Finite Group Databasebeta

← #20246423

Subgroups — #20246423

Order 6016.

688 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093996C211yesmaximal, characteristic
2C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
3C2×#13093980C211yesmaximal, characteristic, complemented
4#15689023C211yesmaximal, characteristic, complemented
5#15689023C211yesmaximal, characteristic, complemented
6#15689018C211yesmaximal, characteristic, complemented
7#15689013C211yesmaximal, characteristic, complemented
8#15689011C211yesmaximal, characteristic, complemented
9#15689003C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C47×#390C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13093996C418yescomplemented
22(C22⋊D47)⋊C4—24no—
23#13093980—24no—
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C22×D4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C42×C47C2211yescharacteristic
54C24×C47C2311yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C2×D4×C47—41no—
58C2×D4×C47—41no—
59C2×D4×C47C2×C414yescomplemented
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—22no—
66C2×C22⋊D47—22no—
67C2×C22⋊D47—41no—
68C2×C22⋊D47—41no—
69C2×C22⋊D47C2×C414yes—
70C2×C22⋊D47C2×C414yescomplemented
71C22×Dic47—22no—
72C22×Dic47—22no—
73C22×Dic47—22no—
74C22×Dic47—22no—
75C22×Dic47—41no—
76C22×Dic47C2×C414yescomplemented
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C2×C4×D47—22no—
85C2×C4×D47—22no—
86C2×C4×D47—41no—
87C4⋊C4×C47—41no—
88C22⋊C4×C47—22no—
89C22⋊C4×C47—22no—
90C22⋊C4×C47—22no—
91C22⋊C4×C47—22no—
92C42×C47—41no—
93C22⋊Dic47—22no—
94C22⋊Dic47—22no—
95C22⋊Dic47—41no—
96C22⋊Dic47C2×C414yescomplemented
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—41no—
100(C2×D47)⋊C4C2×C414yescomplemented
101Dic47⋊C4—22no—
102Dic47⋊C4—41no—
103Dic47⋊C4C2×C414yescomplemented
104Dic47⋊C4D414yescomplemented
105C4×Dic47—22no—
106C4×Dic47—22no—
107C4×Dic47—22no—
108C4×Dic47—22no—
109C4×Dic47—41no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47C22×C412yes—
123C23×C47C22×C412yes—
124C23×C47C2411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47C22×C412yes—
132D4×C47—44no—
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—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47C22×C412yes—
146C2×C4×C47C2×D412yes—
147C2×C4×C47#4112yes—
148C22⋊D47—28no—
149C22⋊D47—44no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—28no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—44no—
166C2×Dic47C22×C412yes—
167C2×Dic47C22×C412yes—
168C2×Dic47C22×C412yes—
169C2×Dic47C2×D412yes—
170C2×Dic47C2×D412yes—
171C2×Dic47#4112yes—
172C2×Dic47#4112yes—
173C4×D47—44no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47C23×C411yescharacteristic
189C22×C47C22×D411yescharacteristic
190C22×C47C2×#4111yescharacteristic
191C22×C47C2×#4111yescharacteristic
192C22×C47C2×#4111yescharacteristic
193C22×C47H(5,𝔽2)11yescharacteristic
194C22×C47H(5,𝔽2)11yescharacteristic
195C2×D47—22no—
196C2×D47—22no—
197C2×D47—22no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C4×C47—22no—
203C4×C47—22no—
204C4×C47—22no—
205C4×C47—41no—
206C4×C47—41no—
207Dic47—22no—
208Dic47—22no—
209Dic47—22no—
210Dic47—22no—
211Dic47—41no—
212Dic47—41no—
213Dic47C4×D414yes—
214#2363—471nomaximal, Sylow
215C2×C47—42no—
216C2×C47—42no—
217C2×C47C2×C4×D411yescharacteristic
218C2×C47C4×#4111yescharacteristic
219C2×C47#51811yescharacteristic
220C2×C47#54611yescharacteristic
221C2×C47#55011yescharacteristic
222C2×C47#55311yescharacteristic
223C2×C47#55511yescharacteristic
224D47—42no—
225C2×#121—471no—
226C2×C4×D4—471no—
227C2×#117—471no—
228#390—471no—
229#390—471no—
230#390D4711yescharacteristic, complemented
231#389—471no—
232#388—471no—
233#388—471no—
234#386—471no—
235#386—471no—
236C4×C4⋊C4—471no—
237C4×C22⋊C4—471no—
238C4×C22⋊C4—471no—
239C4×C22⋊C4—471no—
240C47#236311yescharacteristic, complemented, Sylow
