Finite Group Databasebeta

← #20255700

Subgroups — #20255700

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#15689828C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689453C211yesmaximal, characteristic, complemented
5#15689452C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689380C211yesmaximal, characteristic, complemented
9#15689332C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689285C211yesmaximal, characteristic, complemented
12#15689214C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#417C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094014—21no—
24#13094007—21no—
25#13094005—21no—
26#13094004C2211yescharacteristic
27#13094003—21no—
28#13094003C2211yescharacteristic
29#13094003C2211yescharacteristic
30#13094002—21no—
31#13094000C2211yescharacteristic
32#13093996—21no—
33#13093989C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35C4×C22⋊D47—21no—
36C4×C22⋊D47C2211yescharacteristic
37C2×Dic47⋊C4—21no—
38C4⋊C4×D47C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71#10625352—22no—
72#10625352—41no—
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78M16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—41no—
89#10625335—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109Dic188—41no—
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116D4×C47—21no—
117D4×C47—42no—
118D4×C47#4112yes—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—42no—
125C2×C4×C47—81no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—22no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—81no—
142Dic94—21no—
143Dic94—21no—
144Dic94—21no—
145Dic94—21no—
146Dic94—81no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—22no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C4×C47—21no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47C2×#4111yescharacteristic
166C4×C47H(5,𝔽2)11yescharacteristic
167Dic47—21no—
168Dic47—21no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47#13712yes—
174#3331—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—42no—
177C2×C47#54611yescharacteristic
178C2×C47C2×#13711yescharacteristic
179C2×C47#57711yescharacteristic
180D47—41no—
181#554—471no—
182#547—471no—
183#487—471no—
184#483—471no—
185#483—471no—
186#476—471no—
187#470—471no—
188#470—471no—
189#462—471no—
190#452—471no—
191#452—471no—
192C4×SD16—471no—
193#436—471no—
194#417—471no—
195#417D4711yescharacteristic, complemented
196C47#333111yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C2×#41C2×D4711yescharacteristic
199C2×Q16—471no—
200C2×Q16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C2×M16C2×D4711yescharacteristic
204C4⋊Q8—471no—
205C4⋊Q8—471no—
206#125—941no—
207#123—941no—
208#123—941no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—471no—
212C22⋊Q8—471no—
213C22⋊Q8—941no—
214C22⋊Q8—941no—
215#121—941no—
216C4×Q8—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—941no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222C2×C4⋊C4C2×D4711yescharacteristic
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—
239C4×C8—471no—
240#41—22no—
241#41—41no—
242#41—942no—
243#41—1881no—
244C2×Q8—471no—
245C2×Q8—471no—
246C2×Q8—941no—
247C2×Q8C22×D4711yescharacteristic
248C2×D4—21no—
249C2×D4—471no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—471no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4C22×D4711yescharacteristic
259Q16—1881no—
260Q16—1881no—
261SD16—942no—
262M16—41no—
263M16—1881no—
264C2×C8—471no—
265C2×C8—471no—
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⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4C22×D4711yescharacteristic
282C4⋊C4C22×D4711yescharacteristic
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C42—471no—
291C42—941no—
292C23—21no—
293C23—471no—
294C23D4×D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—941no—
298Q8—941no—
299Q8—941no—
300Q8—941no—
301Q8—3761no—
302D4—21no—
303D4—42no—
304D4—942no—
305D4—1882no—
306D4#1062535012yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—3761no—
324C2×C4—1882no—
325C2×C4—1882no—
326C2×C4D4×D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—22no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22C2×D4×D4711yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—472no—
347C4—941no—
348C4—941no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4C2×#1062535011yescharacteristic
354C4#1309406911yescharacteristic
355C2—41no—
356C2—42no—
357C2—1881no—
358C2#1568976311yescharacteristic
359C2#137×D4711yescharacteristic
360C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3331
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #15689828C2semidirect
3. #15689472C2semidirect
4. #15689453C2semidirect
5. #15689452C2semidirect
6. #15689411C2semidirect
7. #15689381C2semidirect
8. #15689380C2semidirect
9. #15689332C2semidirect
10. #15689286C2semidirect
11. #15689285C2semidirect
12. #15689214C2semidirect
13. #15689199C2semidirect
14. #15689121C2semidirect
15. C47×#417C2semidirect
195. #417D47semidirect
196. C47#3331semidirect