Finite Group Databasebeta

← #20253366

Subgroups — #20253366

Order 6016.

398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689701C211yesmaximal, characteristic
2#15689464C212yesmaximal, complemented
3#15689458C212yesmaximal, complemented
4#15689447C212yesmaximal, complemented
5#15689436C212yesmaximal, complemented
6#15689166C211yesmaximal, characteristic, complemented
7C2×#13093957C211yesmaximal, characteristic, complemented
8#15689122C211yesmaximal, characteristic, complemented
9#15689117C211yesmaximal, characteristic, complemented
10#15689090C211yesmaximal, characteristic, complemented
11C47×#520C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14C22×C47⋊C8C2211yescharacteristic
15#13094003C2212yes—
16#13094000—21no—
17#13093998C2212yes—
18#13093996—22no—
19#13093995—21no—
20C2×C4⋊Dic47C2211yescharacteristic
21#13093957C2212yes—
22#13093957C2212yes—
23#13093957C2212yes—
24#13093955C2212yes—
25#13093947C2211yescharacteristic
26#13093947C2211yescharacteristic
27#13093947C2212yes—
28#13093944C2211yescharacteristic
29#13093944C2211yescharacteristic
30#13093944C2212yes—
31C22⋊(C47⋊C8)C2212yes—
32C22⋊(C47⋊C8)C2212yes—
33C2×#41×C47C2211yescharacteristic
34C4×Q8×C47—21no—
35C4×D4×C47—21no—
36C4×D4×C47—22no—
37#117×C47C2211yescharacteristic
38#117×C47C2212yes—
39C2×C4⋊C4×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2212yes—
41#41×C47—22no—
42#41×C47—22no—
43C2×Q8×C47D411yescharacteristic
44C2×D4×C47D411yescharacteristic
45C2×D4×C47D412yes—
46C22×C4×C47—22no—
47C22×C4×C47—21no—
48C22×C4×C47C2312yes—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C22×Dic47—21no—
53#10625350—22no—
54#10625350—22no—
55C2×D188C2311yescharacteristic
56C2×C4×D47—21no—
57C2×Dic94C2311yescharacteristic
58C4⋊C4×C47—22no—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C4⋊C4×C47C2311yescharacteristic
62C4⋊C4×C47C2311yescharacteristic
63C22⋊C4×C47—22no—
64C22⋊C4×C47—21no—
65C42×C47—22no—
66C42×C47—21no—
67C22⋊Dic47—22no—
68(C2×D47)⋊C4—22no—
69C4⋊Dic47—21no—
70C4⋊Dic47C2312yes—
71Dic47⋊C4—22no—
72#10625329—22no—
73C2×C47⋊C8—22no—
74C2×C47⋊C8C2312yes—
75C2×C47⋊C8C2311yescharacteristic
76C2×C47⋊C8C2311yescharacteristic
77C23×C47C2×D412yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80Q8×C47—22no—
81D4×C47—24no—
82D4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—81no—
89C2×C4×C47—82no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47#4112yes—
93C2×C4×C47#4112yes—
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—42no—
96C22⋊D47—82no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—81no—
100D188—21no—
101D188—21no—
102C4×D47—42no—
103Dic94—21no—
104Dic94—21no—
105C47⋊C8—21no—
106C47⋊C8—21no—
107C47⋊C8—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47—22no—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47#12312yes—
114C22×C47C22×D411yescharacteristic
115C2×D47—41no—
116C2×D47—41no—
117C2×D47—41no—
118C4×C47—22no—
119C4×C47—42no—
120C4×C47—41no—
121C4×C47—41no—
122C4×C47#12312yes—
123C4×C47C2×#4111yescharacteristic
124C4×C47C2×#4111yescharacteristic
