Finite Group Databasebeta

← #26104596

Subgroups — #26104596

Order 12032.

384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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#20243531C212yesmaximal
2#20241211C214yesmaximal
3C4×#125×C47C211yesmaximal, characteristic
4#15688878—22no—
5#15688878—22no—
6#15688878C2214yes—
7C2×#125×C47C411yescharacteristic
8C47×#389C2212yes—
9C47×#387—22no—
10C47×#382C411yescharacteristic
11C4×C4⋊C4×C47—22no—
12C4×C4⋊C4×C47C412yes—
13C43×C47C2211yescharacteristic
14C22×C47⋊C8—24no—
15#125×C47—24no—
16C2×C4⋊C4×C47—22no—
17C2×C4⋊C4×C47—22no—
18C2×C4⋊C4×C47C2×C412yes—
19C2×C4⋊C4×C47C2×C412yes—
20C2×C42×C47—22no—
21C2×C42×C47C2×C411yescharacteristic
22C2×C42×C47C2×C411yescharacteristic
23C2×C42×C47D412yes—
24C2×C42×C47D412yes—
25C2×C42×C47C2311yescharacteristic
26#95×C47—22no—
27#95×C47—22no—
28#95×C47—22no—
29C22×C4×C47—22no—
30C22×C4×C47—22no—
31C22×C4×C47C22⋊C412yes—
32C22×C4×C47C22⋊C411yescharacteristic
33C22×C4×C47C22⋊C411yescharacteristic
34C22×C4×C47C22×C411yescharacteristic
35C22×C4×C47C2×D412yes—
36C4⋊C4×C47—28no—
37C4⋊C4×C47—22no—
38C4⋊C4×C47—42no—
39C4⋊C4×C47—44no—
40C4⋊C4×C47M1614yes—
41C42×C47—22no—
42C42×C47—22no—
43C42×C47—24no—
44C42×C47—42no—
45C42×C47—41no—
46C42×C47—44no—
47C2×C47⋊C8—44no—
48C2×C47⋊C8—44no—
49C2×C47⋊C8—44no—
50C23×C47C2×C22⋊C411yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—24no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—42no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47#10112yes—
68C2×C4×C47C2×M1612yes—
69C2×C4×C47#13514yes—
70C47⋊C8—84no—
71#7650—471nomaximal, Sylow
72C22×C47#40711yescharacteristic
73C22×C47#41011yescharacteristic
74C22×C47C2×#10111yescharacteristic
75C22×C47#41612yes—
76C22×C47#42112yes—
77C4×C47—22no—
78C4×C47—24no—
79C4×C47—22no—
80C4×C47—41no—
81C4×C47—42no—
82C4×C47—44no—
83C4×C47—82no—
84C4×#125D4711yescharacteristic
85#1839—472no—
86#1271—474no—
87C2×C47#146711yescharacteristic
88C2×C47#148812yes—
89C2×C47#152112yes—
90C2×C47#153411yescharacteristic
91C2×C47#154411yescharacteristic
92C2×#125Dic4711yescharacteristic
93#389C2×D4712yes—
94#387—22no—
95#382Dic4711yescharacteristic
96C4×C4⋊C4—22no—
97C4×C4⋊C4Dic4712yes—
98C43C2×D4711yescharacteristic
99#336—474no—
100#336—942no—
101#336—942no—
102C47#765011yescharacteristic, complemented, Sylow
103C22×C8—944no—
104#125—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4C2×Dic4712yes—
108C2×C4⋊C4C2×Dic4712yes—
109C2×C42—22no—
110C2×C42C2×Dic4711yescharacteristic
111C2×C42C2×Dic4711yescharacteristic
112C2×C42C22⋊D4712yes—
113C2×C42C22⋊D4712yes—
114C2×C42C22×D4711yescharacteristic
115#95—22no—
116#95—22no—
117#95—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4C22⋊Dic4711yescharacteristic
121C22×C4C22⋊Dic4712yes—
122C22×C4C22⋊Dic4711yescharacteristic
123C22×C4C22×Dic4711yescharacteristic
124C22×C4C2×C22⋊D4712yes—
125C2×C8—1884no—
126C2×C8—1884no—
127C2×C8—1884no—
128C4⋊C4—28no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—44no—
132C4⋊C4#1062532914yes—
133C42—22no—
134C42—22no—
135C42—24no—
136C42—42no—
137C42—41no—
138C42—44no—
139C23C2×C22⋊Dic4711yescharacteristic
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4#1309394312yes—
157C2×C4C2×#1062532912yes—
158C2×C4#1309404414yes—
159C8—3764no—
160C22#1568908711yescharacteristic
161C22#1568909711yescharacteristic
162C22C2×#1309394311yescharacteristic
163C22#1568911912yes—
164C22#1568914012yes—
165C4—24no—
166C4—22no—
167C4—22no—
168C4—41no—
169C4—42no—
170C4—44no—
171C4—82no—
172C2#2024173211yescharacteristic
173C2#2024182212yes—
174C2#2024196512yes—
175C2#2024201511yescharacteristic
176C2#2024205311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×#125×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×#125D47
hypocenterC47#7650
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
102. C47#7650semidirect

Maximal subgroups

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

subgroupindex
#202435312
#202412112
C4×#125×C472
#765047