Finite Group Databasebeta

← #20252859

Subgroups — #20252859

Order 6016.

484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#13094057C211yesmaximal, characteristic, complemented
2C2×#13094054C211yesmaximal, characteristic, complemented
3#15689669C211yesmaximal, characteristic
4C2×#13093989C211yesmaximal, characteristic, complemented
5#15689348C212yesmaximal, complemented
6#15689344C212yesmaximal, complemented
7#15689332C212yesmaximal, complemented
8#15689322C212yesmaximal, complemented
9#15689146C211yesmaximal, characteristic, complemented
10#15689122C211yesmaximal, characteristic, complemented
11C47×#417C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14#13094057—24no—
15#13094054—24no—
16C2×Dic188C2212yes—
17C2×#10625337C2212yes—
18C2×#10625325C2212yes—
19C2×#10625335C2212yes—
20C2×#10625329C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094013C2211yescharacteristic
24#13094011C2211yescharacteristic
25#13093996—21no—
26#13093996—21no—
27#13093989—21no—
28#13093989—21no—
29#13093989C2212yes—
30#13093989C2212yes—
31C4×C22⋊D47—21no—
32C4×C22⋊D47—21no—
33C2×Dic47⋊C4—21no—
34C2×C4×Dic47—21no—
35C2×C4×Dic47C2211yescharacteristic
36Dic47⋊C8C2212yes—
37Dic47⋊C8C2212yes—
38#13093947C2212yes—
39#13093944C2212yes—
40C2×#41×C47C2211yescharacteristic
41C2×M16×C47C2211yescharacteristic
42C2×C4⋊C4×C47C2211yescharacteristic
43#103×C47C2212yes—
44#102×C47C2212yes—
45#41×C47—22no—
46#41×C47—22no—
47C2×Q8×C47C2311yescharacteristic
48C2×D4×C47—21no—
49C2×D4×C47C2311yescharacteristic
50C22×C4×C47—21no—
51C22×C4×C47—21no—
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—21no—
54C2×C22⋊D47—21no—
55C2×C22⋊D47—21no—
56C22×Dic47—21no—
57C22×Dic47D411yescharacteristic
58C22×Dic47D411yescharacteristic
59#10625350—22no—
60#10625350—22no—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×Dic94—21no—
64C2×Dic94—22no—
65C2×Dic94D414yescomplemented
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2312yes—
68M16×C47—22no—
69C2×C8×C47C2312yes—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2312yes—
72C22⋊Dic47—21no—
73C22⋊Dic47—21no—
74#10625337—24no—
75#10625335—24no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—21no—
81Dic47⋊C4—21no—
82C4×Dic47—22no—
83C4×Dic47—22no—
84C4×Dic47D411yescharacteristic
85C4×Dic47D411yescharacteristic
86C4×Dic47C2311yescharacteristic
87C4×Dic47C2311yescharacteristic
88#10625329—22no—
89C2×C47⋊C8C2312yes—
90Dic188—24no—
91#10625325—24no—
92C23×C47—21no—
93C23×C47C2×D411yescharacteristic
94C22×D47—21no—
95Q8×C47—21no—
96Q8×C47—21no—
97D4×C47—21no—
98D4×C47—21no—
99D4×C47—42no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2×D412yes—
106C2×C4×C47#4112yes—
107C2×C4×C47C2411yescharacteristic
108C22⋊D47—42no—
109C22⋊D47—42no—
110C22⋊D47—42no—
111C2×Dic47—24no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—21no—
115C2×Dic47—41no—
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120D188—21no—
121D188—21no—
122C4×D47—42no—
123Dic94—24no—
124Dic94—22no—
125Dic94—21no—
126Dic94—21no—
127Dic94C2×D414yes—
128C8×C47—22no—
129C47⋊C8—22no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—41no—
133C22×C47—41no—
134C22×C47—41no—
135C22×C47#12112yes—
136C22×C47C22×D411yescharacteristic
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—41no—
141C4×C47—42no—
142C4×C47#12112yes—
143C4×C47C22×D411yescharacteristic
144C4×C47C2×#4111yescharacteristic
145Dic47—24no—
146Dic47—21no—
147Dic47—21no—
