Finite Group Databasebeta

← #20243340

Subgroups — #20243340

Order 6016.

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

normal subgroups only

This group has 620 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×#13094070C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic, complemented
4#15689122C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic, complemented
8#13094070—22no—
9#13094070—22no—
10#13094070—22no—
11#13094070C414yescomplemented
12C2×#10625354—21no—
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×D188—21no—
16C22×D188C2211yescharacteristic
17C2×D4×D47—22no—
18C2×D4×D47—21no—
19C2×#10625329C2211yescharacteristic, complemented
20C2×(C2×D47)⋊C4—22no—
21C2×C4×Dic47C2211yescharacteristic, complemented
22#13093951—22no—
23#13093950—22no—
24#13093947—21no—
25#13093944—21no—
26#13093940—22no—
27C2×#41×C47C2211yescharacteristic
28C2×M16×C47C2211yescharacteristic, complemented
29C2×C4⋊C4×C47C2211yescharacteristic, complemented
30#103×C47—21no—
31#102×C47—21no—
32C23×D47—22no—
33C23×D47D412yes—
34#41×C47—21no—
35#41×C47—21no—
36#41×C47C2×C412yes—
37#41×C47D412yes—
38C2×Q8×C47D411yescharacteristic
39C2×D4×C47—21no—
40C2×D4×C47D411yescharacteristic
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—22no—
45C2×C22⋊D47—21no—
46C22×Dic47—21no—
47#10625354—24no—
48#10625354—24no—
49D4×D47—28no—
50D4×D47—24no—
51D4×D47—28no—
52D4×D47—24no—
53#10625350—24no—
54#10625350—21no—
55#10625350—21no—
56#10625350—24no—
57#10625350C2×C412yes—
58#10625350D412yes—
59C2×D188—22no—
60C2×D188—24no—
61C2×D188—21no—
62C2×D188—21no—
63C2×D188—21no—
64C2×D188—21no—
65C2×D188—24no—
66C2×D188C2×C412yes—
67C2×D188D412yes—
68C2×D188D411yescharacteristic
69C2×C4×D47—22no—
70C2×C4×D47—21no—
71C2×Dic94D411yescharacteristic
72M16×C47—21no—
73M16×C47—21no—
74C2×C8×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77(C2×D47)⋊C4—44no—
78C4×Dic47—21no—
79C4×Dic47—21no—
80#10625329—21no—
81#10625329—21no—
82C2×C47⋊C8—21no—
83C23×C47—21no—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—21no—
87C22×D47—28no—
88C22×D47—22no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47—82no—
92C22×D47—82no—
93C22×D47C22⋊C414yes—
94Q8×C47—21no—
95Q8×C47C22⋊C412yescomplemented
96D4×C47—22no—
97D4×C47—22no—
98D4×C47—21no—
99D4×C47C22⋊C412yescomplemented
100C2×C4×C47—21no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—42no—
104C2×C4×C47—41no—
105C2×C4×C47C22×C411yescharacteristic
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C22⋊D47—28no—
112C22⋊D47—22no—
113C22⋊D47—22no—
114C2×Dic47—21no—
115C2×Dic47—22no—
116C2×Dic47—41no—
117C2×Dic47—41no—
118D188—28no—
119D188—22no—
120D188—22no—
121D188—22no—
122D188—21no—
123D188—22no—
124D188C22⋊C412yescomplemented
125C4×D47—28no—
126C4×D47—22no—
127C4×D47—22no—
128Dic94—21no—
129Dic94C22⋊C412yescomplemented
130C8×C47—41no—
131C47⋊C8—41no—
132C22×C47—21no—
133C22×C47—21no—
134C22×C47—22no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47C2×C22⋊C411yescharacteristic
138C22×C47#12011yescharacteristic
139C22×C47#12011yescharacteristic
140C2×D47—24no—
141C2×D47—22no—
142C2×D47—42no—
143C2×D47—41no—
144C2×D47—42no—
145C2×D47—41no—
146C2×D47—44no—
147C2×D47—82no—
148C2×D47—88no—
149C4×C47—22no—
150C4×C47—81no—
151C4×C47C2×C22⋊C411yescharacteristic
152C4×C47C2×C22⋊C411yescharacteristic
153C4×C47#12011yescharacteristic
154C4×C47#12011yescharacteristic
155Dic47—22no—
156Dic47—42no—
157#1792—471nomaximal, Sylow
158C2×C47—21no—
159C2×C47—21no—
160C2×C47—42no—
161C2×C47#37911yescharacteristic
162C2×C47#45311yescharacteristic
163C2×C47#45511yescharacteristic
164D47—44no—
165D47—42no—
166C2×H(5,𝔽2)—471no—
167C2×#104—471no—
168C2×#104—471no—
169#417—471no—
