Finite Group Databasebeta

← #20255501

Subgroups — #20255501

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#15689830C211yesmaximal, characteristic, complemented
2#15689782C211yesmaximal, characteristic
3#15689483C211yesmaximal, characteristic, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689346C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689231C211yesmaximal, characteristic, complemented
13#15689125C211yesmaximal, characteristic, complemented
14C2×#13093949C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×Dic188C2211yescharacteristic
19C2×Dic188C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094015—21no—
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13094001—21no—
30#13094001—21no—
31#13093998C2211yescharacteristic
32#13093996—21no—
33C4×Dic94C2211yescharacteristic
34C4×Dic94C2211yescharacteristic
35D4×Dic47—21no—
36(C22⋊D47)⋊C4—21no—
37C2×C4⋊Dic47C2211yescharacteristic
38C2×C4⋊Dic47C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47D411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67#10625350—22no—
68#10625350—41no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—22no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94—41no—
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78M16×C47—41no—
79C2×C8×C47—41no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47D411yescharacteristic
85C22⋊C4×C47D411yescharacteristic
86C22⋊C4×C47D411yescharacteristic
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108Dic188—22no—
109Dic188—41no—
110#10625325—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114D4×C47—22no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2411yescharacteristic
124C22⋊D47—42no—
125C22⋊D47—42no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136D188—21no—
137D188—21no—
138C4×D47—42no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143Dic94—21no—
144Dic94—42no—
145Dic94—81no—
146Dic94#4112yes—
147C8×C47—21no—
148C8×C47—21no—
149C8×C47—21no—
150C8×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#13712yes—
157C22×C47C22×D411yescharacteristic
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47C2×#4111yescharacteristic
166C4×C47H(5,𝔽2)11yescharacteristic
167Dic47—22no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3316—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—41no—
177C2×C47#54611yescharacteristic
178C2×C47C2×#13711yescharacteristic
179C2×C47#57711yescharacteristic
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#451—471no—
192#441—471no—
193#435D4711yescharacteristic, complemented
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×M16C2×D4711yescharacteristic
203C22×C8C2×D4711yescharacteristic
204C4⋊Q8—471no—
205#125—941no—
206#124—471no—
207#124—941no—
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—941no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223#106—471no—
224#106—471no—
225#106—471no—
226C4⋊C8C2×D4711yescharacteristic
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237C22⋊C8C2×D4711yescharacteristic
238C22⋊C8C2×D4711yescharacteristic
239#97C2×D4711yescharacteristic
240#41—942no—
241#41—1881no—
242C2×Q8—471no—
243C2×Q8—471no—
244C2×Q8—471no—
245C2×Q8—942no—
246C2×Q8—941no—
247C2×Q8—941no—
248C2×Q8—1881no—
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4D18811yescharacteristic
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259Q16—942no—
260Q16—1881no—
261SD16—1881no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—471no—
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⋊C4—941no—
280C4⋊C4D18811yescharacteristic
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4D18811yescharacteristic
288C22⋊C4D18811yescharacteristic
289C42—941no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—941no—
293C23C2×D18811yescharacteristic
294C23C2×D18811yescharacteristic
295Q8—472no—
296Q8—941no—
297Q8—941no—
298Q8—941no—
299Q8—941no—
300Q8—941no—
301Q8—3761no—
302Q8—1882no—
303D4—22no—
304D4—941no—
305D4—941no—
306D4—1882no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4C2×D18811yescharacteristic
324C2×C4C2×D18811yescharacteristic
325C2×C4C2×D18811yescharacteristic
326C2×C4C2×D18811yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22#1309405712yes—
341C22C22×D18811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—942no—
347C4—1881no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4#41×D4711yescharacteristic
354C4#1309406911yescharacteristic
355C2—22no—
356C2—41no—
357C2—3761no—
358C2#1568976811yescharacteristic
359C2C2×#1309405711yescharacteristic
360C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3316
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689830C2semidirect
3. #15689483C2semidirect
4. #15689454C2semidirect
5. #15689442C2semidirect
6. #15689409C2semidirect
7. #15689381C2semidirect
8. #15689352C2semidirect
9. #15689346C2semidirect
10. #15689287C2semidirect
11. #15689281C2semidirect
12. #15689231C2semidirect
13. #15689125C2semidirect
14. C2×#13093949C2semidirect
15. C47×#435C2semidirect
193. #435D47semidirect
196. C47#3316semidirect