125Dic47—41no—
126Dic47—42no—
127#3098—471nomaximal, Sylow
128C2×C47—22no—
129C2×C47—42no—
130C2×C47C2×#12311yescharacteristic
131C2×C47#57611yescharacteristic
132C2×C47#57811yescharacteristic
133D47—81no—
134#537—471no—
135#520D4711yescharacteristic, complemented
136#485—472no—
137#484—472no—
138#482—472no—
139#480—472no—
140#428—471no—
141C2×#107—471no—
142#417—471no—
143#416—471no—
144#408—471no—
145C47#309811yescharacteristic, complemented, Sylow
146C2×#41—471no—
147C2×#41C2×D4711yescharacteristic
148C2×M16—471no—
149C22×C8—471no—
150C22⋊Q8—472no—
151C22⋊Q8—941no—
152#121—472no—
153#121—941no—
154#121—942no—
155C4×Q8—21no—
156C4×D4—22no—
157C4×D4—21no—
158#117C2×D4711yescharacteristic
159#117C2×D4712yes—
160C2×C4⋊C4—471no—
161C2×C4⋊C4C2×D4711yescharacteristic
162C2×C4⋊C4C2×D4712yes—
163#107—472no—
164#107—472no—
165#107—472no—
166#106—472no—
167#103—471no—
168#103—471no—
169#103—472no—
170#102—471no—
171#102—471no—
172#102—472no—
173C22⋊C8—472no—
174C22⋊C8—472no—
175#41—22no—
176#41—22no—
177#41—942no—
178#41—942no—
179C2×Q8—471no—
180C2×Q8C22⋊D4711yescharacteristic
181C2×D4—471no—
182C2×D4—942no—
183C2×D4—941no—
184C2×D4C22⋊D4712yes—
185C2×D4C22⋊D4711yescharacteristic
186C22×C4—22no—
187C22×C4—21no—
188C22×C4—941no—
189C22×C4—941no—
190C22×C4C22×D4712yes—
191C22×C4C22×D4711yescharacteristic
192M16—942no—
193C2×C8—472no—
194C2×C8—471no—
195C2×C8—471no—
196C2×C8—942no—
197C4⋊C4—22no—
198C4⋊C4—21no—
199C4⋊C4—472no—
200C4⋊C4—942no—
201C4⋊C4—941no—
202C4⋊C4C22×D4711yescharacteristic
203C4⋊C4C22×D4711yescharacteristic
204C4⋊C4C22×D4712yes—
205C22⋊C4—22no—
206C22⋊C4—21no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C42—22no—
210C42—21no—
211C23—941no—
212C23C2×C22⋊D4712yes—
213C23C2×C22⋊D4711yescharacteristic
214Q8—22no—
215Q8—941no—
216Q8—941no—
217D4—24no—
218D4—22no—
219D4—941no—
220D4—941no—
221D4—3762no—
222D4—1882no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—3761no—
233C2×C4—1882no—
234C2×C4#1062535012yes—
235C2×C4#1062535012yes—
236C2×C4C2×C22⋊D4712yes—
237C2×C4C2×C22⋊D4711yescharacteristic
238C2×C4C23×D4711yescharacteristic
239C8—941no—
240C8—941no—
241C8—942no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—1881no—
248C22—1881no—
249C22—1881no—
250C22#1309400712yes—
251C22C22×C22⋊D4711yescharacteristic
252C4—22no—
253C4—42no—
254C4—41no—
255C4—41no—
256C4—1881no—
257C4—1882no—
258C4#1309400712yes—
259C4C2×#1062535011yescharacteristic
260C4C2×#1062535011yescharacteristic
261C2—22no—
262C2—42no—
263C2—3761no—
264C2C2×#1309400711yescharacteristic
265C2#1568992611yescharacteristic
266C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#520C2
socleC22×C47C22×D4
hypercenter#520D47
hypocenterC47#3098
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
2. #15689464C2semidirect
3. #15689458C2semidirect
4. #15689447C2semidirect
5. #15689436C2semidirect
6. #15689166C2semidirect
7. C2×#13093957C2semidirect
8. #15689122C2semidirect
9. #15689117C2semidirect
10. #15689090C2semidirect
11. C47×#520C2semidirect
135. #520D47semidirect
145. C47#3098semidirect