Finite Group Databasebeta

← #20255133

Subgroups — #20255133

Order 6016.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625337C211yesmaximal, characteristic, complemented
2C2×Q16×D47C211yesmaximal, characteristic, complemented
3Q8×C22⋊D47C211yesmaximal, characteristic
4#15689786C211yesmaximal, characteristic
5#15689501C211yesmaximal, characteristic, complemented
6#15689363C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689332C211yesmaximal, characteristic, complemented
9#15689331C211yesmaximal, characteristic, complemented
10#15689281C211yesmaximal, characteristic, complemented
11#15689280C211yesmaximal, characteristic, complemented
12#15689277C211yesmaximal, characteristic, complemented
13#15689215C211yesmaximal, characteristic, complemented
14(C22⋊D47)⋊C8C211yesmaximal, characteristic
15C47×#451C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic
19C2×Dic188C2211yescharacteristic
20C2×Dic188C2211yescharacteristic
21C2×#10625337—24no—
22C2×#10625337C2211yescharacteristic
23C2×#10625337C2211yescharacteristic
24C2×#10625337C2211yescharacteristic
25C2×#10625337C2211yescharacteristic
26C2×#10625337C2211yescharacteristic
27Q16×D47—24no—
28C22×C47⋊C8C2211yescharacteristic
29C2×C8×D47C2211yescharacteristic
30#13094023—21no—
31#13094022—21no—
32#13094022C2211yescharacteristic
33#13094022C2211yescharacteristic
34#13094004C2211yescharacteristic
35#13094003—21no—
36#13094003C2211yescharacteristic
37#13094002—21no—
38#13094001—21no—
39#13094000—21no—
40#13094000C2211yescharacteristic
41Q8×Dic47C2211yescharacteristic
42#13093989C2211yescharacteristic
43C4×C22⋊D47—21no—
44C4×C22⋊D47C2211yescharacteristic
45(C22⋊D47)⋊C4—21no—
46#13093957C2211yescharacteristic
47Dic47⋊C8C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093948C2211yescharacteristic
51#13093947C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic
53C8×Dic47C2211yescharacteristic
54C22×Q8×C47C2211yescharacteristic
55C2×Q16×C47C2211yescharacteristic
56C2×Q16×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59#103×C47C2211yescharacteristic
60C22⋊C8×C47C2211yescharacteristic
61C2×Q8×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47D411yescharacteristic
70C22×Dic47—21no—
71Q8×D47—22no—
72Q8×D47—22no—
73Q8×D47—41no—
74Q8×D47—41no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—22no—
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94—21no—
82C2×Dic94—41no—
83C2×Dic94C2311yescharacteristic
84C2×Dic94C2311yescharacteristic
85C2×Dic94C2311yescharacteristic
86Q16×C47—22no—
87Q16×C47—41no—
88C2×C8×C47C2311yescharacteristic
89C2×C8×C47C2311yescharacteristic
90C4⋊C4×C47—21no—
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47D411yescharacteristic
95#10625337—22no—
96#10625337—22no—
97#10625337—22no—
98#10625337—22no—
99#10625337D414yescomplemented
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4D411yescharacteristic
103C4⋊Dic47—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4D411yescharacteristic
114C4×Dic47—21no—
115C4×Dic47—21no—
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120Dic188—22no—
121Dic188—41no—
122C8×D47—22no—
123C23×C47C2×D411yescharacteristic
124C22×D47C2×D411yescharacteristic
125Q8×C47—21no—
126Q8×C47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—42no—
131Q8×C47C2×D412yes—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—42no—
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C22⋊D47Q1614yescomplemented
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—42no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—42no—
153C4×D47—42no—
154Dic94—21no—
155Dic94—21no—
156Dic94—21no—
157Dic94—21no—
158Dic94—21no—
159Dic94—42no—
160Dic94—42no—
161Dic94—42no—
162Dic94C2×D412yes—
163C8×C47—21no—
164C8×C47—21no—
165C47⋊C8—21no—
166C47⋊C8C2×D412yes—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47C2×Q1612yescomplemented
170C22×C47C22×D411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47C2×Q1612yescomplemented
174C4×C47—21no—
175C4×C47—22no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C22×D411yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—22no—
