Finite Group Databasebeta

← #20256047

Subgroups — #20256047

Order 6016.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689858C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic, complemented
3#15689479C212yesmaximal, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689426C212yesmaximal, complemented
6#15689341C212yesmaximal, complemented
7#15689319C211yesmaximal, characteristic
8#15689247C211yesmaximal, characteristic, complemented
9C4×#10625336C211yesmaximal, characteristic, complemented
10#15689205C212yesmaximal, complemented
11C47×#477C211yesmaximal, characteristic, complemented
12C2×#10625336C2211yescharacteristic
13C2×D376C2212yes—
14#13094021C2211yescharacteristic
15#13094015C2212yes—
16#13094013C2212yes—
17#13094012—21no—
18#13094009—22no—
19#13094004—21no—
20#13094000—22no—
21C4×Dic94C2211yescharacteristic
22C4×D188—21no—
23C4×D188C2211yescharacteristic
24#13093986C2212yes—
25#13093986C2212yes—
26C4⋊C4×D47—21no—
27#13093955C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093948C2211yescharacteristic
30#13093946C2212yes—
31#13093944C2212yes—
32#13093944C2212yes—
33#13093944C2211yescharacteristic
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#107×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188—21no—
44C2×D188—21no—
45C2×D188C2312yes—
46C2×D188C2311yescharacteristic
47C2×C4×D47—21no—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×Dic94D411yescharacteristic
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58#10625336—22no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C4⋊Dic47—22no—
65C4⋊Dic47D411yescharacteristic
66C4⋊Dic47C2311yescharacteristic
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72D376—24no—
73C22×D47—21no—
74C22×D47—22no—
75Q8×C47—21no—
76Q8×C47—21no—
77Q8×C47—81no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—21no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87D188—22no—
88D188—21no—
89D188—22no—
90D188—42no—
91D188—81no—
92D188#4112yes—
93C4×D47—42no—
94C4×D47—82no—
95C4×D47—82no—
96Dic94—22no—
97C8×C47—22no—
98C47⋊C8—21no—
99C47⋊C8—21no—
100C22×C47C22×D411yescharacteristic
101C2×D47—22no—
102C2×D47—41no—
103C2×D47—41no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—21no—
108C4×C47—41no—
109C4×C47—41no—
110C4×C47—42no—
111C4×C47#13512yes—
112C4×C47C2×#4111yescharacteristic
113C4×C472−1+411yescharacteristic
114Dic47—22no—
115Dic47—22no—
116Dic47—41no—
117#3361—471nomaximal, Sylow
118C2×C47#54811yescharacteristic
119C2×C47C2×#13511yescharacteristic
120C2×C47#57611yescharacteristic
121D47—42no—
122D47—82no—
123#559—471no—
124#554—471no—
125#488—472no—
126#486—471no—
127#478—472no—
128#477D4711yescharacteristic, complemented
129#463—472no—
130#459—471no—
131C8×Q8—471no—
132C4×SD16—471no—
133C4×D8—472no—
134C47#336111yescharacteristic, complemented, Sylow
135C2×SD16—471no—
136C2×D8—472no—
137C4⋊Q8C2×D4711yescharacteristic
138#127—471no—
139#125—472no—
140#124—472no—
141#124—941no—
142#123—942no—
143C22⋊Q8—941no—
144C22⋊Q8—942no—
145C4×Q8—471no—
146C4×Q8C2×D4711yescharacteristic
147C4×D4—472no—
148C4×D4—472no—
149C4×D4—471no—
150C4×D4—941no—
151C2×C4⋊C4—941no—
152#107C2×D4712yes—
153#106—471no—
154C4⋊C8—472no—
155C4⋊C8C2×D4711yescharacteristic
156#103—471no—
157#103C2×D4712yes—
158#102—472no—
159#102—471no—
160#102—472no—
161#102—472no—
162C4×C8—472no—
163C4×C8—471no—
164C2×Q8—21no—
165C2×Q8—471no—
166C2×Q8C22×D4711yescharacteristic
167C2×D4—471no—
168C2×D4—472no—
169C2×D4—941no—
170C2×D4—941no—
171C22×C4—942no—
172C22×C4—942no—
173C22×C4—941no—
174SD16—942no—
175D8—944no—
176C2×C8—471no—
177C2×C8—471no—
178C2×C8C22×D4712yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—472no—
182C4⋊C4—471no—
183C4⋊C4—471no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4C22×D4712yes—
187C4⋊C4C22×D4711yescharacteristic
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—941no—
193C42—21no—
194C42—472no—
195C42C22×D4711yescharacteristic
196C23—941no—
197C23—942no—
198Q8—21no—
199Q8—21no—
200Q8—81no—
201Q8—942no—
202D4—472no—
203D4—942no—
204D4—941no—
205D4—942no—
206D4—3761no—
207D4—1882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—472no—
212C2×C4—472no—
213C2×C4—941no—
214C2×C4—3762no—
215C2×C4—3762no—
216C2×C4—1882no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—22no—
221C8—941no—
222C8—941no—
223C22—942no—
224C22—1882no—
225C22—1882no—
226C22—1882no—
227C22—1881no—
228C22—1881no—
229C22C2×D4×D4711yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—42no—
234C4—942no—
235C4—942no—
236C4—1881no—
237C4#1309404712yes—
238C4#41×D4711yescharacteristic
239C4#1309407211yescharacteristic
240C2—3762no—
241C2—1882no—
242C2#1568978311yescharacteristic
243C2C2×#1309404711yescharacteristic
244C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#477C2
socleC22×C47C22×D4
hypercenter#477D47
hypocenterC47#3361
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689834C2semidirect
3. #15689479C2semidirect
4. #15689471C2semidirect
5. #15689426C2semidirect
6. #15689341C2semidirect
8. #15689247C2semidirect
9. C4×#10625336C2semidirect
10. #15689205C2semidirect
11. C47×#477C2semidirect
128. #477D47semidirect
134. C47#3361semidirect