Finite Group Databasebeta

← #26104396

Subgroups — #26104396

Order 12032.

408 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 143 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#20243505C212yesmaximal
2#20241211C214yesmaximal
3C4×#125×C47C211yesmaximal, characteristic
4C2×C4⋊(C47⋊C8)—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—
15C4⋊(C47⋊C8)—44no—
16#125×C47—22no—
17#125×C47C814yescomplemented
18C2×C4⋊C4×C47—22no—
19C2×C4⋊C4×C47—22no—
20C2×C4⋊C4×C47C2×C412yes—
21C2×C4⋊C4×C47C2×C412yes—
22C2×C42×C47—22no—
23C2×C42×C47C2×C411yescharacteristic
24C2×C42×C47C2×C411yescharacteristic
25C2×C42×C47D412yes—
26C2×C42×C47D412yes—
27C2×C42×C47C2311yescharacteristic
28#95×C47—22no—
29#95×C47—22no—
30#95×C47—22no—
31C22×C4×C47—22no—
32C22×C4×C47—22no—
33C22×C4×C47C22⋊C411yescharacteristic
34C22×C4×C47C22⋊C412yes—
35C22×C4×C47C22⋊C411yescharacteristic
36C22×C4×C47C22×C411yescharacteristic
37C22×C4×C47C2×D412yes—
38C4⋊C4×C47—28no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—42no—
41C4⋊C4×C47—42no—
42C4⋊C4×C47—42no—
43C4⋊C4×C47C2×C814yes—
44C42×C47—22no—
45C42×C47—22no—
46C42×C47—22no—
47C42×C47—42no—
48C42×C47—41no—
49C42×C47—44no—
50C42×C47C2×C812yes—
51C42×C47M1612yes—
52C2×C47⋊C8—44no—
53C2×C47⋊C8—44no—
54C2×C47⋊C8—44no—
55C23×C47C2×C22⋊C411yescharacteristic
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—24no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—42no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47C22⋊C814yes—
72C2×C4×C47#10112yes—
73C2×C4×C47C22×C811yescharacteristic
74C2×C4×C47C2×M1611yescharacteristic
75C2×C4×C47AGL(1,ℤ/8)12yes—
76C2×C4×C47#13712yes—
77C47⋊C8—84no—
78#7602—471nomaximal, Sylow
79C22×C47C2×C22⋊C811yescharacteristic
80C22×C47#41011yescharacteristic
81C22×C47C2×#10111yescharacteristic
82C22×C47#41712yes—
83C22×C47#42112yes—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—24no—
87C4×C47—22no—
88C4×C47—22no—
89C4×C47—22no—
90C4×C47—41no—
91C4×C47—44no—
92C4×C47—82no—
93C4×#125D4711yescharacteristic
94#1831—472no—
95#1271—474no—
96C2×C47#146111yescharacteristic
97C2×C47#147712yes—
98C2×C47#151212yes—
99C2×C47#153411yescharacteristic
100C2×C47#156111yescharacteristic
101C2×#125Dic4711yescharacteristic
102C2×C4⋊C8—942no—
103#389C2×D4712yes—
104#387—22no—
105#382Dic4711yescharacteristic
106C4×C4⋊C4—22no—
107C4×C4⋊C4Dic4712yes—
108C43C2×D4711yescharacteristic
109#336—474no—
110#336—942no—
111C47#760211yescharacteristic, complemented, Sylow
112C22×C8—944no—
113#125—22no—
114#125C47⋊C814yescomplemented
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×Dic4712yes—
118C2×C4⋊C4C2×Dic4712yes—
119C2×C42—22no—
120C2×C42C2×Dic4711yescharacteristic
121C2×C42C2×Dic4711yescharacteristic
122C2×C42C22⋊D4712yes—
123C2×C42C22⋊D4712yes—
124C2×C42C22×D4711yescharacteristic
125C4⋊C8—1884no—
126#95—22no—
127#95—22no—
128#95—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4C22⋊Dic4711yescharacteristic
132C22×C4C22⋊Dic4712yes—
133C22×C4C22⋊Dic4711yescharacteristic
134C22×C4C22×Dic4711yescharacteristic
135C22×C4C2×C22⋊D4712yes—
136C2×C8—1884no—
137C2×C8—1884no—
138C2×C8—1884no—
139C4⋊C4—28no—
140C4⋊C4—22no—
141C4⋊C4—42no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4C2×C47⋊C814yes—
145C42—22no—
146C42—22no—
147C42—22no—
148C42—42no—
149C42—41no—
150C42—44no—
151C42C2×C47⋊C812yes—
152C42#1062532912yes—
153C23C2×C22⋊Dic4711yescharacteristic
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—24no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4C22⋊(C47⋊C8)14yes—
170C2×C4#1309394312yes—
171C2×C4C22×C47⋊C811yescharacteristic
172C2×C4C2×#1062532911yescharacteristic
173C2×C4#1309404912yes—
174C2×C4#1309405412yes—
175C8—3764no—
176C22C2×C22⋊(C47⋊C8)11yescharacteristic
177C22#1568909711yescharacteristic
178C22C2×#1309394311yescharacteristic
179C22#1568912412yes—
180C22#1568914012yes—
181C4—22no—
182C4—22no—
183C4—21no—
184C4—21no—
185C4—22no—
186C4—24no—
187C4—44no—
188C4—41no—
189C4—82no—
190C2#2024171211yescharacteristic
191C2#2024177512yes—
192C2#2024192612yes—
193C2#2024201511yescharacteristic
194C2#2024212611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC4×#125×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×#125D47
hypocenterC47#7602
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
17. #125×C47C8semidirect
111. C47#7602semidirect
114. #125C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
#202435052
#202412112
C4×#125×C472
#760247