Finite Group Databasebeta

← #20254064

Subgroups — #20254064

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#15689746C211yesmaximal, characteristic, complemented
2#15689726C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689509C211yesmaximal, characteristic, complemented
5#15689479C211yesmaximal, characteristic, complemented
6#15689468C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689354C211yesmaximal, characteristic, complemented
10#15689232C211yesmaximal, characteristic, complemented
11#15689226C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13#15689205C211yesmaximal, characteristic, complemented
14#15689081C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×D376C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
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#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093934C2211yescharacteristic
49#13093934C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×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—22no—
74M16×C47—22no—
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—22no—
86#10625334—22no—
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
104C2×C47⋊C8—22no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107D376—22no—
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#4112yes—
144C47⋊C8—21no—
145C47⋊C8#4112yes—
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×C47C2×#4111yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—21no—
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171#3179—471nomaximal, Sylow
172C2×C47—41no—
173C2×C47—81no—
174C2×C47#53211yescharacteristic
175C2×C47#57611yescharacteristic
176C2×C47#57711yescharacteristic
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#468D4711yescharacteristic, complemented
187#466—471no—
188#465—471no—
189#442—471no—
190#440—471no—
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×M16C2×D4711yescharacteristic
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—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#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#97—471no—
236C4×C8—471no—
237C4×C8—471no—
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—22no—
253SD16—942no—
254D8—942no—
255D8—942no—
256M16—22no—
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—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—472no—
323C8—941no—
324C8#1062535212yes—
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#41×D4711yescharacteristic
349C4C2×#1062535211yescharacteristic
350C2—41no—
351C2—81no—
352C2—3761no—
353C2—3761no—
354C2#1568966811yescharacteristic
355C2#1568992711yescharacteristic
356C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689726C2semidirect
3. #15689531C2semidirect
4. #15689509C2semidirect
5. #15689479C2semidirect
6. #15689468C2semidirect
7. #15689376C2semidirect
8. #15689357C2semidirect
9. #15689354C2semidirect
10. #15689232C2semidirect
11. #15689226C2semidirect
12. SD16×Dic47C2semidirect
13. #15689205C2semidirect
14. #15689081C2semidirect
15. C47×#468C2semidirect
186. #468D47semidirect
194. C47#3179semidirect