Finite Group Databasebeta

← #20255643

Subgroups — #20255643

Order 6016.

392 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#15689819C211yesmaximal, characteristic, complemented
2#15689782C211yesmaximal, characteristic, complemented
3#15689478C211yesmaximal, characteristic, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689264C211yesmaximal, characteristic, complemented
12C4×#10625325C211yesmaximal, characteristic, complemented
13#15689133C211yesmaximal, characteristic, complemented
14#15689125C211yesmaximal, characteristic, complemented
15C47×#436C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094019—21no—
22#13094016C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094010—21no—
25#13094006—21no—
26#13094003C2211yescharacteristic
27#13094002—21no—
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093996—21no—
32#13093996—21no—
33C4×Dic94C2211yescharacteristic
34C4×D188C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36(C22⋊D47)⋊C4—21no—
37#13093983C2211yescharacteristic
38C2×C4⋊Dic47C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58C4×C8×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—
68#10625350—22no—
69#10625350—41no—
70C2×D188C2311yescharacteristic
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×Dic94—22no—
75C2×Dic94—21no—
76C2×Dic94—41no—
77C2×Dic94C2311yescharacteristic
78C2×Dic94C2311yescharacteristic
79M16×C47—41no—
80M16×C47—41no—
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47D411yescharacteristic
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108D376—41no—
109#10625325—22no—
110#10625325—41no—
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115D4×C47—41no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—42no—
127C22⋊D47—42no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47—81no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141C4×D47—42no—
142C4×D47—81no—
143Dic94—21no—
144Dic94—21no—
145Dic94—21no—
146Dic94—42no—
147Dic94#4112yes—
148C8×C47—21no—
149C8×C47—21no—
150C8×C47—21no—
151C8×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47C22×D411yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—22no—
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177#3326—471nomaximal, Sylow
178C2×C47—41no—
179C2×C47—41no—
180C2×C47#54611yescharacteristic
181C2×C47#57511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—81no—
184D47—81no—
185#553—471no—
186#548—471no—
187#488—471no—
188#483—471no—
189#482—471no—
190#479—471no—
191#469—471no—
192#468—471no—
193#463—471no—
194#449—471no—
195#448—471no—
196C4×SD16—471no—
197#436D4711yescharacteristic, complemented
198#419—471no—
199#417—471no—
200C47#332611yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C22×Q8—471no—
203C2×SD16—471no—
204C2×SD16—471no—
205C2×D8—471no—
206C2×M16C2×D4711yescharacteristic
207C2×M16C2×D4711yescharacteristic
208#126—941no—
209#125—471no—
210#124—471no—
211#124—941no—
212#123—941no—
213C22⋊Q8—471no—
214C22⋊Q8—941no—
215#121—471no—
216#121—471no—
217#121—471no—
218#121—941no—
219#121—941no—
220C4×Q8—471no—
221C4×D4—471no—
222C4×D4—941no—
223C4×D4—941no—
224C4×D4C2×D4711yescharacteristic
225#117—471no—
226C2×C4⋊C4—471no—
227#107—471no—
228#106—471no—
229#106—471no—
230C4⋊C8C2×D4711yescharacteristic
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241C22⋊C8C2×D4711yescharacteristic
242C22⋊C8C2×D4711yescharacteristic
243C4×C8C2×D4711yescharacteristic
244#41—942no—
245#41—1881no—
246C2×Q8—471no—
247C2×Q8—471no—
248C2×Q8—942no—
249C2×Q8—941no—
250C2×Q8—1881no—
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4D18811yescharacteristic
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264SD16—942no—
265SD16—1881no—
266D8—1881no—
267M16—41no—
268M16—41no—
269C2×C8C22×D4711yescharacteristic
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C2×C8C22×D4711yescharacteristic
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4D18811yescharacteristic
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4D18811yescharacteristic
292C22⋊C4D18811yescharacteristic
293C42—941no—
294C42—941no—
295C42C22×D4711yescharacteristic
296C23—941no—
297C23—941no—
298C23C2×D18811yescharacteristic
299C23C2×D18811yescharacteristic
300Q8—472no—
301Q8—941no—
302Q8—941no—
303Q8—941no—
304Q8—1882no—
305D4—41no—
306D4—941no—
307D4—941no—
308D4—941no—
309D4—941no—
310D4—3761no—
311D4—1882no—
312D4—1882no—
313D4—1882no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—3761no—
325C2×C4—3761no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4C2×D18811yescharacteristic
329C2×C4C2×D18811yescharacteristic
330C2×C4C2×D18811yescharacteristic
331C2×C4C2×D18811yescharacteristic
332C2×C4C23×D4711yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C22×D18811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—942no—
355C4—1881no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4#41×D4711yescharacteristic
361C4#1309406911yescharacteristic
362C2—41no—
363C2—41no—
364C2—3761no—
365C2—3761no—
366C2#1568976811yescharacteristic
367C2#1568992311yescharacteristic
368C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3326
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689782C2semidirect
3. #15689478C2semidirect
4. #15689454C2semidirect
5. #15689448C2semidirect
6. #15689431C2semidirect
7. #15689376C2semidirect
8. #15689369C2semidirect
9. #15689339C2semidirect
10. #15689270C2semidirect
11. #15689264C2semidirect
12. C4×#10625325C2semidirect
13. #15689133C2semidirect
14. #15689125C2semidirect
15. C47×#436C2semidirect
197. #436D47semidirect
200. C47#3326semidirect