Finite Group Databasebeta

← #20246996

Subgroups — #20246996

Order 6016.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625352C211yesmaximal, characteristic, complemented
2C2×#13094008C211yesmaximal, characteristic, complemented
3C2×#13093998C211yesmaximal, characteristic, complemented
4C2×#13093996C211yesmaximal, characteristic, complemented
5#15689044C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689036C211yesmaximal, characteristic, complemented
8#15689032C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15689000C211yesmaximal, characteristic, complemented
11#15689000C211yesmaximal, characteristic, complemented
12#15688998C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14C2×C47⋊#95C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C2×#10625352—24no—
17C2×#10625352—24no—
18C2×#10625352—24no—
19C22×Dic94C2211yescharacteristic
20C22×D188C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C22×C22⋊D47C2211yescharacteristic
23C22×C22⋊D47C2211yescharacteristic
24C22×C22⋊D47C2211yescharacteristic
25C23×Dic47C2211yescharacteristic
26C23×Dic47C2211yescharacteristic
27C23×Dic47C2211yescharacteristic
28C22×C4×D47C2211yescharacteristic
29#13094008—24no—
30#13093998—24no—
31#13093996—24no—
32C2×C4⋊Dic47C2211yescharacteristic
33C2×C4⋊Dic47C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C47⋊#95C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C23×C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55#95×C47C2211yescharacteristic
56#95×C47C2211yescharacteristic
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C23×D47C2311yescharacteristic
60C23×D47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47D414yescomplemented
64C22×C4×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
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—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—41no—
83C2×C22⋊D47D414yescomplemented
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—22no—
89C22×Dic47—22no—
90C22×Dic47—22no—
91C22×Dic47—41no—
92C22×Dic47D414yescomplemented
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95C22×Dic47C2311yescharacteristic
96C22×Dic47C2311yescharacteristic
97C22×Dic47C2311yescharacteristic
98C22×Dic47C2311yescharacteristic
99#10625352—232no—
100C2×D188—22no—
101C2×D188—22no—
102C2×D188—41no—
103C2×C4×D47—22no—
104C2×C4×D47—22no—
105C2×C4×D47—22no—
106C2×Dic94—22no—
107C2×Dic94—22no—
108C2×Dic94—22no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47—41no—
112C22⋊Dic47—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118(C2×D47)⋊C4—22no—
119(C2×D47)⋊C4—41no—
120C4⋊Dic47—22no—
121C4⋊Dic47—22no—
122C4⋊Dic47—22no—
123Dic47⋊C4—22no—
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×C47C2×D412yes—
135C23×C47C2×D412yes—
136C23×C47C2×D412yes—
137C23×C47C2×D412yes—
138C23×C47C2411yescharacteristic
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—21no—
152C22×D47C2×D412yes—
153D4×C47—28no—
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×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—44no—
168C2×C4×C47C2×D412yes—
169C2×C4×C47#4112yescomplemented
170C22⋊D47—28no—
171C22⋊D47—28no—
172C22⋊D47—44no—
173C22⋊D47—44no—
174C2×Dic47—28no—
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—21no—
189C2×Dic47—21no—
190C2×Dic47—44no—
191C2×Dic47C2×D412yes—
192C2×Dic47C2×D412yes—
193C2×Dic47C2×D412yes—
194C2×Dic47#4112yescomplemented
195D188—44no—
196C4×D47—28no—
197Dic94—28no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—22no—
205C22×C47—22no—
206C22×C47—22no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47#12014yes—
212C22×C47C22×D411yescharacteristic
213C22×C47C22×D411yescharacteristic
214C22×C47C22×D411yescharacteristic
215C22×C47C2×#4111yescharacteristic
216C22×C47C2×#4111yescharacteristic
217C22×C47H(5,𝔽2)11yescharacteristic
218C22×C472−1+411yescharacteristic
219C2×D47—22no—
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
230C2×D47—41no—
231C2×D47—41no—
232C2×D47—41no—
233C4×C47—22no—
234C4×C47—22no—
235C4×C47—41no—
236C4×C47—41no—
237C4×C47—41no—
238Dic47—22no—
239Dic47—22no—
240Dic47—22no—
241Dic47—22no—
242Dic47—41no—
243Dic47—41no—
244#2430—471nomaximal, Sylow
245C2×C47—24no—
246C2×C47—42no—
247C2×C47C2×#12011yescharacteristic
248C2×C47#53211yescharacteristic
249C2×C47#53711yescharacteristic
250C2×C47#54611yescharacteristic
251C2×C47#54611yescharacteristic
252C2×C47#54711yescharacteristic
253C2×C47#54711yescharacteristic
254D47—42no—
255D47—81no—
256C22×#41—471no—
257C2×#123—471no—
258C2×#121—471no—
