Finite Group Databasebeta

← #20255697

Subgroups — #20255697

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#15689831C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689452C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689379C211yesmaximal, characteristic, complemented
8#15689378C211yesmaximal, characteristic, complemented
9#15689331C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11SD16×Dic47C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094014—21no—
23#13094007—21no—
24#13094005—21no—
25#13094004—21no—
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13094000C2211yescharacteristic
29#13094000C2211yescharacteristic
30#13093996—21no—
31Q8×Dic47C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35C2×C4⋊Dic47C2211yescharacteristic
36C2×Dic47⋊C4—21no—
37C4⋊C4×D47C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72#10625352—22no—
73#10625352—41no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78Q16×C47—41no—
79SD16×C47—22no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—41no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
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
107#10625329—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118D4×C47—21no—
119D4×C47—42no—
120D4×C47#4112yes—
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×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—22no—
130C22⋊D47—42no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137C2×Dic47—81no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—81no—
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#452D4711yescharacteristic, complemented
192C4×SD16—471no—
193#436—471no—
194#417—471no—
195#417—471no—
196C47#333111yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C2×#41C2×D4711yescharacteristic
199C2×Q16—471no—
200C2×Q16C2×D4711yescharacteristic
201C2×SD16C2×D4711yescharacteristic
202C2×M16—471no—
203C2×M16—471no—
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—941no—
213C22⋊Q8—941no—
214C22⋊Q8C2×D4711yescharacteristic
215#121—941no—
216C4×Q8—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—941no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—941no—
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#103—471no—
233#103C2×D4711yescharacteristic
234#102—471no—
235#102—471no—
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8C2×D4711yescharacteristic
239C4×C8—471no—
240#41—22no—
241#41—41no—
242#41—942no—
243#41—1881no—
244C2×Q8—471no—
245C2×Q8—941no—
246C2×Q8C22×D4711yescharacteristic
247C2×Q8C22×D4711yescharacteristic
248C2×D4—21no—
249C2×D4—471no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—471no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4C22×D4711yescharacteristic
259Q16—41no—
260Q16—1881no—
261SD16—22no—
262M16—1881no—
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—471no—
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⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—471no—
285C22⋊C4—471no—
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—21no—
298Q8—21no—
299Q8—941no—
300Q8—941no—
301Q8—3761no—
302D4—21no—
303D4—42no—
304D4—942no—
305D4—1882no—
306D4#1062535212yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—3761no—
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×#1062535211yescharacteristic
354C4#1309406911yescharacteristic
355C2—41no—
356C2—42no—
357C2—1881no—
358C2#1568976011yescharacteristic
359C2#137×D4711yescharacteristic
360C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3331
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #15689831C2semidirect
3. #15689472C2semidirect
4. #15689454C2semidirect
5. #15689452C2semidirect
6. #15689411C2semidirect
7. #15689379C2semidirect
8. #15689378C2semidirect
9. #15689331C2semidirect
10. #15689282C2semidirect
11. SD16×Dic47C2semidirect
12. #15689198C2semidirect
13. #15689124C2semidirect
14. #15689121C2semidirect
15. C47×#452C2semidirect
191. #452D47semidirect
196. C47#3331semidirect