Finite Group Databasebeta

← #26108653

Subgroups — #26108653

Order 12032.

620 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 107 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#20257883C211yesmaximal, characteristic
2#20242116C212yesmaximal
3#20242026C211yesmaximal, characteristic
4#20241899C212yesmaximal
5C47×#1995C211yesmaximal, characteristic
6C47⋊#564—22no—
7#15689852—22no—
8#15689851—22no—
9#15689848C414yescomplemented
10#15689735—22no—
11#15689733—24no—
12#15689680C2212yes—
13#15689180C2212yes—
14#15688871—22no—
15#15688870—22no—
16#15688865—22no—
17#15688859—24no—
18C47×#533C2211yescharacteristic
19C47×#423C2211yescharacteristic
20C47×#376C2211yescharacteristic
21C47×#339—22no—
22#13094024—22no—
23#13094024D412yes—
24#13094024D412yes—
25#13094022—24no—
26#13094017—28no—
27#13094016—22no—
28#13094016—22no—
29#13094015—28no—
30#13094015—24no—
31#13094014—28no—
32#13094014—28no—
33#13094003—22no—
34#13094003D414yes—
35Q8×Dic47—24no—
36C4×Dic94—24no—
37C4×Dic94—22no—
38C4×Dic94C2×C414yes—
39#13093989—24no—
40#13093983—22no—
41C4⋊(C47⋊C8)—22no—
42C22⋊(C47⋊C8)—22no—
43#13093935—22no—
44C2×M16×C47—21no—
45C4⋊Q8×C47C2×C412yes—
46#125×C47D412yes—
47C22⋊Q8×C47—22no—
48C4×Q8×C47—22no—
49#117×C47D412yes—
50C2×C42×C47—21no—
51C2×C42×C47C2311yescharacteristic
52C4⋊C8×C47—22no—
53#95×C47—22no—
54C2×Q8×C47—22no—
55C22×C4×C47—41no—
56C22×C4×C47C2×D411yescharacteristic
57C22×C4×C47C2×D412yes—
58C2×Dic94—22no—
59C2×Dic94C22⋊C414yes—
60M16×C47—42no—
61C2×C8×C47—41no—
62C4⋊C4×C47—22no—
63C4⋊C4×C47—24no—
64C4⋊C4×C47C22⋊C414yes—
65C22⋊C4×C47—22no—
66C42×C47—22no—
67C42×C47—22no—
68C42×C47—41no—
69C42×C47C22×C411yescharacteristic
70C42×C47C2×D411yescharacteristic
71C42×C47C2×D412yes—
72C22⋊Dic47—24no—
73C4⋊Dic47—28no—
74C4⋊Dic47—22no—
75C4⋊Dic47—22no—
76C4⋊Dic47—22no—
77C4⋊Dic47C22⋊C414yes—
78Dic47⋊C4—28no—
79Dic47⋊C4—28no—
80Dic47⋊C4—24no—
81Dic47⋊C4—24no—
82C4×Dic47—28no—
83C4×Dic47—24no—
84C2×C47⋊C8—42no—
85C23×C47#12011yescharacteristic
86Q8×C47—44no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—24no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—82no—
93C2×C4×C47C2×C22⋊C412yes—
94C2×C4×C47C2×C22⋊C411yescharacteristic
95C2×C4×C47#12011yescharacteristic
96C2×C4×C47#12012yes—
97C2×Dic47—24no—
98C2×Dic47—24no—
99Dic94—42no—
100Dic94—42no—
101Dic94—44no—
102C8×C47—81no—
103C47⋊C8—82no—
104#8495—471nomaximal, Sylow
105C22×C47—21no—
106C22×C47—22no—
107C22×C47#37911yescharacteristic
108C4×C47—21no—
109C4×C47—22no—
110C4×C47—22no—
111C4×C47—44no—
112C4×C47—82no—
113C4×C47#45411yescharacteristic
114C4×C47#45611yescharacteristic
115Dic47—44no—
116Dic47—44no—
117#3556—471no—
118#1995D4711yescharacteristic
119#1559—472no—
120#1537—471no—
121#1506—472no—
122C2×C47—41no—
123C2×C47#179311yescharacteristic
124C2×C47#179612yes—
125#564—942no—
126#557—474no—
127#557—942no—
128#557—942no—
129#541—944no—
130#541—942no—
131#533—472no—
132#533C2×D4711yescharacteristic
133#432—472no—
134#423C2×D4711yescharacteristic
135#376C2×D4711yescharacteristic
136#339—22no—
137#333—942no—
138#332—942no—
139#330—942no—
140#328—944no—
141C47#849511yescharacteristic, complemented, Sylow
142C2×M16—21no—
143C4⋊Q8—472no—
144C4⋊Q8—472no—
145C4⋊Q8—942no—
146C4⋊Q8—944no—
147C4⋊Q8C4×D4712yes—
148#126—948no—
149#125—942no—
150#125—944no—
151#125—948no—
152#125—948no—
153#125—948no—
154#125—942no—
155#125D18812yes—
156C22⋊Q8—22no—
157C22⋊Q8—474no—
158C22⋊Q8—942no—
159C4×Q8—22no—
160C4×Q8—474no—
161C4×Q8—944no—
162C4×Q8—944no—
163C4×Q8—944no—
164C4×Q8—942no—
165#117—942no—
166#117C22⋊D4712yes—
167C2×C42—21no—
168C2×C42C22×D4711yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—942no—
171C22⋊C8—942no—
172#97—942no—
173#95—22no—
174C2×Q8—22no—
175C2×Q8—474no—
176C2×Q8—942no—
177C22×C4—41no—
178C22×C4D4×D4712yes—
179C22×C4C2×C22⋊D4711yescharacteristic
180M16—42no—
181C2×C8—41no—
182C2×C8—1882no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—474no—
186C4⋊C4—948no—
187C4⋊C4—948no—
188C4⋊C4—948no—
189C4⋊C4—944no—
190C4⋊C4—942no—
191C4⋊C4—944no—
192C4⋊C4—942no—
193C4⋊C4—942no—
194C4⋊C4(C2×D47)⋊C414yes—
195C22⋊C4—22no—
196C22⋊C4—944no—
197C42—22no—
198C42—22no—
199C42—41no—
200C42—948no—
201C42—944no—
202C42C2×C4×D4711yescharacteristic
203C42C2×D18811yescharacteristic
204C42D4×D4712yes—
205C23#1309399211yescharacteristic
206Q8—44no—
207Q8—1884no—
208Q8—1882no—
209Q8—1882no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—944no—
217C2×C4—944no—
218C2×C4C22⋊C4×D4712yes—
219C2×C4C2×(C2×D47)⋊C411yescharacteristic
220C2×C4#1309399211yescharacteristic
221C2×C4#1309399412yes—
222C8—81no—
223C8—3762no—
224C22—21no—
225C22—22no—
226C22#1568897811yescharacteristic
227C4—21no—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—82no—
232C4—1884no—
233C4—1884no—
234C4#1568929511yescharacteristic
235C4#1568930511yescharacteristic
236C2—41no—
237C2#2024334611yescharacteristic
238C2#2024336212yes—
subgroupG/H
centerC22#15688978
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1995C2
socleC22×C47#379
prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#1995D47
hypocenterC47#8495
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
9. #15689848C4semidirect
141. C47#8495semidirect

Maximal subgroups

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

subgroupindex
#202578832
#202421162
#202420262
#202418992
C47×#19952
#849547