Finite Group Databasebeta

← #20241631

Subgroups — #20241631

Order 6016.

780 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
2C22×C22⋊Dic47C211yesmaximal, characteristic
3C22×C22⋊Dic47C211yesmaximal, characteristic
4C2×C47⋊#95C211yesmaximal, characteristic, complemented
5C2×C47⋊#95C211yesmaximal, characteristic, complemented
6C2×C47⋊#95C211yesmaximal, characteristic, complemented
7C22×C22⋊C4×C47C211yesmaximal, characteristic
8C23×Dic47C2211yescharacteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×Dic47⋊C4—22no—
13C2×Dic47⋊C4—22no—
14C2×Dic47⋊C4—22no—
15C2×C22⋊Dic47—22no—
16C2×C22⋊Dic47—22no—
17C2×C22⋊Dic47—22no—
18C2×C22⋊Dic47—22no—
19C2×C22⋊Dic47—22no—
20C2×C22⋊Dic47C414yescomplemented
21C47⋊#95—22no—
22C47⋊#95—22no—
23C47⋊#95—22no—
24C25×C47C2211yescharacteristic
25C23×C4×C47C2211yescharacteristic
26C23×C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47—22no—
28C2×C22⋊C4×C47—22no—
29C2×C22⋊C4×C47—22no—
30C24×C47—21no—
31C24×C47—21no—
32C24×C47—21no—
33C24×C47—21no—
34C24×C47—21no—
35C24×C47—21no—
36C24×C47—21no—
37C24×C47—21no—
38C24×C47—21no—
39C24×C47—21no—
40C24×C47—21no—
41C24×C47—21no—
42C24×C47C2×C412yes—
43C24×C47D412yes—
44C24×C47Q812yes—
45C24×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47—21no—
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47D412yes—
59C22×C4×C47D412yes—
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82C22×Dic47C2×C412yes—
83C22×Dic47C2×C412yes—
84C22×Dic47D412yes—
85C22×Dic47D412yes—
86C22×Dic47D412yes—
87C22×Dic47D412yes—
88C22⋊C4×C47—28no—
89C22⋊Dic47—28no—
90C22⋊Dic47—28no—
91Dic47⋊C4—28no—
92C23×C47—22no—
93C23×C47—22no—
94C23×C47—22no—
95C23×C47—22no—
96C23×C47—22no—
97C23×C47—22no—
98C23×C47—22no—
99C23×C47—22no—
100C23×C47—22no—
101C23×C47—22no—
102C23×C47—22no—
103C23×C47—22no—
104C23×C47—22no—
105C23×C47—22no—
106C23×C47—22no—
107C23×C47—22no—
108C23×C47—22no—
109C23×C47—22no—
110C23×C47—41no—
111C23×C47—41no—
112C23×C47—41no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47—41no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47—41no—
126C23×C47C4⋊C414yescomplemented
127C23×C47C22×C411yescharacteristic
128C23×C47C2×D411yescharacteristic
129C23×C47C2×D411yescharacteristic
130C23×C47C2×D411yescharacteristic
131C23×C47C2×D411yescharacteristic
132C23×C47C2×D411yescharacteristic
133C23×C47C2×D411yescharacteristic
134C23×C47C2×D411yescharacteristic
135C23×C47C2×Q811yescharacteristic
136C23×C47#4111yescharacteristic
137C23×C47#4111yescharacteristic
138C23×C47#4111yescharacteristic
139C23×C47#4111yescharacteristic
140C23×C47#4111yescharacteristic
141C23×C47#4111yescharacteristic
142C2×C4×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—22no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×Dic47—22no—
157C2×Dic47—22no—
158C2×Dic47—22no—
159C2×Dic47—22no—
160C2×Dic47—22no—
161C2×Dic47—22no—
162C2×Dic47—22no—
163C2×Dic47—22no—
164C2×Dic47—22no—
165C2×Dic47—22no—
166C2×Dic47—22no—
167C2×Dic47—22no—
168C2×Dic47—22no—
169C2×Dic47—22no—
170C2×Dic47—22no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—41no—
176C2×Dic47—41no—
177C2×Dic47—41no—
178C2×Dic47—41no—
179C2×Dic47—41no—
180C2×Dic47—41no—
181C2×Dic47—41no—
182C2×Dic47—41no—
183C2×Dic47C22⋊C414yescomplemented
184C22×C47—24no—
185C22×C47—24no—
186C22×C47—24no—
187C22×C47—42no—
188C22×C47—42no—
189C22×C47—42no—
190C22×C47—42no—
191C22×C47—42no—
192C22×C47—42no—
193C22×C47—42no—
194C22×C47—42no—
195C22×C47—42no—
196C22×C47—42no—
