Finite Group Databasebeta

← #20243348

Subgroups — #20243348

Order 6016.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13094071C211yesmaximal, characteristic
2C2×#13093952C211yesmaximal, characteristic, complemented
3#15689125C211yesmaximal, characteristic, complemented
4#15689124C211yesmaximal, characteristic, complemented
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15689029C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic, complemented
8#13094071—22no—
9#13094071—22no—
10#13094071—22no—
11#13094071C414yescomplemented
12C2×#10625350—21no—
13C2×#10625350C2211yescharacteristic
14C2×#10625352—21no—
15C2×#10625352—22no—
16C22×Dic94—21no—
17C22×Dic94C2211yescharacteristic
18C2×Q8×D47—21no—
19C2×#10625329C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21#13093952—22no—
22#13093949—21no—
23#13093948—21no—
24#13093946—21no—
25#13093945—21no—
26#13093942—22no—
27C47⋊#95—22no—
28C2×#41×C47C2211yescharacteristic
29C2×M16×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31#104×C47—22no—
32#41×C47—21no—
33#41×C47—21no—
34#41×C47C2×C412yes—
35#41×C47D412yes—
36C2×Q8×C47D411yescharacteristic
37C2×D4×C47—21no—
38C2×D4×C47D411yescharacteristic
39C22×C4×C47—21no—
40C22×C4×C47—21no—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—22no—
43C2×C22⋊D47—21no—
44C22×Dic47—22no—
45C22×Dic47—21no—
46C22×Dic47D412yes—
47Q8×D47—24no—
48Q8×D47—24no—
49#10625352—28no—
50#10625352—24no—
51#10625352—24no—
52#10625352—28no—
53#10625350—24no—
54#10625350—21no—
55#10625350—21no—
56#10625350—24no—
57#10625350C2×C412yes—
58#10625350D412yes—
59C2×D188D411yescharacteristic
60C2×C4×D47—22no—
61C2×C4×D47—21no—
62C2×Dic94—22no—
63C2×Dic94—24no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—24no—
69C2×Dic94C2×C412yes—
70C2×Dic94D412yes—
71C2×Dic94D411yescharacteristic
72M16×C47—21no—
73M16×C47—21no—
74C2×C8×C47—21no—
75C42×C47—21no—
76C42×C47—21no—
77C4⋊Dic47—21no—
78C4⋊Dic47—21no—
79#10625329—21no—
80#10625329—21no—
81C2×C47⋊C8—21no—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—21no—
85Q8×C47—21no—
86Q8×C47C22⋊C412yes—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—21no—
90D4×C47C22⋊C412yes—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—41no—
96C2×C4×C47—41no—
97C2×C4×C47C22×C411yescharacteristic
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C22⋊D47—28no—
104C22⋊D47—22no—
105C22⋊D47—22no—
106C2×Dic47—28no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—42no—
111C2×Dic47—41no—
112C2×Dic47C22⋊C414yes—
113D188—21no—
114D188C22⋊C412yes—
115C4×D47—28no—
116C4×D47—22no—
117C4×D47—22no—
118Dic94—28no—
119Dic94—22no—
120Dic94—22no—
121Dic94—22no—
122Dic94—21no—
123Dic94—22no—
124Dic94C22⋊C412yes—
125C8×C47—41no—
126C47⋊C8—41no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—22no—
130C22×C47—41no—
131C22×C47—41no—
132C22×C47C2×C22⋊C411yescharacteristic
133C22×C47#12011yescharacteristic
134C22×C47#12011yescharacteristic
135C2×D47—22no—
136C2×D47—41no—
137C2×D47—41no—
138C4×C47—22no—
139C4×C47—42no—
140C4×C47C2×C22⋊C411yescharacteristic
141C4×C47C2×C22⋊C411yescharacteristic
142C4×C47#12011yescharacteristic
143C4×C47#12011yescharacteristic
144Dic47—24no—
145Dic47—22no—
146Dic47—81no—
147#1793—471nomaximal, Sylow
148C2×C47—21no—
149C2×C47—21no—
