Finite Group Databasebeta

← #20248325

Subgroups — #20248325

Order 6016.

760 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic, complemented
2C2×#13094002C211yesmaximal, characteristic, complemented
3C2×#13094001C211yesmaximal, characteristic, complemented
4C2×#13093997C211yesmaximal, characteristic, complemented
5C2×#13093996C211yesmaximal, characteristic, complemented
6C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
7#15689059C211yesmaximal, characteristic, complemented
8#15689058C211yesmaximal, characteristic, complemented
9#15689032C211yesmaximal, characteristic, complemented
10#15689031C211yesmaximal, characteristic, complemented
11#15689025C211yesmaximal, characteristic, complemented
12#15689023C211yesmaximal, characteristic, complemented
13#15689023C211yesmaximal, characteristic, complemented
14C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C47×#390C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C23×Dic47C2211yescharacteristic
23C22×C4×D47C2211yescharacteristic
24#13094010—24no—
25#13094002—24no—
26#13094001—24no—
27#13093997—24no—
28#13093996—24no—
29(C22⋊D47)⋊C4—24no—
30C2×C4⋊Dic47C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C2×(C2×D47)⋊C4C2211yescharacteristic
45C2×(C2×D47)⋊C4C2211yescharacteristic
46C2×C4×Dic47C2211yescharacteristic
47C2×C4×Dic47C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C47⋊#95C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic
56C2×C42×C47C2211yescharacteristic
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C23×D47C2311yescharacteristic
60C23×D47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—41no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—41no—
80C2×C22⋊D47—41no—
81C22×Dic47—22no—
82C22×Dic47—22no—
83C22×Dic47—22no—
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C2×D188—22no—
91C2×D188—22no—
92C2×D188—41no—
93C2×C4×D47—22no—
94C2×C4×D47—22no—
95C2×C4×D47—22no—
96C2×Dic94—22no—
97C2×Dic94—22no—
98C2×Dic94—22no—
99C4⋊C4×C47—22no—
100C22⋊C4×C47—22no—
101C22⋊C4×C47—22no—
102C22⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C42×C47—41no—
105C22⋊Dic47—22no—
106C22⋊Dic47—22no—
107C22⋊Dic47—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115C4⋊Dic47—22no—
116Dic47⋊C4—22no—
117Dic47⋊C4—22no—
118Dic47⋊C4—22no—
119Dic47⋊C4D414yescomplemented
120Dic47⋊C4D414yescomplemented
121C4×Dic47—41no—
122C4×Dic47D414yescomplemented
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47#4112yes—
137C23×C47C2411yescharacteristic
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47#4112yes—
152D4×C47—44no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47C2×D412yes—
166C2×C4×C47C2×D412yes—
167C2×C4×C47C2×D412yes—
168C22⋊D47—28no—
169C22⋊D47—44no—
170C22⋊D47—44no—
171C22⋊D47—44no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—44no—
185C2×Dic47C2×D412yes—
186C2×Dic47C2×D412yes—
187C2×Dic47C2×D412yes—
188C2×Dic47C2×D412yes—
189C2×Dic47C2×D412yes—
190C2×Dic47C2×D412yes—
191D188—44no—
192C4×D47—44no—
193Dic94—44no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47C22×D411yescharacteristic
209C22×C47C22×D411yescharacteristic
210C22×C47C22×D411yescharacteristic
211C22×C47C2×#4111yescharacteristic
212C22×C47C2×#4111yescharacteristic
213C22×C47H(5,𝔽2)11yescharacteristic
214C22×C472−1+411yescharacteristic
215C2×D47—22no—
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C4×C47—22no—
230C4×C47—22no—
231C4×C47—22no—
232C4×C47—41no—
233C4×C47—41no—
234Dic47—22no—
235Dic47—22no—
236Dic47—22no—
237Dic47—41no—
238Dic47—41no—
239Dic47#12714yes—
240#2540—471nomaximal, Sylow
241C2×C47—42no—
242C2×C47—81no—
243C2×C47#52511yescharacteristic
244C2×C47C2×#12711yescharacteristic
245C2×C47#53711yescharacteristic
246C2×C47#54611yescharacteristic
247C2×C47#54611yescharacteristic
248C2×C47#54811yescharacteristic
249C2×C47#54811yescharacteristic
250D47—42no—
251D47—81no—
252C2×#124—471no—
253C2×C22⋊Q8—471no—
254C2×C22⋊Q8—471no—
255C2×#121—471no—
256C2×#121—471no—
257C2×C4×D4—471no—
258#399—471no—
259#399—471no—
260#392—471no—
261#392—471no—
262#390—471no—
263#390—471no—