197C22×C47—42no—
198C22×C47—42no—
199C22×C47C2×C22⋊C411yescharacteristic
200C22×C47C2×C4⋊C411yescharacteristic
201C22×C47#11711yescharacteristic
202C22×C47C4×D411yescharacteristic
203C22×C47C4×D411yescharacteristic
204C22×C47C4×D411yescharacteristic
205C22×C47C4×D411yescharacteristic
206C22×C47#12011yescharacteristic
207C22×C47#12011yescharacteristic
208C22×C47#12011yescharacteristic
209C22×C47#12111yescharacteristic
210C22×C47#12111yescharacteristic
211C22×C47#12111yescharacteristic
212C22×C47#12111yescharacteristic
213C22×C47#12111yescharacteristic
214C22×C47#12111yescharacteristic
215C22×C47#12111yescharacteristic
216C22×C47#12111yescharacteristic
217C22×C47C22⋊Q811yescharacteristic
218C22×C47C22⋊Q811yescharacteristic
219C22×C47C22⋊Q811yescharacteristic
220C22×C47C22⋊Q811yescharacteristic
221C22×C47C22⋊Q811yescharacteristic
222C22×C47C22⋊Q811yescharacteristic
223C22×C47#12311yescharacteristic
224C22×C47#12311yescharacteristic
225C22×C47#12311yescharacteristic
226C22×C47#12311yescharacteristic
227C22×C47#12311yescharacteristic
228C22×C47#12411yescharacteristic
229C22×C47#12411yescharacteristic
230C22×C47#12411yescharacteristic
231C22×C47#12611yescharacteristic
232C22×C47#12611yescharacteristic
233C22×C47#12711yescharacteristic
234C4×C47—42no—
235C4×C47—42no—
236Dic47—24no—
237Dic47—42no—
238Dic47—42no—
239Dic47—42no—
240#1439—471nomaximal, Sylow
241C2×C47—44no—
242C2×C47#38011yescharacteristic
243C2×C47#38511yescharacteristic
244C2×C47#38511yescharacteristic
245C2×C47#38611yescharacteristic
246C2×C47#38811yescharacteristic
247C2×C47#38811yescharacteristic
248C2×C47#39011yescharacteristic
249C2×C47#39211yescharacteristic
250C2×C47#39311yescharacteristic
251C2×C47#39411yescharacteristic
252C2×C47#39411yescharacteristic
253C2×C47#39611yescharacteristic
254C2×C47#39611yescharacteristic
255C2×C47#39711yescharacteristic
256C2×C47#39911yescharacteristic
257C22×C4⋊C4—471no—
258C22×C22⋊C4—471no—
259C22×C22⋊C4—471no—
260C22×C22⋊C4D4711yescharacteristic
261C2×#95—471no—
262C2×#95—471no—
263C2×#95—471no—
264C47#143911yescharacteristic, complemented, Sylow
265C25C2×D4711yescharacteristic
266C23×C4—471no—
267C23×C4—471no—
268C23×C4—471no—
269C23×C4—471no—
270C23×C4C2×D4711yescharacteristic
271C23×C4C2×D4711yescharacteristic
272C2×C4⋊C4—942no—
273C2×C4⋊C4—942no—
274C2×C4⋊C4—942no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—474no—
279C2×C22⋊C4—942no—
280C2×C22⋊C4—942no—
281C2×C22⋊C4—942no—
282C2×C22⋊C4—942no—
283C2×C22⋊C4—942no—
284#95—942no—
285#95—942no—
286#95—942no—
287C24—21no—
288C24—21no—
289C24—21no—
290C24—21no—
291C24—21no—
292C24—21no—
293C24—21no—
294C24—21no—
295C24—21no—
296C24—21no—
297C24—21no—
298C24—21no—
299C24Dic9412yes—
300C24C4×D4712yes—
301C24C22⋊D4712yes—
302C24C22×D4711yescharacteristic
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—472no—
316C22×C4—472no—
317C22×C4—472no—
318C22×C4—472no—
319C22×C4—472no—
320C22×C4—472no—
321C22×C4—941no—
322C22×C4—941no—
323C22×C4—941no—
324C22×C4—941no—
325C22×C4—941no—
326C22×C4—941no—
327C22×C4—941no—
328C22×C4—941no—
329C22×C4—941no—
330C22×C4—941no—
331C22×C4—941no—
332C22×C4—941no—
333C22×C4—941no—
334C22×C4—941no—
335C22×C4—941no—
336C22×C4—941no—
337C22×C4—941no—
338C22×C4—941no—
339C22×C4—941no—
340C22×C4—941no—
341C22×C4—941no—
342C22×C4—941no—
343C22×C4C22⋊D4712yes—
344C22×C4C22⋊D4712yes—
345C4⋊C4—948no—
346C22⋊C4—28no—
347C22⋊C4—948no—
348C22⋊C4—948no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23Dic47⋊C414yescomplemented
