q8×C47—41no—
47C2×Q8×C47—41no—
48C2×Q8×C47—41no—
49C2×Q8×C47—41no—
50C2×Q8×C47—41no—
51C2×Q8×C47—41no—
52C2×Q8×C47SD1612yes—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—41no—
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47C2×D412yes—
58C22×Dic47—22no—
59C22×Dic47—22no—
60Q16×C47—48no—
61C2×C8×C47—22no—
62C2×C8×C47—41no—
63C2×C8×C47—41no—
64C4⋊C4×C47—24no—
65C4⋊C4×C47—42no—
66C4⋊C4×C47—41no—
67C42×C47—41no—
68C4⋊Dic47—22no—
69C4⋊Dic47—22no—
70C4⋊Dic47—42no—
71C4⋊Dic47—81no—
72C4⋊Dic47—81no—
73Dic47⋊C4—42no—
74Dic47⋊C4—42no—
75C4×Dic47—81no—
76C2×C47⋊C8—24no—
77C2×C47⋊C8—42no—
78C2×C47⋊C8—42no—
79C23×C47#12011yescharacteristic
80Q8×C47—42no—
81Q8×C47—42no—
82Q8×C47—42no—
83Q8×C47—81no—
84Q8×C47—81no—
85Q8×C47—81no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—41no—
92C2×C4×C47—41no—
93C2×C4×C47—41no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—81no—
97C2×C4×C47—81no—
98C2×C4×C47C2×SD1611yescharacteristic
99C2×C4×C47#13512yes—
100C2×C4×C47#13711yescharacteristic
101C2×C4×C47#13712yes—
102C2×Dic47—42no—
103C2×Dic47—42no—
104C2×Dic47—42no—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108C8×C47—42no—
109C47⋊C8—44no—
110#7760—471nomaximal, Sylow
111C22×C47#44811yescharacteristic
112C22×C47#45212yes—
113C22×C47#45311yescharacteristic
114C22×C47#45612yes—
115C22×C47B(4,𝔽2)11yescharacteristic
116C4×C47—21no—
117C4×C47—21no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—42no—
121C4×C47—82no—
122C4×C47—81no—
123Dic47—82no—
124Dic47—82no—
125#2809—471no—
126#2058—472no—
127#2016D4711yescharacteristic
128#1272—471no—
129#1271—472no—
130C2×C47#159611yescharacteristic
131C2×C47#160312yes—
132C2×C47#163411yescharacteristic
133C2×C47#165312yes—
134C2×C47#166011yescharacteristic
135C22×Q16—21no—
136C2×C4⋊Q8C2×D4711yescharacteristic
137C2×#106—942no—
138C2×#103—21no—
139#400—941no—
140#398—942no—
141#391—941no—
142#391C2×D4711yescharacteristic
143#389—472no—
144#387—942no—
145#340—942no—
146#336—472no—
147#336C2×D4711yescharacteristic
148C47#776011yescharacteristic, complemented, Sylow
149C22×Q8—21no—
150C22×Q8C22⋊D4711yescharacteristic
151C2×Q16—42no—
152C2×Q16—42no—
153C2×Q16—42no—
154C22×C8—21no—
155C22×C8—942no—
156C4⋊Q8—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—472no—
160C2×C4⋊C4—941no—
161C2×C4⋊C4—941no—
162C2×C4⋊C4—942no—
163C2×C4⋊C4C22⋊D4711yescharacteristic
164C2×C42—941no—
165C2×C42C22×D4711yescharacteristic
166#106—1884no—
167#103—42no—
168#95—22no—
169#95—941no—
170#95—942no—
171#95—942no—
172#95—942no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8#1062533512yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—942no—
187C22×C4—942no—
188C22×C4D4×D4712yes—
189C22×C4C2×C22⋊D4711yescharacteristic
190Q16—48no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—944no—
195C2×C8—1882no—
196C2×C8—1882no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—942no—
201C4⋊C4—942no—
202C4⋊C4—3761no—
203C4⋊C4—3761no—
204C4⋊C4—1882no—
205C4⋊C4—1882no—
206C4⋊C4—1882no—
207C42—41no—
208C42—3761no—
209C23#1309399211yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—81no—
214Q8—81no—
215Q8—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—1882no—
229C2×C4—1882no—
230C2×C4—1882no—
231C2×C4—1882no—
232C2×C4—1882no—
233C2×C4—1882no—
234C2×C4C2×#1062533511yescharacteristic
235C2×C4#1309404712yes—
236C2×C4#1309405411yescharacteristic
237C2×C4#1309405612yes—
238C8—42no—
239C8—1884no—
240C22#1568926111yescharacteristic
241C22#1568928412yes—
242C22#1568929011yescharacteristic
243C22#1568930412yes—
244C22#1568930911yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—82no—
252C4—3762no—
253C4—3762no—
254C2#2024231011yescharacteristic
255C2#2024235012yes—
256C2#2024253111yescharacteristic
257C2#2024266312yes—
258C2#2024269711yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2016C2
socle, prime radicalC23×C47#120
hypercenter#2016D47
hypocenterC47#7760
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
148. C47#7760semidirect

Maximal subgroups

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

subgroupindex
#202513762
#202447182
#202412142
#202412102
C47×#20162
#776047