Finite Group Databasebeta

← #20255498

Subgroups — #20255498

Order 6016.

388 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#15689834C211yesmaximal, characteristic, complemented
2#15689781C211yesmaximal, characteristic
3#15689452C211yesmaximal, characteristic, complemented
4#15689440C211yesmaximal, characteristic, complemented
5#15689405C211yesmaximal, characteristic, complemented
6#15689380C211yesmaximal, characteristic, complemented
7#15689351C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689280C211yesmaximal, characteristic, complemented
11#15689231C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#489C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625324C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic
23#13094015—21no—
24#13094010—21no—
25#13094004C2211yescharacteristic
26#13094004C2211yescharacteristic
27#13094001—21no—
28#13094000—21no—
29#13094000—21no—
30#13094000C2211yescharacteristic
31#13093997—21no—
32#13093995C2211yescharacteristic
33C4×Dic94C2211yescharacteristic
34C4×Dic94C2211yescharacteristic
35C4×D188C2211yescharacteristic
36#13093986—21no—
37(C22⋊D47)⋊C4—21no—
38C4⋊C4×D47C2211yescharacteristic
39C4⋊C4×D47C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65Q8×D47—22no—
66Q8×D47—41no—
67#10625352—22no—
68#10625352—41no—
69C2×D188D411yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87#10625337—41no—
88#10625335—41no—
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⋊Dic47—21no—
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108Dic188—22no—
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—81no—
117D4×C47—21no—
118D4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—42no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—42no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134D188—22no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—42no—
140C4×D47—81no—
141C4×D47—81no—
142Dic94—21no—
143Dic94—21no—
144Dic94—21no—
145Dic94—42no—
146Dic94#4112yes—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47#13712yes—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47H(5,𝔽2)11yescharacteristic
168Dic47—22no—
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3316—471nomaximal, Sylow
175C2×C47—81no—
176C2×C47#54611yescharacteristic
177C2×C47C2×#13711yescharacteristic
178C2×C47#57711yescharacteristic
179D47—22no—
180D47—41no—
181#554—471no—
182#548—471no—
183#489D4711yescharacteristic, complemented
184#483—471no—
185#481—471no—
186#475—471no—
187#470—471no—
188#465—471no—
189#464—471no—
190#452—471no—
191#451—471no—
192#441—471no—
193#435—471no—
194#417—471no—
195C2×#103—471no—
196C47#331611yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C22×Q8—471no—
199C2×Q16—471no—
200C2×Q16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8C2×D4711yescharacteristic
205#125—941no—
206#124—941no—
207#124C2×D4711yescharacteristic
208C22⋊Q8—471no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212C22⋊Q8—941no—
213C22⋊Q8—941no—
214#121—471no—
215#121—941no—
216C4×Q8—471no—
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—941no—
220C4×D4—941no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103C2×D4711yescharacteristic
233#103C2×D4711yescharacteristic
234#102—471no—
235#102C2×D4711yescharacteristic
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97C2×D4711yescharacteristic
240#41—942no—
241#41—1881no—
242C2×Q8—21no—
243C2×Q8—471no—
244C2×Q8—471no—
245C2×Q8—941no—
246C2×Q8—942no—
247C2×Q8—1881no—
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4C22×D4711yescharacteristic
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259Q16—942no—
260Q16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—1881no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—941no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—21no—
293C23—471no—
294C23—471no—
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—472no—
299Q8—941no—
300Q8—941no—
301Q8—941no—
302Q8—1882no—
303D4—21no—
304D4—21no—
305D4—942no—
306D4—1882no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4—1882no—
324C2×C4—1882no—
325C2×C4D4×D4711yescharacteristic
326C2×C4D4×D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—472no—
336C22—941no—
337C22—941no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—941no—
348C4—941no—
349C4—942no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4#41×D4711yescharacteristic
354C4#1309407011yescharacteristic
355C2—81no—
356C2—942no—
357C2—1881no—
358C2#1568976611yescharacteristic
359C2#137×D4711yescharacteristic
360C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
3. #15689452C2semidirect
4. #15689440C2semidirect
5. #15689405C2semidirect
6. #15689380C2semidirect
7. #15689351C2semidirect
8. #15689342C2semidirect
9. #15689286C2semidirect
10. #15689280C2semidirect
11. #15689231C2semidirect
12. #15689196C2semidirect
13. #15689121C2semidirect
14. #103×D47C2semidirect
15. C47×#489C2semidirect
183. #489D47semidirect
196. C47#3316semidirect