Finite Group Databasebeta

← #20254802

Subgroups — #20254802

Order 6016.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689746C211yesmaximal, characteristic, complemented
2#15689726C211yesmaximal, characteristic, complemented
3#15689432C211yesmaximal, characteristic, complemented
4#15689422C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689374C211yesmaximal, characteristic, complemented
8#15689371C211yesmaximal, characteristic, complemented
9#15689359C211yesmaximal, characteristic, complemented
10#15689341C211yesmaximal, characteristic, complemented
11#15689340C211yesmaximal, characteristic, complemented
12#15689321C211yesmaximal, characteristic, complemented
13#15689317C211yesmaximal, characteristic, complemented
14#15689149C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×D376C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094020C2211yescharacteristic
22#13094019—21no—
23#13094015C2211yescharacteristic
24#13094013C2211yescharacteristic
25#13094010—21no—
26#13094008—21no—
27#13094006—21no—
28#13094006—21no—
29#13094004—21no—
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic
32#13093996—21no—
33#13093995—21no—
34Q8×Dic47C2211yescharacteristic
35D4×Dic47C2211yescharacteristic
36#13093986C2211yescharacteristic
37#13093986C2211yescharacteristic
38#13093983C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C2×D188C2311yescharacteristic
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×Dic94—21no—
73SD16×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47D411yescharacteristic
84C22⋊Dic47D411yescharacteristic
85#10625336—41no—
86#10625334—41no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47D411yescharacteristic
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107D376—41no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—81no—
125C22⋊D47—81no—
126C22⋊D47—81no—
127C22⋊D47—81no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—21no—
136D188—21no—
137D188—21no—
138D188—21no—
139C4×D47—81no—
140C4×D47—81no—
141Dic94—81no—
142C8×C47—21no—
143C8×C47—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47C22×D411yescharacteristic
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47H(5,𝔽2)11yescharacteristic
164C4×C472−1+411yescharacteristic
165Dic47—21no—
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171#3257—471nomaximal, Sylow
172C2×C47—41no—
173C2×C47—81no—
174C2×C47#53711yescharacteristic
175C2×C47#57611yescharacteristic
176C2×C47#57711yescharacteristic
177D47—81no—
178D47—81no—
179#542—471no—
180#540—471no—
181#479—471no—
182#478—471no—
183#476—471no—
184#474—471no—
185#469—471no—
186#468—471no—
187#466—471no—
188#465D4711yescharacteristic, complemented
189#463—471no—
190#463—471no—
191#460—471no—
192#459—471no—
193#424—471no—
194C47#325711yescharacteristic, complemented, Sylow
195C2×SD16—471no—
196C2×SD16C2×D4711yescharacteristic
197C2×D8—471no—
198C2×D8—471no—
199C2×M16—471no—
200C22×C8C2×D4711yescharacteristic
201C4⋊Q8—471no—
202#127—471no—
203#126—941no—
204#125—471no—
205#124—471no—
206#124—941no—
207#123—941no—
208#123—941no—
209#123—941no—
210C22⋊Q8—941no—
211C22⋊Q8C2×D4711yescharacteristic
212#121—471no—
213#121—471no—
214#121—941no—
215#121—941no—
216#121C2×D4711yescharacteristic
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221#117—471no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106C2×D4711yescharacteristic
226C4⋊C8—471no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229C4⋊C8—471no—
230#103—471no—
231#103C2×D4711yescharacteristic
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102C2×D4711yescharacteristic
238C2×Q8—941no—
239C2×Q8C22×D4711yescharacteristic
240C2×D4—21no—
241C2×D4—471no—
242C2×D4—471no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252SD16—41no—
253SD16—1881no—
254D8—1881no—
255D8—1881no—
256M16—1881no—
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22×D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—471no—
285C42—471no—
286C42—941no—
287C23—21no—
288C23—941no—
289C23—941no—
290C23D4×D4711yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—941no—
301D4—3761no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—21no—
323C8—941no—
324C8—941no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—941no—
343C4—941no—
344C4—941no—
345C4—941no—
346C4—1881no—
347C4—1881no—
348C4#1309406911yescharacteristic
349C4#1309407111yescharacteristic
350C2—41no—
351C2—81no—
352C2—3761no—
353C2—3761no—
354C2#1568970011yescharacteristic
355C2#1568992511yescharacteristic
356C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3257
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689726C2semidirect
3. #15689432C2semidirect
4. #15689422C2semidirect
5. #15689412C2semidirect
6. #15689401C2semidirect
7. #15689374C2semidirect
8. #15689371C2semidirect
9. #15689359C2semidirect
10. #15689341C2semidirect
11. #15689340C2semidirect
12. #15689321C2semidirect
13. #15689317C2semidirect
14. #15689149C2semidirect
15. C47×#465C2semidirect
188. #465D47semidirect
194. C47#3257semidirect