Finite Group Databasebeta

← #26117147

Subgroups — #26117147

Order 12032.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#20253423C212yesmaximal
2#20246681C211yesmaximal, characteristic
3#20241816C212yesmaximal
4#20241217C211yesmaximal, characteristic
5C47×#1995C211yesmaximal, characteristic
6C2×C4×Dic94C2212yes—
7#15689456—22no—
8#15689415—22no—
9#15689330—22no—
10#15689278—22no—
11C4×#10625337—24no—
12#15689176C2212yes—
13#15689055—22no—
14#15689044—22no—
15C4×C4⋊Dic47—22no—
16#15688853—24no—
17C47×#533C2211yescharacteristic
18C47×#423C2211yescharacteristic
19C47×#376C2211yescharacteristic
20C47×#339—22no—
21C22×Dic94D412yes—
22C2×#10625337—24no—
23C4×Dic94—22no—
24C4×Dic94—22no—
25C4×Dic94—22no—
26C4×Dic94—22no—
27C2×C4⋊Dic47—24no—
28C2×C4⋊Dic47D412yes—
29C2×Dic47⋊C4—22no—
30C2×C4×Dic47—22no—
31#13093957—24no—
32C4⋊(C47⋊C8)—22no—
33#13093948—24no—
34#13093947—24no—
35C22⋊(C47⋊C8)—22no—
36C4×C47⋊C8D414yes—
37C47⋊#95—22no—
38C47⋊#95—22no—
39C2×M16×C47—21no—
40C4⋊Q8×C47D412yes—
41#125×C47—21no—
42C22⋊Q8×C47—22no—
43C4×Q8×C47—22no—
44#117×C47—21no—
45C2×C42×C47D412yes—
46C2×C42×C47C2311yescharacteristic
47C4⋊C8×C47—22no—
48#95×C47—22no—
49C2×Q8×C47—22no—
50C22×C4×C47—22no—
51C22×C4×C47C2×D412yes—
52C22×C4×C47C2×D411yescharacteristic
53C22×Dic47—22no—
54C22×Dic47—22no—
55C2×Dic94—22no—
56C2×Dic94—22no—
57C2×Dic94—44no—
58M16×C47—42no—
59C2×C8×C47—41no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62C4⋊C4×C47—42no—
63C22⋊C4×C47—41no—
64C42×C47—22no—
65C42×C47—41no—
66C42×C47Q1614yescomplemented
67C42×C47C2×D411yescharacteristic
68C42×C47C2×D412yes—
69C42×C47#4111yescharacteristic
70#10625337—48no—
71C4⋊Dic47—22no—
72C4⋊Dic47—22no—
73C4⋊Dic47—48no—
74Dic47⋊C4—42no—
75Dic47⋊C4—42no—
76C4×Dic47—42no—
77C4×Dic47—42no—
78C2×C47⋊C8—24no—
79C23×C47#12011yescharacteristic
80Q8×C47—44no—
81C2×C4×C47—24no—
82C2×C4×C47—42no—
83C2×C4×C47—44no—
84C2×C4×C47—42no—
85C2×C4×C47#12012yes—
86C2×C4×C47#12112yes—
87C2×C4×C47#12111yescharacteristic
88C2×C4×C47#12711yescharacteristic
89C2×C4×C47C2×Q1612yes—
90C2×C4×C47#13712yes—
91C2×Dic47—24no—
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—44no—
95C2×Dic47—42no—
96Dic94—24no—
97Dic94—24no—
98Dic94—42no—
99Dic94—42no—
100C8×C47—81no—
101C47⋊C8—44no—
102#10017—471nomaximal, Sylow
103C22×C47—22no—
104C22×C47#39211yescharacteristic
105C22×C47#45112yes—
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—44no—
109C4×C47—82no—
110C4×C47#46212yes—
111C4×C47#49411yescharacteristic
112C4×C47#49711yescharacteristic
113Dic47—44no—
114Dic47—82no—
115#3104—472no—
116#2399—471no—
117#1995D4711yescharacteristic
118#1487—472no—
119#1274—471no—
120C2×C47—22no—
121C2×C47#201012yes—
122C2×C47#201611yescharacteristic
123#533C2×D4711yescharacteristic
124C2×C4×Q8—472no—
125#484—942no—
126#477—942no—
127#462—942no—
128#451—942no—
129C4×Q16—944no—
130#431—472no—
131#423C2×D4711yescharacteristic
132#398—942no—
133#395—942no—
134C4×C4⋊C4—942no—
135#376C2×D4711yescharacteristic
136#339—22no—
137Q8⋊C8—944no—
138C47#1001711yescharacteristic, complemented, Sylow
139C22×Q8—472no—
140C2×Q16—944no—
141C2×M16—21no—
142C4⋊Q8D18812yes—
143#125—21no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146C4×Q8—942no—
147C4×Q8—942no—
148C4×Q8—942no—
149C4×Q8—942no—
150#117—21no—
151C2×C4⋊C4—472no—
152C2×C4⋊C4—944no—
153C2×C4⋊C4—942no—
154C2×C42—942no—
155C2×C42C22⋊D4712yes—
156C2×C42C22×D4711yescharacteristic
157#107—944no—
158C4⋊C8—22no—
159C4⋊C8—942no—
160#103—944no—
161#103—944no—
162C22⋊C8—942no—
163C4×C8—474no—
164#95—22no—
165#95—942no—
166#95—942no—
167C2×Q8—22no—
168C2×Q8—942no—
169C2×Q8—942no—
170C2×Q8—1884no—
171C22×C4—22no—
172C22×C4—942no—
173C22×C4—942no—
174C22×C4D4×D4712yes—
175C22×C4C2×C22⋊D4711yescharacteristic
176Q16—1888no—
177M16—42no—
178C2×C8—41no—
179C2×C8—944no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—1888no—
186C4⋊C4—1882no—
187C4⋊C4—1882no—
188C22⋊C4—41no—
189C42—22no—
190C42—41no—
191C42—1882no—
192C42—1882no—
193C42#1062533714yescomplemented
194C42C2×D18811yescharacteristic
195C42#1062535011yescharacteristic
196C42D4×D4712yes—
197C23#1309399211yescharacteristic
198Q8—44no—
199Q8—944no—
200Q8—944no—
201Q8—1882no—
202Q8—1882no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—944no—
208C2×C4—1884no—
209C2×C4—1882no—
210C2×C4—1882no—
211C2×C4—1882no—
212C2×C4#1309399412yes—
213C2×C4#1309399712yes—
214C2×C4#1309399811yescharacteristic
215C2×C4#1309402011yescharacteristic
216C2×C4C2×#1062533712yes—
217C2×C4#1309405412yes—
218C8—81no—
219C8—1884no—
220C22—22no—
221C22#1568903211yescharacteristic
222C22#1568927812yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—82no—
227C4—3762no—
228C4—1884no—
229C4#1568933312yes—
230C4#1568950211yescharacteristic
231C4#1568951811yescharacteristic
232C2—22no—
233C2#2024445412yes—
234C2#2024448711yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1995C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1995D47
hypocenterC47#10017
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
66. C42×C47Q16semidirect
138. C47#10017semidirect
193. C42#10625337semidirect

Maximal subgroups

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

subgroupindex
#202534232
#202466812
#202418162
#202412172
C47×#19952
#1001747