Finite Group Databasebeta

← #26119358

Subgroups — #26119358

Order 12032.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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#20244360C212yesmaximal
2#20244207C211yesmaximal, characteristic
3#20241269C211yesmaximal, characteristic
4#20241269C212yesmaximal
5C47×#2845C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13093947—22no—
8C2×#13093935C2212yes—
9C2×#13093935C2211yescharacteristic
10#15688885—22no—
11#15688885—22no—
12C47×#398—22no—
13C47×#398—22no—
14C47×#398—22no—
15C47×#382C2212yes—
16C47×#382C2211yescharacteristic
17C22×Dic94—21no—
18C22×C47⋊C8—21no—
19C22×C47⋊C8—22no—
20#13094024—22no—
21#13094024—21no—
22#13094024Q812yes—
23C2×C4⋊Dic47—22no—
24#13093947—44no—
25#13093935—22no—
26#13093935—22no—
27#13093935—22no—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47—22no—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D412yes—
33C2×C4⋊C4×C47D412yes—
34C2×C42×C47C2311yescharacteristic
35#95×C47—22no—
36#95×C47—22no—
37#95×C47—22no—
38#95×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47C2×D412yes—
43C22×C4×C47C2×D411yescharacteristic
44C22×Dic47—41no—
45C2×Dic94—22no—
46C2×Dic94—42no—
47C2×Dic94—42no—
48C2×Dic94—41no—
49C4⋊C4×C47—42no—
50C4⋊C4×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—82no—
53C4⋊C4×C47—82no—
54C4⋊C4×C47—82no—
55C42×C47C2×Q811yescharacteristic
56C42×C47#4112yes—
57C42×C47#4111yescharacteristic
58C4⋊Dic47—24no—
59C4⋊Dic47—42no—
60C2×C47⋊C8—22no—
61C2×C47⋊C8—24no—
62C2×C47⋊C8—41no—
63C2×C47⋊C8—42no—
64C2×C47⋊C8—42no—
65C2×C47⋊C8—41no—
66C23×C47#12011yescharacteristic
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47C22⋊Q812yes—
81C2×C4×C47C22⋊Q811yescharacteristic
82C2×C4×C47#12412yes—
83C2×C4×C47#12411yescharacteristic
84C2×Dic47—42no—
85C2×Dic47—81no—
86C2×Dic47—81no—
87Dic94—44no—
88Dic94—82no—
89C47⋊C8—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—
103C4×C47—82no—
104Dic47—82no—
105#2845D4711yescharacteristic
106#1993—472no—
107#1960—471no—
108#1295—471no—
109#1295—472no—
110C2×C47#166112yes—
111C2×C47#166211yescharacteristic
112C2×C47#166311yescharacteristic
113C2×C47#202711yescharacteristic
114C2×C47#202812yes—
115C2×C4⋊Q8—471no—
116C2×#103—942no—
117C2×#97—471no—
118C2×#97—472no—
119#398—22no—
120#398—22no—
121#398—22no—
122#382C2×D4711yescharacteristic
123#382C2×D4712yes—
124#340—942no—
125#340—942no—
126C47#1036111yescharacteristic, complemented, Sylow
127C22×Q8—941no—
128C22×C8—942no—
129C22×C8—941no—
130C4⋊Q8—472no—
131C4⋊Q8—942no—
132C4⋊Q8—941no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—942no—
137C2×C4⋊C4C22⋊D4712yes—
138C2×C4⋊C4C22⋊D4712yes—
139C2×C4⋊C4C22⋊D4712yes—
140C2×C42C22×D4711yescharacteristic
141#103—1884no—
142#97—942no—
143#97—942no—
144#97—942no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—942no—
150C2×Q8—1882no—
151C2×Q8—1882no—
152C2×Q8—1881no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—1881no—
157C22×C4C2×C22⋊D4712yes—
158C22×C4C2×C22⋊D4711yescharacteristic
159C2×C8—942no—
160C2×C8—944no—
161C2×C8—1881no—
162C2×C8—1882no—
163C2×C8—1882no—
164C2×C8—1881no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—82no—
171C4⋊C4—944no—
172C4⋊C4—1882no—
173C42Q8×D4711yescharacteristic
174C42#1062535412yes—
175C42#1062535411yescharacteristic
176C23#1309399311yescharacteristic
177Q8—3762no—
178Q8—1884no—
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—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—3761no—
193C2×C4—3761no—
194C2×C4—1882no—
195C2×C4#1309400012yes—
196C2×C4#1309400011yescharacteristic
197C2×C4#1309401312yes—
198C2×C4#1309401311yescharacteristic
199C8—1882no—
200C8—1884no—
201C22#1568903411yescharacteristic
202C22#1568929111yescharacteristic
203C22#1568929611yescharacteristic
204C22#1568930112yes—
205C22#1568930612yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—3762no—
214C2#2024270512yes—
215C2#2024271111yescharacteristic
216C2#2024271611yescharacteristic
217C2#2024454111yescharacteristic
218C2#2024454612yes—
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2845C2
socle, prime radicalC23×C47#120
hypercenter#2845D47
hypocenterC47#10361
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

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
#202443602
#202442072
#202412692
C47×#28452
#1036147