384C23C2×Dic9411yescharacteristic
385C23C2×C4×D4711yescharacteristic
386C23#1062535011yescharacteristic
387C23#1062535011yescharacteristic
388C23D4×D4711yescharacteristic
389C23D4×D4711yescharacteristic
390C23D4×D4711yescharacteristic
391C23D4×D4711yescharacteristic
392C23#1062535211yescharacteristic
393C23#1062535211yescharacteristic
394C23#1062535211yescharacteristic
395C23#1062535211yescharacteristic
396C23C2×C22⋊D4711yescharacteristic
397C23C2×C22⋊D4711yescharacteristic
398C23C2×C22⋊D4711yescharacteristic
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—474no—
414C2×C4—942no—
415C2×C4—942no—
416C2×C4—942no—
417C2×C4—942no—
418C2×C4—942no—
419C2×C4—942no—
420C2×C4—942no—
421C2×C4—942no—
422C2×C4—942no—
423C2×C4—942no—
424C2×C4—942no—
425C2×C4—942no—
426C2×C4—942no—
427C2×C4—942no—
428C2×C4—942no—
429C2×C4—1881no—
430C2×C4—1881no—
431C2×C4—1881no—
432C2×C4—1881no—
433C2×C4—1881no—
434C2×C4—1881no—
435C2×C4—1881no—
436C2×C4—1881no—
437C2×C4—1881no—
438C2×C4—1881no—
439C2×C4—1881no—
440C2×C4—1881no—
441C22—24no—
442C22—24no—
443C22—24no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22C22⋊C4×D4711yescharacteristic
457C22C2×Dic47⋊C411yescharacteristic
458C22#1309398011yescharacteristic
459C22(C22⋊D47)⋊C411yescharacteristic
460C22(C22⋊D47)⋊C411yescharacteristic
461C22C4×C22⋊D4711yescharacteristic
462C22C4×C22⋊D4711yescharacteristic
463C22#1309399211yescharacteristic
464C22#1309399211yescharacteristic
465C22#1309399311yescharacteristic
466C22#1309399511yescharacteristic
467C22#1309399511yescharacteristic
468C22#1309399611yescharacteristic
469C22#1309399611yescharacteristic
470C22#1309399611yescharacteristic
471C22#1309399611yescharacteristic
472C22#1309399711yescharacteristic
473C22#1309399711yescharacteristic
474C22#1309400111yescharacteristic
475C22#1309400111yescharacteristic
476C22#1309400111yescharacteristic
477C22#1309400111yescharacteristic
478C22#1309400311yescharacteristic
479C22#1309400311yescharacteristic
480C22#1309400511yescharacteristic
481C22#1309400511yescharacteristic
482C22#1309400611yescharacteristic
483C22#1309400611yescharacteristic
484C22#1309400711yescharacteristic
485C22#1309401011yescharacteristic
486C22#1309401011yescharacteristic
487C22#1309401111yescharacteristic
488C22#1309401711yescharacteristic
489C22#1309401711yescharacteristic
490C22#1309402011yescharacteristic
491C4—42no—
492C4—42no—
493C4—944no—
494C4—1882no—
495C4—1882no—
496C4—1882no—
497C2—44no—
498C2#1568898111yescharacteristic
499C2#1568899511yescharacteristic
500C2#1568899611yescharacteristic
501C2#1568899911yescharacteristic
502C2#1568901111yescharacteristic
503C2#1568901711yescharacteristic
504C2#1568902311yescharacteristic
505C2#1568903111yescharacteristic
506C2#1568903511yescharacteristic
507C2#1568903711yescharacteristic
508C2#1568903811yescharacteristic
509C2#1568904611yescharacteristic
510C2#1568904611yescharacteristic
511C2#1568905111yescharacteristic
512C2#1568905911yescharacteristic
subgroupG/H
center, FrattiniC24C22×D47
commutatorC23×C47C22×C4
FittingC22×C22⋊C4×C47C2
socleC24×C47C23
hypercenterC22×C22⋊C4D47
hypocenterC47#1439
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×Dic47⋊C4C2semidirect
4. C2×C47⋊#95C2semidirect
5. C2×C47⋊#95C2semidirect
6. C2×C47⋊#95C2semidirect
20. C2×C22⋊Dic47C4semidirect
126. C23×C47C4⋊C4semidirect
183. C2×Dic47C22⋊C4semidirect
264. C47#1439semidirect
383. C23Dic47⋊C4semidirect