Finite Group Databasebeta

← #20255381

Subgroups — #20255381

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689782C211yesmaximal, characteristic, complemented
2#15689777C211yesmaximal, characteristic, complemented
3#15689483C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689369C211yesmaximal, characteristic, complemented
8#15689359C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689264C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689125C211yesmaximal, characteristic, complemented
14C2×#13093949C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352—21no—
18C22×Dic94C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×D376C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094008—21no—
26#13094008—21no—
27#13094004—21no—
28#13094003C2211yescharacteristic
29#13094002—21no—
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic
32#13093998C2211yescharacteristic
33#13093996—21no—
34C4×Dic94C2211yescharacteristic
35C4×D188C2211yescharacteristic
36(C22⋊D47)⋊C4—21no—
37C2×C4⋊Dic47C2211yescharacteristic
38C2×C4⋊Dic47C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093946C2211yescharacteristic
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—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69#10625352—44no—
70#10625350—22no—
71#10625350—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94—22no—
77C2×Dic94—21no—
78C2×Dic94—21no—
79C2×Dic94—41no—
80C2×Dic94C2311yescharacteristic
81C2×Dic94C2311yescharacteristic
82M16×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47D411yescharacteristic
89C22⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109D376—41no—
110#10625325—22no—
111#10625325—41no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116D4×C47—22no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—42no—
127C22⋊D47—42no—
128C22⋊D47—42no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—21no—
143C4×D47—42no—
144C4×D47—42no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148Dic94—42no—
149Dic94—42no—
150Dic94#4112yescomplemented
151C8×C47—21no—
152C8×C47—21no—
153C8×C47—21no—
154C8×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47AGL(1,ℤ/8)12yes—
161C22×C47C22×D411yescharacteristic
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—22no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3308—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—41no—
183C2×C47#54611yescharacteristic
184C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C47#57811yescharacteristic
186D47—81no—
187D47—81no—
188#548—471no—
189#547—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#477—471no—
194#468—471no—
195#466—471no—
196#463—471no—
197#449—471no—
198#448—471no—
199#440—471no—
200#435D4711yescharacteristic, complemented
201#417—471no—
202C2×#103—471no—
203C47#330811yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C2×#41—941no—
206C22×Q8—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×D8—471no—
210C2×M16C2×D4711yescharacteristic
211C22×C8C2×D4711yescharacteristic
212C4⋊Q8—471no—
213#124—471no—
214#124—941no—
215#123—941no—
216#123—941no—
217C22⋊Q8—471no—
218C22⋊Q8—941no—
219C22⋊Q8—941no—
220#121—471no—
221#121—471no—
222#121—471no—
223#121—941no—
224C4×Q8—471no—
225C4×D4—471no—
226C4×D4—941no—
227C4×D4C2×D4711yescharacteristic
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8C2×D4711yescharacteristic
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#103—471no—
239#103—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244C22⋊C8C2×D4711yescharacteristic
245C22⋊C8C2×D4711yescharacteristic
246#97C2×D4711yescharacteristic
247#41—942no—
248#41—1881no—
249#41—1884no—
250C2×Q8—471no—
251C2×Q8—471no—
252C2×Q8—942no—
253C2×Q8—941no—
254C2×Q8—941no—
255C2×Q8—1881no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4D18811yescharacteristic
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270SD16—942no—
271SD16—1881no—
272D8—1881no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D4711yescharacteristic
276C2×C8C22×D4711yescharacteristic
277C2×C8C22×D4711yescharacteristic
278C2×C8C22×D4711yescharacteristic
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4D18811yescharacteristic
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4D18811yescharacteristic
297C22⋊C4D18811yescharacteristic
298C42—941no—
299C42C22×D4711yescharacteristic
300C23—941no—
301C23—941no—
302C23C2×D18811yescharacteristic
303C23C2×D18811yescharacteristic
304Q8—472no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308Q8—1882no—
309Q8—1882no—
310D4—22no—
311D4—941no—
312D4—941no—
313D4—941no—
314D4—941no—
315D4—1882no—
316D4—1882no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4—1882no—
333C2×C4—1882no—
334C2×C4C2×D18811yescharacteristic
335C2×C4C2×D18811yescharacteristic
336C2×C4C2×D18811yescharacteristic
337C2×C4C2×D18811yescharacteristic
338C2×C4C23×D4711yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1309405212yes—
355C22C22×D18811yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—942no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—41no—
370C2—3761no—
371C2—3761no—
372C2#1568976811yescharacteristic
373C2C2×#1309405211yescharacteristic
374C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3308
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. #15689782C2semidirect
2. #15689777C2semidirect
3. #15689483C2semidirect
4. #15689459C2semidirect
5. #15689437C2semidirect
6. #15689419C2semidirect
7. #15689369C2semidirect
8. #15689359C2semidirect
9. #15689339C2semidirect
10. #15689270C2semidirect
11. #15689264C2semidirect
12. #15689225C2semidirect
13. #15689125C2semidirect
14. C2×#13093949C2semidirect
15. C47×#435C2semidirect
150. Dic94#41semidirect
200. #435D47semidirect
203. C47#3308semidirect