Finite Group Databasebeta

← #20255125

Subgroups — #20255125

Order 6016.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094044C211yesmaximal, characteristic, complemented
2C22×#10625337C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4#15689505C211yesmaximal, characteristic, complemented
5#15689362C211yesmaximal, characteristic, complemented
6#15689357C211yesmaximal, characteristic, complemented
7#15689345C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689262C211yesmaximal, characteristic, complemented
12#15689261C211yesmaximal, characteristic, complemented
13C4×#10625337C211yesmaximal, characteristic, complemented
14D4×C47⋊C8C211yesmaximal, characteristic, complemented
15C47×#548C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18#13094044—24no—
19C2×#10625337—24no—
20C2×#10625337C2211yescharacteristic
21C2×#10625337C2211yescharacteristic
22C2×#10625337C2211yescharacteristic
23C2×#10625337C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C22×C47⋊C8C2211yescharacteristic
30C22×C47⋊C8C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094010—21no—
33#13094003C2211yescharacteristic
34#13094002—21no—
35#13093998C2211yescharacteristic
36#13093996—21no—
37C4×Dic94C2211yescharacteristic
38(C22⋊D47)⋊C4—21no—
39#13093957C2211yescharacteristic
40C4⋊(C47⋊C8)C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic
49C4×C47⋊C8C2211yescharacteristic
50C2×#41×C47C2211yescharacteristic
51C22×Q8×C47C2211yescharacteristic
52#124×C47—21no—
53#124×C47C2211yescharacteristic
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47C2211yescharacteristic
56#121×C47—21no—
57#121×C47C2211yescharacteristic
58C4×Q8×C47C2211yescharacteristic
59C4×D4×C47—21no—
60C4×D4×C47C2211yescharacteristic
61#41×C47—22no—
62#41×C47—41no—
63C2×Q8×C47—21no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47D411yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C22×Dic47—21no—
79#10625350—22no—
80#10625350—41no—
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×Dic94—22no—
84C2×Dic94—21no—
85C2×Dic94—41no—
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47D411yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47D411yescharacteristic
97C22⋊C4×C47D411yescharacteristic
98C42×C47—21no—
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101#10625337—22no—
102#10625337—22no—
103#10625337—22no—
104#10625337D414yescomplemented
105#10625336—22no—
106#10625336—41no—
107#10625335—22no—
108#10625335—41no—
109#10625334—22no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116C4×Dic47—21no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127Q8×C47—21no—
128Q8×C47—21no—
129Q8×C47—21no—
130Q8×C47—42no—
131Q8×C47C2×D412yes—
132D4×C47—22no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—42no—
136D4×C47—42no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2411yescharacteristic
151C22⋊D47—42no—
152C22⋊D47—42no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—42no—
157D188—21no—
158D188—21no—
159C4×D47—42no—
160Dic94—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—42no—
164Dic94C2×D412yes—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C47⋊C8—21no—
168C47⋊C8C2×D412yes—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47#13512yescomplemented
178C22×C47C22×D411yescharacteristic
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—22no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—22no—
192Dic47—41no—
193Dic47—41no—
194#3285—471nomaximal, Sylow
195C2×C47—22no—
196C2×C47—41no—
197C2×C47—81no—
198C2×C47D4211yescharacteristic
199C2×C47C2×#13511yescharacteristic
200C2×C47#57811yescharacteristic
201D47—81no—
202C2×#135—471no—
203C22×Q16—471no—
204#548—471no—
205#548D4711yescharacteristic, complemented
206#495—471no—
207#467—471no—
208#466—471no—
209#464—471no—
