Finite Group Databasebeta

← #20246825

Subgroups — #20246825

Order 6016.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093996C211yesmaximal, characteristic, complemented
2C2×#13093996C211yesmaximal, characteristic, complemented
3C2×#13093996C211yesmaximal, characteristic, complemented
4C2×D4×Dic47C211yesmaximal, characteristic, complemented
5C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689045C211yesmaximal, characteristic, complemented
8#15689038C211yesmaximal, characteristic, complemented
9#15689037C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic, complemented
13#15689002C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C2×#121×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22#13093996—24no—
23#13093996—24no—
24#13093996—24no—
25D4×Dic47—24no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4—24no—
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C22⋊Dic47C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C2×C4×Dic47C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C22×D4×C47C2211yescharacteristic
52C23×C4×C47C2211yescharacteristic
53#121×C47—24no—
54C2×C4⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic
56C2×C22⋊C4×C47C2211yescharacteristic
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C24×C47C2311yescharacteristic
60C23×D47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—22no—
64C2×D4×C47—22no—
65C2×D4×C47—22no—
66C2×D4×C47—22no—
67C2×D4×C47—22no—
68C2×D4×C47—41no—
69C2×D4×C47D414yescomplemented
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—41no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—22no—
83C2×C22⋊D47—22no—
84C2×C22⋊D47—22no—
85C2×C22⋊D47—41no—
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—22no—
89C22×Dic47—22no—
90C22×Dic47—22no—
91C22×Dic47—22no—
92C22×Dic47—22no—
93C22×Dic47—41no—
94C22×Dic47D414yescomplemented
95C22×Dic47C2311yescharacteristic
96C22×Dic47C2311yescharacteristic
97C22×Dic47C2311yescharacteristic
98C22×Dic47C2311yescharacteristic
99C22×Dic47C2311yescharacteristic
100C22×Dic47C2311yescharacteristic
101C22×Dic47C2311yescharacteristic
102C4⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47—22no—
107C22⋊Dic47—22no—
108C22⋊Dic47—22no—
109C22⋊Dic47—22no—
110C22⋊Dic47—41no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—41no—
115C4⋊Dic47—22no—
116Dic47⋊C4—22no—
117Dic47⋊C4—22no—
118Dic47⋊C4—22no—
119Dic47⋊C4—22no—
120Dic47⋊C4—22no—
121Dic47⋊C4D414yescomplemented
122C4×Dic47—22no—
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—21no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—21no—
140C23×C47C2×D412yes—
141C23×C47C2×D412yes—
142C23×C47C2×D412yes—
143C23×C47#4112yes—
144C23×C47C2411yescharacteristic
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47—21no—
152D4×C47—28no—
153D4×C47—44no—
154D4×C47—44no—
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×C47—44no—
166C2×C4×C47C2×D412yes—
167C2×C4×C47C2×D412yes—
168C22⋊D47—44no—
169C22⋊D47—44no—
170C22⋊D47—44no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—28no—
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—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—44no—
189C2×Dic47—44no—
190C2×Dic47C2×D412yes—
191C2×Dic47C2×D412yes—
192C2×Dic47C2×D412yes—
193C2×Dic47C2×D412yes—
194C2×Dic47#4112yes—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47—41no—
212C22×C47—41no—
213C22×C47—41no—
214C22×C47—41no—
215C22×C47#12114yescomplemented
216C22×C47C22×D411yescharacteristic
217C22×C47C22×D411yescharacteristic
218C22×C47C22×D411yescharacteristic
219C22×C47C2×#4111yescharacteristic
220C22×C47C2×#4111yescharacteristic
221C22×C47H(5,𝔽2)11yescharacteristic
222C22×C472−1+411yescharacteristic
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
230C4×C47—22no—
231C4×C47—22no—
232C4×C47—41no—
233C4×C47—41no—
234Dic47—22no—
235Dic47—22no—
236Dic47—41no—
237Dic47—41no—
238Dic47—41no—
239Dic47—41no—
240Dic47#12114yescomplemented
241#2416—471nomaximal, Sylow
242C2×C47—24no—
243C2×C47—42no—
244C2×C47—81no—
245C2×C47C2×#12111yescharacteristic
246C2×C47C2×#12111yescharacteristic
247C2×C47#53711yescharacteristic
248C2×C47D4211yescharacteristic
