Finite Group Databasebeta

← #20255249

Subgroups — #20255249

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D47C211yesmaximal, characteristic, complemented
2#15689774C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689453C211yesmaximal, characteristic, complemented
5#15689452C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689355C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689327C211yesmaximal, characteristic, complemented
10#15689263C211yesmaximal, characteristic, complemented
11#15689262C211yesmaximal, characteristic, complemented
12#15689208C211yesmaximal, characteristic, complemented
13C8×C22⋊D47C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C2×#103×C47C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×Q8×D47C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094022—21no—
24#13094022C2211yescharacteristic
25#13094009—21no—
26#13094007—21no—
27#13094003—21no—
28#13094003C2211yescharacteristic
29#13094002—21no—
30#13094000—21no—
31#13094000C2211yescharacteristic
32#13093999C2211yescharacteristic
33#13093998C2211yescharacteristic
34Q8×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic
36C4×C22⋊D47—21no—
37C4×C22⋊D47C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69Q8×D47—22no—
70Q8×D47—41no—
71#10625350—44no—
72C2×D188—21no—
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×Dic94—21no—
79C2×Dic94—21no—
80C2×Dic94C2311yescharacteristic
81C2×C8×C47—41no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47—21no—
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47D411yescharacteristic
89#10625336—22no—
90#10625336—41no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325—41no—
111C8×D47—41no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47C2×D411yescharacteristic
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—42no—
119Q8×C47#4112yescomplemented
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47SD1614yescomplemented
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—21no—
139D188—21no—
140D188—42no—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—42no—
144C4×D47—42no—
145C4×D47—42no—
146Dic94—21no—
147Dic94—21no—
148Dic94—42no—
149Dic94—42no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47C2×SD1612yes—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47C2×SD1612yes—
164C4×C47—22no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—21no—
172Dic47—21no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47C2×SD1612yes—
177#3298—471nomaximal, Sylow
178C2×C47—22no—
179C2×C47#54611yescharacteristic
180C2×C47C22×SD1611yescharacteristic
181C2×C47#57811yescharacteristic
182D47—22no—
183D47—81no—
184D4×Q8—471no—
185#547—471no—
186#487—471no—
187#483—471no—
188#483—471no—
189#475—471no—
190#465—471no—
191#465—471no—
192#461—471no—
193#448—471no—
194#448—471no—
195C4×SD16—471no—
196C8×D4—471no—
197C2×#103—471no—
198C2×#103D4711yescharacteristic, complemented
199C47#329811yescharacteristic, complemented, Sylow
200C2×#41—941no—
201C22×Q8—471no—
202C22×Q8C2×D4711yescharacteristic
203C2×SD16—471no—
204C2×SD16—471no—
205C2×SD16—471no—
206C22×C8—471no—
207C22×C8C2×D4711yescharacteristic
208C4⋊Q8—471no—
209C4⋊Q8—471no—
210C4⋊Q8—941no—
211#123—941no—
212#123—941no—
213C22⋊Q8—471no—
214C22⋊Q8—471no—
215C22⋊Q8—941no—
216C22⋊Q8—941no—
217C22⋊Q8—941no—
218#121—471no—
219#121—471no—
220C4×Q8—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—941no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4C2×D4711yescharacteristic
226#106—471no—
227#106—471no—
228#106—471no—
229C4⋊C8—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103C2×D4711yescharacteristic
236#103C2×D4711yescharacteristic
237#103C2×D4711yescharacteristic
238#103C2×D4711yescharacteristic
239#102—471no—
240C22⋊C8—471no—
241C22⋊C8—471no—
242C4×C8—471no—
243#41—1884no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—471no—
248C2×Q8—941no—
249C2×Q8—941no—
250C2×Q8—942no—
251C2×Q8—1881no—
252C2×Q8C22×D4711yescharacteristic
253C2×Q8C22×D4711yescharacteristic
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—941no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—471no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4C22×D4711yescharacteristic
265SD16—942no—
266SD16—1881no—
267SD16—1881no—
268C2×C8—41no—
269C2×C8—471no—
270C2×C8—471no—
271C2×C8—1881no—
272C2×C8C22×D4711yescharacteristic
273C2×C8C22×D4711yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—471no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4C22×D4711yescharacteristic
286C4⋊C4C22×D4711yescharacteristic
287C22⋊C4—471no—
288C22⋊C4—471no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—471no—
295C42—941no—
296C23—471no—
297C23—941no—
298C23D4×D4711yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—941no—
304Q8—941no—
305Q8—1882no—
306Q8—1882no—
307Q8#1062535012yescomplemented
308D4—474no—
309D4—941no—
310D4—941no—
311D4—1882no—
312D4—1882no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—471no—
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×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—21no—
340C22—472no—
341C22—941no—
342C22—941no—
343C22—1881no—
344C22—1881no—
345C22—1881no—
346C22SD16×D4712yes—
347C22C2×D4×D4711yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—472no—
354C4—941no—
355C4—941no—
356C4—1881no—
357C4—1881no—
358C4—1881no—
359C4C2×#1062535011yescharacteristic
360C4#1309406911yescharacteristic
361C2—22no—
362C2—942no—
363C2—3761no—
364C2#1568976311yescharacteristic
365C2C2×SD16×D4711yescharacteristic
366C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC22×C47C22×D4
hypercenterC2×#103D47
hypocenterC47#3298
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D47C2semidirect
3. #15689472C2semidirect
4. #15689453C2semidirect
5. #15689452C2semidirect
6. #15689406C2semidirect
7. #15689355C2semidirect
8. #15689352C2semidirect
9. #15689327C2semidirect
10. #15689263C2semidirect
11. #15689262C2semidirect
12. #15689208C2semidirect
13. C8×C22⋊D47C2semidirect
14. #103×D47C2semidirect
15. C2×#103×C47C2semidirect
119. Q8×C47#41semidirect
131. C22⋊D47SD16semidirect
198. C2×#103D47semidirect
199. C47#3298semidirect
307. Q8#10625350semidirect