210#464—471no—
211#452—471no—
212#452—471no—
213#448—471no—
214#448—471no—
215C4×Q16—471no—
216C8×D4—471no—
217C47#328511yescharacteristic, complemented, Sylow
218C2×#41—471no—
219C2×#41C2×D4711yescharacteristic
220C22×Q8—471no—
221C22×Q8C2×D4711yescharacteristic
222#135—944no—
223C2×Q16—471no—
224C2×Q16—471no—
225C2×Q16—471no—
226C2×Q16—471no—
227C2×Q16—944no—
228C2×SD16—471no—
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×D8—471no—
233C22×C8—471no—
234C22×C8—471no—
235#124—21no—
236#124—471no—
237#124—941no—
238#124C2×D4711yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—471no—
241C22⋊Q8—941no—
242C22⋊Q8C2×D4711yescharacteristic
243#121—21no—
244#121—471no—
245#121—941no—
246#121C2×D4711yescharacteristic
247C4×Q8—471no—
248C4×Q8C2×D4711yescharacteristic
249C4×D4—21no—
250C4×D4—941no—
251C4×D4C2×D4711yescharacteristic
252#107—471no—
253C4⋊C8—471no—
254#103—471no—
255#103—471no—
256#103—471no—
257#103—471no—
258#102—471no—
259#102—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C4×C8—471no—
263#41—22no—
264#41—41no—
265#41—942no—
266#41—1881no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—471no—
271C2×Q8—471no—
272C2×Q8—942no—
273C2×Q8—941no—
274C2×Q8—1881no—
275C2×Q8C22×D4711yescharacteristic
276C2×Q8C22×D4711yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—471no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4C22⋊D4711yescharacteristic
283C2×D4C22×D4711yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290Q16—474no—
291Q16—942no—
292Q16—942no—
293Q16—942no—
294SD16—942no—
295SD16—942no—
296SD16—1881no—
297SD16—1881no—
298D8—942no—
299C2×C8—471no—
300C2×C8—471no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—942no—
304C2×C8—942no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—471no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C4⋊C4C22⋊D4711yescharacteristic
311C4⋊C4C22×D4711yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4C22⋊D4711yescharacteristic
321C22⋊C4C22⋊D4711yescharacteristic
322C42—21no—
323C42—941no—
324C42C22×D4711yescharacteristic
325C23—21no—
326C23—941no—
327C23C2×C22⋊D4711yescharacteristic
328C23C2×C22⋊D4711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—472no—
334Q8—941no—
335Q8—941no—
336Q8—941no—
337Q8—1882no—
338Q8D4×D4712yes—
339D4—22no—
340D4—21no—
341D4—21no—
342D4—42no—
343D4—42no—
344D4—941no—
345D4—941no—
346D4—1882no—
347D4—1882no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—1882no—
361C2×C4—1882no—
362C2×C4C2×C22⋊D4711yescharacteristic
363C2×C4C2×C22⋊D4711yescharacteristic
364C2×C4C2×C22⋊D4711yescharacteristic
365C2×C4C2×C22⋊D4711yescharacteristic
366C2×C4C23×D4711yescharacteristic
367C8—472no—
368C8—941no—
369C8—941no—
370C8—941no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22#1309404412yescomplemented
383C22C22×C22⋊D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—942no—
392C4—1881no—
393C4—1881no—
394C4C2×D4×D4711yescharacteristic
395C4#1309406911yescharacteristic
396C2—22no—
397C2—41no—
398C2—81no—
399C2—3761no—
400C2D4×C22⋊D4711yescharacteristic
401C2C2×#1309404411yescharacteristic
402C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#548C2
socleC22×C47C22×D4
hypercenter#548D47
hypocenterC47#3285
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13094044C2semidirect
2. C22×#10625337C2semidirect
3. #15689782C2semidirect
4. #15689505C2semidirect
5. #15689362C2semidirect
6. #15689357C2semidirect
7. #15689345C2semidirect
8. #15689342C2semidirect
9. #15689285C2semidirect
10. #15689283C2semidirect
11. #15689262C2semidirect
12. #15689261C2semidirect
13. C4×#10625337C2semidirect
14. D4×C47⋊C8C2semidirect
15. C47×#548C2semidirect
104. #10625337D4semidirect
177. C22×C47#135semidirect
205. #548D47semidirect
217. C47#3285semidirect
382. C22#13094044semidirect