241C22×D4—471no—
242C22×D4—471no—
243C22×D4C2×D4711yescharacteristic
244C23×C4—471no—
245C23×C4—471no—
246C23×C4—471no—
247#121—478no—
248C4×D4—944no—
249#117—944no—
250C2×C4⋊C4—471no—
251C2×C4⋊C4—471no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4C2×D4711yescharacteristic
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—471no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4C2×D4711yescharacteristic
264C2×C22⋊C4C2×D4711yescharacteristic
265C2×C22⋊C4C2×D4711yescharacteristic
266C2×C22⋊C4C2×D4711yescharacteristic
267C2×C42—471no—
268C2×C42—471no—
269C2×C42—471no—
270C2×C42—471no—
271C2×C42—471no—
272C2×C42C2×D4711yescharacteristic
273#95—471no—
274#95—471no—
275#95—471no—
276#95—471no—
277#95—471no—
278#95—471no—
279C24—471no—
280C24C22×D4711yescharacteristic
281C24C22×D4711yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—474no—
285C2×D4—474no—
286C2×D4—942no—
287C2×D4—942no—
288C2×D4—1881no—
289C2×D4—1881no—
290C2×D4C4×D4714yescomplemented
291C22×C4—471no—
292C22×C4—474no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—942no—
300C22×C4—942no—
301C22×C4—942no—
302C22×C4—942no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4—1881no—
306C22×C4—1881no—
307C22×C4C22×D4711yescharacteristic
308C22×C4C22×D4711yescharacteristic
309C22×C4C22×D4711yescharacteristic
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—474no—
314C4⋊C4—474no—
315C4⋊C4—942no—
316C4⋊C4—1881no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—474no—
322C22⋊C4—474no—
323C22⋊C4—942no—
324C22⋊C4—942no—
325C22⋊C4—942no—
326C22⋊C4—942no—
327C22⋊C4—1881no—
328C22⋊C4—1881no—
329C42—41no—
330C42—942no—
331C42—942no—
332C42—942no—
333C42—942no—
334C42—1881no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—472no—
348C23—941no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23C2×C4×D4712yes—
355C23C2×C4×D4712yes—
356C23C23×D4711yescharacteristic
357D4—44no—
358D4—948no—
359D4—1884no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—472no—
373C2×C4—472no—
374C2×C4—472no—
375C2×C4—472no—
376C2×C4—472no—
377C2×C4—472no—
378C2×C4—472no—
379C2×C4—948no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—1884no—
395C2×C4—1884no—
396C2×C4C2×C4×D4712yes—
397C2×C4D4×D4712yes—
398C2×C4#1062535212yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—942no—
414C22—942no—
415C22—942no—
416C22—1881no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22C22×C4×D4711yescharacteristic
421C22C2×D4×D4711yescharacteristic
422C22#41×D4711yescharacteristic
423C22#41×D4711yescharacteristic
424C22C2×#1062535211yescharacteristic
425C22#1309406911yescharacteristic
426C22#1309406911yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—474no—
433C4—942no—
434C4—942no—
435C4—942no—
436C4—942no—
437C4—1881no—
438C4—1881no—
439C2—42no—
440C2—42no—
441C2—1882no—
442C2C4×D4×D4711yescharacteristic
443C2C4×#1062535211yescharacteristic
444C2#1568959611yescharacteristic
445C2#1568976211yescharacteristic
446C2#1568979311yescharacteristic
447C2#1568981611yescharacteristic
448C2#1568983511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#390C2
socleC23×C47C24
hypercenter#390D47
hypocenterC47#2363
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D47)⋊C4C2semidirect
3. C2×#13093980C2semidirect
4. #15689023C2semidirect
5. #15689023C2semidirect
6. #15689018C2semidirect
7. #15689013C2semidirect
8. #15689011C2semidirect
9. #15689003C2semidirect
10. #15688999C2semidirect
11. C4×Dic47⋊C4C2semidirect
12. C22⋊C4×Dic47C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C47×#390C2semidirect
21. #13093996C4semidirect
59. C2×D4×C47C2×C4semidirect
70. C2×C22⋊D47C2×C4semidirect
76. C22×Dic47C2×C4semidirect
96. C22⋊Dic47C2×C4semidirect
100. (C2×D47)⋊C4C2×C4semidirect
103. Dic47⋊C4C2×C4semidirect
104. Dic47⋊C4D4semidirect
230. #390D47semidirect
240. C47#2363semidirect
290. C2×D4C4×D47semidirect