Finite Group Databasebeta

← #20255132

Subgroups — #20255132

Order 6016.

482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×#13094046C211yesmaximal, characteristic, complemented
2C2×Q16×D47C211yesmaximal, characteristic, complemented
3#15689783C212yesmaximal, complemented
4#15689508C211yesmaximal, characteristic, complemented
5#15689360C211yesmaximal, characteristic, complemented
6#15689348C212yesmaximal, complemented
7#15689283C212yesmaximal, complemented
8#15689263C212yesmaximal, complemented
9#15689217C211yesmaximal, characteristic, complemented
10C8×C22⋊D47C211yesmaximal, characteristic, complemented
11C47×#467C211yesmaximal, characteristic, complemented
12C2×#10625350C2212yes—
13C2×Q8×D47C2212yes—
14#13094046—24no—
15C2×Dic188C2211yescharacteristic
16C2×#10625337C2212yes—
17Q16×D47—24no—
18C2×#10625325C2212yes—
19C2×#10625336C2212yes—
20C2×D376C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094013C2212yes—
23#13094010—22no—
24#13094002—22no—
25#13093999C2212yes—
26#13093997—22no—
27#13093989C2212yes—
28#13093986—22no—
29C4×C22⋊D47C2211yescharacteristic
30Dic47⋊C8C2211yescharacteristic
31#13093947C2212yes—
32#13093944C2212yes—
33C22⋊(C47⋊C8)C2211yescharacteristic
34(C2×D47)⋊C8C2211yescharacteristic
35C8×Dic47C2211yescharacteristic
36C2×Q16×C47C2211yescharacteristic
37C22×C8×C47C2211yescharacteristic
38C22⋊Q8×C47C2212yes—
39#107×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—22no—
44C2×C22⋊D47D411yescharacteristic
45Q8×D47—24no—
46Q8×D47—42no—
47#10625350—24no—
48#10625350—42no—
49C2×D188—22no—
50C2×D188C2312yes—
51C2×C4×D47—22no—
52C2×C4×D47—22no—
53C2×C4×D47C2311yescharacteristic
54C2×Dic94—22no—
55C2×Dic94C2312yes—
56Q16×C47—22no—
57C2×C8×C47—22no—
58C2×C8×C47C2311yescharacteristic
59C2×C8×C47C2311yescharacteristic
60C4⋊C4×C47—22no—
61C4⋊C4×C47C2312yes—
62C22⋊C4×C47—22no—
63C22⋊Dic47D411yescharacteristic
64#10625337—24no—
65#10625336—42no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4D411yescharacteristic
70Dic47⋊C4—22no—
71Dic47⋊C4D411yescharacteristic
72C4×Dic47—22no—
73C4×Dic47C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76Dic188D414yescomplemented
77D376—22no—
78#10625325—24no—
79C8×D47—22no—
80C23×C47C2×D411yescharacteristic
81C22×D47—22no—
82C22×D47C2×D411yescharacteristic
83Q8×C47—22no—
84Q8×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2411yescharacteristic
91C22⋊D47—22no—
92C22⋊D47—44no—
93C2×Dic47—22no—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97D188—22no—
98D188—22no—
99D188—44no—
100C4×D47—21no—
101C4×D47—21no—
102C4×D47—44no—
103C4×D47—44no—
104Dic94—22no—
105Dic94—44no—
106Dic94C2×D414yes—
107C8×C47—21no—
108C8×C47C2×D412yes—
109C47⋊C8—21no—
110C47⋊C8—21no—
111C22×C47—21no—
112C22×C47—21no—
113C22×C47—21no—
114C22×C47C22×D411yescharacteristic
115C2×D47—21no—
116C2×D47—21no—
117C2×D47—42no—
118C2×D47—42no—
119C2×D47—42no—
120C2×D47#13512yescomplemented
121C4×C47—21no—
122C4×C47—42no—
123C4×C47—42no—
124C4×C47C22×D411yescharacteristic
125C4×C47H(5,𝔽2)11yescharacteristic
126Dic47—24no—
127Dic47—21no—
128Dic47—21no—
129Dic47—21no—
