Finite Group Databasebeta

← #26125711

Subgroups — #26125711

Order 12032.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#20252023C211yesmaximal, characteristic
2#20245197C212yesmaximal, complemented
3#20241338C212yesmaximal, complemented
4#20241324C211yesmaximal, characteristic
5C47×#1320C211yesmaximal, characteristic
6C2×#13093983C411yescharacteristic
7#15689181—22no—
8#15689181—22no—
9#15689146C411yescharacteristic
10#15689146C2211yescharacteristic
11#15689087C411yescharacteristic
12M16×Dic47C411yescharacteristic
13M16×Dic47C2211yescharacteristic
14#15688943—22no—
15#15688905C2212yes—
16#15688900—22no—
17C47×#407C2211yescharacteristic
18C47×#349C2212yes—
19C2×#10625329C2×C411yescharacteristic
20C2×#10625329C2×C411yescharacteristic
21#13093983—21no—
22#13093983—21no—
23#13093983—22no—
24C2×C4⋊Dic47—21no—
25C2×C22⋊Dic47—21no—
26C2×C4×Dic47C2×C411yescharacteristic
27C2×C4×Dic47C2×C411yescharacteristic
28#13093964—22no—
29Dic47⋊C8—22no—
30Dic47⋊C8—22no—
31C22⋊(C47⋊C8)—22no—
32#13093934—21no—
33#13093934D412yes—
34C8×Dic47—21no—
35C8×Dic47D412yes—
36C23×C4×C47C2×C411yescharacteristic
37C2×M16×C47C2×C411yescharacteristic
38C2×M16×C47C2311yescharacteristic
39M32×C47—22no—
40C22⋊C8×C47—22no—
41C24×C47M1611yescharacteristic
42C22×C4×C47—21no—
43C22×C4×C47—21no—
44C22×C4×C47—41no—
45C22×C4×C47—41no—
46C22×C4×C47M1611yescharacteristic
47C22×C4×C47C22×C411yescharacteristic
48C22×Dic47—21no—
49C22×Dic47—21no—
50M16×C47—41no—
51M16×C47—41no—
52C2×C8×C47—21no—
53C2×C8×C47C2×D412yes—
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60C4×Dic47C22⋊C411yescharacteristic
61C4×Dic47C22⋊C411yescharacteristic
62C4×Dic47M1612yes—
63#10625329—41no—
64#10625329—41no—
65C2×C47⋊C8—21no—
66C2×C47⋊C8C22⋊C412yes—
67C16×C47—42no—
68C47⋊C16—42no—
69C23×C47—21no—
70C23×C47—41no—
71C23×C47—81no—
72C23×C47C2×M1611yescharacteristic
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—42no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47C2×C22⋊C411yescharacteristic
81C2×C4×C47C2×M1611yescharacteristic
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—81no—
86C2×Dic47—81no—
87C8×C47—22no—
88C8×C47—41no—
89C47⋊C8—22no—
90C47⋊C8—41no—
91#11522—471nomaximal, Sylow
92C22×C47—21no—
93C22×C47—41no—
94C22×C47—42no—
95C22×C47—41no—
96C22×C47—82no—
97C22×C47#40711yescharacteristic
98C4×C47—21no—
99C4×C47—41no—
100C4×C47#41011yescharacteristic
101C4×C47#41311yescharacteristic
102Dic47—41no—
103Dic47—41no—
104Dic47—42no—
105#2921—471no—
106#2165—472no—
107#1327—472no—
108#1320—471no—
109#1320D4711yescharacteristic
110C2×C47—21no—
111C2×C47—41no—
112C2×C47—81no—
113C2×C47#146411yescharacteristic
114C2×#117—471no—
115#433—942no—
116#433—942no—
117#423—471no—
118#423—471no—
119#407—471no—
120#407C2×D4711yescharacteristic
121C4×M16—471no—
122C4×M16—471no—
123#364—942no—
124#349—472no—
125#349C2×D4712yes—
126#347—942no—
127C47#1152211yescharacteristic, complemented, Sylow
128C23×C4C4×D4711yescharacteristic
129C2×M16—471no—
130C2×M16—471no—
131C2×M16C4×D4711yescharacteristic
132C2×M16C22×D4711yescharacteristic
133#117—942no—
134#117—941no—
135#117—941no—
136C2×C4⋊C4—941no—
137C2×C22⋊C4—941no—
138C2×C42—471no—
139C2×C42—471no—
140M32—22no—
141M32—942no—
142C4⋊C8—942no—
143C4⋊C8—942no—
144C22⋊C8—22no—
145C22⋊C8—942no—
146#97—472no—
147#97—941no—
148C4×C8—472no—
149C4×C8—941no—
150C24#1062532411yescharacteristic
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—941no—
156C22×C4—941no—
157C22×C4#1062532411yescharacteristic
158C22×C4C2×C4×D4711yescharacteristic
159M16—41no—
160M16—41no—
161M16—1881no—
162M16—1881no—
163C2×C8—21no—
164C2×C8—472no—
165C2×C8—941no—
166C2×C8D4×D4712yes—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C22⋊C4—942no—
170C22⋊C4—942no—
171C42—471no—
172C42—471no—
173C42—472no—
174C42—941no—
175C42—941no—
176C16—42no—
177C16—1882no—
178C23—21no—
179C23—41no—
180C23—81no—
181C23C2×#1062532411yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—941no—
190C2×C4—941no—
191C2×C4—942no—
192C2×C4—3761no—
193C2×C4—3761no—
194C2×C4C22⋊C4×D4711yescharacteristic
195C2×C4M16×D4711yescharacteristic
196C8—22no—
197C8—41no—
198C8—942no—
199C8—1881no—
200C22—21no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22—82no—
205C22#1568908511yescharacteristic
206C4—21no—
207C4—41no—
208C4—1881no—
209C4—1881no—
210C4—1882no—
211C4#1568909511yescharacteristic
212C4#1568910411yescharacteristic
213C2—21no—
214C2—41no—
215C2—81no—
216C2#2024171911yescharacteristic
subgroupG/H
centerC4#15689095
commutatorC22×C4×C47C22×C4
FrattiniC2×M16C22×D47
FittingC47×#1320C2
socleC2×C47#1464
prime radicalC24×C47M16
cosocleC2×M16×C47C23
hypercenter#1320D47
hypocenterC47#11522
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #20245197C2semidirect
3. #20241338C2semidirect
127. C47#11522semidirect

Maximal subgroups

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

subgroupindex
#202520232
#202451972
#202413382
#202413242
C47×#13202
#1152247