Finite Group Databasebeta

← #20244390

Subgroups — #20244390

Order 6016.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#10625336C211yesmaximal, characteristic, complemented
2C2×#13094000C211yesmaximal, characteristic, complemented
3C2×#13093999C211yesmaximal, characteristic
4C2×#13093946C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188—21no—
9C22×D188C2211yescharacteristic
10C22×C4×D47C2211yescharacteristic
11C2×#10625336—22no—
12C2×#10625336—22no—
13C2×#10625336—22no—
14C22×C47⋊C8C2211yescharacteristic
15#13094000—22no—
16#13094000—22no—
17#13093999—22no—
18#13093999—22no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4—21no—
21C2×(C2×D47)⋊C4—21no—
22C2×(C2×D47)⋊C4—21no—
23#13093946—22no—
24(C2×D47)⋊C8—22no—
25C22×Q8×C47C2211yescharacteristic
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#103×C47—22no—
29C23×D47—21no—
30C23×D47D411yescharacteristic
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—21no—
36C2×Q8×C47D412yescomplemented
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47C2311yescharacteristic
40C22×Dic47—21no—
41C22×Dic47D411yescharacteristic
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—24no—
47C2×D188—21no—
48C2×D188—42no—
49C2×D188—42no—
50C2×D188D412yes—
51C2×C4×D47—21no—
52C2×C4×D47—21no—
53C2×C4×D47—21no—
54C2×C4×D47—21no—
55C2×C4×D47—21no—
56C2×C4×D47—21no—
57C2×C8×C47—21no—
58C2×C8×C47—21no—
59C2×C8×C47—21no—
60C4⋊C4×C47—21no—
61C4⋊C4×C47D412yes—
62#10625336—28no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—24no—
65C4⋊Dic47—21no—
66C4⋊Dic47D412yescomplemented
67Dic47⋊C4—24no—
68C2×C47⋊C8—21no—
69C2×C47⋊C8—21no—
70C2×C47⋊C8D412yescomplemented
71C23×C47C2×D411yescharacteristic
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—21no—
78C22×D47—22no—
79C22×D47—41no—
80C22×D47—41no—
81C22×D47—41no—
82C22×D47—41no—
83C22×D47—41no—
84C22×D47—41no—
85C22×D47SD1612yescomplemented
86Q8×C47—22no—
87Q8×C47—22no—
88Q8×C47—41no—
89Q8×C47—41no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—41no—
93C2×C4×C47—41no—
94C2×C4×C47—41no—
95C2×C4×C47—41no—
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47#4111yescharacteristic
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47—41no—
107C2×Dic47—41no—
108D188—22no—
109D188—22no—
110D188—48no—
111D188—41no—
112D188—41no—
113C4×D47—41no—
114C4×D47—41no—
115C4×D47—41no—
116C4×D47—41no—
117C8×C47—41no—
118C47⋊C8—22no—
119C22×C47#12011yescharacteristic
120C22×C47#12011yescharacteristic
121C22×C47#12111yescharacteristic
122C22×C47C2×SD1611yescharacteristic
123C22×C47#13511yescharacteristic
124C22×C47AGL(1,ℤ/8)11yescharacteristic
125C22×C47#13711yescharacteristic
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—41no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—81no—
137C2×D47—81no—
138C2×D47—81no—
139C2×D47—81no—
140C4×C47—42no—
141C4×C47—42no—
142C4×C47#12011yescharacteristic
143C4×C47#12111yescharacteristic
144C4×C47#12111yescharacteristic
145C4×C47#12711yescharacteristic
146Dic47—41no—
147Dic47—42no—
148#2000—471nomaximal, Sylow
149C2×C47#39211yescharacteristic
150C2×C47#44811yescharacteristic
151C2×C47#44911yescharacteristic
152C2×C47#45011yescharacteristic
153C2×C47#45211yescharacteristic
154C2×C47#46511yescharacteristic
155C2×C47#46811yescharacteristic
156D47—42no—
157D47—82no—
158C22×SD16—471no—
159C2×C22⋊Q8—471no—