150C2×C47—42no—
151C2×C47#37911yescharacteristic
152C2×C47#45411yescharacteristic
153C2×C47#45611yescharacteristic
154D47—42no—
155C2×2−1+4—471no—
156C2×#104—471no—
157C2×#104D4711yescharacteristic, complemented
158#417—471no—
159#417—471no—
160C2×#101—471no—
161#391—471no—
162C47#179311yescharacteristic, complemented, Sylow
1632−1+4—474no—
1642−1+4—942no—
1652−1+4—942no—
1662−1+4—942no—
167C2×#41—471no—
168C2×#41—941no—
169C2×#41—942no—
170C2×#41—941no—
171C2×#41C2×D4711yescharacteristic
172C22×Q8—471no—
173C22×Q8—941no—
174C22×Q8—941no—
175C2×M16—471no—
176C2×M16C2×D4711yescharacteristic
177C2×C4⋊C4—471no—
178C2×C42C2×D4711yescharacteristic
179#104—22no—
180#104—942no—
181#103—941no—
182#103—941no—
183#102—941no—
184#102—941no—
185#101—942no—
186#95—942no—
187#41—21no—
188#41—21no—
189#41—472no—
190#41—472no—
191#41—944no—
192#41—944no—
193#41—948no—
194#41—948no—
195#41—944no—
196#41—944no—
197#41—941no—
198#41—941no—
199#41C4×D4712yes—
200#41C22⋊D4712yes—
201C2×Q8—472no—
202C2×Q8—472no—
203C2×Q8—471no—
204C2×Q8—944no—
205C2×Q8—942no—
206C2×Q8—944no—
207C2×Q8—944no—
208C2×Q8—944no—
209C2×Q8—941no—
210C2×Q8—941no—
211C2×Q8—941no—
212C2×Q8—941no—
213C2×Q8D18811yescharacteristic
214C2×D4—21no—
215C2×D4—471no—
216C2×D4—942no—
217C2×D4—941no—
218C2×D4D18811yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—472no—
222C22×C4—942no—
223C22×C4—942no—
224C22×C4—941no—
225C22×C4—941no—
226C22×C4C22×D4711yescharacteristic
227M16—21no—
228M16—21no—
229M16—941no—
230M16—941no—
231C2×C8—21no—
232C2×C8—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C42—21no—
236C42—21no—
237C23—21no—
238C23—941no—
239C23D4×D4711yescharacteristic
240Q8—21no—
241Q8—472no—
242Q8—948no—
243Q8—942no—
244Q8—942no—
245Q8—942no—
246Q8—941no—
247Q8—942no—
248Q8(C2×D47)⋊C412yes—
249D4—22no—
250D4—22no—
251D4—21no—
252D4—472no—
253D4—948no—
254D4—942no—
255D4—942no—
256D4—941no—
257D4(C2×D47)⋊C412yes—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—474no—
265C2×C4—948no—
266C2×C4—948no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—941no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—1882no—
273C2×C4—1881no—
274C2×C4C2×C4×D4711yescharacteristic
275C2×C4C2×D18811yescharacteristic
276C2×C4D4×D4711yescharacteristic
277C2×C4D4×D4711yescharacteristic
278C2×C4D4×D4711yescharacteristic
279C2×C4C2×C22⋊D4711yescharacteristic
280C8—41no—
281C8—1881no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—942no—
288C22—1881no—
289C22—1881no—
290C22C22⋊C4×D4711yescharacteristic
291C22#1309399211yescharacteristic
292C22#1309399411yescharacteristic
293C4—22no—
294C4—42no—
295C4—944no—
296C4—942no—
297C4—3761no—
298C4C22⋊C4×D4711yescharacteristic
299C4C2×(C2×D47)⋊C411yescharacteristic
300C4#1309399211yescharacteristic
301C4#1309399411yescharacteristic
302C2—21no—
303C2—21no—
304C2—42no—
305C2—1882no—
306C2#1568897811yescharacteristic
307C2#1568929711yescharacteristic
308C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#1793
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#13093952C2semidirect
3. #15689125C2semidirect
4. #15689124C2semidirect
5. C2×#13093942C2semidirect
6. #15689029C2semidirect
7. C2×#104×C47C2semidirect
11. #13094071C4semidirect
157. C2×#104D47semidirect
162. C47#1793semidirect