Finite Group Databasebeta

← #26119418

Subgroups — #26119418

Order 12032.

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

normal subgroups only

This group has 364 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#20244369C211yesmaximal, characteristic
2#20241886C212yesmaximal
3#20241291C212yesmaximal
4#20241217C211yesmaximal, characteristic
5C47×#2402C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689176C2212yes—
8#15689147C2211yescharacteristic
9#15688883—22no—
10#15688859—22no—
11#15688859—22no—
12C47×#400—22no—
13C47×#398—22no—
14C4×C4⋊C4×C47—22no—
15C4×C4⋊C4×C47C2212yes—
16C47×#376C2211yescharacteristic
17C2×#10625329—21no—
18#13094024Q812yes—
19#13094016—21no—
20#13094003—22no—
21C4×Dic94—22no—
22#13093983—21no—
23C4⋊(C47⋊C8)—22no—
24C4⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)—22no—
26C4×C47⋊C8—22no—
27C2×C4⋊C4×C47—22no—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C42×C47—22no—
31C2×C42×C47D412yes—
32C2×C42×C47C2311yescharacteristic
33#95×C47—22no—
34#95×C47—22no—
35#95×C47—22no—
36#95×C47D412yes—
37#95×C47D412yes—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47C2×D411yescharacteristic
43C2×Dic94—22no—
44C4⋊C4×C47—44no—
45C4⋊C4×C47—44no—
46C4⋊C4×C47—44no—
47C42×C47—22no—
48C42×C47—22no—
49C42×C47—42no—
50C42×C47—42no—
51C42×C47C2×Q811yescharacteristic
52C42×C47#4112yes—
53C42×C47#4111yescharacteristic
54C22⋊Dic47—41no—
55C4⋊Dic47—22no—
56C4⋊Dic47—22no—
57Dic47⋊C4—42no—
58C4×Dic47—41no—
59#10625329—42no—
60C2×C47⋊C8—42no—
61C2×C47⋊C8—41no—
62C23×C47#12011yescharacteristic
63C2×C4×C47—24no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47C22⋊Q812yes—
74C2×C4×C47C22⋊Q811yescharacteristic
75C2×C4×C47#12412yes—
76C2×C4×C47#12411yescharacteristic
77C2×C4×C47#13512yes—
78C2×C4×C47#13712yes—
79C2×Dic47—42no—
80Dic94—82no—
81C47⋊C8—82no—
82C47⋊C8—81no—
83#10373—471nomaximal, Sylow
84C22×C47—22no—
85C22×C47#39311yescharacteristic
86C22×C47#45212yes—
87C4×C47—22no—
88C4×C47—22no—
89C4×C47—44no—
90C4×C47—82no—
91C4×C47—82no—
92C4×C47#47912yes—
93C4×C47#48811yescharacteristic
94C4×C47#49111yescharacteristic
95Dic47—82no—
96#2402D4711yescharacteristic
97#1995—471no—
98#1503—472no—
99#1303—472no—
100#1274—471no—
101C2×C47—22no—
102C2×C47#202611yescharacteristic
103C2×C47#203112yes—
104#533—471no—
105#431—472no—
106#423—471no—
107#400—22no—
108#398—22no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4C2×D4712yes—
111#376C2×D4711yescharacteristic
112#339—942no—
113#328—942no—
114#328—942no—
115C47#1037311yescharacteristic, complemented, Sylow
116C2×M16—941no—
117C4⋊Q8—472no—
118#125—941no—
119C22⋊Q8—942no—
120C4×Q8—942no—
121#117—941no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D4712yes—
127C2×C42C22×D4711yescharacteristic
128C4⋊C8—942no—
129C4⋊C8—942no—
130C22⋊C8—942no—
131C4×C8—942no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95C22⋊D4712yes—
136#95C22⋊D4712yes—
137C2×Q8—942no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C2×C22⋊D4712yes—
142C22×C4C2×C22⋊D4711yescharacteristic
143M16—1882no—
144C2×C8—1882no—
145C2×C8—1881no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—44no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—1882no—
152C22⋊C4—1881no—
153C42—22no—
154C42—22no—
155C42—42no—
156C42—42no—
157C42—1881no—
158C42Q8×D4711yescharacteristic
159C42#1062535411yescharacteristic
160C42#1062535412yes—
161C23#1309399311yescharacteristic
162Q8—3762no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—1882no—
174C2×C4#1309400012yes—
175C2×C4#1309400011yescharacteristic
176C2×C4#1309401312yes—
177C2×C4#1309401311yescharacteristic
178C2×C4#1309404412yes—
179C2×C4#1309405412yes—
180C8—3762no—
181C8—3761no—
182C22—22no—
183C22#1568903411yescharacteristic
184C22#1568928512yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—3762no—
191C4#1568942712yes—
192C4#1568948011yescharacteristic
193C4#1568949311yescharacteristic
194C2—22no—
195C2#2024453611yescharacteristic
196C2#2024455712yes—
subgroupG/H
centerC2×C4#13094013
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2402C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#2402D47
hypocenterC47#10373
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
115. C47#10373semidirect

Maximal subgroups

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

subgroupindex
#202443692
#202418862
#202412912
#202412172
C47×#24022
#1037347