Finite Group Databasebeta

← #20245071

Subgroups — #20245071

Order 6016.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689669C211yesmaximal, characteristic
2#15689107C211yesmaximal, characteristic, complemented
3#15688921C212yesmaximal, complemented
4#15688919C212yesmaximal, complemented
5C47×#413C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic
7C2×#10625329—21no—
8#13094022C2211yescharacteristic
9#13094020C411yescharacteristic
10#13094013C2211yescharacteristic
11#13094011C411yescharacteristic
12#13093996—21no—
13#13093996—21no—
14C4×C22⋊D47—21no—
15C4×C22⋊D47—21no—
16C2×C4×Dic47C411yescharacteristic
17#13093943C2212yes—
18#13093941—21no—
19C2×#41×C47C2211yescharacteristic
20C2×M16×C47—21no—
21#101×C47C2212yes—
22#100×C47—21no—
23#41×C47—41no—
24#41×C47—41no—
25C2×Q8×C47C2311yescharacteristic
26C2×D4×C47C2×C411yescharacteristic
27C2×D4×C47D411yescharacteristic
28C2×D4×C47D411yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C22×Dic47—21no—
36#10625350—41no—
37#10625350—41no—
38C2×D188C2×C411yescharacteristic
39C2×C4×D47—21no—
40C2×Dic94C2×C411yescharacteristic
41M16×C47—22no—
42M16×C47—41no—
43C2×C8×C47—41no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50C4×Dic47—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47C2×C411yescharacteristic
53#10625329—22no—
54#10625329—41no—
55C2×C47⋊C8—41no—
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22⋊C411yescharacteristic
58C23×C47C22⋊C411yescharacteristic
59C22×D47—21no—
60Q8×C47—41no—
61D4×C47—41no—
62D4×C47—41no—
63D4×C47—41no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47C22⋊C411yescharacteristic
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C22⋊D47—42no—
75C22⋊D47—42no—
76C22⋊D47—42no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—42no—
81D188—41no—
82C4×D47—41no—
83C4×D47—41no—
84Dic94—41no—
85C8×C47—42no—
86C47⋊C8—42no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47C2×C22⋊C411yescharacteristic
94C2×D47—41no—
95C2×D47—41no—
96C2×D47—41no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47#9911yescharacteristic
101C4×C47#9911yescharacteristic
102Dic47—22no—
103Dic47—41no—
104Dic47—41no—
105#2132—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—41no—
108C2×C47—41no—
109C2×C47—41no—
110C2×C47C2×#9911yescharacteristic
111D47—81no—
112#532—471no—
113#413—471no—
114#413D4711yescharacteristic, complemented
115#356—472no—
116#355—472no—
117C47#213211yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C2×#41C2×D4711yescharacteristic
120C2×M16—21no—
121C2×M16—941no—
122C4⋊Q8—471no—
123#127—471no—
124#124—471no—
125#124—471no—
126#121—941no—
127#121—941no—
128C4×D4—941no—
129C4×D4—941no—
130C2×C42—471no—
131#101—472no—
132#101C2×D4712yes—
133#100—21no—
134#100—941no—
135#41—41no—
136#41—41no—
137#41—1881no—
138#41—1881no—
139C2×Q8—471no—
140C2×Q8C22×D4711yescharacteristic
141C2×D4—471no—
142C2×D4—941no—
143C2×D4—941no—
144C2×D4—941no—
145C2×D4C4×D4711yescharacteristic
146C2×D4D18811yescharacteristic
147C2×D4C22⋊D4711yescharacteristic
148C22×C4—941no—
149C22×C4—941no—
150C22×C4C4×D4711yescharacteristic
151C22×C4D18811yescharacteristic
152C22×C4C22⋊D4711yescharacteristic
153M16—22no—
154M16—41no—
155M16—942no—
156M16—1881no—
157C2×C8—41no—
158C2×C8—1881no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—941no—
164C22⋊C4—941no—
165C42—471no—
166C42—471no—
167C42—941no—
168C23—941no—
169C23(C2×D47)⋊C411yescharacteristic
170C23(C2×D47)⋊C411yescharacteristic
171C23(C2×D47)⋊C411yescharacteristic
172Q8—41no—
173Q8—1881no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—1881no—
178D4—1882no—
179D4—1882no—
180D4—1882no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—941no—
188C2×C4—941no—
189C2×C4—941no—
190C2×C4—1882no—
191C2×C4—1881no—
192C2×C4—1881no—
193C2×C4(C2×D47)⋊C411yescharacteristic
194C2×C4C2×C4×D4711yescharacteristic
195C2×C4C2×D18811yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—42no—
198C8—1882no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—1881no—
206C22—1881no—
207C22—1881no—
208C22C2×(C2×D47)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—942no—
213C4—1881no—
214C4—1881no—
215C4#1309393811yescharacteristic
216C4#1309393811yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—3761no—
222C2C2×#1309393811yescharacteristic
subgroupG/H
centerC4#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC47×#413C2
socleC2×C47C2×#99
hypercenter#413D47
hypocenterC47#2132
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #15689107C2semidirect
3. #15688921C2semidirect
4. #15688919C2semidirect
5. C47×#413C2semidirect
114. #413D47semidirect
117. C47#2132semidirect