Finite Group Databasebeta

← #20253580

Subgroups — #20253580

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689726C211yesmaximal, characteristic, complemented
2#15689606C211yesmaximal, characteristic, complemented
3#15689439C211yesmaximal, characteristic, complemented
4#15689437C211yesmaximal, characteristic, complemented
5#15689432C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689321C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689232C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689208C211yesmaximal, characteristic, complemented
13D8×Dic47C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18#13094020C2211yescharacteristic
19#13094015C2211yescharacteristic
20#13094008—21no—
21#13094006—21no—
22#13093998C2211yescharacteristic
23#13093996—21no—
24#13093995—21no—
25Q8×Dic47C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27D4×Dic47—21no—
28D4×Dic47—21no—
29D4×Dic47C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093983—21no—
34#13093983C2211yescharacteristic
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77SD16×C47—22no—
78D8×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47D411yescharacteristic
87C22⋊Dic47D411yescharacteristic
88#10625336—22no—
89#10625334—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47D411yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114D4×C47—24no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119D4×C47#4112yes—
120C2×C4×C47—24no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—81no—
128C22⋊D47—81no—
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—21no—
142D188—21no—
143C4×D47—81no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—22no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—22no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C47C2×#4111yescharacteristic
166Dic47—21no—
167Dic47—21no—
168Dic47—21no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173#3119—471nomaximal, Sylow
174C2×C47—41no—
175C2×C47—42no—
176C2×C47—81no—
177C2×C47#52511yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57711yescharacteristic
180D47—81no—
181#540—471no—
182#520—471no—
183#481—471no—
184#480—471no—
185#479—471no—
186#478—471no—
187#460—471no—
188#459—471no—
189#449—471no—
190#449D4711yescharacteristic, complemented
191#442—471no—
192#440—471no—
193C4×SD16—471no—
194C4×D8—471no—
195#433—471no—
196C47#311911yescharacteristic, complemented, Sylow
197C2×#41C2×D4711yescharacteristic
198C2×SD16—471no—
199C2×SD16C2×D4711yescharacteristic
200C2×D8—471no—
201C2×D8C2×D4711yescharacteristic
202#127—471no—
203#125—471no—
204#123—941no—
205#123—941no—
206#121—471no—
207#121—941no—
208#121—941no—
209#121C2×D4711yescharacteristic
210C4×Q8—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—941no—
217C4×D4—941no—
218#117—471no—
219#117—941no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227C4⋊C8—471no—
228#103—471no—
229#103C2×D4711yescharacteristic
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102C2×D4711yescharacteristic
236C22⋊C8—471no—
237C22⋊C8C2×D4711yescharacteristic
238#97—471no—
239C4×C8—471no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D4711yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C2×D4C22×D4711yescharacteristic
251C22×C4—21no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—22no—
259SD16—942no—
260D8—22no—
261D8—942no—
262C2×C8—471no—
263C2×C8—471no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—471no—
279C22⋊C4—471no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C42—471no—
286C42—471no—
287C42—941no—
288C42—941no—
289C23—21no—
290C23—21no—
291C23—941no—
292C23D4×D4711yescharacteristic
293Q8—21no—
294Q8#1062535212yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—941no—
301D4—941no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305D4#1062535212yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—3761no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4D4×D4711yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—21no—
326C8—21no—
327C8—941no—
328C8—941no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—941no—
346C4—941no—
347C4—941no—
348C4—941no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4C2×#1062535211yescharacteristic
353C4C2×#1062535211yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—3761no—
358C2#1568962911yescharacteristic
359C2#1568992511yescharacteristic
360C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689726C2semidirect
2. #15689606C2semidirect
3. #15689439C2semidirect
4. #15689437C2semidirect
5. #15689432C2semidirect
6. #15689421C2semidirect
7. #15689321C2semidirect
8. #15689316C2semidirect
9. #15689268C2semidirect
10. #15689232C2semidirect
11. #15689224C2semidirect
12. #15689208C2semidirect
13. D8×Dic47C2semidirect
14. #15689181C2semidirect
15. C47×#449C2semidirect
190. #449D47semidirect
196. C47#3119semidirect