Finite Group Databasebeta

← #20255285

Subgroups — #20255285

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689820C211yesmaximal, characteristic, complemented
2#15689783C211yesmaximal, characteristic, complemented
3#15689479C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689433C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689214C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13#15689120C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094017—21no—
22#13094015C2211yescharacteristic
23#13094013C2211yescharacteristic
24#13094010—21no—
25#13094005—21no—
26#13094002—21no—
27#13093999C2211yescharacteristic
28#13093997—21no—
29#13093995—21no—
30#13093995C2211yescharacteristic
31#13093989C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093986—21no—
34C4×C22⋊D47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36#13093983C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093955C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
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⋊D47D411yescharacteristic
66C22×Dic47—21no—
67Q8×D47—22no—
68Q8×D47—41no—
69#10625350—22no—
70#10625350—41no—
71C2×D188—21no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79SD16×C47—41no—
80C2×C8×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47D411yescharacteristic
92#10625335—22no—
93#10625334—41no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4D411yescharacteristic
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—81no—
120C2×C4×C47—21no—
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—22no—
128C22⋊D47—42no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188—21no—
139D188—42no—
140C4×D47—21no—
141C4×D47—21no—
142C4×D47—42no—
143C4×D47—42no—
144C4×D47—81no—
145Dic94—21no—
146Dic94—42no—
147Dic94#4112yes—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47#13512yes—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—22no—
172Dic47—21no—
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177#3301—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—81no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—22no—
184D47—81no—
185#553—471no—
186#548—471no—
187#488—471no—
188#485—471no—
189#481—471no—
190#479—471no—
191#466—471no—
192#465D4711yescharacteristic, complemented
193#463—471no—
194#449—471no—
195#448—471no—
196C4×SD16—471no—
197C8×D4—471no—
198#416—471no—
199C2×#103—471no—
200C47#330111yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C22×Q8—471no—
203C2×SD16—471no—
204C2×SD16C2×D4711yescharacteristic
205C2×D8—471no—
206C22×C8—471no—
207C22×C8C2×D4711yescharacteristic
208#126—941no—
209#125—471no—
210#124—471no—
211#124—941no—
212#123—941no—
213C22⋊Q8—941no—
214C22⋊Q8C2×D4711yescharacteristic
215#121—471no—
216#121—471no—
217#121—941no—
218#121—941no—
219#121C2×D4711yescharacteristic
220C4×Q8—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—941no—
224C4×D4—941no—
225#117—471no—
226C2×C4⋊C4—471no—
227#107—471no—
228#106—471no—
229#106C2×D4711yescharacteristic
230C4⋊C8—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103C2×D4711yescharacteristic
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241C22⋊C8—471no—
242C22⋊C8—471no—
243C4×C8—471no—
244#41—942no—
245#41—1881no—
246C2×Q8—471no—
247C2×Q8—941no—
248C2×Q8—942no—
249C2×Q8—1881no—
250C2×Q8C22×D4711yescharacteristic
251C2×D4—21no—
252C2×D4—471no—
253C2×D4—471no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—471no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4C22×D4711yescharacteristic
264SD16—41no—
265SD16—942no—
266D8—1881no—
267C2×C8—41no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—1881no—
271C2×C8C22×D4711yescharacteristic
272C2×C8C22×D4711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4C22×D4711yescharacteristic
282C4⋊C4C22×D4711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—471no—
286C22⋊C4—471no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—471no—
294C42—941no—
295C42—941no—
296C23—21no—
297C23—471no—
298C23—941no—
299C23D4×D4711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—472no—
303Q8—941no—
304Q8—1882no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—942no—
309D4—941no—
310D4—941no—
311D4—1882no—
312D4—1882no—
313D4—1882no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—471no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—3761no—
328C2×C4—3761no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—21no—
334C8—21no—
335C8—941no—
336C8—941no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—472no—
344C22—941no—
345C22—941no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C2×D4×D4711yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—941no—
355C4—942no—
356C4—941no—
357C4—941no—
358C4—1881no—
359C4—1881no—
360C4#41×D4711yescharacteristic
361C4#1309406911yescharacteristic
362C2—41no—
363C2—81no—
364C2—942no—
365C2—3761no—
366C2#1568976211yescharacteristic
367C2#135×D4711yescharacteristic
368C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3301
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. #15689820C2semidirect
2. #15689783C2semidirect
3. #15689479C2semidirect
4. #15689461C2semidirect
5. #15689443C2semidirect
6. #15689433C2semidirect
7. #15689358C2semidirect
8. #15689340C2semidirect
9. #15689266C2semidirect
10. #15689260C2semidirect
11. #15689214C2semidirect
12. C8×C22⋊D47C2semidirect
13. #15689120C2semidirect
14. #103×D47C2semidirect
15. C47×#465C2semidirect
192. #465D47semidirect
200. C47#3301semidirect