Finite Group Databasebeta

← #20254850

Subgroups — #20254850

Order 6016.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689746C212yesmaximal, complemented
2#15689416C212yesmaximal, complemented
3#15689402C212yesmaximal, complemented
4#15689371C212yesmaximal, complemented
5#15689359C211yesmaximal, characteristic
6#15689347C212yesmaximal, complemented
7#15689341C212yesmaximal, complemented
8#15689149C211yesmaximal, characteristic, complemented
9C47×#467C211yesmaximal, characteristic, complemented
10C2×#10625336C2212yes—
11C2×D376C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13#13094023C2212yes—
14#13094019—22no—
15#13094013C2212yes—
16#13094010—22no—
17#13094006—22no—
18#13094004—22no—
19#13093998C2212yes—
20Q8×Dic47C2212yes—
21#13093986C2212yes—
22#13093983C2211yescharacteristic
23#13093958C2211yescharacteristic
24#13093957C2212yes—
25Dic47⋊C8C2212yes—
26Dic47⋊C8C2212yes—
27#13093948C2212yes—
28#13093946C2212yes—
29#13093944C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#107×C47C2211yescharacteristic
34#103×C47C2212yes—
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—22no—
38C2×D188C2312yes—
39C2×C4×D47—22no—
40C2×Dic94—22no—
41Q16×C47—41no—
42C2×C8×C47—41no—
43C2×C8×C47C2311yescharacteristic
44C2×C8×C47C2311yescharacteristic
45C4⋊C4×C47—22no—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—22no—
48C22⋊Dic47D412yes—
49#10625336—42no—
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47D411yescharacteristic
56C4⋊Dic47D411yescharacteristic
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C4×Dic47C2312yes—
61#10625329—41no—
62C2×C47⋊C8C2312yes—
63D376—41no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66Q8×C47—22no—
67Q8×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2411yescharacteristic
74C22⋊D47—82no—
75C2×Dic47—22no—
76C2×Dic47C2×D412yes—
77C2×Dic47C2×D412yes—
78D188—22no—
79D188—22no—
80C4×D47—82no—
81Dic94—82no—
82C8×C47—21no—
83C8×C47—21no—
84C47⋊C8—22no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47C22×D411yescharacteristic
89C2×D47—42no—
90C2×D47—42no—
91C2×D47—42no—
92C4×C47—21no—
93C4×C47—42no—
94C4×C47—42no—
95C4×C47H(5,𝔽2)11yescharacteristic
96C4×C472−1+411yescharacteristic
97Dic47—22no—
98Dic47—22no—
99Dic47—42no—
100#3262—471nomaximal, Sylow
101C2×C47—41no—
102C2×C47#53711yescharacteristic
103C2×C47#57611yescharacteristic
104C2×C47#57811yescharacteristic
105D47—82no—
106#542—472no—
107#477—472no—
108#474—472no—
109#468—472no—
110#467D4711yescharacteristic, complemented
111#466—471no—
112#464—472no—
113#463—472no—
114#424—471no—
115C47#326211yescharacteristic, complemented, Sylow
116C2×Q16C2×D4711yescharacteristic
117C2×SD16—472no—
118C2×D8—471no—
119C2×M16—471no—
120C22×C8C2×D4711yescharacteristic
121C4⋊Q8—472no—
122#126—942no—
123#124—472no—
124#124—942no—
125#123—942no—
126C22⋊Q8—942no—
127C22⋊Q8C2×D4712yes—
128#121—472no—
129C4×Q8—472no—
130C4×D4—472no—
131#117—471no—
132#107—471no—
133#107—472no—
134#107C2×D4711yescharacteristic
135C4⋊C8—472no—
136C4⋊C8—472no—
137#103—472no—
138#103C2×D4712yes—
139#102—472no—
140#102—472no—
141C2×Q8—942no—
142C2×Q8C22×D4712yes—
143C2×D4—472no—
144C2×D4—942no—
145C22×C4—942no—
146C22×C4C22×D4711yescharacteristic
147Q16—41no—
148SD16—1882no—
149D8—1881no—
150M16—1881no—
151C2×C8—41no—
152C2×C8—472no—
153C2×C8C22×D4711yescharacteristic
154C2×C8C22×D4711yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—471no—
157C4⋊C4—471no—
158C4⋊C4—472no—
159C4⋊C4—942no—
160C4⋊C4—942no—
161C4⋊C4C22×D4712yes—
162C22⋊C4—22no—
163C22⋊C4—472no—
164C22⋊C4—942no—
165C22⋊C4—942no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C42—472no—
169C42—942no—
170C23—942no—
171C23D4×D4711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—3762no—
175D4—942no—
176D4—942no—
177D4—3762no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—472no—
183C2×C4—472no—
184C2×C4—942no—
185C2×C4—3762no—
186C2×C4D4×D4711yescharacteristic
187C2×C4C23×D4711yescharacteristic
188C8—21no—
189C8—21no—
190C8—942no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—1882no—
195C22—1882no—
196C22—1882no—
197C22C2×D4×D4711yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—942no—
202C4—942no—
203C4—1882no—
204C4#1309406911yescharacteristic
205C4#1309407111yescharacteristic
206C2—41no—
207C2—3762no—
208C2#1568970011yescharacteristic
209C2#1568992511yescharacteristic
210C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3262
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689416C2semidirect
3. #15689402C2semidirect
4. #15689371C2semidirect
6. #15689347C2semidirect
7. #15689341C2semidirect
8. #15689149C2semidirect
9. C47×#467C2semidirect
110. #467D47semidirect
115. C47#3262semidirect