Finite Group Databasebeta

← #26119308

Subgroups — #26119308

Order 12032.

416 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 123 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#20248630C211yesmaximal, characteristic
2#20244337C212yesmaximal
3#20241271C211yesmaximal, characteristic
4#20241228C212yesmaximal
5C47×#1956C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)C2212yes—
7#15689062—22no—
8#15689022—22no—
9#15688988—22no—
10C4×C4⋊Dic47C2212yes—
11#15688885—22no—
12#15688885—22no—
13C2×C4⋊Q8×C47C2211yescharacteristic
14C2×#103×C47—22no—
15C2×C4×C8×C47C2211yescharacteristic
16C47×#384C2211yescharacteristic
17C22×C47⋊C8—22no—
18C2×C4⋊Dic47—22no—
19C2×C4⋊Dic47D412yes—
20C2×C4⋊Dic47D412yes—
21C2×C4×Dic47—22no—
22C4⋊(C47⋊C8)—22no—
23C4⋊(C47⋊C8)—22no—
24C47⋊#95—22no—
25C47⋊#95—24no—
26C47⋊#95—22no—
27C22×Q8×C47—21no—
28C22×C8×C47—21no—
29C4⋊Q8×C47—22no—
30C4⋊Q8×C47—21no—
31C4⋊Q8×C47Q812yes—
32C2×C4⋊C4×C47—22no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36#103×C47—44no—
37C4×C8×C47—22no—
38C2×Q8×C47—22no—
39C2×Q8×C47—42no—
40C2×Q8×C47—42no—
41C2×Q8×C47—41no—
42C22×C4×C47—22no—
43C22×C4×C47—41no—
44C22×C4×C47C2×D411yescharacteristic
45C22×C4×C47C2×D412yes—
46C22×Dic47—22no—
47C22×Dic47—22no—
48C2×C8×C47—22no—
49C2×C8×C47—41no—
50C2×C8×C47—41no—
51C4⋊C4×C47—24no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—42no—
55C4⋊C4×C47—42no—
56C42×C47C2×Q811yescharacteristic
57C42×C47#4111yescharacteristic
58C42×C47#4112yes—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47—82no—
64C4×Dic47—42no—
65C4×Dic47—42no—
66C2×C47⋊C8—42no—
67C2×C47⋊C8—42no—
68C2×C47⋊C8—42no—
69C23×C47#12011yescharacteristic
70Q8×C47—44no—
71Q8×C47—82no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—42no—
75C2×C4×C47—44no—
76C2×C4×C47—42no—
77C2×C4×C47—81no—
78C2×C4×C47—81no—
79C2×C4×C47C22⋊Q812yes—
80C2×C4×C47C22⋊Q811yescharacteristic
81C2×C4×C47#12412yes—
82C2×C4×C47#12411yescharacteristic
83C2×C4×C47#13512yes—
84C2×C4×C47#13512yes—
85C2×C4×C47#13712yes—
86C2×C4×C47#13712yes—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93C8×C47—42no—
94C47⋊C8—82no—
95#10352—471nomaximal, Sylow
96C22×C47#39311yescharacteristic
97C22×C47#45212yes—
98C22×C47#45212yes—
99C22×C47#45311yescharacteristic
100C22×C47#45411yescharacteristic
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—82no—
104C4×C47—82no—
105C4×C47#47912yes—
106C4×C47#47912yes—
107C4×C47#48812yes—
108C4×C47#49112yes—
109Dic47—82no—
110Dic47—82no—
111#2571—471no—
112#1987—472no—
113#1956D4711yescharacteristic
114#1296—471no—
115#1279—472no—
116C2×C47#163011yescharacteristic
117C2×C47#163411yescharacteristic
118C2×C47#163812yes—
119C2×C47#202612yes—
120C2×C47#202711yescharacteristic
121C2×C4⋊Q8C2×D4711yescharacteristic
122C2×C4⋊C8—472no—
123C2×#103—22no—
124C2×C4×C8C2×D4711yescharacteristic
125#400—942no—
126#389—942no—
127#384C2×D4711yescharacteristic
128#382—942no—
129C4×C4⋊C4—472no—
130#340—942no—
131#340—942no—
132C47#1035211yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C22×C8—21no—
135C22×C8—942no—
136C4⋊Q8—21no—
137C4⋊Q8—22no—
138C4⋊Q8Dic9412yes—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—942no—
144C2×C4⋊C4C22⋊D4712yes—
145C2×C42—942no—
146C2×C42C22×D4711yescharacteristic
147C4⋊C8—942no—
148C4⋊C8—942no—
149#103—44no—
150C4×C8—22no—
151#95—942no—
152#95—944no—
153#95—942no—
154C2×Q8—22no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—41no—
158C22×C4—22no—
159C22×C4—41no—
160C22×C4—942no—
161C22×C4—942no—
162C22×C4D4×D4712yes—
163C22×C4C2×C22⋊D4711yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—1882no—
168C2×C8—1882no—
169C2×C8—1882no—
170C4⋊C4—24no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—3762no—
180C42—1882no—
181C42—1882no—
182C42C2×Dic9411yescharacteristic
183C42#1062535011yescharacteristic
184C42#1062535212yes—
185C23#1309399211yescharacteristic
186Q8—44no—
187Q8—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4#1309400112yes—
202C2×C4#1309400311yescharacteristic
203C2×C4#1309401012yes—
204C2×C4#1309401111yescharacteristic
205C2×C4#1309404512yes—
206C2×C4#1309404712yes—
207C2×C4#1309405312yes—
208C2×C4#1309405612yes—
209C8—42no—
210C8—3762no—
211C22#1568903511yescharacteristic
212C22#1568928212yes—
213C22#1568928412yes—
214C22#1568929011yescharacteristic
215C22#1568929511yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—3762no—
221C4—3762no—
222C4#1568942812yes—
223C4#1568943212yes—
224C4#1568947912yes—
225C4#1568949012yes—
226C2#2024250711yescharacteristic
227C2#2024253111yescharacteristic
228C2#2024255712yes—
229C2#2024453712yes—
230C2#2024454411yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1956C2
socle, prime radicalC23×C47#120
hypercenter#1956D47
hypocenterC47#10352
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
132. C47#10352semidirect

Maximal subgroups

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

subgroupindex
#202486302
#202443372
#202412712
#202412282
C47×#19562
#1035247