Finite Group Databasebeta

← #20254741

Subgroups — #20254741

Order 6016.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689659C212yesmaximal, complemented
2#15689432C212yesmaximal, complemented
3#15689426C212yesmaximal, complemented
4#15689359C211yesmaximal, characteristic
5#15689354C212yesmaximal, complemented
6#15689347C212yesmaximal, complemented
7#15689341C212yesmaximal, complemented
8C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
9C47×#467C211yesmaximal, characteristic, complemented
10C2×#10625336C2212yes—
11C2×D376C2211yescharacteristic
12C22×C47⋊C8C2211yescharacteristic
13#13094019—22no—
14#13094015C2212yes—
15#13094013C2212yes—
16#13094008—22no—
17#13093998C2212yes—
18Q8×Dic47C2212yes—
19#13093986C2212yes—
20(C22⋊D47)⋊C4—22no—
21#13093982—22no—
22C2×C4×Dic47C2211yescharacteristic
23#13093958C2211yescharacteristic
24#13093955C2212yes—
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—
38C22×Dic47D411yescharacteristic
39C22×Dic47D411yescharacteristic
40C2×D188C2312yes—
41C2×C4×D47—22no—
42Q16×C47—41no—
43C2×C8×C47—41no—
44C2×C8×C47C2311yescharacteristic
45C2×C8×C47C2311yescharacteristic
46C4⋊C4×C47—22no—
47C4⋊C4×C47C2312yes—
48C22⋊C4×C47—22no—
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⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58C4×Dic47—22no—
59C4×Dic47D412yes—
60C4×Dic47C2312yes—
61C2×C47⋊C8—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—44no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—41no—
78C2×Dic47C2×D412yes—
79C2×Dic47C2×D412yes—
80D188—22no—
81D188—22no—
82C4×D47—44no—
83C8×C47—21no—
84C8×C47—21no—
85C47⋊C8—22no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47#13512yes—
89C22×C47C22×D411yescharacteristic
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—42no—
93C4×C47—21no—
94C4×C47—42no—
95C4×C47—42no—
96C4×C47H(5,𝔽2)11yescharacteristic
97C4×C472−1+411yescharacteristic
98Dic47—22no—
99Dic47—22no—
100Dic47—42no—
101#3250—471nomaximal, Sylow
102C2×C47—22no—
103C2×C47#53711yescharacteristic
104C2×C47C2×#13511yescharacteristic
105C2×C47#57511yescharacteristic
106D47—82no—
107#529—472no—
108#479—472no—
109#478—472no—
110#467D4711yescharacteristic, complemented
111#466—471no—
112#465—472no—
113#464—472no—
114#463—472no—
115C2×C4⋊C8—471no—
116C47#325011yescharacteristic, complemented, Sylow
117C2×Q16C2×D4711yescharacteristic
118C2×SD16—472no—
119C2×D8—471no—
120C22×C8—471no—
121C22×C8C2×D4711yescharacteristic
122#126—942no—
123#125—472no—
124#124—472no—
125#123—942no—
126C22⋊Q8C2×D4712yes—
127#121—472no—
128C4×Q8—472no—
129C4×D4—472no—
130C4×D4—942no—
131#117—942no—
132C2×C42—471no—
133#107—471no—
134#107C2×D4711yescharacteristic
135#106—472no—
136C4⋊C8—472no—
137C4⋊C8—472no—
138#103—472no—
139#103C2×D4712yes—
140#102—472no—
141#102—472no—
142C2×Q8C22×D4712yes—
143C2×D4—472no—
144C2×D4—942no—
145C22×C4—471no—
146C22×C4—471no—
147C22×C4—942no—
148C22×C4C22×D4711yescharacteristic
149Q16—41no—
150SD16—1882no—
151D8—1881no—
152C2×C8—41no—
153C2×C8—472no—
154C2×C8—1881no—
155C2×C8C22×D4711yescharacteristic
156C2×C8C22×D4711yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—472no—
159C4⋊C4—942no—
160C4⋊C4—942no—
161C4⋊C4—942no—
162C4⋊C4C22×D4712yes—
163C22⋊C4—22no—
164C22⋊C4—942no—
165C22⋊C4—942no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C42—472no—
169C42—472no—
170C42—942no—
171C23—942no—
172C23D4×D4711yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—942no—
176D4—942no—
177D4—1884no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—472no—
183C2×C4—472no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—1884no—
187C2×C4—1881no—
188C2×C4D4×D4711yescharacteristic
189C2×C4C23×D4711yescharacteristic
190C8—21no—
191C8—21no—
192C8—942no—
193C22—21no—
194C22—21no—
195C22—1882no—
196C22—1882no—
197C22—1882no—
198C22#1309404712yes—
199C22C2×D4×D4711yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—942no—
204C4—942no—
205C4—1882no—
206C4#1309406911yescharacteristic
207C4#1309407111yescharacteristic
208C2—22no—
209C2—3762no—
210C2#1568970011yescharacteristic
211C2C2×#1309404711yescharacteristic
212C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3250
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. #15689659C2semidirect
2. #15689432C2semidirect
3. #15689426C2semidirect
5. #15689354C2semidirect
6. #15689347C2semidirect
7. #15689341C2semidirect
8. C2×Dic47⋊C8C2semidirect
9. C47×#467C2semidirect
110. #467D47semidirect
116. C47#3250semidirect