259C2×#121—471no—
260#395—471no—
261#394—471no—
262#393—471no—
263#392—471no—
264#386—471no—
265#386—471no—
266#386—471no—
267#386D4711yescharacteristic, complemented
268#385—471no—
269#385—471no—
270C2×#95—471no—
271C47#243011yescharacteristic, complemented, Sylow
272C2×#41—944no—
273C2×#41—944no—
274C2×#41—944no—
275C22×Q8—471no—
276C22×D4—471no—
277C22×D4—471no—
278C22×D4—471no—
279C22×D4—471no—
280C22×D4—471no—
281C22×D4C2×D4711yescharacteristic
282C23×C4—471no—
283C23×C4—471no—
284C23×C4—471no—
285C23×C4—471no—
286C23×C4C2×D4711yescharacteristic
287#123—944no—
288#121—944no—
289#121—944no—
290C2×C4⋊C4—471no—
291C2×C4⋊C4—471no—
292C2×C4⋊C4—471no—
293C2×C4⋊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⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305#95—471no—
306#95—471no—
307#95—471no—
308#95—471no—
309#95—471no—
310#95—471no—
311#95C2×D4711yescharacteristic
312#95C2×D4711yescharacteristic
313C24—471no—
314C24—471no—
315C24C22×D4711yescharacteristic
316C24C22×D4711yescharacteristic
317#41—9432no—
318C2×Q8—942no—
319C2×Q8—942no—
320C2×Q8—942no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—474no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—942no—
333C2×D4—942no—
334C2×D4—942no—
335C2×D4—942no—
336C2×D4—1881no—
337C2×D4—1881no—
338C2×D4D18814yescomplemented
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—474no—
343C22×C4—471no—
344C22×C4—471no—
345C22×C4—471no—
346C22×C4—471no—
347C22×C4—471no—
348C22×C4—471no—
349C22×C4—942no—
350C22×C4—942no—
351C22×C4—942no—
352C22×C4—942no—
353C22×C4—942no—
354C22×C4—942no—
355C22×C4—942no—
356C22×C4—942no—
357C22×C4—942no—
358C22×C4—942no—
359C22×C4—1881no—
360C22×C4C22×D4711yescharacteristic
361C22×C4C22×D4711yescharacteristic
362C22×C4C22×D4711yescharacteristic
363C22×C4C22×D4711yescharacteristic
364C22×C4C22×D4711yescharacteristic
365C4⋊C4—942no—
366C4⋊C4—942no—
367C4⋊C4—942no—
368C4⋊C4—942no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—41no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—942no—
376C22⋊C4—942no—
377C22⋊C4—942no—
378C22⋊C4—942no—
379C22⋊C4—1881no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—472no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23—941no—
402C23—941no—
403C23—941no—
404C23C2×D18812yes—
405C23C2×D18812yes—
406C23D4×D4712yes—
407C23D4×D4712yes—
408C23C23×D4711yescharacteristic
409Q8—948no—
410D4—28no—
411D4—948no—
412D4—948no—
413D4—1884no—
414D4—1884no—
415D4—1884no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—472no—
431C2×C4—472no—
432C2×C4—472no—
433C2×C4—472no—
434C2×C4—948no—
435C2×C4—948no—
436C2×C4—948no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—941no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—941no—
449C2×C4—941no—
450C2×C4—941no—
451C2×C4—1884no—
452C2×C4C2×D18812yes—
453C2×C4#1062535212yescomplemented
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—942no—
468C22—942no—
469C22—942no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22—1881no—
474C22—1881no—
475C22—1881no—
476C22—1881no—
477C22—1881no—
478C22—1881no—
479C22—1881no—
480C22—1881no—
481C22#1309399414yes—
482C22C2×D4×D4711yescharacteristic
483C22C2×D4×D4711yescharacteristic
484C22C22×D18811yescharacteristic
485C22#41×D4711yescharacteristic
486C22C2×#1062535211yescharacteristic
487C22#1309406911yescharacteristic
488C22#1309407111yescharacteristic
489C4—22no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—942no—
495C4—942no—
496C4—942no—
497C4—942no—
498C4—1881no—
499C4—1881no—
500C2—24no—
501C2—42no—
502C2—3761no—
503C2—1882no—
504C2C2×#1309399411yescharacteristic
505C2#1568966811yescharacteristic
506C2#1568970011yescharacteristic
507C2#1568976011yescharacteristic
508C2#1568976811yescharacteristic
509C2#1568977111yescharacteristic
510C2#1568977711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2430
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×#13094008C2semidirect
3. C2×#13093998C2semidirect
4. C2×#13093996C2semidirect
5. #15689044C2semidirect
6. #15689039C2semidirect
7. #15689036C2semidirect
8. #15689032C2semidirect
9. #15689001C2semidirect
10. #15689000C2semidirect
11. #15689000C2semidirect
12. #15688998C2semidirect
13. #15688997C2semidirect
14. C2×C47⋊#95C2semidirect
15. C47×#386C2semidirect
63. C2×D4×C47D4semidirect
83. C2×C22⋊D47D4semidirect
92. C22×Dic47D4semidirect
169. C2×C4×C47#41semidirect
194. C2×Dic47#41semidirect
267. #386D47semidirect
271. C47#2430semidirect
338. C2×D4D188semidirect
453. C2×C4#10625352semidirect