Finite Group Databasebeta

← #20254069

Subgroups — #20254069

Order 6016.

374 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#15689745C211yesmaximal, characteristic, complemented
2#15689724C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689509C211yesmaximal, characteristic, complemented
5#15689479C211yesmaximal, characteristic, complemented
6#15689468C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689372C211yesmaximal, characteristic, complemented
9#15689360C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×D376C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094018—21no—
24#13094015C2211yescharacteristic
25#13094013C2211yescharacteristic
26#13094012—21no—
27#13094009—21no—
28#13094007—21no—
29#13094006—21no—
30#13094002—21no—
31#13094000C2211yescharacteristic
32#13093999C2211yescharacteristic
33#13093999C2211yescharacteristic
34#13093998—21no—
35#13093997—21no—
36#13093995C2211yescharacteristic
37C4×D188C2211yescharacteristic
38C4×D188C2211yescharacteristic
39#13093981C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×D188—21no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47C2311yescharacteristic
72C2×Dic94—21no—
73SD16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C42×C47—21no—
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83#10625336—22no—
84#10625334—22no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
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)⋊C4D411yescharacteristic
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105D376—22no—
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—21no—
113Q8×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—81no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—81no—
124C22⋊D47—81no—
125C22⋊D47—81no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131D188—21no—
132D188—21no—
133D188—21no—
134D188—21no—
135D188—81no—
136D188—81no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—81no—
140C4×D47—81no—
141Dic94—81no—
142C8×C47—21no—
143C8×C47#4112yes—
144C47⋊C8—21no—
145C47⋊C8#4112yes—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47C22×D411yescharacteristic
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C47C2×#4111yescharacteristic
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171#3179—471nomaximal, Sylow
172C2×C47—81no—
173C2×C47#53211yescharacteristic
174C2×C47#57611yescharacteristic
175C2×C47#57711yescharacteristic
176D47—41no—
177D47—81no—
178D47—81no—
179#542—471no—
180#540—471no—
181#501—471no—
182#496—471no—
183#488—471no—
184#486—471no—
185#469—471no—
186#468—471no—
187#466—471no—
188#465—471no—
189#442—471no—
190#440D4711yescharacteristic, complemented
191C4×SD16—471no—
192C4×D8—471no—
193#405—471no—
194C47#317911yescharacteristic, complemented, Sylow
195C2×SD16—471no—
196C2×SD16C2×D4711yescharacteristic
197C2×D8—471no—
198C2×D8—471no—
199C2×M16—471no—
200C22×C8—471no—
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—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—471no—
214#121—471no—
215#121—941no—
216#121—941no—
217C4×Q8C2×D4711yescharacteristic
218C4×D4—471no—
219C4×D4—471no—
220C4×D4C2×D4711yescharacteristic
221#117—471no—
222#107—471no—
223#107C2×D4711yescharacteristic
224#106—471no—
225#106—471no—
226#103—471no—
227#103C2×D4711yescharacteristic
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102C2×D4711yescharacteristic
234#97—471no—
235#97C2×D4711yescharacteristic
236C4×C8—471no—
237C4×C8—471no—
238C2×Q8—941no—
239C2×Q8C22×D4711yescharacteristic
240C2×D4—471no—
241C2×D4—471no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—471no—
250C22×C4—941no—
251C22×C4—941no—
252SD16—22no—
253SD16—942no—
254D8—942no—
255D8—942no—
256M16—942no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—942no—
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—471no—
275C22⋊C4—471no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—21no—
285C42—471no—
286C42C22×D4711yescharacteristic
287C23—21no—
288C23—471no—
289C23—941no—
290C23—941no—
291Q8—21no—
292Q8—21no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—941no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—3761no—
301D4—3761no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—472no—
323C8—941no—
324C8#1062535012yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—941no—
329C22—941no—
330C22—941no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—941no—
344C4—941no—
345C4—941no—
346C4—1881no—
347C4—1881no—
348C4#41×D4711yescharacteristic
349C4C2×#1062535011yescharacteristic
350C2—81no—
351C2—3761no—
352C2—3761no—
353C2—1881no—
354C2#1568967011yescharacteristic
355C2#1568992711yescharacteristic
356C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689745C2semidirect
2. #15689724C2semidirect
3. #15689531C2semidirect
4. #15689509C2semidirect
5. #15689479C2semidirect
6. #15689468C2semidirect
7. #15689375C2semidirect
8. #15689372C2semidirect
9. #15689360C2semidirect
10. #15689349C2semidirect
11. #15689236C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625334C2semidirect
14. #15689080C2semidirect
15. C47×#440C2semidirect
190. #440D47semidirect
194. C47#3179semidirect