Finite Group Databasebeta

← #26104552

Subgroups — #26104552

Order 12032.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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
2#20241214C214yesmaximal
3C4×C4⋊Q8×C47C211yesmaximal, characteristic
4C2×#13093935—22no—
5#15688878—22no—
6#15688878C2214yes—
7C2×C4⋊Q8×C47C411yescharacteristic
8C2×C4×Q8×C47C412yes—
9C47×#391C2212yes—
10C47×#389—22no—
11C47×#384C411yescharacteristic
12C4×C4⋊C4×C47—22no—
13C43×C47C2211yescharacteristic
14C22×C47⋊C8—24no—
15#13093935—28no—
16C22×Q8×C47C2×C412yes—
17C4⋊Q8×C47—24no—
18C4×Q8×C47—44no—
19C2×C4⋊C4×C47—22no—
20C2×C4⋊C4×C47—22no—
21C2×C4⋊C4×C47—22no—
22C2×C4⋊C4×C47C2×C412yes—
23C2×C42×C47—22no—
24C2×C42×C47C2×C411yescharacteristic
25C2×C42×C47C2×C411yescharacteristic
26C2×C42×C47D412yes—
27C2×C42×C47D412yes—
28C2×C42×C47C2311yescharacteristic
29#95×C47—24no—
30C2×Q8×C47—22no—
31C2×Q8×C47—42no—
32C2×Q8×C47—42no—
33C2×Q8×C47M1614yes—
34C22×C4×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47C22⋊C411yescharacteristic
37C22×C4×C47C22⋊C411yescharacteristic
38C22×C4×C47C22⋊C412yes—
39C22×C4×C47C22×C411yescharacteristic
40C22×C4×C47C2×D412yes—
41C4⋊C4×C47—28no—
42C4⋊C4×C47—44no—
43C4⋊C4×C47—42no—
44C4⋊C4×C47—44no—
45C42×C47—22no—
46C42×C47—24no—
47C42×C47—22no—
48C42×C47—24no—
49C42×C47—41no—
50C42×C47—44no—
51C2×C47⋊C8—28no—
52C2×C47⋊C8—44no—
53C2×C47⋊C8—44no—
54C23×C47C2×C22⋊C411yescharacteristic
55Q8×C47—44no—
56Q8×C47—44no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—24no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—42no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—44no—
71C2×C4×C47#10012yes—
72C2×C4×C47#10414yes—
73C2×C4×C47C2×M1612yes—
74C2×C4×C47#13714yes—
75C47⋊C8—48no—
76#7639—471nomaximal, Sylow
77C22×C47#40711yescharacteristic
78C22×C47#41011yescharacteristic
79C22×C47C2×#10011yescharacteristic
80C22×C47#41912yes—
81C22×C47C2×#10412yes—
82C4×C47—22no—
83C4×C47—22no—
84C4×C47—24no—
85C4×C47—24no—
86C4×C47—44no—
87C4×C47—41no—
88C4×C47—82no—
89C4×C4⋊Q8D4711yescharacteristic
90#1745—472no—
91#1272—474no—
92C2×C47#146611yescharacteristic
93C2×C47#149112yes—
94C2×C47#150612yes—
95C2×C47#152511yescharacteristic
96C2×C47#155811yescharacteristic
97C2×C4⋊Q8Dic4711yescharacteristic
98C2×C4×Q8Dic4712yes—
99C2×#97—942no—
100#391C2×D4712yes—
101#389—22no—
102#384Dic4711yescharacteristic
103C4×C4⋊C4—22no—
104C43C2×D4711yescharacteristic
105#336—474no—
106#336—942no—
107C47#763911yescharacteristic, complemented, Sylow
108C22×Q8C2×Dic4712yes—
109C22×C8—944no—
110C4⋊Q8—24no—
111C4×Q8—44no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4C2×Dic4712yes—
116C2×C42—22no—
117C2×C42C2×Dic4711yescharacteristic
118C2×C42C2×Dic4711yescharacteristic
119C2×C42C22⋊D4712yes—
120C2×C42C22⋊D4712yes—
121C2×C42C22×D4711yescharacteristic
122#97—948no—
123#95—24no—
124C2×Q8—22no—
125C2×Q8—42no—
126C2×Q8—42no—
127C2×Q8#1062532914yes—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4C22⋊Dic4711yescharacteristic
131C22×C4C22⋊Dic4711yescharacteristic
132C22×C4C22⋊Dic4712yes—
133C22×C4C22×Dic4711yescharacteristic
134C22×C4C2×C22⋊D4712yes—
135C2×C8—948no—
136C2×C8—1884no—
137C2×C8—1884no—
138C4⋊C4—28no—
139C4⋊C4—42no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C42—22no—
143C42—24no—
144C42—22no—
145C42—24no—
146C42—41no—
147C42—44no—
148C23C2×C22⋊Dic4711yescharacteristic
149Q8—44no—
150Q8—44no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4#1309394112yes—
166C2×C4#1309395114yes—
167C2×C4C2×#1062532912yes—
168C2×C4#1309405514yes—
169C8—1888no—
170C22#1568908711yescharacteristic
171C22#1568909711yescharacteristic
172C22C2×#1309394111yescharacteristic
173C22#1568913212yes—
174C22C2×#1309395112yes—
175C4—22no—
176C4—24no—
177C4—22no—
178C4—24no—
179C4—41no—
180C4—44no—
181C4—82no—
182C2#2024172911yescharacteristic
183C2#2024183512yes—
184C2#2024190012yes—
185C2#2024198011yescharacteristic
186C2#2024211411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×C4⋊Q8×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×C4⋊Q8D47
hypocenterC47#7639
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
107. C47#7639semidirect

Maximal subgroups

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

subgroupindex
#202431372
#202412142
C4×C4⋊Q8×C472
#763947