Finite Group Databasebeta

← #20252230

Subgroups — #20252230

Order 6016.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094056C211yesmaximal, characteristic
2#15689605C211yesmaximal, characteristic
3#15689599C211yesmaximal, characteristic, complemented
4#15689227C211yesmaximal, characteristic, complemented
5#15689226C211yesmaximal, characteristic, complemented
6#15689225C211yesmaximal, characteristic, complemented
7Q16×Dic47C211yesmaximal, characteristic, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9C4×#10625336C211yesmaximal, characteristic, complemented
10#15689210C211yesmaximal, characteristic, complemented
11#15689162C211yesmaximal, characteristic, complemented
12#15689118C211yesmaximal, characteristic
13#103×D47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#441C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18#13094056C418yescomplemented
19C2×#10625337C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic
28#13093989—21no—
29#13093989C2211yescharacteristic
30C4×D188—21no—
31C4×D188C2211yescharacteristic
32#13093986—21no—
33#13093986C2211yescharacteristic
34#13093982—21no—
35#13093982C2211yescharacteristic
36#13093981—21no—
37#13093981—21no—
38#13093981C2211yescharacteristic
39C4⋊C4×D47—21no—
40C4⋊C4×D47C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C4×C47⋊C8C2211yescharacteristic
52C8×Dic47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59#97×C47C2211yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62#10625354—22no—
63#10625354C2×C414yes—
64Q8×D47—22no—
65Q8×D47C2×C414yescomplemented
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94C2311yescharacteristic
76Q16×C47C2×C414yescomplemented
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C42×C47—21no—
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86#10625337C2×C414yescomplemented
87#10625336C2×C414yescomplemented
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4D411yescharacteristic
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325C2×C414yescomplemented
111#10625324C2×C414yescomplemented
112C8×D47—22no—
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47C22×C412yes—
118Q8×C47C22×C412yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—24no—
133D188—21no—
134D188C22×C412yes—
135C4×D47—24no—
136C4×D47—24no—
137C4×D47—81no—
138C4×D47—81no—
139C4×D47—81no—
140C4×D47C22×C412yes—
141C4×D47#4112yes—
142Dic94—21no—
143Dic94—24no—
144Dic94C22×C412yes—
145C8×C47—21no—
146C8×C47C22×C412yes—
147C47⋊C8—21no—
148C47⋊C8C22×C412yes—
149C22×C47C22×D411yescharacteristic
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47C4×D412yes—
156C4×C47—22no—
157C4×C47—22no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47C23×C411yescharacteristic
163C4×C47C2×#4111yescharacteristic
164Dic47—22no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47C4×D412yes—
170#2947—471nomaximal, Sylow
171C2×C47C2×C4×D411yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57811yescharacteristic
174D47—22no—
175D47—42no—
176C2×#137—471no—
177#520—471no—
178#519—471no—
179#441—471no—
180#441D4711yescharacteristic, complemented
181#440—471no—
182#440—471no—
183C4×Q16—471no—
184C4×Q16—471no—
185C4×SD16—471no—
186C4×SD16—471no—
187#428—471no—
188#416—471no—
189C2×#103—471no—
190#405—471no—
191C47#294711yescharacteristic, complemented, Sylow
192C2×#41—471no—
193C22×Q8—471no—
194#137—478no—
195C2×Q16—471no—
196C2×Q16C2×D4711yescharacteristic
197C2×SD16—471no—
198C2×SD16—471no—
199C2×M16—471no—
200C22×C8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×Q8—941no—
206C4×Q8—941no—
207C4×Q8C2×D4711yescharacteristic
208C4×Q8C2×D4711yescharacteristic
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—941no—
212C4×D4—941no—
213#117—471no—
214#117—471no—
215#117—941no—
216#117—941no—
217#117—941no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—941no—
220#107—471no—
221#107—471no—
222#106—471no—
223#106C2×D4711yescharacteristic
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103C2×D4711yescharacteristic
229#103C2×D4711yescharacteristic
230#102—471no—
231#102—471no—
232#97—471no—
233#97C2×D4711yescharacteristic
234C4×C8—471no—
235C4×C8—471no—
236#41—474no—
237#41—942no—
238C2×Q8—474no—
239C2×Q8—471no—
240C2×Q8—941no—
241C2×Q8—942no—
242C2×Q8C22×D4711yescharacteristic
243C2×Q8C22×D4711yescharacteristic
244C2×D4—471no—
245C2×D4—941no—
246C22×C4—471no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252Q16—474no—
253Q16C4×D4714yescomplemented
254SD16—474no—
255SD16—474no—
256M16—474no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—942no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—21no—
281C42—21no—
282C42—471no—
283C42—941no—
284C42—941no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C23—471no—
290C23—941no—
291Q8—21no—
292Q8—21no—
293Q8—472no—
294Q8—944no—
295Q8—941no—
296Q8C2×C4×D4712yes—
297Q8C2×C4×D4712yes—
298D4—472no—
299D4—944no—
300D4—941no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—471no—
306C2×C4—472no—
307C2×C4—472no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—944no—
311C2×C4—944no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—3761no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—472no—
323C8—941no—
324C8C2×C4×D4712yes—
325C22—472no—
326C22—941no—
327C22—941no—
328C22—942no—
329C22—1881no—
330C22—1881no—
331C22C2×D4×D4711yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—472no—
339C4—942no—
340C4—941no—
341C4—941no—
342C4—1881no—
343C4—1881no—
344C4C22×C4×D4711yescharacteristic
345C4#41×D4711yescharacteristic
346C2—942no—
347C2—1882no—
348C2C4×D4×D4711yescharacteristic
349C2#1568993211yescharacteristic
350C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#2947
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #15689599C2semidirect
4. #15689227C2semidirect
5. #15689226C2semidirect
6. #15689225C2semidirect
7. Q16×Dic47C2semidirect
8. C4×#10625337C2semidirect
9. C4×#10625336C2semidirect
10. #15689210C2semidirect
11. #15689162C2semidirect
13. #103×D47C2semidirect
14. #15689080C2semidirect
15. C47×#441C2semidirect
18. #13094056C4semidirect
65. Q8×D47C2×C4semidirect
76. Q16×C47C2×C4semidirect
86. #10625337C2×C4semidirect
87. #10625336C2×C4semidirect
110. #10625325C2×C4semidirect
111. #10625324C2×C4semidirect
180. #441D47semidirect
191. C47#2947semidirect
253. Q16C4×D47semidirect