160C2×#121—471no—
161C2×#103D4711yescharacteristic, complemented
162C2×#102—471no—
163C2×C22⋊C8—471no—
164#340—471no—
165C47#200011yescharacteristic, complemented, Sylow
166C22×Q8C2×D4711yescharacteristic
167C22×D4—471no—
168C22×D4—941no—
169C23×C4—471no—
170C2×SD16—942no—
171C2×SD16—942no—
172C2×SD16—942no—
173C22×C8—471no—
174C22×C8C2×D4711yescharacteristic
175C22⋊Q8—942no—
176C22⋊Q8—942no—
177#121—942no—
178#121—942no—
179C2×C4⋊C4—471no—
180C2×C4⋊C4—941no—
181C2×C4⋊C4C2×D4711yescharacteristic
182C2×C22⋊C4—941no—
183C2×C22⋊C4—941no—
184#103—22no—
185#102—942no—
186C22⋊C8—942no—
187C24—471no—
188C24—941no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8D18812yescomplemented
195C2×D4—472no—
196C2×D4—944no—
197C2×D4—941no—
198C2×D4—941no—
199C2×D4—941no—
200C2×D4—941no—
201C2×D4—941no—
202C2×D4—1882no—
203C2×D4—1882no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—471no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—941no—
213C22×C4—941no—
214C22×C4C22×D4711yescharacteristic
215SD16—948no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—472no—
220C2×C8—941no—
221C2×C8—941no—
222C4⋊C4—21no—
223C4⋊C4—472no—
224C4⋊C4—944no—
225C4⋊C4—941no—
226C4⋊C4C22⋊D4712yes—
227C22⋊C4—944no—
228C22⋊C4—944no—
229C23—472no—
230C23—941no—
231C23—941no—
232C23—941no—
233C23—941no—
234C23—941no—
235C23—941no—
236C23—942no—
237C23—1881no—
238C23—1881no—
239C23—1881no—
240C23—1881no—
241C23—1881no—
242C23—1881no—
243C23D4×D4711yescharacteristic
244Q8—22no—
245Q8—22no—
246Q8—41no—
247Q8—41no—
248D4—942no—
249D4—942no—
250D4—1888no—
251D4—1881no—
252D4—1881no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—941no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—1881no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4C2×D18811yescharacteristic
270C2×C4#1062535011yescharacteristic
271C2×C4D4×D4711yescharacteristic
272C2×C4D4×D4711yescharacteristic
273C2×C4D4×D4711yescharacteristic
274C2×C4C2×C22⋊D4711yescharacteristic
275C8—41no—
276C8—942no—
277C22—942no—
278C22—942no—
279C22—942no—
280C22—3761no—
281C22—3761no—
282C22—3761no—
283C22—3761no—
284C22—1882no—
285C22—1882no—
286C22—1882no—
287C22—1881no—
288C22—1881no—
289C22—1881no—
290C22—1881no—
291C22#1309399211yescharacteristic
292C22#1309399411yescharacteristic
293C22#1309399711yescharacteristic
294C22SD16×D4711yescharacteristic
295C22#1309404711yescharacteristic
296C22#1309405111yescharacteristic
297C22#1309405611yescharacteristic
298C4—42no—
299C4—42no—
300C4—1882no—
301C4—1881no—
302C4#1309399411yescharacteristic
303C4#1309399711yescharacteristic
304C4#1309399811yescharacteristic
305C4#1309402011yescharacteristic
306C2—3762no—
307C2—1882no—
308C2#1568903211yescharacteristic
309C2#1568926311yescharacteristic
310C2#1568927111yescharacteristic
311C2#1568927211yescharacteristic
312C2#1568928411yescharacteristic
313C2#1568935511yescharacteristic
314C2#1568937211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2000
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#10625336C2semidirect
2. C2×#13094000C2semidirect
4. C2×#13093946C2semidirect
5. C2×(C2×D47)⋊C8C2semidirect
6. #15688885C2semidirect
7. C2×#103×C47C2semidirect
36. C2×Q8×C47D4semidirect
66. C4⋊Dic47D4semidirect
70. C2×C47⋊C8D4semidirect
85. C22×D47SD16semidirect
161. C2×#103D47semidirect
165. C47#2000semidirect
194. C2×Q8D188semidirect