130#3285—471nomaximal, Sylow
131C2×C47—41no—
132C2×C47D4211yescharacteristic
133C2×C47C2×#13511yescharacteristic
134C2×C47#57811yescharacteristic
135D47—22no—
136D47—82no—
137C2×#135—471no—
138C22×Q16—471no—
139#548—472no—
140#495—471no—
141#467D4711yescharacteristic, complemented
142#466—471no—
143#464—472no—
144#452—472no—
145#448—472no—
146C4×Q16—471no—
147C8×D4—471no—
148C47#328511yescharacteristic, complemented, Sylow
149C2×#41—472no—
150C22×Q8—472no—
151#135—944no—
152C2×Q16—472no—
153C2×Q16—471no—
154C2×Q16—944no—
155C2×Q16C2×D4711yescharacteristic
156C2×SD16—472no—
157C2×SD16—472no—
158C2×D8—471no—
159C22×C8—471no—
160C22×C8C2×D4711yescharacteristic
161#124—472no—
162#124—942no—
163C22⋊Q8—942no—
164C22⋊Q8C2×D4712yes—
165#121—472no—
166#121—942no—
167C4×Q8—472no—
168C4×D4—471no—
169C4×D4—942no—
170#107C2×D4711yescharacteristic
171C4⋊C8—471no—
172#103—472no—
173#103C2×D4712yes—
174#102—472no—
175C22⋊C8—471no—
176C22⋊C8—471no—
177C4×C8—471no—
178#41—944no—
179#41—1882no—
180C2×Q8—472no—
181C2×Q8—942no—
182C2×Q8—944no—
183C2×Q8—1882no—
184C2×Q8C22×D4712yes—
185C2×D4—471no—
186C2×D4—472no—
187C2×D4—942no—
188C2×D4—942no—
189C22×C4—471no—
190C22×C4—942no—
191C22×C4—942no—
192C22×C4C22×D4711yescharacteristic
193Q16—22no—
194Q16—474no—
195Q16—944no—
196SD16—944no—
197SD16—1882no—
198D8—942no—
199C2×C8—22no—
200C2×C8—471no—
201C2×C8—471no—
202C2×C8—942no—
203C2×C8C22×D4711yescharacteristic
204C2×C8C22×D4711yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—471no—
207C4⋊C4—942no—
208C4⋊C4C22×D4712yes—
209C22⋊C4—22no—
210C22⋊C4—471no—
211C22⋊C4—471no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C22⋊C4—942no—
215C42—471no—
216C42—942no—
217C23—471no—
218C23—942no—
219C23D4×D4711yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—474no—
223Q8—942no—
224Q8—1884no—
225D4—942no—
226D4—942no—
227D4—942no—
228D4—1884no—
229D4—1884no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—471no—
235C2×C4—471no—
236C2×C4—471no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4—1884no—
241C2×C4—1884no—
242C2×C4D4×D4711yescharacteristic
243C2×C4C23×D4711yescharacteristic
244C8—21no—
245C8—941no—
246C8—941no—
247C8D4×D4712yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—472no—
252C22—941no—
253C22—941no—
254C22—1882no—
255C22—1882no—
256C22—1882no—
257C22C2×D4×D4711yescharacteristic
258C4—21no—
259C4—42no—
260C4—42no—
261C4—941no—
262C4—944no—
263C4—941no—
264C4—941no—
265C4C2×D4×D4711yescharacteristic
266C4#1309407011yescharacteristic
267C2—41no—
268C2—942no—
269C2—3762no—
270C2#1568975711yescharacteristic
271C2#135×D4711yescharacteristic
272C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3285
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. C2×#13094046C2semidirect
2. C2×Q16×D47C2semidirect
3. #15689783C2semidirect
4. #15689508C2semidirect
5. #15689360C2semidirect
6. #15689348C2semidirect
7. #15689283C2semidirect
8. #15689263C2semidirect
9. #15689217C2semidirect
10. C8×C22⋊D47C2semidirect
11. C47×#467C2semidirect
76. Dic188D4semidirect
120. C2×D47#135semidirect
141. #467D47semidirect
148. C47#3285semidirect