Finite Group Databasebeta

← #20254707

Subgroups — #20254707

Order 6016.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689668C211yesmaximal, characteristic, complemented
2#15689654C211yesmaximal, characteristic, complemented
3#15689426C211yesmaximal, characteristic, complemented
4#15689425C211yesmaximal, characteristic, complemented
5#15689417C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689352C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689337C211yesmaximal, characteristic, complemented
11#15689336C211yesmaximal, characteristic, complemented
12#15689322C211yesmaximal, characteristic, complemented
13#15689316C211yesmaximal, characteristic, complemented
14C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
15C47×#466C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094017—21no—
24#13094015C2211yescharacteristic
25#13094011C2211yescharacteristic
26#13094010—21no—
27#13094005—21no—
28#13094003C2211yescharacteristic
29#13093998C2211yescharacteristic
30#13093996—21no—
31#13093989C2211yescharacteristic
32D4×Dic47—21no—
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic
36(C22⋊D47)⋊C4—21no—
37#13093980—21no—
38C2×C4×Dic47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093944C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47D411yescharacteristic
70C22×Dic47D411yescharacteristic
71#10625352—44no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×Dic94—21no—
75C2×Dic94C2311yescharacteristic
76D8×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89#10625335—41no—
90#10625334—41no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—41no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—42no—
118D4×C47—42no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—42no—
127C22⋊D47—42no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47—42no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188—21no—
141C4×D47—42no—
142Dic94—21no—
143Dic94—21no—
144Dic94—42no—
145C8×C47—21no—
146C8×C47—21no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47AGL(1,ℤ/8)12yes—
158C22×C47C22×D411yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47H(5,𝔽2)11yescharacteristic
166C4×C472−1+411yescharacteristic
167Dic47—21no—
168Dic47—21no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47#13512yes—
174#3247—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—81no—
177C2×C47—81no—
178C2×C47#53711yescharacteristic
179C2×C47C2×#13511yescharacteristic
180C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
181D47—81no—
182#532—471no—
183#529—471no—
184#478—471no—
185#478—471no—
186#477—471no—
187#476—471no—
188#466—471no—
189#466D4711yescharacteristic, complemented
190#465—471no—
191#465—471no—
192#463—471no—
193#463—471no—
194#460—471no—
195#459—471no—
196C2×C4⋊C8—471no—
197C47#324711yescharacteristic, complemented, Sylow
198C2×#41—941no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8C2×D4711yescharacteristic
203C22×C8—471no—
204C22×C8C2×D4711yescharacteristic
205C4⋊Q8—471no—
206#127—471no—
207#126—941no—
208#125—471no—
209#124—471no—
210#124—941no—
211#123—941no—
212C22⋊Q8—471no—
213#121—471no—
214#121—941no—
215#121C2×D4711yescharacteristic
216#121C2×D4711yescharacteristic
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221C4×D4—941no—
222C4×D4—941no—
223#117—941no—
224C2×C42—471no—
225#107—471no—
226#107C2×D4711yescharacteristic
227#106—471no—
228#106—471no—
229C4⋊C8—471no—
230C4⋊C8—471no—
231C4⋊C8—471no—
232C4⋊C8—471no—
233#103—471no—
234#103—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102C2×D4711yescharacteristic
240#102C2×D4711yescharacteristic
241#41—1884no—
242C2×Q8—471no—
243C2×Q8—941no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4C22×D4711yescharacteristic
251C2×D4C22×D4711yescharacteristic
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—1881no—
259SD16—1881no—
260D8—41no—
261D8—1881no—
262C2×C8—41no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—1881no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C42—471no—
288C42—471no—
289C42—471no—
290C42—941no—
291C23—21no—
292C23—21no—
293C23—941no—
294C23D4×D4711yescharacteristic
295Q8—941no—
296Q8—941no—
297Q8—1882no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—42no—
304D4—941no—
305D4—941no—
306D4—1882no—
307D4—1882no—
308D4—1882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—942no—
318C2×C4—942no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—1882no—
323C2×C4—1882no—
324C2×C4—1882no—
325C2×C4D4×D4711yescharacteristic
326C2×C4C23×D4711yescharacteristic
327C8—21no—
328C8—21no—
329C8—941no—
330C8—941no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22#1309404812yes—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—472no—
348C4—941no—
349C4—941no—
350C4—941no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4#1309406911yescharacteristic
355C4#1309407111yescharacteristic
356C2—22no—
357C2—81no—
358C2—81no—
359C2—3761no—
360C2#1568970011yescharacteristic
361C2#135×D4711yescharacteristic
362C2C2×#1309404811yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3247
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #15689668C2semidirect
2. #15689654C2semidirect
3. #15689426C2semidirect
4. #15689425C2semidirect
5. #15689417C2semidirect
6. #15689411C2semidirect
7. #15689357C2semidirect
8. #15689352C2semidirect
9. #15689350C2semidirect
10. #15689337C2semidirect
11. #15689336C2semidirect
12. #15689322C2semidirect
13. #15689316C2semidirect
14. C2×Dic47⋊C8C2semidirect
15. C47×#466C2semidirect
189. #466D47semidirect
197. C47#3247semidirect