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187Dic47C2×Q1612yescomplemented
188D4×Q16—471nomaximal, Sylow
189C2×C47—22no—
190C2×C47D4211yescharacteristic
191C2×C47C22×Q1611yescharacteristic
192C2×C47#57811yescharacteristic
193D47—22no—
194C22×Q16—471no—
195C22×Q16—471no—
196D4×Q8—471no—
197D4×Q8—471no—
198#494—471no—
199#467—471no—
200#467—471no—
201#462—471no—
202#462—471no—
203#451—471no—
204#451—471no—
205#451—471no—
206#451D4711yescharacteristic, complemented
207C4×Q16—471no—
208C8×D4—471no—
209C47D4×Q1611yescharacteristic, complemented, Sylow
210C22×Q8—471no—
211C22×Q8—471no—
212C22×Q8—471no—
213C22×Q8C2×D4711yescharacteristic
214C2×Q16—471no—
215C2×Q16—471no—
216C2×Q16—471no—
217C2×Q16—471no—
218C2×Q16—471no—
219C2×Q16—471no—
220C2×Q16—471no—
221C2×Q16—944no—
222C2×Q16—944no—
223C2×Q16C2×D4711yescharacteristic
224C2×Q16C2×D4711yescharacteristic
225C22×C8—471no—
226C22×C8—471no—
227C4⋊Q8—471no—
228C4⋊Q8—471no—
229C4⋊Q8—941no—
230C4⋊Q8—941no—
231C22⋊Q8—471no—
232C22⋊Q8—471no—
233C22⋊Q8—471no—
234C22⋊Q8—941no—
235C22⋊Q8—941no—
236C22⋊Q8—941no—
237C22⋊Q8—941no—
238C22⋊Q8C2×D4711yescharacteristic
239C4×Q8—471no—
240C4×Q8—471no—
241C4×D4—471no—
242C4×D4—941no—
243C4×D4—941no—
244#107—471no—
245C4⋊C8—471no—
246#103—471no—
247#103—471no—
248#103—471no—
249#103—471no—
250#103C2×D4711yescharacteristic
251#103C2×D4711yescharacteristic
252C22⋊C8—471no—
253C22⋊C8C2×D4711yescharacteristic
254C4×C8—471no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—471no—
259C2×Q8—471no—
260C2×Q8—471no—
261C2×Q8—941no—
262C2×Q8—941no—
263C2×Q8—942no—
264C2×Q8—941no—
265C2×Q8—942no—
266C2×Q8—942no—
267C2×Q8—1881no—
268C2×Q8—1881no—
269C2×Q8—1881no—
270C2×Q8C22×D4711yescharacteristic
271C2×Q8C22×D4711yescharacteristic
272C2×Q8C22×D4711yescharacteristic
273C2×D4—471no—
274C22×C4—21no—
275C22×C4—471no—
276C22×C4—941no—
277C22×C4—941no—
278C22×C4—941no—
279C22×C4C22×D4711yescharacteristic
280Q16—22no—
281Q16—41no—
282Q16—474no—
283Q16—942no—
284Q16—942no—
285Q16—942no—
286Q16—942no—
287Q16—942no—
288Q16—1881no—
289C2×C8—471no—
290C2×C8—471no—
291C2×C8—942no—
292C2×C8—942no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—941no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C4⋊C4C22×D4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—471no—
310C22⋊C4—471no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C42—471no—
315C42—941no—
316C42—941no—
317C23—471no—
318C23D4×D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—472no—
326Q8—941no—
327Q8—941no—
328Q8—941no—
329Q8—941no—
330Q8—941no—
331Q8—1882no—
332Q8—1882no—
333Q8—1882no—
334Q8D4×D4712yes—
335D4—474no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—471no—
344C2×C4—471no—
345C2×C4—471no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—1882no—
353C2×C4—1882no—
354C2×C4—1882no—
355C2×C4D4×D4711yescharacteristic
356C2×C4C23×D4711yescharacteristic
357C8—21no—
358C8—21no—
359C8—472no—
360C8—941no—
361C22—21no—
362C22—21no—
363C22—472no—
364C22—941no—
365C22—941no—
366C22Q16×D4712yescomplemented
367C22C2×D4×D4711yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—472no—
374C4—941no—
375C4—942no—
376C4—941no—
377C4—1881no—
378C4—1881no—
379C4—1881no—
380C4C2×D4×D4711yescharacteristic
381C4#1309406911yescharacteristic
382C2—22no—
383C2—942no—
384C2#1568975511yescharacteristic
385C2C2×Q16×D4711yescharacteristic
386C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47D4×Q16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C22×#10625337C2semidirect
2. C2×Q16×D47C2semidirect
5. #15689501C2semidirect
6. #15689363C2semidirect
7. #15689362C2semidirect
8. #15689332C2semidirect
9. #15689331C2semidirect
10. #15689281C2semidirect
11. #15689280C2semidirect
12. #15689277C2semidirect
13. #15689215C2semidirect
15. C47×#451C2semidirect
99. #10625337D4semidirect
141. C22⋊D47Q16semidirect
169. C22×C47C2×Q16semidirect
173. C2×D47C2×Q16semidirect
187. Dic47C2×Q16semidirect
206. #451D47semidirect
209. C47D4×Q16semidirect
366. C22Q16×D47semidirect