Finite Group Databasebeta

← #26107204

Subgroups — #26107204

Order 12032.

444 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 151 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#20243137C212yesmaximal
2C2×#15688865C212yesmaximal
3#20241269C212yesmaximal
4C4×#125×C47C211yesmaximal, characteristic
5C2×#13093935C2214yes—
6#15688878—22no—
7#15688878—22no—
8#15688865C418yescomplemented
9C2×#125×C47C2211yescharacteristic
10C47×#389C412yes—
11C47×#387—22no—
12C47×#382C2211yescharacteristic
13C4×C4⋊C4×C47—22no—
14C4×C4⋊C4×C47C412yes—
15C43×C47C2211yescharacteristic
16C22×C47⋊C8—24no—
17#13093935—24no—
18#13093935C2×C418yes—
19#125×C47—22no—
20#125×C47C2×C414yes—
21C2×C4⋊C4×C47—22no—
22C2×C4⋊C4×C47—22no—
23C2×C4⋊C4×C47C2×C412yes—
24C2×C4⋊C4×C47C2×C412yes—
25C2×C42×C47—22no—
26C2×C42×C47C2×C411yescharacteristic
27C2×C42×C47C2×C411yescharacteristic
28C2×C42×C47D412yes—
29C2×C42×C47D412yes—
30C2×C42×C47C2311yescharacteristic
31#95×C47—22no—
32#95×C47—22no—
33#95×C47—22no—
34C22×C4×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47C22⋊C412yes—
37C22×C4×C47C22⋊C411yescharacteristic
38C22×C4×C47C22⋊C411yescharacteristic
39C22×C4×C47C22×C411yescharacteristic
40C22×C4×C47C2×D412yes—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—28no—
43C4⋊C4×C47—44no—
44C4⋊C4×C47—42no—
45C4⋊C4×C47C4214yes—
46C42×C47—22no—
47C42×C47—41no—
48C42×C47—42no—
49C42×C47—42no—
50C42×C47—44no—
51C42×C47C22×C412yes—
52C42×C47#4112yes—
53C2×C47⋊C8—28no—
54C2×C47⋊C8—44no—
55C2×C47⋊C8—44no—
56C23×C47C2×C22⋊C411yescharacteristic
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—24no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47#10112yes—
74C2×C4×C47C2×C4211yescharacteristic
75C2×C4×C47#11711yescharacteristic
76C2×C4×C47C4×D414yes—
77C47⋊C8—48no—
78#8225—471nomaximal, Sylow
79C22×C47C4×C22⋊C411yescharacteristic
80C22×C47C2×#10111yescharacteristic
81C22×C47#41311yescharacteristic
82C22×C47#42112yes—
83C22×C47#42112yes—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—24no—
87C4×C47—22no—
88C4×C47—41no—
89C4×C47—44no—
90C4×C47—42no—
91C4×C47—82no—
92C4×#125D4711yescharacteristic
93#1745—472no—
94C2×#330—472no—
95#1295—472no—
96C2×C47#153411yescharacteristic
97C2×C47#153512yes—
98C2×C47#153711yescharacteristic
99C2×C47C4×#10111yescharacteristic
100C2×C47#175912yes—
101C2×#125C2×D4711yescharacteristic
102C2×#97—474no—
103#389Dic4712yes—
104#387—22no—
105#382C2×D4711yescharacteristic
106C4×C4⋊C4—22no—
107C4×C4⋊C4Dic4712yes—
108C43C2×D4711yescharacteristic
109#336—942no—
110#336—942no—
111#330—478no—
112C47#822511yescharacteristic, complemented, Sylow
113C22×C8—944no—
114#125—22no—
115#125C4×D4714yes—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4C2×Dic4712yes—
119C2×C4⋊C4C2×Dic4712yes—
120C2×C42—22no—
121C2×C42C2×Dic4711yescharacteristic
122C2×C42C2×Dic4711yescharacteristic
123C2×C42C22⋊D4712yes—
124C2×C42C22⋊D4712yes—
125C2×C42C22×D4711yescharacteristic
126#97—478no—
127#97—944no—
128#95—22no—
129#95—22no—
130#95—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4C22⋊Dic4711yescharacteristic
134C22×C4C22⋊Dic4712yes—
135C22×C4C22⋊Dic4711yescharacteristic
136C22×C4C22×Dic4711yescharacteristic
137C22×C4C2×C22⋊D4712yes—
138C2×C8—948no—
139C2×C8—1884no—
140C2×C8—1884no—
141C4⋊C4—22no—
142C4⋊C4—28no—
143C4⋊C4—42no—
144C4⋊C4—44no—
145C4⋊C4C4×Dic4714yes—
146C42—22no—
147C42—41no—
148C42—42no—
149C42—42no—
150C42—44no—
151C42C2×C4×D4712yes—
152C42#1062535012yes—
153C23C2×C22⋊Dic4711yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#1309394312yes—
171C2×C4C2×C4×Dic4711yescharacteristic
172C2×C4#1309398311yescharacteristic
173C2×C4C4×C22⋊D4714yes—
174C8—1888no—
175C22C4×C22⋊Dic4711yescharacteristic
176C22C2×#1309394311yescharacteristic
177C22#1568910711yescharacteristic
178C22#1568914012yes—
179C22#1568914012yes—
180C4—22no—
181C4—21no—
182C4—21no—
183C4—24no—
184C4—42no—
185C4—41no—
186C4—44no—
187C4—82no—
188C2#2024201511yescharacteristic
189C2#2024201912yes—
190C2#2024202611yescharacteristic
191C2C4×#1309394311yescharacteristic
192C2#2024319812yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC4×#125×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×#125D47
hypocenterC47#8225
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
8. #15688865C4semidirect
112. C47#8225semidirect

Maximal subgroups

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

subgroupindex
#202431372
C2×#156888652
#202412692
C4×#125×C472
#822547