Finite Group Databasebeta

← #26119359

Subgroups — #26119359

Order 12032.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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#20251663C211yesmaximal, characteristic
2#20244362C212yesmaximal
3#20241270C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#1960C211yesmaximal, characteristic
6C2×#13093935C2212yes—
7#15689057—22no—
8#15689056—22no—
9#15689055—22no—
10#15688989C2212yes—
11#15688885—22no—
12#15688885—22no—
13C2×C4⋊Q8×C47C2211yescharacteristic
14C2×#103×C47—22no—
15C2×#97×C47C2211yescharacteristic
16C47×#382C2211yescharacteristic
17C22×C47⋊C8—22no—
18C2×C4⋊Dic47—22no—
19C2×C4⋊Dic47D412yes—
20C2×C4⋊Dic47D412yes—
21C2×Dic47⋊C4—22no—
22C2×Dic47⋊C4—22no—
23#13093935—22no—
24#13093935—22no—
25C47⋊#95—22no—
26C47⋊#95—22no—
27C47⋊#95—22no—
28C22×Q8×C47—21no—
29C22×C8×C47—21no—
30C4⋊Q8×C47—22no—
31C4⋊Q8×C47—21no—
32C4⋊Q8×C47Q812yes—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36#103×C47—44no—
37#97×C47—22no—
38#95×C47—22no—
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C2×Q8×C47—42no—
42C2×Q8×C47—41no—
43C22×C4×C47—22no—
44C22×C4×C47—41no—
45C22×C4×C47C2×D412yes—
46C22×C4×C47C2×D411yescharacteristic
47C22×Dic47—22no—
48C22×Dic47—22no—
49C2×C8×C47—22no—
50C2×C8×C47—41no—
51C2×C8×C47—41no—
52C4⋊C4×C47—24no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—42no—
55C42×C47C2×Q811yescharacteristic
56C42×C47#4111yescharacteristic
57C42×C47#4112yes—
58C4⋊Dic47—42no—
59C4⋊Dic47—42no—
60C4⋊Dic47—82no—
61Dic47⋊C4—82no—
62Dic47⋊C4—82no—
63C2×C47⋊C8—24no—
64C2×C47⋊C8—42no—
65C2×C47⋊C8—42no—
66C23×C47#12011yescharacteristic
67Q8×C47—44no—
68Q8×C47—82no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
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×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C8×C47—42no—
90C47⋊C8—44no—
91#10361—471nomaximal, Sylow
92C22×C47#39311yescharacteristic
93C22×C47#45311yescharacteristic
94C22×C47#45411yescharacteristic
95C22×C47#45512yes—
96C22×C47#45612yes—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—82no—
102C4×C47—82no—
103Dic47—82no—
104Dic47—82no—
105#2845—471no—
106#1993—472no—
107#1960D4711yescharacteristic
108#1295—472no—
109#1295—471no—
110C2×C47#166112yes—
111C2×C47#166211yescharacteristic
112C2×C47#166311yescharacteristic
113C2×C47#202711yescharacteristic
114C2×C47#202812yes—
115C2×C4⋊Q8C2×D4711yescharacteristic
116C2×#103—22no—
117C2×#97—472no—
118C2×#97C2×D4711yescharacteristic
119#398—942no—
120#398—942no—
121#398—942no—
122#382—472no—
123#382C2×D4711yescharacteristic
124#340—942no—
125#340—942no—
126C47#1036111yescharacteristic, complemented, Sylow
127C22×Q8—21no—
128C22×C8—21no—
129C22×C8—942no—
130C4⋊Q8—21no—
131C4⋊Q8—22no—
132C4⋊Q8Dic9412yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4—942no—
137C2×C4⋊C4—942no—
138C2×C4⋊C4—942no—
139C2×C4⋊C4C22⋊D4712yes—
140C2×C42C22×D4711yescharacteristic
141#103—44no—
142#97—22no—
143#97—942no—
144#97—942no—
145#95—22no—
146#95—942no—
147#95—942no—
148#95—942no—
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—942no—
156C22×C4—942no—
157C22×C4D4×D4712yes—
158C22×C4C2×C22⋊D4711yescharacteristic
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—944no—
163C2×C8—1882no—
164C2×C8—1882no—
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—3762no—
169C4⋊C4—3762no—
170C4⋊C4—3762no—
171C4⋊C4—1882no—
172C4⋊C4—1882no—
173C42C2×Dic9411yescharacteristic
174C42#1062535011yescharacteristic
175C42#1062535212yes—
176C23#1309399211yescharacteristic
177Q8—44no—
178Q8—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—1882no—
190C2×C4—1882no—
191C2×C4—1882no—
192C2×C4—1882no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4#1309400112yes—
196C2×C4#1309400311yescharacteristic
197C2×C4#1309401012yes—
198C2×C4#1309401111yescharacteristic
199C8—42no—
200C8—1884no—
201C22#1568903511yescharacteristic
202C22#1568929011yescharacteristic
203C22#1568929511yescharacteristic
204C22#1568929912yes—
205C22#1568930412yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—3762no—
213C4—3762no—
214C2#2024270212yes—
215C2#2024270911yescharacteristic
216C2#2024271411yescharacteristic
217C2#2024454411yescharacteristic
218C2#2024454712yes—
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1960C2
socle, prime radicalC23×C47#120
hypercenter#1960D47
hypocenterC47#10361
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
126. C47#10361semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202443622
#202412702
#202412692
C47×#19602
#1036147