Finite Group Databasebeta

← #20255394

Subgroups — #20255394

Order 6016.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic, complemented
2#15689487C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689434C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#15689119C211yesmaximal, characteristic, complemented
15C47×#550C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625334C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094019—21no—
22#13094016C2211yescharacteristic
23#13094006—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26#13093996—21no—
27C4×D188C2211yescharacteristic
28(C22⋊D47)⋊C4—21no—
29#13093983C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C2×#41×C47C2211yescharacteristic
50#127×C47—21no—
51#127×C47C2211yescharacteristic
52#121×C47—21no—
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47D411yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C22×Dic47—21no—
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47D411yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625336—22no—
93#10625334—41no—
94#10625334—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116Q8×C47—21no—
117Q8×C47#4112yes—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—41no—
123D4×C47—42no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—81no—
127D4×C47—81no—
128D4×C47—81no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—81no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—81no—
148D188—21no—
149D188—21no—
150C4×D47—81no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47C22×D411yescharacteristic
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—22no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47C2×#4111yescharacteristic
178C4×C47H(5,𝔽2)11yescharacteristic
179Dic47—41no—
180Dic47—41no—
181Dic47—41no—
182#3309—471nomaximal, Sylow
183C2×C47—41no—
184C2×C47—41no—
185C2×C47—81no—
186C2×C47—81no—
187C2×C47#54611yescharacteristic
188C2×C47#57511yescharacteristic
189C2×C47#57611yescharacteristic
190D47—81no—
191#553—471no—
192#550D4711yescharacteristic, complemented
193#490—471no—
194#482—471no—
195#480—471no—
196#479—471no—
197#469—471no—
198#466—471no—
199#459—471no—
200#449—471no—
201#449—471no—
202#440—471no—
203#435—471no—
204#417—471no—
205#416—471no—
206C47#330911yescharacteristic, complemented, Sylow
207C2×#41C2×D4711yescharacteristic
208C2×#41C2×D4711yescharacteristic
209C2×SD16—471no—
210C2×D8—471no—
211C2×D8—471no—
212C2×M16—471no—
213C22×C8—471no—
214#127—21no—
215#127C2×D4711yescharacteristic
216#126—941no—
217#125—471no—
218#123—941no—
219#121—21no—
220#121—21no—
221#121—471no—
222#121—471no—
223#121—941no—
224#121C2×D4711yescharacteristic
225#121C2×D4711yescharacteristic
226C4×Q8C2×D4711yescharacteristic
227C4×D4—21no—
228C4×D4—471no—
229C4×D4—941no—
230C4×D4C2×D4711yescharacteristic
231#117—471no—
232C2×C4⋊C4—471no—
233#107—471no—
234#107—471no—
235#106—471no—
236C4⋊C8—471no—
237#103—471no—
238#103—471no—
239#103—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247C22⋊C8—471no—
248C22⋊C8—471no—
249#97—471no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—471no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4C22⋊D4711yescharacteristic
265C2×D4C22×D4711yescharacteristic
266C2×D4C22×D4711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273SD16—942no—
274D8—1881no—
275D8—1881no—
276M16—1881no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—471no—
281C2×C8—1881no—
282C4⋊C4—21no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—471no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4C22⋊D4711yescharacteristic
290C4⋊C4C22×D4711yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4C22⋊D4711yescharacteristic
298C22⋊C4C22⋊D4711yescharacteristic
299C42—21no—
300C42—941no—
301C42C22×D4711yescharacteristic
302C23—21no—
303C23—21no—
304C23—941no—
305C23C2×C22⋊D4711yescharacteristic
306C23C2×C22⋊D4711yescharacteristic
307Q8—21no—
308Q8#1062535212yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—941no—
321D4—941no—
322D4—3761no—
323D4—1882no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—3761no—
336C2×C4—3761no—
337C2×C4C2×C22⋊D4711yescharacteristic
338C2×C4C2×C22⋊D4711yescharacteristic
339C2×C4C2×C22⋊D4711yescharacteristic
340C2×C4C2×C22⋊D4711yescharacteristic
341C2×C4C23×D4711yescharacteristic
342C8—941no—
343C8—941no—
344C8—941no—
345C8—941no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22C22×C22⋊D4711yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—1881no—
369C4—1881no—
370C4—1881no—
371C4C2×#1062535211yescharacteristic
372C4#1309406911yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—3761no—
378C2#1568976711yescharacteristic
379C2#1568992111yescharacteristic
380C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#550C2
socleC22×C47C22×D4
hypercenter#550D47
hypocenterC47#3309
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689487C2semidirect
3. #15689444C2semidirect
4. #15689434C2semidirect
5. #15689430C2semidirect
6. #15689374C2semidirect
7. #15689357C2semidirect
8. #15689315C2semidirect
9. #15689268C2semidirect
10. #15689268C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. #15689119C2semidirect
15. C47×#550C2semidirect
192. #550D47semidirect
206. C47#3309semidirect