170#417D4711yescharacteristic, complemented
171C2×#100—471no—
172#390—471no—
173C47#179211yescharacteristic, complemented, Sylow
174H(5,𝔽2)—474no—
175H(5,𝔽2)—942no—
176H(5,𝔽2)—942no—
177H(5,𝔽2)—942no—
178C2×#41—471no—
179C2×#41—941no—
180C2×#41—941no—
181C2×#41C2×D4711yescharacteristic
182C22×D4—471no—
183C22×D4—941no—
184C22×D4—942no—
185C22×D4—941no—
186C2×M16—471no—
187C2×M16C2×D4711yescharacteristic, complemented
188C2×C4⋊C4C2×D4711yescharacteristic, complemented
189C2×C22⋊C4—942no—
190C2×C42—471no—
191#104—942no—
192#104—942no—
193#103—21no—
194#103—941no—
195#102—21no—
196#102—941no—
197#100—942no—
198C24—472no—
199C24—942no—
200#41—21no—
201#41—21no—
202#41—472no—
203#41—472no—
204#41—944no—
205#41—944no—
206#41—944no—
207#41—944no—
208#41—941no—
209#41—941no—
210#41C4×D4712yes—
211#41D18812yes—
212C2×Q8—471no—
213C2×Q8C22⋊D4711yescharacteristic
214C2×D4—21no—
215C2×D4—472no—
216C2×D4—471no—
217C2×D4—472no—
218C2×D4—944no—
219C2×D4—942no—
220C2×D4—944no—
221C2×D4—948no—
222C2×D4—948no—
223C2×D4—944no—
224C2×D4—942no—
225C2×D4—941no—
226C2×D4—944no—
227C2×D4—941no—
228C2×D4—941no—
229C2×D4—941no—
230C2×D4—941no—
231C2×D4C22⋊D4711yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—942no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4C22×D4711yescharacteristic
238M16—21no—
239M16—21no—
240M16—941no—
241M16—941no—
242C2×C8—21no—
243C2×C8—941no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C22⋊C4—1884no—
247C42—941no—
248C42—941no—
249C23—21no—
250C23—474no—
251C23—948no—
252C23—942no—
253C23—941no—
254C23—942no—
255C23—3762no—
256C23—3762no—
257C23—1882no—
258C23—1882no—
259C23D4×D4711yescharacteristic
260Q8—21no—
261Q8—472no—
262Q8—941no—
263Q8(C2×D47)⋊C412yescomplemented
264D4—22no—
265D4—22no—
266D4—21no—
267D4—472no—
268D4—948no—
269D4—948no—
270D4—942no—
271D4—942no—
272D4—942no—
273D4—942no—
274D4—942no—
275D4—941no—
276D4—942no—
277D4(C2×D47)⋊C412yescomplemented
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—948no—
284C2×C4—941no—
285C2×C4—942no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4C2×C4×D4711yescharacteristic
291C2×C4C2×D18811yescharacteristic
292C2×C4D4×D4711yescharacteristic
293C2×C4D4×D4711yescharacteristic
294C2×C4D4×D4711yescharacteristic
295C2×C4C2×C22⋊D4711yescharacteristic
296C8—41no—
297C8—1881no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—41no—
302C22—41no—
303C22—942no—
304C22—944no—
305C22—3762no—
306C22—3768no—
307C22—1884no—
308C22—1881no—
309C22—1882no—
310C22—1881no—
311C22—1882no—
312C22C22⋊C4×D4711yescharacteristic
313C22#1309399211yescharacteristic
314C22#1309399411yescharacteristic
315C4—22no—
316C4—81no—
317C4—942no—
318C4—1882no—
319C4C22⋊C4×D4711yescharacteristic
320C4C2×(C2×D47)⋊C411yescharacteristic
321C4#1309399211yescharacteristic
322C4#1309399411yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2—1882no—
327C2—1884no—
328C2#1568897811yescharacteristic
329C2#1568928911yescharacteristic
330C2#1568929911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#120
hypercenter#417D47
hypocenterC47#1792
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
2. C2×#13093951C2semidirect
3. C2×#13093950C2semidirect
4. #15689122C2semidirect
5. C2×#13093940C2semidirect
6. #15689024C2semidirect
7. C47×#417C2semidirect
11. #13094070C4semidirect
19. C2×#10625329C22semidirect
21. C2×C4×Dic47C22semidirect
28. C2×M16×C47C22semidirect
29. C2×C4⋊C4×C47C22semidirect
95. Q8×C47C22⋊C4semidirect
99. D4×C47C22⋊C4semidirect
124. D188C22⋊C4semidirect
129. Dic94C22⋊C4semidirect
170. #417D47semidirect
173. C47#1792semidirect
187. C2×M16C2×D47semidirect
188. C2×C4⋊C4C2×D47semidirect
263. Q8(C2×D47)⋊C4semidirect
277. D4(C2×D47)⋊C4semidirect