264#390—471no—
265#390D4711yescharacteristic, complemented
266C4×C4⋊C4—471no—
267C47#254011yescharacteristic, complemented, Sylow
268C22×Q8—471no—
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—471no—
272C22×D4—471no—
273C22×D4—471no—
274C22×D4C2×D4711yescharacteristic
275C23×C4—471no—
276C23×C4—471no—
277#124—944no—
278C22⋊Q8—944no—
279C22⋊Q8—944no—
280#121—944no—
281#121—944no—
282C4×D4—944no—
283C2×C4⋊C4—471no—
284C2×C4⋊C4—471no—
285C2×C4⋊C4—471no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4—471no—
289C2×C4⋊C4C2×D4711yescharacteristic
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—471no—
294C2×C22⋊C4—471no—
295C2×C22⋊C4—471no—
296C2×C22⋊C4—471no—
297C2×C22⋊C4—471no—
298C2×C22⋊C4—471no—
299C2×C22⋊C4—471no—
300C2×C22⋊C4C2×D4711yescharacteristic
301C2×C22⋊C4C2×D4711yescharacteristic
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C42—471no—
305C2×C42—471no—
306C2×C42C2×D4711yescharacteristic
307#95—471no—
308#95—471no—
309C24—471no—
310C24—471no—
311C24C22×D4711yescharacteristic
312C24C22×D4711yescharacteristic
313C2×Q8—942no—
314C2×Q8—942no—
315C2×Q8—942no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—942no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—942no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—1881no—
332C2×D4—1881no—
333C2×D4—1881no—
334C22×C4—471no—
335C22×C4—471no—
336C22×C4—471no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—942no—
341C22×C4—942no—
342C22×C4—942no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4C22×D4711yescharacteristic
347C22×C4C22×D4711yescharacteristic
348C22×C4C22×D4711yescharacteristic
349C22×C4C22×D4711yescharacteristic
350C22×C4C22×D4711yescharacteristic
351C4⋊C4—22no—
352C4⋊C4—474no—
353C4⋊C4—474no—
354C4⋊C4—942no—
355C4⋊C4—942no—
356C4⋊C4—942no—
357C4⋊C4—942no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—942no—
363C22⋊C4—942no—
364C22⋊C4—942no—
365C22⋊C4—942no—
366C22⋊C4—942no—
367C22⋊C4—942no—
368C22⋊C4—942no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C42—41no—
373C42—474no—
374C42—1881no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—472no—
389C23—941no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23—941no—
402C23#1062535012yes—
403C23C23×D4711yescharacteristic
404Q8—1884no—
405D4—44no—
406D4—948no—
407D4—1884no—
408D4—1884no—
409D4—1884no—
410D4—1884no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—472no—
424C2×C4—472no—
425C2×C4—472no—
426C2×C4—472no—
427C2×C4—472no—
428C2×C4—472no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—1884no—
442C2×C4—1884no—
443C2×C4D4×D4712yes—
444C2×C4D4×D4712yes—
445C2×C4D4×D4712yes—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—942no—
461C22—942no—
462C22—942no—
463C22—1881no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22—1881no—
474C22C2×D4×D4711yescharacteristic
475C22C2×D4×D4711yescharacteristic
476C22C2×D4×D4711yescharacteristic
477C22#41×D4711yescharacteristic
478C22C2×#1062535011yescharacteristic
479C22#1309406911yescharacteristic
480C22#1309407111yescharacteristic
481C4—22no—
482C4—22no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—474no—
487C4—942no—
488C4—942no—
489C4—942no—
490C4—1881no—
491C4—1881no—
492C2—42no—
493C2—81no—
494C2—3761no—
495C2—1882no—
496C2#1568963211yescharacteristic
497C2#127×D4711yescharacteristic
498C2#1568970011yescharacteristic
499C2#1568976211yescharacteristic
500C2#1568976311yescharacteristic
501C2#1568978111yescharacteristic
502C2#1568978211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2540
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. C2×#13094002C2semidirect
3. C2×#13094001C2semidirect
4. C2×#13093997C2semidirect
5. C2×#13093996C2semidirect
6. C2×(C22⋊D47)⋊C4C2semidirect
7. #15689059C2semidirect
8. #15689058C2semidirect
9. #15689032C2semidirect
10. #15689031C2semidirect
11. #15689025C2semidirect
12. #15689023C2semidirect
13. #15689023C2semidirect
14. C4×Dic47⋊C4C2semidirect
15. C47×#390C2semidirect
119. Dic47⋊C4D4semidirect
120. Dic47⋊C4D4semidirect
122. C4×Dic47D4semidirect
265. #390D47semidirect
267. C47#2540semidirect