Finite Group Databasebeta

← #26110781

Subgroups — #26110781

Order 12032.

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

normal subgroups only

This group has 412 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#20244217C211yesmaximal, characteristic
2#20242176C212yesmaximal, complemented
3#20242050C211yesmaximal, characteristic
4#20241220C212yesmaximal, complemented
5C47×#2979C211yesmaximal, characteristic
6#15689176C2212yes—
7#15689147C2211yescharacteristic
8C2×#13093951—22no—
9C42×Dic47C2211yescharacteristic
10#15688875—22no—
11#15688873—22no—
12#15688872C412yescomplemented
13#15688867C411yescharacteristic, complemented
14#15688867C411yescharacteristic, complemented
15C47×#532C2211yescharacteristic
16C47×#436—22no—
17C8×D4×C47—22no—
18C47×#431C2212yes—
19C47×#408—22no—
20C2×#10625329—21no—
21C2×C4×Dic47—21no—
22C2×C4×Dic47—22no—
23C4⋊(C47⋊C8)—22no—
24C4⋊(C47⋊C8)C2×C412yes—
25C4⋊(C47⋊C8)C2×C412yes—
26#13093951—44no—
27C22⋊(C47⋊C8)—22no—
28C4×C47⋊C8—22no—
29C2×#41×C47D412yes—
30C2×M16×C47—22no—
31C22×C8×C47—22no—
32C4⋊Q8×C47C2×C411yescharacteristic
33#127×C47C2×C411yescharacteristic
34#124×C47Q812yes—
35#121×C47—22no—
36C4×D4×C47—22no—
37C2×C42×C47C2311yescharacteristic
38C4⋊C8×C47D412yes—
39C4⋊C8×C47D412yes—
40C22⋊C8×C47—24no—
41C22⋊C8×C47—22no—
42C4×C8×C47—22no—
43#41×C47—42no—
44#41×C47—42no—
45C2×Q8×C47C4⋊C412yes—
46C2×D4×C47—22no—
47C2×D4×C47—22no—
48C2×D4×C47C4⋊C412yes—
49C22×C4×C47—22no—
50C22×C4×C47C2×D411yescharacteristic
51C22×C4×C47#4112yes—
52C22×Dic47—41no—
53M16×C47—82no—
54C2×C8×C47—22no—
55C2×C8×C47—22no—
56C2×C8×C47—82no—
57C4⋊C4×C47—22no—
58C22⋊C4×C47—24no—
59C42×C47C22×C411yescharacteristic
60C42×C47C2×D412yes—
61C42×C47C2×Q811yescharacteristic
62C4×Dic47—22no—
63C4×Dic47—24no—
64C4×Dic47—42no—
65C4×Dic47—41no—
66#10625329—42no—
67C2×C47⋊C8—22no—
68C2×C47⋊C8—22no—
69C2×C47⋊C8—41no—
70C23×C47—22no—
71C23×C47#12311yescharacteristic
72Q8×C47—42no—
73D4×C47—42no—
74D4×C47—42no—
75D4×C47—42no—
76D4×C47—82no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47C2×C4⋊C411yescharacteristic
85C2×C4×C47C4×D412yes—
86C2×C4×C47#12011yescharacteristic
87C2×C4×C47C22⋊Q812yes—
88C2×Dic47—42no—
89C2×Dic47—44no—
90C8×C47—42no—
91C8×C47—42no—
92C47⋊C8—42no—
93C47⋊C8—42no—
94C47⋊C8—81no—
95#8934—471nomaximal, Sylow
96C22×C47—21no—
97C22×C47—22no—
98C22×C47—42no—
99C22×C47—44no—
100C22×C47#38511yescharacteristic
101C4×C47—21no—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47#44312yes—
105C4×C47#44412yes—
106C4×C47#45311yescharacteristic
107C4×C47#45511yescharacteristic
108Dic47—44no—
109#2979D4711yescharacteristic
110#1962—471no—
111#1574—472no—
112#1543—471no—
113#1276—472no—
114C2×C47—41no—
115C2×C47—82no—
116C2×C47#185611yescharacteristic
117C2×C47#186612yes—
118#532C2×D4711yescharacteristic
119#436—22no—
120C8×D4—22no—
121#431—472no—
122#431C2×D4712yes—
123#423—471no—
124C2×#104—942no—
125#408—22no—
126C43—471no—
127#335—942no—
128#334—942no—
129#333—472no—
130#331—471no—
131#331—471no—
132C47#893411yescharacteristic, complemented, Sylow
133C2×#41C22⋊D4712yes—
134C2×M16—22no—
135C2×M16—941no—
136C22×C8—22no—
137C4⋊Q8C4×D4711yescharacteristic
138#127C4×D4711yescharacteristic
139#124Dic9412yes—
140#121—22no—
141C4×D4—22no—
142C2×C42—942no—
143C2×C42—941no—
144C2×C42C22×D4711yescharacteristic
145C4⋊C8—472no—
146C4⋊C8—472no—
147C4⋊C8—942no—
148C4⋊C8C22⋊D4712yes—
149C4⋊C8C22⋊D4712yes—
150#104—1884no—
151C22⋊C8—24no—
152C22⋊C8—22no—
153C22⋊C8—942no—
154C4×C8—22no—
155C4×C8—942no—
156#41—42no—
157#41—42no—
158C2×Q8Dic47⋊C412yes—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4Dic47⋊C412yes—
162C22×C4—22no—
163C22×C4—1881no—
164C22×C4#1062535012yes—
165C22×C4C2×C22⋊D4711yescharacteristic
166M16—82no—
167M16—1882no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—82no—
171C2×C8—942no—
172C2×C8—942no—
173C2×C8—1881no—
174C4⋊C4—22no—
175C22⋊C4—24no—
176C42—942no—
177C42—944no—
178C42—1882no—
179C42—1881no—
180C42C2×Dic9411yescharacteristic
181C42C2×C4×D4711yescharacteristic
182C42C2×C22⋊D4712yes—
183C23—22no—
184C23#1309400711yescharacteristic
185Q8—42no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—1882no—
198C2×C4—1884no—
199C2×C4C2×Dic47⋊C411yescharacteristic
200C2×C4C4×C22⋊D4712yes—
201C2×C4#1309399311yescharacteristic
202C2×C4#1309400312yes—
203C8—42no—
204C8—42no—
205C8—3761no—
206C8—1882no—
207C8—1882no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—44no—
212C22#1568899611yescharacteristic
213C4—21no—
214C4—22no—
215C4—42no—
216C4—1884no—
217C4#1568923812yes—
218C4#1568924312yes—
219C4#1568929111yescharacteristic
220C4#1568930111yescharacteristic
221C2—41no—
222C2—82no—
223C2#2024359811yescharacteristic
224C2#2024366312yes—
subgroupG/H
centerC2×C4#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2979C2
socleC22×C47#385
prime radicalC47×#532C22
cosocleC2×C42×C47C23
hypercenter#2979D47
hypocenterC47#8934
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #20242176C2semidirect
4. #20241220C2semidirect
12. #15688872C4semidirect
13. #15688867C4semidirect
14. #15688867C4semidirect
132. C47#8934semidirect

Maximal subgroups

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

subgroupindex
#202442172
#202421762
#202420502
#202412202
C47×#29792
#893447