Finite Group Databasebeta

← #26109677

Subgroups — #26109677

Order 12032.

554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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#20243150C212yesmaximal
2#20241269C214yesmaximal, complemented
3C2×C47×#382C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5C2×#13093935C2214yes—
6#15688878—22no—
7C22×C4⋊C4×C47C411yescharacteristic
8C22×C4⋊C4×C47C411yescharacteristic
9C22×C42×C47C2211yescharacteristic
10C47×#382—22no—
11C47×#382C412yes—
12C47×#382C2212yes—
13C2×#95×C47—22no—
14C22×C47⋊C8—24no—
15C22⋊(C47⋊C8)—28no—
16#13093935—28no—
17C23×C4×C47—21no—
18C23×C4×C47—21no—
19C23×C4×C47C2×C411yescharacteristic
20C23×C4×C47D412yes—
21C2×C4⋊C4×C47—21no—
22C2×C4⋊C4×C47—21no—
23C2×C4⋊C4×C47—42no—
24C2×C4⋊C4×C47—42no—
25C2×C4⋊C4×C47C2×C412yes—
26C2×C4⋊C4×C47C2×C412yes—
27C2×C42×C47—24no—
28C2×C42×C47C2×C411yescharacteristic
29C2×C42×C47D412yes—
30C2×C42×C47C2311yescharacteristic
31#95×C47—24no—
32#95×C47—24no—
33C24×C47C22⋊C411yescharacteristic
34C22×C4×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47—22no—
37C22×C4×C47—24no—
38C22×C4×C47—24no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—42no—
42C22×C4×C47—44no—
43C22×C4×C47—42no—
44C22×C4×C47—42no—
45C22×C4×C47—44no—
46C22×C4×C47C22⋊C412yes—
47C22×C4×C47C22⋊C411yescharacteristic
48C22×C4×C47C22×C411yescharacteristic
49C22×C4×C47C2×D412yes—
50C4⋊C4×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C42×C47—22no—
55C42×C47—24no—
56C42×C47#4114yes—
57C2×C47⋊C8—28no—
58C2×C47⋊C8—44no—
59C2×C47⋊C8—44no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—22no—
63C23×C47#10012yes—
64C23×C47#10414yes—
65C23×C47C2×C22⋊C411yescharacteristic
66C2×C4×C47—28no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—48no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—44no—
80C2×C4×C47—44no—
81C2×C4×C47—84no—
82C2×C4×C47—84no—
83C2×C4×C47#10112yes—
84C2×C4×C47#11712yes—
85C2×C4×C47#12314yes—
86C47⋊C8—48no—
87#8718—471nomaximal, Sylow
88C22×C47—22no—
89C22×C47—24no—
90C22×C47—24no—
91C22×C47—22no—
92C22×C47#32914yes—
93C22×C47#38111yescharacteristic
94C22×C47C2×#10011yescharacteristic
95C22×C47C2×#10111yescharacteristic
96C22×C47C2×#10412yes—
97C22×C47#42112yes—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47—24no—
101C4×C47—42no—
102C4×C47—82no—
103C4×C47—82no—
104C2×#382D4711yescharacteristic
105#1749—472no—
106#1295—474no—
107C2×C47—24no—
108C2×C47C2×#32911yescharacteristic
109C2×C47#152812yes—
110C2×C47#153311yescharacteristic
111C2×C47#182111yescharacteristic
112C2×C47#182612yes—
113C22×C4⋊C4Dic4711yescharacteristic
114C22×C4⋊C4Dic4711yescharacteristic
115C22×C42C2×D4711yescharacteristic
116C2×C22⋊C8—942no—
117C2×#97—474no—
118#382—22no—
119#382Dic4712yes—
120#382C2×D4712yes—
121C2×#95—22no—
122#336—942no—
123C47#871811yescharacteristic, complemented, Sylow
124C23×C4—21no—
125C23×C4—21no—
126C23×C4C2×Dic4711yescharacteristic
127C23×C4C22⋊D4712yes—
128C22×C8—944no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4C2×Dic4712yes—
134C2×C4⋊C4C2×Dic4712yes—
135C2×C42—24no—
136C2×C42C2×Dic4711yescharacteristic
137C2×C42C22⋊D4712yes—
138C2×C42C22×D4711yescharacteristic
139C22⋊C8—948no—
140#97—948no—
141#95—24no—
142#95—24no—
143C24C22⋊Dic4711yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—24no—
148C22×C4—24no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—44no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—44no—
156C22×C4C22⋊Dic4712yes—
157C22×C4C22⋊Dic4711yescharacteristic
158C22×C4C22×Dic4711yescharacteristic
159C22×C4C2×C22⋊D4712yes—
160C2×C8—948no—
161C2×C8—1884no—
162C2×C8—1884no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C42—22no—
168C42—24no—
169C42#1062535014yes—
170C23—21no—
171C23—21no—
172C23—22no—
173C23#1309394112yes—
174C23#1309395114yes—
175C23C2×C22⋊Dic4711yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—84no—
192C2×C4—84no—
193C2×C4#1309394312yes—
194C2×C4#1309398312yes—
195C2×C4#1309400714yes—
196C8—1888no—
197C22—22no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22#1568886314yes—
202C22#1568898611yescharacteristic
203C22C2×#1309394111yescharacteristic
204C22C2×#1309394311yescharacteristic
205C22C2×#1309395112yes—
206C22#1568914012yes—
207C4—22no—
208C4—22no—
209C4—24no—
210C4—42no—
211C4—82no—
212C4—82no—
213C2—24no—
214C2C2×#1568886311yescharacteristic
215C2#2024199012yes—
216C2#2024201211yescharacteristic
217C2#2024346811yescharacteristic
218C2#2024348712yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#382C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#382D47
hypocenterC47#8718
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #20241269C2semidirect
123. C47#8718semidirect

Maximal subgroups

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

subgroupindex
#202431502
#202412692
C2×C47×#3822
#871847