Finite Group Databasebeta

← #26109798

Subgroups — #26109798

Order 12032.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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#20245974C211yesmaximal, characteristic
2#20243312C211yesmaximal, characteristic
3#20241297C214yesmaximal
4C47×#1784C211yesmaximal, characteristic
5C2×#13093983C412yes—
6C2×#13093943—22no—
7#15689087C2212yes—
8#15689030—22no—
9#15689030—22no—
10#15688986C412yes—
11#15688986C2212yes—
12C23×Q8×C47C2211yescharacteristic
13C2×#101×C47—22no—
14C47×#407C2212yes—
15C2×#10625329—22no—
16#13093983—44no—
17C2×C4⋊Dic47—22no—
18C2×C22⋊Dic47C2×C414yes—
19C2×C4×Dic47—22no—
20#13093943—44no—
21C22⋊(C47⋊C8)—24no—
22C47⋊#95—24no—
23C47⋊#95—22no—
24C47⋊#95—22no—
25C22×Q8×C47—24no—
26C22×Q8×C47—44no—
27C22×Q8×C47D412yes—
28C22×Q8×C47D412yes—
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47C2×C411yescharacteristic
31C23×C4×C47C2311yescharacteristic
32C2×M16×C47—22no—
33#101×C47—44no—
34C22⋊C8×C47—24no—
35C24×C47C22×C411yescharacteristic
36C2×Q8×C47—24no—
37C2×Q8×C47—24no—
38C2×Q8×C47—24no—
39C2×Q8×C47—24no—
40C2×Q8×C47—42no—
41C2×Q8×C47—42no—
42C2×Q8×C47—416no—
43C22×C4×C47—22no—
44C22×C4×C47—24no—
45C22×C4×C47—22no—
46C22×C4×C47—42no—
47C22×C4×C47—42no—
48C22×C4×C47C22⋊C412yes—
49C22×C4×C47C22⋊C412yes—
50C22×C4×C47C2×D411yescharacteristic
51C22×C4×C47C2×D411yescharacteristic
52C22×C4×C47#4114yes—
53C22×Dic47—24no—
54M16×C47—44no—
55C2×C8×C47—42no—
56C22⋊Dic47—44no—
57C4⋊Dic47—44no—
58C4×Dic47—44no—
59#10625329—44no—
60C2×C47⋊C8—42no—
61C23×C47—22no—
62C23×C47—42no—
63C23×C47C2×C22⋊C411yescharacteristic
64C23×C47#11712yes—
65Q8×C47—48no—
66Q8×C47—48no—
67C2×C4×C47—28no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—44no—
76C2×C4×C47—44no—
77C2×C4×C47#9914yes—
78C2×C4×C47#12312yes—
79C2×C4×C47#12312yes—
80C2×Dic47—48no—
81C2×Dic47—44no—
82C8×C47—82no—
83C47⋊C8—82no—
84#8753—471nomaximal, Sylow
85C22×C47—22no—
86C22×C47—22no—
87C22×C47—24no—
88C22×C47—44no—
89C22×C47#38111yescharacteristic
90C22×C47C2×#9912yes—
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—24no—
94C4×C47—42no—
95Dic47—84no—
96#2310—471no—
97#1784—471no—
98#1784D4711yescharacteristic
99#1306—474no—
100C2×C47—22no—
101C2×C47—42no—
102C2×C47#181911yescharacteristic
103C2×C47#183012yes—
104C23×Q8C2×D4711yescharacteristic
105C2×#117—472no—
106C2×#101—22no—
107C2×#101—942no—
108#407—472no—
109#407C2×D4712yes—
110#391—942no—
111#391—942no—
112#381—472no—
113#381—472no—
114C47#875311yescharacteristic, complemented, Sylow
115C22×Q8—24no—
116C22×Q8—44no—
117C22×Q8D18812yes—
118C22×Q8C22⋊D4712yes—
119C23×C4C4×D4711yescharacteristic
120C23×C4C4×D4711yescharacteristic
121C23×C4C22×D4711yescharacteristic
122C2×M16—22no—
123C2×M16—942no—
124#117—1884no—
125C2×C4⋊C4—942no—
126C2×C22⋊C4—474no—
127C2×C42—942no—
128#101—44no—
129#101—1884no—
130C22⋊C8—24no—
131C22⋊C8—944no—
132#95—944no—
133#95—942no—
134#95—942no—
135C24C2×C4×D4711yescharacteristic
136C2×Q8—24no—
137C2×Q8—24no—
138C2×Q8—24no—
139C2×Q8—24no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—416no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—22no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—944no—
149C22×C4(C2×D47)⋊C412yes—
150C22×C4(C2×D47)⋊C412yes—
151C22×C4C2×D18811yescharacteristic
152C22×C4#1062535214yes—
153C22×C4C2×C22⋊D4711yescharacteristic
154M16—44no—
155M16—1884no—
156C2×C8—42no—
157C2×C8—1882no—
158C4⋊C4—1884no—
159C22⋊C4—1884no—
160C42—1884no—
161C23—22no—
162C23—42no—
163C23C2×(C2×D47)⋊C411yescharacteristic
164C23#1309398012yes—
165Q8—48no—
166Q8—48no—
167C2×C4—28no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—1888no—
178C2×C4—1884no—
179C2×C4#1309393814yes—
180C2×C4#1309400512yes—
181C2×C4#1309400812yes—
182C8—82no—
183C8—3762no—
184C22—22no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22#1568898411yescharacteristic
189C22C2×#1309393812yes—
190C4—22no—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—3764no—
195C2—22no—
196C2—42no—
197C2#2024346011yescharacteristic
198C2#2024350012yes—
subgroupG/H
centerC22#15688984
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1784C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1784D47
hypocenterC47#8753
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
114. C47#8753semidirect

Maximal subgroups

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

subgroupindex
#202459742
#202433122
#202412972
C47×#17842
#875347