249C2×C47#54711yescharacteristic
250C2×C47#54811yescharacteristic
251C2×C47#55311yescharacteristic
252D47—81no—
253C2×#121—471no—
254C2×#121—471no—
255C2×#121—471no—
256C2×#121D4711yescharacteristic, complemented
257C2×C4×D4—471no—
258C22×C4⋊C4—471no—
259#396—471no—
260#396—471no—
261#394—471no—
262#394—471no—
263#390—471no—
264#389—471no—
265#386—471no—
266#386—471no—
267#380—471no—
268C47#241611yescharacteristic, complemented, Sylow
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—471no—
272C22×D4C2×D4711yescharacteristic
273C22×D4C2×D4711yescharacteristic
274C22×D4C2×D4711yescharacteristic
275C23×C4—471no—
276C23×C4—471no—
277C23×C4—471no—
278C23×C4C2×D4711yescharacteristic
279#121—24no—
280#121—944no—
281#121—944no—
282#121—944no—
283C4×D4—944no—
284C2×C4⋊C4—471no—
285C2×C4⋊C4—471no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4—471no—
289C2×C4⋊C4—471no—
290C2×C4⋊C4—471no—
291C2×C4⋊C4—944no—
292C2×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
301C2×C22⋊C4—471no—
302C2×C22⋊C4—471no—
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305C2×C42—471no—
306#95—471no—
307#95—471no—
308#95—471no—
309#95—471no—
310C24—471no—
311C24C22×D4711yescharacteristic
312C24C22×D4711yescharacteristic
313C24C22×D4711yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—41no—
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—1881no—
331C2×D4C22⋊D4714yescomplemented
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—471no—
336C22×C4—474no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—1881no—
351C22×C4C22×D4711yescharacteristic
352C22×C4C22×D4711yescharacteristic
353C22×C4C22×D4711yescharacteristic
354C22×C4C22×D4711yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—474no—
357C4⋊C4—942no—
358C4⋊C4—942no—
359C4⋊C4—942no—
360C4⋊C4—942no—
361C4⋊C4—942no—
362C4⋊C4—942no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—942no—
366C22⋊C4—942no—
367C22⋊C4—942no—
368C22⋊C4—942no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—1881no—
374C22⋊C4—1881no—
375C42—942no—
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—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23D4×D4712yes—
401C23#1062535212yes—
402C23C2×C22⋊D4712yes—
403C23C2×C22⋊D4712yes—
404C23C23×D4711yescharacteristic
405D4—28no—
406D4—44no—
407D4—44no—
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—44no—
422C2×C4—472no—
423C2×C4—472no—
424C2×C4—472no—
425C2×C4—472no—
426C2×C4—472no—
427C2×C4—948no—
428C2×C4—941no—
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—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—1884no—
445C2×C4—1884no—
446C2×C4D4×D4712yes—
447C2×C4C2×C22⋊D4712yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22—1881no—
474C22—1881no—
475C22#1309399614yescomplemented
476C22C2×D4×D4711yescharacteristic
477C22C2×D4×D4711yescharacteristic
478C22C22×C22⋊D4711yescharacteristic
479C22#41×D4711yescharacteristic
480C22C2×#1062535211yescharacteristic
481C22#1309406911yescharacteristic
482C22#1309407111yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—474no—
488C4—942no—
489C4—942no—
490C4—1881no—
491C4—1881no—
492C4—1881no—
493C4—1881no—
494C2—24no—
495C2—42no—
496C2—81no—
497C2—3761no—
498C2#121×D4711yescharacteristic
499C2C2×#1309399611yescharacteristic
500C2#1568970011yescharacteristic
501C2D4×C22⋊D4711yescharacteristic
502C2#1568977211yescharacteristic
503C2#1568977911yescharacteristic
504C2#1568981611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2416
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13093996C2semidirect
2. C2×#13093996C2semidirect
3. C2×#13093996C2semidirect
4. C2×D4×Dic47C2semidirect
5. C22×Dic47⋊C4C2semidirect
6. #15689046C2semidirect
7. #15689045C2semidirect
8. #15689038C2semidirect
9. #15689037C2semidirect
10. #15689023C2semidirect
11. #15689018C2semidirect
12. #15689003C2semidirect
13. #15689002C2semidirect
14. #15688981C2semidirect
15. C2×#121×C47C2semidirect
69. C2×D4×C47D4semidirect
94. C22×Dic47D4semidirect
121. Dic47⋊C4D4semidirect
215. C22×C47#121semidirect
240. Dic47#121semidirect
256. C2×#121D47semidirect
268. C47#2416semidirect
331. C2×D4C22⋊D47semidirect
475. C22#13093996semidirect