Finite Group Databasebeta

← #20255503

Subgroups — #20255503

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#15689831C211yesmaximal, characteristic, complemented
2#15689784C211yesmaximal, characteristic
3#15689484C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689378C211yesmaximal, characteristic, complemented
8#15689354C211yesmaximal, characteristic, complemented
9#15689347C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11#15689230C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14C2×#13093948C211yesmaximal, characteristic, complemented
15C47×#451C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094014—21no—
22#13094013—21no—
23#13094013C2211yescharacteristic
24#13094004—21no—
25#13094001—21no—
26#13094000—21no—
27#13094000C2211yescharacteristic
28#13094000C2211yescharacteristic
29#13093998—21no—
30#13093998C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×Q16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70#10625354—22no—
71#10625354—41no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78Q16×C47—22no—
79Q16×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊Dic47D411yescharacteristic
86#10625336—41no—
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
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—42no—
120Q8×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C22⋊D47—42no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—81no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188—21no—
141D188—42no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—42no—
145C4×D47—81no—
146Dic94—81no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47#13712yes—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—22no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47H(5,𝔽2)11yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—21no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3316—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47#54611yescharacteristic
177C2×C47C2×#13711yescharacteristic
178C2×C47#57711yescharacteristic
179D47—41no—
180D47—81no—
181#554—471no—
182#548—471no—
183#489—471no—
184#483—471no—
185#481—471no—
186#475—471no—
187#470—471no—
188#465—471no—
189#464—471no—
190#452—471no—
191#451D4711yescharacteristic, complemented
192#441—471no—
193#435—471no—
194#417—471no—
195C2×#103—471no—
196C47#331611yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C22×Q8C2×D4711yescharacteristic
199C2×Q16C2×D4711yescharacteristic
200C2×Q16C2×D4711yescharacteristic
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—471no—
205#125—941no—
206#124—471no—
207#124—941no—
208C22⋊Q8—471no—
209C22⋊Q8—471no—
210C22⋊Q8—941no—
211C22⋊Q8—941no—
212C22⋊Q8—941no—
213C22⋊Q8C2×D4711yescharacteristic
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#102—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8C2×D4711yescharacteristic
239#97—471no—
240#41—942no—
241#41—1881no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—941no—
246C2×Q8C22×D4711yescharacteristic
247C2×Q8C22×D4711yescharacteristic
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—471no—
251C2×D4—941no—
252C2×D4—941no—
253C22×C4—21no—
254C22×C4—471no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4C22×D4711yescharacteristic
259Q16—22no—
260Q16—41no—
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—471no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—471no—
283C22⋊C4—471no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—471no—
290C42—941no—
291C42—941no—
292C23—471no—
293C23—941no—
294C23D4×D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—3761no—
302Q8#1062535212yes—
303D4—942no—
304D4—941no—
305D4—941no—
306D4—1882no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—3761no—
324C2×C4—3761no—
325C2×C4—1882no—
326C2×C4D4×D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—941no—
335C22—941no—
336C22—941no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22#1309405612yes—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—941no—
348C4—941no—
349C4—941no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4C2×#1062535211yescharacteristic
354C4#1309406911yescharacteristic
355C2—22no—
356C2—3761no—
357C2—1881no—
358C2#1568976011yescharacteristic
359C2C2×#1309405611yescharacteristic
360C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689484C2semidirect
4. #15689452C2semidirect
5. #15689442C2semidirect
6. #15689406C2semidirect
7. #15689378C2semidirect
8. #15689354C2semidirect
9. #15689347C2semidirect
10. #15689284C2semidirect
11. #15689230C2semidirect
12. #15689191C2semidirect
13. #15689123C2semidirect
14. C2×#13093948C2semidirect
15. C47×#451C2semidirect
191. #451D47semidirect
196. C47#3316semidirect