Finite Group Databasebeta

← #20254558

Subgroups — #20254558

Order 6016.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689657C211yesmaximal, characteristic
2C2×#13094016C211yesmaximal, characteristic, complemented
3#15689525C212yesmaximal, complemented
4#15689478C212yesmaximal, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689454C211yesmaximal, characteristic, complemented
7#15689442C211yesmaximal, characteristic
8#15689437C211yesmaximal, characteristic
9#15689431C212yesmaximal, complemented
10#15689424C212yesmaximal, complemented
11C47×#431C211yesmaximal, characteristic, complemented
12#13094018—21no—
13#13094016—21no—
14#13094016—21no—
15#13094016C2212yes—
16#13094016C2211yescharacteristic
17#13094016C2212yes—
18#13094012C2211yescharacteristic
19#13094007—21no—
20#13094003C2211yescharacteristic
21#13093998C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×C22⋊D47—21no—
25#13093981—21no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30#13093958C2212yes—
31#13093958C2212yes—
32#13093956C2212yes—
33#13093956C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36#13093946C2212yes—
37#13093946C2212yes—
38C2×C42×C47C2211yescharacteristic
39C4⋊C8×C47C2212yes—
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42C4×C8×C47C2212yes—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D411yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49C2×D188C2311yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47C2312yes—
53C2×C8×C47C2312yes—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58C22⋊Dic47—21no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2312yes—
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76Dic47⋊C4—21no—
77C4×Dic47—21no—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—41no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C22⋊D47—42no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97D188—22no—
98C4×D47—42no—
99Dic94—22no—
100C8×C47—22no—
101C8×C47—22no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47#13512yes—
105C22×C47C22×D411yescharacteristic
106C2×D47—41no—
107C2×D47—41no—
108C2×D47—41no—
109C4×C47—21no—
110C4×C47—21no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47—21no—
114C4×C472−1+412yes—
115Dic47—41no—
116Dic47—42no—
117Dic47—41no—
118Dic47—41no—
119Dic47—42no—
120#3232—471nomaximal, Sylow
121C2×C47—22no—
122C2×C47#53611yescharacteristic
123C2×C47C2×#13511yescharacteristic
124C2×C47#57511yescharacteristic
125D47—81no—
126#529—471no—
127C2×#125—471no—
128#499—472no—
129#488—472no—
130#484—471no—
131#483—471no—
132#481—471no—
133#480—471no—
134#479—472no—
135#478—472no—
136#431D4711yescharacteristic, complemented
137C47#323211yescharacteristic, complemented, Sylow
138#126—941no—
139#125—472no—
140#125—472no—
141#125—471no—
142#125—941no—
143#125—941no—
144#124—471no—
145#123—941no—
146C22⋊Q8—471no—
147#121—471no—
148C4×Q8—471no—
149C4×D4—471no—
150C4×D4—941no—
151#117—941no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—471no—
154C2×C4⋊C4—941no—
155C2×C4⋊C4—941no—
156C2×C42C2×D4711yescharacteristic
157#107—472no—
158#107—472no—
159#106—472no—
160#106—472no—
161C4⋊C8C2×D4712yes—
162#103—472no—
163#103—472no—
164#102—472no—
165#102—472no—
166C22⋊C8C2×D4711yescharacteristic
167C22⋊C8C2×D4711yescharacteristic
168C4×C8C2×D4712yes—
169C2×Q8—471no—
170C2×D4—471no—
171C2×D4—941no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4—941no—
175C22×C4D18811yescharacteristic
176C22×C4D18811yescharacteristic
177C22×C4C22×D4711yescharacteristic
178C2×C8C22×D4712yes—
179C2×C8C22×D4712yes—
180C4⋊C4—472no—
181C4⋊C4—472no—
182C4⋊C4—471no—
183C4⋊C4—471no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C22⋊C4—941no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C42—941no—
200C42D18811yescharacteristic
201C42D18811yescharacteristic
202C42C22×D4711yescharacteristic
203C42C22×D4711yescharacteristic
204C23—941no—
205C23C2×D18811yescharacteristic
206Q8—942no—
207D4—942no—
208D4—1882no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—1882no—
218C2×C4—1882no—
219C2×C4—1882no—
220C2×C4C2×D18811yescharacteristic
221C2×C4C2×D18811yescharacteristic
222C2×C4C2×D18811yescharacteristic
223C2×C4C2×D18811yescharacteristic
224C2×C4C2×D18811yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—1881no—
231C22—1881no—
232C22—1881no—
233C22#1309404612yes—
234C22C22×D18811yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—1882no—
241C4—1881no—
242C4—1881no—
243C4—1882no—
244C4—1881no—
245C4#1309407112yes—
246C2—22no—
247C2—3761no—
248C2#1568969911yescharacteristic
249C2C2×#1309404611yescharacteristic
250C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3232
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×#13094016C2semidirect
3. #15689525C2semidirect
4. #15689478C2semidirect
5. #15689459C2semidirect
6. #15689454C2semidirect
9. #15689431C2semidirect
10. #15689424C2semidirect
11. C47×#431C2semidirect
136. #431D47semidirect
137. C47#3232semidirect