Finite Group Databasebeta

← #20254285

Subgroups — #20254285

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689701C211yesmaximal, characteristic, complemented
2#15689458C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689436C211yesmaximal, characteristic, complemented
5#15689434C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689362C211yesmaximal, characteristic, complemented
9#15689357C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689283C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689266C211yesmaximal, characteristic, complemented
14#15689090C211yesmaximal, characteristic, complemented
15C47×#537C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25#13094000—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093996—21no—
29#13093996—21no—
30#13093995—21no—
31C2×C4⋊Dic47C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093957C2211yescharacteristic
35#13093957C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C2×#41×C47C2211yescharacteristic
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47—21no—
54#121×C47—21no—
55#121×C47—21no—
56#121×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—41no—
60#41×C47—41no—
61#41×C47—41no—
62#41×C47—41no—
63C2×Q8×C47D411yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47D411yescharacteristic
70C2×D4×C47D411yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C22×Dic47—21no—
81#10625350—41no—
82#10625350—41no—
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×Dic94C2311yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625337—41no—
98#10625336—41no—
99#10625335—41no—
100#10625334—41no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108#10625329—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C23×C47C2×D411yescharacteristic
117C23×C47C2×D411yescharacteristic
118C22×D47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47—41no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—41no—
125D4×C47—41no—
126D4×C47—41no—
127D4×C47—42no—
128D4×C47—81no—
129D4×C47—81no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—42no—
140C2×C4×C47—81no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2411yescharacteristic
145C22⋊D47—42no—
146C22⋊D47—81no—
147C22⋊D47—81no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—81no—
152D188—21no—
153D188—21no—
154C4×D47—42no—
155Dic94—21no—
156Dic94—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47C22×D411yescharacteristic
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47H(5,𝔽2)11yescharacteristic
184C4×C47H(5,𝔽2)11yescharacteristic
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188#3203—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47—41no—
191C2×C47—41no—
192C2×C47—81no—
193C2×C47#53411yescharacteristic
194C2×C47#57611yescharacteristic
195C2×C47#57811yescharacteristic
196D47—81no—
197#537—471no—
198#537D4711yescharacteristic, complemented
199#484—471no—
200#484—471no—
201#480—471no—
202#480—471no—
203#468—471no—
204#468—471no—
205#467—471no—
206#466—471no—
207#452—471no—
208#452—471no—
209#449—471no—
210#449—471no—
211#408—471no—
212C47#320311yescharacteristic, complemented, Sylow
213C2×#41—471no—
214C2×#41C2×D4711yescharacteristic
215C2×#41C2×D4711yescharacteristic
216C2×Q16—471no—
217C2×SD16—471no—
218C2×SD16—471no—
219C2×D8—471no—
220C2×M16—471no—
221C22×C8—471no—
222C22⋊Q8—21no—
223C22⋊Q8—471no—
224C22⋊Q8—471no—
225C22⋊Q8—941no—
226C22⋊Q8C2×D4711yescharacteristic
227C22⋊Q8C2×D4711yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—471no—
232#121—471no—
233#121—941no—
234#121—941no—
235#121—941no—
236#121C2×D4711yescharacteristic
237#121C2×D4711yescharacteristic
238C2×C4⋊C4—471no—
239C2×C4⋊C4C2×D4711yescharacteristic
240#107—471no—
241#107—471no—
242#107—471no—
243#107—471no—
244#103—471no—
245#103—471no—
246#103—471no—
247#103—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252C22⋊C8—471no—
253C22⋊C8—471no—
254C22⋊C8—471no—
255C22⋊C8—471no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—1881no—
261#41—1881no—
262C2×Q8—471no—
263C2×Q8C22⋊D4711yescharacteristic
264C2×Q8C22×D4711yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—471no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4C22⋊D4711yescharacteristic
273C2×D4C22⋊D4711yescharacteristic
274C2×D4C22⋊D4711yescharacteristic
275C2×D4C22×D4711yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282C22×C4C22×D4711yescharacteristic
283Q16—1881no—
284SD16—1881no—
285SD16—1881no—
286D8—1881no—
287M16—1881no—
288C2×C8—471no—
289C2×C8—471no—
290C2×C8—471no—
291C2×C8—471no—
292C2×C8—1881no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—941no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4C22×D4711yescharacteristic
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C23—21no—
312C23—941no—
313C23C2×C22⋊D4711yescharacteristic
314C23C2×C22⋊D4711yescharacteristic
315C23C2×C22⋊D4711yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—941no—
320Q8—941no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—941no—
330D4—941no—
331D4—3761no—
332D4—3761no—
333D4—1882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—3761no—
349C2×C4—1882no—
350C2×C4C2×C22⋊D4711yescharacteristic
351C2×C4C2×C22⋊D4711yescharacteristic
352C2×C4C2×C22⋊D4711yescharacteristic
353C2×C4C23×D4711yescharacteristic
354C8—941no—
355C8—941no—
356C8—941no—
357C8—941no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C22×C22⋊D4711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1881no—
381C4—1881no—
382C4—1881no—
383C4#1309406911yescharacteristic
384C4#1309406911yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—3761no—
390C2#1568968211yescharacteristic
391C2#1568992611yescharacteristic
392C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#537C2
socleC22×C47C22×D4
hypercenter#537D47
hypocenterC47#3203
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #15689701C2semidirect
2. #15689458C2semidirect
3. #15689456C2semidirect
4. #15689436C2semidirect
5. #15689434C2semidirect
6. #15689371C2semidirect
7. #15689367C2semidirect
8. #15689362C2semidirect
9. #15689357C2semidirect
10. #15689285C2semidirect
11. #15689283C2semidirect
12. #15689268C2semidirect
13. #15689266C2semidirect
14. #15689090C2semidirect
15. C47×#537C2semidirect
198. #537D47semidirect
212. C47#3203semidirect