148Dic47—21no—
149Dic47—41no—
150Dic47#13712yescomplemented
151#3037—471nomaximal, Sylow
152C2×C47—22no—
153C2×C47—81no—
154C2×C47C2×#12111yescharacteristic
155C2×C47C2×#13711yescharacteristic
156C2×C47#57511yescharacteristic
157D47—81no—
158C2×#137—471no—
159C2×#137—471no—
160#532—471no—
161C2×C4×Q8—471no—
162#464—472no—
163#464—472no—
164#462—472no—
165#460—472no—
166#423—471no—
167#417—471no—
168#417D4711yescharacteristic, complemented
169C47#303711yescharacteristic, complemented, Sylow
170C2×#41—471no—
171C2×#41C2×D4711yescharacteristic
172C22×Q8—471no—
173#137—944no—
174#137—944no—
175C2×Q16—472no—
176C2×Q16—472no—
177C2×SD16—472no—
178C2×SD16—472no—
179C2×M16—471no—
180C2×M16C2×D4711yescharacteristic
181C4⋊Q8—471no—
182#127—471no—
183#124—471no—
184#124—471no—
185#121—941no—
186#121—941no—
187C4×Q8—472no—
188C4×Q8—472no—
189C4×Q8—941no—
190C4×Q8—941no—
191C4×D4—941no—
192C4×D4—941no—
193C2×C4⋊C4—941no—
194C2×C4⋊C4C2×D4711yescharacteristic
195C2×C42—471no—
196C2×C42—941no—
197C4⋊C8—472no—
198C4⋊C8—472no—
199#103—472no—
200#103C2×D4712yes—
201#102—472no—
202#102C2×D4712yes—
203#41—22no—
204#41—22no—
205#41—942no—
206#41—942no—
207C2×Q8—474no—
208C2×Q8—472no—
209C2×Q8—471no—
210C2×Q8—942no—
211C2×Q8—941no—
212C2×Q8C22×D4711yescharacteristic
213C2×D4—21no—
214C2×D4—471no—
215C2×D4—941no—
216C2×D4—941no—
217C2×D4—941no—
218C2×D4C22×D4711yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—471no—
222C22×C4—471no—
223C22×C4—941no—
224C22×C4—941no—
225C22×C4C22×D4711yescharacteristic
226Q16—944no—
227Q16—944no—
228SD16—944no—
229SD16—944no—
230M16—22no—
231M16—942no—
232C2×C8—472no—
233C2×C8C22×D4712yes—
234C4⋊C4—21no—
235C4⋊C4—942no—
236C4⋊C4—942no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4C22×D4712yes—
240C22⋊C4—941no—
241C22⋊C4—941no—
242C22⋊C4—941no—
243C22⋊C4—941no—
244C42—471no—
245C42—471no—
246C42—471no—
247C42—471no—
248C42—942no—
249C42—942no—
250C23—21no—
251C23—941no—
252C23D4×D4711yescharacteristic
253Q8—21no—
254Q8—21no—
255Q8—474no—
256Q8—944no—
257Q8—942no—
258Q8—941no—
259Q8—941no—
260D4—21no—
261D4—21no—
262D4—42no—
263D4—941no—
264D4—941no—
265D4—1882no—
266D4—1882no—
267D4—1882no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—471no—
273C2×C4—471no—
274C2×C4—471no—
275C2×C4—471no—
276C2×C4—942no—
277C2×C4—944no—
278C2×C4—942no—
279C2×C4—941no—
280C2×C4—1881no—
281C2×C4—1882no—
282C2×C4#1062535012yes—
283C2×C4D4×D4711yescharacteristic
284C2×C4D4×D4712yes—
285C2×C4C23×D4711yescharacteristic
286C8—22no—
287C8—942no—
288C22—21no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—1881no—
294C22—1881no—
295C22—1881no—
296C22#1309399712yes—
297C22C2×D4×D4711yescharacteristic
298C4—41no—
299C4—42no—
300C4—472no—
301C4—944no—
302C4—941no—
303C4—941no—
304C4—941no—
305C4—1881no—
306C4#1309399712yes—
307C4C2×D4×D4711yescharacteristic
308C4C2×#1062535011yescharacteristic
309C2—22no—
310C2—81no—
311C2—3761no—
312C2C2×#1309399711yescharacteristic
313C2#137×D4711yescharacteristic
314C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3037
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C2×#13094054C2semidirect
4. C2×#13093989C2semidirect
5. #15689348C2semidirect
6. #15689344C2semidirect
7. #15689332C2semidirect
8. #15689322C2semidirect
9. #15689146C2semidirect
10. #15689122C2semidirect
11. C47×#417C2semidirect
65. C2×Dic94D4semidirect
150. Dic47#137semidirect
168. #417D47semidirect
169. C47#3037semidirect